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Overview

Project website gitlab.com/libre-money-projects/theorie-relative-de-la-monnaie
Project maintainers User avatar kapis User avatar Moul User avatar PifPafPouf
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Source code repository git@git.duniter.org:documents/theorie-relative-de-la-monnaie.git
Repository branch master
Last remote commit Pipfile matching the requirements f4849b8
Toover authored 6 months ago
Last commit in Weblate Translated using Weblate (Spanish) 2506d96
User avatar nenamaca authored 6 months ago
Weblate repository https://weblate.duniter.org/git/trm/theorie-relative-de-la-monnaie/
File mask source/locale/*/LC_MESSAGES/appendice-2.po
Translation file Download source/locale/en_US/LC_MESSAGES/appendice-2.po
Last change March 24, 2023, 8:55 p.m.
Last author Pif Paf Pouf

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User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

Une borne minimale simple apparaît pour les :math:`\alpha` positif, si :math:`\alpha \approx c` on a :math:`DU(t+dt) \approx DU(t)`, et une autre borne minimale simple apparaît pour les :math:`\alpha` petits et négatifs, que nous sommes heureux de retrouver sous cette forme, puisqu'elle est très proche de la définition : :math:`DU(t) = c \, \frac{M(t)}{N(t)}`.
A simple lower bound appears for :math:`\alpha` positive if :math:`\alpha \approx c` we have :math:`DUD(t+dt) \approx DUD(t)`, and another simple lower bound appears for :math:`\alpha` small and negative, that we are happy to find in this form, since it is very close to the definition: :math:`DUD(t) = c \, \frac{M(t)}{N(t)}`.
6 months ago
User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

N(t) est inconnu, aussi afin d'évaluer la forme d'une méthode générale de génération pratique, nous devons établir une méthode des plus simples et des plus lisibles, que nous pouvons approcher via une modélisation de la variation de N sous la forme :math:`dN(t)=\alpha N(t)` ou encore :math:`N(t+dt)=N(t)+dN(t)=(1+\alpha)N(t)` et nous prenons une approximations pour M conforme à :math:`M(t+dt) \approx (1+c) M(t)`.
N(t) is unknown, so to assess the form of a general method of practical generation, we need a method simpler and more readable, we can approach via modeling of the variation of N in the form :math:`dN(t)=\alpha N(t)` or :math:`N(t+dt)=N(t)+dN(t)=(1+\alpha)N(t)` and take an approximation for M according to :math:`M(t+dt) \approx (1+c) M(t)`.
6 months ago
User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

Notamment on se convaincra par la réflexion de la nécessité d'aborder la solution pratique en prenant en considération des cas extrêmes, comme celui du cas de forte hausse du nombre de participants d'une monnaie libre (équivalente à une pseudo-initialisation de monnaie), où le DU calculé en relatif ( :math:`DU(t)=c\left(\frac{M}{N}\right)(t)` ) subira une forte discontinuité, détruisant la continuité de la progression, et deviendrait extrêmement bas vis-à-vis des participants initiaux, peu nombreux, et qui posséderaient dans ce cas une part monétaire extrêmement forte par rapport aux nouveaux entrants, sans rapport avec le DU calculé.
In particular, one should be convinced by thinking of the necessity to approach the practical solution by taking into consideration these extreme cases, as the one of the strongest growth of the number of members of a fair money (equivalent to a pseudo-initialization of the money), where the calculated UD in relative ( :math:`DUD(t)=c\left(\frac{M}{N}\right)(t)` ) will suffer a huge discontinuity, destroying the continuity of the progression, and would become extremely low compared to initial fewer participants, and would own in this case a huge share of money compared to the new entrants, unrelated to the calculated UD.
6 months ago
User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

Étant donné ce qui précède il faut garder à l'esprit que c'est la convergence de demie vie qui est l'objectif atteint par une monnaie libre, les nouveaux entrants remplaçant les morts (voir à ce propos les formes :eq:`eq4` et :eq:`eq14` concernant la condition temporelle valable pour tout individu).
Given prior analyze, one should bear in mind that it's the convergence of half life that is the target reached by a fair money, new entrants replacing dead human being (see about this the forms :eq:`eq4` et :eq:`eq14` concerning the time condition valid for any individual).
6 months ago
User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

On remarque immédiatement que lorsque le compte vaut la moyenne, la taxe théorique s'applique au compte directement et sans approximation intermédiaire.
We immediately note that when the account is worth the average, the theoretical tax is applied directly to the account without intermediary approximation.
6 months ago
User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

Cette forme reprend le taux de la taxe :math:`(c_1 - c_2)` appliqué au compte augmenté du RdB (visant sa valeur en "t+1", sans taxe), et ramené de cette valeur approchée en "t+1" vers sa valeur en "t" par la division par :math:`(1+c_1)`.
This form use again the tax rate :math:`(c_1 - c_2)` applied to the account increased of the UBI (targeting its value in "t+1", without tax), and brought back to this value approximated in "t+1" to its value in "t" by the division by : :math:`(1+c_1)`.
6 months ago
User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

Nous avons donc bien ici le calcul instantané de la "taxe apparente" dans :math:`R_{2}` à partir de données directement issues de :math:`R_{1}`, permettant un affichage :math:`RdB_{R_{2}} = DU_{R_{2}} + (taxe \, apparente)_{R_{2}}`.
We have here the instantaneous calculation of the "apparent tax" in :math:`R_{2}` from data directly taken from :math:`R_{1}`, letting a display :math:`RdB_{R_{2}} = DUD_{R_{2}} + (apparent tax)_{R_{2}}`.
6 months ago
User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

La présence du facteur :math:`(1+c_2)` n'est pas étonnante puisque c'est le taux d'expansion discret de :math:`R_{2}`, qui multiplié par des données "t" donne une approximation des données en "t+1". On doit donc comprendre que cela produit une bonne valeur intermédiaire du numérateur entre "t" et "t+1".
The presence of the factor :math:`(1+c_2)` is not surprising since it is the expansion rate discrete of :math:`R_{2}`, which multiplied by the data "t" gives an approximation of the data in "t+1". We should now understand that it produces a good intermediary value of the numerator between "t" and "t+1".
6 months ago
User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

Tous les termes de droite étant déjà calculés par transformation directe depuis :math:`R_1`.
All the right terms being already calculated by direct transformation from :math:`R_1`.
6 months ago
User avatar PifPafPouf

Translation changed

TRM / appendice-2 — English (United States)

Dans :math:`R_{1}` nous avons l'égalité :
In :math:`R_{1}` we will have the equality :
6 months ago
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