Essay Abstract

With the vast scientific knowledge-base available to us, why is it still so hard to accurately predict things like stock market prices and biological evolution? In this essay, I connect several concepts from computability, predictability, data science, and physics together to understand why some systems are so difficult to model. After addressing the important role of navigating particular state spaces in each field, I conclude that modularity may be an under-appreciated and under-utilized tool in our ability to compute our complex world.

Author Bio

Alyssa is currently a postdoc at UW-Madison in Bacteriology. They got their PhD in Physics at Arizona State University, where they studied the difference between living systems and non-living ones. Alyssa also did an internship at Microsoft Research, where they implemented one-shot machine learners directly into Minecraft. For two years after graduation, Alyssa worked at VEDA Data Solutions, a local data-science-as-a-service company focused on making messy healthcare data accurate. Now, Alyssa develops fast and improved software for bioinformatics while studying how complex systems (like microbiomes) work together to perform robust functions.

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5 days later

Holism is such an interesting and fascinating issue. I really appreciate the thoughtfulness of your essay with respect to how necessary it is to normative accounts of reasoning and decision-making. Perhaps the systematic errors people make in psychology experiments on these tasks are due to the necessity of an efficient representation that allows dependencies among very "distant" states within state space.

From a normative perspective, what do you believe is the best approach to start making progress on tackling the problems? From the psychological perspective, how do you think people get by despite these issues? (We probably don't wait for our mind to halt an uncomputable problem when a lion appears in our visual field, we act near immediately.)

Joe Austerweil

    Hi Joe!

    Great questions! For humans, I would guess that we make state spaces that are small enough to make intractable problems tractable. I'd be really interested to know how state spaces are created from an environment, and how humans are able to build these spaces from scratch, switch between one state space and other, and expand them (like adding a new word to their vocabulary). I'd also be interested to know if each problem requires its own state space.

    In general, I'd be very interested to know what these mechanisms are and how they compare to other things within biology. For example, do cells "create their own state spaces" based on the kinds of proteins they can encode? How would this space change with protein interactions with other cells? I think it would take some clever modeling that is driven by empirical analysis to get these answers. Luckily, there's already a goldmine of data thanks to technology!

    Cheers!

    Alyssa

    6 days later

    Dear Dr.Alyssa Adams,

    I applaud you for addressing unpredictability from a pragmatic point of view. Even when theory permits computations, decidability and predictability we usually have state spaces too vast for us to traverse through for a meaningful solution. Modularity, and its promise of helping us manage all the different state spaces confronting us, rightfully merits emphasis in our conversation of the 3 uns.

    A natural question is how do you know if modularity is theoretically possible? To return to the million dollar question of stock market, how do you know we can shrink the state space, and use it to gain useful answers?

    Modularity from what I understood as a layperson is overlooking certain details differentiating states. In the case of statistical physics, we overlook details of individual movements of atoms and instead see their behavior at a collective level. What if for our million dollar question of stock market, we if we need to know the behavior of every single Wall Street trader, buyers, seller, and the flap of random butterfly somewhere in the Amazon? In other words, all the details separating the states?

    Since I am very much a layperson, I will apologize if I misunderstood the technical aspects of your work.

    Kind Regards,

    Raiyan Reza

      Cool essay! I like the data-driven bent (e.g. assuming the stock market can be 'solved', the 'true' rules don't matter as much as our ability to predict their output does).

      What do you mean when you reference biology being uncomputable? That it's computationally hard or impossible to 'optimize' fitness in the context of evolution?

      Your operational definition of uncomputable seems to be "hard to do in practice" rather than undecidable in the mathematical sense. After thinking about it, I think this is probably for the best, because there are no real world undecidable problems. For example, every real program will halt, if only because all programmers will eventually die and the computer will eventually break down. So I think the heuristic of 'can we make it in a reasonable amount of time?', a la the desk weird ornaments, is much more useful.

      I agree that modularity is an important part of why we can solve problems and understand the world at all. To give an example related to your essay, we can make desks without having a complete quantum theory of gravity---and that's pretty amazing, if you think about it! It's also pretty amazing, as you mention, the way that organisms' overall phenotype can be relatively insensitive to many genetic and epigenetic details. If a single random mutation can turn us into formless slime, then evolution probably would have been unsuccessful, and we wouldn't exist. I'm thankful our developmental algorithms are so robust.

      P.S. Do you know Kevin L.? He's a grad student at UW Madison working on microbiome-related stuff.

      John

        These are excellent questions! Actually, I'd be very curious to know how systems naturally use modularity and then build from there. It would likely require an extensive empirical review of all kinds of systems. But maybe, as a start, doing a meta-analysis of tons of machine learning models might provide an answer to this. As far as I know, machine learning models (including deep learning, etc) are very good at picking which data features (or things that could be called variables, or states from various possible state spaces) are needed to make a meaningful prediction about a particular problem. I don't know enough about the field of machine learning to know if this has already been done in some way. But if it hasn't, I would start there.

        Then, it would be fascinating to compare those results to the ability of each model to make accurate predictions. Are successful models good because they were able to select the right "state-space" by choosing modular features? Also, for a given data set or set of observations, how many features could possibly be engineered? How does a feature engineer which features to engineer? I'm sure there's been some excellent work on feature selection for machine learning, I can't wait to read it and see what others have to say!

        I could see the whole field of machine learning providing us with some interesting and unintended insights for understanding systems as a whole!

        Cheers!

        Alyssa

        Hi John!

        Thank you so much for your comments! These are very good points. It seems that many of the hallmarks of biology (like open-ended evolution and emergence) are likely uncomputable:

        "As time grows, the stated complexity measures allow for the existence of complex states during the evolution of a computable dynamical system. We show, however, that finding these states involves undecidable computations." from this paper here: https://www.mitpressjournals.org/doi/full/10.1162/ARTL_a_00254

        But regardless of that, biology still continues to evolve forward and instantiates itself physically. It seems to me that modeling approaches in fields like artificial life could be deeply flawed in a fundamental sense and we need to understand what state-space computation is being performed, and what it says about other state spaces within the exact same system.

        For example, in video games, it would be fun to understand the mechanisms that drive the open-ended evolution of strategies used by players. However, the open-endedness is only seen from the "strategy" state-space, not the state space of the player chat or the micro-movements of the players. It would be possible to train a machine learning agent to mimic the movements of players, and even win against a competitive human team, but it would still not provide answers to understanding the apparent open-endedness on the level (state-space) of strategies. So some aspects of this system are probably computable while other aspects aren't.

        I love your point about modularity being related to robustness! It's very good to highlight that explicitly, and I'll also add to it by saying it's extremely interesting when information about smaller levels of organization isn't necessary to do a task on a larger level! There's some pretty cool work about it in information theory, I should see if this idea has been explored for large systems with multiple state spaces.

        Cheers!

        Alyssa

        PS: I don't think I've met him before! I'll keep an eye out though whenever campus opens up so I can say hello!

        Hi Alyssa,

        What a great essay! It was very well written and very easy to follow. Well done!

        Going into every computation, knowning as many primes as possible is surely the best way to compute something with maximum predictability, but certainly at a cost! There is just to much information. Elon Musk tweet is the prime you care about, the blade of grass moving in the wind is might contain some signal, but is likely noise. You made this idea crystal clear and how it to learning and Turing machines and stochastic processors.

        If you increase your state space to include all information, your not really learning everything, you're just memorising stuff. You need to forget and ignore stuff to learn and thus, follow well worn tracks through your massive state space. As you point, out biology figured all this out long ago.

        Great work, I completely agree with your thesis and loved the essay! We certainly have a lot of overlap in our ideas. My essay 'noisy machines' covered a lot of the same topics, but focused on the thermodynamics and computation. I'd love to get your feedback if you have the time!

        Thanks,

        Michael

          Dear Dr.Alyssa Adams,

          Thanks for presenting an excellent essay. You discussed well about the predictability. Your fig 2. shows an algorithm that is something EXACTLY like my essay "A properly deciding, Computing and Predicting new theory's Philosophy".

          In that philosophy I gave some additional practical points like truth fullness, forcing and manipulation ( fixing) of results, some cheating etc., that you did not include. Probably at your age you did not see the world.

          I want to give the best rating to your essay, but at least make a visit to my essay and leave some comment please......

          Best

          =snp

            Dear Dr Alyssa Adams. Nice essay.you have my high rating. I liked your take on modularity.Seems like you struck the same chord with me here https://fqxi.org/community/forum/topic/3525.kindly read/review on bias.Thanks and wish you all the best in the essay contest.

              Dear Dr.Alyssa Adams,

              First, I am really sorry for a late reply. I somehow missed update on my email ( which is linked to this competition).

              Thanks for your detailed answer!

              And, yes indeed I think machine learning can provide us with strong insight in multiple fields!

              I think the good models indeed selected the right modular features; because a good model has to be computable. For instance, in gravitational physics, we narrowed down the state spaces by simple caring about the mass of an apple, not the arrangement of the particles, its color, etc.

              At the end of the day Newton with the scant data at hand, and no computational capacity could not have reasoned otherwise! Simply focusing on the mass led him to shrink the state space vastly.

              And, I think as we are confronting more and more sophisticated problems, we are realizing we cannot shrink many state spaces as drastically, and this is where machine learning and other modern tools of computation comes in handy!

              (PS: As a layman my response can be completely invalid ofc)

              Kind Regards,

              Raiyan Reza

              Hi Michael!

              It is interesting to think about the process of just memorizing stuff vs. understanding an underlying process (compressing the data into an algorithm). I wish we knew more about the physical instantiation of knowledge in space, since it would clear up a lot of misunderstandings on causality. As an example, it is currently difficult to understand what processes caused the human brain to have the physiology that it currently has. Or, more simply, it's difficult to understand why the grains of sand on a beach are exactly arranged in the way that they are currently. It's too difficult to extract this information and move backward, since for each effect there could be several causes (even if many possible causes are the most likely because they are short explanations (Occam's Razor)).

              I hope you find my posted questions on your essay helpful and interesting! I really loved reading it!

              Cheers!

              Alyssa

              Hi Alyssa,

              thank you for laying out the computing state space so clearly! These are some rather interesting tools to play with.

              So I get how the human brain might be said to 'shrink the state space' of the sense data available to it by massively simplifying what we experience in terms of cross modal sensory perception, object perception, short term memory, attention and so on. I'd be really interested to hear your thoughts on how these sorts of observational processes are being or might be modelled in this computational sense, and especially in terms of any developments in evolutionary biology.

              Is anyone looking at morphogenesis in evo-devo from this computing perspective? I've been playing around with various philosophical and biological notions regarding the modern concept of morphogenesis, and trying to think of it as fundamentally an informational process that organizes matter. And not just in terms of the evolution of the individual organism but more in terms of how biology is a terraforming biosphere process (cf. Sara Imari Walker's work)

              Specifically do you think there might be a way to model an observer-dependent perspective as an information feedback loop driving morphogenetic processes?

              Cheers,

              Malcolm

              Je suis, nous sommes Wigner!

                Dear Alyssa,

                thank you for writing this essay - very enjoyable. Regarding the relation between computation and implementation (your figures 1 and 2) I was wondering if you know the framework of "Abstract representation theory" by Dominic Horsman et al. They deal with the question of what physical systems compute, i.e. which of them are implementing a computation. I was wondering how their perspective fits or compares to your framework.

                Thanks again and best regards,

                Gemma

                  Dear Alyssa,

                  My first thought was, do we see, between the essays, an ad selling a get-rich-quick scheme? Just kidding, but it made me curious, and after reading your essay, I became indeed richer, intellectually. Also had a lot of fun, I like your style. In addition, I could relate with your essay in many ways (you mention CNC, I worked 8 years for a company making cad/cam software for CNC. I didn't trade, but a friend, one of my former colleagues there, left the company to trade Forex, won 0.25m, then lost 1m. He's fine now, but still not allowed to trade.) I loved your explanations and your ideas, about the limits of computation (indeed, even Laplace's daemon has some serious trouble). I liked especially the ideas you presented about how to beat these limitations by constraining the state space and by modularity. I'll tell my friend these tricks, once the law will allow him again to trade, he can use them. I will not try, I'll let him do this, anyway he said at some point that if he wins big time he'll finance my research :-)

                  Thank you for the excellent essay, and I wish you success in the contest!

                  Cheers,

                  Cristi

                    Absolutely! It makes me curious to wonder if there is a nice mathematical framework that would help us shrink the state space in an appropriate way for a particular problem. It makes me think about set theory, and also makes me wish I knew way more about discrete mathematics than I do. The thing is that it's difficult because it depends so much on the problem in question, which has the subjective abilities of the observer built right in.

                    Hello SNP!

                    Yes! I definitely see a lot of overlap between our two essays! I have some questions and comments for you as well, but I will post them on your essay page.

                    Cheers!

                    Alyssa

                    Thank you so much for reading! I look forward to posting my questions about your essay and having a great conversation!

                    Cheers!

                    Alyssa

                    Hi Malcom!

                    Actually, this is my exact interest as well! I can't help but think a mathematical model that captures the subjectivity of an observer could be represented with some kind of set theory.

                    On one hand, you have an observer who is only able to make particular observations of the world, due to the lack of complete knowledge of the entire world. On the other hand, you have the rest of the world, which also includes the observer itself, which is often the case in biology.

                    I think this "cut" between an observer and the world should have a big impact on the dynamics of both the world and an observer, especially if the observer's dynamics are not fixed in time.

                    Plus, there's the physical arrangement of these entities in the world. The physical limits of computation put bounds on the actual tasks any entity could possibly take. I think what makes humans so interesting is our ability to extend our computation power beyond the brain, which I personally think why computers and machines are so important to collective human tasks (this is the extended model of cognition in psychology). It makes me think that humans are extremely good at manipulating state spaces to complete computational tasks. There's a lot of fascinating work in psychology about this, so I think, if anything, we should look to the empirical results of human cognition and other biological computation tasks (like chemical networks in metabolism, viral evolution, etc).

                    There are so many moving parts here, but it is my hope that some mathematical model could formalize these ideas so we get a better picture of the computational landscape we have to work with, then if we're lucky, we could see if it has any explanatory power over real data.

                    Cheers!

                    Alysas