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The structures of computation and the mathematical structure of nature (2010) (rutherfordjournal.org)
137 points by ege_erdogan 13 days ago | hide | past | web | favorite | 24 comments

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.


That's not a new idea.


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.


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.


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.

I am pleased that it pleased you, but allow me to correct the misconception arising due to the parallax between your view of me and my view of me.

Quantum Entanglement is computation, which makes me a monist and a materialist/physicalist. Computers reify our formal languages by manipulating matter.


In the language of comp-sci: Code is data - data is code. Homoiconicity.

In the language that has fallen out of fashion as of late...

In the beginning was the Word, and the Word was with God, and the Word was God. —John 1:1

I intended for my phrase “confident realist materialism founded on a certain anthropocentric presumption of Cartesian dualism,” in all its entirety, to refer to the object of the critique. I apologize if my carelessness caused you to interpret the second half of the phrase (the part after the word “materialism”) as a mischaracterized signifier of you, the subject or cause of the critique. Regardless, I thank you for providing an organization of your advanced philosophy and the fundamental mechanics of it.

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.

You can never determine this with 100% certainty - that is what we have falsification for.

The non-compressibility of a sequence is a falsifiable claim.

All it takes is a single demonstration of successful compression.

for limited runtime you can

So you were unable to compress the stream given the allocated time.

Perhaps you could've compressed it had you kept running for just a second longer?

i mean run all the shorter bitstrings until time runs out or they terminate.

How does “time run out” in practice other than you putting an upper bound on your computation?

Obviously, the code will not halt until it compresses the stream successfully.

enumerate all bitstrings of length 10.

run them for N steps.

if none terminate on the target bitstring of length 100, then we've eliminated the computation hypothesis for 10 bits and N runtime

if we continue this approach and eliminate all the available storage and time available, then we eliminate the computation hypothesis altogether for our scenario

You understand that "Number of bitstrings of length 10" is a function of the cardinality of your alphabet, right?

A binary alphabet has 2^10 such strings. A decimal alphabet has 10^10 such strings.

So before you can make the assertion you've made you first have to answer two question:

1. How many symbols does your alphabet contain? 2. How did you choose that number?

Down that path you arrive the Linear speedup theorem. https://en.wikipedia.org/wiki/Linear_speedup_theorem

bit is base 2 as far as i know

yes, there is always a turing machine that can generate the target with any performance characteristics

so, the key is to keep the reference turing machine fixed

You can’t keep the reference Turing machine fixed in light of the linear speed up theorem.

Hence the argument for compression.

A Turing machine with a better language is faster.

It compresses time.

Yes, I agree there is always a faster Turinng machine for a particular target. With this sort of argument, all bitstrings have a compression of zero bits. I.e. you pick a TM that has the target bitstring as output for the null string. And if it starts with the target on the output tape, there is also zero time. Thus, every bitstring can be generated with zero space and time, with some TM.

So, thats why when talking about compression in general, we keep the reference TM fixed.

When testing, there is the possibility with a single test maybe we have the wrong reference machine. But as the number of tests grows, that probability approaches zero. So, with enough testing we can eliminate the linear speedup theorem loophole, at least with high probability.

As a practical application of this sort of thing, check out the 'normalized information distance'. It is based on algorithmic mutual information, which in theory is not approximatable, as you argue. However, in practice it works surprisingly well, even without prior knowledge of the domain.

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

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