How many people can live in space?

[Frank]

Oh please, who does food anymore?? By 2030 we'll all be size 0's. You don't need food to live. Just lots of water and drugs.

Well, food is easy and can be perfectly healthy. Just don't try to order steak and expect it to originate from a cow.

Then again, even that can be done. But if you want real farmers, greenery and livestock, you need a lot more space, mass and energy. It's at least an order of magnitude more expensive.

 

[CarstenB]

None! You need a biosphere of some kind.

 

[Frank]

None! You need a biosphere of some kind.

That's so last century thinking...

 

[DemoCoder]

AFAIK, diagonalization argument is a proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers... but i don't understand a whole lot about it so I would appreciate it if you could elaborate a bit on why it is so.

No, diagonalization can be used for many proofs.

Look up Turing Computable functions or computable numbers. It's not hard to define numbers which definately exist, for which a calculation procedure exists, but never the less, are non-computable by Turing machines.

Chaitin's number Omega is a case in point. People have even computed up to 64-bits of it. Unfortunately, even given infinite storage and computational power, one still can't calculate it, because the inherent problem is metamathematical, just like one can't prove all theorems true as Godel showed, since there will either be inconsistency or incompleteness.

There is no way around these limits, for the problem is not one of how much CPU and memory you've got, but fundamental to mathematics.

If you turned the entire universe into one big computer, and if this universe was countably infinite in size, you'd still never be able to compute Omega.

This is besides the point that an infinite number of events doesn't a guarantee a particular pattern will exist. I can create an infinite cellular automaton, say the Game of Life, and seed it a certain way, such it will NEVER produce any patterns but the ones I want. One can easily imagine infinitely sized universes like our own, that never develop life or complexity, because the initial conditions or physical constants are such to preclude universal automatons from arising.

 

[Npl]

@Democoder:
What do you consider a "Program"?
Its a finite sequence of instructions (however large) for me, and in that case you can certainly find a bijection between natural numbers & programms.

 

[DemoCoder]

@Democoder:
What do you consider a "Program"?
Its a finite sequence of instructions (however large) for me, and in that case you can certainly find a bijection between natural numbers & programms.

Define finite sequence. Do you mean countably infinite? The classic model for computation is the Turing Machine, and Turing Machines can have infinite inputs and outputs.

You can only construct a bijection between Turing computable functions/numbers and the natural numbers. The bijection defines the limits to which numbers are computable, for example.

But consider this:

You write down a list of every possible Turing Machine program, numbered 1,2,3,... You have a bijection between every program and the natural numbers, right?

I will now construct a program that is not on your list:

for(int step=1; ; step++)
{
   run_for_one_step(complement(your_program_list[step])));
}

Don't concern yourself with how "complement" is implemented right now, it's not important. ( It just means "behave differently than the input program", which could just be logical negation, permutation of output, etc.)

This program steps through your list, and at each step I, it runs a program that behaves differently than program I for a single step. This program will behave differently than every program on your list (on step 1, it behaves differently than program 1, on step 2, it behaves different than program 2, etc), and therefore, it is not on your list, therefore your list does not ennumerate all possible programs. (for any possible program on your list, call it N, my new constructed program will behavior differently than your program at step N and therefore cannot be program N)

This is a very real program, since the enumeration procedure itself can be constructed. For example, I could simply represent programs as bitstrings, and program N simply becomes N in binary, so I need no array to 'store' the bijection. Whether or not bitstring 'N' represents a program which halts immediately (invalid) or not is irrelevent, since this is a list of all possible programs, is it not? You might be tempted to add my program to you list, but I assure you, there are an infinitely more of these type.

The fact of the matter is, size of the set of theorems which are true, or algorithms that can be specified are larger than the set of programs. This is a fundamental result of complexity theory or metamathematics if you prefer.

You can't avoid this unless you drastically limit the expressiveness of your instructions, and especially don't allow universal quantifiers. (for all x...there exists...) since the quantifiers encode potentially infinite work.

 

[alexsok]

DemoCoder
On a related but a bit beside the point note, doesn't it sort of prove that God can't exist because even in an infinitely complex universe, he/she/it wouldn't be able to compute all the functions?

 

[Frank]

DemoCoder
On a related but a bit beside the point note, doesn't it sort of prove that God can't exist because even in an infinitely complex universe, he/she/it wouldn't be able to compute all the functions?

He could have pushed the initial button and might take a peek inside every now and then.

 

[alexsok]

He could have pushed the initial button and might take a peek inside every now and then

I don't think the initial conditions could be of such complexity (or alternatively, simplicity) to set off a paththat would go beyond their initial capacities in the far off future; that would be illogical.

 

[Frank]

I don't think the initial conditions could be of such complexity (or alternatively, simplicity) to set off a paththat would go beyond their initial capacities in the far off future; that would be illogical.

Yes, but it might just be random. Try and see what happens.

 

[alexsok]

s, but it might just be random. Try and see what happens.

With life maybe (game theory and all), but not with the universe. The appearance of life can indeed be attributed to a random mutation/accident or whatever but not the appearance of the universe. The chances of that happening were calculated I think and needless to say they're the lowest this side of Planck scale allows.

Life had a solid structure for it's appearance & development and unless the universe has a similar buttress that is invisible to a naked our or to our scientific apparatus, it will forever remain unknown how exactly could the seeds be sown. Again, every TOE (Theory of Everything) to this day only discusses the "how" (how were the dimensions formed, how did the Big Bang expand in rapid inflation, how our universe might be a single event in a multiverse of parallel dimensions and other universe, etc), not the question of "why". The more theories we propose, the closer we come to answering the "how" question and the farther away we're taken from the "why" question.

 

[Npl]

Define finite sequence. Do you mean countably infinite? The classic model for computation is the Turing Machine, and Turing Machines can have infinite inputs and outputs.

You can only construct a bijection between Turing computable functions/numbers and the natural numbers. The bijection defines the limits to which numbers are computable, for example.

For all whats worth, I was speaking about "real" programms and "real" computers. Real as in running in finite( yes I mean finite if I write it ), but arbitrary big resources. In that case you could simply enumerate the programms of each size ( that even includes non-terminating programs ).

 

[Frank]

With life maybe (game theory and all), but not with the universe. The appearance of life can indeed be attributed to a random mutation/accident or whatever but not the appearance of the universe. The chances of that happening were calculated I think and needless to say they're the lowest this side of Planck scale allows.

Life had a solid structure for it's appearance & development and unless the universe has a similar buttress that is invisible to a naked our or to our scientific apparatus, it will forever remain unknown how exactly could the seeds be sown. Again, every TOE (Theory of Everything) to this day only discusses the "how" (how were the dimensions formed, how did the Big Bang expand in rapid inflation, how our universe might be a single event in a multiverse of parallel dimensions and other universe, etc), not the question of "why". The more theories we propose, the closer we come to answering the "how" question and the farther away we're taken from the "why" question.

That is the same argument as used for intelligent design. You say, that it is very unlikely (perhaps even impossible) that you could figure out in advance what initial conditions you need to end up with this particular universe.

Well, this might simply be Random_uiverse_3456789.

 

[alexsok]

Well, this might simply be Random_uiverse_3456789.

That doesn't really explain anything. What it does instead is contribute to the metaphysical language game. These things which we can't talk about we must remain silent. We are both guilty as charged of commiting this grave error

 

[DemoCoder]

That doesn't really explain anything. What it does instead is contribute to the metaphysical language game. These things which we can't talk about we must remain silent. We are both guilty as charged of commiting this grave error

Asserting that our universe was setup by God because the laws of physics seem tailored for us doesn't explain anything, because it's a tautology.

Pointing out that such an argument fails because of selection bias is not tautological or a game, it is pointing out a logical flaw in the original argument.

There could be many many explanations for why the laws of physics are the way they are:

1) many universes. Universes with every allowable combination of physics exists. Any universes with physics that allows life to evolve leads to those beings in those universes thinking they are "special" and that the universe was tweaked just for them.

2) It can't be any other way. Right now, the parameters of physical theories are empircally derived. Perhaps, they are logical neccessities, and can't be any other value just like PI can't be any value but what it is. In this case, God has no freedom to tweak the parameters because they are logical imperatives. It may turn out that the parameters must be universal, and therefore, the universe *JUST IS* and life was predestined to evolve, period.


3) Life influences the beginning of the universe at its far future lightcone boundary. A pre-destination paradox.

I could come up with dozens more, all plausible explanations. I'm not really interested in defending them, just showing the flaw in the idea that the existence of life logically implies a Deist designer of the universe.

 

[pcchen]

But what if there are an infinite number of computers placed all over the universe all running an infinite amount of programs? Obviously, one computer couldn't do it at the same time, but an infinite number might be up to the task.

I have no formal proof, but to me it seems that one computer can simulate infinite number of computers. It goes like this:

Suppose that you have infinite computers with infinite programs. We call the first instruction of the program of the first computer I(1, 1). The second instruction of the first computer is I(1, 2). The first instruction of the second computer is I(2, 1), etc.

Now, we can use a single computer to run all the programs by running the instructions as the following order: I(1, 1), I(2, 1), I(1, 2), I(1, 3), I(2, 2), I(3, 1) ... and at the same time keeps the recording spaces by the same order (i.e. the memory space for each computers as M(1, 1), M(2, 1), M(1, 2), ...)

This way, you can run all programs of all these infinite computers with one computer. If one of these computers solve the program and halt, the one computer should also halt at some point.

 

[alexsok]

Democoder

just showing the flaw in the idea that the existence of life logically implies a Deist designer of the universe.

I never actually defended the view that the existence of life implies a supernatural creator. I merely pointed out that whatever we propose is simply a metaphysical language game (for example, an infinite amount of universes where the laws of physics are not the same as in ours is simply a modification (multiplication) of the concept of the entire cosmos which we happened to name "universe" and now keep adding together just because some interpretations of QM necessitate this).

Now... I always viewed the existence of life as being separate from the existence of the universe, for life evolved billions of years after the universe (there weren't humans back at the BB - if this theory is correct - to witness the birth of the cosmos, etc). I am not sure the idea of a creator or lack thereof satisfies me since I'm unable to comprehend either one - the scales are just too astronomical and the my imagination can't cope with that.

 

[Frank]

I am not sure the idea of a creator or lack thereof satisfies me since I'm unable to comprehend either one - the scales are just too astronomical and the my imagination can't cope with that.

Good thinking. When you cannot prove it's existence or the lack thereof, and there is nothing that requires it, use Occam's razor. Because there is any amount of things that can be proposed that go by the same rules, and it's a seriously safe bet to say that more than 99% of them simply don't exist.

 

[alexsok]

Good thinking. When you cannot prove it's existence or the lack thereof, and there is nothing that requires it, use Occam's razor. Because there is any amount of things that can be proposed that go by the same rules, and it's a seriously safe bet to say that more than 99% of them simply don't exist.

Exactly I love Occam's razor