Hacker News new | comments | show | ask | jobs | submitlogin
The structures of computation and the mathematical structure of nature (2010) (www.rutherfordjournal.org)
137 points by ege_erdogan 15 days ago | hide | past | web | 24 comments | favorite





Either the structure of the universe is computational or the structure of the instrument we use to understand the universe with is computational: our minds.

It is difficult to distinguish the two cases in practice.

https://en.wikipedia.org/wiki/Mind_projection_fallacy


That's not a new idea.

https://en.wikipedia.org/wiki/Thing-in-itself

I don't think it follows that either the universe or our minds are computational. For one, we don't have a satisfactory definition of "mind", so that question has to remain open until we do.

And the universe could be "computational" in a completely unfamiliar way. It might even be humanly unimaginable.

As a wild speculation, consider the extreme case: the universe actually functions as an indivisible whole.

We use math to make predictions about repeating causal patterns, and invariably they work in a time- and precision-limited way. If the universe was a true thing-in-itself on its own terms, it could be "computational", but our models would always be incomplete and imperfect.

We would never be able to understand it fully, because we would never be able to build a complete and accurate representation of its computational mechanisms.


Note how you insist on a definition for “mind”, but if we are going to keep raising the bar on missing definitions let’s just go for the sacred cow. What is a definition anyway?

Could you give me a definition for “definition”?

At some point you have to be content that your inability to define every single term in your vocabulary doesn’t hinder your ability to use that term in practice.

All we have in way of creating/communicating knowledge is symbol manipulation. Language.

Turing machines are language recognisers, and I am comfortable using them as practically sufficient (for the purposes of conversation) models of minds.

To be sure you see my point, defining “definition” is recursive and that puts you on the computer science turf.

I am a computer. Mathematics is a language; or more precisely - it is a grammar. Our Mathematical models of the universe are computational, and since Mathematics can only prove things up to isomorphism that is as far as colourless, formal, linguistic reductionism will take us.

As for Kantian transcendentalism. Look no further than Jean-Yves Girard’s work on Linear Logic, Geometry of Interaction and transcendental syntax. Is all computer science intersecting with Quantum Physics.


> I am a computer.

You are a biological system. A massive, noisy and dynamical system of interactions we can never hope to model in fidelity. You exist because of unstable equilibria and tiny little proteins pushing against entropy.

> All we have in way of creating/communicating knowledge is symbol manipulation. Language.

We can communicate with more than abstract symbol language. A dog grows and bears its teeth. A thunderstorm communicates its approach.

We're pattern recognizers, but messy, soupy ones.


>You are a biological system.

That is the language of systems theory.

You are welcome to use the Church-Turing-Deutsch principle as a semantic.

>A massive, noisy and dynamical system of interactions we can never hope to model in fidelity.

https://en.wikipedia.org/wiki/Geometry_of_interaction

We are already modeling it.

The only argument here is the degree of fidelity required or possible.

> You exist because of unstable equilibria and tiny little proteins pushing against entropy >We can communicate...

Begging the question: why do proteins exist?

Entropy, Information, Communication. Heh! That is the language of Information Theory.

>We’re pattern recognisers

Yes. That is what I said - computer/language recogniser. If there's no pattern/structure you can't parse it.

https://en.wikipedia.org/wiki/Pattern_recognition

However you define/conceptualise us, every time you use the word “I” or “we” you are exemplifying recursion.

That is the great thing about self-locating beliefs - they are unfalsifiable.


An inspiring critique of and response to confident realist materialism founded on a certain anthropocentric presumption of Cartesian dualism. It exemplified skill—its own powerful confidence—and experience, deserving great commendation. The education born from witnessing such activity has a high aesthetic value to me.

Even if our mind were computational, we could detect if the universe was not.

Not really. You are still in the paradigm of computation.

Detecting anything is signal processing.

And if I am wrong about this - all the better! It is exactly the right kind of wrongness we need to progress science.


Let's say I have a computer that can only store 10 bits worth of information, but generates 100 bits of information. Then obviously the information cannot entirely originate in the computer.

Sure it can. Compression. Kolmogorov complexity.

I don't need to 'store' the infinite set of natural numbers - that would require infinite space (memory).

But I can describe the infinite set in a single line of Python. Nat = lambda x=0: Nat(x+1)

It's just a space-time tradeoff.


If the sequence isn't compressible, then you can eliminate that possibility.

Wonderfully large article, I often dig in history of CS and science but there was a lot to learn about connection between different research fields.

Thanks a lot




Guidelines | FAQ | Support | API | Security | Lists | Bookmarklet | DMCA | Apply to YC | Contact

Search: