Is computation synonymous with functions in computer science?

[Jarvis323]

@Fooality, assuming randomness based on incomplete knowledge is no different than assuming a deterministic universe based on incomplete knowledge, it's an act of faith. Theoretical computer science doesn't take any such leaps, nothing is assumed except simple fundamental axioms. Everything is built from layers of logical/mathematical proofs. Talk about unknown input and such things may be a fun philosophical topic, but it really doesn't fit into theory of computing at all.

@Boing3000, the topic is not real computers, but theory of computation. This again is a pure math, and is almost entirely defined through set theory, and mathematical functions. Read about the Turing Machine or Lambda Calculus They are pretty much the foundations of computability theory.

The Church Turing Thesis essentially says that a Turing Machine can compute that which is computable. The question of the OP is essentially about the robustness of the Church Turing Thesis, considering the possibility that something which could be considered computation, but cannot be described through functions, could exist. This brings real computers into the picture, purely based on the idea that they can take analog signals, which introduces some question about the physical nature of the universe, and whether a non-deterministic universe could imply physical devices could compute something a Turing Machine cannot.

Of course trying to consider some chunk of text in the syntax of a programming language as a mathematical function, as written, is not going to always work. It doesn't even make sense to do. It's just text in a non-mathematical language that indirectly maps to some lower level instructions, that again gets mapped to lower level instructions, and then movements of electricity... Of course the fact that you can write some programming function who's signature doesn't look like a mathematical function, doesn't break the Church Turing Thesis. If turning over the long lived foundations of theoretical computer science was as easy as pointing to some arbitrary text based code, of for example a pseudo-random number generator, and saying look, it's not a function, then don't you think it would have been done long ago. Don't you think Turing and Church would have noticed and the Church Turing Thesis never had existed?

 

[FactChecker]

@Fooality, assuming randomness based on incomplete knowledge is no different than assuming a deterministic universe based on incomplete knowledge, it's an act of faith.

Don't argue with us. Argue with Heisenberg and his uncertainty principle. It is much more profound than many imagine. There is unavoidable random behavior in the physical world. Also. saying that something is deterministic, when you can not predict, repeat, or even explain the results afterword is a poor use of the word "deterministic". One can say that coin tosses are deterministic, but till there is a successful theory to explain and predict coin toss results, the word "random" is more fitting. And there are formal mathematical methods that can be applied.

That being said. Even with unknown inputs to a "computation", I agree that we can define the resulting computation as theoretically deterministic. That part is a function.

 

[Boing3000]

the topic is not real computers, but theory of computation.

I understand that its your understanding of the the question, and I disagree. The OP ask a about the relationship between the mathematical notion of function, and the computer notion of function. I have quote its sentences for a reason.

This again is a pure math, and is almost entirely defined through set theory, and mathematical functions.

Yes. Set theory is pure math. Nobody is questioning that. I am explaining that computer science is not pure math. I especially draw a connection with physics which is also not pure math. My intent is not to start a feud between mathematics and other field which deal "in logic" currency. There are also a lot of other field science filed, like medicine, geology. None of them is pure math either. Pure math is not an all encompassing ensemble. Pure math ensemble is big and full of treasure, and most of it is useless, as it should be.
Einstein equivalence principle is not part of math. It is physics.
x86 instruction set is not pure math. It is just a natural disaster ;-)

The question of the OP is essentially about the robustness of the Church Turing Thesis, considering the possibility that something which could be considered computation, but cannot be described through functions, could exist.

Listen I am not saying mathematical concept do not cross breed and enhance some part of some code. I have precisely stated the opposite.
But my take on "Church Turing Thesis" is that is is a case where actually it is the other way round.

This brings real computers into the picture, purely based on the idea that they can take analog signals, which introduces some question about the physical nature of the universe, and whether a non-deterministic universe could imply physical devices could compute something a Turing Machine cannot.

Wow. All this is surely interesting, and philosophical debates are funny (espacially in QM) but I'd like to keep my posting focused on the OP question, which is clearely not about "the nature of the universe"

Of course trying to consider some chunk of text in the syntax of a programming language as a mathematical function, as written, is not going to always work. It doesn't even make sense to do.

That's absolutely right. A very tinny percentage of the codes is written in mathematical language. Computing/er have its own domain, with a lot of different language and a lot of different sub domains/purpose (database, whatnot) ... as does have math and physics.

Don't you think Turing and Church would have noticed and the Church Turing Thesis never had existed?

I am quite confident that absolutely zero knowledge in pure mathematics is needed to build computers and the codes that they runs. I am not diminishing the importance of Turing's work. I just say they are complementary not opposite nor depending of each others.
It is just another kind of plumbing, more akin to car technology, than math. That's why teenagers can write code. No math degree is needed. And very few of my college have a bigger math level than I (that is: high school).
Computer science is more technology. Math is more theory. There is no conflict between them.

 

[Jarvis323]

@Boing3000, what I got out of that was that you know nothing about Theoretical Computer Science at all,did not understand the OP, and did not understand anything I said, but disagree with all of it. How do I respond to that?

@FactChecker, you can define things however you want. I believe the meanings I intended to be used for the terms random and deterministic, should have been clear from the context, and are not abnormal usage in the context. If you can wrap you head around the way I used the words enough to understand my arguments that's good enough for me.

 

[Boing3000]

@Boing3000, what I got out of that was that you know nothing about Theoretical Computer Science at all,did not understand the OP, and did not understand anything I said, but disagree with all of it. How do I respond to that?

Your are projecting too much. You are entitle to your interpretation of the OP question, and I also am. The only truth is that only the OP knows. Does that piece of logic is mathematically correct enough for you ?

I m not really into "Theoretical Computer", but contrary to your claims, I stated aver and over again, that it can be useful.
You've said d a lot of things that I agree on (even if not on the OP subject). But you also said things I disagree, and provide the reasons for my opinions.

If you are not interested to have a conversation (that is : without the childish "you don't understand"), just don't respond. It would be the logical thing to do.

 

[Dale]

Closed pending moderation.

 

[berkeman]

Thread has gone off track from the OP's question, so it will remain closed.