Chess and the number of atoms in the universe.

[scguy]

I read that when IBM were building deep blue they had to find innovative ways to get around the fact that chess can produce more combinations of moves than all the atoms in the universe, this is obviously beyond what any computer can currently cope with. How did they work out the total number of moves?

And, i dont know if this is a viable question but say i wanted to work out how many connections could be made between every atom in the universe ie every atom is connected to every other atom regardless of distancs etc. How would this be calculated and would the number be of any significance?

[YT2095]

actualy the number of possible game permutations is Finite.

 

I`ve no idea how it was worked out though

[matt grime]

Define "connection". If every atom is connected to every other atom then it owuld depend on what a "connection" was, or more precisely how many ways to connect two atoms. The number would then be a simple function of this and the number of atoms in the universe.

[zaphod]

actualy the number of possible game permutations is Finite.

 

I`ve no idea how it was worked out though

 

to be fair, so is the number of atoms in the universe.

[the tree]

Why would they need to work out a tottal number of moves?

Thinking ten moves ahead from the first move, there's probably less than a million things that can happen in those ten moves, as you go through the game there will be less and less things that can happen so it can think even more moves ahead using the same memory.

It'd be pointless to have every possible game already thought out.

[scguy]

The further ahead the computer can calculate then the better it can play chess, as u say its unfeasable at the moment for a computer to think of every single possible move for the whole game but maybe in the future lol. I think thats when casparov won't have a chance

[Dak]

Why would they need to work out a tottal number of moves?

Thinking ten moves ahead from the first move' date=' there's probably less than a million things that can happen in those ten moves, as you go through the game there will be less and less things that can happen so it can think even more moves ahead using the same memory.

It'd be pointless to have every possible game already thought out.[/quote']

This would only be useful if you were >10 moves from winning the game... the heuristics involved in deep blue must be pretty impressive!

[YT2095]

actualy to think 10 moves ahead is quite common amongst players, esp when you`re in a superior tactical positioning (regardless of material taken).

Check mate in 4 moves isn`t uncommon either, infact many resign the game at that point and occasionaly before that point.

(it`s actualy a neat way to teach also, swap sides and see if your opponent can figure out HOW to do the CM).

 

I think the algorythms that worry me the most are the one cappable of Learning!

and if it ever DOES come to a computer that "knows" every permutation, topple your king, you`ve lost before you move!

[bmaxwell]

The next generation of Chess playing software will not think about moves that it can make or even think about moves in the future or play out the game to the end a finite number of times based on a difficulty setting.

Chess programs for a long time "thought" their way through games. Programmers tried to recreate the human chess players thought process or patterns with code. This is not an attainable goal with in the confines of contemporary computer hardware or our understanding of the human mind for that matter.

The future of Chess software will abandon this path for a more enlightened approach to the problem, that uses the true strengths of the modern machine, instead of the brute force approach that our brains use to solve problems.

[bmaxwell]

And' date=' i dont know if this is a viable question but say i wanted to work out how many connections could be made between every atom in the universe ie every atom is connected to every other atom regardless of distancs etc. How would this be calculated and would the number be of any significance?[/quote']

 

The eqation would be trivial if you knew the number of connections between any two given atoms and had a ball park figure for how many atoms exist in the universe.

 

Assuming that each atom has 1 connection to all other atoms then the equation would be something like this:

 

a=number of atoms in the universe

t= total number of connections

 

t= a(a-1)

 

assuming that an atom is not connected to its self

 

maybe I am missing something because that seems so easy

 

a simple atempt to prove my theory

 

if the universe has 4 atoms in it and each atom has 1 and only one connection to every other atom then the total number of connections in the system is

 

4(4-1)=t

or

t=12

 

I would say that a simple drawing will let you know weather this is true or not

if I draw a square and connect the corners with differnt color pens to each other corner I will see that there are 3 lines of any given color. 3 x 4 is 12.

So the real question is how do I figure out how many atoms in the universe and is there really a connections between them all?

 

Well we know that there is a connection between every object in the universe and every other object in the universe its called gravity.

however is the total number of gravitational connections between atoms in the universe relevant to my reality? i dont think so.

 

But in case you want to go further with your speculations. I would suggest ball parking the number of atoms. I think many theoretical physicists have already done this.

Take all the mass in the universe and add it up.

 

tm=total mass in universe

 

now find the average wieght of a atom in kilos

 

aaw=average atomic wieght

 

Lets assume this is a constant for now because figuring that value would involve knowing all the ratios of atoms to the total number of atoms in existence. you can ball park it if you assume 90% of mass is hydrogen and 9% is helium and so on and o forth. But even the .000001% of heavy shit can have a impact on average because its 1000s of times heavier than Hydrogen.

Anyway

 

tm/aaw= number of atoms in existance so

 

(tm/aaw)((tm/aaw-1)) = t

 

This has absolutely nothing to do with chess but it did help me blow off a chuck of my work day.

 

PS

To answer your second question... No

[AtomicMX]

Hmmm.... where to start.

 

1st- YT makes references that there is a calculable finite number of permutations in chess that is not tooo high, just the recursive ones then it would tent to infinite, the correct algorithm would be then when it draws.

 

2nd.- The number of atoms in the universe is not consistent, i am amazed of the ignorance in this fact. people, remember fussion and fision and radiation.

 

3th.- The number of atoms in the universe is far very very far beyond the permutations of a chess table, compare them gets to seem stupid.

 

4th.- Deep Blue is algorithmic not heuristic.

 

5th.- In the universe the atoms have plenty lots of conections, not going far a quick example is the electric field (Kq/d^2) or gravity perhaps despreciable in a long distance, but important.

 

6th-

How would this be calculated and would the number be of any significance?

Well this wont be made for a start but the way the the atoms connect its inverse proportional to the distance. so they would get what in science are called, significative cifers.

 

7th-

I think thats when casparov won't have a chance

Actually he didn't have a chance. but the computer took the playing protocol. (let him move then calculate and then and then, its quite simple).

[ecoli]

I believe they came up with a formula of moves, where, if you white can always win or black can always tie. I don't remember a source or if this is true, anybody hear similiar?

[scguy]

Bmaxwell, the equation u came up with seems ok but u forgot that if 2 points are connected then there is only 1 connection and not 2 so the answer of 12 u got for 4 connected particles would actually be 6 which can be seen from the drawing. BTW the reason i asked the question was because i thought it might have something to do with the so called singularity, and thus the number might have some significance. I admit i strayed away from the chess topic but i thought that would get people interested.

[BigMoosie]

I believe they came up with a formula of moves, where, if you white can always win or black can always tie. I don't remember a source or if this is true, anybody hear similiar?

 

No

 

3th.- The number of atoms in the universe is far very very far beyond the permutations of a chess table, compare them gets to seem stupid.

 

Many sites offer an estimate close to [math]10^{80}[/math] for example http://en.wikipedia.org/wiki/Atoms#Atoms_in_the_universe_and_our_world. This could easily be beaten by the number of games in chess. Imagine, on the first move you have 12 options, later at times you may have about 30 or more, it is common for games to go to 50 full moves (50 for white, 50 for black), it can be seen from this that just up to that number, at the least would have [math]12^100[/math] options, that already exceeds the atoms...

 

...just looked up wolfram, he thinks it is [math]10^{10^{50}}[/math]: http://mathworld.wolfram.com/Chess.html

 

t= a(a-1)

 

Points in space being connected is the same as points on a plane being connect so must follow the tringaular formula of [math]t={{a(a-1)}/2}[/math]

[Ophiolite]

Hmmm.... where to start.

2nd.- The number of atoms in the universe is not consistent' date=' i am amazed of the ignorance in this fact. people, remember fussion([i']sic[/i]) and fision(sic) and radiation.

1. I did not observe any ignorance of this fact on the part of the other posters: what I observed was the very practical recognition that the uncertainty in our knowlege of the number of atoms in the Universe is at least an order of magnitude greater than the change over the course of a human lifetime in the number of those atoms due to fusion or fission.

2. Please cite an instance where radiation changes the number of atoms in the Universe (other than being involved as part of the fission or fusion process)..

3th.- The number of atoms in the universe is far very very far beyond the permutations of a chess table, compare them gets to seem stupid.

Oh, go on. Give it a go. How many atoms in the Universe? How many permutations on the chess table?

My, look at this! http://www.aaai.org/AITopics/html/chess.html

Number of atoms in the Universe 10^75

Number of possible chess moves 10^120

Hmm! What was that you were saying about stupid?

4th.- Deep Blue is algorithmic not heuristic.

Yes, just like chess players.

 

Please explain the words "despreciable" and "significative".

 

If this seems to you a rather agressive response to your post - you are right: it is a pure reaction to you presumptive, and inaccurate, use of the qualifiers "ignorant" and "stupid".

[BigMoosie]

The thing about deep blue is that it discards paths that are not looking good, it also build statistics on what makes a good layout without having to apply much thought to it. Also, it doesnt have to think about every move as half of them it can control, the other half it cant, that changes things alot.

[AtomicMX]

In the hidrogen bomb the idea is to join 2 atoms of H into 1 atom of He for example.

so... the cuantity of atoms is not constant in the same system.

Thas why we have electrons and quarks.

 

And i only like to debate against Sayonara rookie.

 

Number of possible chess moves 10^120 <- You are of those statistics freaks aren't you?.

 

Well if i have a queen and a king and my opponent has a queen and a king, they can move into circles forever in the ethernity. so there is not a real number of chess movements.

 

I did not observe any ignorance

Its quite hard for ignorants to discover themselves in ignorance.

 

and please, think before posting.

[zaphod]

2nd.- The number of atoms in the universe is not consistent' date=' i am amazed of the ignorance in this fact. people, remember fussion and fision and radiation.[/quote']

 

*clears throat*

 

i dont think i said that the number of atoms is "consistent" (? did you mean constant ?)

 

i said that it is finite.

 

thats all i said. i didnt make any references to the comparison with the number of moves in chess or anything like that. so calm down.

[Ophiolite]

and please, think before posting.

I believe that is the request myself, Big Moosie and Zaphod are making of you. Inaccuracy and rudeness do not further the cause of your argument. Thank you.

[bmaxwell]

Points in space being connected is the same as points on a plane being connect so must follow the tringaular formula of [math]t={{a(a-1)}/2}[/math]

 

Why are we dividing by 2? I dont understand?

[bmaxwell]

Bmaxwell, the equation u came up with seems ok but u forgot that if 2 points are connected then there is only 1 connection and not 2 so the answer of 12 u got for 4 connected particles would actually be 6 which can be seen from the drawing. BTW the reason i asked the question was because i thought it might have something to do with the so called singularity, and thus the number might have some significance. I admit i strayed away from the chess topic but i thought that would get people interested.

 

I think this is incorrect. The number of connections between any point and 3 other points is 12.

 

Each point has 3 connections. One to each other point. 3 x 4 is 12 not 6.

[BigMoosie]

Try drawing it!

 

How many connections between a point and 1 other point. According to you there will be 2: each connection has 1 connection. 1 x 2 = 2. But this is absurd, the two connections are identicle.

 

You must realise that whenever you do [math]a(a-1)[/math] you are getting a value that has each connection twice:

 

#----#
|\  /|
| \/ |
| /\ |
|/  \| 
#----#

 

^ 6 connections

[Ophiolite]

The formula gives the totalnumber of connections between particles. So it considers both the connection from a to b, and from b to a. But that can reasonably be taken as the same connection. So, to get the total number of connections we must divide the result by two. Does that make sense?

[bmaxwell]

Now I see what you are saying. I guess I was looking at it as a physics problem related to the number of gravitational forces exerted on each atom in the universe.

 

The connection from a->b is not the same connection from b->a.

For instance the gravitational force that atom a exerts on atom b is not the same force that atom b exerts on a. They dont even have to be equal. They are seperate forces. Therefore they should be counted as unique connections.

 

This is all relative to the original post and my assumption that the connection between all the atoms in the universe the Original poster refered to was in fact gravity.

[BigMoosie]

The connection from a->b is not the same connection from b->a.

For instance the gravitational force that atom a exerts on atom b is not the same force that atom b exerts on a. They dont even have to be equal. They are seperate forces. Therefore they should be counted as unique connections.

 

If you are going to be this silly you might as well take into account the possibility of light being emmitted from a particle, orbiting a black hole and striking itself again