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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
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RECENT POSTS IN THIS TOPIC

Ian Durham: on 5/20/20 at 0:58am UTC, wrote Hi Simon, I apologize for not getting to this sooner. This was a very...

Rick Searle: on 5/18/20 at 1:51am UTC, wrote Dear Prof. DeDeo, This was an awesome essay and is tied with the paper by...

Paul Davies: on 5/17/20 at 23:09pm UTC, wrote Near the end you touch on something I myself have come back to many times:...

Kevin Knuth: on 5/17/20 at 16:36pm UTC, wrote Dear Simon, Thank you for your interesting and engaging essay. I...

David Jewson: on 5/5/20 at 13:06pm UTC, wrote Dear Simon, Thanks for your essay. I have now come to the dreadful...

Alyssa Adams: on 5/1/20 at 0:03am UTC, wrote Hi Simon! Fantastic essay! I love how you talk about KC in your examples. ...

Cristinel Stoica: on 4/26/20 at 19:52pm UTC, wrote Dear Simon, I liked very much your essay, both how it's written, the...

Simon DeDeo: on 4/26/20 at 19:37pm UTC, wrote Lovely, Flavio. Looking forward to reading it. It’s worth thinking about...


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FQXi FORUM
September 19, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Mutual Explainability, or, a Comedy in Computerland by Simon DeDeo [refresh]
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Author Simon DeDeo wrote on Apr. 19, 2020 @ 22:21 GMT
Essay Abstract

Many people believe that the universe is a giant computer. This view implies that what is uncomputable has no causal power. We propose that, to the contrary, at least one uncomputable object, Kolmogorov Complexity, does play a causal role in the physical world, and that we have good scientific reasons to therefore believe it exists. We use a simple set of arguments, based on the probabilistic extension of algorithmic information theory, to show that such a causal role is not only consistent with the best evidence from cosmology, but also predicts an otherwise mysterious feature of our environment: mutual explainability. Mutual explainability is the fact that things that tend to correlate with each other also tend to explain each other.

Author Bio

Simon DeDeo is external faculty at the Santa Fe Institute, and assistant professor in the Department of Social and Decision Sciences at Carnegie Mellon University, where he runs the Laboratory for Social Minds. http://santafe.edu/~simon

Download Essay PDF File

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 20, 2020 @ 15:08 GMT
Dear Prof Simon DeDeo,

Thank you for giving us a wonderful essay on what computers can't do ( Uncomputability). The KC is complex program, and it is even not came in a full program form till now. Is this Artificial intelligence in some other words? They say full AI is also very complex....

Hope you will get some spare time to have look at my essay " A properly deciding, Computing and Predicting new theory’s Philosophy" also, and give your valuable comments....

Best regards

=snp

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Author Simon DeDeo replied on Apr. 20, 2020 @ 15:11 GMT
Hello SNP —

Thank you. I think getting these questions right is crucial for GAI, so I’m glad you asked. I’m currently in the middle of Reza Negarestani’s book Intelligence and Spirit, which you might like if you find this style sympathetic.

Some great essays this year, looking forward to reading yours.

Simon

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Satyavarapu Naga Parameswara Gupta replied on Apr. 21, 2020 @ 04:52 GMT
Dear Simon,

What is that book "Reza Negarestani’s book Intelligence and Spirit" and tell a few words about it and how to get it?

By the way what is GAI? And please clarify my question about AI, and when you can spare some time visit my essay ....

Best

=snp

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Jochen Szangolies wrote on Apr. 21, 2020 @ 05:30 GMT
Dear Simon,

this is an exceptionally well written, and more importantly, well argued essay that brings a novel, and intriguing, perspective to the question of whether non-computable objects matter in the world.

It's an interesting perspective to try to accord an abstract quantity causal significance. On the face of it, it seems to invite some strange notions---if I say, 'the real...

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Author Simon DeDeo replied on Apr. 21, 2020 @ 06:24 GMT
Hello Jochen —

Thank you for your gracious comments here. I'm drawing that notion of cause in part from the scientific naturalism of Ladyman et al ("Every Thing Must Go"), who say that our ontologies should be those of the best scientific explanations. But I doubt they'd agree with me after that! I do think it's possible to be a scientific naturalist at the same time as rejecting...

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Jochen Szangolies replied on Apr. 21, 2020 @ 14:59 GMT
Dear Simon,

regarding this:

I do think it's possible to be a scientific naturalist at the same time as rejecting computational naturalism (the computerland) though.

I have to say I emphatically agree. I think computationalism is a very attractive idea---in part, because the 'linkage' of concrete physical entities with abstract objects, like computations, seems to hold a...

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Author Simon DeDeo replied on Apr. 21, 2020 @ 20:23 GMT
So I think the grueniverse does actually work in this case. First we condition on the Universes being "safe enough for intelligent life" that we get to the world historical moment of us having this discussion right now. The concern is that these have to have mutual explainability—let's take that as given.

We have two hypotheses: KC (the argument of this paper), and CN (computational naturalism, random generation w/o use of Kolmogorov Complexity). By assumption, right now, our experiences are such that:

P( E | KC) = P( E | CN ) = 1 (or so)

Now wait ten minutes and get experiences E2. Sadly, no unicorns emerge inexplicably from the asphalt.

P( E2 | KC ) = 1

P( E2 | CN ) = epsilon

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André C. R. Martins wrote on Apr. 23, 2020 @ 21:34 GMT
Dear Simon,

Great piece, I am glad you mentioned it in my own entry, as I had some time to read essays today and came soon to yours. Let see what it does to my primacy effect (I'll love to know what my own article does with your effect also). And, indeed, there are nice similarities in our opening sentences.

Your description for a possible KC-universe generating scenario is intriguing and reminds me of something similar I heard about some time ago. I can't recall the source, but it was about universes being created as consequences of other universes and there was some kind of evolutive pressure on the process. I need to hunt that one down.

Anyway, I must say I have a problem with the suggestion that simplicity might be a good way to pick correct theories. You do not say that explicitly but you do suggest that as an argument. I do like simplicity and I think it does have a role in science. But, unlike other physicists, I think the role simplicity (and, with that, measures of complexity) does play is based on human limitations. Simple, assuming human language and knowledge, is easier to use and that makes it preferable. But that is not the same as claims of truth - which should not be made - or even probabilistic truth.

Best,

André

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Author Simon DeDeo replied on Apr. 23, 2020 @ 23:27 GMT
Hey André! I think you're thinking about Lee Smolin's proposals regarding black holes forming baby universes—rather clever, though focused on the capacity of universes to create baby universes, rather than to be efficiently explainable.

"Simplicity" is a powerful concept, and the question is why it works. There are IMO two answers:

1. it works because the world is explainable—it turns out things do have simple descriptions, so let's prefer those.

2. it serves as a regularization term, or a block against overfitting. Certainly this is why something like LASSO or sparsity constraints work in machine learning. It's a bit of #1, but includes the fact that we also have noise, and noise is uncompressible, so you can penalize things that model noise by penalizing complex things.

Physicists do also like a #3: simple things are easy to communicate! These come from cognitive constraints. But we certainly wouldn't say "X is likely to be correct because I can understand it" (we might say "X is likely to be correct because it's simple, and by virtue of that second fact, it happens that I can understand it").

Yours,

Simon

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André C. R. Martins replied on Apr. 24, 2020 @ 01:06 GMT
Yes, it was Smolin's idea. Much easier to track now, thanks.

I am not saying simplicity does not work, it did in the past, and it will probably work well in the future also. But there is a clear bias we introduce in explanations as we do start looking at the simpler ones. Assuming there are several equally good explanations (probabilistic underdeterminancy), we would find the simpler ones first, just because we are looking there first. That does fit nicely with your #3.

The world is explainable might mean different things, as you know. It might even be just partially correct, in that we can get part of the answer but not the complete version, in principle. And yes, avoidance of overfitting is important. In principle, Bayesian methods do penalize more complicated models, so you would not need that. But, even in simple cases of model comparison, you crash into problems with the priors.

In any case, I think it is essential not to assume more than we actually can say from observation. Introducing new theories is fundamental, even metaphysical ones, but we must withdraw judgment far more often than it is done in the physics community.

Yours,

André

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Flavio Del Santo wrote on Apr. 25, 2020 @ 12:26 GMT
Dear Prof. DeDeo,

thank you for a nicely written essay, very accessible and with a lot of food for tought. I enjoyed very much reading it. I found particulerly appealing your section 4, where the main thrust comes. I believe there is some element of convergence between our views, for instance when you say that "a mathematical object exists if it plays a causal role in the natural world". In my essay you will find an argument based, if not on simplicity, on some principles that tries of finiteness (of the Kolmogorov complexity, in fact) that tries to disentangle the mathematical abstraction with the physical meanings. I would appreciate your opinion on that.

Best wishes and good luck for the contest!

Flavio

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Author Simon DeDeo replied on Apr. 26, 2020 @ 19:37 GMT
Lovely, Flavio. Looking forward to reading it. It’s worth thinking about how to flesh out that rather off the cuff remark about causality...

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Cristinel Stoica wrote on Apr. 26, 2020 @ 19:52 GMT
Dear Simon,

I liked very much your essay, both how it's written, the connections it makes, and particularly the idea to refute the physical Church-Turing Thesis by showing that Kolmogorov complexity plays a causal role in the universe through the mutual explainability.

It's relieving to know that the chances we're not in a simulation went down :) OK, I'm not really worried about the possibility that the world is a simulation. The reason for this is expressed better than I can do by Sam Harris: "whether or not you're already in the Matrix or in a dream or in some other way distant from the base layer of reality, the fact that it's like something to be you is the fact of consciousness, and it's the one thing that can never be in doubt." This works I think whether or not consciousness is reducible to computation. If it's reducible, then a consciousness in a simulation is as good as one in a real world. If it's irreducible, then even if it is plugged into a simulation like a role playing character or like in the Matrix, the argument from Sam's quote shows that there's something real about it.

Cheers,

Cristi

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Alyssa Adams wrote on May. 1, 2020 @ 00:03 GMT
Hi Simon!

Fantastic essay! I love how you talk about KC in your examples.

I was wondering if you could talk a bit more about this: "The idea that mutual explainability provides evidence against the physical Church-Turing Thesis is radical." I think this is generally true and also extremely interesting. But I'm also wondering how much that depends on a and b are encoded. For A, there are several different ways to realize it, and on top of that, far more ways to encode its realization into a state. Have you considered this distinction before? For example, a person who is deaf would encode states of the world completely differently than a person who is blind. I'm wondering if this encoding has an impact on the compatibility of a problem or the physical realization of an object. Maybe there is no such encoding that a and b have mutual explainability, or perhaps a explains b only when encoded in a particular way.

I'd be really curious to know what you'd think! I also talk about this idea in my own essay, I probably do a much better job explaining it there.

Cheers!

Alyssa

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David Jewson wrote on May. 5, 2020 @ 13:06 GMT
Dear Simon,

Thanks for your essay.

I have now come to the dreadful realisation that, in my essay, I have created a computerland world with the future predicted by a simple algorithm that has to be run over and over again, possibly a billion or more number of times, to predict how a certain set up will develop after a certain time t.

In that world there is just one algorithm that continually loops: it returns results, then acts again on those results and so on, until time t is reached.

But then it occurred to me that perhaps (just perhaps) I can measure the Kolmogorov Complexity of that algorithm. What if I defined complexity as the inverse of the number of times that the algorithm had to completely loop to get to time t (on the basis that the simpler a program, the more loops it will have to make to achieve a result)? Indeed, the algorithm could be adjusted so that it could also tell me how many loops it had performed, thereby telling me its own complexity without the need for a different KC program. I could also compare my algorithm with other algorithms that predicted the future using the same sort of looping process and then be able to say which was the simplest by comparing the number of loops to get to time t. What then? Would that mean this type of KC is actually computable?

What do you think?

All the best. I really enjoyed your essay and learned a lot from it.

David

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Member Kevin H Knuth wrote on May. 17, 2020 @ 16:36 GMT
Dear Simon,

Thank you for your interesting and engaging essay.

I appreciated your discussion on KC, and I was pleased to find that your essay got me thinking about a good many things.

Your focus on self-reference and KC made me think more deeply about consciousness. I studied neuroscience during posdtdoctoral years in the mid-1990s. At that time, the field referred to consciousness as "The C Word", and serious discussion was somewhat taboo.

The topic interested me, and my thinking about the research performed by colleagues led me to believe that consciousness was more or less an illusion that arose from the brain modeling and describing itself. It wasn't until, I read your essay that I was forced to think about this idea of something modeling or describing itself as a form of self-reference.

- Do you have any thoughts on this perspective?

- Could this self-reference by one of the reasons why we intuitively feel that consciousness is so magical??

- And what are the prospects for an AI that models itself?

I was struck by the point that you made stating that a computer simulation can only use computable numbers. If we were in a computer simulation, there would be many holes. Would these be detectable?

Are these hidden because the rationals are dense?

Or would they be unnoticeable precisely because we too are simulations?

Thank you for the thought-provoking essay!

Kevin

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Member Paul Davies wrote on May. 17, 2020 @ 23:09 GMT
Near the end you touch on something I myself have come back to many times: the universe admits of explanation. That means the universe is structured in such a way that a (small) subset of itself can construct a compression of the whole. You cite a counter-example of Robert Wilson. Another, which I have often thought about, is Jung and Pauli's synchronicity. We can imagine correlations between events in different causal chains, and even spacelike separated events (beyond EPR) that would demand a very different mode of 'explanation'. How can we explore the possible existence of patterns of events scattered over the spacetime manifold that are not captured by standard Lagrangian dynamical evolution?

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Member Rick Searle wrote on May. 18, 2020 @ 01:51 GMT
Dear Prof. DeDeo,

This was an awesome essay and is tied with the paper by Flavio Del Santo for my favorite of all the essays I have read for this contest.

Your application of Kolmogorov Complexity to the universe as a whole was brilliant,but it was the way you expressed these deep thoughts with style and humor that left me most impressed.

My two favorite lines were:

"A being equipped with only RLKC can use simplicity to decide between explanations, but can’t consider explanations that themselves invoke simplicity. Among other things, this means it will be unable to judge this paper."

And:

"The equation on the t-shirt is simple, but the t-shirt is a mess."

Best of luck in the contest!

Rick Searle

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Member Ian Durham wrote on May. 20, 2020 @ 00:58 GMT
Hi Simon,

I apologize for not getting to this sooner. This was a very interesting essay! KC is something I have thought a bit about at various times in my career. Anyway, there's lots to digest here and I feel like I need some time to do the digesting (but I love the reference to Robert Anton Wilson!).

Ian

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