Wittgenstein, Occam, and the Scientific Method

(3.24) If a sign is not necessary then it is meaningless. That is the meaning of Occam’s razor.

and again,

(5.57321) Occam’s razor is, of course, not an arbitrary rule nor one justified by its practical success. It simply says that unnecessary elements in a symbolism mean nothing.

But also,

(5.453) The solution of logical problems must be simple for they set the standard of simplicity.

Thus, the scientific rationalist extrapolation of Occam’s razor (that simpler explanations for natural phenomena are superior to more complex ones) has grounding if the relation between mathematics and the natural world obtains. However, with even a small dose of Humean skepticism, this relation is impossible to know for certain: at best, the relationship between mathematics and nature can be a statistically significant conjunction, but nothing more. For this reason, Wittgenstein says,

(6.363)  The process of induction is the process of assuming the simplest law that can be made to harmonize with our experience.

(6.3631) This process, however, has no logical foundation… It is clear that there are no grounds for believing that the simplest course of events will really happen.

Empiricist approaches to scientific knowledge are built on rationalist foundations. At best, the natural laws we invoke in our mechanical descriptions of the universe are “forms of laws” of causality.


Mathematics and Aesthetics

The following is an unfinished, obtuse, and probably bad post I wrote at the end of last semester. I hope to revise it soon—but the gist of the idea, that mathematics is not an exercise of “pure reason,” but it heavily relies on the mathematician’s “aesthetic” sense. This sense is still rational, but not explicitly logical.

I’ve often thought of mathematics as a mere exercise in necessity. Something about the pure logical foundations of higher math—the way that theorems and propositions of such significance were supported ineluctably on pillars of axioms reasoning that seemed so indubitable as to be tautological—something about that computerized, Spock-like ideal of ironclad reasoning attracted me. But I’ve been somewhat mistaken.

Now that I’ve tried (and more often than not failed) to do mathematics, I’ve begun to think it more proper to say that the material of mathematics is logic: without consistent, logical relations between concepts, mathematics would not exist. But a thing’s material reality is, at best, only half the picture. Logic can limit the number of things you can say that are useful in discovering or describing truth—by guiding the statement of valid claims and restricting the statement of invalid ones—but it does not tell you with necessity what should be said, what should be claimed. If logic were the only guiding principle of mathematics, Euclid had already finished his elements as soon as he formulated his axiomatic definitions of lines and points and planes. Since an ironclad and ineluctable chain of reasoning connects the definitions of Euclidian geometry with the Pythagorean theorem, to state the (reduced) former thing is, in a sense, to state everything. This level of reductionism is akin to thinking that you are a carpenter once you know what wood is, or that to look at a timber forest from 50 years ago is to have seen every boat, home, and kitschy bear statue that would be made from it.

But this is obviously not the case. Just as a kind of formal principle is needed for carpentry to be carpentry, Mathematics itself needs a formal principle, a principle of what should be said, not merely what can be said. And, in my limited experience with mathematics, these formal principles seem to be largely aesthetic. Why should points and lines be constructed so as to join three of each of these elements and make a triangle, and to further compute the relations between the side lengths of the figure? It is either by a principle in the mind of the mathematician to represent the triangles he sees in nature or, else, by an exploring, pioneering, experimenting principle in the geometer to sound the depths of what can be constructed within the possibility space that founded on Euclid’s axioms.

Not only this, but all development in mathematics seems to stem from exploration and attempts to build bridges to these explorations with the necessary building materials of consistent logical statements. It was the futile attempts of ancient geometers to square the circle that clued us into the existence of mathematical concepts inaccessible by geometric construction.

There is also an aesthetic principle of symmetry—in the sense of both true mathematical symmetry and of a parity and evenhandedness and fittingness—that rules mathematical development in addition to those of exploration and a drive for natural representation. The basis of most mathematical conjectures is that a theorem or principle that applies to one type of space or one region of consideration should hold for another space or region deemed similar enough. Even though logic in no way occasions or guarantees the extension of particular truth claims to other spaces, such a belief is the default position of the mathematician when conjecturing, and this jumping off point allows him some formal handhold onto the sheer wall of necessity. [To use another analogy, he can see whether the brick he has picked up actually fits into the wall he is attempting to build.] For example, in topology, the functioning of derived space topologies—in quotient-, product-, and subspaces—is distinct, and there is no necessary reason that these three spaces should function similarly, but what we do know about each of these derived spaces is based off their similarity and correspondence: that connectedness is preserved by projection mappings and identity mappings alike, [there are more examples here which I have not yet listed], etc.   

My concept of aesthetics likely has a definition (or the beginnings of one) that begs the question: aesthetics are concerned with formal principles and relationships between things that are not merely necessary. Such relationships are much easier to see in terms of a superstructure instead of in single propositions itself. The content of 2+2=4 is mostly a matter of necessity. [I hope to develop this idea a bit more with revision]


Rhetorical Nihilism, Tyrrany, and Memes?

In the early days of his campaign, it was conceivable to read Donald Trump like a book with an unreliable narrator. The content was absurd & offensive, but the absurdity was strangely calculated so that the act of being offensive still carried rhetorical value: Trump’s offensiveness wasn’t captained by personal conviction or robust political philosophy, but was reactionary. Trump said precisely the things which would provoke backlash from anyone remotely left-of-center: minorities aren’t an “economic burden,” they’re “rapists.” Hillary doesn’t merely “lack integrity,” she should be “locked up.”

It worked.

The “provoking-qua-provoking” (i.e., forcefully stating beliefs he may not even have held), was the very source of Trump’s electoral power. He perceived that people were annoyed with the monotony of “political correctness,” so he offended and offended—even letting his offenses contradict one another. It was doubly-effective: offensiveness also got him the most airtime of any 2016 candidate, and airtime directly correlates with public support. Target those moves at swing audiences (Pennsylvania, etc.) and you’ve got yourself an election.

The Alt-Right had it First.

The same tactics were already being developed in the growing alt-right movement, a mutated political ideology which incubated in dark corners of the Internet, where casual holocaust jokes and anonymously-shared memes were infused with 1) male bravado and 2) honest disgust at the ineffectiveness of American politics. The internet had cheapened all talk, and unbreakable cultural myths practically made debate meaningless. Joining the alt-right, which claimed to both explain and rise above fruitless politics, yielded a sense of enlightenment. Even freedom from futility, Hope.

Memes—more properly memetics, the ideology behind them—are not incidental to the alt-right (nor American culture at large). They define the alt-right’s conceptions of society’s problem and the rules by which to fix it, as follows:

  1. Standards of “political correctness” (support for minorities, political & religious tolerance, &c.) have been co-opted by virtue signaling.
  2. Thus, standards of “political correctness” don’t exist to be truthful; instead they exist to perpetuate themselves in culture. In other words, “being PC” is a meme.
  3. The reproduction of this meme leaves its host (namely the American public) unable to think outside the “politically correct” box. This causes an inability to absorb any ideas which do not adopt the strictures of political correctness, thwarting discourse.
  4. Since memes operate by the rules of natural selection, the only thing which can kill a meme is another meme which catches and reproduces faster (is more “fit”).
  5. Therefore, to remove the memetic roadblock to public discourse, we must destroy “political correctness” with a rival, fitter meme.

This formulation of the problem is incredibly appealing. Thus, the alt-right co-opted Pepe, uncorked the finely-aged bottles of racially-insensitive jokes and misogynist opinions, and harnessed the power of backlash. Since the very point of the rhetoric was to prod those who hosted the “political correctness” meme, the outrage of those people only stoked the flames. A self-amplyfying, feedback loop began.

Trump Saw an Opportunity for Power, Not for Cultural Renovation.

Trump, seeing the unrest, frustration, and dissatisfaction, spied opportunity. As a businessman, he didn’t care about political philosophies, but merely about value. Power is valuable, and sometimes even lucrative. There was a power vacuum in the presidency following Obama, and the skill set needed to fill the vacuum was precisely Trump’s: marketing.

But now, now that the marketing campaign worked, what does he… do?

The answer is simple: exactly the same thing as before. You market, which for Trump means saying exactly what is desired to the people who want to hear it. (Cf. Evangelicals at Liberty University, and Trump’s use of “Two Corinthians.”)

The point has been accomplished. Trump got power, and he can continue to exert enough control using the same tactics. The only thing which is of concern now is losing power. Sure, he’s relatively safe as president (impeachment proceedings are still rare and inefficient enough that he might weather them), but that all depends on his relations with the public. There’s still some standard of decency which must not be crossed. He nearly hit it with Charlottesville.

That explains why Trump fired Bannon. In the aftermath of last weekend, Trump cut it a little too close to the critical mass of offensiveness which would genuinely tip public opinion. As ardent as white supremacists are in supporting Trump, they have zero—nay, negative—electoral power. He can’t stay in power using fringe groups alone. He must remain painfully tolerated by the establishment until his 4 years are up. So, in an effort to save face after his double-talk on Charlottesville was too agitating, Trump dumped Bannon, the most controversial and alt-right-associated member of his cabinet. That’s scapegoating (another memetic tactic): it creates an illusion that Trump’s administration has been purified, and it creates a independent object (Bannon/Breitbart) which will absorb public hatred.

So Here’s the Extant Danger.

Trump is a jester. In the classic sense. He is not afraid to speak literally meaningless words—emptied of meaning through self-contradiction—because it pleases disparate groups of people and maintains power. However, in front of the backdrop of a perversely democratic* society, Trump is de facto fulfilling the role of the tyrant. “Tyrant” there isn’t just a synonym for “bad president, me no like.” Here’s how Plato describes the genesis of a tyrannical leader and society:

What about when the possessions of his father and mother give out? With that great swarm of pleasures inside him, won’t he first try to break into someone’s house or snatch someone’s coat late at night? … [E]rotic love lives like a tyrant within him, in complete anarchy and lawlessness as his sole ruler, and drives him—as if he were a city—to dare anything that will provide sustenance for itself and the unruly mob around it. … [If the mob] chance to live in a time of peace and quiet, they’ll remain in the city and bring about lots of little evils. … [And] when such people become numerous and conscious of their numbers, it is they—aided by the foolishness of the people—who create a tyrant.

Republic, Book IX

Trump isn’t consciously being tyrannical (if such a thing is possible). But his key tactic in governing is the textbook definition of tyrrany: supplying words, funds, power, “anything that will provide sustenance for [himself] and the unruly mob around [him].”

But notice the last line. It’s on me. (And you. And our neighbors.)

The essential premise of the alt-right’s political engagement—that of memetic thinking, which has spread only with the modern cultural phenomenon that is the Internet—is that rhetoric has value, but no meaning. All opinions are jokes, because all opinions can and will be contradicted as needed. Self-consistency, and with it integrity, is jettisoned. The only virtue is a kind of non-conformity, a kind of brash and brutal honesty that, ironically, simply has nothing to say. This rhetorical nihilism is antithetical to any sort of genuine political discourse, and needs to be refuted. Memetics drives the wedge deeper, and splitting the log won’t solve the problem.

The alt-right adopted offense for a subversive purpose, and in the process have constructed a cultural peninsula for white supremacists and neo-Nazis—the ones who really believe the ideological horrors which alt-righters merely joke about believing. Their nihilism is what allows the bright-eyed and vile idealism of the extremists to flourish. The alt-right, in turn has already surpassed the intended limits of Trump’s opportunist joke by believing it to have cultural value.

So, what will I try to do?

  • Reject the dialectic of memetics. I want to remind myself that there’s more to life and truth than surviving and spreading. I think that looks like having a warm and joyful heart toward my peers and the institutions I’m a part of.
  • Respond with a cool temper. I’m giving up Facebook comment wars, and I’m  putting myself on guard against scapegoating. As a child of the internet, these societal problems have an efficient cause in my heart.
  • Stop virtue signaling. Sharing this on Facebook probably seems like I’m negating myself here. But I’ve been one of those idiots mired in endless shouting matches on the internet. I often select who I talk to and befriend by the cultural (political, religious, etc.) phenomena they identify with. Putting this post here is my attempt to reach outside my echo chamber.
  • Think before I joke. My words are more than mere sounds, and actually mean what I think they mean. I want to add constructive contributions to conversations rather than try to get a quick laugh.

I would love responses and critiques of this perspective from anyone who reads this. If you can’t contact me via Facebook or the comment section, my email is rsquared.reynolds (at) gmail.com. Let’s dialogue about where America, politics, and the Internet are—and how to better them.

* This goes back to Plato again. To him, Democracy wasn’t a positive thing. Instead, it was a far-devolved point of social affairs where the only political and societal value is freedom. In Plato’s estimation, it is “democracy’s insatiable desire for” freedom that is the very mechanism of its destruction.


The First (and Last) Annual Reynolds Collegiate Review

So, I get a lot of college mail.


Like, a LOT of college mail.

And it comes in envelopes.


A LOT of envelopes.


With such a preponderance of collegiate marketing, I decided to hold the First (and Last, since I’m a senior this year) Annual Reynolds Review of College Mail (Uncensored Snarkiness Edition).


I took the PSAT. And you know that little bubble where they ask you if you want to participate in the “Student Search Service?” Yeah? Well, I filled that out. And then every time I got college mail after that, I put it in a box. Finally, on October the Fourteenth, Anno Domini Two-Thousand and Fourteen, when I felt like it, I poured said box onto my bed and sorted out the envelopes from the flyers from the letters. The award categories were determined by the most cynical thought that came to my mind while performing said “sorting.”


And the winners are…

“Most Likely To Deforest a Small Latin-American Country”

Winner: UChicago. In addition to sending me two viewbooks and myriad little postcards displaying their obvious affection for my intellect, the University of Chicago also managed to send me a 4 foot by 3 foot poster of Chicago.



The “Useless Postal Billboard” Award

Winners: all of the following colleges who sent me full size envelopes inviting me to apply—online.


Yep. Absolutely no paper applications included whatsoever. Merely oversized envelopes with two sheets of paper inside telling me to go apply on the internet. (+500 GreenPoints)

Most enigmatic was the mailing from the Colorado School of Mines, a school I just found was not made up and not only attended by dwarves.

Runner up for the UPB Award: University of Minnesota, which somehow was able to fit the following poster in the mail:


Seriously, I don’t even know how it got to me. It’s way bigger than the size of my mailbox. I’m guessing they either employ wizards or bribe the postal carriers.

“Making-Me-Feel-Intellectual” Award

Winners: all of the Ivy League universities that sent me mail.


I got mail from Harvard, Yale, Princeton, Cornell, Brown, UPenn, and Columbia. (And I got viewbooks from Harvard, Yale, and Princeton, so I’m basically as good as accepted.) The only college that didn’t send me mail is Dartmouth. Well, same to you, Dartmouth. And I will not perform surgery on your oral lacerations once I become a doctor after earning my medical degree at Harvard, Yale, and/or Princeton.

***UPDATE*** I received a letter from Dartmouth inviting me to apply! One catch: the deadline had passed. Oh, and the letter was postmarked in November and I received it in January. Thanks.

“Most Incomprehensible Page Layout” Award

Winner: Soka University, which sent a viewbook containing the following beauty:


Yes. That is two completely different paragraphs, interspersed— line by line—between each other. In all caps. However, if you read it straight through, it’s great practice for acting schizophrenic.

“Most Flattering College Mailing” Award

Winner: University of New Mexico, which decided to send me my diploma early.


…with my last name spelled horribly wrong. I am thinking of framing it.

(To be fair, this was technically my fault. Did I forget to mention that when I took the PSAT, I accidentally put a “Q” in my last name rather than an “O?” Yeah, well, they’re only one letter apart, and they were both capitalized and the bubbles looked really similar, OK? It’s still funny, though.)

“Viewbook Title That Made Me Giggle the Most” Award


Winner: “Limitless Swarthmore,” by Swarthmore College. It was a very swarthy book. Yes, very swarthy; though less swarthy than I expected from an institution which promises to swarth more than the average college swarths.

“Surprisingly Concise and Efficient” Award

Winner: UPenn. They only sent me one mailing (that I saved, at least), and it had all of their important information packed into the letter and on the envelope itself.


I don’t actually have much snarkiness here. I just really appreciated that this college didn’t send me copious correspondance.

The “Giving-Me-Every-Single-Brochure-They-Had-In-Their-Admissions-Office” Award

Winner: Williams College.


They sent me five brochures and a letter in a paper folder. It reminded me of what the developer gave us when my parents bought our house, except with fewer forms claiming freedom from liability when the various structural flaws take effect. Hopefully Williams College doesn’t also go bankrupt within six years.

The “I Might Actually Use This” Award

Winner: Reed College. They sent me a periodic table for no apparent reason.


And it’s actually a good-quality periodic table, too. I mean, look at all the significant figures in the atomic weight of Fluorine!


TEN? TEN??? The table in my school’s chemistry lab doesn’t even have that many! (OK, chemistry nerd rant over. But it’s three-hole-punched for putting in my notebook.)

The “Most Blatant Lie on a Front Page” Award

Winner: Carleton College.


It says, “This Is Carleton” in big letters, but right below it in the fine print, it gives the man’s name as Ben. Wow, at least try to make your deceptions believable, Carleton College.*

The Final Verdict

Once it was all done, I was left with two things. A thirteen-pound box of brochures:


And a ream of new scratch paper for my scratch paper drawer (courtesy of hundreds of colleges):


My main point in all of this: college marketing is wasting a crapload of paper, especially since much of it can be (and is) done online. Send me a viewbook, maybe—if I request it. But otherwise, just email me. I’ll find out about your college soon enough.

*Please understand that this whole thing was completely sarcastic. Uncensored Snarkiness, remember? That also goes for all of the other colleges that I “insult.” (And if you are an admissions officer from one of those colleges, Hello! I would actually be honored to attend your institution! And please don’t incinerate my application!)