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A Complex Meeting
I had the fortune of getting coffee in the city with one of my best friends from college over the holidays. A simple meet-up made rare and especially delightful due to his infrequent flights to New York from New Mexico, where he works as a researcher at The Santa Fe Institute. Initially unfamiliar with the institute's work, I came to understand the interdisciplinary studies conducted there via a book my friend recommended called Complexity: A Guided Tour by Melanie Mitchell, who happens to work at the institute. For those unfamiliar, what ties all work in complexity theory together is the importance of emergent structure from the interaction of individuals.
Structured Notetaking
The research in complexity set me off and I began raving about Obsidian, a notes app I had recently begun using after meeting a D.E. Shaw trader at the Stock Slam sessions in NYC, which are worth a post about them in and of themselves. To avoid going on a tangent, see the tweet below for more info on those.
Announcement:
— Kris (@KrisAbdelmessih) September 9, 2022
Please join @moreproteinbars and I for 1 of 3 evenings in NYC in the first week of October.
We are calling them the StockSlam Sessions.
I'll explain the details below but know they are 100% free (although space is limited)
Apply here:https://t.co/OU41w6nJEi
Obsidian is a lightweight note-taking app that serves as a Personal Knowledge Management system. I use the word lightweight because Obsidian is:
- free
- easy to use
- small (380 MB)
- does not overwhelm the user with a billion tabs and features that you can’t even begin to understand how to use.
- [”the”, “ambitious”, “dog”, “drove”, “quickly”, “to”, “the”, “supermarket”].
- [”robot”, “ivory”, “corporate”, “stochastic”, “red”, “keyboard“, “robot”, “ocean”].
Aside from the graph view that shows the web of your connected notes, there is a convenient linking feature that allows the user to create what I like to call his or her own “personal Wikipedia”. My 2 biggest gripes with trying to learn via Wikipedia are citation-needed issues and the endless rabbit hole every entry I click seems to be.
I explained to my friend how I am able to take notes on exactly as much detail as I need including the meat of concepts directly in the note in my own words while providing source and author tags meta-data for further learning and future reference if needed. Giving due credit, my methodology was taken from Robert Martin’s posts on Molecular Notes, with some tweaks and edits to the tag types so the system works best for me.
Emergent Structure
Everything about Obsidian promotes emergent structure, a phrase I first recall hearing in biology when learning of the cellular components that give rise to what we call life. My friend paused me here to speak of ongoing research that lo and behold was focused on emergent structure. To be more precise while still being vague enough to not leak his research paper before an arXiv preprint is available, he is studying individuality. The individual is interesting because it is something we often take for granted. What constitutes an individual? If you find yourself struggling to give a formal definition like I was, it’s probably because you are making an implicit assumption about what an individual really is.
As we sat on our stools discussing the a rigorous definition of an individual, I began to realize the intricacies of his work. Very rarely are we actually working with individuals. Let us look at a subset of subjects belonging to the field of Complexity: the natural sciences.
For a long time, we thought atoms were the fundamental unit of matter. Then came the subatomic particles — protons, neutrons, electrons — but further still, there exist quarks making up the protons and neutrons. In the study of chemistry, we learn how subatomic particles combine to make different atoms called elements which combine to make molecules, some of which are essential to life. In biology, one such molecule is ATP. ATP along with many othe molecules keep our cells running, which collectively constitue our organs which themselves depend on one another to keep the organism they belong to alive.
Note the whether or not something is an individual is not binary, because almost everything can be broken down into further sub-levels, and influences by other factors that may or may not be immediately apparent at each level. he degree to which we can understand how something “works” by understanding how related factors “work” varies tremendously. Take for example training a regression model to predict the price of an apartment in NYC.
Designing a good model for tasks like this is a data-driven way to try and answer the question “What makes the value of an apartment, the value of that apartment?”. In a typical regression model, this means learning the weights of the features that minimize the chosen loss function. We could view a house as an individual entity, and perhaps you will see them referred to as one when Bloomberg reports on house purchasing activity, but really a house is a complex system — a function of many other variables, which themselves may be functions of other variables, leading to spurious correlation. Consider an urban neighborhood and the Broken windows theory: is it the case that visible signs of crime encourages further crime (causual relationship), or is simply that visible signs of crime (which are frequently a variety of minor crime i.e. vandalism, public drinking, fare evasion) are correlated with more serious crime (i.e. theft, drug trafficking, murder) in the area? Thus, complicating the question of what makes an entity an “individual” is whether the entity we are measuring is caused by the features we have selected or rather just correlated.
Markets and Individualism
Markets are some of the lowest signal-to-noise (SNR) environments people operate in. The severity of low SNR ratio environments, and thus high volatility environments, is even excaerbated by strategies employed by some hedge funds. Why is this? Take for instance your typical Long/Short Equity fund, where changes to anything in production would take weeks or not months to observe and try to determine at a statistically significant level that the new full model is better at predicting the target variable than the prior reduced model.
Returning to the theme of emergent structure, market dynamics are a function of traders — be it informed traders or noise traders — and those traders’ actions are a function of the dynamics of other traders. Quickly, this becomes the “Guess 2/3 of the average game”, which I mentioned previously here in my review of Fooled by Randomness by Taleb. Having mentioned such correlation measures and game theoretic ideas, I pose the question of individuality again but worded slightly differently: who makes an individual?
Of course we can get a better idea of who makes an indivdual by including more and more variables from the system in which they operate, which is what happens when growing the number of parameters in model and using only R-squared to choose a best-fit model. I brought up the F1 score in the context of binary classification to my friend, which can be extended for multi-class classification .
Essentially, the F-Test is useful in deciding whether or not to reject a reduced model (fewer explanatory variables) in favor of the full model (more explanatory variables). Still even with all these fancy statistical tests, we are obtaining a correlation relationship between our predictor variables and the output variable, not evidence of a causal relationship. For that, we would need counterfactual data on the predictor variables obtained by time traveling to the past, changing just one of the predictor variables, and then re-measuring the fit of a regression model. We could call this an altnerative history or, in the case of time-series, an alternative path. The importance of alternative paths is expanded upon by Nicholas Taleb in Fooled by Randomness, and is a prominent pillar in his theory of Black Swans and how the market consistently misprices exceedingly rare, severe loss scenarios. The essense of his argument is that people (generally speaking) attribute events presently happening to events that happened at some preceeding time on the basis of correlation. That is, people assign causation to correlation. Why people do this is out of the scope of Fooled by Randomness, and I will leave it to the reader to ponder. if I had to guess, it would be human tendency to crave understanding of unexplained and/or mysterious phenonema. This could explain why conspiracy theories are able to gain mainstream traction, and why so many different theories arise from a limited set of undisputed for-a-fact information.
