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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