Space being continuous or discrete

Is there any proof of space being continous or discrete?

Space is discrete. I guarantee it.

It is both discrete and continuous.  Hasn't quantum theory taught you anything?

So is time?

>>4
Time is discrete as well.

As far as I know about quantum particles, they are described by wavefunctions which has wavepackets which have a minimum amount of energy..or something. That doesn't have anything to do with space and time though.

There is nothing to suggest time is discrete.

>>7
We used to think everything in nature was continuous. Slowly we found all kinds of levels of discreteness (all the way down to things like photons currently). There is a pattern there.

The word I would use for the continuum would be relative, but appearently discrete works.

What's there to suggest that space is discrete? Quantum theories are about particles which is not the same as space.

>>10
What's there to suggest that everything is discrete, except spacetime?

>>11
1/0

>>11
Because particles and forces etc. are different from the thing that they are in maybe

>>13
How is that a reason for spacetime not to be discrete?

Also, if spacetime were continuous, it cannot be computed by a Turing machine. Yet within the universe, it seems it is not possible to perform hypercomputation. If it is in fact not possible (this cannot be proved, but all signs point to it), then it seems inexplicably wasteful for the universe itself to not be computable.

>>14
I said space doesn't have to be discrete because particles are.

And what are you going on about computation?

>>15
Fail.

Thread over.

>>14
You conveniently ignore the fact that "computable" does not necessarily mean "discrete." For example, suppose that spacetime coordinates are made up of only rational numbers. Then it's feasible (though not necessarily possible) that the universe could computed in the sense that a machine could take in a time t and output the position of every single particle with infinite precision.

Assume that spacetime coordinates are made up of only real numbers.  Then it's feasible (though not necessarily possible) that the universe could be computer in a sense that a machine could take in a time t and output the position of every single particle with infinite precision.

>>17,18
Except it would take an infinite amount of computing power (memory/time), which means you'd need super-Turing computation if you ever want a single calculation to complete.

>>19
only if the position that >>17 talks about that you get from time t has to be infinitely precise.

>>20
If you cut off the values at a certain level of precision, the range of values becomes discrete.

We don't know whether the universe is discrete or not. There is nothing to suggest either.

>>19
Do you even know what computable means? The number sqrt(2) is computable, yet requires infinite memory and infinite time to compute for obvious reasons.

Furthermore, even if our "machine" had finite memory and needed to compute an output in finite time, you haven't proven that it won't work. The input and output both require only finite memory, so without additional knowledge of what needs to be stored there is no reason to believe that the memory required would necessarily be infinite. We have no idea what the computations would involve, and hence making comments on how long it would take to complete these computations is meaningless at best and intellectual dishonesty at worst.

In short, I suggest you actually learn something about computability theory before trying to shoehorn it into a discussion.

>>18
Alright, I'll assume that spacetime coordinates are made up of only real numbers. Let p be a particle at (x,y,z,t) = (0,0,c,t) in some frame of reference, with c being Chaitin's constant. Oops! Guess we can't compute that particle's position at time t to infinite precision, since Chaitin's constant can only be computed to a finite number of digits. The reason I chose rationals over computables is because (a) they're all computable, and (b) >>14 doesn't seem like he knows very much about computability theory and thus may not know what the computable numbers are.

>>23
BTW, now that I think of it, is 1/0 computable?

>>21
yea but you can decide what level of discreteness it is, ie. you can decide the precision.

I HAVE NO IDEA WHAT YOU ARE TALKING ABOUT. PLEASE EXPLAIN "COMPUTABLE".

There is no evidence to suggest the universe is either discrete or not discrete.

>>26
Can a computer calculate it to a 100% degree of accuracy?

>>23
The number sqrt(2) is computable, yet requires infinite memory and infinite time to compute for obvious reasons.
The program wouldn't halt, so no, the entire number is not computable in that sense. A computable number is understood to be one for which a program can produce any desired digit (and then halt), which is possible for sqrt(2). The result is finite use of memory and time.

The input and output both require only finite memory
Given a continuous range, there are infinitely many possibilities for the values. Logically, these cannot all be stored in some limited number of digits.

>>25
Then the model would only be an approximation of reality, and therefore it wouldn't say anything about the computability of reality.

>>28
"The program wouldn't halt, so no, the entire number is not computable in that sense. A computable number is understood to be one for which a program can produce any desired digit (and then halt), which is possible for sqrt(2). The result is finite use of memory and time."

Right, just like the program to compute the position of every particle in the universe given a time t might not halt, but may still be computable. What is your point?

"Given a continuous range, there are infinitely many
possibilities for the values. Logically, these cannot all be
stored in some limited number of digits."

All I said was that the input and output are finite, not that they are less than some natural number N.

I really think, reading this post, that you are getting confused about definitions. A "Turing machine" with finite memory is not, in fact, a Turing machine. Saying a function is "computable" does not mean "it will produce an answer in finite time," it means that it can be expressed as a Turing machine. If your conjecture is that, with rational-valued coordinates, the universe could not be computed by a Turing machine which halts in finite time for any given input, you may be correct (although you have yet to prove this). However, that is not the issue I was addressing, and it is not the issue that >>14 brought up.

A "Turing machine" with finite memory is not, in fact, a Turing machine.
I am aware of this. It is probably better to speak of unbounded memory though. No Turing machine will be able to use an infinite amount of memory (see next answer for why), the infinite memory is only there so that any certain amount of information can theoretically be processed.

Saying a function is "computable" does not mean "it will produce an answer in finite time," it means that it can be expressed as a Turing machine.
No. A Turing machine that does not halt does not really express anything. A computable function can be expressed as a Turing machine which halts when it has the answer.

Right, just like the program to compute the position of every particle in the universe given a time t might not halt, but may still be computable. What is your point?
My point is that it is pointless to speak of a Turing machine with infinite runtime (as explained above), and therefore you cannot define the concept of 'computable numbers' using that (as you seem to do). Therefore, computable numbers are defined as those that can be approximated by a Turing machine to any desired level of precision (or the equivalent digit based definition I gave earlier). In the same vein, describing the universe using a Turing machine with infinite runtime (as would be necessary if it contained variables with a continuous range), is just as silly; If there's no halting Turing machine to calculate the universe, then the universe would not be computable, just as sqrt(2) is not fully computable.

All I said was that the input and output are finite
Why is that? I'd like to see you try to put the values on a continuous number line (say, reals from 0 to 1) each in a finite number of bits.

THIS THREAD IS MADE OF TROLL AND FAIL. COMPUTABLE? WHAT THE FUCK!!!!!!!

>>30
"just as sqrt(2) is not fully computable."

0, as a real number, is not "fully computable" by that definition, since it requires infinite memory to store all of the digits and infinite time to write them. The same goes for any real number. "Fully computable" is a concept you have just made up out of a lack of understanding of the subject. I reiterate that I am talking about whether or not the universe is computable, which is the subject as initially brought up by >>14. You seem to be talking about whether or not the universe is a DFA, which is a different issue.

>>32
You made that concept up. You were talking about how sqrt(2) is computable but requires an infinite amount of memory/time to compute. Well, guess what? Then it's not computable. Because the notion of computable functions when applied to numbers pretty much boils down to just the rational numbers (those that can be fully computed in finite time), it is a useless concept, and 'computable number' was therefore instead defined to instead mean a number that can be approximated to any degree by a Turing machine. Thus your whole idea of computable functions that require infinite resources is wrong.

This ties in to >>14 because if the universe is computable (likely, otherwise why wouldn't we, inside the universe, be given access to this hypercomputing power?), then it also does not require infinite computational resources to run, and then it cannot be continuous. All these concepts of discreteness, computability, DFAs, etc, are highly interrelated.

PS:
0, as a real number, is not "fully computable" by that definition, since it requires infinite memory to store all of the digits and infinite time to write them.
What? The tape starts out with all zeroes, the machine's first instruction is to halt. Presto: The result of the computation is zero.

>>34
The first smart point you've made so far. Replace 0 with 1/3.

>>33
"Well, guess what? Then [sqrt(2) is] not computable."

If your argument relies on redefining "computable," then there isn't any point in carrying on with this discussion, and if you're claiming that sqrt(2) is not computable under the accepted definition then please provide a proof of this. You keep repeating that sqrt(2) is not computable but can be calculated to any degree by a (single) Turing machine - that is EXACTLY WHAT COMPUTABLE MEANS.

>>35
IT'S ONLY WHAT COMPUTABLE MEANS IN THE CONTEXT OF NUMBERS. There is a subtle difference with the meaning of computable wrt functions (which I've explained several times now), and it is only that meaning that would apply to the universe. A computable function can be implemented in a Turing machine which produces an answer in finite time (and therefore memory), a computable number only needs a Turing machine which generates arbitrary digits in finite time.

Replace 0 with 1/3.
Extend the set of symbols with some to mark repeating groups of digits, eg "{}". The machine then only has to output ".{3}".

There is nothing to suggest the universe is continuous or discrete.