Digital resolution to zeno's paradoxes?

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Reply Tue 18 Nov, 2008 02:33 pm
Hi everyone,

I was wondering what your thoughts are on using digital physics or cellular automata to solve zeno's paradoxes on motion. Are there any problems with the idea?
Reply Tue 18 Nov, 2008 03:35 pm
Fibonacci sequence and the 1/2 1/4 1/8 1/16 .... merge well. The 1/2... is to the hypotenuse of a triangle as the Fibonacci sequence is to the length of one of the other sides (both of equal length).

I'm not sure why cellular automata is useful here, I'd love to read your thoughts on this though. And digital physics sounds cool.
Reply Tue 18 Nov, 2008 08:04 pm
Oh, sorry. I never really explained myself, did I?

Basically, I'm saying space and time are quantized. There's even some support for this from current physics- look up the Planck units.

Anyway, I'm starting to think that the universe is a cellular automaton, similar to Conway's game of life. A cellular automaton is an n-dimensional grid of cells with at least 2 different states for a cell, which are determined by the states of it's neighbors. In conway's game of life, for example, the cellular automaton is a 2-D square lattice with only the states "on" and "off". A cell changes from on to off iff it has less than one or greater than four neighbors. A cell changes from off to on iff it has 3 neighbors, and remains on if it has 2 or 3 neighbors.

In this simulation, movement, growth, and even pattern self-replication can occur. As holiday pointed out, it may explain certain constants found throughout nature, like phi. However, there are some more interesting ramifications-

For example, if our universe is indeed a cellular automaton, and it is finite in size, then it can only have a finite number of states- meaning, at some point in the future, the universe must either cease to exist or repeat it's past states.

And if our universe is computable, then strong AI is possible, and this universe may be simply a computer simulation.
Reply Wed 19 Nov, 2008 01:46 pm

Uh, am I being like this guy:

Or, am I just not explaining myself well?
Reply Wed 19 Nov, 2008 02:59 pm
jknilinux wrote:

I can be blamed for incoherency too. But your thoughts are rather to the point here. You just need to explain yourself more. Why do you think the universe is computable?

Also, a cellular automation, sure, its a way of showing how things influence eachother. But the number of influences perceived are irrational, meaning that there are an undefined number. As for the actual influences like the fundamental forces of nature, constants, etc. I do not think cells are the right words to describe the actuality of such interactions between them all, as if there is a defined syntax of cosmic interaction within every single place in the universe. An obvious example of what I mean would be like saying it is silly to assume that in the whole universe planck's constant is the same, or of the same influence.
Reply Wed 19 Nov, 2008 05:23 pm
The universe must be computable if it is a cellular automaton. All a cellular automaton is is just cells whose states depend on other cells. So, for any cellular automaton (CA) you make, it must be computable.

If you are not a dualist, then this means that our consciousness arises out of a certain pattern in the CA, which means that given a big enough computer, if it can simulate the area of the CA that is my mind, then it can simulate me.

So, yes, basically I'm saying that there is a very simple syntax that governs whether a cell is on or off, and patterns of these cells are what constitutes matter.

See here: Digital philosophy - Wikipedia, the free encyclopedia
here: Digital physics - Wikipedia, the free encyclopedia
and here: Cellular automaton - Wikipedia, the free encyclopedia

For better explanations.
Reply Wed 19 Nov, 2008 05:43 pm
If space is infinetly divisible, it does not take an infinite amount of time to transverse an infinetly smaller distance, rather the opposite.

It is a challenge to show that space is infinetly divisible when you are faced with general relativity and the Heisenberg uncertainty principle see Physical significance Planck length - Wikipedia, the free encyclopedia It is only the meaningful measurement that becomes impossible. Now if something is not measureable is it sensible to assign it existence, is a tough cookie indeed.

I do not think that space and time are quantized. Rather I see it as the information available to define objects and events is quanitized.
Reply Wed 19 Nov, 2008 06:03 pm
If something is unmeasurable, then it makes no more sense to assign it existence than to assign the existence of a huge 4-d tomato which our universe is really enveloped by. Unprovable, therefore nonexistent.

So, even if you're right that only the information becomes quantized as distance decreases, then that means space-time must also be quantized, since it only exists in the presence of an observer- otherwise it is unprovable and meaningless.
Reply Sat 22 Nov, 2008 08:45 pm
So, is this silence because of awe? Very Happy

Seriously though, did I misunderstand anyone?
Reply Sun 23 Nov, 2008 07:18 am
Here are some thoughts from Tobias Dantzig, a favourite mathematician of Einstein's. I think they show why Zeno's paradoxes cannot be solved by quantising spacetime into Planck lengths or conceptual infinitessimals.

"Herein I see the genesis of the conflict between geometrical intuition, from which our physical concepts derive, and the logic of arithmetic. The harmony of the universe knows only one musical form - the legato; while the symphony of numbers knows only its opposite, - the staccato. All attempts to reconcile this discrepancy are based on the hope that an accelerated staccato may appear to our senses as legato. Yet our intellect will always brand such attempts as deceptions and reject such theories as an insult, as a metaphysics that purports to explain away a concept by resolving it into its opposite."

"The axiom of Dedekind - "if all points of a straight line fall into two classes, such that every point of the first class lies to the left of any point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions" - this axiom is just a skillful paraphrase of the fundamental property we attribute to time. Our intuition permits us, by an act of the mind, to sever all time into the two clasess, the past and the future, which are mutually exclusive and yet together comprise all of time, eternity: The now is the partition which separates all the past from all the future; any instant of the past was once a now, any instant of the future will be a now anon, and so any instant may itself act as such a partition. To be sure, of the past we know only disparate instants, yet, by an act of the mind we fill out the gaps; we conceive that between any two instants - no matter how closely these may be associated in our memory - there were other instants, and we postulate the same compactness for the future. This is what we mean by the flow of time.

Furthermore, paradoxical though this may seem, the present is truly irrational in the Dedekind sense of the word, for while it acts as partition it is neither a part of the past nor a part of the future. Indeed, in an arithmetic based on pure time, if such an arithmetic was at all possible, it is the irrational which would be taken as a matter of course, while all the painstaking efforts of our logic would be directed toward establishing the existence of rational numbers.

Finally, when Dedekind says that "if we knew for certain that space was discontinuous, there would be nothing to prevent us, in case we so desired, from filling up its gaps in thought and thus making it continuous," he states post factum. This filling-out process was accomplished ages ago, and we shall never dicover any gaps in space for the simple reason that we cannot conceive of any gaps in time."

Tobias Dantzig
Number - The Language of Science (182)
Pearson Education 2005 (1930)

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