cheater_1's math and physics lesson.

Combinations of atoms don't work the way most of you have calculated. They exist in space, not on a sequence.

you are correct on one point, infinity is a concept, it does not exist. However, googol is a number and therefore so is googol! (though it is a really big number). Each number is as real as the number that came before it.

Ugh, all this topic has proved is that cheater_1 is a sophist, unwilling to listen to any arguments that may actually disprove what he's saying.   I would like to know whether he has any qualifications or ANY ACTUAL KNOWLEDGE to back up his so-called "theory."  His last post demonstrates this precisely...

The most logical reasoning has failed to sway him and he has failed to produce anything to back him up, it is clear he is not going to be swayed from an idea that is to all intents and purposes wrong.

This topic should have closed a long time ago and been identified as trolling.

broze

Cheater_1 fails to appreciate the difference between  holism and reductionism.

He is just a stirrer and wants us to respond . In that respect, all of us, including myself in this very post, are feeding this bot's desires to seem more intelligent than he really is.

This post is making not contribution to thought, and cheater_1 should be exposed as to what he is - a cheater.

careface.

cheater_1, My last attempt to make you use that head of yours. Nobody is arguing that gogoplex! is a made up number but so is 10. Explain to me how the number 10 is real.

What confuses me (wich is probably the point) is that you havn't given any definition of what distinguish a real and imaginary number because it sure doesn't follow the standard mathematical definitions of imaginary numbers. If what you mean is that in a system with 10^80 elements there can never be more than 10^80 of anything then you're already proven wrong. All it takes is one counter example to disprove the rule and the number of ways to sort the 10^80 elements is a higher number than the number of elements.

I think the problem here is that cheater_1 doesn't seem to understand that numbers are only true by definition. There is nothing inheritly true about a mathematical system.

cheater_1 should read basic mathematical books and get the concept of real and imaginary, finite and infinite  numbers cleared up.

A real number may be either rational or irrational; either algebraic or transcendental; and either positive, negative, or zero. Real numbers measure continuous quantities. They may in theory be expressed by decimal representations that have an infinite sequence of digits to the right of the decimal point; these are often represented in the same form as 324.823122147... The ellipsis (three dots) indicate that there would still be more digits to come. (-Wikipedia)

An imaginary number (in maths) is a complex number whose squared value is a real number not greater than zero.

Hence by definition, a googol (though it is greater than the number of elementary particles in the observable universe, which has been variously estimated from 10⁷⁹ up to 10⁸¹) is a real, finite number (there are larger numbers). A googolplex is the number 10^googol (though it cannot be imagined or represented by anything in the physical universe) by definition is also a real, finite number (larger numbers exist, like Graham's Number).

I've been a teacher for a number of years, and now I teach teachers.

There are a few golden rules to observe:

1) You need to understand the concept you are teaching yourself or else you will end up looking extremely foolish.

2) You need to understand the ability of your students and aim your lessons appropriately otherwise you will alienate some, demotivate others and achieve nothing.

3) If you go into a classroom and state your own opinion, repeatedly, loudly, without sufficient research and ignore very valid comments from those who are more intelligent and well informed than yourself then you will be ridiculed, ignored and eventually removed from your post.

In England we have inspectors who assess teacher performance. Unfortunately Cheater_1's performance is very poor.

Inspectorate report on Cheater_1:

You are a failing teacher and need to be trained properly if you wish to continue in your role. You are hereby removed from your self-appointed post until you receive further training. Feel free to contact me should you wish to be reinstated.

So if we're going to store every possible chess move in a tablebase, how big will that tablebase be?

What do you mean by a real number ?

So if I understand you correctly, numbers below 10^81 (or whatever the number of atoms in the universe might be) are real, while bigger numbers are not ? Real in what sense ? Are they physical entities wandering around above our heads ?

Then what do you do with complex numbers ? Are they also real ?

cheater_1, it seems like you are using the number of atoms in the universe to determine what numbers are real and what numbers are not real.  If the universe can hold at most X number of atoms then I agree that the universe cannot hold X + 1 atoms.  However, that doesn't mean that X + 1 is not a real number.  What if I want to count the number of protons or electrons in the universe?  Each atom has at least one proton and one electron.  It is true that an atom can lose its electrons but then it would be no longer called an atom.  If I counted the number of electrons in the universe then I would expect that total to be greater than X since I know that hydrogen (only having one electron) is not the only element in the universe.  Why would you not consider that a real number?

Also, real numbers is not restricted to counting matter.  It can also count ideas or thoughts like combinations and permutations.  :) 

Also, isn't the set of real numbers a group under addition?  So if X is the number of atoms in the universe and it is a real number then by definition X + X is also a real number.  :)  If you are rusty on group theory then here is a site:

http://en.wikipedia.org/wiki/Elementary_group_theory

The integers Z and the real numbers R are groups under addition '+'. For all elements a, b, and c of either Z or R:

A1: Adding any two numbers yields another number of the same kind.

A2: (a+b)+c=a+(b+c).

A3: a+0=a. Hence 0 is an identity element.

A4: -a+a=0. Hence -a denotes inverse and 0 is an inverse element.

Also, I do believe that there is an upper limit in the number of moves in a chess game due to the 50 move rule and the 3-fold repetitions that end in draws.  If we take away those two rules then the game can go on forever repeating 1 Nf3 Nf6 2 Ng1 Ng8 3 Nf3 Nf6...  :)  Each pawn has up to 6 moves in a game.  They will either end in promoting, get captured, or they will get blocked off by other pieces.  Since pawns cannot move backwards then every pawn move will create a unique position that has not been previously reached in that game.  So this would mean that pawn pushes would avoid board repetition but each pawn can only do this up to 6 times.  And when the pawns don't move there are a limited number of squares and pieces on the board for maneouvers and capturing to avoid any kind of repetition.  Even if you take the 50 move rule away you would have to end up with checkmate, stalemate, or repeating a certain position at least 3 times because pawns can't move forever.  :)

hi im new to this and i aint/am not educated so bere with me please,hence give me easaly understood anolagies.

Is there more possible DIFFERENT posibilities in chess than there are atoms in the universe?? iv read sumwere that there are roughly 10 to the power of 120 DIFFERENT possibilities in chess is this true?? and is this number bigger than total estimate(i assume no ones eva counted precisely;))of  atoms in the universe?

cheater 1 i find ur writing easy to understand so please dont get more complex!

I NEVER REALY CHECK FOR REPLYS SO PLEASE SEND MESSAGE TO ,WILL08,THANKS!

Numbers are concepts and are only true by definition (neneko)

The number 10^200 denotes the number of 200 digit numbers in existence. Just because there are only 10^81 atoms in the universe, doesn't mean that only 40% of the 200 digit numbers can exist and the rest are just imaginary. Stop being foolish. 

And once again, I repeat, how about you stop rewriting your same line of bullshit and try (I repeat try) to address the arguments that have disproved your line of bullshit.

There has been much great debate. Whether you disagree with me or agree with some or all of what I said, I respect ANYONE who at least expand upon what they are talking about. It's the DUNDERHEADS who just say I'm a troll or I'm wrong or blah blah blah. The poster Einstein6910 exemplifies a respectable response (even though he cited wikipedia as a source ...OUCH!)

Heavyop also made a great point by saying, "Each number is as real as the number that came before it." However, at what point do we consider real ending and unreal beginning? It's like the old saying that If we drop a ball from 10 feet and it bounces 1/2 as high (5 feet) and then bounces half as high (2.5 feet) etc etc etc, then it will never hit the ground because you can divide numbers in half FOREVER. THE REALITY IS THAT YOU CANNOT DIVIDE NUMBERS IN HALF FOREVER and that fact is proven by the ball actually coming to a rest. There is a point when theoretical numbers come into play. There are IMPOSSIBLY large and impossibly small numbers that cannot exist in reality....otherwise youd have a ball never settling on the ground...and likewise....youd have a chessgame (a mere 32 pieces on a mere 64 squares, with a single maximum move number of 7) accounting for more combinations than all the atoms in the known universe. HOGWASH!!!!!

Let me just put into perspective something for you all. If you were to a single grain of salt or sand and count the total # of atoms in just that one grain, youd have 1.2x10^18 atoms http://www.physlink.com/education/askexperts/ae342.cfm

Now, the odds of winning a typical powerball lottery which equates to picking 5 of 55 white balls and 1 of 42 red balls is 1.46 x 10^8.

There is 8.2 x 10^9 more atoms in a single grain of sand than in the odds of picking 5 out of 55 and 1 out of 42. Can you all wrap your heads around that one? Can you fathom all the grains of sand on all the planets and all the hydrogen atoms in all the stars still not equalling the number of moves in a paltry game of chess? TO the visionaries, the deep thinkers, the expanded minds like me, it is PREPOSTEROUS!

lol.

its notjust the move itself that come ino consideration, its every move before that move, every move before that move and every combination of every move previous to that move. then you have to account of every move that could come after that, then you have to start again with another situation and another position. and even one position can be done severall different ways and look the same, becausethe rooks could be different or the knights might be different or the pawnsmight have sqitchd, or there might have been a promotion of a pawn. the ammount of possibilities exeeds the capabilities of the human mind. its not preposterous its entirly plausable just because you cant imagine it being so doesnt mean it isnt.

THE REALITY IS THAT YOU CANNOT DIVIDE NUMBERS IN HALF FOREVER  - cheater1

wow, just wow. 

if you can show me a number that cannot be divided in half then i'll believe you.  if, instead, you want to say that the number is "too impossibly small to fathom" then just multiply it by 2 until it gets big enough for you to understand. 

OK. This is driving me crazy. I am a professional musician and make a really good living from it which facilitates a a finite amount of free time to do things like go to school, play chess, etc. Before there was Dr. Gregory House, there was me. In my spare time I picked up advanced degrees in Chemistry, Physics, and Abstract Mathematics (however, spelling is not a strong point so spare me the grammatical corrections). My IQ (I think IQ testing is a flawed system, since I have taken while teaching Chemistry and Mathematics, below average students and helped them in developing their mental capacities. Not to mention, a high IQ doesn't always ensure that you can pay your bills) is 174. With this said, I believe your theory is flawed on a number of levels. It is a bit too simplistic for the theoretic arena you're using. Mathematically speaking the concept is swimming in uncertain waters. Given the applications of chaos driven mathematics as applied to your analogy, you might want to fortify your argument a bit. Sometimes, as you find out when you apply textbook theory to universal reality, the words within the textbook tend to fall apart and harsh reality sets in. I do applaud you for your ego driven personality. You probably are the smartest man alive. After all, what do I know. I'm just a average chess player who plays simply because he loves the game. I don't care whether I win or loose in the arena of chess because I am rewarded with a learning experience from any game I play. I may not be the best theoretical thinker of my time, but I hold my own. As for my music, well, I sell CDs so I guess some one other than my wife loves my music....

Of course, you do know my last post was done with a bit of satire and sarcasm (although I really do know more than most people do). Well, it time to take my pain medication and hit the recording studio. Bucket of pins indeed. How about a bucket of pinheads?

There's an easy way to settle this, how many atoms are there in a chess move. The obvious answer is that there are none, but it could be argued that there are as many as there are in a Queen and another Queen (Or whichever two pieces are the largest). For the sake o the debate, you can argue that.

Now how many atoms are there in two moves. OK, maybe there are two different pieces involved. Maybe a rook and a king. The atom count nearly doubles. Nearly being the important word. If you use the atoms in the board as the constant (Graphically speaking the y-intercept), or the number of atoms in 0 moves, as it exists regardless of moves made, then your graph will be (Very approximately) the reflection of a quadratic, and after 32 or more moves, the atom count will go no higher. Ever, not at all.

Let's imagine that chess board was comprised of all of the atoms in the universe, then if you argued that three movements of the same pawn resulted in the number of atoms used tripling, then logically a full game using all pieces would utilise more atoms than there are atoms in the universe (See your first post for the impossibility of this.)

However the possibilities in a game of chess, or a game of Go as even though this argument has centred around chess, Go is equally valid as by Cheater_1's argument it too could not have a game-tree larger than the number of atoms. In fact, to make a point it would be valid to make a new game, one played on a board 100x100 with each side having 19 pieces with the ability to move to any square instantly, plus 1 piece each (named Akuni and Cheater_1, why not) with the movement of a King which is to be sourrounded or his army destroyed to win the game. For each of these equally valid games I mentioned, the number of possibilities in any given position after x amount of moves would increase approximately exponentially because you would have to account for every single branch of the game tree after said number of moves.

Now I did some very very rough calculations and after only 2 moves by each player there are more than 20 million positions reachable.

Now back to the board, the game, and the graphs. We have established that there is a finite numbers of atoms, and therefore the graph denoting the number of atoms used will eventually have a slope equalling zero, it will grow no more. However the graphs for the can grow upwards, in the last case infinitely as there is no rule for creating a draw.

Now had you argued that there are more possible conifgurations of all the atoms in the universe that there are possibilitties in a game of chess, then you would have been correct. But instead you decided to forget that all numbers are imaginary. And all numbers pertain to something in the universe. Even infinite, even complex numbers.

Even your last ditch effort of trying to impress us with the number of atoms in a grain of salt failed because to impress because, as I hopefully explained, any single board game even one that I just invented, with a game-tree complexity greater than the number of atoms in the universe, even your imaginary universe where apparently scientists are capable of forgetting about free-floating atoms when making a simple count, invalidates your entire argument.

I seem to recall you mentioning there is a point in the real number system when nubers get so large that they become merely theoretical in terms of human experience and observation and the universe as a whole. And you are of course correct, and that point is infinitely far away from any number on that number line. it is not 1x10^80, as real ideas can be expressed beyond there.