There is an stellar system.
This stellar system has planets.
The planets are arranged as follows:
- 6 internal planets (1 to 6), in what is known as the "hot zone".
- 5 intermediate planets (7 to 11), in what is known as the "goldilocks zone".
- 49 exterior planets (12 to 61), in what isknown as the "cold zone".
There are some extrange creatures that inhabit this plants. All the planet has population.
In both the hot zone and the cold zone, there exists some magic shields that are put in place to protect the fetus as soon as pregancy starts. These shields protect the individual from the extreme temperatures of the planets. The shield stay with the baby and young individual as it grows. Other individuals can reach into the shield and interact with the infant.
The shield of an individual will eventually weaken and stay on only intermittently, this allows the individual to develop its natural resitence to the natural temperature, which they should have as adults.
The time until they reach a point where they no longer need the shield varies from planet to planet.
In planet 1 - which is the closer to the star - the shield will last for 26 years, while the sixth planet from the star it will last only 13 years.
A creature from a cold region will have more brown fat (Warming up kind of fat) than white fat (energy reserves in case there isn't enough glucose). This means that the creature needs a high amount of glucose.
Given the year boundaries for the shields and the fact that for the other planets in the hot zone and cold zone it is proportional, how can I calculate how many years the number will have the shield on part time and thus how many years it will have the shield on from birth?
We have these two data points:
- At planet 1, it takes 26 years.
- At planet 6, it takes 13 years.
And we are assuming that this "year" is the same unit. That means that those measurements are not in the years of each respective planets. Because if they are... then we need the orbital period of the planets, and as such the answer is: there is not enough information.
As I understand it, the number of years for the shields goes abrubtly form 13 years in planet 6 to 0 years in planet 7 (the first one of the goldilocks zone). So, there would not be a single smooth curve that describe the number of years for all the planets.
Now, because there are no more data points, the simpler aproximation is to say that the function - at least of the hot zone - is linear.
We can calculate the delta of year from planet to planet: The diffence from planet 1 to planet 6 is 26 years - 13 years = 13 years. So it changes 13 along 6 planets, or 13/6 years per planet.
Since 13 is prime I will not simplify the expression, and I will not try to convert it to months or days, because I don't know how those play out on your system - if they exists at all.
The economics is complex here. For a given type of currency (...) the exchange rate is 1:1, even if it isn't nearly that in real life. Each planet has a different currency. So 2 planets can have dollars but the dollars might be completely different.
Currently the interplanetary money transport is like this:
Production -> Teleportation (which relies partly on electricity) -> Conversion through base (unit) after it lands on the planet that needs money.
But I want the conversion step to essentially be lost. So how can I make it automatically convert from 1 base to another while it is being sent?
The way the equivalent is done currently in the real world, is that each electronic account has a defined currency. And whatever ammount of money is in the account, it is in that currency. When an electronic transaction occurs, it is responsability of the machine to do the appropiate conversions.
If we assume that we are not shipping the money from planet to planet, then the unit conversion has to happen in the machines used to do the electronic transaction^1.
Now, let's assume that we ship the money. In that case, the recieving party in the destination planet will now have some money that belongs to another planet. If this money is not accepted currency in this planet, they will have to go to the bank and change it for the accepted currency. It is now the bank at the destination planet the one that's doing the exchange (not some mahcine that convert bills from one kind to the other)...
But what does the bank do with the alien money? They could loan it to the original planet, where there is people who want it, and demand some interest in payment. Or they could use it to buy stuff from the other planet - and that way the money goes back to its original planet.
^1: The OP, had the idea that each planet uses a different numeric base. Such that planet 1 uses Base 2 (which coincidently is the name of the planet), the planet 2 uses base 3, and so on... But the question is... do the machines also internally use these bases? Or - by any chance - they are all using binary internally?
If the machines share base, and the conversion rate is 1:1, there is no conversion needed.
On the other hand, if they use different bases, the machines still require a common physical protocol (that dictates how to encode information for transmission) that is understood by the machines of all planets (which may suggest they share origin). And in this common physical protocol the ammounts will have to be encoded in some base.
You may argue: "Oh.. they send the number and send in what base it is!" well no. Because you have to send the number (and the number of the base for that matter) in some base. And I supect you were imagining base 10, all bases are base 10 in themselves.
So, the simple solution is to have the machines share base.
Now, the elephant in the room.
Whatever or not you ship money phisically or electronically, you are causing the ammount of currency available in one planet to chance. As one currency becomes more escarse, it is only natural that the exchange rate will no longer be 1:1.
For the exchange rate to remain 1:1, all the planets need to belong to a single economic zone - an economic zone is often a country. This probably means that there is - at most - only one - official - emissor of money. That emmisor may or may not be phsically located on one of the planets, it could be an institution spread across the different planets, and able to emit more money form any of them.
Since there is - at most - a single emmisor, there could be a prefered numerical base for money.
Note: it is possible that there are no emmisors at all. It could be the case that the economy is based on a fixed available ammount of currecny. We know that this doesn't work for small economies, because some regions may run out, which in turn changes the
value demand of the currency. Another case is to have the equivalent of the gold standard, with no official emmissors. Instead anybody who can mint gold, well... is creating currency. In that case you don't convert it, you just weigh it.
All the planets belonging to a single political institution makes sense, after all, they seem to share language, they have commerce, and have similar culture - with the shields and stuff.
And the OP claim, they are all numbers - so, I guess they are the same race too.
In abstract, for the economic question there are only two simple solutions:
- The planets quickly diverge their exchange rate.
- The planets join in a single economic zone, with a single currency.
Note: Lets assume that because of some brain impediment the - average - creatues of this planets can only understand one numeric base. If that is the case, then all the changes are in the visualization. The money is not changing, just what is presented to the user changes. Just how you may have a software be localized to different countries that use different languages and units, but you don't - usually - have to put the software into a machine that conversts it, instead the translation is provided and you choose which one you want.