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Regis Petit's Website

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Contents

  1. Keyboard shortcuts
  2. Additional topics
  3. Site map
  4. Design and Accessibility rules
  5. Partner schools and organizations
  6. Weblinks that deal with Website Design and Checking
  7. About the Author of this Website

1. Keyboard shortcuts

The following keyboard shortcuts can be used on this Website. Access key is a figure from 0 to 9.

These keyboard shortcuts can be used via a combination of keyboard keys. The list of these combinations sorted by Operating System then by Browser is as follows.
Warning : Shift is sometimes useless on some keyboards (including the QWERTY and QWERTZ keyboards).


Sources :
Wikipedia, Access key.
Mozilla, Accesskey.


2. Additional topics


The site hosts several additional short and synthetic topics. See Contents.

A. Art and culture

A1. Optic illusions
A1.1. Luminous paintings by Bardula
Picture Luminous paintings by Bardula - Blue Interferences Picture Luminous paintings by Bardula - Blue ice


Bardula is a pseudonym created by a Belgian artist who currently lives and works in France.
Bardula creates luminous paintings including the hypnotic paintings "Blue Interferences" and "Blue ice" (see Figures 1 and 2 above).

Sources :
Light ZOOM Lumière.
Bardula.


A1.2. Motion illusions
Picture Motion illusions 1     Picture Motion illusions 2     Picture Motion illusions 3

Picture Motion illusions 4     Picture Motion illusions 5     Picture Motion illusions 6


Here is a selection of the best motion illusions (see above Figure 1 cf [GomboDigital], Figures 2 to 5 cf [Sélection.ca] and Figure 6 cf [Akiyoshi Kitaoka]) :
1. Rotating vortex (Vectordivider image via Getty Images)
2. Rotating spirals (Vectordivider image via Getty Images)
3. Mesmerizing effect (Mark Grenier image via Shutterstock)
4. Scroll (Guten Tag Vector image via Shutterstock)
5. Glitter Grid (Mark image via Shutterstock)
6. "Expanding pupils" (Image from Akiyoshi Kitaoka)

Sources :
Sélection du Reader's Digest (Canada) - 24 illusions d'optique complètement étourdissantes.
GomboDigital - 5 illusions d'optique qui vont vous scotcher/.
Akiyoshi Kitaoka - Anomalous motion illusions 35.


A2. Heritage of Gers Lomagne
picture Heritage of Gers Lomagne


The following files describe the monumental and architectural heritage of 140 municipalities located less than 20 km from the towns of Lectoure or Condom in Gers (France), and including Gers Lomagne and its surroundings.

List of municipalities :
The municipalities are listed alphabetically, each followed by the department number: Gers (32 by default), Lot-et-Garonne (47), Tarn-et-Garonne (82).
Each pdf file weighs approximately 500 KB, the heaviest being Lectoure (3.3 MB).


Sources :
- Wikipedia, Descriptif de chaque commune dont département, toponymie, histoire, maire, nombre d'habitants, altitude, lieux et monuments.
- Ministère de la Culture, Immeubles protégés au titre des Monuments Historiques, par département et par commune. N'inclut pas les sites protégés.
- Ministères Ecologie Energie Territoires, Liste des servitudes des sites et monuments du Gers jusque janvier 2015, par commune et incluant la protection des sites et des monuments au titre des Monuments Historiques.
- SDAP renommé STAP (Services Territoriaux de l'Architecture et du Patrimoine), Liste des monuments historiques et des sites du Lot-et-Garonne, par commune et jusqu'en 2006.
- DREAL Midi-Pyrénées (Direction Régionale de l'Environnement, de l'Aménagement et du Logement Midi-Pyrénées), Bilan des sites classés et inscrits du Tarn-et-Garonne, avril 2013, par commune.
- Ministère de la Culture, Base Mérimée du patrimoine monumental français, par commune et par monument incluant date d'origine, lieu, descriptif et propriété.
- Comet Anaïs Villages et bourgs de la Gascogne gersoise à la fin du Moyen Age (1250-1550), par commune, Thèse d'histoire, 2017, Volume 1 : Synthèse (405 p), Volume 2 : Figures (442 p), Volume 3 : Notices (680 p), Volume 4 : Atlas (391 p).
- Google, Recherche par commune (histoire, origine du nom, bastide, castelnau, castrum, fortification, rempart, château, fossé, vestige) ou par monument (protection récente des monuments et des sites au titre des Monuments Historiques)
- Google Images et Google Vidéos, Recherche par commune (monument, "carte postale", vidéo Youtube).
- IGN (Institut Géographique National, renommé Institut National de l'information Géographique et forestière), Géoportail, par commune (situation graphique des lieux-dits et des rues).
- Google, Google Maps, par commune (situation GPS des lieux-dits, rues principales, photos par Street View).
- Google, Recherche par commune (cadrans solaires, moulins, pigeonniers, puits, fontaines, lavoirs).
- Mapio, Photos d'internautes avec titre et géolocalisation précise. Recherche par Région, Département, Arrondissement, Commune.


A3. Unusual sculptures
A3.1. Wind sculptures of Berrac
Picture Wind sculpture of Berrac - Elegante Picture Wind sculpture of Berrac - Extravagante Picture Wind sculpture of Berrac - Endurante Picture Wind sculpture of Berrac - Fascinante


The Author of this site has made four wind sculptures installed in his garden in Berrac (Gers).

Description :


Design :
These sculptures are made with recycled products (aluminum rails for thermal insulation frame, PVC camping bowls, plastic jerrycan sides, tennis ball, rebar, etc.).
All moving parts are carried on ball bearings.
All the fixed elements are assembled by stainless steel screws.
The sculptures are fixed to the ground by a vertical mast (galvanized steel fence post or old steel water pipe).

A3.2. Wind sculpture by Pierre Luu
Picture Wind sculpture by Pierre Luu - plan 1 Picture Wind sculpture by Pierre Luu - plan 2 Picture Wind sculpture by Pierre Luu - plan 3


Pierre Luu is a French sculptor who has created sculptures with unpredictable movements, driven by wind or water, including the "wind turbine with random motion" (see Figures above, and video "Mobile eolien art cinétique" in [Pierre Luu]).

Description :
Figure 1 above : general view (cf [Art et Eau]).
Figure 2 above : zoom on blades twist angle (video clip 0:12).
Figure 3 above : zoom on blades lenght (video clip 0:22).
The "wind turbine with random motion" is made up of 5 moving parts in unstable equilibrium (cf [Pierre Luu - Quelque chose ne tourne pas rond][Art et Eau - Quelque chose ne tourne pas rond]).
The balance is all the more unstable as there is no weather vane to orient the sculpture in the wind direction. The blue ball is aesthetic and symbolizes the Earth (cf my email of March 5, 2023 from Pierre Luu to Régis Petit).
The two blades are of different size with a secondary rotation nested within the primary rotation (cf [Pierre Luu - Eolide].
The sculpture slowly comes to life and changes shape thanks to the wind action. The movement is maintained by inertia due to the balance of the masses (cf [Art et Eau - Quelque chose ne tourne pas rond]).
The sculpture unfolds in an enigmatic choreography and only finds temporary stability when the blades reach a certain speed (cf [Pierre Luu - Quelque chose ne tourne pas rond]).

Design :
The whole is designed in a search for balance between the masses, the gravity centers, the surfaces exposed to the wind and the relative angles of the surfaces (cf [Pierre Luu - Quelque chose ne tourne pas rond]).
The mobile elements are fixed by ball bearings for all sculptures in project version (cf email of March 7, 2023 from Pierre Luu to Régis Petit). This combination allows fluid rotations and movements even in light winds (cf [Pierre Luu - Fragments mobile éolien).
Material : stainless steel and composite materials (cf [Art et Eau - Quelque chose ne tourne pas rond]).
Height : 3 m 50 (cf [Art et Eau - Quelque chose ne tourne pas rond]).

Sources :
Pierre Luu - Mobile eolien art cinétique (YouTube, 01:57).
Pierre Luu - Un art en mouvement - Sculptures éoliennes et mobiles.
Pierre Luu - Un art en mouvement - Quelque chose ne tourne pas rond.
Pierre Luu - Un art en mouvement - Fragments mobile éolien.
Pierre Luu - Un art en mouvement - Eolide.
Pierre Luu - Un art en mouvement - Solaris : sculpture éolienne et solaire autonome en énergie.
Art et Eau - Ellipse, quelque chose ne tourne pas rond.


A3.3. Kinetics sculptures by Jeff Kahn
Picture Kinetic sculpture by Jeff Kahn - Astrolabe Picture Kinetic sculpture by Jeff Kahn  - Naked Alien Picture Kinetic sculpture by Jeff Kahn - I Ching


Jeff Kahn is an American sculptor who created kinetic sculptures, titled "Invisible Forces", from aluminum and stainless steel.
These sculptures explore balance and gravity and how almost imperceptible air currents interact with them. They are extremely sensitive to the surrounding environment (light breezes, sun heat, weight of the morning dew). See above Figures 1, 2 and 3 showing three particular sculptures : "Astrolabe", "Naked Alien" and "I Ching".
Jeff Kahn's studio is located in Lenhartsville, Pennsylvania, USA.

Sources :
Jeff Kahn - Bio.
Jeff Kahn - Catalog.
Jeff Kahn - Videos.


A3.4. Hypnotic sculpture by Anthony Howe
Picture Hypnotic sculpture by Anthony Howe Picture Hypnotic sculpture by Anthony Howe - zoom of each arm Picture Hypnotic sculpture by Anthony Howe - zoom of each bearing


Anthony Howe is an American sculptor who has created hypnotic mobile sculptures including "Di-Octo" in 2014 (see Figures 1, 2 and 3 above, and "Di-Octo" video in [Anthony Howe] and [KULTT]).
Anthony Howe currently lives in Eastsound, Orcas Island, San Juan County, Washington State (USA).

Description :
Di-Octo is a half-octopus, half-star, wind-driven and near-silent mobile sculpture.
The original Di-Octo, designed and made by Anthony Howe, has been industrialized in two identical copies by Show Canada Inc (Laval steelworks in Quebec) as follows (cf email of March 10, 2023 from David Boulay (Show Canada Inc) to Régis Petit) :


Design :
Di-Octo is 8 meters high, 3 meters in diameter, weighs 725 kilograms and requires only 2 km/h of wind for its moving parts to activate (cf [Concordia University]).
Di-Octo is composed of 36 arms each carrying 16 very thin steel domes and rotating around a vertical circular ring. The inter-arm connections are of the intermediate wheel type with drive fingers. See detail in Figure 3 above (cf [Show Canada]).
The arms always turn in the same direction, regardless of the wind direction. This is due to the domes shape (cf email of March 19, 2023 from David Boulay to Régis Petit).
Di-Octo is entirely made of 316 stainless steel, which gives it better corrosion resistance as well as non-magnetic properties (cf [Show Canada]).

Other similar sculptures :
Anthony Howe designed and made other sculptures similar to Di-Octo (cf [Anthony Howe, https://www.howeart.net/about]) :


Sources :
Anthony Howe.
Anthony Howe - Shindahiku (Fern pull).
The DC Blike Blogger - Shindahiku (Fern Pull).
KULTT - Les sculptures hypnotiques d'Anthony Howe.
Anthony Howe - Di-Octo (Youtube 1:10).
Anthony Howe - Di-Octo (long version) (Youtube 1:33).
Université Concordia - Di-Octo : captivant, cinétique et unique.
Show Canada.
JuanG3D : Di-Octo 3D Model.
What's on - Check out these alien-esque kinetic sculptures in Dubai.
UAE - Famous American artist brings kinetic sculptures to Dubai.
reddit - "Octo II", Anthony Howe, stainless steel, 2013..

A3.5. Hypnotic sculpture by Jennifer Townley
Picture Hypnotic sculpture by Jennifer Townley Picture Hypnotic sculpture by Jennifer Townley - bricks zoom


Jennifer Townley is a Dutch artist who has created hypnotic mobile sculptures including "Asinas" in 2015 (see Figure 1 above, and video "Asinas").
When viewed at a standstill from the front, it looks like a double helix like the usual representation of DNA.

Description (cf [Jennifer Townley]) :
"Asinas" is a mobile sculpture composed of two helixes that intertwine and slide into each other, producing a fluid and natural movement.
The two helixes slowly rotate in opposite directions and at slightly different speeds, gradually transforming the sculpture.
A demonstration of how this sculpture works helps to better understand this description (see video "Asinas Working Demonstration" in [Amogh Jadhav] and video "SolidWorks Mechanical Sculpture" in [tecnoloxia.org]).

Design :
The sixty-five white wooden bricks that form the two helixes increase in size towards the middle of the sculpture, giving it a conical shape.
Each brick has the shape of a Z with 90 degree angles. The bricks of a helix are fixed on the rotation axis. The bricks of the other helix are connected to one another through small spacers (see Figure 2 above from [Amogh Jadhav]).
The bricks are made from painted wood. The frame is made of steel as well as all the parts connecting the gears to their axes, the bearings to the frame, etc.
Then there are all the other parts : an electric motor, heavy steel spur gears and sprockets, two belts and lots of bearings (cf [The Plus Paper]).

Sources :
Asinas - Jennifer Townley - 2015 - Kinetic art (Youtube 2:31).
Jennifer Townley - Asinas.
L'Usine Nouvelle - Hypnotiques, ces sculptures cinétiques vous étonneront.
Amogh Jadhav - Asinas.
Amogh Jadhav - Asinas Working Demonstration (Youtube 2:14).
tecnoloxia.org - As esculturas cinéticas de Jennifer Townley.
MadCadSkills : Jennifer Townley - SolidWorks Mechanical Sculpture (Youtube 3:43).
The Plus Paper - Asinas : Fluent Movement ( http://www.thepluspaper.com/2015/03/23/asinas-fluent-movement/ ).


A3.6. Walking robot by Theo Jansen
Picture Walking robot - one legWalking robot - six legsPicture Walking robot


Theo Jansen is a Dutch sculptor who in 1991 created strange creatures including the walking robot (see Figures 1 and 2 above).

Working :
This walking robot is a mechanism with very light legs which can move on a horizontal plane under the wind action or on an inclined plane under the action of its own weight (see video cf [Jansen, Plaudens Vela]).
The only actuator in the robot is a central crankshaft making the connection between the legs and the robot body (see red while on Figure 2, and also [Exergia]).
For a robot with three pairs of legs, the crankshaft has three cranks offset successively by 120 to have a constant movement of the robot during the propulsion phase (see Figure 2).

Body description :
The robot body consists of a horizontal platform (length 2a) and vertical fixed supports (length l) carrying the crankshaft (eccentricity m). See Figure 3 above.
The double length (a) of the platform is calculated to ensure non-collision between the front legs and the rear legs.
The length (l) of the supports can be modified to ensure an overall horizontal movement of the robot. Increasing or decreasing the length (l) amounts to pivoting all the bars of each leg around each fixed point F.

Legs description :
Each leg consists of ten articulated bars (bars b to k) of which two form a rigid link (bars e and h)). See Figure 3 above.
The two legs of the same pair are identical and mirror each other on each side of the crankshaft.
The foot of each leg describes an ovoid curve whose lower part is almost flat and horizontal, thus allowing the foot to be in contact with the ground during the propulsive phase.
In the return phase, the foot lifts off the ground and the robot can step over small obstacles without lifting its body too much.
The table of Figure 3 gives the length of each bar according to different authors :


Sources :
Jansen - Plaudens Vela.
Jansen - plaudens vela 1 (Youtube 0:53).
Wikipedia - Mécanisme de Jansen.
Exergia - Simulation von Theo Jansen's Strandbeest.
Giesbrecht Daniel - Design and optimisation of a one-degree-offreedom eight-bar leg mechanism for a walking machine.

B. Games

B1. Labyrinths


How to get out of a labyrinth for sure ?

Picture Labyrinth1


Introduction

Imagine any labyrinth made up of many crossroads and multiple corridors connecting these crossroads. How to get out of this labyrinth for sure ?
Figure 1 above gives an example of a simple labyrinth made up of 7 crossroads (numbered 1 to 7) including a dead end (crossroads 3), 10 corridors and 4 minimal loops ((55), (464), (2452) and (4564)).
The simplest rule for navigating a labyrinth, called the "hand rule", consists of crossing crossroads and corridors, always leaving the same hand (right or left) placed on the wall. This strategy allows you to never get lost in the labyrinth but does not guarantee finding the exit. Either the traveler possibly discovers one of the exits during his journey, or he automatically returns to his start crossroads.
Thus, on the example of Figure 1, with the right hand rule, a visitor lost at crossroads 5 will go indefinitely in circles in the loop (5245) by entering the corridor (52), and in the loop (5465) by entering the corridor (54).
The "rule of the hand" therefore only applies if the start crossroads corresponds to the entrance to the labyrinth, in which case the traveler is guaranteed to cross the labyrinth without getting lost along the way.

A general rule exists. It allows the lost traveler to definitely escape from the labyrinth when it has an outcome (entrance or exit) and, otherwise, to visit it completely before finding himself at his start crossroads. Two search strategies exist :
- In-depth search, when the traveler is completely lost in the labyrinth. Two different rules were published : rule of Charles-Pierre Trémaux in 1882 [LUC], and rule of Gaston Tarry in 1895 [TAR][TOU][ROS1] which is more general.
- Search by concentric circles (or breadth search), when the traveler knows that he is not too far from the entrance to the labyrinth (less than 3 or 4 crossroads for example). The rule was published by Oystein Ore in 1959 [OYS][WAL].
These three rules (Trémaux, Tarry and Oystein Ore) applie to any flat labyrinth, that is to say spread out on a relatively flat surface, as well as to any three-dimensional labyrinth that may include stairs and rooms with multiple floors.


Tarry : in-depth search

When the traveler is completely lost in the labyrinth, the General Rule of the French mathematician Gaston Tarry is a double rule which is stated as follows :

At each crossroads of the labyrinth :
Rule no. 1 : Only retake the corridor of first visit to this crossroads as a last resort (Tarry's rule [TAR]).
Rule no. 2 : Never take a corridor twice in the same direction (remark from Pierre Tougne [TOU]).

Rule no. 1 allows you to escape the labyrinth with certainty. If the labyrinth does not have an outcome (entrance or exit), all crossroads are visited by traveling through each corridor exactly twice before returning to the start crossroads.
Rule no. 2 avoids wasting time by retracing paths already taken.

This double rule has many practical advantages :
- It is easy to remember.
- Subject to correctly marking certain particular corridors, it allows you to commute, at any time and without getting lost, between any finish crossroads and any start crossroads, and this without having to go through all the corridors already covered on the way there. This makes it possible in particular to return to a start crossroads (for example to pick up a person left there waiting) then to return to the finish crossroads (for example to bring the person back with you and continue the search together) [PET].
- It allows you to completely clean a labyrinth by passing through all the crossroads without exception.
- It allows you to successively cut each of the two sides of each corridor in a hedge labyrinth by passing through all the corridors twice without exception.


Proof of Tarry's general rule :

We will demonstrate that Tarry's rule allows us to visit all the crossroads of the labyrinth when it has no outcome (entrance or exit), which means that we certainly exit the labyrinth otherwise.
In the following, we consider that :
- A labyrinth is a set of crossroads whose exits are all connected to corridors ;
- Any two crossroads are connected by at least one continuous path passing through one or more corridors between crossroads (connected labyrinth) ;
- All corridors are two-way ;
- The start crossroads is a crossroads already visited by a fictitious arrival corridor.

Proposition no. 1 : Crossroads all completely visited (quick demonstration according to [TAR]) :
Since the corridors of the labyrinth are all two-way, any crossroads has as many exits as entrances. The traveler is therefore never stuck when visiting or revisiting a crossroads in the labyrinth. Consequently, if the labyrinth has no exit (entrance or exit) and if the rule no. 2 is scrupulously applied, the traveler will eventually stop at the start crossroads. At this moment, all the crossroads of the labyrinth are then necessarily completely visited, with all the corridors traveled exactly twice.

Proposition no. 2 : Crossroads all completely visited (complete demonstration by the Author of this Website) :
Since the corridors of the labyrinth are all two-way, any crossroads has as many exits as entrances.
Consequently (see Figure 4 below), the traveler who enters a crossroads via an arrival corridor (type R or T corridor) necessarily exits via a departure corridor not already taken in this direction (cf rule no. 2). This departure corridor can be the arrival corridor (with R rebound on the crossroads) or any other departure corridor (with T transit through the crossroads).
The first arrival at the crossroads (PV corridor) corresponds to the discovery of the crossroads via its corridor of first visit, followed by a departure via any corridor.
The last arrival at the crossroads (DV corridor) corresponds to the last visit to the crossroads with a return in the opposite direction to the corridor of first visit (cf rule no. 1).
The traveler is therefore never stuck when he visits or revisits a crossroads in the labyrinth.
Consequently, if the labyrinth has no outcome (entrance or exit) and if rule no. 2 is scrupulously applied, the traveler will eventually stop at the start crossroads after having visited a certain number of crossroads.
Any crossroads visited for the first time is via a corridor traveled from another crossroads necessarily visited for the first time. Consequently, any crossroads visited at least once is on a tree whose trunk is the start crossroads and whose branches are the first visit corridors of each crossroads (see example in Figure 5 below).
Suppose that there is on this tree a crossroads whose first visit corridor is never taken in the opposite direction. In this case, the upstream crossroads located on the tree just before this downstream crossroads finds itself in the same situation (see rule no. 1). Step by step, the start crossroads located at the base of the tree (first crossroads visited) also finds itself in the same situation, which is contradictory with the fact that the traveler always ends up returning to the start crossroads. Consequently, if the rule no. 1 has been scrupulously applied at each crossroads, all crossroads in the tree are completely visited.
Furthermore, the labyrinth being connected, any crossroads (C) not already visited and connected to a crossroads of the tree at the distance of a corridor will therefore visited, which extends the tree and makes crossroads C completely visited. Step by step, all the crossroads of the labyrinth will therefore be completely visited, with all the corridors of the labyrinth traveled exactly twice (once in the arrival direction and once in the starting direction).

On a practical level, the completely visited crossroads of the labyrinth are therefore successively visited in the form of downstream-upstream fallbacks which necessarily end at the start crossroads. On the example of Figure 2 above, if crossroads 7 is not an exit but a simple dead end, the path is as follows :
- The route between the departure from crossroads 1 and the arrival at crossroads 7 is given by the succession of corridors (12)(24)(45)(52)(25)(55)(56)(64)(43)(34)(46)(67). See following paragraph.
- The route to then return to the crossroads 1 is given by the succession of corridors (76)(64)(46)(65)(55)(54)(42)(21).
The fallback corridors are (34) then (76) then (65) then the series (54)(42)(21)), and correspond to the branches of the tree of the corridors of first visit to each crossroads (see Figure 5 below).

Conclusion :
The traveler therefore visits all the crossroads of the labyrinth when it has no outcome (entrance or exit), which means that one will certainly exit the labyrinth otherwise.
picture Labyrinth2


Tarry : course with overview

In the fun case where the traveler has an overview of the labyrinth, the traveler must analyze each crossroads and its adjoining corridors as follows :
A. Just before entering a crossroads, the traveler must mark the Corridor of first Visit to the crossroads (PV) which is the corridor through which the visitor enters the crossroads for the first time. To do this, he creates a PV mark at the right end of the arrival corridor.
B. Just before leaving the crossroads, the traveler must mark the Last departure corridor from the crossroads (D) which is the most recent corridor through which the visitor exits the crossroads. To do this, he creates a D mark at the right entrance to the departure corridor.

Let's see this course on the example of Figure 1.
The crossroads are marked by the numbers 1, 2... 7 where 1 is the start crossroads of the lost traveler and 7 the only outcome of the labyrinth (entrance and exit). The route of a corridor is noted by the number of the start crossroads followed by the number of the end crossroads, for example (24).
Initially, the traveler finds himself lost at crossroads 1 and seeks to reach the exit of the labyrinth (crossroads 7).

Figure 2 above shows a possible course accompanied by the marks created at the end of each arrival corridor (PV or no mark) and at the entrance to each departure corridor (D).
In the case of a dead end (single-exit crossroads), the PV and D marks are not useful since the traveler will never return to this crossroads (see crossroads 3 in Figure 2).
Let's start from the crossroads (1) and take the only possible corridor (12).
At crossroads 2, choose one of the four unexplored corridors, for example (24). At crossroads 4, let's choose, for example, corridor (45). At crossroads 5, let's choose for example corridor (52). Until now, it has been easy to apply the general rule because there was, at each crossroads visited, an unexplored corridor and each crossroads was visited for the first time.
At crossroads 2 (already visited), we cannot take corridor (21) which is the corridor of first visit to the crossroads (cf rule no. 1), nor corridor (24) already taken in this direction (cf rule no. 2). The only option left is to turn back via the corridor (25).
At crossroads 5 (already visited), let's choose for example the right corridor which is in fact a loop (55). Back at crossroads 5, let's choose for example the corridor (56). At crossroads 6, let's choose for example the corridor (64).
At crossroads 6, let's choose, for example, corridor (64).
At crossroads 4 (already visited), by application of rules no. 1 and 2, we can only take one of the two unexplored corridors (43) or (46), or turn back via the other corridor (46).
The first tactic is called "Crazy Ariadne", the second "Sage Ariadne or Trémaux Algorithm". These two tactics are equivalent if we seek to explore the entire labyrinth. The "Crazy Ariadne" tactic is, however, preferable if we are looking for a way out. Let's choose this tactic and take the corridor (43).
At crossroads 3 (dead end), we must turn back via corridor (34).
At crossroads 4 (already visited), let's choose for example the unexplored corridor (46) then, arriving at crossroads 6, the corridor (67) leading to exit 7.
In total, the course between start 1 and exit 7 of the labyrinth is given by the succession of corridors (12)(24)(45)(52)(25)(55)(56)(64)(43)(34)(46)(67).
The corridors of first visit to each crossroads are indicated in bold font.


Tarry : course without overview

In the real case where the traveler does not have an overview of the labyrinth, the traveler must stop at each crossroads and go completely around it in order to analyze all the adjoining corridors as follows :
A. Just before entering a cossroads, the traveler must temporarily mark the arrival corridor as the assumed corridor of First Visit to the crossroads. To do this, it creates a P mark at the right end of the arrival corridor. This mark also allows you to go completely around the crossroads, returning calmly to the P mark.
   - If the assumption is true (crossroads having no PV mark), the traveler must change the P mark to PV mark in order to be able to apply rule no. 1 during a next visit to the crossroads.
   - If the assumption is false (crossroads already having a PV mark), the traveler must cancel the P mark by crossing it out ("P crossed out") in order to return to initial conditions during a next visit to the crossroads.
B. Just before leaving the crossroads, the traveler must mark two particular departure corridors at the right entrance to each corridor. He must first cancel the D mark of the last corridor explored by crossing it out ("D crossed out"). He must then create a D mark on the corridor he is going to take. The "crossed out D" mark is only useful if the traveler plans to commute through the labyrint between an finish crossroads and a start crossroads. Note that, although crossed out, this mark remains a mark of a corridor already explored, therefore eligible for rule no. 2.
Figure 3 above shows the same course as that of Figure 2, accompanied by the marks created at the end of each arrival corridor (P, then PV or P crossed out) and at the entrance to each departure corridor (D crossed out if D exists, then D).
In the case of a dead end (single-exit crossroads), the P, PV and D marks are not useful since the traveler will never return to this crossroads (see crossroads 3 in Figure 3).

In the case where the traveler has nothing to mark the walls of the corridors but where he has small stones (like Tom Thumb), then the marks can be advantageously replaced as follows.
But be careful not to confuse the right entrance and left entrance to each corridor when going around the crossroads !

MarkStone management
PJust before entering a crossroads, place 1 stone at the right end of the arrival corridor.
PVAfter a complete tour of the crossroads without discovering a pair of stones at the left entrance to a corridor, add 1 stone to the stone placed.
P crossed outDuring the complete tour of the crossroads with discovery of a pair of stones at the left entrance to a corridor, finish the tour and pick up the stone placed.
D crossed outDuring the complete tour of the crossroads with discovery of a pair of stones at the right entrance to a corridor, pick up 1 stone out of the 2.
DJust before leaving the crossroads, place 2 stones at the right entrance to the departure corridor.


Tarry : shuttle between two crossroads of the labyrinth

If the traveler has made sure to keep only one D mark at each crossroads (see point B above), he can then commute, at any time and without getting lost, between two crossroads of the labyrinth as following :
- Returning to a start crossroads (for example to pick up a person left there waiting) then becomes possible and easy. At each crossroads, simply take the corridor marked PV at the left entrance to the corridor in the opposite direction, without generating new marks [PET]. The return path from an finish crossroads to any start crossroads in fact constitutes a tree whose trunk is this start crossroads and whose branches are the corridors marked PV (see Figure 5 below).
Proof : Any crossroads visited the first time is via a corridor traveled from another crossroads necessarily visited the first time. Consequently, any crossroads visited for the first time is on a tree whose trunk is the start crossroads and whose branches are the corridors of first visit to each crossroads.
This tree is called "tree of corridors of first visit to each crossroads" or "tree of crossroads visited the first time".
- Then returning to the finish crossroads (for example to bring the person back with you and continue the search together) also becomes possible and easy. At each crossroads, simply take the corridor marked D at the right entrance to the corridor in the same direction, without generating new marks [PET]. The return path from a start crossroads to any finish crossroads also constitutes a tree whose trunk is this finish crossroads and whose branches are the corridors marked D (see Figure 6 below).
Proof : Any crossroads visited the last time is via a corridor traveled from another crossroads necessarily visited the last time. Consequently, any crossroads visited last time is on a tree whose trunk is the finish crossroads and whose branches are the last departure corridors from each crossroads.
This tree is called "tree of last departure corridors from each crossroads" or "tree of crossroads visited last time".

picture Labyrinth3


Oystein : search by concentric circles

When the lost traveler knows that he is not too far from the entrance to the labyrinth (less than 2 or 3 crossroads for example), the general rule of the Norwegian mathematician Oystein Ore allows this entrance to be reached by concentric circles from the start crossroads, without the need to explore the labyrinth in depth.
The general rule is then the following [WAL] :

1. From the start crossroads, travel the corridors leading to a distance of 1 crossroads one by one, marking with a line each of the two ends of each corridor traveled.
2. Block both ends of the corridor by changing the marks to a cross in the following four cases :
   A. the corridor marked with a line is a dead end (corridor (43) in step 3 below) ;
   B. the corridor marked with a line is a loop connecting two exits from the same crossroads (corridor (55) in step 3 below) ;
   C. the corridor marked with a line leads to a crossroads already visited (corridors (45), (46) and (56) in step 3 below) ;
   D. the corridor leads to a crossroads from which all exits are blocked (corridor (25) in step 4 below).
3. Return to the start crossroads following the marks.
4. Repeat the operation by traveling all the non-condemned corridors leading to a distance of 2 crossroads, following the marks, and adding a line at each of the two ends of each corridor during its outward journey.
   E. The outward and return marks tracking is simple : their number decreases by 1 at each crossroads crossed on the way out and increases by 1 at each crossroads crossed on the way back.
5. Return to the start crossroads following the marks.
6. Repeat the operation as many times as necessary, going at a distance of 3 crossroads, then 4, etc.


Proof of Oystein's general rule :
(Complete demonstration by the Author of this Website)

Oystein's general rule is to travel the labyrinth by gradually expanding the search in concentric circles passing through the crossroads.
The level 0 circle (denoted C0) is the start crossroads.
The circle of level n (denoted Cn) whatever n > 0, passes through all the crossroads a crossroads away from the circle Cn - 1.
An outward corridor is a corridor connecting a crossroads of the circle Cm to a crossroads of the circle Cm + 1 whatever m ≥ 0. It is always traversed by marking it with an additional line at each end.
A return corridor is a corridor connecting a crossroads of the circle Cm + 1 to a crossroads of the circle Cm whatever m ≥ 0. It is always traveled without generating additional marks.
Having established these definitions, exploring a new circle Cn + 1 for given n consists of visiting at least once all the crossroads of the circle Cn + 1 using the following strategy :
- Reach each crossroads of the Cn circle via the route of outward and/or return corridors following the marks (see law E above), then travel through all the new outward corridors (unmarked and not condemned) connecting this crossroads to the crossroads of the circle Cn + 1.
- Return to the start crossroads via the return corridor route following the marks (see law E above).
Moreover :
- Condemning any corridor connecting two crossroads already visited (see law C above) amounts to removing any loop internal to the labyrinth passing through at least two crossroads (loops (4524), (464) and (5645) in step 3 below), which transforms the labyrinth into a tree whose trunk is the start crossroads and whose foliage is all the uncondemned corridors.
- Condemning any dead end (see law A above) amounts to removing any blind corridor connected to the crossroads (corridor (43) in step 3 below), which simplifies the tree by removing the terminale branches.
- Condemning any loop connecting two exits from the same crossroads (see law B above) amounts to removing any internal loop at the crossroads (corridor (55) in step 3 below), which simplifies the tree by removing the branches folded on themselves.
- Condemning any corridor leading to a crossroads where all exits are condemned (see law D above) amounts to simplifying the tree even further by removing the "dead" branches (corridor (25) in step 4 above). below).
The labyrinth finally transforms into a tree whose foliage gradually passes through all the crossroads not yet visited, including inevitably through the exit crossroads from the labyrinth.


In the fun case where the traveler has an overview of the labyrinth, the general rule applies without difficulty.
Figure 7 below shows a possible course from the start crossroads of the labyrinth in Figure 1, accompanied by the marks created on each corridor traveled (lines or crosses).
The succession of corridors traveled is as follows. Condemned corridors are indicated in bold font.
- Remote exploration of 1 crossroads : (12)(21)
- Remote exploration of 2 crossroads : (12)(24)(42)(25)(52)(21)
- Remote exploration of 3 crossroads : (12)(24)(45)(54)(46)(64)(46)(64)(43)(34)(42)(25)(55)(56)(65)(52)(21)
- Remote exploration of 4 crossroads : (12)(25)(52)(24)(46)(67)
The exit from the labyrinth (also corresponding to the entrance) is found after exploration by concentric circles at a distance of 4 crossroads.

In the real case where the traveler does not have an overview of the labyrinth, the traveler must stop at each crossroads, take a complete tour in order to analyze all the adjoining corridors, then take the return corridor in possibly condemning him. The traveler can then take the wrong corridor when a crossroads has several exits marked with a single line. For example, for crossroads 5 in step 3 below, when taking the return corridor (54), the traveler may mistakenly take the corridor (52) traveled in step 2.
The general rule must therefore be supplemented as follows :
4 bis - Just before entering a crossroads via a new corridor (unmarked and not condemned), when marking the corridor end with a simple line, the traveler must add a different mark (for example P). This particular mark will allow you to calmly take the complete tour of the crossroads and take the return corridor without mistake.

image Labyrinthe4


Distinction between crossroads and corridor

A labyrinth described in the form of a graph does not present ambiguity between crossroads and corridors, a crossroads being a node of the graph and a corridor an arc connecting two nodes.
But in reality, a crossroads or a corridor is a navigation area that can be complex to analyze at the topological level : more or less vast, more or less narrow area, with the possible presence of niches, shallow dead ends, protusions or small islets. In a crossroads already visited, the traveler may, for example, not find the exact location of an exit or worse, see new corridors appear within the same crossroads. When traveling (in the opposite direction) through a corridor already traveled, the traveler can also, for example, see new crossroads appear within the same corridor.

To avoid any ambiguity, the vocabulary must be rigorously defined as follows :
- A Labyrinth is a set of Crossroads whose Exits are all connected to Corridors.
- A Crossroads is a Navigation area with 1 Exit, 3 Exits, or more than 3 Exits (see example in Figure 8 below). The "1 Exit" case corresponds to a dead end, which is the end of a blind Corridor (crossroads 3 in Figure 1 above), or any single-corridor crossroads that may be a start crossroads (crossroads 1 in Figure 1) or an outcome from the labyrinth (crossroads 7 in Figure 1).
- A Corridor connects two Crossroads by a single Section or by a succession of several consecutive Sections (see example in Figure 8). A Corridor can form a loop when it connects two Exits from the same Crossroads (case of Figure 8).
- A Section is a Navigation area with exactly 2 Exits (see example in Figure 8). A Section is generally empty (without islets) and narrow. It can also be presented in reduced form in length, such as a doorway between two Crossroads.
- A Navigation area is a connected space (in one piece) as large as possible, having all its points intervisible or quasi-intervisible, and delimited by one or more Exits. The space may include niches, shallow dead ends, protusions and small islets. Figure 8 below gives an example of three Navigation areas : 1. a Crossroads (indicated in bold font) including five Exits (S1, S2, S3, S4, S5), a niche (N), a shallow dead end (C), a protusion (A) and two small islets (I1, I2)) ; 2. an empty Section (S3, S) ; 3. a Section (S, S4) with a small islet ; these two Sections forming a Corridor between the S3 and S4 Exits of the Crossroads.
- An Exit is the limit of a Crossroads or a Section, beyond which the intervisibility criterion for a Navigation Area is no longer respected.

image Labyrinthe5


Modeling a labyrinth and shortest path :

When we have an overview of a labyrinth, it can be modeled by an incidence matrix (M) whose rows and columns are the crossroads numbers and each element of the matrix indicates the number of corridors (0, 1, 2, etc.) connecting one crossroads to another [WAL]. Figure 10 above shows an example of a labyrinth and its corresponding incidence matrix.
The incidence matrix also makes it possible to model a labyrinth with one-way corridors [WAL] provided that these corridors do not form a loop connecting two exits from the same crossroads or a loop connecting two crossroads.

For study purposes, any labyrinth can be simplified as follows :
1. Any dead end can be removed by considering that it is integrated (as a shallow dead end) into the crossroads leading to it.
2. Any loop connecting two exits from the same crossroads can be removed by considering that it is integrated (as a small islet) into the crossroads.
3. Any loop connecting two crossroads can be reduced to a single corridor between these crossroads by considering that it is integrated (as a small islet) into this corridor.
4. Any crossroads whose number of corridors is reduced to 2 by one or more of the preceding simplifications can be removed by directly connecting the two corridors.
5. Any crossroads with n corridors such that n > 3 can be replaced by a ring formed by n crossroads with 3 corridors each [STE] on condition of agreeing to violate rule no. 2 in the modified crossroads in order to be able to travel the ring between any two crossroads (see Figure 9 above).
If the traveler knows how to navigate the modified labyrinth, then he or she can also find a path through the original labyrinth by restoring the original crossroads and corridors.
Figure 10 shows the labyrinth equivalent to that of Figure 1 by applying simplifications 1 to 4.

The incidence matrix of a labyrinth makes it possible to find the number of corridors of the shortest path connecting one crossroads to another [WAL].
By multiplying the matrix M by itself (see Figure 10), we obtain a new matrix (M2) whose elements indicate the number of different ways of going from one crossroads to another via a path made up of 2 corridors. By repeating the operation n times, we obtain a matrix (Mn) whose elements indicate the number of different ways of going from one crossroads to another by a path made up of n corridors [WAL].
To find the shortest path connecting one crossroads to another, it is then sufficient to raise the matrix M to a power such that the element corresponding to the connection between these two crossroads becomes non-zero. The power then gives the number of corridors of the shortest path [WAL].
Figure 10 above shows that the shortest path to go from crossroads 1 to crossroads 7 is obtained for n = 4 with 2 possible paths made up of n = 4 corridors.


Sources relating to labyrinth
[LUC] Edouard Lucas, Le jeu des labyrinthes, in Récréations mathématiques, tome I (2ème édition, Paris, 1882), chapitre 3, pp. 41-55.
[OYS] Oystein Ore, An excursion into labyrinths, in The Mathematics Teacher, pp. 367-370, Vol. 52, N5, May 1959.
[PET] Régis Petit, Labyrinthes et arbres, article de la revue "CANAL.N7", journal de l'association des ingénieurs de l'I.E.T.- E.N.S.E.E.I.H, N33 de septembre 1994.
[ROS1] Pierre Rosensthiel, Les mots du labyrinthe, Revue CoEvoluion. N11. Hiver 1983.
[ROS2] Pierre Rosensthiel, Labyrintologie mathématique, in Mathématiques et sciences humaines, tome 33 (1971), p.5-32.
[STE] Ian Stewart, Algorithmes labyrinthiques, article de la revue Pour la science, rubrique Visions mathématiques, N162 d'avril 1991.
[TAR] Gaston Tarry, Le problème des labyrinthes, Nouvelles annales de mathématiques 3e série, tome 14 (1895), p. 187-190.
[TOU] Pierre Tougne, Comment explorer un labyrinthe ?, article de la revue Pour la science, rubrique Jeux mathématiques, N60 d'octobre 1982, réactualisé dans Pierre Tougne, L'exploration d'un labyrinthe, Dossier Pour la science, Avril/Juin 2008.
[WAL] Jearl Walker, Comment traverser un labyrinthe sans se perdre ni tourner en rond, article de la revue Pour la science, rubrique Expériences d'amateur, février 1987.

B2. Benford's law
picture Benford's law     picture Benford's law


Introduction :

Benford's law, or Newcomb-Benford law, or law of abnormal numbers, or law of the first significant digit, shows that in everyday life, the first significant digit of numbers is not equiprobable : the number 1 is more frequent than 2, itself more frequent than 3, etc.
This curiosity is observed in many fields such as the human and social sciences, tables of numerical values, genetics, construction, economics (exchange rates) or even in the street numbers in one's address book [WIK].
Open the page of a newspaper at random, note all the numbers you find there. Then look at the first significant digit of each number. It is the leftmost digit, which is not zero. Do not take into account either the sign or the place of the decimal point : for example, the first significant digit of the numbers 0.038   3.14159 and -32 is 3.
To your great surprise, you will notice that the digit 1 appears for almost a third of the numbers, the digit 2 approximately once in 6, and that the frequency of appearance decreases until the digit 9 (less than once in 20) [ROU].

Definition :
Benford's law gives the theoretical value (f) of the frequency of appearance of the first significant digit (c) of a measurement result expressed in a given base (b) [WIK] : fc = logb(1 + 1/c)
We verify that the sum of the frequencies fc is worth : ∑i = 1 to (b-1)[logb(1 + 1/i)] = logb(b) = 1
In the decimal system (base b = 10), the law is therefore : fc = log10(1 + 1/c)
For example, the Benfordian probability that a base 10 number begins with the digit c = 1 is as follows : f1 = log10(2) = 30.1 %
The table above gives the frequency fc in percentage for each value of the first digit c between 1 and 9.
Benford's law remains invariant by changing the number base and also by multiplication by a constant, particularly when changing units.

Application areas :
Benford's law applies all the better when the series of numbers is "rich", with numbers of varied origins (case of a good mixture of any series) and/or relatively well spread over a range covering several orders of magnitude (sizes of cities for example) [ROU][DEL2].
Thus, the house numbers found in an address directory satisfy Benford's law quite well [DEL1]. If a street has 50 numbers, then more than a fifth of the numbers start with a 1 (because of 10, 11, 12... 19). If it has 20 or 200, more than half of the numbers start with a 1. It is therefore normal to find on average more often numbers starting with a 1 than with 9 (and more generally with the digit c than with c + 1) [LED1].
Benford's law does not apply for various cases, including the following [WIK][DEL1] :
- Numbers drawn at random (the digits c will then all be equally probable).
- Numbers whose first digit is imposed, for example telephone numbers or vehicle registration numbers.
- Restricted scale of possible values, for example the height of individuals in meters (almost all measurements starting with the digit 1) or the selling price of a particular model of new car (the price varies little from one dealer to another) to another).

Benford's law is mainly used to detect tax, financial, accounting and scientific fraud. The principle is as follows : if they regularly extend over several orders of magnitude, the numbers appearing in accounts or statistics must, unless there are special reasons, verify Benford's law. If these are invented numbers, then the forger must have wanted to create as many starting with 1 as with 2, 3, etc., which will contradict Benford's law [DEL2].
On doctored digital images, we can in particular distinguish artificial images from natural images, or identify images from a series containing hidden data (steganography) [DEL2].

Explanation :
Benford's law remains imperfectly explained to this day [DEL1]. The best explanation seems to be this :
We demonstrate mathematically that the sequence of natural integers (1, 2, 3... n) satisfies a "weak" form of Benford's law (in the sense of Cesàro's iterated averages) [DEL1].
This is why it seems legitimate, when the data set is "rich" (see Application areas above), to find statistically in everyday life, series of numbers whose first significant digit is not equiprobable and approximately follows Benford's law.

Case of the digits following the first :
1. Case of a block of digits in first position [WIK] : The Benfordian probability that a number in base b begins with the digit block (cde) is as follows : fcde = logb(1 + 1/cde)
For example, for the block cde = "314" in base 10, we have : f314 = log10(1 + 1/314) = 0.138 %
Another example, for the block cde = "10" in base 3 (i.e. cde = 3 in base 10), we have : fcde = log3(1 + 1/3) = 26.2 %
2. Case of a digit in position k [WIK] : The Benfordian probability that a digit (c) is at a given position (k > 1) in a number in base b is as follows : fc = ∑i = bk-2 to bk-1 - 1[logb(1 + 1/(i b + c))]
For example, the Benfordian probability in base 10 that the digit c = 0 appears in the second position (k = 2) is : log10(1 + 1/10) + log10(1 + 1/20) + ... + log10(1 + 1/90) = 12.0 %.
This law quickly approaches a uniform law with a value of 10 % for each of the ten digits (see Table above).

Case of the sequence of natural integers :

For the sequence of natural integers (1, 2, 3... n), the digits c in base b are only equally distributed (of frequency M = 1/(b - 1))) when n is exactly (b - 1), (b2 - 1)... (bp - 1) for p integer ≥ 1, which almost never happens [CHA].

Otherwise, the frequencies of the first digit c in base b constantly oscillate between two extreme values Msup and Minf taken respectively at nsup and ninf, such that [WIK][CHA] :
nsup = (c + 1) bp - 1 - 1
ninf = c bp - 1
Msup = ( (bp - 1)/(b - 1) ) / nsup   which tends to   Msupapp = b/( (c + 1)(b - 1) )   for p = +∞
Minf = ( (bp - 1)/(b - 1) ) / ninf   which tends to   Minfapp = 1/( c (b - 1) )   for p = +∞
We have the relation :   Minf ≤ Minfapp ≤ M ≤ Msupapp < Msup   since we always have :   1 ≤ c ≤ b - 1   and   b > 1

In base 10 and for p = 1, the value of the couple (Msup, Minf) is :
    (1, 1/9) for the digit 1, obtained in (nsup, ninf) = (1, 9),
    (1/5, 1/49) for the digit 5, obtained in (nsup, ninf) = (5, 49),
    (1/9, 1/89) for the digit 9, obtained in (nsup, ninf) = (9, 89).
In base 10 and for p = 2, the value of the couple (Msup, Minf) is :
    (11/19, 11/99) for the digit 1, obtained in (nsup, ninf) = (19, 99),
    (11/59, 11/499) for the digit 5, obtained in (nsup, ninf) = (59, 499),
    (11/99, 11/899) for the digit 9, obtained in (nsup, ninf) = (99, 899).
In base 10 and for p = +∞, the value of the couple (Msupapp, Minfapp) is :
    (5/9, 1/9) for the digit 1,
    (5/27, 1/45) for the digit 5,
    (1/9, 1/81) for the digit 9.
For example, the graph above shows the frequency curve of the first digit 1 (in red) and that of the first digit 9 (in blue) for integers from 1 to 10,000, in logarithmic scale [WIK].

The sequence fc(n) therefore does not converge and oscillates indefinitely between two extreme values. To smooth these oscillations [DEL1], we take the average sc(n) = (1/n) ∑k = 1 to n[fc(k)], called Cesro average. The new sequence sc(n) still does not converge but varies in a narrower interval.
By repeating this averaging process (tc(n) = (1/n) ∑k = 1 to n[sc(k)]), we obtain successive sequences (tc(n), uc(n), etc.) which vary in increasingly narrow intervals and B. Flehinger demonstrated in 1966 that the interval that we obtain by continuing these calculations of averages of averages approaches, to infinity, the expected value of the Benford's law, i.e. logb(1 + 1/c)
Thus, the frequency of integers starting with the digit c satisfies a "weak" form of Benford's law (in the sense of Cesro's iterated averages), each frequency converging towards the value logb(1 + 1/c)
This convergence in the Cesàro sense makes it possible to converge sequences which were divergent. Known example, the sequence "01010101..." converges to 1/2 in the Cesàro sense.

Case of numerical sequences :
Certain remarkable numerical sequences satisfy Benford's law at infinity, that is to say that the proportion of the terms of the sequence up to n, the first digit of which is c, tends towards the value log10(1 + 1 /c) when n tends to infinity.
This is the case of the sequences 2n, nn and (n!), as well as the coefficients of Newton's binomial [DEL1].
It is the same for any sequence rn where r is a positive real such that log10(r) is not a rational number (that is to say a ratio of two integers) [DEL1].
It is also the same for any sequence defined by a recurrence relation of type : u(n) = a1 u(n - 1) + a2 u(n - 2) + ... + ap u(n - p), in particular for the Fibonacci sequence (defined by : u(0) = u(1) = 1 and u(n) = u(n - 1) + u(n - 2)) [DEL1].

Sources relating to Benford's law
[CHA] Jean-Marie Champeau, Les illusions - La loi de Benford.
[DEL1] Jean-Paul Delahaye, L'étonnante loi de Benford, article de la revue Pour la science, rubrique Logique et calcul, N351 de janvier 2007.
[DEL2] Jean-Paul Delahaye, Une explication pour la loi de Benford, article de la revue Pour la science, rubrique Logique et calcul, N489 de juillet 2018.
[ROU] Thierry de la Rue, Gaëlle Chagny, L'incroyable statistique des premiers chiffres, Université de Rouen.
[WIK] Wikipedia, Loi de Benford.

C. Natural sciences

C1. Climat change
Picture Climat change over the past 2000 years    Picture Climat change over the past 150 years


Left Figure : evolution of the global average annual temperature of the earth's surface from year 1 to 2019, relative to the pre-industrial reference (1850-1900) [HAW].

Right Figure : evolution of the global average annual temperature of the earth's surface from 1850 to 2020, relative to the pre-industrial reference (1850-1900) [MTE3]. The connected dots show the data year by year. The solid black curve is a rolling average of the annual totals over 11 years (average of years N-5 to N+5 for year N) making it possible to overcome the modulation due to the cycle of solar activity (11 years) [POI].



Introduction :

Climate change, also called "global warming", is the significant increase in the average temperature of the earth's surface since the beginning of the 20th century.
Be careful not to confuse "climate" and "weather". Weather refers to the weather over a short period (a day, a week). Climate refers to past and future time over long periods (year, century, millennium).

The graph above in left Figure shows that this increase (from 1900 to 2019) is unprecedented in the last 2000 years. The graph is a reconstruction including data from a wide variety of records such as tree rings, cave deposits, corals, etc. Added some relevant world events such as major volcanic eruptions, the Maunder Solar Minimum and historical dates of scientific discoveries. The oft-cited Medieval Warm Period and Little Ice Age are real phenomena, but small compared to recent changes [HAW].
The graph above in right Figure shows that the decade 2011-2020 was 1.1 C warmer than the pre-industrial reference (1850-1900), with warming being greater on the continents (+1.6 C) than in above the oceans (+0.9 C) [TSP][GIE][MTE3].

The IPCC (Intergovernmental Panel on Climate Change) is a scientific body created in 1988, responsible for assessing the extent, causes and consequences of ongoing climate change.
The IPCC position confirms this warming and attributes it unequivocally to greenhouse gas (GHG) emissions of human origin, called "additional or additive or anthropogenic greenhouse effect" [WIK1].
A very broad scientific consensus endorses the IPCC position and agrees that solar irradiation is not the cause of climate change for two reasons [NAS1][NAS2] :
- Since the beginning of the 20th century, the average amount of solar energy received by the Earth has remained constant within 0.1 % [BLA] ;
- If the Sun were responsible for global warming, this warming would act in all layers of the atmosphere, from the surface to the upper atmosphere (stratosphere). However, the observations instead show warming at the surface and cooling in the stratosphere, which is consistent with the fact that the warming is caused by an accumulation of heat-trapping gases near the Earth's surface.


Controversial :

Some people, called "climate skeptics", express denial of global warming and are divided into four main trends [WIK7] :
1. those who deny global warming ;
2. those who admit global warming but deny its human origin ;
3. those who admit global warming but deny its impacts ;
4. those who have no opinion on global warming but deny the scientific consensus on the topic (conspiracy theory).
The motivations are varied and lie essentially between two positions : doubt in good faith and doubt proclaimed out of interest [POI].

In the United States, in 2023, one in two inhabitants is climate skeptic [RFI] with motivations essentially oriented towards economic interest. Positions of denial, sometimes violent, are mainly held by "skeptical bloggers", supporters of conservative economic policies, industrialists opposed to the taxation of CO2 emissions and some groups financed by the tobacco and fossil fuel industries [ WIK7][RFI].
In the "top 3" of the most climate-sceptical countries, we find Saudi Arabia at the top, then come the United States and Australia, these countries being also three major producers of hydrocarbons (oil, gas and coal) [RFI].

In France, in 2022, 37 % of people consider themselves climate skeptics, including 8 % belonging to trend no. 1 [FJJ]. We can cite :


The controversy is therefore not scientific but societal [AFI].
When the doubt is in good faith, the controversy is rather passive, experienced in public opinion as a possible, probable and uncertain scenario, in a word a "discreet" and silent catastrophe [MDS].
When the doubt is proclaimed out of interest, the controversy is active, often polluted with verbal violence, particularly on the X platform (formerly Twitter).



Greenhouse gas :

The Earth constantly receives energy from the sun in the form of visible light. 30 % is reflected by the atmosphere and the earth's surface, 20 % is absorbed by ozone and water vapor in the atmosphere, 50 % is absorbed by the earth's surface which heats up and emits infrared radiation from all the more intense as the surfaces are hot.
10 % of this radiation is emitted towards the universe, 90 % is absorbed by some gases called "greenhouse gases" and partly reradiated towards the surface, thereby slowing the loss of heat into space and causing global warming.
The Earth thus maintains an average temperature of +15 C by a natural balance between the energy of the sun absorbed and that re-emitted in the form of infrared radiation. Without these gases, the average temperature on Earth would be -18 C, and life as we know it would become impossible [NAS1][MTE1][DUF][WIK2][WIK3].
Since the beginning of the 20th century, man has considerably increased the quantity of greenhouse gases naturally present in the atmosphere, thus modifying the climatic balance through an additional greenhouse effect [MTE1].

These gases are essentially made up of the following elements [NAS1][WIK1][DUF][CDE][FRA1][ADT][CAR][BEN] :


In summary, according to these figures, global warming of human origin (additional greenhouse effect) is mainly due to fossil fuels (47 %), agriculture (25 %) and deforestation (20 %).

In France, the transport sector constitutes the largest source of greenhouse gas emissions, accounting for 30 % of national emissions.
Over the entire life cycle of vehicles (extraction and processing of raw materials, manufacturing, transportation and use of the vehicle), these emissions are attributable as follows : passenger cars (53 %), heavy goods vehicles (27 %), utility vehicles light (15 %), air transport (3 %) and other modes of transport (2 % : two-wheelers, rail and maritime) [GRE].



Carbon footprint :

The carbon footprint (or GHG balance) of a product, a person, a company, a sector of activity or a territory is a measure of the cumulative quantity of all greenhouse gas emissions that can be attributed to it. This measure can be evaluated according to two conventions :
    - either in direct emissions due to the use of energy by the final consumer ;
    - either in life cycle analysis taking into account emissions due to the use of energy but also indirect emissions due to all upstream energy transformations (research and development, production, transport, distribution ), or even downstream (recycling, dismantling) [WIK4].
Example of carbon footprint for different modes of transport (in CO2 equivalent per passenger over 100 km) : plane (20 kg), motorcycle (19 kg), gasoline car (15 kg), diesel car (14 kg), electric car (10 kg), coach (3 kg), TGV (0.2 kg) [SEL].
For a greenhouse gas, its contribution to the greenhouse effect is measured by its Global Warming Potential (GWP) defined as the radiative forcing (i.e. the radiative power that the gas returns to the ground), accumulated over a reference period of 100 years and measured relative to the same mass of CO2.
The GWP is 1 for CO2 ; 8 for water vapor ; 30 for CH4 ; 300 for N2O ; 700 to 15,000 for CFC, HFC and PFC ; 17,000 for the NF3 ; 25,000 for SF6.
The carbon footprint of gas is then expressed in grams of CO2 equivalent per kilowatt-hour (gCO2eq/kWh) corresponding to the product of the mass of gas (mog) by its Global Warming Potential (GWP).
The carbon footprint of gas is sometimes also expressed by a Carbon Equivalent (CE) which only measures the mass of carbon (C) contained in the CO2 emitted. We then have the relationship : CE = 0.2727 x mog x PRG

The Bilan Carbone is a method of calculating the carbon footprint according to three distinct scopes of emissions (direct induced by the combustion of fossil fuels, indirect induced by energy consumption, indirect other).
It takes into account the six greenhouse gases designated by the Kyoto Protocol (CO2, CH4, N2O, hydrofluorocarbons (HFC), perfluorocarbons (PFC) and sulfur hexafluoride (SF6)), as well as trifluoride nitrogen (NF3), and water vapor in the case of air transport [WIK5].

The ecological footprint (or environmental footprint) covers a broader spectrum and consists of estimating the quantity of land and water necessary for an individual or population to meet its needs without depleting natural resources or disrupting the ecosystem.
More than half of the French ecological footprint is due to the carbon footprint [WIK6].



Impacts :

The main effect of global warming is [NAT1] :


By the end of the century, if GHG emissions follow their current trajectory without additional climate policy and with high population growth (IPCC SSP3-7.0 scenario), warming will be +4 C with sea levels rising 1 m relative to the pre-industrial reference (1850-1900) [MTE4].
In this probable scenario, particularly if States engage in regional or global conflicts to the detriment of international climate policies, the IPCC identifies several key risks for Europe, which directly concern France [RCA1] :


Solutions :

The fight against climate change relies on two levers :


The recommended solutions are as follows [RCA2] [MTE2][MTE3] :


Sources relating to climat change :
[ADT] Académie des technologies, Le méthane - d'où vient-il et quel est son impact sur le climat ?.
[AFI] Afis Science, Le "climato-scepticisme" : un concept fourre-tout.
[ALL] Vanessa Allnutt, Les climatosceptiques contre la science.
[AMB] Valentine Ambert, Va-t-on manquer d'eau ?, Youmatter.
[BEN] Marc Benoît, Pollutions agricoles, CNRS Editions.
[BLA] Guillaume Blanc, Le réchauffement climatique.
[CAR] Carbone4, L'ozone des basses altitudes, une épée à double tranchant.
[CCE] Cour des Comptes Européenne, Lutte contre la désertification dans l'UE : le phénomène s'aggravant, de nouvelles mesures s'imposent.
[CDE] CDE - Connaissance des Energies, Gaz à effet de serre : d'où proviennent les émissions de méthane ?.
[DEL] Céline Deluzarche, Pourquoi manque-t-on de plus en plus d'eau alors que les pluies augmentent ?, Futura.
[DUF] Jean-Louis Dufresne, L'effet de serre, Planet Terre.
[FJJ] Fondation Jean Jaurès, Climatoscepticisme : Le nouvel horizon du populisme français.
[FRA1] Franceinfo, COP26 : on vous explique ce qu'est le méthane, l'autre gaz à effet de serre qui réchauffe le climat.
[FRA2] Franceinfo, Changement climatique : on vous explique pourquoi sécheresse et inondations sont parfois liées.
[FRI] France Inter, Algorithmes : les meilleurs amis des climatosceptiques.
[GIE] GIEC, Synthèse du rapport AR6 du GIEC publié le 27/03/2023.
[GRE] Greenly, Les transports, premier secteur émetteur en France.
[HIL] David Hiler, Réchauffement climatique : comprendre ceux qui n'y croient pas, Le Temps.
[IDV] idverde, Comment réduire les risques de pénurie d'eau ?.
[LAP] Pascal Lapointe, Les réseaux sociaux favorisent le discours climatosceptique ? Vrai, Agence Science-Presse.
[LAR] Larousse, Désertification.
[MDS] Martin de La Soudière, Le changement climatique, une "grande peur" collective ?.
[MEF1] Meteo France, Climat HD.
[MEF2] Meteo France, Tempêtes en France métropolitaine.
[MTE1] Ministère de la transition écologique et de la cohésion des territoires, Pourquoi la Terre chauffe ? 14 septembre 2018.
[MTE2] Ministère de la transition écologique et de la cohésion des territoires, Dossier de presse - 1er Plan national d'adaptation au changement climatique, 20 juillet 2011.
[MTE3] Ministère de la transition écologique et de la cohésion des territoires, Observations du changement climatique.
[MTE4] Chiffres clés du climat - France, Europe et Monde (décembre 2022).
[NAS1] NASA, Les causes du changement climatique.
[NAS2] NASA, Le Soleil est-il à l'origine du réchauffement climatique ?.
[NAT1] Nations Unis, Causes du changement climatique.
[NAT2] Nations Unis, L'eau - au coeur de la crise climatique.
[ONE] ONERC, Les évènements météorologiques extrêmes dans un contexte de changement climatique.
[POI] Jean Poitou, Climat : distinguer le vrai du faux, Progressistes.
[RCA1] Réseau Climat Action France, 6e rapport du GIEC : quelles sont les conséquences réelles du changement climatique ? 28-02-2022.
[RCA2] Réseau Climat Action France, Synthèse du 6e rapport du GIEC : l'urgence climatique est là, les solutions aussi, 20-03-2023.
[RCA3] Réseau Climat Action France, 6e rapport du GIEC : quelles solutions face au changement climatique ? 04-04-2022.
[REP1] Reporterre, Le réchauffement des sous-sols, une "menace silencieuse".
[REP2] Reporterre, Déni de réalité : pourquoi le climatoscepticisme progresse.
[RFI] RFI, Pourquoi y a-t-il encore autant de climatosceptiques aux Etats-Unis et dans le monde ?.
[RIV] Johan Rivalland, La Démocratie des crédules - Critique du dernier livre de Gérald Bronner.
[ROY] Florentin Roy, Les forêts en Méditerranée vont-elles disparaître ?, Youmatter.
[SEL] Selectra, Empreinte Carbone : calcul, définition et conseils de réduction.
[SEN] Sénat, Adapter la France aux dérèglements climatiques à l'horizon 2050 : urgence déclarée.
[TSP] The Shift Project, Climat : synthèse vulgarisée du 6ème rapport du GIEC (mars 2023).
[WIK1] Wikipedia, Gaz à effet de serre.
[WIK2] Wikipedia, Effet de serre.
[WIK3] Wikipedia, Changement climatique.
[WIK4] Wikipedia, Empreinte carbone.
[WIK5] Wikipedia, Bilan carbone.
[WIK6] Wikipedia, Empreinte écologique.
[WIK7] Wikipedia, Déni du réchauffement climatique.
[WIK8] Wikipedia, Elévation du niveau de la mer.
[ZEK] Marie Zekri, 37 % des Français se considèrent climato-sceptiques, National Geographic.


C2. Footprints of mammals and birds
Picture Mammal footprints     Picture Bird footprints


Footprints printed on the ground or in the snow allow most mammals and birds to be identified.
For birds, the identification method is based on each Isolated footprint, a bird being able to only walk or hop on the ground.
For mammals, the identification relies on the joint use of three different methods based on the following observations :
- Isolated footprint,
- Succession of footprints, giving the movement pattern of the animal,
- Droopings of the animal.





Isolated footprint

Mammal footprints are all Hand type (with 3, 4 or 5 fingers per paw, excluding palm), Pads type (with 4 or 5 digital pads per paw, excluding palm) or Hooves type (with 1, 2, 3 or 4 fingers per paw, excluding foot sole).
Bird footprints are all Hand type comprising, with some exceptions, 3 fingers per paw supplemented by a fourth opposite finger (thumb) which may be reduced or completely absent.
The 4 slides below present a method of identifying mammals and birds from their isolated footprints.

Sources :
(empreintes des mammifères) Ma Chasse, Les mammifères.
(empreintes des mammifères) France Nature Environnement - Haute-Savoie, Les empreintes.
(empreintes des mammifères) Gilles Christophe, FRAPNA, Les mammifères de Rhne-Alpes- les empreintes.
(empreintes des mammifères) Salamandre, Empreinte de mammifères.
(empreintes des oiseaux) Ma Chasse, Les oiseaux.
(oiseaux) Zadi Bridge, Combien les oiseaux ont-ils de doigts ?.
(ongulés) Puverel Camille, Leprince Julie, Atlas des mammifères de Rhône-Alpes - Les ongulés.

Picture Footprints : page1
Picture Footprints : page2
Picture Footprints : page3
Picture Footprints : page4



Succession of footprints

The slide below presents a method of identifying quadrupedal mammals from their movement pattern.
The legs are marked as follows : 1 left front leg, 2 right front leg, 3 left hind leg, 4 right hind leg, P projection in the air (hanging time).
The main movement patterns are as follows :


Nota :
- Walking exists in all quadrupedal mammals. For some, it is sometimes slow and infrequent (that of the squirrel for example).
- For the first five movement patterns (Walk, Trot, Back up, Amble, Gallop), the order of legs movement is always the same : 1 4 2 3, with some legs sometimes being moved together, being part of the same diagonal or the same side.

Sources :
(amble) Wikipedia, Amble.
(amble et galop du cheval) Dictionnaire visuel - Allures du cheval.
(bond du renard, lièvre et écureuil) Espaces, Suivre à la trace.
(bond de la belette) J'ai suivi une petite belette sauvage (Youtube, 5:45).
(bond de l'écureuil) Pilon Michel, Forum Image et Nature.
(démarche des mammifères) Les Chasseurs à l'Arc de la Réunion, LES TRACES D'ANIMAUX DANS LA FORET (EUROPE).
(démarche des mammifères) Couzi Laurent, Planche N1 intitulée "Empreintes animales" du livre Phénomènes, Juzeau C. , Rébulard M., Caradec C., Editions du Chêne, 2023.
(marche, amble et bonds) La Presse+, Jouer au détective dans la neige.
(marche, amble et bonds) Fédération Canadienne de la Faune, A la découverte du monde du pistage d'animaux.
(pas, trot et galop du cheval) Le Monde des Chevaux, Les allures.
(pas, trot et galop du cheval) Wikipedia, Allure (équitation).
(pas, trot et galop du cheval) Lenoble du Teil Jules, Etude sur la locomotion du cheval et des quadrupèdes en général, 1873, LENOBLE_ETUDE_SUR_LA_LOCOMOTION_1873.pdf (accompagné d'un atlas de 23 planches).
(reculer du cheval) Blog Equitation Nord, Hippologie : les allures.
(reculer du cheval) Devos Emma, chevalogie.free.fr, Le reculer.
(vidéos du cheval) Hippologie.fr, Les allures du cheval.
(vidéo du trot du cerf) Cerf qui court et au trot (Youtube, 4:11).
(vidéo du galop du cheval) galop au ralenti (Youtube, 1:08).
(vidéo du galop du chameau) Course de chameaux en Egypte (Youtube, 1:54).
(vidéo du bond du chevreuil) CHEVREUIL/Sauts et Course ! BRUITX (Youtube, 2:00).

Picture Footprints : page5



Droppings

The slide below presents a method of identifying mammals from the shape and texture of their droppings.
Size is another clue. It is generally proportional to the length of the animal's rectum, therefore also to the size of the animal.
Color is also another clue, but it depends on the freshness of the deposit and the ingestion of some foods. For examples :
- Fresh mouse droppings are black and turn brown after about 24 hours.
- The color of hedgehog droppings can vary from black to brown to different shades of gray, depending on its diet which mainly consists of insects, molluscs and small vertebrates.
- A dog that eats too many bones or industrial food containing too much animal flour will produce white droppings. In the sun, the white color will be even more pronounced because the water contained in the droppings evaporates, bringing out the calcium.
- A wolf that swallows the bones of its prey will produce white droppings.

The deposit of droppings is generally done on the paths taken by the animal. For carnivores, in addition to the natural evacuation function, the deposit corresponds to the visual and odorous marking of the territory, often at crossroads between paths.

Sources :
(détail) Gilles Christophe, FRAPNA, Les mammifères de Rhne-Alpes - Les fèces.
(détail) Martin Alexis, Petit guide illustré des crottes de mammifères.
(détail) Salamandre, Crottes de mammifères.
(général) Espace pour la vie Montréal, Des crottes qui en ont long à dire.
(images) Lahaye Romain, Atlas préliminaire des Mammifères sauvages de Bourgogne.
(tableau) France Nature Environnement - Haute-Savoie, Les crottes.
(tableau) Carbala, Espace outil pédagogique.

Picture Footprints : page6



D. Sciences and technologies

D1. Scientific approach and systemic modeling
Picture Scientific approach


The scientific approach consists mainly of six steps :
    1. Observation and measurement of a phenomenon ;
    2. Systemic modeling and formulation of the simplest theory correctly accounting for all the observed facts ;
    3. Experimentation and validation of the theory ;
    4. Comparison with existing theories ;
    5. Communication of the results obtained to his peers for revalidations and possible criticisms ;
    6. Use of the theory to predict or reproduce the phenomenon.
Warning : Any criticism must be constructive to be admissible, that is to say be factual, without value judgment and without ironic or disrespectful remarks, in short, be worthy of the critic.

The systemic modeling is a stage of the scientific approach which consists in describing physical phenomena in the form of systems. The challenge is to find the right level of model : neither too simple to take into account all the physical observations, nor too complex to set the model parameters from these observations.
Systemic modeling also aims to divide systems into subsystems in an optimal way according to four main principles of systemes urban planning :

1. "Divide to conquer" or modularity principle. The goal is to cut the system into subsystems of optimal size and each having its autonomy of exploitation and use.
The temporary unavailability of a subsystem does not prevent the other subsystems from operating.

2. "Group to simplify" or subsidiarity principle. The goal is to pool what can be pooled and to treat each specificity as a differential with respect to the general case.
Complexity is isolated in easily manageable special case subsystems and does not put generic subsystems at risk.

3. "Distribute to better communicate" or reducing adhesions principle. The goal is to minimize the adhesions between subsystems and to compensate by a dynamic cooperation between them.
The data exchanged between subsystems are only created and modified in a single subsystem (notion of proprietary subsystem).
The information exchanges between subsystems are done via standardized interfaces.

4. "Start small but think big" or progressiveness principle. The goal is to provide for an evolution of the system in stages and starting from the existing one.


D2. Digital optical disk (CD, DVD and BD)
Picture Digital optical disk


Definition :
The Digital Optical Disk (DON) is a removable flat disk used to store digital data in the fields of computers, audio and video.
The best known disks are CD, DVD and BD :


The acronym CD, DVD or BD is followed by the burning mode : ROM (Read-Only Memory) for read-only disk, ±R (Recordable) for disk that can only be written to once, ±RW (Rewritable) or ±RE for rewritable disk.
The acronym ± of burning mode corresponds to two different DVD standards, the old players not being compatible with the + standard which is more recent.

Constitution :
A digital optical disk is a stack of several layers (see Figure above) :


Data is written in the base layer for ROM, in the dye layer for ±R and in the reflective layer for ±RW, on a spiral-shaped track that is almost 5 km long for disks CD, from the center outwards.
Optical reading is binary (0 or 1). The information is made up of micro-pits and lands. Any state change (land to micro-pit or vice versa) is translated by a '1', and all the lengths of lands and micro-pits by '0'.

Lifetime :
The objective lifetime of a digital optical disk ranges from 2 years to 20 years, and sometimes longer if all precautions are taken. It strongly depends on the choice of media, the use conditions and the storage conditions of the disk.

Choice of media :


Use :


Conservation :


Sources :
Wikipedia - Disque Compact.
Wikipedia - DVD.
Wikipedia - Disque Blu-ray.
Level - Quelles sont les différences entre un CD et un DVD ?.
Infobidouille - La question technique 6 : CD, DVD, BLU-RAY, RW... Comment ça marche les supports optiques ?.
FISTON production - Inquiétudes sur la durée de vie des DVD enregistrables.
Maxicours - Stockage optique.
expert multimedia - Caractéristiques techniques d'un DVD.
Chaumette O., AGIR/PHYSIQUE/CHAP 20 - Le principe de la lecture d'un disque optique (CD, DVD, BluRay...).
Gouvernement du Canada - Durabilité des CD, des DVD et des disques Blu-ray inscriptibles.
Centre de conservation du Québec - Critères de choix d'un disque optique, guide d'entretien et de manipulation.
SOSORDINATEURS - Quelle est la durée de conservation des CD, DVD et Blu-Ray.
VERBATIM - Les différences significatives de performance entre les couches réfléchissantes en argent et en aluminium soulignent l'importance de savoir ce que vous achetez.
Que Choisir - Durée de vie des DVD - Conseils.
Ballajack - Durée de vie d'un CD ou DVD gravé, comment les conserver ?.

E. Social sciences

E1. The life laws


A small number of truth seekers, notably Svâmi Prajnânpad, have simply described the laws of life as follows (from the book [Petit Régis, Une approche scientifique du silence]).

  1. Definitions
  2. Law of difference
  3. Law of change
  4. Law of causality
  5. Law of the psyche
  6. The life purpose
  7. Silence and fullness
  8. To love
  9. To desire
  10. To act
  11. To live in society
  12. To give
  13. To help others
  14. To die
  15. Sources



E1.1. Definitions

* Svâmi Prajnânpad, the truth, emotion / feeling, to think / to see

Svâmi Prajnânpad (alias Svâmiji, 1891-1974) was a Bengali Brahmin who had received dual training, classical Vedantic and modern scientific trainings.
A master of wisdom and lucidity, his rigorous approach is a dive into the heart of the unconscious which reveals the difficulties hindering the silence of mental. No God, no ritual, no paradise.
André Comte-Sponville said about him : "This master is content to see, to be one with what he indifferently calls truth or reality, which is neutral, neither good nor bad, neither pleasant nor painful, and promised only change or death." [PDS 2]
According to the specific vocabulary of his teaching [EHM 1] :

* Inner peace, truth, science

* Ego, attachment, mental, identification

* Thought, emotion, desire

* To be

* Spirituality



E1.2. Law of difference : Every thing is different and unique
Picture The life laws - Difference



E1.3. Law of change : Everything that comes goes away
Picture The life laws - Change



E1.4. Law of causality : For every effect there is a cause
Picture The life laws - Causality



E1.5. Law of the psyche : The mental creates a "second", the truth is "one without a second"
Picture The life laws - The mental creates a second



E1.6. The life purpose
Picture The life laws - The life purpose



E1.7. Silence and fullness
Picture The life laws - Silence and fullness



E1.8. To love
Picture The life laws - To love



E1.9. To desire
Picture The life laws - To desire



E1.10. To act
Picture The life laws - To act



E1.11. To live in society
Picture The life laws - To live in society



E1.12. To give
Picture The life laws - To give



E1.13. To help others
Picture The life laws - To help others



E1.14. To die
Picture The life laws - To die



E1.15. Sources


[ARI 1] Association pour le Rayonnement Culturel Indien, Citation de Mata Amritanandamayi, La Lettre N3 de l'ARCI, 2ème trimestre 1987
[BTC 1] Bouchet Christian, Gurdjieff - qui suis-je, Pards 2001
[CSA 1] Comte-Sponville André, De l'autre côté du désespoir - Introduction à la pensée de Svâmi Prajnânpad, Accarias-L'Originel 1997
[CSO 1] Cambessédès Olivier, Le quotidien avec un maître Svami Prajnanpad, Accarias L'Originel 1995
[DAF 1] Desjardins Arnaud et Farcet Gilles, Confidences impersonnelles, Critrion 1991
[DAF 2] Desjardins Arnaud et Farcet Gilles, Regards sages sur un monde fou, La Table Ronde 1997
[DAL 3] Desjardins Arnaud et Loiseleur-Desjardins Véronique, La voie et ses pièges, La Table Ronde 1992
[DAL 4] Desjardins Arnaud et Loiseleur-Desjardins Véronique, L'ami spirituel, La Table Ronde 1996
[DEA 1] Delaye Alain, Sagesses concordantes - Quatre maîtres pour notre temps : Etty Hillesum, Vilama Thakar, Svâmi Prajnânpad, Krishnamurti, Volume I, Accarias-L'Originel 2003, 2011
[DSA 7] Desjardins Arnaud, A la recherche du Soi 1 - Adhyatma yoga, La Table Ronde 1977
[DSA 8] Desjardins Arnaud, A la recherche du Soi 2 - Le vedanta et l'inconscient, La Table Ronde 1978
[DSA 9] Desjardins Arnaud, A la recherche du Soi 3 - Au-delà du moi, La Table Ronde 1979
[DSA 10] Desjardins Arnaud, A la recherche du Soi 4 - Tu es cela, La Table Ronde 1980
[DSA 15] Desjardins Arnaud, La voie du coeur, La Table Ronde 1987
[DSA 17] Desjardins Arnaud, Zen et Vedanta - Commentaire du Sin sin ming, La Table Ronde 1995
[DSA 19] Desjardins Arnaud, Retour à l'essentiel, La Table Ronde 2002
[DSA 21] Desjardins Arnaud, Bienvenue sur la voie, La Table Ronde 2005
[DSA 23] Desjardins Arnaud, Lettres à une jeune disciple, La Table Ronde 2006
[DSD 1] Desjardins Denise, De naissance en naissance, La Table Ronde 1977
[DSD 3] Desjardins Denise, Mère sainte et courtisane, La Table Ronde 1983
[DSD 7] Desjardins Denise, La route et le chemin - Carnet de voyage et d'ascèse, La Table Ronde 1995
[DSD 9] Desjardins Denise, Conteurs, Saints et Sages - Des Pères du désert à Swâmi Prajnânpad, La Table Ronde 1998
[DSD 10] Desjardins Denise, Petit traité de l'action, La Table Ronde 1999
[EHM 1] Edelmann Eric, Humbert Olivier et Dr Massin Christophe, Swâmi Prajnânpad et les lyings, La Table Ronde 2000
[FTG 1] Farcet Gilles, Arnaud Desjardins ou l'aventure de la sagesse, La Table Ronde 1987
[FTG 3] Farcet Gilles, La transmission selon Arnaud Desjardins, Le Relié 2009
[GKG 1] Guéshé Kelsang Gyatso, Vivre une vie pleine de sens - Mourir dans la joie, Tharpa France 2017
[GKG 2] Guéshé Kelsang Gyatso, Transformez votre vie. Un voyage plein de félicité, Tharpa France 2009
[LRF 1] Leboyer Frédérick, Portrait d'un homme remarquable - Svami Prajnanpad, Critérion 1991
[LRV 1] Loiseleur-Desjardins Véronique, Anthologie de la non dualité, La Table Ronde 1981
[MAM 1] Mâ Ananda Moyî, L'enseignement de Mâ Ananda Moyî, traduit par Josette Herbert, Albin Michel 1974
[MRD 1] Marol et Roumanoff Daniel, Sois sage, La Table Ronde 1994
[NIL 1] Nduwumwami Louis, Krishnamurti et l'éducation, Du Rocher 1991
[OPD 1] Ouspensky Petr Demianovitch, L'homme et son évolution possible, Denoël 1961 puis Accarias L'Originel 1999
[OPD 2] Ouspensky Petr Demianovitch, Fragments d'un enseignement inconnu, Stock 1974
[PDS 1] Prajnanpad Svami, L'art de voir, Lettres à ses disciples - Tome 1, Traduction de Colette et Daniel Roumanoff, Accarias-L'Originel 1988
[PDS 2] Prajnanpad Svami, Les yeux ouverts, Lettres à ses disciples - Tome 2, Traduction de Colette et Daniel Roumanoff, Accarias-L'Originel 1989
[PDS 3] Prajnanpad Svami, La vérité du bonheur, Lettres à ses disciples - Tome 3, Traduction de Colette et Daniel Roumanoff, Accarias L'Originel 1990
[PDS 4] Prajnanpad Svami, A B C d'une sagesse, Paroles choisies par Daniel Roumanoff, La Table Ronde 1998 puis Albin Michel 2009
[PDS 5] Prajnanpad Svami, L'éternel présent - Questions et réponses - Entretiens avec Pierre Wack, Traduction de Daniel Roumanoff, Accarias-L'Originel 2002
[PDS 6] Prajnanpad Svami, Les formules de Swâmi Prajnânpad commentées par Arnaud Desjardins, Formules et commentaires rassemblés par Véronique Desjardins, La Table Ronde 2003
[PDS 7] Prajnanpad Svami, Le but de la vie - Un été plein de sagesse, Entretiens avec Roland de QuatreBarbes été 1966, traduits par Daniel Roumanoff, Accarias-L'Originel 2005
[PDS 8] Prajnanpad Svami, Svâmi Prajnânpad pris au mot - Les Aphorismes, Recueillis et traduits par Frédérick Leboyer, Accarias-L'Originel 2006
[PDS 9] Prajnanpad Svami, Ceci Ici A présent - Seule et unique réalité, Entretiens avec Frédérick Leboyer (première série, janvier et février 1963), Traduction de Colette et Daniel Roumanoff, Accarias-L'Originel 2006
[PDS 10] Prajnanpad Svami, La connaissance de soi - Citations commentées des Upanishad et histoires (tome 1), Mises en forme par Daniel Roumanoff, Accarias-L'Originel 2008
[PSP 1] Prakash Sumangal et Prajnanpad Svami, L'expérience de l'unité, Traduction de Colette et Daniel Roumanoff, Accarias-L'Originel 1986 puis 2013
[RFD 1] Roumanoff Daniel, Svâmi Prajnânpad - Tome 1 Un maître contemporain - Manque et plénitude, La Table Ronde 1989, puis regroupé avec le Tome 3 chez Albin Michel 2009 sous le titre "Tome 1 Les lois de la vie"
[RFD 2] Roumanoff Daniel, Svâmi Prajnânpad - Tome 2 Le quotidien illuminé, La Table Ronde 1990, puis Albin Michel 2009
[RFD 3] Roumanoff Daniel, Svâmi Prajnânpad - Tome 3 Une synthèse Orient Occident, La Table Ronde 1991, puis regroupé avec le Tome 1 chez Albin Michel 2009 sous le titre "Tome 1 Les lois de la vie"
[RFD 4] Roumanoff Daniel, Candide au pays des Gourous - Journal d'un explorateur de l'Inde spirituelle, Dervy 1990
[RFD 5] Roumanoff Daniel, Svâmi Prajnânpad - Biographie, La Table Ronde 1993
[RFD 6] Roumanoff Daniel, Psychanalyse et sagesse orientale - Une lecture indienne de l'inconscient, Accarias L'Originel 1996
[SNR 1] Srinivasan Ramanuja, Entretiens avec Svami Prajnanpad, Traduction de Colette Roumanoff, Accarias-L'Originel 1984


E2. Smells and flavors


Smell and taste are the two senses that aroused the least interest from scientific researchers until the 1960s.
Today, we know that the sensory perception of smells and flavors is a subtle mix between universal principles, personal perception and culture.



Smells

Picture Smells


Smells are molecules detected chemically by olfactory receptors located in the nasal cavity.
They can take two distinct routes : a direct route, called orthonasal, located in the nose (concept of "smell") or an indirect route, called retro-nasal, located in the back of the throat (concept of "aroma" released by food in the mouth).
There is to date no universal consensus on the categorization of smells. Only perfumery and oenology have produced specific classifications.
The table below allows you to simply categorize smells according to their effects (unpleasant/pleasant) and their origins (mineral, plant, animal, human).


Sources :
Claude Boisson, "La dénomination des odeurs : variations et régularités linguistiques", Intellectica, 1997/1, 24, pp. 29-49.
Sophie David, Danièle Dubois, Catherine Rouby, Benoist Schaal, "L'expression des odeurs en français : analyse lexicale et représentation cognitive", Intellectica, 1997/1, 24, pp. 51-83.
Dico du Vin, Odeurs du vin, nouvelle classification, Dico-du-Vin 2023.
Danièle Dubois, "Des catégories d'odorants à la sémantique des odeurs", Terrain, 47 | 2006, 89-106.
Camille Gaubert, 03.05.2022, "Notre perception des odeurs n'est que très peu liée à notre culture", Cerveau et Psy.
André Holley, "Le physiologiste et la catégorisation des odeurs", Intellectica, 1997/1, 24, pp. 21-27.
L'Atelier du Vin, Guide des arômes du vin et de leur perception en oenologie.
Hervé-Pierre Lambert, "L'imaginaire, les neurosciences et l'olfactif : confirmations et extrapolations", IRIS, 33 | 2012, 37-51.
C. Sulmont-Rossé, I. Urdapilleta, "De la mise en mots des odeurs", chapitre 28 (pp. 373-382) du livre : Odorat et Goût : de la neurobiologie des sens chimiques aux applications agronomiques, industrielles et médicales, Edition QUAE.
Luca Poyo Vallina, 24 nov. 2022, "Les 10 principales odeurs perçues par l'odorat humain", Divain, .
Wikipedia, Rétro-olfaction.



Flavors

Picture Flavors


Flavors are molecules detected chemically by taste receptors located on the taste buds of the tongue.
Other sensations in the mouth, also called "flavors" in the broad sense, do not involve the taste buds and are sensory (olfactory, auditory, visual) and somesthetic (thermal, tactile, proprioceptive (position and movement) and nociceptive (pain)).
The table below describes the basic flavors, "flavors" being taken in the broad sense. They can then combine with each other to form more elaborate taste sensations.


Sources :
Le Thi Maï Allafort, Connaissez-vous les mots du goût ? Lorsque les textures font le plaisir !, Marie Claire.
Christine Belloir, Récepteurs gustatifs humains : étude des relations structure-fonction, Thèse 2019, Université de Bourgogne.
Diane Boivineau, Evaluation gnoso-praxique linguale des enfants avec trouble structurel du langage oral, Mémoire 2013/2014, Université Paris VI.
Loïc Briand, "La chimie du goût", CultureSciences-Chimie.
Juliette Defossez, Vers un langage du goût : approche expérimentale d'une communication multimodale à destination des mangeurs, Thèse 2014, Université de Bourgogne.
Audrey Dufour, 24/01/2017, "Comment reconnaît-on les saveurs ?", La Croix.
Goûts et Papilles, C'est quoi le goût ? Odeur, saveur, flaveur....
FasterCapital, Au-delà du goût : comment la texture influence notre perception des aliments.
Claire Gresser, Contribution à l'étude de la composante trigéminale dans la posture cervico-faciale, Thèse 2005, Université de Lorraine.
Tanya Lewis, 5 octobre 2021, "Ce que les piments peuvent nous apprendre sur la douleur", Pour la Science.
Christophe Otte, Olivier Otte, Régulation des dysfonctions maxillo-faciales de l'enfant, Clinique OPS.
Dale Purves, George J. Augustine, David Fitzpatrick, Lawrence C. Katz, Anthony-Samuel LaMantia, James O. McNamara, Neurosciences - Les sens chimiques, DeBoeck
Rapport du groupe PNNS - Qualité gustative des aliments et environnement des repas : restauration scolaire, hospitalière et aide alimentaire, décembre 2010.
Si on me coupait la langue, pourrais-je toujours savourer mes repas ?, La sensation trigéminale.
Wikipedia, Goût.
Wikipedia, Thermorécepteur.


F. Society

F1. Planned obsolescence and consumer products
Picture Consumer products


Current or durable consumer products offered on the markets do not always have the expected quality. The main causes are the following :

A. "Construction" defect of the product
Three types of fault exist :


In France nearly 10 % of electronic devices purchased on the Internet are returned due to non-compliance.
For domestic electrical devices, the faulty component is often the electronic block of the device (examples : freezer, steam iron, thermal resistance of towel dryers, lighting of bathroom cabinets with touch control, outdoor solar light garland, DVD player).

B. Non-optimal user manual
The product user manuel is sometimes succinct, poorly structured, roughly translated into French or written only in English, which does not allow consumers to use the product easily and appropriately.

C. Non-optimal consumer service
Access to consumer service is not always easy (examples : unclear access methods, premium rate telephone number, unspecified waiting time).
Furthermore, the processing of requests and complaints is sometimes disconcerting or even flawed, with some operators not always having sufficient training in the products and services in the catalog, in internal procedures and in IT tools.

D. Premature and planned obsolescence of the product
Planned obsolescence is a market practice justified by manufacturers for economic (see Consumer society), technical and risk prevention reasons. The consumer suffers the consequences : he is frustrated when he notices that the effective lifespan of his product does not correspond to the lifespan he expects.
But the causes of obsolescence are not only linked to the producer. They may occur during sale, distribution or consumption. This is why we speak more widely of premature obsolescence.
Different types of premature obsolescence can shorten the life of consumer products [CLI][HIP] :


France is the first country in the world to have criminalized planned obsolescence through article L. 441-2 of the Consumer Code dated March 14, 2016.
Law n 2021-1485 of November 15, 2021 relating to the reduction of the digital environmental footprint in France (REEN law) then modified this article by redefining the offense as follows : "The practice of planned obsolescence is prohibited which is defined by the use of techniques, including software, by which the person responsible for placing a product on the market aims to deliberately reduce its lifespan".
Warning : there may be "obsolescence" without it being planned. It is up to the consumer to provide proof of the voluntary intention of the manufacturer to reduce the life of the product : difficult or even impossible task.

One of the solutions aimed at combating planned obsolescence is the services rental. Instead of owning a good, we would pay for the service rendered. Companies would then benefit from manufacturing durable and easily repairable goods (example : Xerox in the professional photocopier market) [WIK].

Sources relating to planned obsolescence :
[HIP] HIPPOCAMPE, Usages numériques et terminaux.
[CLI] LE CLIMATOSCOPE, L'obsolescence prématurée de nos produits de consommation : un débat à remodeler.
[WIK] WIKIPEDIA, Obsolescence programmée.

F2. Consumer society
Picture Consumer society


Introduction :

The consumer society is a type of society within which consumers are encouraged to consume goods and services on a regular and abundant basis [JDN].
It appeared in Western countries from the second half of the 20th century, at the same time as some trends such as the women emancipation, industrial and technological innovation, globalization of trade.
The economy will then rely on the production capacities of companies as well as on the consumption capacities of citizens. It will increase the living standard of a large number of citizens in terms of comfort and material well-being, by increasing access to goods and services in volume and diversity.
But gradually a new paradigm is emerging : "consume more, produce more, earn more". Producers and consumers then mechanically become hyper-producers and hyper-consumers. The first ones offer an abundant supply based on products with a limited lifespan (Premature obsolescence). The seconds have demands that go well beyond their primary needs.


Results :

This situation, where producers and consumers are closely linked around the industry of "desire", has resulted in the following consequences on the individual and their environment :

1. On an information level, the media (press, edition, poster, radio, television, cinema, Internet network, telecommunications) broadcast to the consumer (reader, listener, spectator, Internet user) a mass of more or less accurate information, amplified by social networks and content sharing platforms.
Broadcast can take different forms :


2. On an audiovisual communication level, the media, whose concern is to preserve a market more than to ensure the civic education of the masses, become a source of sensory pollution and overstimulation of the senses to the detriment of useful information [BEN]. See Media violence.

3. On an ecological level, overconsumption encourages waste and the production of waste which pollutes, even if progress is made to recycle it as cleanly as possible.

4. On a nutritional level, overconsumption promotes the appearance of pathologies such as diabetes and obesity.

5. On a professional level, the perpetual creation of new needs can lead to over-indebtedness, overwork or insecurity.

6. On a psychological level, the search for "always more" can lead to continual frustration which generates discomfort, depressive and even aggressive behavior.

7. On a social level, the human being has also become a "product" who must "know how to sell himself", who must enter into "competition", "at war" with everyone and others.

8. On a moral level, consumer objects become ends in themselves leading to a loss of "true purpose".

9. On the human level, social relations become simple means and are therefore artificial. We must then differentiate ourselves from others, in particular by impressing others with symbols of wealth and power to the detriment of the authenticity and depth of human relationships.

10. On a spiritual level, having replaces being, depth, introspection, reflection on identity based on something other than possessions [GUI].


Conclusions :

Today the consumer society, which has become a society of overconsumption, is beginning to move towards a society of deconsumption along four axes :

1. Individual sufficiency which consists of consuming less and differently, favoring quality rather than quantity.
To be applicable at the level of each consumer, this sobriety must be "happy", that is to say without the idea of restriction or sacrifice. Examples : second-hand purchase, recourse to repair, return to essential needs.
This trend would be driven in France by the elderly (with fewer needs), women (attracted towards ecology) and the most qualified (attracted towards a form of daily asceticism) [GOL][CAS].

2. Collaborative economy based on the sharing or exchange between individuals of goods (car, housing, parking, drill, etc.), services (passenger transport, DIY, etc.) or knowledge (computer courses, communities of learning, etc.), with or without monetary exchange, with or without digital networking platform.
By reducing or even eliminating intermediaries, this economic system allows you to moderate your expenses and save money.

3. Circular economy focused on a sustainable strategy which consists of sharing, reusing, repairing, renovating and recycling products and materials for as long as possible so that they retain their value.
In France, we can cite the following examples :


4. Waste management which consists of collecting it and then transforming it, prioritizing in order: reuse, recycling, elimination [MTE].

In France, in 2018, 66 % of treated waste is recycled, 7 % is incinerated with or without energy recovery and 27 % is landfilled [NOT].


Sources relating to consumer society :
[ADE1] ADEME, Economie circulaire : notions, 2013.
[ADE2] ADEME, Potentiels d'expansion de la consommation collaborative pour réduire les impacts environnementaux, 2016.
[AGE] Agence Lucie, L'économie circulaire.
[ALT] Altermaker, Economie circulaire : définition et exemple.
[BEN] Abdellatif Bensfia, "François HEINDERYCKX (2003), La malinformation. Plaidoyer pour une refondation de l'information", Communication, Vol. 23/2 | 2005, 259-265..
[CAS] Jean-Laurent Cassely, Les diplômés, bons élèves ou cancres de l'alterconsommation ?, in Constructif, juin 2021 (N59).
[CHI] Chilowé, Comment vivre la sobriété heureuse au quotidien ?.
[DES] Cécile Désaunay, Vers la déconsommation ?, in Constructif, juin 2021 (N 59).
[GOL] Mathilde Golla, La société de déconsommation commence à faire son chemin, Novethic.
[GUI] Valérie Guillard, La société de consommation, cours PSL Paris-Dauphine.
[IMP] impots.gouv.fr, Economie collaborative et plateformes numériques.
[JDN] JDN - Journal du Net, Consommation : définition simple.
[MAR] Margaux, Société d'hyperconsommation : comment en sommes-nous arrivés là ? Comment changer demain ?, Suricates Consulting.
[ODI] ODI - Observatoire de la Déontologie et de l'Information, L'information au coeur de la démocratie - Rapport Annuel 2017.
[RUM] Yannick Rumpala, Quelle place pour une "sobriété heureuse" ou un "hédonisme de la modération" dans un monde de consommateurs ?, in Dans L'Homme & la Société 2018/3 (n 208), pages 223 à 248.
[TOU] La Toupie, Toupictionnaire.
[WIK1] Wikipedia, Société de consommation.

Sources relating to waste management :
[ADE3] ADEME, Déchets chiffres-clés - Edition 2023.
[MTE] Ministère de la transition écologique et de la cohésion des territoires, Traitement des déchets.
[NOT] notre-environnement, Le traitement des déchets.
[REC] Recygo, Poubelles de tri sélectif, comprendre les codes couleurs.
[SEN1] Sénat, Les nouvelles techniques de recyclage et de valorisation des déchets ménagers et des déchets industriels banals.


F3. Surveys
picture Surveys


Introduction :
A survey is, by definition, a statistical method of analyzing a population based on a sample of this population.
It are mainly used for political purposes (to help with decision-making), electoral purposes (to exist in the political landscape), commercial purposes (to anticipate sales of a product or find out customer satisfaction), activist purposes (to defend a cause) or media purposes (to build audience).
The quality of the information collected depends largely on the rigor surrounding the completion of the survey and the interpretation of results.
The important parameters of a survey are as follows :

Sample size [GUM][SER] :
Sample size is a determining factor in obtaining reliable results.
The following formula (Cochran's formula) determines the number of people (n) to question based on the margin of error (m) that can be tolerated on a proportion of responses (p).
n = σ2 x p (1 - p) / m2
p is the expected proportion of responses relative to the sample size n (when p is unknown, we use p = 0.5).
m is the error margin tolerated for the proportion p, the confidence interval equal to [p - m, p + m].
NC is the confidence level (or probability) that the answers are within the error margin (m).
z is the quantile of order α/2 of the reduced centered normal distribution for a given confidence level NC = 1 - α (z = 1.96 for NC = 95 %, z = 2.58 for NC = 99 %).
With a confidence level of 95 % and an error margin of 5 %, the calculation gives : n = 384.16
With a confidence level of 99 % and an error margin of 2 %, the calculation gives : n = 4144.14
For a sufficiently reliable market study, we most often accept a confidence level of 95 % and an error margin of 5 %, which requires interviewing 400 people.

Note that the error margin only takes into account random error, that is to say the possible differences between sample and reference population due solely to random sampling [TOU]. It does not take into account all other errors (representativeness of the sample, quality of the questionnaire, conduct of the survey, analysis of the results).

Proof of Cochran's formula [WIK1][WIK2][WIK3] :

We seek to estimate the real proportion (p) of a population likely to respond positively to a questionnaire.
To do this, we carry out a survey on a restricted population by submitting the questionnaire to a number (n) of individuals drawn at random.
The survey is assumed to be based on a simple random sample from a large population.
If we repeat the operation several times, the proportion of responses obtained then follows a binomial law with mean p and standard deviation σ = (p (1 - p) / n)1/2
For n sufficiently large, this binomial law is very close to a normal law with mean p and standard deviation σ
To obtain the margin of error (m) on the proportion p, we simply multiply the standard deviation σ by the factor z of the reduced centered normal distribution for a given confidence level (NC), which gives :
m = z σ = z (p (1 - p) / n)1/2
Hence the formula :
n = σ2 x p (1 - p) / m2
Note that the margin of error is maximum for p = 0.5


Representativeness of the sample :
The sample must be representative of the reference population if we want to extrapolate the survey results to the entire population.
it is necessary to ensure that the sampling frame is complete, up to date and without repetition, and containing all categories of society - If it is a random survey carried out from a sample drawn at random from the entire population, it must be ensured that the sampling base is complete, up to date and without repetition, and containing all categories of society (origin , sex, age, profession, region, etc.) [GUM][LAL]. This is the method used for example for major surveys carried out by INSEE [TOU].
- If it is a selection survey with judicious choice (quota methods), it must be ensured that the quotas are substantially proportional to the fraction of the population represented by each category. This option is favored by polling institutes in France and applied to much smaller samples, generally 1000 or 2000 people [TOU].
- Internet surveys allow you to interview large numbers of people at low cost. However, email lists are generally not representative and 20 % of the population, not "connected to the Internet", is omitted [LAL].

Clarity of the questionnaire :
- Indicate the total estimated time to answer the questionnaire, which should not be too long as it risks tiring the participant.
- Limit the questionnaire to 15 questions and each question to a single subject comprising 20 words maximum. For example, asking "How do you rate the quality of our product and customer service ?" leads to confusion which leads to ignoring the question.
- Avoid sensitive questions linked in particular to money, religion, intimacy, sexuality or family conflicts.
- Adapt the vocabulary to that of the population interviewed. For example, the question "France devotes around a quarter of national income to financing social protection. Do you consider this to be excessive, normal or insufficient ?" can be advantageously simplified by the question "Do you think that enough is spent on social protection ?".
- Give a definition of acronyms, technical words and little-used words.
- Do not use restrictive words such as "always", "never", "all" or "none", which prevent people from qualifying their comments and responding objectively.
- Do not ask imprecise questions, such as : "Have you been to the cinema recently ?" or "How much gasoline do you consume on average ?".
- Do not ask questions based on statements, such as : Do you agree with the statement "The police should not intervene" ?
- Do not ask questions containing superlatives or subjective adjectives, even emotionally charged or controversial, such as : "Was our customer service excellent ?" or "How amazing was your stay at our hotel ?".
- Do not ask questions containing implying words, such as : "Are you afraid of noise in your home ?" or "Are you excited to discover our new online store ?".
- Do not ask questions containing negative terms, such as : "Do you prefer not to use electrically assisted bicycles during your bike rides ?".
- Never use a double negative such as : "In your opinion, is the use of glycophate not without danger ?".

Effectiveness of the questionnaire :
- Prefer closed questions (single choice or multiple choices, to be selected from a list of options) to open questions (collection of opinions), the latter leading to a long and difficult statistical analysis of the responses.
- For each closed question, limit the number of options, without forgetting the "Not concerned" or "Without opinion" option.
- Avoid imprecise options, such as "usually" or "often", replace with a clear concept such as "every day" or "more than twice a week".
- Avoid the single binary choice "Yes"/"No" which leads people to respond in a less thoughtful way and favors the "Yes" answer to appear more pleasant (positivity bias or tendency to acquiesce [JAC][SOU]). Instead, offer a single choice between two or more response options.
- For single choices with more than 2 options, prefer the choice with 4 balanced options, such as : "Very satisfied", "Satisfied", "Dissatisfied", "Very dissatisfied".
- For single choices with more than 2 options consisting of ranges, ensure that they are mutually exclusive, such as : "2 years or less", "3 to 5", "6 or more".
- For single choices with more than 2 options consisting of grades (1 to 4 for example), explicitly mention that grade 1 corresponds to the lowest grade.
- For multiple choices, classify them in alphabetical order, without forgetting the "Other" option.
- Add contextual information to explain and guide the participant in their responses.

Neutrality of the questionnaire :
You should only give credit to surveys whose questions are as neutral as possible. Some questions call for answers. For example [LAL] :
- IF we ask "Do you prefer to use the old version or this improved version of the website ?", this is a biased question since the question implies by the word "improve" that the latest version of the site is best.
- If we ask "Do you think airlines should allow the use of cell phones in flight ?" the answers will not be the same as if we ask "Do you think airlines should ban cell phone use in flight ?"
- If we ask "Do you find it important that security rules at airports are tightened ?", most people will answer in the affirmative. However, if we tell them about the conditions that will accompany this greater security (longer waits, increased police presence, increased ticket costs, etc.), their opinion may be different.
- If we ask "Are you in favor or against sanctioning judges in the event of a fault leading to a judicial error ?", who would not want to sanction someone who has committed a fault ?

Conduct of the survey :
When the survey is carried out in the "field" (face-to-face or telephone survey), it is necessary to ensure that :
- The investigators are serious, professional, well trained, neutral in appearance, welcoming and relational.
- The place, time and circumstances are propitious. For example, only launch the survey when the media context is relatively neutral in relation to the subject of the survey.
- The participant is available to answer the questionnaire.

Analysis of results :
The understanding and interpretation of the results are sometimes very different depending on the analyst. For example [LAL] :
- If business travelers are asked "Do you often, occasionally, rarely or never use Internet access in your hotel room ?", the results will differ greatly depending on the groupings that we will provide answers. Does the "yes" result corresponding to the "often" case also include the "occasionally" case, or even the "rarely" case ?
- If the results show that "60 % of Canadians use their credit card to pay for their vacations", then the information should not be condensed into the form "Canadians travel on credit".

Adjustment of results [DAN] :
Adjustment is a common practice in the world of surveys.
It consists of applying weightings to individuals to increase the weight of those belonging to categories under-represented in the sample surveyed compared to the reference population, and to simultaneously reduce the weight of those who are over-represented.
Adjustment on a single variable corresponds to a simple rule of 3. Adjustment on several variables at the same time is more complex and requires lengthy computer calculations.
But be careful, excessive weightings pose a certain risk to the quality of the results. Thus, it seems absurd to give 10 times more weight to the answers of the only person we managed to interview in a given category.
It is also possible that the calculations do not allow the sample questioned to converge towards the desired distribution.
Thus, if data is false from the start, if it was poorly collected, incorrectly entered, or if it contains too much missing data, there will be no point in trying to correct it.
Hence the extreme importance of ensuring that samples consistent with the reference population are obtained in advance.

Publication of results :
Any published survey must be accompanied by certain information.
The French law of July 19, 1977 regulates surveys made public on the national territory and linked to the electoral debate. They must mention at least the purpose of the survey, the name of the organization, the name of the sponsor, the number of people questioned, the date, the exact wording of the questions asked and the proportion of "unanswered" [DOC].

Reliability of surveys :
Concerning the reliability of the surveys, opinions are divided :
For some people, despite their faults, surveys are good indicators of trends and opinions [LAL]. They are not wrong when they are well done and observed in a trending manner.
For others, surveys reflect an opinion formed on the spot. Responding to a pollster doesn't commit you to anything. This can even be an opportunity to play, or even to express your anger at the moment.
The surveys also reflect an opinion drowned out in the media noise surrounding the question asked.
But most often, the survey is used to build audience. Its relevance is almost never mentioned.
Only in-depth surveys, repeated from year to year, are of interest in understanding changes in values over the long term [COS].

Sources relating to surveys :
[COS] Centre d'observation de la société, Le sondage - un mauvais outil pour comprendre la société.
[DAN] Gérard Danaguezian, Le redressement d'échantillons, Survey Magazine.
[DOC] Doctrine, Loi n 77-808 du 19 juillet 1977 relative à la publication et à la diffusion de certains sondages d'opinion.
[GUM] Hervé Gumuchian et Claude Marois, Chapitre 6 - Les méthodes d'échantillonnage et la détermination de la taille de l'échantillon, in Initiation à la recherche en géographie, Presses de l'Université de Montréal.
[JAC] Marc Jacquemain, Méthodologie de l'enquête, Institut des Sciences Humaines et Sociales, Université de Liège.
[LAL] Michèle Laliberté, L'art des sondages ou comment éviter les pièges, Réseau Veille Tourisme.
[PER] Anne Perrut, Cours de probabilités et statistiques.
[SER] Zineb Serhier, Comment calculer la taille d'un échantillon pour une étude observationnelle ?.
[SOU] Dr. Ghomari Souhila, Techniques d'Enquête, Université de Tlemcen.
[TOU] Hugo Touzet, Connaître et mesurer l'opinion publique : utilité et limites des sondages, Ressources en Sciences Economiques et Sociales.
[WIK1] Wikipedia, Intervalle de confiance.
[WIK2] Wikipedia, Marge d'erreur.
[WIK3] Wikipedia, Loi normale.


F4. Statistics
picture Fun statistics


F4.1. Introduction :

When we have a data set, for example from numerous measurements, it is often useful to characterize it by parameters of central tendency (such as the arithmetic mean or the median) and dispersion (such as the standard deviation or the interquartile range).
It is also important to know the influence of aberrant data on these parameters.
Finally, the statistical method has a certain number of traps into which even experienced users can fall.

Consider a list of n data xi, the index i ranging from 1 to n. The most common statistical parameters are then the following :


F4.2. Aberrant data [WIK5]

Aberrant data is data that contrasts greatly with other data, in an abnormally low or high manner.
Aberrant date is due to :
- either a measurement error in which case it is necessary to delete the aberrant data or use robust statistical indicators in the face of aberrant data,
- or to a highly asymmetrical data distribution in which case one must be very careful in using tools or reasoning designed for a normal distribution.

Different methods exist to identify aberrant date present in a dataset.
The simplest [KHA] consists of classifying the data in ascending order then identifying the first quartile (Q1), the third quartile (Q3) and the interquartile range EI = Q3 - Q1.
Any data xi verifying one of the following relationships will then be considered aberrant :
xi < Q1 - 1,5 EI    or    xi > Q3 + 1,5 EI

The Figure above shows an example dataset with aberrant data (shown in bold font).
The table on the right shows the influence of these aberrant data on the calculation of the various common statistical parameters for four particular cases :
   case a : set of 5 data without any aberrant data
   case b : set of 6 data including those of case a supplemented by an abnormally low data
   case c : set of 6 data including those of case a supplemented by an abnormally high data
   case d : set of 7 data including those from case a supplemented by aberrant data from cases b and c
The analysis of this table is given below for each statistical parameter.



F4.3. Parameters of central tendency

The main parameters of central tendency are as follows, including the median which is robust to aberrant data.


Generalized mean Mp [WIK2] :

For n strictly positive data xi, the generalized mean of non-zero order p (or Hlder mean) is the quantity : Mp = ( (1/n) ∑i[xip] )(1/p)
This mean is used in practice with :
   p → -∞ for the data minimum Min{xi}
   p = -1 for the harmonic mean MH
   p → 0 for the geometric mean MG
   p = 1 for the arithmetic mean MA
   p = 2 for the root mean square MQ
   p → +∞ for the data maximum Max{xi}
Between different means, we have the following relationship : Min{xi} ≤ MH ≤ MG ≤ MA ≤ MQ ≤ Max{xi}
The generalized mean does not depend on the order of the data.
The generalized mean is homogeneous : for any strictly positive constant k, we have the relation : Mp(k xi) = k Mp(xi)
The generalized mean is cumulative : if the data list is divided into several sublists, the mean of the overall list is the weighted mean of the means of the sublists, with the coefficients of each sublist being the number of terms concerned.
The generalized mean can be expressed in the form of a norm of order p :

Proof of the generalized mean for p → 0 [WIK3] :

For p → 0, Mp takes the indeterminate form 1
We then rewrite Mp in the form : Mp = exp[X] with :
X = ln[ ( (1/n) ∑i[xip] )(1/p) ] = (1/p) ln[ (1/n) ∑i[xip] ] = f(p)/g(p)
f(p) = ln[ (1/n) ∑i[xip] ]
g(p) = p
Having furthermore f(0) = ln[1] = 0 and g(0) = 0, we can apply the Hospital rule subject to the existence of f'(p) and g'(p) :
f'(p) = ∑i[ xip ln[xi] ] / ∑i[xip] using the relations ln'(u) = u'/u and (xp)' = xp ln[x], and provided that x is strictly positive.
g'(p) = 1
Hence (Hospital rule) :
lim(p → 0)(X) = lim(p → 0)( f(p)/g(p) ) = f'(0)/g'(0) = (∑i[ 1 ln[xi] ] / ∑i[1]) / 1 = ∑i[ ln[xi] ] / n = ln[ Produiti[xi] ] / n
The exponential function being continuous everywhere and defined at 0, we can then write :
lim(p → 0)(Mp) = lim(p → 0)(exp[X]) = exp[ lim(p → 0)(X) ] = exp[ ln[ Produiti[xi] ] / n ] = (exp[ ln[ (Produiti[xi] ] ])1/n = (Produiti[xi])1/n
which is indeed the expression of the geometric mean.



Harmonic mean MH [WIK1] :

For n strictly positive data xi, the harmonic mean is the quantity : MH = ( (1/n) ∑i[xi-1] )(-1) which can also be written : 1/MH = (1/n) ∑i[1/xi]
The harmonic mean is to be used when we seek to mean a quantity which influences according to an inverse proportionality in a physical phenomenon (example : mean speed of a vehicle on journeys of the same length).
The harmonic mean minimizes the squared deviation defined by the sum ∑i[ (1/x - 1/xi)2 ]
Example [BIB] : you take a bike ride. You start by climbing a hill of length L at speed v1 = 20 km/h, then you go back down this same hill at speed v2 = 30 km/h. What is your mean speed v ? Please note, this is not 25 km/h found by taking the arithmetic mean.
If t1 = L/v1 is the time taken to ascend and t2 = L/v2 the time to descend, then the total time t = 2 L/v is written : t = t1 + t2 = L/v1 + L/v2 , or again : 2/v = 1/v1 + 1/v2
The mean speed v is therefore the harmonic mean of the two speeds v1 and v2, i.e.: v = 24 km/h.

The MH harmonic mean is highly sensitive to aberrant data when it is abnormally low relative to other data (see Table above).



Geometric mean MG [WIK1] :

For n strictly positive data xi, the geometric mean is the quantity : MG = ( Produiti[xi] )1/n which can also be written : ln[MG] = (1/n) ( ∑i[ ln[xi] ] )
The geometric mean is to be used when we seek to have a balanced representation of the influence of low data and high data thanks to their logarithmic transformation.
The geometric mean minimizes the squared deviation defined by the sum ∑i[ (ln[x] - ln[xi])2 ]
Example [BIB] : at the end of a demonstration, the police announce x1 = 10,000 demonstrators and the organizers x2 = 100,000. What is the real number x of demonstrators ? Please note, this is not 55,000 found by taking the arithmetic mean.
If we assume that the police and the organizers "cheat" in the same way, then the police announce (x/k) demonstrators and the organizers (x k), k being a multiplier coefficient. By taking the geometric mean, we then find the exact result : x = [(x/k) (x k)]1/2 = 31,600.

The MH geometric mean is highly sensitive to aberrant data when they are abnormally low relative to other data (see Table above).



Arithmetic mean MA (or "usual mean") [WIK1] :

For any n data xi, the arithmetic mean (or "usual mean") is the quantity : MA = (1/n) ∑i[xi]
The arithmetic mean minimizes the squared deviation defined by the sum ∑i[ (x - xi)2 ]

The arithmetic mean MA is sensitive to aberrant data (see Table above). It should only be calculated on a normal distribution or after identifying and removing aberrant data.



Root mean square MQ [WIK1] :

For any n data xi, the quadratic mean is the quantity : MQ = ( (1/n) ∑i[xi2] )(1/2) which can also be written : MQ2 = (1/n) ∑i[xi2]
The quadratic mean is to be used when we seek to mean a quantity which has a square influence in a physical phenomenon (example : mean speed of a particle involved in kinetic energy) or which includes values oscillating around zero (example : electrical signal).
The square mean minimizes the squared deviation defined by the sum ∑i[ (x2 - xi2)2 ]

The Root mean square Mq is highly sensitive to aberrant data (see Table above).



Weighted mean [WIK1] :

When the data are individually assigned coefficients mi (called weights), positive and not all zero, the previous means each have a weighted version as follows :
- Weighted generalized mean : Mp = ( ∑i[mi xip] / ∑i[mi] )(1/p)
- Weighted harmonic mean : MH = ∑i[mi] / ∑i[mi/xi]
- Weighted geometric mean : MG = ( Produiti[ximi] )1/∑i[mi])
- Weighted arithmetic mean (or barycenter) : MA = ∑i[mi xi] / ∑i[mi]
- Weighted quadratic mean : MQ = ( ∑i[mi xi2] / ∑i[mi] )(1/2)
If the weights are of integer value, they define the number of repetitions of each data.
When all weights are equal, the weighted mean is the same as the unweighted mean.



Median Q2 [WIK4] :

picture median filter


For any n data xi, the median (or second quartile) is the data Q2 located in the middle of the data xi when classified in ascending order [WIK6] :
- If n is odd, then Q2 = x(1/2)(n + 1)
- If n is even, then Q2 = (1/2)(xn/2 + x(n/2 + 1))
The median should be used when we seek to minimize, or even ignore, the influence of aberrant data.
The median minimizes the difference defined by the sum ∑i[ |x - xi| ]
Example : in digital image processing, the median filter reduces noise while preserving the contours of the objects in the image. The Figure above shows the example of an aberrant pixel (value 97) replaced by the median value (equal to 4) of its neighborhood made up of the eight surrounding pixels.

The Q2 median is robust to aberrant data (see Table above) and should be preferred over other means.



Weighted median [WIK9] :

When the data is individually assigned coefficients mi (called weights), which are positive and not all zero, the median has a weighted version which is the data xk which divides the mass of the weights in two when the data is classified in ascending order. We can also say that xk is the data having a cumulative weight equal to half the sum of all the weights.
k is then solution of : ∑ i = 1, k-1[mi] ≤ (1/2) ∑i[mi]    and    ∑ i = k+1, n[mi] ≤ (1/2) ∑i[mi]
When two values of k satisfy the above condition (k inf and k sup), then the weighted median is : (1/2)(xk inf + xk sup)
If the weights are of integer value, they define the number of repetitions of each data.
When all weights are equal, the weighted median is the same as the unweighted median.




F4.4. Dispersion parameters

The main dispersion parameters are as follows, including the interquartile range which is robust to aberrant data.


Scope e [WIK4] :

For any n data xi, the scope (or amplitude) is the quantity : e = Max{xi} - Min{xi}.

The range e is highly sensitive to aberrant data (see Table above).



Mean deviation EM [WIK4] :

For any n data xi, the mean deviation is the quantity : EM = (1/n) ∑i[ |xi - MA| ]
where MA is the arithmetic mean of the data xi.
The mean deviation is to be used when trying to calculate the arithmetic mean of the absolute value of the deviations from the arithmetic mean.
The absolute value function not being differentiable is sometimes incompatible with certain analyses. To make the differences positive, we then resort to squaring and use the standard deviation.

The mean deviation EM is highly sensitive to aberrant data (see Table above).



Standard deviation σ [WIK4] :

For any n data xi, the standard deviation is the quantity : σ = ( (1/n) ∑i[ (xi - MA)2 ] )(1/2) = ( (1/n) ∑i[ xi2] - MA2 )(1/2)
where MA is the arithmetic mean of the data xi.
The standard deviation is to be used when trying to calculate the square mean of the deviations from the arithmetic mean.
We have the relation : EM ≤ σ

The standard deviation σ is highly sensitive to aberrant data (see Table above). It should only be calculated on a normal distribution or after identifying and removing aberrant data.



Interquartile range EI [WIK4] :

For any n data xi, the interquartile range is the quantity EI = Q3 - Q1
Q1, called lower quartile (or first quartile), is the data below which 25 % of the data xi is found when classified in ascending order [WIK6] :
- If the rank (1/4)(n + 3) is integer, then Q1 = x(1/4)(n + 3)
- If this rank ends with 0.25 then Q1 = (1/4)(3 xinf + xsup)
- If this rank ends with 0.50 then Q1 = (1/2)(xinf + xsup)
- If this rank ends with 0.75 then Q1 = (1/4)(xinf + 3 xsup)
Q3, called upper quartile (or third quartile), is the data below which 75 % of the data xi is found when classified in ascending order [WIK6] :
- If the rank (1/4)(3 n + 1) is integer, then Q3 = x(1/4)(3 n + 1)
- If this rank ends with 0.25 then Q3 = (1/4)(3 xinf + xsup)
- If this rank ends with 0.50 then Q3 = (1/2)(xinf + xsup)
- If this rank ends with 0.75 then Q3 = (1/4)(xinf + 3 xsup)
with xinf = xlower integer rank and xsup = xupper integer rank

Interquartile range EI is robust to aberrant data (see Table above) and should be preferred over scope e, mean deviation EM and standard deviation σ.



F4.5. Misleading statistics

Statistics, like any other technique, is not always handled with care, discernment and good faith.
It is the subject of traps, misleading evidence and even scams.


The right definition :

Statistics calculated on a variable only have meaning relative to its definition.
Example [INS][WIK8][MON][JAI] : in March 2017, the number of unemployed in mainland France was 2.7 million according to INSEE and 3.7 million according to the Ple Emploi. Where does this gap come from ?
For INSEE, an unemployed person is officially an "unemployed active" person (i.e. aged 15 or over, unemployed, actively looking for work and available within two weeks), which excludes so-called "inactive" people ( young people under 15 ; student ; retired ; people in training ; discouraged people ; women with young children, not available quickly ; people unable to work ; etc.
For Pôle Emploi, an unemployed person is a person registered with an agency, unemployed and actively looking for work (category A).
20 % of the unemployed identified by INSEE are not registered with Pôle Emploi (people at the end of their rights, people removed for administrative reasons, etc.). Conversely, 40 % of unemployed people registered with Pôle emploi are not recorded by INSEE, often to benefit from certain measures.
The unemployment rate is then defined as the ratio between the number of unemployed and the number of active people, the number of active people being the sum of the number of employed people and the number of unemployed people.
In 2022, according to the INSEE survey, employment is distributed as follows : 68.7 % employed active, 5.3 % unemployed active (unemployed) and 26.0 % inactive [UNE], the unemployment rate being 7.2 %


Cumulative percentages :

When we combine increases and decreases in percentages, a multiplicative perception of the percentages is necessary.
Example [DEL2] : a price increases by 15 % then decreases by 6 %. What is the percentage price change ? The answer is not +9 %
You must in fact multiply the price by 1.15 then by 0.94, which gives 1.081 and corresponds to an increase of 8.1 %.
Note that the reversed operation "decrease by 6 % then increase by 15 %" gives the same result, the multiplication being commutative.


Percentage and absolute value :

A quantity can decrease in percentage each year at the same time as it increases in absolute value.
Example [DEL2] : A member of the government assures that the increase in deficit which was 15 % last year has been reduced to 14 % this year. The opposition claims on the contrary that the deficit which was 15 billion euros last year has increased again this year by more than a billion euros. Who is right ?
The 15 billion euros of last year's deficit corresponds to 15 % of the initial deficit (from two years ago). This was therefore 100 billion euros. Last year, the deficit increased from 100 billion to 115 billion. If, as the first statement indicates, the increase in deficit was 14 %, this year the increase therefore reached 14 % of 115 billion, or 16.1 billion. This is consistent with the second statement that the deficit increased by more than a billion. The two statements are perfectly compatible.


The aberrant mean :

The arithmetic mean has little meaning when the data distribution is unbalanced.
Example [DAN] : in a company of 200 people, 80 % of the workforce receives 1,500 euros per month and the remaining 20 % receives 10,000 euros per month. The average remuneration then amounts to 3,200 euros per month, which is an unrepresentative result when we take a simple arithmetic mean.


The hidden common cause :

Confusion is frequently made between correlation of factors (often linked by a common cause) and causality of facts (meaning cause and effect relationship).
Example 1 [ANI] : a person who has diabetes will have high blood sugar levels and feel excessive hunger. The two factors are linked and come from the same cause, which is diabetes. But high sugar levels do not cause feelings of excessive hunger, and vice versa. These are related facts but not by causality.
Example 2 [TER] : people who wear shoes larger than 45 commit three times more murders than those who wear shoes between 40 and 42. Does this mean that large shoes induce murderous behavior ? The real correlation is actually linked to gender : it turns out that homicidal behavior is found primarily in male individuals.


Law of small numbers :

The law of small numbers pushes individuals to believe that a small number of observations can accurately reflect the general population.
Example 1 [ANI] : if we count 70 % women at a meeting and we use this proportion of 70 % to guess the number of women in the world, this generalization is false because it is not representative of reality nor the randomness of the sample.
Example 2 [ANI] : it is not because we were cured using a grandmother's remedy that it really works for the entire population. This is why in medicine many tests are carried out to find out whether or not a treatment has a beneficial effect.


Paradox of the average number of children :

"Taking a family at random" and "taking a child at random" are not the same thing.
Example [DEL2] : An exhaustive survey carried out in a city indicates that families with children under 18 are distributed as follows : 10 % families with 1 child, 50 % with 2 children, 30 % with 3 children , 10 % to 4 children. The average number of children per family (among those with children) is therefore (10 + 100 + 90 + 40)/100 = 2.4.
To check this statistic, the administrative authorities carry out a survey. We survey 1,000 children under the age of 18 carefully chosen at random and ask them how many children there are in their family, including themselves. By averaging the answers, we get 2.67 ! Why is this gap so significant with the 2.4 in the statistic which took into account all families with children ?
The answer lies in the fact that by interviewing children at random, you will interview 4 times more children from families with 4 children than you will from families with 1 child, which skews the average. If there are 1000 families, there will be 100 only children, 1000 children belonging to a family of 2 children, 900 children belonging to a family of 3 children, 400 children belonging to a family of 4 children. In total, the answers given by these 2,400 children will lead to the result of 2,666... children per family.
The survey carried out does not evaluate the average number of children in a family taken at random, but the average number of children found in the family of a child taken at random.


Simpson paradox :

picture Simpson paradox


A phenomenon observed in several groups of data can be reversed when the groups are brought together. If we want to obtain sensible conclusions, the aggregation of results must respect certain rules of homogeneity [DEL2].
Example [WIK7][SCI][DEL1] : A patient has kidney stones. His doctor offers him two alternatives: treatment A and treatment B. To help him make his choice, the doctor informs him that a study was carried out on 700 patients. Half of them (i.e. 350) received treatment A for which there were 273 cures (i.e. 78 % of cases), and the others received treatment B for which there were 289 cures (i.e. 83 % of cases).
We also know that there are two types of calculations : small and large (see small table above).
- Treatment A is successful in 81 cases out of 87 for small stones (i.e. 93 % of cases) and in 192 cases out of 263 for large stones (i.e. 73 % of cases).
- Treatment B is successful in 234 cases out of 270 for small stones (i.e. 87 % of cases) and in 55 cases out of 80 for large stones (i.e. 69 % of cases).
In both cases (small or large stones), treatment A is more effective, while for the overall result, treatment B is more effective.
What creates the paradox, and the erroneous impression that B is more effective overall, is that treatment A was given much more often for large stones, which are more difficult to treat.
To occur, the paradox requires two conditions :
- existence of an often hidden variable (called a confounding factor) which significantly influences the final result. In this example, the size of the stones affects the likelihood of treatment success.
- heterogeneous distribution of the sample studied. Treatment A is in fact more often given to large stones and B to small ones.
In science, we carry out "randomized" experiments, which ensure a homogeneous distribution : for example, if you have kidney stones and you participate in an experiment to compare treatments, you are randomly assigned treatment A or B , without the size of the calculations influencing the decision. We thus erase the heterogeneity of distribution, and the paradox disappears : treatment A will be clearly seen as being the best [MAT].
When Simpson's paradox occurs, one of the solutions to eliminate it is to make the distribution homogeneous by modifying the numbers in each data group while retaining the percentages. In the "Small calculations" line, the ratio 81/87 can be replaced by 251.38 /270 giving the same percentage 93 %. In the "Large calculations" line, the ratio 55/80 can be replaced by 180.81 /263 giving the same percentage 69 %. The "Total" line then gives a ratio of 443.38 /533 = 83.17 % for treatment A and 414.81 /533 = 77.83 % for treatment B, which confirms that treatment A is the best.

Arithmetic proof [DEL1] :

If we denote A, B, C, D the four successive numbers of the "Total" line, a,b,c,d those of the "Small calculations" line and a', b', c', those of the "Large calculations" line, then we have the following relationships :
A = a + a' ; B = b + b' ; C = c + c' ; D = d + d'
A/B < C/D ; a/b > c/d ; a'/b' > c'/d'
The astonishment comes from the fact that we believe that the double inequality { a/b > c/d and a'/b' > c'/d' } leads to { A/B > C/D }, or even with only small letters: { (a + a')/(b + b') > (c + c')/(d + d') }
But in fact, the three inequalities can sometimes be true simultaneously on an arithmetic level.
When the data have same effect within each group (b = d and b' = d') or between groups (b = b' and d = d'), Simpson's paradox cannot occur, the double inequality { a/b > c/d and a'/b' > c'/d' } always resulting in { A/B > C/D }.


F4.6. Sources relating to statistics :
[ANI] Animafac, Les pièges de l'utilisation des chiffres.
[BIB] Bibm@th.net, Diverses moyennes.
[CAN1] Statistique Canada, Mesures de la tendance centrale.
[CAN2] Statistique Canada, Mesures de la dispersion.
[DAN] Gérard Danaguezian, Attention, statistiques !, Survey Magazine.
[DEL1] Jean-Paul Delahaye, L'embarrassant paradoxe de Simpson, Pour la Science, n429 de juillet 2013.
[DEL2] Jean-Paul Delahaye, Déjouer les pièges des statistiques, Pour la Science, Hors-Série n98 de février-mars 2018.
[KHA] Khan Academy, Identification des valeurs aberrantes avec la règle 1,5 x écart interquartile
[MAT] Johan Mathieu, Le paradoxe de Simpson.
[UNE] Unédic, Comprendre le halo du chômage.
[SCI] Science étonnante, Le paradoxe de Simpson.
[TER] Marc Tertre, Pourquoi faut-il se méfier des statistiques ?, Le Club de Mediapart.
[WIK1] Wikipedia, Moyenne.
[WIK2] Wikipedia, Moyenne d'ordre p.
[WIK3] Wikipedia, Discussion : Moyenne d'ordre p.
[WIK4] Wikipedia, Indicateur de dispersion.
[WIK5] Wikipedia, Donnée aberrante.
[WIK6] Wikipedia, Quartile.
[WIK7] Wikipedia, Paradoxe de Simpson.
[WIK8] Wikipedia, Chômage en France.
[WIK9] Wikipedia, Médiane pondérée.


F5. Media violence
Picture Media violence


Introduction :

In a society of excessive consumption there is commodification of the whole of society. Information becomes a commodity, subject to the laws of the market and competition, just like television programs, cinema, film producers, the media.
To capture the audience, the media have different means such as sensationalism, controversy, fake news. Violence is also one of these means, hence the media violence which is, by definition, human violence shown or suggested by media. It can be verbal, physical, sexual or psychological.


Human violence :

The animal does not seek to kill or cause suffering. It kills to feed, reproduce or defend its territory. It is neither peaceful nor cruel and never acts excessively [GAN].
The human being is also an animal, but an animal of excess. It is distinguished from animals by the anatomical and functional importance of its brain [GAN], in particular the neocortex devoted to thought, imagination and anticipation, which allows it to explore and exploit an increasingly extensive environment.
Since the beginning of humanity, around two million years ago, human beings have been inventive with an exploring, manipulative, conquering and aggressive side. This fundamentally creative character tears him away from nature and makes him enter into excess and transgression. He then becomes ingenious in matters of violence, torture and horror, reinforced by his primitive animality in the form of celebration, sacrifice, cruelty and warlike orgy [GAN].
Today, modern man is no more violent than in the past. Wars have become increasingly deadly in the 20th century, but they are becoming rarer. Criminal violence has been on the decline since the 19th century. However, it appears worse than before because we approach criminal phenomena with different standards from those used in the past, being accustomed to increasingly broad security [GAN].
The reduction in violence is thus a massive and incontestable phenomenon. But there can be periods of relapse, setback, regression. Man is civilized but he does not change in depth. The impulses, the frustrations, the violent temptations remain [PIN].

Violence is a universal fact. Wisdom consists of accepting it rather than repressing it [GAN]. But wisdom also consists of discovering that all conflict is good as long as it reveals a truth, in particular that we are obliged to agree in order to live and that the conflict does not need to be violent for that [MIC].
Svâmiji said : "The animal is subject to nature. Man fights against nature. The wise man achieves unity with nature by accompanying it in its movement".


Results :

On human being, the effects of media violence are mainly those of violent images (bloodshed, beatings, torture, killings, bombings, road accidents, suicide, rape, etc.).
On this topic, more than 50 years of scientific research shows that prolonged exposure to violent images makes people more violent, increases the fear of becoming a victim themselves and reduces the feeling of sympathy towards victims of violence in real life [COU][WIK9].

On children and adolescents, the effects of media violence are as follows [CBS] :
- From 0 to 2 years : high vulnerability to sound effects (noises and screams).
- From 2 to 7 years : vulnerability to intense, trivialized, antisocial or gratuitous violence.
- From 7 to 12 years old : vulnerability to intense, trivialized, antisocial or intellectual violence.
- From 12 to 18 years old : vulnerability to antisocial or spiritual violence.
The most harmful programs for young people are violent films, including some cartoons, and realistic television news. The greatest impact is achieved by the association of violence with erotic images [KUC].

Also note [KUC] :
- The number of programs for young people, especially of good quality, seems insufficient (less than 10%), which encourages young people to watch programs for adults that are totally unsuitable for their age.
- Some boys with an aggressive character identify more easily with combative heroes whose behavior they reproduce in reality as well as in the fiction they have watched (mimetic effect).
- On American television, 20 to 25 violent acts per hour are broadcast in children's programs.
- On Canadian television, sexual relations between unmarried partners are shown 24 times more than those between spouses [NIH].

The following alphabetical list gives the main forms of media violence against human beings, ranging from simple annoyance to extreme violence.


Many people do not believe in the effects of media violence. There are six reasons for this [COU] :


Conclusions :

The remedy for media violence consists of finding a better balance between producers of violent images and consumers. This mainly involves the following actors [COU] :


Sources relating to media violence :
[ART] ARTE Radio, Prise de son : les 15 erreurs du débutant.
[BEN] Abdellatif Bensfia, "François HEINDERYCKX (2003), La malinformation. Plaidoyer pour une refondation de l'information", Communication, Vol. 23/2 | 2005, 259-265..
[BIL] Philippe Bilger, Pourquoi le son français est-il si mauvais ?.
[BOU] Marie-Claude Bourdon, Médias culture et violence.
[CBS] CBSC, Canadian Broadcast Standards Council, Classement des émissions en fonction de la violence - Guide de référence.
[CLE] CLEMI Le centre pour l'éducation aux médias et à l'information, Ecrans et violence.
[CNR] CNRTL, Centre National de Ressources Textuelles et Lexicales, Sexisme.
[COU] Courbet D. & Fourquet-Courbet M.P. (2014), "L'influence des images violentes sur les comportements et sur le sentiment d'insécurité chez les enfants et les adultes", Rapport Technique de Recherches, Université d'Aix-Marseille, Institut de Recherche en Sciences de l'Information et de la Communication IRSIC.
[CSA] CSA - Conseil supérieur de l'Audiovisuel, Réflexion sur les émissions dites "de téléréalité".
[FLA] Jean-Yves Flament, Téléréalité et idéologie.
[FMV] Fondation Marie-Vincent, Qu'est-ce que la violence sexuelle ?.
[FRI] France Inter, Algorithmes : les meilleurs amis des climatosceptiques.
[GAG] Christophe Gagne, "Un bon clash pour faire le buzz", Corela, 19-2 | 2021.
[GAN] René-François Gagnon, Cinq conceptions de la violence quotidienne, Mémoire 1999, Université Laval.
[GDC] Gouvernement du Canada, Ravaler sa douleur - Etude des liens entre l'anorexie, la boulimie et la violence contre les femmes et les filles.
[GDQ] Gouvernement du Québec, Le sexe dans les médias, Editions du Conseil du statut de la femme.
[GOU] Vincent Goulet, "Violence et médias", séances du Réseau Thématique n 37 "Médias" du 3e congrès de l'Association Française de Sociologie, Paris, 14-17 avril 2009.
[HIL] David Hiler, Réchauffement climatique : comprendre ceux qui n'y croient pas, Le Temps.
[KUC] Corinne Kucharscki, Jean-Luc Saladin, Daniel Godefroy et Matthieu Blondet, La télévision nourrit la violence, Reporterre - Le média de l'écologie.
[LER] Pierre Leroux et Philippe Riutort, Intégrer les politiques aux divertissements.
[LOO] Joséphine Loock, Violence institutionnelle de l'administration publique.
[MAT] Philippe Mathieu, Pour une histoire et une esthétique de l'écran fragmenté au cinéma, Thèse 2010, Université de Montréal.
[MCC] Ministère de la Culture et de la Communication, La violence à la télévision.
[MDT] Ministère du travail, La protection contre les discriminations.
[MIC] Yves Michaud, La violence apprivoisée.
[NIH] NIH, National Library of Medicine, Les répercussions de l'usage des médias sur les enfants et les adolescents.
[PAG] PagesJaunes/PagesConseil/Droit/, Atteinte à la dignité.
[PIN] Steve Pinker, La diminution de la violence dans le monde est un phénomène massif et incontestable, Libération.
[RFI] RFI, Les ados et le sexe sur internet : attention danger!.
[RIM] Pierre Rimbert, Interdire l'information en continu ?, Le Monde diplomatique.
[SEN2] Sénat, Enfants et publicité télévisuelle.
[SEN3] Sénat, L'audiovisuel à l'ère du numérique.
[SIX] Nicolas Six, Pourquoi les dialogues sont-ils parfois aussi inaudibles dans les films et les séries ?, Le Monde.
[TOU] La Toupie, Toupictionnaire.
[TRO] Pauline Trouillard, "Atteinte à la dignité humaine et autres contenus toxiques à la télévision française : le Conseil d'Etat a t-il ouvert la boîte de Pandore ?", La Revue des droits de l'homme, 24 | 2023.
[WIK2] Wikipedia, Cyberharcèlement.
[WIK3] Wikipedia, Perversion.
[WIK4] Wikipedia, Violence conjugale.
[WIK5] Wikipedia, Violence psychologique.
[WIK6] Wikipedia, Télé poubelle.
[WIK7] Wikipedia, Téléréalité.
[WIK8] Wikipedia, Violence policière.
[WIK9] Wikipedia, Education parentale.
[WIK10] Wikipedia, Entertainment Software Rating Board.
[YAP] yapaka.be, Les images violentes ne sont pas nécessairement celles que l'on croit.


3. Site map

This Web site contains 63 html pages.
The pages translated in English are preceded by a star.

  1. * Accueil/Contact  (Home/Contact)
  2. * Billard  (Billiards)
    1. * Théorie du jeu  (Theory of the Game)
    2. * La pratique du billard  (The Art of Billiards Play)
    3. * Bibliographie  (Bibliography)
    4. C'est du billard, reportage ARTE
  3. * Bélier hydraulique  (Hydraulic ram)
    1. Pages de Hervé de Baillenx
    2. Principe de fonctionnement
    3. Théorie
    4. Pratique
    5. Annexe
    6. Notations
    7. Glossaire
    8. * Bibliographie  (Bibliography)
    9. * Sommaire général  (Overall Table of contents)
  4. * Système Nerveux Humain  (Human Nervous System)
    1. Introduction
    2. Piaget
    3. Description fonctionnelle
    4. Glossaire
    5. * Bibliographie  (Bibliography)
    6. * Sommaire général  (Overall Table of contents)
  5. * Relativité  (Relativity)
  6. Botanique
    1. Liste des plantes ligneuses dont le nom commun commence par la lettre A
    2. Liste des plantes ligneuses dont le nom commun commence par la lettre B
    3. Liste des plantes ligneuses dont le nom commun commence par la lettre C
    4. Liste des plantes ligneuses dont le nom commun commence par la lettre D, E ou F
    5. Liste des plantes ligneuses dont le nom commun commence par la lettre G
    6. Liste des plantes ligneuses dont le nom commun commence par la lettre H, I, J, K ou L
    7. Liste des plantes ligneuses dont le nom commun commence par la lettre M, N ou O
    8. Liste des plantes ligneuses dont le nom commun commence par la lettre P
    9. Liste des plantes ligneuses dont le nom commun commence par la lettre Q, R ou S
    10. Liste des plantes ligneuses dont le nom commun commence par la lettre T, U, V, W, X, Y ou Z
  7. Musique
  8. Ornithologie
    1. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre A
    2. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre B
    3. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre C
    4. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre D, E ou F
    5. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre G
    6. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre H, I, J, K ou L
    7. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre M, N ou O
    8. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre P
    9. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre Q, R ou S
    10. Catalogue des oiseaux d'Europe dont le nom commun commence par la lettre T, U, V, W, X, Y ou Z
  9. Météorologie
  10. * Aide  (Help)
  11. * (Warning)



4. Design and Accessibility rules

At the time of last update of this page (see bottom of this page), all Web pages of this site have the following properties :
- they comply with W3C normes (HTML and CSS) ;
- they comply with Web Content Accessibility Guidelines (WCAG) 2.0 with Level AA conformance.

Design and Accessibility rules of this site :

  1. Web design
    1. Structuration du site en pages : selon une arborescence hiérarchique limitée à une profondeur de trois (règle des "trois clics").
    2. Version bilingue : version français/anglais de (presque) chaque page.
    3. Homogénéité des pages : même présentation et mêmes couleurs.
    4. Liens entre pages du site : depuis chaque page, accès a minima aux pages "Accueil/Contact", "Aide", ainsi qu'aux pages de type père, oncles, frères et fils.
    5. Page d'accueil : présentation simple, sur un seul écran, avec moteur de recherche interne.
  2. Web ergonomy (presentation and browsing)
    1. Page : présentation structurée verticalement selon Barre de menu puis Contenu puis Pied de page, et tenant horizontalement dans l'écran.
    2. Barre de menu : avec bouton "English/Français" de type bascule.
    3. Contenu d'une page : structuration linéaire selon titre (rappel de la page père), chapitre (nom de la page courante), sommaire local (uniquement si page longue), paragraphe, sous-paragraphe, sous-sous-paragraphe...
    4. Pied de page : avec mention du copyright, année de création, nom de l'auteur et date de dernière mise à jour de la page.
    5. Liens : (presque) tous commençant par une lettre majuscule, et de couleur différente selon le type de lien (non visité, visité, survolé, activé).
    6. Liens vers fichier téléchargeable : avec indication du type de fichier (.gif, .jpeg, etc.) et de sa taille (en Ko ou Mo).
    7. Liens extra-page : avec texte court, explicite quant à la page destination.
    8. Liens intra-page : uniquement dans les pages longues.
    9. Liens "Précédent/Suivant" : uniquement entre chapitres, entre paragraphes et entre sous-paragraphes.
    10. Images porteuses d'information : avec texte alternatif (attribut "alt"), court et explicite quant à la fonction et à l'aspect.
    11. Plan de page : existe.
    12. Paragraphes : justifiés (à gauche et à droite) et indentés en première ligne.
    13. Typographie : aucun soulignement, ni texte en majuscule, et avec style "italique" uniquement dans des cas précis.
  3. Accessibility to sensory handicapped
    1. Changements de langue : indiqué systématiquement (attribut "lang" dans chaque objet de type tableau, liste, bloc (balise "span"), etc.).
    2. Objets multimédias (animation, vidéo, son) : ni clignotement, défilement ou mise à jour automatique d'information, ni image animée ou à zone réactive cliquable, ni fenêtre pop-up, ni son, ni listes déroulantes, ni boîtes de dialogue. Les boutons de désactivation des animations et du son sont en effet impossibles à trouver rapidement par un non-voyant.
    3. Couleurs (utilisation) : rien ne repose uniquement sur la couleur (indication d'une action, sollicitation d'une réponse, distinction d'un élément visuel).
    4. Couleurs (standardisation) : prises parmi les 16 couleurs de base du standard HTML 4.01 (voir tableau ci-dessous, avec Nom HTML, Nom français et Code hexadécimal selon la notation #RRVVBB).
    5. Couleurs (contraste) : contraste particulièrement adapté aux daltoniens déficients en vert (soit 80 % des daltoniens, ces derniers représentant 8 % des hommes et 0,5 % des femmes), selon les règles suivantes (voir tableau ci-dessous) :
         - Arrière-plan : sans motifs ni texte (donc fond uni) ; couleur "white" pour le fond de page ; couleurs "aqua", "silver" et "white" pour les fonds de menu ; couleurs "yelow" et "red" pour les fonds de lien (respectivement survolé et activé) situés en arrière-plan par rapport au texte de lien.
         - Premier plan : couleur "black" pour le texte de page ; couleur "blue" et "purple" pour les textes de lien (respectivement non visité et visité) ; couleur "yellow" et "red" pour les fonds de lien situés en premier plan par rapport au fond de page ou de menu.
    6. Police de caractères : sans empattements, ni embellissements, ni enluminures (police sans sérif).
    7. Images : suivies si nécessaire d'un équivalent textuel expliquant le contenu de l'image.
    8. Titres : balises "h1", "h2", "h3"... logiquement enchaînées et en cohérence avec la présentation des pages en titre, chapitre, paragraphe...
    9. Tableaux : avec résumé indiquant la fonction menu/données et le nombre de colonnes (attribut "summary"), avec en-têtes de colonnes (attribut "th"), avec si nécessaire correspondance entre cellule et colonne (attributs "id" et "headers").
    10. Listes : avec numérotation systématique.
    11. Formules mathématiques : écriture littérale, y compris les fonctions mathématiques (exemple : sin[x]).
    12. Clefs d'accès des raccourcis clavier : chiffres de 0 à 9 (dont les touches couramment utilisées : 0 Aide ; 1 Accueil).

    The following table gives the contrast between each foreground color (in lines) and each background color (in rows) for the 16 basic color from HTML 4.01
    This website uses only 24 contrasts indicated by the text "OUI", especially suited to green colorblind deficient.

    Nom HTMLblacknavybluegreenteallimeAQUAmaroonpurpleoliveGRAYSILVERREDfuchsiaYELLOWWHITE
    Nom françaisnoirbleu foncébleuvertbleu vertvert brillantcyanmarronvioletvert olivegris foncégris clairrougerosejauneblanc
    Code hexa0000000000800000FF00800000808000FF0000FFFF800000800080808000808080C0C0C0FF0000FF00FFFFFF00FFFFFF
    BLACKnonnonnonnonnonnonOUI01nonnonnonOUI02OUI03nonnonnonOUI04
    navynonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    BLUEnonnonnonnonnonnonOUI05nonnonnonOUI06OUI07OUI08nonOUI09OUI10
    greennonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    tealnonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    limenonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    aquanonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    maroonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    PURPLEnonnonnonnonnonnonOUI11nonnonnonOUI12OUI13OUI14nonOUI15OUI16
    olivenonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    graynonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    silvernonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    REDnonnonnonnonnonnonOUI17nonnonnonOUI18OUI19nonnonnonOUI20
    fuchsianonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon
    YELLOWnonnonnonnonnonnonOUI21nonnonnonOUI22OUI23nonnonnonOUI24
    whitenonnonnonnonnonnonnonnonnonnonnonnonnonnonnonnon

  4. Html code
    1. Balises "!DOCTYPE", "html" et "head" : efficaces et en nombre restreint (pour les moteurs de recherche type Google).
    2. Feuille de style (.css, 3 Ko) : feuille externe unique avec attributs de taille redéfinis en relatif ("em" ou pourcentages) plutôt qu'en absolu (pixels).
    3. Balise "body" : avec attribut "bgcolor" en doublon de la feuille de style (pour compatibilité avec versions de code html inférieures à 3.2).
    4. Cadres (ou "frame") : aucun.
    5. Fenêtres secondaires : aucune.
    6. Liens javascript : aucun (hormis éventuel cassage du nom de domaine).
    7. Paragraphes : tous explicites (avec balise "p") afin de pouvoir jouer dessus avec la feuille de style.
    8. Mathematical symbols : coded in html when the code exists (examples : ≤ ∞ Δ ◊).
    9. Fichiers : nommage représentatif des deux premiers niveaux de la structure du site, sans blanc, ni caractère accentué (car problème sur serveurs Unix). Majuscules évitées au maximum.
    10. Temps d'accès aux pages : très court, avec quelques pages "pesant" au plus 100 Ko.



5. Partner schools and organizations

The following schools or organizations used this website :
Caption :
CPGE : Classes Préparatoires aux Grandes Ecoles
PFE : Projet de Fin d'Etude
TIPE : Travaux d'Initiative Personnelle Encadrée
TPE : Travaux Pratiques Encadrés

About the topic "Billiards physics" :

  1. Bordeaux, Lycée Michel Montaigne, TIPE : Le billard, Maxime Plottu, CPGE 2ème année, PSI*, 2024.
  2. Bourg-en-Bresse, Lycée Lalande, TIPE : Le billard, Mickaël Jacques, CPGE 2ème année, PC, 2012.
  3. Caen, Lycée Victor Hugo, TIPE : Le billard, Wilfried Lerot, CPGE 2ème année, PSI, 2008.
  4. Dijon, Lycée Carnot, TIPE : Le bowling, Pierre Goguelat, CPGE 2ème année, MP, 2011.
  5. La Flèche, Lycée Prytanée, TIPE : La physique du billard, Matthieu Dolliou, CPGE 2ème année, MP*, 2014.
  6. Lille, Lycée Faidherbe, TIPE : Le billard, Vincent Bolle, CPGE 1ère année, MPSI, 2008.
  7. Lille, Lycée Faidherbe, TIPE : Le billard, Sylvain Capelle, CPGE 2ème année, PC, 2011.
  8. Lille, Lycée Faidherbe, TIPE : Le billard, Maxime Duprez et Romain George, CPGE 2ème année, PSI, 2014.
  9. Lyon, ECAM, TIPE : Le billard, Jérémy Crétin et Jérémy Quentin, CPGE 2ème année intégrée, PT, 2012.
  10. Lyon, Lycée Aux Lazaristes, TIPE : Le billard, Florian Carra, CPGE 2ème année, MP, 2011.
  11. Nancy, Lycée Henri-Poincaré, TIPE : La physique du billard, Julien Vukasin, CPGE 2ème année, MP, 2011.
  12. Nantes, Lycée Clémenceau, TIPE : La mécanique du billard, Baptiste Martin, CPGE 2ème année, PSI, 2024.
  13. Neuilly-sur-Seine, Lycée Pasteur, TIPE : La physique du billard, Swann Bareilhe, CPGE 2ème année, MP, 2012.
  14. Nice, Lycée Masséna, TIPE : Le billard, Siméon Nenoff, Frédéric Bieber et Adrien Génin, CPGE 2ème année, MP et PC, 2008.
  15. Paris, Lycée Saint-Louis, TIPE : La dynamique du billard, Laura Sobra, CPGE 2ème année, PC, 2011.
  16. Perpignan, Lycée Arago, TIPE : Le billard, Baudoin Espieux, CPGE 2ème année, PSI, 2013.
  17. Reims, Lycée Roosevelt, TIPE : Le billard, Chloé Deflandre, Ellyn Dubecq, CPGE 1ère année, MPSI, 2016.
  18. Saint-Etienne, Lycée Fauriel, TIPE : La mécanique du billard, Victor Soriano, CPGE 2ème année, MP, 2011.
  19. Valbonne, Lycée International, TIPE : Le billard, Caroline Boyer, CPGE 2ème année, MP, 2012.

About the topic "Hydraulic ram" :

  1. Besançon, Lycée Victor Hugo, TIPE : Le bélier hydraulique, Anthony Doubey, CPGE 2ème année, PSI, 2015.
  2. Brest, ENSTA ParisTech, Projet de pompe hydraulique autonome basé sur un multiplicateur de pression, Vincent Macaigne, 2014.
  3. Burundi, Faculté des sciences appliquées, Département de Génie Electromécanique, PFE : Possibilité technique et énergétique du pompage pour l'irrigation d'une région agricole du Nord du Burundi, Claude Nkonji, 2009.
  4. Clermont-Ferrand, Lycée Blaise Pascal, TIPE : Le bélier hydraulique, Baptiste Durand, CPGE 2ème année, PSI, 2014.
  5. Cluny, Lycée La Prat's, TIPE : Le bélier hydraulique, Geoffroy de Saint-André, CPGE 2ème année, PT, 2011.
  6. Grenoble, INP-ENSE3, Maquette transparente de bélier hydraulique (YouTube, 03:19) ; Bélier hydraulique : Maquette transparente (YouTube, 06:43) Cyril Benistand, Matthieu Villevieille, Robin Vallée, Thomas Fayer, Pierre Coutouly et Alexandre Wettstein, Atelier d'ingénierie, 2015.
  7. Grenoble, INP-ENSE3, Modélisation de bélier hydraulique, Jean-Côme Biscay, Kenza Taoussi, Erwan Tardy, Raphaël D'Oliveira, Laurent Dumas, El Bachir Chakir et Pierre Boucher, Atelier d'ingénierie, 2015.
  8. Grenoble, INP-ENSE3, Projet de bélier hydraulique en haute montagne ; Alex Croutz et Jérémie Serfass, 2ème année, Filière Hydraulique, Ouvrages et Environnement, Option Génie Hydraulique et Ouvrages, 2016.
  9. Longwy, IUT Longwy, Université Henri Poincaré Nancy1, Projet tutoré : le bélier hydraulique, Quentin Ducassou, Julien Breemersch, Clément Malliard, 2ème année, GTE, 2009.
  10. Louvain-La-Neuve (Belgique), Ecole polytechnique, Construction d'un bélier dans une ferme près de Kinshasa en RDC, Manon Kummeler, 2024.
  11. Lyon, ECAM, TIPE : Le bélier hydraulique, Johanna Ankri, Justine Abou Chacra, CPGE 2ème année intégrée, PT, 2015.
  12. Lyon, INSA, PFE : HydroRam (.pptx, 2.5 Mo), Quentin Letellier, 2012.
  13. Lyon, Lycée du Parc, TIPE : Du coup de bélier dévastateur au bélier hydraulique salvateur, Florent Joyet, CPGE 1ère et 2ème années, MPSI et PSI, 2007 & 2008.
  14. Lyon, Lycée La Martinière-Monplaisir, TIPE : Le bélier hydraulique, Tristan Jardel et Ilham Hamdame, CPGE 1ère année, MPSI, 2008.
  15. Margency, Lycée Notre-Dame de Bury, TPE : Le bélier hydraulique, Nadir Bouchene, Marie Magana, Victor Gillibert, 1ère S, 2010.
  16. Montpellier, Ecole d'ingénieur SupAgro, Institut des Régions Chaudes, Le bélier hydraulique : mémoire de fin d'études d'ingénieur en agronomie tropicale spécialisé en gestion sociale de l'eau, Adrien Busson, 2010.
  17. Nantes, Lycée Clémenceau, TIPE : Le bélier hydraulique, David Rousseleau, Jonathan Coueraud et Jules Douet, CPGE 1ère année, MPSI, 2008.
  18. Nantes, Lycée Eugène Livet, TIPE : Le bélier hydraulique, Romain Leluc et Gwenhael Darcy, CPGE 1ère et 2ème années, PTSI et PT, 2008 & 2009.
  19. Nice, Lycée Masséna, TIPE : Le bélier hydraulique, Martin Roux, CPGE 2ème année, PC, 2019.
  20. Nogent-sur-Oise, Lycée Marie-Curie, Projet : Le bélier hydraulique, Louison Richet, Terminale STI2D, 2013.
  21. Paris, AgroParisTech, PFE : Le bélier hydraulique (projet de valorisation patrimoniale sur le canal de Gignac), Pauline Poutrain, Maelle Delabre, Félicie Aulanier, Christophe Abraham, Paul-Emile Noirot-Cosson, 3ème année, Ingénierie de l'Environnement, 2012.
  22. Paris, Institut de France, Panneaux descriptifs du fonctionnement d'un bélier hydraulique, dans le cadre du Printemps de l'Industrie (Pavillon de Manse, mars 2009) et des Journées de la Rose (Abbaye royale de Chaalis et musée Jacquemart-André - Chaalis, juin 2009), J.M. Vasseur, Service culturel et pédagogique.
  23. Paris, Lycée Claude Bernard, TIPE : Principe du bélier hydraulique, Baptiste Mathae, CPGE 2ème année, PSI, 2015 : Le bélier en action (.jpg, 100 Ko), Constitution (.jpg, 100 Ko).
  24. Paris, Lycée Saint-Louis, TIPE : Le bélier hydraulique, Mickael Roucou, CPGE 2ème année, PSI, 2011.
  25. Paris, Lycée Stanislas, TIPE : Le bélier hydraulique, Matthieu Ansart, CPGE 2ème année, PC, 2015.
  26. Pau, Université de Pau et des Pays de l'Adour, Projet : Etude et Conception d'un bélier hydraulique, David Béritault et Luc Champault, Master Ingénierie des Systèmes Industriels (ISI), 2007.
  27. Rouen, Lycée Corneille, TIPE : Le bélier hydraulique, L. Duflot, CPGE 2ème année, PSI, 2011.
  28. Tananarive (Madagascar), Université d'Antananarivo, ESPA, Contribution à l'étude et réalisation d'un bélier hydraulique : mémoire de fin d'étude d'ingénieur grade Master 2 en Génie Mécanique et Industriel (.pdf, 2.6 Mo), Jean Harson Rakotonoely, 2019 ( http://biblio.univ-antananarivo.mg/pdfs/rakotonoelyJeanH_ESPA_MAST2_19.pdf ).
    A noter que ce mémoire reprend quasi-intégralement le texte et les équations des pages Web du Sujet Internet "Bélier hydraulique", comme suit :
    - Chapitre Principe : recopie intégrale des Phases de fonctionnement (sans mention de la source) : pages 10 à 11 du mémoire.
    - Chapitre Théorie : recopie quasi-intégrale de tout le chapitre (sans mention de la source) : pages 12 à 38 du mémoire.
    - Chapitre Pratique : recopie adaptée des paragraphes "Calcul d'un bélier" et "Bélier prototype à construire soi-même" : pages 42 à 47, et 54 à 55 du mémoire.
  29. Toulouse, Lycée Déodat de Séverac, TIPE : Le bélier hydraulique, Pauline Vie, Marc Chauchat, Gautier Combelles, CPGE 2ème année, PSI, 2015.
  30. Valbonne, Lycée International, TIPE : Le bélier hydraulique, Raphael Chattot, CPGE 2ème année, PSI, 2011.
  31. Valbonne, Lycée International, TIPE : Le bélier hydraulique, Samuel Franch, CPGE 2ème année, PC, 2021.

About the topic "Ornithology" :

  1. Vanves, Editions du Chêne, "Phénomènes - De la pollinisation à l'origine des comètes en 124 planches illustrées", Planche n32 intitulée "Chants des oiseaux", Editions du Chêne 2023, Suzanne Labourie, contributeur en Recherches et Coordination scientifique.



6. Weblinks that deal with Website Design and Checking

Site UKO.
Tutoriel HTML

Josselin Willette.
Les bases du HTML

Sébastien Laoût.
Balises nécessaires pour faire une page HTML 4.01 Strict

Alexandre Alapetite.
Caractères spéciaux et entités HTML

Web Design Group.
HTML 4 Reference

Alsacreations - Tutoriels et astuces.
Apprendre les standards Web, HTML, CSS, JavaScript, design et développement...

W3C.
HTML 4.01 Specification

WDG HTML Validator ( http://gnu.univ.gda.pl/wdg-html-validator/ ).
Le validateur HTML du WDG (World Design Group) pour site entier

W3C - Markup Validation Service.
Le validateur HTML du W3C (World Wide Web Consortium)

Validateur HTML/XML.
Le validateur HTML Aborla du HTACG (HTML Tidy Advocacy Community Group) associé au W3C (World Wide Web Consortium)

W3C - Link Checker.
Le validateur W3C (World Wide Web Consortium) des liens, ancres et objets référencés en page Web

WDG - CSSCheck.
Le validateur CSS du WDG (Web Design Group)

W3C - CSS Validation Service.
Le validateur CSS du W3C (World Wide Web Consortium)



7. About the Author of this Website

Overall

Régis Petit, former engineer in Computing at EDF (Electricity of France) is a specialist in Systemic modeling. In 2005, he created this scientific information site which is used by numerous schools and organizations, in particular within the framework of projects at the studies end.
Through his research for nearly twenty years and the rigor of the results obtained, the author is one of the world referents of Billiards physics as well as French referents of hydraulic ram.

The various models made by the author are as follows :

Publications

Training

Régis Petit was born on February 24, 1958.
- Engineer in Mechanics ("Arts et Métiers" - E.N.S.A.M. - Paris)
- Engineer in Applied Mathematics (E.N.S.E.E.I.H.T. - Toulouse)
- P.H.D. in Computing, Artificial Intelligence and Robotics (I.N.P.T. - Toulouse)
- Independent researcher in systemic modeling. France.



Copyright © 2005 Régis Petit.         CopyrightFrance.com        Last page update : June 11, 2024.