Everything can be represented by ones and zero

[Avichal]

Studying computer science I noticed that such complicated software and programs are basically just ones and zeros lined up. Everything is just a yes or no.

Can everything be broken down into a yes or no? By everything I mean human behavior, laws of physics etc.

 

[DiracPool]

Studying computer science I noticed that such complicated software and programs are basically just ones and zeros lined up. Everything is just a yes or no.

Can everything be broken down into a yes or no? By everything I mean human behavior, laws of physics etc.

I find that a real left-field question, Avichal. I like it though, made me think. My initial response would be "yes" but with a qualification. That qualification is that our understanding of everything can be broken down into yes's and no's because our minds evolved in a manner that organizes information in a hierarchical, sequential fashion. That is why I am writing this sentence in the fashion that I am, and obviously a digital computer can present that sentiment, or else you wouldn't be reading it right now. So now you can say, well, what about emotions and intuition, etc., you can't digitize that? Well, you can actually, because we can only express those feelings or even reflect on what they mean through an internal dialog. And that dialog is organized in the same fashion this sentence is.

 

[Avichal]

I find that a real left-field question, Avichal. I like it though, made me think. My initial response would be "yes" but with a qualification. That qualification is that our understanding of everything can be broken down into yes's and no's because our minds evolved in a manner that organizes information in a hierarchical, sequential fashion. That is why I am writing this sentence in the fashion that I am, and obviously a digital computer can present that sentiment, or else you wouldn't be reading it right now. So now you can say, well, what about emotions and intuition, etc., you can't digitize that? Well, you can actually, because we can only express those feelings or even reflect on what they mean through an internal dialog. And that dialog is organized in the same fashion this sentence is.

I am for a "yes" too.
Everything works according to laws of physics so if we are able to represent matter and laws in terms on ones and zeros we are done.
As for the emotions and intuition that's a biology problem. We haven't yet figured out how they work. When we know how it works we might be able to digitize that.

I'd like to hear more though from other people

 

[kith]

I have two of objections:
1) Most theories are built upon analog mathematics which means they include irrational numbers. These can't be represented by ones and zeros.
2) Consciousness and emotions can not be captured by theories at all because they are subjective experiences. Describing what happens in the body of a living being while it experiences an emotion doesn't tell you what the subjective experience is.

 

[Office_Shredder]

1) Most theories are built upon analog mathematics which means they include irrational numbers. These can't be represented by ones and zeros.

What is digital mathematics supposed to be?

Anyway, we can represent irrational numbers in 0s and 1s as well as we can represent irrational numbers with any other characters (for example I could represent the square root of 2 using 0s and 1s as long as I have a way of converting between binary strings and English letters). It is true that we can only represent countably many irrational numbers, but that's a problem with our ability to write down only countably many characters and finite length strings, not a problem with binary language in general

 

[ModusPwnd]

I say no. "Everything" includes properties we conceptualize as "mass", "charge", etc. We can represent such properties as ones and zeros, but we cannot break down those properties into ones and zeros. So I think your post and the title to your post are different questions. Yes, everything can be represented by ones and zeros, but not everything can be broken down into ones and zeros. I would water it down even further by noting that everything can be represented by anything unless you have some sort of clause requiring accuracy or precision. I think I would also say that nothing outside of mathematics can be broken down into ones and zeros, it can only be represented by them.

 

[jim mcnamara]

I define represent as meaning an operation (usually arithmetic) completes correctly.

So using some of what I've seen above, how does one deal with repeated floating point operations on numbers that have no correct finite representation, i.e. in IEEE 754 floating point registers? Computers cannot represent sqrt(2) correctly in IEEE 754 floating point registers. Anyone who thinks this is possible should stick to an 'integer operations only' approach when programming. Do not attempt to balance my 401K transactions, please. Why do you suppose that COBOL comp variables are packed decimals, or oracle arithmetic operations are all BCD?

Questions, quibbles? consult:
http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

 

[Number Nine]

Let $X = \{0,1\}^{\mathbb{N}}$ be the set of all binary strings; then $|P(X)| > |X|$, and so we cannot denote every such subset with a binary string.

 

[Office_Shredder]

I define represent as meaning an operation (usually arithmetic) completes correctly.

So using some of what I've seen above, how does one deal with repeated floating point operations on numbers that have no correct finite representation, i.e. in IEEE 754 floating point registers? Computers cannot represent sqrt(2) correctly in IEEE 754 floating point registers. Anyone who thinks this is possible should stick to an 'integer operations only' approach when programming. Do not attempt to balance my 401K transactions, please. Why do you suppose that COBOL comp variables are packed decimals, or oracle arithmetic operations are all BCD?

You don't have to represent numbers with floating point decimals - algebra packages can represent the square root of two exactly

 

[Evo]

As long as this remains a discussion of math, it is ok. Getting into speculation (philosophy) of consciousness, etc..., will not be ok.

 

[D H]

It is true that we can only represent countably many irrational numbers, but that's a problem with our ability to write down only countably many characters and finite length strings, not a problem with binary language in general

It is an inherent problem with using a digital computation model. Almost all of the reals are not computable.

 

[Q_Goest]

The question of whether or not the world can be represented by zeros and ones, or even by a classical mechanical computing machine has been addressed by Deutsch and also by Feynman. They both came to the same conclusion and the answer is no, you can’t simulate the world using ANY classical mechanical computing machine. Their papers can be found here:
Deutsch: http://www.ceid.upatras.gr/tech_news/papers/quantum_theory.pdf
Feynman: http://www.cs.berkeley.edu/~christos/classics/Feynman.pdf

 

[jim mcnamara]

Almost all of the reals are not computable

We agree.

 

[StevieTNZ]

If those 0's and 1's represent binary code, I go with the answer yes. We could potentially store everything on a computer, which is represented by 0's and 1's.

 

[Rick890]

As long as this remains a discussion of math, it is ok. Getting into speculation (philosophy) of consciousness, etc..., will not be ok.

You seem to have an odd, and narrow, definition of what philosophy is. Being that logic is a sub-field of philosophy , it's kind of hard to avoid completely in discussions like this.

 

[DragonPetter]

The question of whether or not the world can be represented by zeros and ones, or even by a classical mechanical computing machine has been addressed by Deutsch and also by Feynman. They both came to the same conclusion and the answer is no, you can’t simulate the world using ANY classical mechanical computing machine. Their papers can be found here:
Deutsch: http://www.ceid.upatras.gr/tech_news/papers/quantum_theory.pdf
Feynman: http://www.cs.berkeley.edu/~christos/classics/Feynman.pdf

Are there any counter arguments to the conclusions made in these papers?

Edit: by counter arguments, I mean papers written by authors who address the conclusions made in these papers or similar ideas. While the papers are not entirely rigorous, they make good points. Some things said raise my eyebrow because the assumptions are somewhat weak or seem obvious (like a finite computer cannot truly simulate an infinite universe beyond approximation).

 

[Bandarigoda]

I heard a news to similar to the OPs question before. It is some a mathematician in past, he was Pythagoras if I remember clearly.
That he tried to show everything using maths.

 

[Evo]

You seem to have an odd, and narrow, definition of what philosophy is. Being that logic is a sub-field of philosophy , it's kind of hard to avoid completely in discussions like this.

No, I am referring to speculations about consciousness, we're not going to go there.

 

[Number Nine]

If those 0's and 1's represent binary code, I go with the answer yes. We could potentially store everything on a computer, which is represented by 0's and 1's.

Not so. I can construct any number of sets whose cardinality is greater than the set of all possible strings of 0's and 1's. It's clearly not possible to represent every element of such a set in a binary computer.

 

[lurflurf]

^It depends what represent means. That is equally a limitation of paper. We cannot write disricptions of some sets on a finite amount of paper either.

 

[micromass]

I think this has been dicussed enough. Locked.