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quadrays in a cube (philosophy of mathematics)

My paragraphs here are aphoristic in the sense that I jump around quite a bit, but then keep coming back to certain themes. The paragraphs somewhat stand on their own. I’ve been inspired by several role models here, including Norman O. Brown in Love’s Body, Nietzsche in Will to Power, and Ludwig Wittgenstein in Philosophical Investigations. Plus we live in the age of hypertext, wherein non-linear browsing is somewhat the norm. We tend to think in “deliberately non-straight lines” these days, to cite one of the Bucky Fuller memes.

I watch a lot of Youtubes, extending habits I’ve cultivated over a lifetime. At Firestone Library, at Princeton, I’d dive into hard-to-find newspapers and magazines, as well as microfilm, to dig up stories and test my research skills. The process is somewhat “non-linear” in that once I’ve accessed a specific collection on a certain floor, the efficient thing is to browse adjacent sources (neighboring books on the shelf). “Who knows when I’ll get back here? Now is the time.”

“Browsing” was the name of the game (not an idle activity, but a deliberate kind of reading), and this was before “web browser” had entered the vernacular. I dreamed of hypertext back then, but Tim Berners-Lee had not yet open sourced the protocol we would all end up using. Computer networks existed in those days, but not yet the web. I learned to program in APL from a terminal.

Just this morning, I was watching an interview with professor Hillary Putnum. He was talking about the philosophy of the mind, and how what we mean by “mind” has no real equivalent much before Descartes. Aristotle’s “psyche” included digestion and reproduction, according to Hillary. The question then arises: will what we mean by “mind” in our day and age, gradually morph into something else? I think of Gregory Bateson’s Steps to an Ecology of Mind.

If academic philosophy is really about ethics, or has to be, to preserve its identity as philosophy, which is what Hillary Putnum claims, then the question becomes “what is ethics?”. A tendency I see in philosophical debates is to carve out some safe and not very controversial topics to keep coming back to, in order to practice justifying this or that position in ethical terms. What have philosophers written about Nine Eleven (as we call it)? What are the ethics around sending US-branded soldiers to Arabia (today’s news)? Should we leave it entirely to congressional representatives such as Tulsi Gabbard to make that call?

How is Machine Learning, especially Deep Learning, going to alter how we think of the mind? AlphaGo has learned to play a few games really well by this time and the raw input is always the same kind of thing: snapshots of what a pro would do in such and such a situation. One basically registers before and after pix, saying “in this situation, these count as good moves, these as bad moves”. The objective is to get a reflex or response mechanism that recognizes what counts as a good move, or next action, given such and such a situation. How are humans that much different?

I could say John Dewey was influential on my thinking in the following sense: given a library I’m using is organized by the Dewey decimal system, and given I’m prone to browse in nearby books, the physical arrangement of books by subject is going to help determine what I access next.

I connect Nine Eleven to the JFK assassination in the following way: the official theories of what really happened, as advanced by various media, are based on long shot unlikely plans actually panning out. If you had been told of the plans in each case ahead of time and asked to give odds on the plans actually achieving their objectives, what would have been your assessment?

Would a lone gunman acting alone have the skill and nerve to get off those shots in a public setting, from a long distance, with a crummy gun, and then feign innocence? Would the hijackers of those jets have any prayer of actually bringing down those buildings? Perhaps turning those giant skyscrapers and WTC 7 into piles of rubble was never the plan? According to the official theory, we don’t actually know if that was the objective, but looking back, we would have to say, if it was, such an outcome was unlikely.

What links Nine Eleven and the JFK assassination together is that those who count themselves as skeptics (called “conspiracy theorists” by others) are in the business of seeking what to them appear less far fetched explanations, i.e. they look for plans less likely to fail, meaning more shooters in more locations, in the case of JFK, and charges already set to go off in the buildings, in the case of Nine Eleven. These skeptics believe they’ve found evidence for their alternative theories, in both cases.

My view is it’s ethical to express skepticism regarding the so-called official explanations of these events and I have no problem with people having opposing views. Sometimes a counter objection is raised, that out of respect and empathy for those seeking “closure”, doubts should never be raised. Yet we know that squelching doubt, including the public expression of doubt, is a path towards oppressive authoritarianism. My inclination is to resist going down this path.

The same goes for people expressing skepticism regarding whether the moon landings actually happened: I encourage skeptics to exercise their freedom to express doubt. In all of these cases, I believe we are dealing with empirical questions, meaning any theory is in principle falsifiable. We’re not arguing about terminology or tautologies, which philosophers distinguish from empirically true or false statements.

I currently believe the Apollo moon landings did occur, that Oswald never fired a shot at JFK, and that WTC 7, at least, was brought down with explosives. I could be wrong in each case, and I should be willing to change my beliefs based on the evidence presented to me. I respect the right of others to say I’m likely wrong in my beliefs, based on their own understanding.

Wittgenstein, in his later investigations, puts emphasis on the phrase “now I can go on” in the context of someone seeking new understanding. I may be stumped about what next move would be a good one. I don’t understand the number sequence for example: 1, 12, 42, 92… what’s next? I don’t see the rule, and might say “if I only knew the rule, I could tell you the next number”. Then you tell me the rule: assign each term a number in sequence starting from 0 (0, 1, 2…), then multiply the term number by itself, then by 10, add 2, except term 0 is 1 (not 2).

If the term number is 1, for example, multiply 1 by itself to get 1, then by 10 and add 2 to get 12. If the term number is 2, multiply 2 by itself to get 4, then multiply by 10 and add 2 to get 42. “Now I can go on!” The next term after 92 would be 162 (10 times 4 times 4, plus 2).

H.S.M. Coxeter, the geometer and mathematician, thought Bucky Fuller, the generalist, should get some acknowledgement for coming up with the above rule, which gives the number of balls in successive layers of a cuboctahedral packing, as shown below:

Sometimes people get uncomfortable when they see official views being questioned. People who call themselves philosophers, or who claim to think philosophically, have an opportunity to weigh in here. That’s what I’m doing. I’m encouraging skepticism, but also encouraging recognizing when debates have strayed from arguing about something provable or falsifiable.

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