A Board for Paper-Based Spaced Repetition Memorization

I’ve been using spaced repetition for quite some time now. My favorite program is Anki, even if I have also tried a few others. I had actually developed one myself before I even knew the SuperMemo algorithm existed back in the late 1990’s, that was more than 10 years before the first Anki release.

Interestingly, spaced repetition has been around since the democratization of computers. That’s for a reason: spaced repetition is very easy to do on computers, but not so easy with physical supports. Although Piotr Wozniak, the inventor of Spaced Repetition, used paper to do his studies, he switched to computerized version as soon as he got a computer. I have been wondering for a while how it could be achieved without too much hassle from the user’s point of view. I finally came up with a rather easy and elegant solution.

The problem with regular flashcards

Who didn’t try to make paper cards of things they wanted to remember? You write a question on the front side, the answer on the back side. It could be anything, including pictures. When picking that card, you have to remember the answer. By repeating the process, you’ll learn that information, eventually.

However, without a planned schedule, that process is very inefficient. You often get exposed to cards that you already know perfectly, which is frustrating, especially if there are so many of them. The sensation that you’re losing your time is taking over. Then you’re tempted to put them away for good. Only to realize a few months later that you forgot the information they hold. Similarly, you sometimes get exposed to cards that you have already forgotten.

This is why Spaced Repetition has been invented: it is optimizing the interval at which you are exposed to the different cards.

Spaced Repetition principles

So, just as a reminder, what is Spaced Repetition?

Basically, it is taking advantage of how our memory works. When exposed to some information for the first time, the brain remembers it for a short time. It could be just an hour or a day. Then it filters this information out, to give space to new information. But when exposed to this information again before it is wiped out, the brain starts giving some bigger importance to it. Thus it will remember it longer. Maybe 2 or 3 days.

Again, after a few days, that information will be deleted. Unless you get exposed to it again before it is erased, in which case it will get an even stronger importance. This time, the brain will remember it for a week or two. And so on. Basically, every time you remember that information before it gets deleted, the brain sort of doubles its importance. This means that it will take double the time before it forgets it. “Double” is a rough estimate, the actual rate varies from person to person, and heavily depends on the knowledge to be learned itself, along with the eagerness of the learner.

So the goal is to be exposed to the information at increasing intervals. The key being that the information should reappear before it is erased.

Attempts

There are people who have attempted to do that. Of course, the inventor himself came up with tables where he marks the intervals.

Although it works, it uses up some paper, and you need a cache to cover the words that need to be learned.

Other people have invented something which is closer to my goal. The idea is to have several boxes, each one of them contains a different interval. The first time you’re exposed to a card, you’ll put it in the first box, which is the daily interval. Once it is learned, it goes to the second box, which could be the weekly interval. And so on.

There is still a problem with this method: if you pick cards from the weekly box every Sunday, then you’ll pick cards from Saturday, which is not good.

In other words, the question is: how do you know how many cards to pick from the weekly box and when to pick them? How do you know 7 days have really passed since that card was put in the box? You don’t know. Which can cause problems. Especially when moving to longer intervals.

Thinking of a board

I thought about developing a board on which it would be easy to know when to pick cards, especially on longer intervals.

Just like the boxes, the goal is to have several zones on the board, with increasing intervals. Thus when remembering a card in a certain zone, it is then moving up to the next zone. This way, the intervals for a card are increasing, similar to the boxes.

However, for a card in a long interval zone, we can add markers to show where we are in the interval. Luckily, it is not difficult to make markers.

Besides, everything depends on the size of the cards you want. I chose the “compact” route, with cards that are square and not bigger than an inch (actually 2 cm in my prototype). But of course, the same principle could just be used with bigger cards, it would simply take more space.

The final result and its explanations

Here is the model of the board I have come up with, which I then printed with a 3D printer.

The column on the right represents the shortest intervals. Every column has two parts: the left part with larger holes in which the cards can be kept, and the right part that contains small holes in which little pegs can be inserted. These pegs are the markers that help keep track of where we are in time.

Moving Pegs

Basically, you just move every peg one step further. They show you directly which cards need to be reviewed that day. Here is what happens when you start a new day:

For the longest intervals, the pegs are moved forward only when the last daily peg reaches one of the marked spots, as seen in this picture:

This way, the two last columns move forward only when the “Daily Move” column reaches one marked spot. This happens every week and every month, respectively.

Note that the last 3 columns have more “peg holes” than “card holes”. Therefore, you don’t need to review cards in these three columns right away when the peg comes to a new spot with cards. Instead, you can pick them gradually, for instance on less busy days.

Learning cards

Every day, you pick cards from the spots that are marked by the pegs. If you forgot the contents of the card, then that card goes back to daily learning, at the bottom right of the board.

If you did remember what was on a card, then you can move it to the next zone, just behind the next zone’s marker. This way, you will have to wait a full cycle of the marker to review that card again.

Here is the representation of the movements of the cards, according to the current peg positions on that board:

Conclusion

This board, which I have already been using for a while now, is very convenient for spaced repetition without the need of a computer. It is quite compact, in fact I have calculated that it could hold no less than 5000 cards. Of course, other boards can be printed if this is not sufficient! It still needs to get a decent cover so that it could be easily transportable.

The board is available to print on Thingiverse: https://www.thingiverse.com/thing:3974248

It is also available on my gitlab: https://gitlab.com/jytou/3d-paper-spaced-repetition

I have also written a converter to print your anki decks: https://gitlab.com/jytou/anki2papergenerator

Broken Stuff 0 – 3D Printing 1

Recently, I got a package with broken stuff in it. It was actually some shelves with doors, and the broken part was that plastic part that contains magnets which hold the doors closed. Here is a picture of what I received:What generally happens in this kind of circumstance is that people will complain and return the package, then get another brand new article. That’s a lot of wasted transport and energy for such a little missing piece.

So I decided to 3D print the part. In the process, I decided to make it more ergonomic. Those white plastic parts are generally a little sharp and can even scratch your hand if you’re not careful. So I designed a round one. I also had some round magnets around and I decided to use those rather than the stock ones which are rectangular.

As the shelves were made of wood, I also printed that part with wood PLA. Here is the resulting piece with the original near it:

Then I glued the magnets in place:

And here is the final result:

Isn’t that much cooler than the original? I love 3D printing!

Planned Obsolescence, 0 – 3D Printer, 1

It is not the first time that I fix something with 3D printing. But this one was an interesting one!

The problem

A few years ago, I bought two stands for my microphones. Okay, they were inexpensive, and maybe it was a bad long-term choice. Maybe I should have opted for more expensive ones. But I have noticed that higher prices don’t always mean better quality. These days, they often mean higher reseller margins.

Anyway, both stands were poorly designed. Even though they did last several years, they finally broke recently, roughly at the same time. Unsurprisingly, the faulty piece is a part made of plastic. It sustains high pressure on a very small surface. And after a while, it just gave in. I believe that, without me noticing, cracks developed over time, until they became big enough to break the piece completely:

As you can see, it is pretty bad. Of course, I couldn’t find spare pieces, especially as these are already “old” (anything beyond a year is “old” nowadays). And without this piece, the stands are totally unusable.

Reflexes…

The first reflex was: it’s cheap stuff, I can buy new stands! Why bother for 20 euros?

But apart from this broken piece, those stands are in perfect condition and they could serve their purpose for many more years. Why pay? Why extract more metals from the Earth, build more plastic pieces mostly from petroleum, more rubber from trees or worse from petroleom again, use energy to forge, heat, assemble, then use again more energy to ship those new stands to me or go and fetch them from a local store – where they would have been shipped from somewhere anyway? And dispose from transport boxes that kill trees? As well of course as disposing from the broken stands. And as a result buy new stands in a few years when those new ones will break?

I didn’t actually want any of that, especially as I have the “Planned Obsolescence Killer” at home : a 3D printer!

Compared to all the waste of buying brand new stands, printing a piece is quite environment-friendly: it does use some electricity (not much), and I mainly print using PLA, which is basically made of… corn. This material does have its pros and cons, but it is certainly better than petroleum-based plastic.

Designing a solution

I spent some time designing a solution. This piece allows the axis to be rotated to the desired angle, and it is a functionality that is really needed for this kind of object! So even though there were many alternative ways of fixing that stand, I wanted to stick with the original design as much as possible.

On the other hand, printing this kind of piece with PLA was going to get me in the exact same trouble in a few years: the plastic would certainly not resist the pressure. I could also print with nylon, but I try to avoid it as much as possible due to environmental concerns. Besides, given the pressure on that piece, I wouldn’t be so sure that even nylon would resist for a long time.

I first thought of adding washers to maximize the surface in contact, but I finally came up with using nuts with a ring base.

3D modelling and printing

Here is one part of the final model:

I heated the printer and printed the pieces:

Results

That piece has two other pieces which hold the nuts in place and stop them from turning, even if the pressure actually isn’t a rotating one but a pulling one.

Mounting the nuts in place and putting one of the pieces in its socket:

The socket for the second piece is clearly visible. The final mounted piece:

And now it was just a matter of putting it instead of the old piece:

Et voilà ! Both stands are fixed with just a few grams of PLA. I think they will last some more years. In fact, I believe this kind of thing should last at least for a lifetime. But then, how would we sustain “economic growth” to pay for growing banking interests?

Une page web pour le système majeur de mémorisation des nombres

Cher lecteur, si tu connais déjà tout sur le système majeur, tu peux sauter directement à la solution. Pour les autres, vous apprendrez quelque chose en lisant l’article en entier ! Et pour les plus impatients, la page web est là : https://jytou.fr/majeur/?n=15

Pour la plupart des gens, mémoriser des grands nombres est un défi qui s’arrête très vite. À grand peine, on arrive avec le temps à mémoriser des grands nombres par la répétition, année après année, comme le numéro de sécurité sociale ou les numéros de téléphone, qu’on arrive enfin à mémoriser le jour où on en change.

Le système majeur

Et pourtant, nous avons à notre disposition des méthodes qui permettent de mémoriser des grands nombres, dont une très populaire qui fonctionne par associations de sons : le système majeur, parfois aussi appelé « Grand Système » en français. Nous devrions tous apprendre cette méthode à l’école ! Cette méthode peut être utilisée dans beaucoup de langues avec quelques modifications basiques. Et pourtant, quel pourcentage de la population connaît cette méthode ? Combien l’utilisent vraiment ? Le pourcentage doit se compter sur les doigts d’une main.

Pour résumer, il s’agit juste de trouver des mots dont les consonnes prononcées correspondent aux chiffres à retenir. Par exemple, pour le chiffre « 0 » on cherchera un mot avec un son « s » ou un « z », pour un chiffre « 1 » on aura un « t » ou un « d », etc.

Voilà le tableau des correspondances généralement utilisées pour la langue française :

Nombre

Lettre

Associations visuelles

0 s, z Le chiffre 0, zéro, produit un son sifflant.
1 t, d Un seul trait vertical
2 n Deux traits verticaux
3 m Trois traits verticaux
4 r La lettre r se retrouve dans quatre en français, four en anglais, vier en allemand, etc.
5 l La lettre L ressemble au chiffre romain L (50)
6 j, ch, sh La lettre j manuscrite ressemble à un 6 inversé
7 k, c, g La lettre K ressemble à deux 7 accolés. G est phonétiquement proche de k.
8 f, v, ph Deux lettres f ressemblent à un 8. V est phonétiquement proche de f et de ph.
9 p, b La lettre P ressemble à un 9 inversé. P et b sont phonétiquement proches.

Bien évidemment, il ne s’agit que de conventions et comme l’apprentissage est très personnel, chacun peut faire des choix différents quant aux correspondances. En revanche, chaque changement nécessite de se poser de nombreuses questions : en choisissant telle correspondance, ne vais-je pas me retrouver dans des situations difficiles parce que je n’avais pas prévu que telle lettre n’est pas très présente dans la langue, par exemple ? Dans tous les cas, chaque changement doit être mûrement réfléchi et résister à l’épreuve de la pratique.

Une fois les conventions adoptées, il s’agit de les tester avec des cas concrets et des chiffres à retenir. L’un des défis est de trouver rapidement des mots correspondant aux chiffres puis de les assembler en une suite de mots qui veut dire quelque chose, même si c’est un peu loufoque. D’ailleurs, plus c’est loufoque, plus ce sera facile à retenir. Nous mémorisons ce qui fait appel à l’émotion et à l’imagination. Si c’est trop « plat », on oublie tout de suite.

Tables apprises par cœur

Pour gagner du temps, une technique courante consiste à mémoriser des mots déjà tout prêts pour des combinaisons de deux chiffres, comme 10=tasse, etc. Voici un exemple d’un tel tableau, qu’on appelle « table de rappel » :

 0
s, z
1
t, d
2
n
3
m
4
r
5
l
6
j, ch
7
k, g
8
f, v
9
p, b
0
s, z
0
as
10
tasse
20
nasse
30
masse
40
race
50
lasso
60
chasse
70
casse
80
face
90
passe
1
t, d
1
tas
11
tata
21
natte
31
maths
41
rate
51
latte
61
château
71
cata
81
fête
91
patte
2
n
2
nez
12
tanin
22
nana
32
manne
42
reine
52
laine
62
chaîne
72
canne
82
fan
92
panne
3
m
3
mât
13
tamis
23
nem
33
maman
43
rame
53
lame
63
chameau
73
came
83
femme
93
pomme
4
r
4
rat
14
tare
24
nerf
34
mare
44
rare
54
lard
64
char
74
car
84
phare
94
part
5
l
5
la
15
talus
25
nylon
35
mâle
45
râle
55
lolo
65
châle
75
cale
85
fil
95
pelle
6
j, ch
6
chat
16
tache
26
niche
36
machin
46
ruche
56
lâche
66
chéchia
76
cache
86
facho
96
pacha
7
k, g
7
cas
17
taquin
27
nuque
37
mac
47
rack
57
laque
67
chèque
77
caca
87
fac
97
pack
8
f, v
8
feu
18
tif
28
nef
38
mafia
48
raffut
58
louve
68
chef
78
café
88
fief
98
pif
9
p, b
9
pas
19
tape
29
nappe
39
myope
49
râpe
59
lapin
69
chapeau
79
cape
89
fip
99
papa

Certains vont même jusqu’à mémoriser 3 chiffres, soit 1000 mots à associer aux 1000 premiers nombres. Bien sûr, c’est très utile pour ceux qui en font un grand usage comme les champions des concours de mémorisation. En revanche, pour les autres, c’est beaucoup de sport cérébral qui finalement risque de ne pas servir à grand-chose, à part peut-être pour briller occasionnellement en société. De manière générale, le tableau ci-dessus suffit pour un usage occasionnel. Pour ma part, je préfère mémoriser trois mots au lieu d’un pour chaque paire de chiffres : un nom, un adjectif et un verbe. Cela permet de faire des phrases qui se retiennent beaucoup plus facilement. L’inconvénient est une petite perte de temps à choisir le mot pour chaque paire afin de former une phrase.

Voyons comment ça se passe dans la pratique avec un exemple.

Défis

Tentons de mémoriser 15807020 avec la table présentée au-dessus :

15807020
talusfacecassenasse

Avec ces mots, on peut facilement faire une phrase qui utilise tous ces mots dans l’ordre, en se rappelant que seuls les noms, adjectifs et verbes sont importants et que le reste compte pour du beurre : « Un talus en face, tu casses ta nasse ». Pour retrouver le nombre, il suffit de se rappeler de cette phrase puis reprendre les noms et les codes de chaque lettre. C’est une technique simple, mais il reste encore à mémoriser cette phrase, ce qui n’est pas toujours évident. Surtout que, dans certains cas, c’est beaucoup moins évident de faire une phrase avec : chameau, lame, panne, mâle. Pas de verbe, pas d’adjectif. Un bon petit casse-tête.

Aller plus loin

Dans le cas d’une mémorisation rapide, il est préférable d’utiliser une table comme celle qui vient d’être présentée. En revanche, pour des mémorisations où on a tout le temps du monde pour élaborer une technique, il est préférable d’optimiser un peu. Plutôt que d’utiliser des « mots tout prêts », on va chercher des mots plus longs, une phrase facile à retenir et qui fait sens plutôt que des mots imposés.

L’un des défis avec ce système est de trouver rapidement des mots « mémorables » et qui se combinent bien pour une certaine combinaison de chiffres. Or, lorsqu’on se retrouve face à 15807020, il n’est pas toujours évident de trouver des mots assez longs pour rivaliser avec la simple mémorisation des mots à 2 chiffres. Sans entraînement, on peut y passer beaucoup de temps. Et même avec de l’entraînement, la combinaison que l’on trouve est souvent loin d’être optimale.

Parfois, il peut aussi être intéressant de former une suite de mots directement à partir du nombre à mémoriser avec des mots de taille variable. Par exemple, pour mémoriser 15807020, on pourrait se rappeler de suite de mots suivante :

Télé visqueuse et niaise
tele visk ø z e njɛ z
1 5 8 07 0 2 0

Facile de se faire une image mentale de cette phrase, il suffit d’avoir un peu d’humour.

Sans aucun doute, il est plus facile de mémoriser moins de mots choisis dans le vocabulaire courant plutôt qu’une grille fixe. Par ailleurs, leur longueur n’a aucune importance car, dans la tête, un mot est une entité mémorisable directement quelle que soit sa longueur, comme on l’a fait plus haut avec la télé visqueuse et niaise.

Il existe déjà un excellent logiciel nommé 2know qui permet de trouver tous les mots correspondant à une suite de chiffres donnée. Malheureusement, je trouve cette application un peu trop limitée car on ne peut chercher qu’une suite de chiffres à la fois. Il faut alors tester toutes les combinaisons pour trouver des mots adéquats. Par ailleurs, ce logiciel ne fonctionne que sous Windows, même s’il est utilisable sous linux et wine, c’est loin d’être idéal.

La solution

Par conséquent, j’ai développé une page internet qui permet de donner toutes les combinaisons de mots qui peuvent se rapporter à une suite de chiffres. L’avantage est que l’on de dépend pas de la plateforme, elle peut être visitée et utilisée à partir de n’importe quel terminal informatique pour peu qu’il dispose d’un navigateur.

Lorsqu’on lui présente un nombre, elle calcule toutes les possibilités de mots qui peuvent être trouvés avec la suite de chiffres en question. Ainsi, elle affiche les possibilités dans un tableau, les mots les plus longs sont placés en haut du tableau, chaque ligne est ensuite complétée avec les mots plus petits. On peut ainsi voir les possibilités intéressantes de combinaisons de mots. Par ailleurs, la page affiche également les mots par type grammatical, car il peut être pratique d’enchaîner un nom, un adjectif, un verbe puis finalement un nom pour former une phrase syntaxiquement correcte.

Il suffit de naviguer là pour voir comment cela fonctionne : https://jytou.fr/majeur/?n=15807020

On retrouve facilement la télé visqueuse et niaise, mais on peut également inventer d’autres combinaisons facilement.

Quelques petits réglages peuvent être paramétrés comme le style plutôt noir sur fond blanc ou l’inverse et le tri des mots. La page reste très simple et épurée de toute distraction.

Et après ?

À l’origine, je visais un peu plus compliqué. J’envisageais que la page fasse également des suggestions de phrases, en utilisant des règles simples permettant de prendre des mots à la suite ayant de fortes chances de faire des phrases correctes. On peut imaginer par exemple : interjection, article/démonstratif…, nom, adjectif, verbe, nom, adjectif. Et ainsi de suite. Pour l’instant, la page telle qu’elle est me suffit – le rasoir d’Okham a encore frappé ! N’hésite pas à commenter si la page plus élaborée t’intéresse et si celle-ci te sert déjà à quelque chose !

Pour les techniciens…

Pour ceux qui se posent la question du développement de cette page, j’ai récupéré le dictionnaire du français avec classification grammaticale et phonétique ici : https://github.com/WhiteFangs/lexique.sql

Ce lexique est issu du projet suivant : http://www.lexique.org/

Il contient 150.000, mots du pain bénit ! J’ai fait un petit peu de ménage dans la classification et gardé seulement le strict nécessaire dans la table SQL, c’est-à-dire l’orthographe, la phonétique, la correspondance en système majeur, la classification grammaticale ainsi que le masculin/pluriel et la fréquence du mot pour afficher les mots les plus courants en premier.

Ensuite, il m’a fallu faire un petit programme java pour calculer la correspondance entre prononciation et équivalent en système majeur, également stocké en base de données.

Enfin, une page en php permet de faire la recherche des mots qui correspondent au nombre recherché et les affiche dans un tableau, simple comme bonjour !

The Relative Theory of Money – English Translation of the Leibnitz Module

This is the translation of the Leibnitz Module of the RTM, which follows the Bresson Module.

Leibnitz Module

(a) Thoughts on the Relativity of Prices (N)

Let’s assume that for a short time compared to life expectancy (a few years), the prices of some known values are relatively stable in the M/N frame of reference. Given this hypothesis, simulate:

  • create the spreadsheet of a Libre Currency in both Quantitative and Relative (UD) frames while the population is composed of N individuals
    including I1, I2 and I3 ; N is a variable represented in a column, during 80 years, one line per month (80×12 lines) as well as a newcomer I4 who enters when N varies,
  • on a short period of time, express the relative price in the frame M/N during a few years of an economic value V ; translate the quantitative price in UD,
  • express during the same period the price of V compared to the accounts of every individual,
  • simulate cases where “N increases strongly” and “N decreases strongly” in a few years, create the charts of the prices of V (which remains quite stable in the quantitative frame), in the 3 units as well as relative to the 4 individuals,
  • Compare and interpret the results.

(b) Reflections on the formula of the UD when N is unstable

  • In the same spreadsheet, simulate two strong local variations of N (10 times growth/reduction) during a small period of time (2 years), N remains stable otherwise,
  • add I4 who is a newcomer during the variation of N,
  • express for the 4 individuals the variations of the price of V (which we will assume is still stable in the quantitative frame) in the 3 units (quantitative, UD, M/N) and relative to the accounts of each individual, during a period of 20 years around the variations of N (before and after),
  • try to find a possible range for the UD’s formula between minimal and maximal values by studying the case of the 4 individuals,
  • Compare and interpret.

(c) Studying different UD formulas

  • In the same spreadsheet, simulate two strong local variations of N (x 10) on a short period (2 years), N remains stable otherwise,
  • Simulate for the 4 individuals different formulas for the UD that can be studied in a 20 year interval before and after the variation of N,
  • simulate the same formulas when N is stable in another spreadsheet,
  • compare each formula graphically by comparing it to M/N when N is stable,
  • calculate for each of these formulas the standard deviation with the stable case,
  • Compare and interpret the results.

(d) General interpretation on relativity

(e) Conclude the publication

My Yolland Bresson Module – Part 2

Welcome to the second part of my version of the Yolland Bresson Module, started in Part 1.

(d) Exchanging values during 50 years in a Libre currency

In this part, we’ll see what happens when individuals do some exchanges, since it is actually what money is here for! So we’ll have generations of 10 people which replace each other over time and watch the impacts on the accounts of these exchanges over time.

Simple exchanges

To begin with, the sample given in the Module is to have exchanges at 5, 15 and 30 years. Besides, in my sample, I’ve given a very unfair distribution to my individuals with the oldest having a lot of money while the youngest has 0. I also chose to use the relative scale for the exchanges so that we can actually compare the relative amounts which don’t change over time, with an average of 10 UDs for all individuals. Finally, the amounts that are exchanged are quite big, making the individuals’ accounts switch from “rich” to “poor” and vice-versa at every exchange:

Year I1 I4 I5 I7 I11
5 -10 UD   10 UD    
15   -8 UD   8 UD  
30       -10 UD 10 UD

Just for the record, this corresponds in the absolute scale to the following exchanges:

Year I1 I4 I5 I7 I11
5 -72.47   72.47    
15   -150.4   150.4  
30       -785.2 785.2

As expected, the same amounts in UD correspond to exponentially growing numbers in the absolute scale.

Visualizing the impacts of simple exchanges

Unfortunately, the absolute graph doesn’t show anything because of the exponential curve, so we’ll directly switch to the log view:

While we do see the exchanges, they seem to have extremely little impact on the overall curves. Consequently, let’s switch to the relative scale:

What happened is pretty obvious now: although they have exchanged very big amounts of money, in the end the result is that when they die their accounts converge toward 0 and new generations (after a few decades) are not impacted by what has been done by the previous generations. Therefore, these new generations can choose their own path and their own values, regardless of what their parents have done and valued.

Focusing on one individual

We can also have a look at the account of one of them only, for instance I7 who has done two transactions:

Obviously, because he has gained quite a bit at year 15, his account has inevitably decreased in relative terms after that compared to other accounts so that all of them reach the mean of all accounts. But then as he becomes “poor” at year 30, his account starts tending toward the mean again, this time by “growing”. And of course, as death takes him away, his account tends toward 0, as everyone else (except for vampires of course).

Double accounting

Until now, we have only considered transactions between humans, who generally exchange money to compensate another exchange in real life: buying some object or service. However, we could express that in a “double-entry” table for each individual where we don’t consider only monetary exchanges:

Year I1 – Credit I1 – Debit
5 +motorcycle -10 UD

With that in mind, we can actually fill the previous table with the double accounting for each event and each individual:

Year I1 I4 I5 I7 I11
5 -10 UD
+motorcycle
  10 UD
-motorcycle
   
15   -8 UD
+boat
  8 UD
-boat
 
30       -10 UD
received coaching
10 UD
spent time coaching

Obviously, every monetary exchange has its own counterpart in the “real world”, either by transferring the property of something from someone to someone else, either by giving one’s time/expertise/work, whatever you call it, to someone else.

Double accounting – including the UD

In the meantime, there is really something missing in this table. In the balance of every individual’s account, a Universal Dividend is created every year. For everyone of them. So if we forget about their exchanges, the balance sheet is somehow missing something:

Year I1 I4 I5 I7 I11
5 +1 UD +1 UD +1 UD +1 UD +1 UD
15 +1 UD +1 UD +1 UD +1 UD +1 UD
30 +1 UD +1 UD +1 UD +1 UD +1 UD

Think about it, isn’t there something missing? We have UDs that are added, but nothing is subtracted to make the sheet balanced.

Year I1 – Credit I1 – Debit
5 +1 UD ???

Or is it really so?

The counterpart of the UD

Well, it isn’t. Every one of us is alive and is somehow always doing “something”. During our life, we give our time and energy to things that are meaningful to us. In addition, sometimes without even noticing it we create value in society, even in the smallest acts of our lives.

For instance, say you watched a football match yesterday while drinking beer and eating junk food. That doesn’t seem much of a contribution to society. I actually don’t like football, if you ask me, you’ve wasted your evening, and wasted yourself with the alcohol as well!… 😀 the fact is that my opinion here is not relevant since here we’re interested about you.

Due to the match you watched, maybe the next day at work you’ll have a nice chat with your colleagues and somehow, with that simple chat and some jokes about the match, you’ll have created a relaxed atmosphere at work that will make everyone positive for the next few hours. Isn’t that a contribution after all? Frankly, do you really think that brightening the day of someone else is a waste of your time?

Furthermore, it gets even more interesting if you produce some “things” that are not recognized by your peers (or even by yourself!) but that may be recognized as great achievements in the future, such as Mozart’s compositions or Vincent van Gogh’s paintings. As we’ve already seen in the Galileo module, we can call these ğvalues. We may not all be geniuses, but we all make contributions that are not recognized today as full “values”, and which have the potential of becoming values in the future.

Furthermore, other people in another part of the Earth might also be interested in your creations because the cultural biases of another society will be able to recognize them as values, while the society you live in don’t recognize them as values – think for instance metaphysical, meditation-related discoveries that would be considered utter b**lshit in the West but greatly valued in the East.

Let’s fill the blanks

With that in mind, let’s get back to our table. We can now fill it with the appropriate negative accounts of your time that you spend being alive and contributing to society as a whole by focusing on your own values and creating ğvalues:

Year I1 I4 I5 I7 I11
5 +1 UD
-ğvalues
+1 UD
-ğvalues
+1 UD
-ğvalues
+1 UD
-ğvalues
+1 UD
-ğvalues
15 +1 UD
-ğvalues
+1 UD
-ğvalues
+1 UD
-ğvalues
+1 UD
-ğvalues
+1 UD
-ğvalues
30 +1 UD
-ğvalues
+1 UD
-ğvalues
+1 UD
-ğvalues
+1 UD
-ğvalues
+1 UD
-ğvalues

Hurray, we do have a balanced double-accounting sheet now.

In conclusion, we have filled the double-entry table and everything is balanced now, thanks to the notion of ğvalue, which is the counterpart of the UD.

Multiplying exchanges

I have also played a little with more exchanges.

Here is the graph of many exchanges made by the exact same individuals:

Ok, I’ll have to agree that it’s quite messy. However the first thing we can notice is that, although they did make a lot of very unbalanced exchanges, the conclusion is always the same: whatever they did, their accounts never became excessively high (up to 2.5 times the average of all accounts) and they always go back to 0 after their death.

Nevertheless, these exchanges are not random – let’s detail what happened here in more detail.

Hoarding “things”

There are many questions that arise about Libre Currencies. One of them is the fact that people would be tempted to get away from their money and buy “something” that would be a store of value for them (think “gold”, for instance). Then later, by selling those things back, they would have an advantage since they wouldn’t have lost their purchasing power, unlike storing libre units of value which statistically lose value exponentially in time.

I have simulated exactly that with one individual, I10. During the first part of his life, he systematically spends his money to buy things. After that, as he reaches his 59th birthday, he sells those things back. Note here that I have considered that the price of those “things” he bought have not changed in the relative scale. For instance, that could be true for something like gold, but you could also imagine many other things. I have isolated the graph for this individual and the people he exchanged with:

It is apparent here that he seems to be “cheating” during the first part of his life. Obviously, he refuses to go to the mean of all accounts so his account gets always filled with money, while other people’s accounts get higher.

Conversely, toward the end of his life, by selling what he has been hoarding during his whole life, he suddenly becomes very rich compared to the others, while everyone else is getting poorer.

Thoughts on I10

Obviously, this technique could be used to “optimize” your account in Libre Currency. I have seen people do that during Ğeconomicus games. However, this technique did not seem to be as fruitful as it could appear at first sight. That is because as the person is “buying” things he is actually not using, he is depriving himself of a very important tool: money itself. In other words, instead of using money for what it is, a means of exchange, he is using it for hoarding things, therefore giving himself a penalty because he cannot exchange with money much anymore.

Furthermore, he takes a great risk. Who knows if the “things” he bought will be considered as having any “value” at all in 30 years when he plans to sell them back? Nobody can guarantee that. Therefore, he’s taking a big chance, and may find himself with no money in his account and be surrounded with useless objects that nobody wants to buy. Certainly, that was not a very smart move! Besides, he could be having problems if he bought a lot of similar things: as he is selling them back, their price will inevitably get lower.

Additionally, we can also wonder how much of those “things that are stores of value” he will be able to buy, as everyone else will also value those things as such. So there will inevitably be a balance to be found on the prices of those objects, while money is circulating around, which is exactly what it was invented for!

Finally, although I10 did manage to get richer somehow toward the end of his life, he did not get “insanely” rich. So such a scheme is not a huge problem overall as he has paid a strong penalty for the rest of his life.

Inheritance

Another interesting question is the one of inheritance. Therefore, I have simulated a family that would try to transmit its monetary riches to its descendance in the hopes of getting richer and richer, as it happens with today’s monetary system. Indeed, despite all inheritance taxes and efforts by the State to grab whatever it can, the rich manage to get richer, generation after generation.

Without further ado, here is the graph of the “inheritance scheme” family who pass on the wealth to the spouse then to the children when one of their member dies:Indeed, they do manage to get a little richer than the average, thanks to the inheritance. Let’s say maybe twice as rich on average. Undoubtedly, that’s absolutely ridiculous compared to the rich today who are millions of times richer than the average population. Besides, everyone else will probably do the same thing, so there is no inequality here. The main point here being that even if trying to pass on great wealth, nobody can get hundreds of times richer than the others.

(e) General interpretation on Relativity

As a conclusion, we have first seen that in a Libre Money system, everything has its own counterpart: the UD is balancing the ğvalues created by humans.

Besides, this balance ensures that no minority manages to tip the scale in their favor since everyone’s contribution is always pushing the global scale to be symmetrically balanced in space and in time as well.

My Yolland Bresson Module – Part 1

Here is my version of the Yolland Bresson Module which follows the Galileo Module.

As the data has already been gathered in the last part of the Galileo Module, we can switch directly to part (b) and create the charts. Note that I based most of my data on the spreadsheet by Inso. I’ve added to it most of the data since 2014 until 2019.

(b) Create Relative Charts

In the Galileo module, I have already discussed the price of gold over time especially compared to different currencies and even compared to real estate prices in Paris.

The Gold Standard effect

One very interesting graph is the long term one which compares the USD to gold:

This is an unusual graph in which we observe the purchasing power of the USD compared to gold. The two steps of the gold standard, before and after 1929, are clearly visible. Then in 1971 as Nixon breaks the gold standard, the fall of the dollar compared to gold. One could say that, by forcing the gold standard, officials have tried the impossible: forcing one value to be equal to another one, although those values were appreciated quite differently in people’s minds.

The point here is that we can always compare any value to any other value, and no value stays equivalent to another one over time.

Looking from another perspective

We always look at prices “in euros” or “in dollars” but we never compare random values together, such as real estate and welfare.

So let’s do this just now and draw the chart of real estate prices expressed in units of welfare!

We’ve seen in the Galileo module that if you own gold, then the price of a flat is actually going down since the 1990s. But if you’re on welfare, the price has more than doubled in the same period of time.

(c) Charts

The point of this part is to look at prices not only over time, but also across geographical regions. Cuckooland has done a tremendous job which allows to see the prices of real estate change over time as the raise in price clearly starts in the center of the Capital, and diffuses first to the West (the richest suburbs) then to the rest of the area. Play with it, it is excellent! He has also rewritten some of it into a new app which he even translated to English. It is also available as a block. Enjoy!

Real Estate around the World

This is all about Paris. But what about the rest of the world? Are real estate prices all going up? You can download the spreadsheet real-estate-world.

Here is a chart of real estate prices worldwide since the early nineties, gathered from the IMF.

Obviously, some prices are going up, but some others are going down!

The geographical changes are also not uniform at all. For instance, in the UK, the prices between the London area and the rest of the UK are absolutely not following the same trend:

While London prices are skyrocketing, doubling between 2005 and 2019, prices elsewhere are not that crazy.

Wheat prices in the US

There are many other interesting values to be considered when it comes to geographical differences.

You may think that prices of wheat, for instance, are pretty much the same everywhere. Well, they are definitely not. The spreadsheet for this is available for download wheat-us. Here is a chart of wheat prices in the US over time:

From Denver to Portland, there has been a point in 2017 when you would pay double the price of wheat in Portland compared to Denver. I’m no expert in wheat crops in the US, but obviously Denver is a big producing area while Portland is not as big.

One other apparent trend here is that prices have diverged during mid 2016 and are getting closer again at the beginning of 2018. Many factors can explain this, such as a bad harvest which is actually confirmed for 2016. When the area already produces very little, a bad harvest means you may even need to import some wheat from elsewhere. But for a big producer, it has less impact. Although it may affect your exports, you still have more than enough locally.

Now that we know that we can actually compare any value with any other, we can actually compare the wheat price in Portland to the Denver price and create the corresponding chart:

We see here that Portland paid an immediate toll for the bad harvest in 2016 and only recovered in mid 2018, 2 years later.

Conclusion

Every value evolves with time, but also in space, always relative to other values. Many factors drive these changes: geography, climate, natural resources, social bias and trends of values in society, individual preferences, etc.

That’s it for Part 1, I will continue in part 2.

The Relative Theory of Money – Yoland Bresson Module Translated to English

Following the Galileo Module, the Yoland Bresson Module is the second module proposed to go deeper in the RTM. Here is a translation of the module in English.

The Yoland Bresson Module

(a) Get some data in a spreadsheet

The data has already been gathered during the last part of the Galileo Module:

(b) Create charts

Long term graphs of: Gold/$, Silver/$, Silver/Gold, Gold/€, Silver/€, Gold/M3€ , Silver/M3€, Gold/JSI-Welfare, Silver/JSI-Welfare.

Create the reverse graphs ($/Gold, $/Silver, etc.).

(c) Charts on Real Estate

Real Estate prices in Paris vs €, Gold, Silver, JSA/Welfare, M3€.

Same charts with real estate prices in another location, preferably a low density populated area.

Animate the results on a map with time. Change the reference frame (rather than €, use Gold, Silver, or any other reference frame).

Compare and discuss the results.

(d) Exchanging values during 50 years in a Libre currency

  • Create spreadsheets in absolute and relative frames for 30 individuals I1-I30 during 160 years.
  • Simulate large exchanges at t1=5 years, t2=15 years and t3=30 years,
  • Discuss numerical values as well as graphically, using double-entry accounting (think about Ğ(x) – eg. values that are not monetized because they are not recognized as values),
  • Summarize your thoughts about how humans, values and money, flow with time.

(e) General interpretation on Relativity

The next module is the Leibnitz Module.

My Galileo Module – Part 5

Here comes the last part of the Galileo Module: the relativity of values.

The aim of this module is to understand that no value is absolute, and that all values are relative to one another.

(e) Establish long term relative variations of different values

Metals

First I will study the price of gold, which we all now for sure is one very stable reference, right?

Let’s have a look at this very stable value:

Hmm, it doesn’t look as stable as we thought. Someone in the US who would buy gold in early 1980 thinking that this thing is definitely going up would absolutely be astounded to see he has lost half of the value 2 years later compared to the USD. Of course, the one who bought gold in 1975 with USD would probably have been very happy to sell his gold to get back some USD in 2012 (x10!).

But enough of the Gold. Silver must be probably better than gold, and reassure us on the fact that those metals are very stable in value:

Oh, it seems silver is even more unstable than gold compared to the USD. What about this rare metal called Palladium?

Well, it’s not so different. Okay, maybe it’s the dollar that is not stable?

Holly Gold

Let’s have a look at Holly Gold compared to different currencies:

What a Christmas Tree! This is total nonsense! Especially in July 2018, are we supposed to think that gold is “going up” or “going down”???

The truth is that nothing is going up or down by itself. Values are always “going up” and “going down” compared to another value. So these variations are totally normal, as nothing has such a thing as “intrinsic value”. Objects have “properties” that are then valued by humans to be “better”, “similar”, “worse”, than other properties of other objects. Gold is rarer than silver? Maybe that’s a reason why it’s valued more. But isn’t it also “better” because it doesn’t get oxydized while silver does? On the other hand, gold is “soft” and can barely be used in its pure state. Silver, on the other hand, is a hard metal, isn’t it better then? See, there are many things that drive the “value” in our minds of one thing, even if it seems simple. But it is always “relative to something else”. A hunter-gatherer tribe will have no business with you if you try to give them a golden bar, they can’t eat it! But for sure, they absolutely could use that big axe you have in your hand to hunt game, so they will value that axe much more than your gold bar.

XDR

Next, let’s see the value of gold compared to something that is a worldwide reference: the SDR (code XDR), Special Drawing Rights. Never heard about it? It’s a world currency, a basket of different currencies (USD, EUR, GBP, JPY, and more recently CNY). Here is the chart:

Unsurprisingly, it bears a resemblance with the charts involving the USD and EUR. But still not stable, which we know now is quite normal.

Real-Estate in Paris

We all know (especially French people) that the prices of houses and flats in Paris is surging for the last decades. Unfortunately, it may be true when counting in units of euros, but if we compare the prices to the total number of euros in circulation, let’s see what happens:

In fact, the price of a Parisian flat seems to be quite stable compared to M3, which is the total amount of euros in circulation. Surprisingly enough, it is even plummeting since 2011!

Last but not least, let’s compare the price of a Parisian flat if we were to buy it with Gold:

That’s not cool, the price of a Parisian flat lost almost 20% since the 1990s compared to gold. Surprised? I’m not.

Conclusion on the Galileo Module

Nothing is absolute. Everything is relative. In other words, every “value” you measure is actually measured “in a specific frame of reference”.

In everyday life, we tend to forget that fact about some values and tend to allow ourselves to think that “things have intrinsic value”. Objects and services never have an intrinsic value.

On the other hand, in everyday life, we are also more precise when it comes to other things. What if I tell you that my house is 50 away? 50 what? Meters? Kilometers? Yards? Nautical Miles? Minutes if you walk fast? We always use a “unit”, which is in fact a frame of reference.

We should not forget that every single value is, in itself, a frame of reference that can be used to compare it to other values.

Depending on the frame of reference we choose, we can conclude on very different results, as we have seen when we discussed monetary accounts in “absolute monetary units” and in “relative UD”.

My Galileo Module – Part 4

In part 3, we have simulated unbalanced exchanges between three individuals in a Libre currency. Now it is time to look what happens when new generations replace old ones. You can download the file for this part here.

(c) Changing frames of reference in time: replacement of generations

As humans do not live forever and new humans also come to this world, we will study what happens when new generations replace old ones.

First let’s have a look a the absolute amounts in the accounts of 20 individuals with only 10 of them present in the economic zone at all times. Every 8 years, one individual dies while another one is born. Here is what it looks like for 80 years:

We see that every account grows when a new individual is born, and then stays at the same value when he dies – these are the horizontal lines on the right of the graph. Let’s extend that to 160 years:

No surprise, as we have an exponential curve, things get “compressed” in the graph.

As it is a little messy to mix all accounts, let’s isolate one, for instance I12:

It is very clear that he starts at 0, then his presence creates money exponentially, finally the monetary creation stops when he dies.

The absolute graphs are not so interesting so let’s have a look at the logarithmic version (which is actually log(x+1) to be able to see the 0 values):

Given that graph, we now see the newcomers who start at 0 and who catch up quickly during their lifetime with the previous individuals, until they die and their account gets as flat as their heartbeats…

While absolute values are interesting, the relative values in the UD scale are even more interesting. Here is the graph on 80 years:

It is already obvious that when an individual dies, his relative account tends toward 0, while when a new individual enters the economic space, his account tends toward a common fixed value. Let’s observe the same over 160 years:

Indeed, all individuals follow the same scheme, let’s isolate I12 as we already did in the absolute scale, but this time in the relative scale:

In the relative scale, we see how I12 catches up very fast with the others during the first half of his life, then plateaus, and finally goes back very fast to 0 after his death. In the relative scale, it becomes clear that dead people’s economic doings “fade” over time, giving space to the new generations.

See you in Part 5, the last part of my Galileo Module.