cheater_1's math and physics lesson.

cheater_1, The ball will have a acceleration towards the ground that is constant. There is no dividing involved to calculate exactly when the ball will stop bouncing.

"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!"

This is a argument used alot in discussions by people arguing against science. For example in debates about religion, alternative to modern science or conspiracy theories. It can be summed up with "I can't imagine anything that big so it can't exist". It's not a very good rational argument.

"THE REALITY IS THAT YOU CANNOT DIVIDE NUMBERS IN HALF FOREVER"

I can't stop laughing, seriously.

Once again cheater, you are wrong (and not surprisingly its the same reason that you have been wrong in every single post so far: NUMBERS ARE DIFFERENT THAN ATOMS) since nothing is every at rest, the ball is continually bouncing less and less, just not visible to the human eye. 

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.

I have never heard of that saying.  :)  I have heard of a boy jumping half of the remaining distance to the other side of the room will never reach the other side.  If a ball reaches only half of its original height then it must have lost a lot of energy upon impact with the earth because I believe in theory it is suppose to come close to its original drop height.  In actuallity it won't because some of the ball's energy is converted to sound, heat, and maybe some wave energy when it hits the ground.  Therefore, the ball will not have as much energy on the way back up.  :)  And the conservation of momentum will tell us that the earth should change momentum upon impact (not much) which means the ball's momentum before the impact should equal the total momentum of the ball and the earth after the impact.  :)

As far as Im concerned, Id just as soon believe that there will always be a question that needs answering. If Chess is solved then the next logical question is ?what?

And what if it is solved it will take a tool to utilize it and to make the solution work thus the the human player it is worthless.

Now going to the moon and getting  a few pounds of moon rocks makes more sence. At least you have some material to hang on to. SO Im all for forgetting about solving chess. I ant remember my name 1/2 the time how would I remember the 14th move of such a tool I cant there for it seems worth less than 0 to any human player. Do the players here have to use computers to play chess by moves? If so I dont need to waste my time.

I think we all understand cheater_1's views on this issue.  Perhaps a better word to describe number like 10^100 as "non-practical" as they do not have real use in the real world.  However I propose this to you Cheater_1.  Lets take a beaker that represents the universe.  Let's assume the beaker's length is 1 meter (even though the universe is of "infinte distance" lets just assume this).  Is it not possible to say that thee beaker is 10^100 * 1/(10^100) M?  What i mean is that a one meter length is the same as 10 decimeter, or 100 centimeters, or 1000 milimeters ect.  By this logic, although a very trivial way of describing the length, it would be accurate to say that it is 10^100 of units of measurement which represent 1/(10^100) of a meter.  Obviously these obscenely large numbers cancel out to 1 but they can still be used in this trivial calculation.  Highly imparactical, but not unreal.

erm, 10^100 is very practical.  For example, the number 10^123 which is even bigger has a very practical use.  It tells us how many possible chess games there are.  This is a very real use in the real world. 

When I was an undergraduate the last time I ran through college, I was 38 and decided after giving physics, mathematics (and almost a complete degree in painting) my attention, I would go to medical school because I had an interest in heart surgery. I had planned on going through the University of California's complete program. I got a full scholarship and hit the books. I didn't know it at the time but I would be pulled away from medical school by a subject I flunked in high school (I was always stoned during my classes). That subject was chemistry.

I had plenty of experience having gone through the University's Physics and Math (abstract or non linear as opposed to linear) with science classes, but only  touched upon chemistry. The first lab class hooked me completely. Why? Because it was like magic. Chemicals were effortlessly mixed together and, like magic they were transformed into something completely different. Now, we all know that chemical reactions are simply the rearrangement of molecules, the mutual attraction of electrons doing the dance that makes the world so varied. Well the first year was wonderful as was the second. However, by the third year I had learned many of the chemical magician's secrets. By the time I finished with the degree and moved on to both fuel cell research and teaching, a lot of that initial magic had worn away. So what does my long winded speech have to do with chess?

     To me, chess is a lot like that first year of chemistry. It's also a lot like playing music. As you improve your playing you learn, and as you learn, you see that strategies and tactics you once saw Chess Masters effortlessly pull out of the bag of tricks as a bit less magical. When I learned how to play guitar it was the same thing. You develop your skills and after a while you can play those guitar leads you once thought impossible to play.

     I think we don't need to answer the big chess question. Do we really need to see how the trick is done to appriciate and enjoy it? I still view the game with the eyes of a child, entranced by the magic. I for one, don't need the question answered to love the game. Listen folks, I have been doing research for years looking for answers to my questions. Why? Because research grants dictated the terms of my work. I can say with some authority that this is a question that will not change the game's core, at least for a good portion of us. I get science, I do science, and after years of it, I have realized that I don't need it to answer most of the questions that matter in my life. Well, there you go, another man's opinion. Good, bad or indifferent, it's food for thought!

I think it's clear that because chess moves are really ideas, devoid of mass, density or any other quality that locks them into a time-space continuum, the highest possible number of moves in a game bears no relationship to the ultimate number of atoms in the universe.

But that does not mean that the  number of moves possible in a game of chess is infinite. It is not infinite, and the reason is really quite simple: the rule that allows no more than fifty moves without a piece capture or a pawn move would force a draw, as would the threefold repetition of the position rule.

I think a more pointed question would be "Why is chess so fascinating?" I believe that when the purity of its abstraction is combined with a high level of creativity,  the resulting esthetic beauty is what draws us to the game. To me, it is this capicity of chess to delight us that seems infinite. In this context, calculating the highest number of possible moves is absurdly pointless.

Can't wait for the next lesson :)

Like the new garb cheater_1

I will say this cheater, you've demonstrated that there are really great thinkers here at chess.com. I have really enjoyed reading every persons opinions and ideas. It seems that, unlike most of the emotional environment around us in the outside world, we can agree to disagree in some cases. Like Maradonna, I can't wait for the next lesson.

WHO CARES?

This reminds me of Godel's Thoerem.  The basics of it are, that if you have an infinite list of decimals, and you go to the first number in the list, and change the first digit (the digit in the tenths spot), and then go to the second number in the list and change the digit in the 100th's spot, and then go to the 3rd number, and change the digit in the 1000th's  spot, etc., then you take all the digits that you changed and create a new number that you can add to the bottom of the list...  well, the point being, the list was infinite to begin with, yet you were able to create a new number that wasn't in the original list.  This has profound implications in mathematics and science, of which the foremost is that our current number system is not resilient enough to model everything in reality.  The are a great many paradoxes that arise because of this.

For more info, check out:

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

For more info about solving Chess:

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

It is highly unlikely that Chess will be solved during our lifetimes.

Hmmm.... if I follow your instructions and attempt to create a new number derived from a process that involves looking at every number in an infinite list... then I will never get to the end of that process, since I will never reach the end of the list!  Am I missing something?

Chess may be solved, but that will take a very long time as chess is finite, but in such a very very VERY large number.

For example, the first 2 moves. 20 possible moves for white and 20 possible moves for black. That is already 400 different possibilites. Also, there can be resignations after the first moves of white, which is 20 (20 moves) possibilites and white may also resign after black's first move which is 400 possibilites (400 possible positions). That should show that there are 821 possibilites of positions after the first two moves. (20 moves for white x 20 moves for black + 20 possibilites of black resigning after white's first move + 400 positions of white resigning to black + 1 which is white forfeiting the game)

Now, that means that 821 possible combinations after the FIRST MOVE, that means that the number will be considerably large.

resigning is not a move that is necessary for a computer to analyze, it is the number of possible positions (which is somewhere around 10^120 if i'm not mistaken)

 I think you are right.