The structures of computation and the mathematical structure of nature (2010) • Hacker News Board

Re: The structures of computation and the mathematical structure of nature (2010)

#21

Post by webdva » Fri, Mar 27, 2020, 4:10 PM UTC

ukj wrote: post #9

echelon wrote: post #7

Earlier quoted context omitted.

> 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 t…

>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 unsta…

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.

Re: The structures of computation and the mathematical structure of nature (2010)

#22

Post by yters » Fri, Mar 27, 2020, 7:14 PM UTC

ukj wrote: post #20

yters wrote: post #19

Earlier quoted context omitted.

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 theore…

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

Re: The structures of computation and the mathematical structure of nature (2010)

#23

Post by ukj » Sat, Mar 28, 2020, 6:43 AM UTC

webdva wrote: post #21

ukj wrote: post #9

Earlier quoted context omitted.

>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 unsta…

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.

https://www.quantamagazine.org/landmark-computer-science-pro...

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

Re: The structures of computation and the mathematical structure of nature (2010)

#24

Post by webdva » Sat, Mar 28, 2020, 8:14 PM UTC

ukj wrote: post #23

webdva wrote: post #21

Earlier quoted context omitted.

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. https://www.quantamagazine.org/landmark-computer-science-pro... In the language of comp-sci: Code is data - data is code…

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.

Re: The structures of computation and the mathematical structure of nature (2010)

#25

Post by ukj » Sun, Mar 29, 2020, 7:54 AM UTC

yters wrote: post #22

ukj wrote: post #20

Earlier quoted context omitted.

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 theore…

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.

Re: The structures of computation and the mathematical structure of nature (2010)

#26

Post by yters » Sun, Mar 29, 2020, 2:06 PM UTC

ukj wrote: post #25

yters wrote: post #22

Earlier quoted context omitted.

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.