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#1 2005-10-31 12:08:49

Chaotic Neutral
Member
Registered: 2005-10-31
Posts: 55

World Mechanics

Beware, my question is long and absurd (mostly absurdly long), and I give quite poor explainations and have ugly drawings.Please excuse my sometimes bad English.

Take 2 exact worlds. Add 1000 random humans to each world, shake well so they are equally distributed over all continents.

Check how they are after, let's say, 1000 years.
Are they the same? If yes, of course there would be a margin of
exactness (consider one group recieved a super-genius and
the other didn't) but the evolvement of the two groups will probably
be the same.

Proof: if x1 roughly equals x2 and y1=y2
then (x1+y1) roughly equals (x2+y2)

This means that every group of factors in disbalance will restore complete balance after time.
This also means that one can write a formula for mankind.
It will be put together like this:

consider xm=male xf=female

xm+xf=n% chance on 0-20 xm/xf

(n=whether they will mate or not, if the xf will bear the child successfully or not, all those factors)

0-20 (0 is minimum possible kids for one xf, and I THINK (sorry girls if I'm wrong) that a woman can produce 20 kids if needed.

the outcoming chance of xm/xf is now presumed to be 1/2

Add the fact that people USUALLY get kids after 18 and before 40 years, USUALLY die in 60-80 years after birth, USUALLY have 1-3 kids , time factors of birth-becoming adult etc, and you have a formula which (with known elements such as availability of food, tech advance .....) can give you the idea of human population growtf/decrease rate.

Then, let's throw away all our friendly philanthropistic thoughts and be realistic.

|   y
|
| .
|   .
|      .
|          .
|            .
|
|____________________________    x

x=intellegence rate in %

y=% of population

You see, higher intellegence=less people with that intellegence

Now consider that people with approximately equal intellegence rate would gang together, giving us several groups of people (ex: 25& dumb brutes, 40% averages, 25% intellectual and 10% hyper-intellectual), consider social means (ex: an intellectual may grow up in a poor area, become either a criminal mastermind or someone who would help people, [70% chance of becoming a criminal]) and we will get factions, represented by sub-cultures by the youngsters and society classes (intellegent businessmen would not side themselves with small-minded factory workers). Those variables will be very flexible but will balance each other (one faction may draw power by hypnotizing the population through mass-media, conquering the world, when the other smaller faction will come up with a masterplan to bring the new empire down, or something else will bring it down, it's a FACT that empires do not last forever)

Now the question:
How do I (and don't tell me it's impossible) write all that as a formula?
Which things do I need to include that I have not mentioned yet?
I guess it would be something like this:

growth formula [calculation] intellegence-group forming formula [calc.] global variables* divided by Time?

*global variables: the world's climate, size, amounts of food.Tech advance (we all know tech makes us lazy and decadent)

Now, the calculation signs between those formulae, are they known to us like +,-,x,: or are they completely new?
In this case it isn't about numbers but about HOW a factor is (war-like, peaceful, dead if thrown in boiling water, intellegent, brown-skinned etc)
I guess there are endlessly many factors, but some of them can be shortened down (ex: instead of calculating sperm speed and maneuverability, I just say there is a 50/50 chance that it will be a boy or a girl.)

So, guys, how to write such a formula?If it's not possible, then why?Could it be MADE possible?
And if it is possible, could we bring the entire universe (material and fictional, both movement of stars and fictional but existant (and therefore calculable) things such al love, trust, lies, memory, ....) on a hypermathematic map?



Thank you for your time


As at night, we realise we will never Know and further thinking is pointless....Yet we start again and again

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#2 2005-10-31 16:54:46

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: World Mechanics

In theory all those factors can be represented by formulas, and could be put together into one enormous and complicated formula, (and not much use because of its complexity).

But perhaps you would be better off putting it together as a "Model", like economists or weather forecasters use.

You could start one in Excel:
* pick a small enough time interval (start with 1 Year with the option of reducing to months).
* run all your births/deaths/marriages etc that would occur in the first year
* calculate the new status at the end of the year, and put that as the start of the next year
* process again and again

Now you will have a set of years, maybe 100 and you can then produce graphs, etc to show how the populations behave. Compare this with historical data to fine-tune your model.

You could probably build an entire career out of this!

You would probably outgrow just Excel, and would need to start programming in C or Java as you got more and more sophisticated.

Sounds like fun.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#3 2005-10-31 23:16:27

Chaotic Neutral
Member
Registered: 2005-10-31
Posts: 55

Re: World Mechanics

Thank you for your response. I guess i'll be busy writing population matrices now big_smile

But I've been thinking..

A conversation between people is nothing else than exchange of factors, which, determined by it's context, have a specific outcome.
For example, if I would say to you: your life or your jewels, you would know it's a joke because we're on the internet and I could not possibly rob you.

global variables: internet, anonymity of forum use
information variables: "Your life or your jewels"->50/50 chance of survivial depending on choice
possibility of dying: 0% (determined by global variables)
Context possibilities: you can fill in this



But if a person would say that on one of those dark November nights, it would look like:

global variables: Dark night, lonely street, evil-looking man
information variables: "Your life or your jewels"->same 50/50 chance of survival
personal variables: largely unknown to either you or the spectator*)
                           -visible: you see the masked man's eyes, you see it's a young kid who isn't 
                                        experienced
                            -mental: without revealing yourself you grab your pocket knife (if you
                                         would hesitate for a while the thug would notice it)

*note: if one would write a model for the thug person, knowing all the psychological data of the "basic" person, with the "added" (his childhood, his education, his experience, his alignment....) factors, one could roughly (or exactly) determine his actions at the moment of the example.


Outcome (forgive me for bad formulae, I'm just trying)

dark night (visibility decreases by 10% by each meter after 10 meters from target)
lonely street (possible helping hand would be 100+ meters away, check above formula for his visibility)
evil-looking man: nx chance of survival, with n=[your fighting/running/negotiations skill]
                          and x being the same of the thug

Context of inf. var.: 90% chance of not being a joke/bluff

Chance of survival: 50(if giving money)/50{calc} nx+(possibility of police car passing by) or something

Now work the data above with the personal variables and you'll get the outcome. Of course, if you was mistaken about the look in his eyes and did not notice the desperacy, you could be shot trying to defend yourself.And so on....

Every situation, conversation could be mapped like this (for conversations it would be terribly long), so my question is now

I know fate is a believer's excuse, but the things above makes me thinking that everything could be determined.

How would it then look?

-Is there a COMPLETELY random "something" that changes the course of events?(I haven't seen any random things in math)

-Is there a homeostatic system, that would automatically by some to us unknown, hyper-mechanic way restore the balance if it would be pulled too hard to one side?

-Or does the system not interact, but are we just shaped self-balancing (for example, an evil but nerdy kid has a plan on conquering the world.The plan would work out perfectly, but regarding that the average human being would bully a supernerd when in high school tongue by those means the fluctuacy has been made even with the rest, and self-balance restored*)

Does this look like this [cathegory x    {sub-cathegory y} cathegory x]

Where the element y is free to do anything between his brackets but would never affect anything outside them (in the x-cath)
Or, if the element y becomes too "cool" and tries to interact with x, the x would "push" it back, hence restoring the balance?

Last edited by Chaotic Neutral (2005-10-31 23:21:23)


As at night, we realise we will never Know and further thinking is pointless....Yet we start again and again

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#4 2005-11-01 10:41:31

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: World Mechanics

All very interesting stuff, your name is very apt considering what you're doing.

The only mistake I can see is that you've said that the lower the level of intelligence, the more people of that level there are, but there are only small amounts of uber-stupid people, just as there are only small amounts of hyper-intellectual people. Frequency of intelligence follows a 'normal distribution', or a bell shape to you and me.


Why did the vector cross the road?
It wanted to be normal.

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#5 2005-11-02 13:26:54

Chaotic Neutral
Member
Registered: 2005-10-31
Posts: 55

Re: World Mechanics

Your comment is true, the intellegence distribution should look more like a square function.


y
|
|
|
|
|                             _
|
|                  /                        \
|
|        /                                               \                   
|_______________________________________x

        1           2          3            4           5
(or something like that)




x= intellegence quotent (in numbers 1-5, 1 being a complete goon and 5 being a super genius)
y= amount


The average joe is now on top of the parabole.


Draw all other factors that we people cope with as a function. for example the determined-ness of all people, and then you can see how many smart people ever reach high functions so you get an idea why there are so many incompetent government employees tongue
With some more functions you can determine what the chance is of a person of becoming good/evil (or stay neutral), become law-obeying or not.... Can not do that myself yet, haven't seen much about analysing and functions at school yet, will see more next year.


But guys, this whole idea, is it worth to work further with or am I mistaken in many things (or am inventing the wheel for the second time) and should go spending my time on something else?

Being only in high-school, I only have a limited skill in math.


As at night, we realise we will never Know and further thinking is pointless....Yet we start again and again

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#6 2005-11-03 02:45:44

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: World Mechanics

By all means, continue with it while you still find it interesting. I don't want to dampen your spirits or anything, but this seems like the kind of thing that will take so long that you will eventually be bored of it and leave it half-done. I hope that doesn't happen, because a world simulator like that could be applied to all kinds of situations and then you'd get a Nobel prize or something. It's not just maths you'll need to know more of, though. You'd need IT to program it, psychology to decide the outcome probabilities of the situations like the one that you were talking about earlier (your life or your jewels) and lots more that I can't think of. As you refine this thing more, it's going to get more and more complicated, so it will probably be more than a 1-person task.


Why did the vector cross the road?
It wanted to be normal.

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#7 2005-11-03 09:46:35

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: World Mechanics

Definitely worth pursuing, particularly if it fires your interest. At least you will pick up a lot of skills.

If you go to Uni there may be times you get asked to do a project, and you can just get out some of the work you have already done, package it neatly and hand it in.

BTW, I found this article from the Rockefeller University: http://phe.rockefeller.edu/poppies/
(like all technical articles it is written to sound impressive, so don't be worried if it sounds complicated, if you had just done that research you would be using the longest words possible too)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#8 2005-11-03 12:24:54

Chaotic Neutral
Member
Registered: 2005-10-31
Posts: 55

Re: World Mechanics

What I've been thinking of is not a world simulator but rather a probability calculator.

For example: my current project: the Thief's Algorithm


A thief needs to sneak into a castle, steal a diamond and escape. The castle is guarded by 25 guards with spears and crossbows.
Conditions: visibility 60%, weather: rain .... (following a complete list of descriptions

In a on-paper "program language" it will look like this:

goal: retrieve [diamond] from [castle], (avoid) the [guards], use {rain} as cover

the words in [] brackets are local constants, described like: [door]: in earth-like conditions, mankind evolving process 35% (middle ages), {iron} or {wooden} structures with usually a keyhole .....

a door with no keyhole is written like: [door[no keyhole]

a completely undefined door, (when the thief sees a door but does not have the slightest idea about what kind of door it may be), is written as ]door[

(avoid): actions, described like: (here): not coming in contact with guards, by those and those means....

{rain]: constants, active for {plane of action}, here medieval Britain.

the more factors you add, it will get more and more precise (as to tell you NOT to wear shoes that make noise)
add all factors included in a theft, process those together, and you will get the way (and chance) of getting that diamond.
Algorithm possibly rewritten on banks, department stores ....
Or let's just change the factors and use it to improve people's lives tongue (reverse and get a Police Algorithm)

And concerning world simulations.... also possible. Write a lot of interacting factors (like above, (avoid) interacts in a way with [guard], let those factors interact with themselves for time necessary (like people being born ...) give a course by which the interaction will take place (a world powered by Pi, someone?Pi is infinite!)

With the right balance of factors they will interact forever, if getting a starting push or being powered by something. Then, make it possible for yourself to manage that world by using "lever" factors that would change the cource of your world without disturbing it (for example, create a major fluctuacy that in real life would look like Hurricane Katrina)

Now you are God.





But guys, how do I get probability chances out of functions? For example, if I would draw the possibility of myself being eaten by wolves in a forest as a function, and then draw the "possibility that I will kill the wolf with my bare hands" as a function, where exactly would I be able to read my chance to survive?


I will keep you up to date with some models and algorithms (at least if someone is interested) so you could correct my mistakes (like the one with the stupidity factor).I really have the idea that this will work and I don't leave a thing unfinished. However a computer calculates with digits. not with described logically interacting factors, so it would probably never get to a computer.And thank you for the article.

Last edited by Chaotic Neutral (2005-11-03 12:31:06)


As at night, we realise we will never Know and further thinking is pointless....Yet we start again and again

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#9 2005-11-03 17:02:41

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: World Mechanics

Chaotic Neutral wrote:

However a computer calculates with digits. not with described logically interacting factors, so it would probably never get to a computer.And thank you for the article.

On the contrary ... the computer is all about logic, and would do the job very well. There are even Artificial Intelligence langages such as Lisp and Prolog. But I think good old C++, Java, etc are a better choice - you get a lot more control.

I have worked with people who simulate mining operations. Every major piece of equipment has failure history (excavators, conveyors, etc), and these can be reduced to statistics.

You can then run a one-year simulation hour-by-hour. Every hour each piece of equipment has a certain likelihood of failing, and the computer program uses random numbers to decide what will happen.

If tuned well it starts to behave like a real mine: equipment breaking down randomly, taking time to be fixed and returned to service.

They can then add (for example) a new truck, and rerun the simulation. If the simulation shows their productivity increases enough to pay for the truck, they might then actually buy it!

These guys really enjoyed coming to work and playing with their pretend mine.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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