Thought Experiment no.1
Imagine an ageless man sitting up a hill and counting. Also imagine he would count till the end of his life, it means up to infinite! For each number he counts there should be a corresponding brain state. But the problem is the brain states at most are dependent on the difference between molecules and there should be a finite (although huge) number of them.
Where is the problem? He should represent infinite numbers where there are finite numbers of states in his brain.
I think it's a good support for the compositionality of meaning in ones mind. When counting, the man would represent one number by analyzing and breaking it down to meaningful pieces.
But still there are finite numbers of combinations!
Is the experiment a correct one or it has flaws? Why can't we imagine a man living for ever?
posted by Siamak @ 11:43 PM
9 Comments:
An interesting experiment. I'm saying why we should suppose a human with an infinite power of thinking, [Forgetting about possibility of existence of a spiritual part in each of us called soul -- come on it's just a possibility ;) ] By finite number of molecules in our brain we would have finite number of states in our mind. A machine with a finite amount of memory can't have infinite power of computation. This is why we couldn't even imagine some concepts. Which concepts ? how could I tell you when I can't even imagine them, by the way there are an accepted belief in most of religions that nobody can find out about the true nature of GOD, isn't this an implicit declaration of a finite computation power of human-kind by religions ( though they even believe is soul :-?) .
Finally although there seems to be an upper limit for the thinking power of human but as it seems (regarding you nice post) we have still lots of thinking remains to get to that limit.
So you mean the man would stop some where when his capacity of counting is fully deployed?
can you imagine such a time?
when the man is sitting there but he can't count because there is no more room for that.
I know, something else should happen, say he might die, but he is ageless!
why do you think that we have infinite states IN OUR MIND? the man has this number on the ground:
11111111........
and counts: one one one...
this is a simple input-output operation without any internal proccessing(internal states).
The fully detailed procedure:
1.man adds a '1' symbol to the number written on the ground.
2.he begins from the left and says 'one' for each '1' detected untill he reaches end of number.
3.he returns to step1.
what is wrong with this argument?
you may argue that he has the full number IN HIS MIND not on the ground. now, I say that nobody can image arbitrary big numbers. At least, I myself cannot image any desired big number in my mind. after a while ,simply, I get confused!
Your argument implies a valuable point: each number has a distinct concept(so, has a distinct mental state). Now, I am not sure if the meaning of numbers are compositional or not.
You're right but to some extend!
As I said you're justifying it using the compositionality theory.
But I argue easier:
The way you've solved it, the mental state of the man trying to say 222 and is pronouncing twenty is the same as when he wants to say 223 and is in the same position(twenty). but if it's so. and the states are the same, why he doesn't say 222 again. so there should be more memmory, but how much?!!
In my view you've given the best solution but still it might have the same problem, and of course it maight not!?
There shouldn't be more memory. The man has not the whole number in his head. For him, 222 and 223 are different, only because there will be different sequences of mental states when counting them.
Think sometime on this:
Is there anybody who can imagine this number in his head: 22222222222222222222222222222222222222
22222222222222222222222222222222222222
22222222222222222222222222222222222222
22222222222222222222222222222222222222
.........??
nobody can. and nobody has a mental state for this number. this number is not mapped to a concept at all.
I know what you mean... as I said...
first, this is the idea of compositionality, and I argue about it before.
second!, using this idea, you haven't still answered my previous comment's question! heve you?
if two states of 2222222 and 2222223 are the same and have no difference for some one who has reached the third 2 and it's just a matter of sequence, what makes him to know they are different?
I know what you would say: They are the same for him, but when he looks up and see the number written on the sands he would recognize the difference.
but consider the case of no sand. The case becomes really different. where should he look? in his memmory? how much he has? :> you see!
What do you mean by "imagineing" a number? I can surely work with arbitrarily large numbers. E.g. let f(m) = 2^{f(m-1)}. What about f(100)? I can do all sort of computations with it. And you do not need to stop at finite number. The key is the representation. You can represent arbitrarily large numbers (by magnitude) using "short codes" (cf. Kolmogorov's complexity/compression).
Back to the counting man. If our brain is a finite state machine then we cannot think of infinitely many possible things. I tend to believe this. So the poor counting person will get confused. However, we are limited in so many other ways that I am not surprised at that we cannot count *indefinitely*.
So you might be able to imagine him stop somewhere, and say: unfortunately I can not count anymore!
:)
At last he is presumably immortal.
there are two possibilities: he either recognizes or not that he cannot count any more.
both are equally possible.
I have no problem with this.
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