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

                    Hi Gemma!

                    I haven't! Thank you so much for sharing this, this is absolutely fascinating. Actually, I think these ideas would fit nicely into Constructor Theory, which I think was missing this exact component. I'll learn AR theory in much more detail because I'd be extremely interested to see how the idea of different observers with access to different knowledge could fit in, especially how observers could be seen as computers using other computers. I think that last part sums up what I think is missing between biology and computation: How do computers use computers?

                    Cheers!

                    Alyssa

                    Ha ha ha, best of luck to him! Maybe, we could all engineer some weird machine learning algorithm to process the logical arguments of these essays, then see if it could come up with some reduced logical set! Then we could apply this to trading XD Glad you enjoyed my essay!

                    Dear Dr.Alyssa Adams,

                    I gave the best rating as i promised. Thank you for your post on my essay, i am replying there. We will communicate further with Email for bio problems, please check mail....

                    Best wishes to your essay

                    =snp

                    Hi Alyssa:

                    Besides novelty in your thinking, you are also an excellent writer, and should get a higehr rating.

                    It is not quite the same, perhaps, but Descartes' philosophy of reductionism, somehow can lead to your suggestion of "modularize" complex problems into small segments [ https://en.wikipedia.org/wiki/Reductionism ]. That is the only way for humans, with their limited mind and, especially, starting originally from complete ignornce about the laws of the universe.

                    Being an experimental physicist, I have dissected the essential steps behind data gathering in all of our experimental apparatuses. In the process, I have found that nature has saddled us with a perpetual bottleneck to obtain the COMPLETE knowledge about anything. Humans have started with complete ignorance about the laws of nature; and we can understand one bit at a time. We have to keep on gathering more and more bits. However, how the newer COMPLETE set of bits will fit together, will always keep changing as we keep gathering more and more bits.

                    We have no choice but to iteratively advance to higher levels of knowledge, leveraging one "working theory" after another "working theory", and so on. However, instead of re-structuring the fundamental postulates of the older working theory to complement the newer "working theory", we have been accepting, as religious dogmas, the older theories and build something above it as the n-th story over the old building, instead of rebuilding a newer edifice. It is very hard; but that is the only way we can INCH towards the ontological reality.

                    Even though I do not have proper understanding how my Holobiota keeps generating these sentences; my ontological existence is validated by this writing on this computer. My Holobiont is transcribing my thoughts; therefore I exist; at elast as an assembly of trillions of cells! I am a partial reality of the universe because I am trying to unravel the realities of the universe.

                    Many of my earlier papers have also articulated this position. They can be downloaded from:

                    http://www.natureoflight.org/CP/

                    You can also download the paper: "Next Frontier in Physics--Space as a Complex Tension Field"; Journal of Modern Physics, 2012, 3, 1357-1368,

                    http://dx.doi.org/10.4236/However, mp.2012.310173

                    You can directly contact me at:

                    Chandra.Roychoudhuri@uconn.edu

                    Stay happy.

                    Stay healthy.

                    That is the surest way to keep the Covid-19, and their earlier friends, under control. Avoiding exposure to them forever is impossible.

                    Sincerely,

                    Chandra.

                      Dear Alyssa Adams!

                      Thanks for the interesting essay. This is essentially a bold original article for an important newspaper!

                      I liked your unexpected association of the current pandemic with the collapse of the financial market. At the 2018 World Philosophical Congress in Beijing, I publicly said: "Soon the world will face a financial crisis. It will be a controlled demolition of the stock market. Market makers want to destroy fictitious capital. For`s this purpose the threat of war is organized!"

                      Before that, I wrote several articles about the fact that they will try to mask the coming economic crisis with international military conflicts. But I did not imagine that they use a pandemic scarecrow for this. Let's hope that all these experiences will remain in the past.

                      Otherwise, our views are similar. You are also looking for algorithms and calculations in the objective world around us. Yes, it's clear that in a flying fly, very specific calculations take place that control the flight. But what calculations take place in the solar system? It is known that Newton believed that the solar system is unstable, and God constantly intervenes, controlling and coordinating the movement of all the planets. Laplace proved that there are certain mechanisms that determine stability. Can these feedback mechanisms be called computation?

                      I wish you success in your scientific work!

                      Sincerely, Pavel Poluian.

                        I must first point out a minor but not insignificant error. The complexity class P does, indeed, mean Polynomial-time, however, the complexity class NP means Non-deterministic Polynomial-time. It does not mean Non-polynomial time because, if it did, then that would mean that P does not equal NP, but this is an open question.

                        I think a simple joke expresses why the stock will never be predictable, but also not unpredictable either and also why I think the ("scientific") concept of predictability is intrinsically flawed. Two hunters are in the woods when they suddenly encounter a bear. The bear then proceeds to charge them and the hunters turn and frantically run away. While running away one of the hunters says to the other hunter, "Why are we running? There is no way we can outrun the bear!" To which the other hunter responds, "I don't need to outrun the bear. I only need to outrun you."

                        The stock market simply does not have an "intrinsic value." This concept is a myth. Simply look at the Black-Scholes option pricing model or the Discounted Cash Flow (DCF) method of evaluting equity securities. The most pertinent aspect of both of these pricing mechanisms is the assumptions that must be made. With Black-Scholes it is the risk-free rate. With DCF it is the terminal value. Even the slightest adjustment to these number can produce wide fluctuations in the present value. These methods were chosen as simply a representative sampling. The fundamental point is that is that it ultimately comes down the the judgment of the analyst who is trying to be "more right" than any of the other analysts. (Note: these comments do not apply to simple arbitrage, which is (successfully) more formulaic.)

                        A great example of this is the Asian financial crisis and the "collapse" of LTCM (Long Term Capital Managment) in the late 1990's. Once the unpredictable is made predictable then the unexpected happens, which is predictably the "one factor" that was not considered.

                        Time for a riddle. Whenever you lose something, such as your keys or the TV remote, why is it always (infuriatingly) "in the last place you look?" Because once you find it you stop looking.

                        These are not merely antidotes. A Nobel prize was recently won with the ideas being presented here. I am referring to Richard H. Thaler and the invention of Behavioral Finance, which he discusses in his book Misbehaving. (He talks about the broader idea of Behavioral Economics, but I think his real insight is contained in the more limited idea of Behavioral Finance. I think his ideas about Behavioral Economics takes the insight too far.)

                        So, what does all this have to do with your essay? It appears you used the abstract as a metaphor for the subjective factor and the physical as a metaphor for the objective factor. But I am not sure the human factor can be considered abstractly, which thus changes the objective. But maybe I misunderstood your premise? It was an interesting thesis nonetheless, which obviously spurred many thoughts.

                          Dear Alyssa,

                          This is a systemic look at systems. I enjoyed the essay and part of the reason I liked this work was how it was organized. Ideas were categorized like in the life sciences instead of the instruction manual style of writing Physicists (like me) fall into. What is the smallest amount of information needed to find a pattern and make predictions? How could we determine there is no pattern and we can stop wasting our time looking for a pattern? If we find a pattern can we generalize the function to a whole category instead of a single problem? This reflects the issues presented to science everyday.

                          Sincerely,

                          Jeff Schmitz

                            Dear Alyssa,

                            I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

                            While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability".

                            I hope that my modest results of work will provide you with information for thought.

                            Warm Regards, `

                            Vladimir

                              Dear Alyssa,

                              This is a very high-class piece of work. Your development of this reminds me of the Bayesian approach to statistics, in which expectations and models play a role - not just an objective "probability" out there.

                                Hi Alyssa,

                                and yes I agree, lots of moving parts!

                                "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."

                                To paraphrase Husserl's notion that 'consciousness is consciousness of something' one might say that 'observation is observation of sets of something'? Would an intuitionistic set theory then be a good place to start?

                                "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."

                                What if the observer simply IS their observable world which includes observations of their own and others bodies, and the unobserved remainder is the potentially observable world? The cut would then be between the model's observable world (as a dynamic flux of observations) and its potentially observable world; or between the phenomenal actuality of - and non-phenomenal potentiality for - observational experience. Something like an 'objective world' could then emerge from the observational flux as an abstraction of that flux.

                                I think the 'cut' between observer and world, or subject and object, is just such a philosophical abstraction, and an unhelpful one at that.

                                So in terms of modelling an observable universe, such a universe would by simple definition have an observer at its centre, and there would be no need to separate the two. Much like it's difficult to physically separate a photon emitted from a distant star and its incidence on a retina with the subsequent neuronal stimulations and behavioural outputs ... where's the non-arbitrary 'cut'? The totality of the potentially observable universe is, in principle at least, described by the wave function for that universe, with the flux of actual observations being the ongoing, finite and actual 'measurement' outcome. Is this a quantum computing problem? And does the fact that the observational sub-system can also feed back on the whole system complicate things?

                                "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)."

                                Embodied cognition and Clark and Chalmers' extended mind theory are all part of what appears to me to be an increasingly commonly held notion that the 'individuated, isolated subject/observer' is something of an abstract concept and possibly a dead end path for thinking. Even Everett conceived of his observer sub-system as a physical automaton 'in' its branch world 'in' the universe. But I can't see how this third-person godlike analytic perspective can logically be part of a perspectival model for an observer dependent reality. Cos if we're all Wigner, and God is dead, then who's observing us?

                                9 days later

                                Thank you so much! And I really love Bayes Theory, I'm constantly thinking about how it applies to information theory. I wish I studied it more!

                                Thank you for reading and sharing! I am also glad I do not think in abstract thoughts XD

                                24 days later

                                Hi Malcom!

                                I think these are all extremely good points. I've been thinking about this a lot since I first read your latest response and this is what's been baking in my mind since then:

                                "I think the 'cut' between observer and world, or subject and object, is just such a philosophical abstraction, and an unhelpful one at that."

                                Absolutely. The more I think about it, the more it seems that these "state spaces" only exist WITHIN an interaction between an observer and something else (could also be itself). It reminds me of the old philosophical question of whether physical laws exist independently of objects. In other words, could Coulomb's law exist in the complete absence of charged particles? I don't know enough field theory to find an answer for physics, but at least for biology, it seems that the answer is "no". In biology, evolution acts on populations/genes/individuals/phenotypes that are physically present. Each example of evolution within biology is so dependent on the properties of physically present individuals that it's even become helpful to think of DNA as the "program" that drives the expression of organisms. But DNA isn't an abstract program in some abstract space, much like the laws of physics. Instead, genetic code itself is subject to evolutionary changes because it is a physical part of the evolutionary process.

                                If biological entities were charged particles, then Coulomb's law would change according to whatever spatial configuration those particles are arranged it.

                                So now I'm thinking how it could be possible to map out the complete state space between two generalized interacting individuals. So far, I think it's been successful to do for systems of humans and physical space, but what about cases of virus-bacterial host systems?

                                Hi Chandra!

                                Thank you so much for your comments and reading my essay! I like your point about information bottlenecks preventing us from having complete information. I think that humans are really good at inventing tools to access additional information that we couldn't reach otherwise. In fact, I think that's what makes humans quite special.

                                Do you think it would be possible to say "how much information" a person could possibly hold in their brain? Like, if we had a complete map of the neural connections in a brain, could it be possible to say "a human brain can store X number of bits, maximum?" We can do this for computers, but I think it gets more complicated for real biological systems because a "bit" of information can mean so many different things. As an example, language has many "layers" of information. There are letters, words, sentences, but also stories, cultural references, inside jokes. Performing Shannon-based information measures on words would look much different than doing it on letters, which would be different than doing it on the cultural reference space, etc. All of these layers make it seem so difficult and I'm wondering if there's any way to "flatten" it.

                                Hi Pavel!

                                Thank you so much for reading my essay! I like your points very much, especially about the feedback mechanisms. I definitely think they are computation. One of my favorite things about humans is how we raise children. Parents spend a ton of energy and resources into raising children to be effective members of society. This is in contrast to "feral" children who were not raised by other humans, or suffered unimaginable abuse to the point where they cannot function at all in society. To me, this says that the role of parents/guardians/caretakers is to "program" children so they can be successful adults, but they are actively intervening on a child's behavior. Parenting is almost entirely a feedback mechanism that results in some kind of "programming."

                                Cheers!

                                Alyssa

                                Hi Jason!

                                Oh, that's a great point about N vs NP, thank you for pointing that out! I will correct that!

                                And these are all extremely good points, all of which are crucial for this topic. After thinking about these for quite some time now, I feel more comfortable moving away from the idea of abstract vs. physical and going to the "other side" of the Church-Turing thesis. Turing machines are a very useful abstract tool, but it is only one way to understand a system. But rather than focusing on lambda calculus, I'm now more concerned about where these spaces for abstractions "come from."

                                Here's what I mean. I can think of a Turing machine in two ways. One is the configuration of the abstract machine (the lookup table) and the other is the states that it produces by running it. As it runs, it marches from one state to another state and given all possible initial conditions, one could map out the entire state space and the "legal" transitions between states. Because of the Halting Problem, it is impossible to look at an abstract Turing Machine and decide whether or not it will eventually halt. It is like looking at a lookup table and asking if it is possible to know some properties of the resulting state-space map. I think the reason this is the case is the entire Turing machine system is described in two ways: A lookup table and a state-space map. In that sense, these two "languages" to describe the same system are encoded in two different spaces of their own. There's the state-space map space, and the lookup-table space.

                                But are these two spaces the best way to represent a dynamical system? The Church-Turing thesis says this representation is equivalent to a world where programs and data are really the same things. But are there other possibilities?

                                This gets extremely difficult because it's essentially asking if there exists an "optimal" description for a system, which suggests some kind of objective reality. But I assert that for at least trying to understand biological systems, "optimality" makes no sense without the context of an observer.

                                So now I'm thinking that state spaces only exist within an interaction between something and something, like an observer and a dynamical system (possibly another observer or even itself). The state space of all possible interactions between me and my cat depends entirely on our current physical configurations at that exact time. Without ears, I couldn't hear him meow, although I could see him do it if he was in my view. Without feet, we would need to invent a new way to play.

                                Going back to the stock market, I think your points are absolutely correct. For an individual broker, their goal isn't to create a perfect model of the financial world, but rather to make a slightly better prediction than everyone else. I am mostly comfortable thinking that the human factor, just a human by themself, is entirely physical, but then the abstract is only defined by the human's interaction with other "stuff."

                                I like the old philosophical question: "Does Coulomb's law exist in absence of charged particles?" I don't know enough field theory to answer this for physics, but for biology, I think the answer is a resounding "no." Conservative/liberal politics do not exist without humans, species cannot exist without niches, and fish cannot exist without water. I think the notion of abstract exists within interactions.

                                Hi Jeff!

                                Thank you so much for reading my essay! I'm very glad you enjoyed it. I really enjoy your questions, I'm constantly thinking about them too! I also add, how do our tools and physical abilities allow us to find these patterns? It would be quite difficult to find patterns in chemistry and thermodynamics without a thermometer, and it would be difficult to study astronomy without telescopes. This tells me that our ability to find patterns and extrapolate depends a lot on our ability to access that information. I like to think of the two extreme limits where God is an observer who can observe all possible things, and also the other limit of being a tiny particle that lives in a tiny box for all of eternity.

                                Cheers!

                                Alyssa

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