Not even in art

As many of you may have noticed, I’ve had a bit of an obsession with pottery as of late. For the past three weeks, this has been exactly the case.

Last semester, during the Art History final, we obviously weren’t actually taking a final, so we convinced Houchins to let us try to use the wheel. Obviously, this didn’t go anywhere. After the AP test (for the two people that took it), we again had nothing to do in Art History. Instead of leaving the class every day, I eventually decided that I should try to get Houchins to teach me how to use the Potter’s wheel.

The first, and quite frankly, hardest, step of throwing pottery is centering the clay. This step is surprisingly hard. First, one presses the clay on the bat (the part that spins), making sure to seal the edges to the bat, which, if not properly attached and sealed, will cause the piece to fly off at the most inopportune times and force one to start over. Then, spin the wheel up to full speed, and try to push the clay center with as steady of a hand as possible.

This task sounds simple; what is to stop one from simply pushing the clay inwards until it is completely circular? The answer here is that it is extremely difficult to hold one’s hands exactly steady. When trying to push clay into center, if one’s hands aren’t completely steady the following process occurs: first, the clay will have some places where it isn’t round; the force of the wheel spinning pushes these against the hands. Then, the beginner reacts to this force, pushing back against the clay. However,  as one reacts to the force of the clay, the wheel has already turned to the other side, where, as the clay is skewed towards the other side, offers even less resistance. As such, the clay is pushed even more off center.

I don’t have any pictures of this step (as it’s not very interesting), but after I managed to learn that step with some consistency, I began to learn to form basic shapes.

This is the first thing that I threw. It’s an attempt at a bowl; the sides and bottom, however, are exceedingly thick. The following day, I made the much better attempt number 2:

To form pottery on the wheel, one centers the clay and shapes it into a roughly square cylinder (height=diameter); then, one presses into the center until the desired depth is reached. Next, one inserts a finger into that hole and carefully pulls the sides out and up. This thus forms another challenge: on each of these steps, one must be careful to go slowly, or some aspect, such as the thickness or height, may be off center; these imperfections accumulate, until a piece is irredeemably off center, after which one’s only option is to throw it away and start over. These pictures document only attempts that made it off the wheel; things thrown, but immediately discarded, were not counted, and occurred with great frequency especially towards the beginning.

Here is my third attempt at making a bowl, and a successful one. I neglected to take a picture of the bowl after it was thrown, but this is a picture of it after trimming. After a cup or bowl is thrown, it is then cut off the bat, and mounted upside down on the wheel; cutting tools are then used to precisely shape the bottom to form features such as a lip, grooves, or more importantly, a perfectly centered base. As you can see, the bowl, after trimming, is mostly circular, although not without imperfections.

I believe that, at least with low fire clay, making cups is more difficult than bowls; when pulling up clay, it tends to go outwards as well, thus naturally forming a bowl. When throwing a cup; one must overcome this to keep the edges straight up. Of course, as with any complication, this introduces an additional place to mess up and get off center. The first cup I made (pictured above), was discarded during trimming because it was far too much off center.

This second cup, on the other hand, was acceptably centered, and made it to completion, complete with a handle (pictured here upside down, because the handle was not yet completely dry).

After successfully making a cup (with, as you can see, pretty thin walls), I went back to try to make a similarly circular and thin bowl.

And finally, a smaller cup:

In addition to these four, I also made a pencil cup, bowl, and another cup out of high fire clay, and finally,  a teapot. In the end, I went way further than I thought I was going to, and actually want to make pottery again at some point in the future, which definitely would have been a surprise to past me from 3 weeks ago.

A speech that I would never give


Often, speeches such as this one feature speakers who have accomplished the impossible; they tell you that as long as you work hard or follow your passions as they did, you will find success. The statisticians out there are quick to note that such speeches should include a disclaimer about survivorship bias: for any given speaker telling you about all the things they accomplished through whatever virtues he peddles, there are hundreds who haven’t gotten quite what they wanted, and, as a result, aren’t the speaker.

The example often presented is that of allied bombers in the second world war. On the surface, it would seem obvious to reinforce the most damaged parts on each bomber; however, as it turns out, and as most statistics students are taught, one should instead do exactly the opposite. One should add armor to the parts on returning planes without bullet holes, since because the planes with damage to those parts must not have returned, those parts must have been important.

This means not just considering what we want to do, and what rewards there are for doing that; I mean that we should also try to keep as many options open as possible. As you’ve probably already picked out your majors, and maybe even planned out classes for your first year in college, you probably have most of this part down. Not to hate on liberal arts majors, but I’m sure even English majors already have potential careers lined up, and if you don’t, I’m sure you already have enough people lined up to tell you to major in something else.

What I mean for this to extend to, then, is the incredibly vague notion that you should just keep backups in mind. If you’re taking math classes, don’t take ‘finance math’ or some other applied math useful only to a specific field you have no interest in; if you have to take some science class to graduate, don’t just pick the one your friends tell you is the easiest, but actually put some thought into which one would best advance your career or open up other career opportunities. If you’re doing something in the summer, by all means take your dream internship, but think about how it will help you advance your goals or what you will do if it falls apart.

For me, that has meant doing a wide variety of things in high school, pursuing universally applicable skills like math and physics, and, in college, will mean taking a wide variety of classes easily applicable to a number of fields from data science to electrical engineering and computer science or even pure math. For you, this should mean maybe paying more attention in that one class you hate on the off chance you decide that you want to move your career in that direction in the future.

In summary, then, I mean that even though college is supposed to be a time to narrow our fields and pursue our dreams, that doesn’t mean we can abandon a wide field of study. We should keep in mind the possibility of a change of plans.

And, on this somber note, I conclude: have fun in college. Just don’t be dumb.

What really grinds my gears?

I was going to talk about what literally grinds my gears — bad meshing, bad alignment, loose housings, excessive load, contaminated lubricant, etc. — but instead, here’s a rant about mathematics education in school. My complaint:

No mathematics is taught in school, and students do not solve any problems.

Let me explain.

First, ask the question: what is mathematics, and what does it mean to solve a math problem? These two definitions are intrinsically linked; mathematics is the posing and solving of math problems. Solving math problems, then, is when one takes a question for which the solution is not known, and finds the solution.

At this point, distinguish between the term solution and answer. An answer to a problem is the exact entity that satisfies its premise; a solution is the process to obtaining that answer. For a problem such as x^2 – 1 = 0, x = 1,-1 is the answer, while

Factor x^2 – 1 = 0 as (x-1)(x+1) = 0. Then, either (x-1) = 0 or (x+1) = 0. Therefore, x = 1 or x = -1.

is the solution.

My point then, is that no problems are solved in school math because for all questions encountered, the solution is already known; only the answer is unknown. If a geometry teacher gives a student two similar triangles and asks them to fill in side lengths from three known lengths, the student surely already knows the solution to the problem, as a similar premise albeit with different numbers has most certainly been presented already in class. Especially with common questions such as this one, the process may have been fully fleshed out in some form of notes.

In this manner, I attribute the general attitude against mathematical aptitude as not some intrinsic quality of mathematics as a whole, but a result of the fact that students don’t learn math in school. All that is taught is basically arithmetic, which everyone hates, including those who love math.

Students never get to see concepts such as rigor and mathematical ‘beauty,‘ despite these concepts being well within the reach of the tools that they are taught. For example, consider the following well-known theorem (Ceva’s Theorem):

For a triangle ABC, for cevians AD, BE, and CF, the three cevians are concurrent if and only if (AF*BD*CE)/(AD*BF*CE) = 1.

One half of the proof (=>) is quite simply as follows:

 Call the intersection of AD, BE, and CF X. Draw a line through A parallel to BC, and extend CF to hit that line at G, and BE to hit that line at H.

Looking at triangles with bases AG and BC, From GH || BC, BFC~AFG => BF/AF=BC/AG and DCX~AGX => CD/AG=DX/AX.

Looking at triangles with bases AH and BC, From GH || BC, BEC~HEA => CE/AE=BC/HA and BXD~HXA => BD/AH=DX/AX.



Substituting for AG and AH, we obtain (CD*BF)/(BC*AF) = (BD*CE)/(BC*AE). Rearranging, the BC term in the denominators cancel, and we get (AF*BD*CE)/(AE*BF*CD) = 1, which is exactly what we set out to prove.

This proof uses a technique — extend two Cevians, draw a parallel, and make similar triangles — simple enough to be easily be independently conceived of and remembered, and uses techniques — AAA similarity and properties of similar triangles — that are mandatory for geometry students to learn. Any geometry student, with enough time to explain, could understand (although not necessarily reproduce) this proof. If perhaps asked to split into groups and solve this problem, geometry students would be solving a math problem.

In this manner, I conclude that students of school mathematics classes do not learn math. Self study, y’all. I recommend Art of Problem Solving.


The students are ready; unfortunately, the teachers are not.

In my current class (Math 409; ‘Advanced Calculus I,’ but really just intro to Real Analysis), the largest group (by specialization) is math teachers.

Exams in the class consist of 7 questions, each worth 10 points. We received 40 and 50 points on the first and second test, respectively, just for showing up. On the second test, 2/7 questions would have been passing.

Different Bad Time, Different Bad Channel

This week, we’re supposed to listen to a podcast, and write about it. Sounds familiar? No, more than that. Sounds dreadful. Thanks, Pratt.

I was going to either follow the same recipe as before (Freakonomics + transcript => ez) or write up some podcast that I already listen to (WAN show, Freakonomics, etc), but instead, I was urged to listen to This American Life. I chose episode 611, Vague and Confused. In this episode, the message — that clear and consistent rule-making is essential to Government — is established as an important consideration in current events int he prologue, and then presented in two stories.

Anyone who has been paying attention to current events should be more than aware that inconsistent government is extremely harmful not necessarily in its effects, but in the fear of its potential effects; between Muslim bans and deportations, Trump has consistently and clearly demonstrated his commitment to generating inconsistent and unclear policy. As such, the effects of vague and confusing rule need little introduction. From here, though, instead of repeating national news, the podcast moves into small, random, and, in the first case, odd samples of American life.

In the first section, This American Life describes an island, “Niihau,” in Hawaii that I had to look up, which is portrayed as basically North Korea. The people there all say it’s paradise, where everything is taken care of; the people who aren’t there speak much less highly of it, complaining of arbitrary rules and cases of people being kicked off the island for no good reason. Information is bad, and reports about the island range largely — one source cited says the island has a population of 25; the island’s ‘management’ claims a population of 125. I’m not sure what this teaches; if anything, it’s just a strange thing that exists in Hawaii that would be an interesting conversation starter. The sources they cite as evidence for an inconsistent and arbitrary government largely come from disgruntled “expats” (again, going with the assessment that the island is a de facto state); even, for example, the United States, which we view as having (mostly) consistent and clear rules, has its share of disgruntled residents.

The second section tells the story of a Judge who has taken it upon himself not just to make fair rulings, but make an impression among defendants that they have been treated fairly. The show follows, among other defendants for which the Judge takes extraordinary measures such as getting a Polish translator, then new court date for a Ukrainian translator, just so he can educate someone who is trying to plead guilty, one of the show’s producers. There, the show’s producer is contesting a ticket, which he views as unfair; beforehand, he agreed to plea guilty to a lesser offense, obstructing the flow of traffic, with the prosecutor; however, as he is talking to the judge, in an attempt to get the judge to throw the ticket out, he claims that there were no cars on the road. This therefore renders the plea bargain of ‘obstructing the flow of traffic’ devoid of factual basis, and the producer is forced to accept the original charge. Asked later, the producer answers that while he wasn’t satisfied with the result, he was satisfied that the process was fair, which was the goal all along. Thus, the lesson here is three-fold: first, one should distinguish between satisfaction with the result from satisfaction with the process of obtaining that result; second, that satisfaction with the process — “fairness” — is more important that satisfaction with the actual result; and finally, pay attention in court. Seriously.

Overall, This American Life, in the episode Vague and Confused, doesn’t contain anything too revolutionary or insightful, but still does present a different perspective on the concept of consistency and clarity.

You should totally hire me to be an accountant

Our unfortunate friend owes $2423.41.

As it turns out, doing taxes is really easy. Although I was tricked into reading the instructions, I totally could have done it without reading the instructions (except for looking up the appropriate tax amount in that monstrous table, obviously). Each blank (of which there are few) is very self explanatory, except for maybe the EIC, but even that should be obvious that it doesn’t apply to our example taxpayer.

Of course, this risk is easy to justify because these aren’t my taxes.

Pollock would not have qualified for VASE.


Number 1A, by Jackson Pollock, is complete gibberish. I’ve never quite understood art; that this work is famous — that this painting is considered ‘good’ — further exacerbates that feeling that the visual arts, especially in a more contemporary context, are completely arbitrary. In a sense, it appears to me that the value of a work is determined more by the prestige of its’ creator than any more logical value like aesthetic value or intrinsic meaning, both of which there are none. Pollock’s earlier works such as Mural  (1943), for example, are much more legible than Number 1A:


Here, there are legible lines forming what appears to me as vaguely humanoid, entangled figures. In this earlier work, there exists enough order to derive meaning as opposed to the pure randomness of Number 1A (of which by definition can contain no meaning).

Thus, if anything, Pollock’s Number 1A is famous because of the profile of its’ painter. It is good only because others say it is good. It has meaning only because others find meaning in it. Analysis of Number 1A is akin to recursively feeding white noise into a neural network and asking it to identify meaning: from just a bit of randomness, we get vivid, psychedelic imagery.

Such is “Number 1 by Jackson Pollock (1948),” by Nancy Sullivan.

No name but a number.
Trickles and valleys of paint
Devise this maze
Into a game of Monopoly
Without any bank. Into
A linoleum on the floor
In a dream. Into
Murals inside of the mind.
No similes here. Nothing
But paint. Such purity
Taxes the poem that speaks
Still of something in a place
Or at a time.
How to realize his question
Let alone his answer?

To summarize the poem, Sullivan makes a number of metaphors to describe the randomness of the piece, then to express her opinion that the piece is a look into Pollock’s mind. Then, she notes the resulting timelessness of the piece, and ends with the realization that it is impossible to note any underlying meaning — Pollock’s question and answer — in Number 1A.

Let’s work our way through the metaphors. First, “trickles and valleys of paint” creates imagery comparing Pollock’s abstract work (referred to as a maze) to a landscape. Then, it is compared to a “game of Monopoly without any bank”; that is, a normally ordered game of monopoly with the one element of order, the Bank, removed. These metaphors create a sense of a lack of order, but in a grandeur way: trickles and valleys are not streams and ditches, but monumental landscapes.

Next, we talk about Pollock’s thoughts. “Into a linoleum on the floor in a dream” calls to mind the abstract patterns one might find on standard one foot floor tiles (that also happens to made completely randomly) and associates that with Pollock’s dreams, that is, subconscious thoughts. “Murals inside the mind” continue the monumental tone the speaker approaches Pollock’s appropriately monumentally sized works with.

Finally, we get to the speaker’s conclusion: that Pollock’s works, precisely because they are pure paint and devoid of references to humans, culture, or even shapes, are timeless and universal. The speaker again makes a metaphor, and compares Number 1A to a poem that “speaks still of something in a place or at a time,” of which are undefined. To close off the argument, a rhetorical question asserts that we will never know what Pollock was thinking when he created this work.

One thing to note though, about the timelessness of Pollock’s works, is that many things are in fact timeless. Constants like pi, e, the speed of light, the universal gravitation constant, and others are also timeless, but even that would be too generous, for timelessness of Pollock’s works is the timelessness of randomness, for that which has no meaning has no meaning for which to be misunderstood.

The Play that’s so Meta, Even This Acronym

Metatheater is great. As such, Tom Stoppard’s Rosencrantz and Guildenstern are Dead ranks as the best piece of hamlet fan fiction, in front of Richard Curtis’s The Skinhead Hamlet (not school appropriate). I absolutely love it when artists try to subvert their respective genres and cultures — Steely Dan sneaking dark references into everything, the last episode of Sherlock showing a detective strangely not in control — and Stoppard’s use of metatheater is no exception.

In Rosencrantz and Guildenstern, metatheater is everywhere. Even from the beginning, Stoppard includes notes clearly intended only for the reader of the play: in the stage instructions establishing the setting, and thus not heard by a theatrical audience, Stoppard writes:

… However, he is nice enough to feel a little embarrassed at taking so much money off his friend. Let that be his character note.

And for Guildenstern:

GUIL is well alive to the oddity of it […] aware but not going to panic about it — his character note.

And little jokes making fun of theater:

his attention being directed at his environment or lack of it

And sarcastic comments inserted into stage directions for no purpose other that to make reading the text much more interesting:

GUIL, examining the confines of the stage, flips over two more coins as he does so […].

Not just the stage directions seek to emphasize the fact that R&G Are Dead is, in fact, a play. Rosencrantz and Guildenstern frequently recognize the fact that they are, in fact, in a play.

They yell fire in the  crowded theater:

ROS: Fire!

(GUIL Jumps up)

GUIL: Where?

ROS: It’s all right — I’m demonstrating the misuse of free speech. To prove that it exists. (He regards the audience, that is the direction, with contempt — and the other directions, then front again.) Not a move. They should burn to death in their shoes.

(NOTE: the “yelling fire in a crowded theater” quote is frequently misused. Please be careful.)

And reference the play in which they exist in ways ranging from the obvious, like that fire comment addressed to the audience, to the subtle:

Come, come, Alfred, this is no way to fill the theatres of Europe.

And, of course, there’s the whole being-part-of-Hamlet thing, with the eerily familiar:

… and with a look so piteous, he takes her by the wrist and holds her hard, then he goes to the length of his arm, and with his other hand over his brow, falls to such perusal of her face as he would draw it …

And straight-up identical:

[…] so shall you hear
of carnal, bloody, and unnatural acts,
of accidental judgements, casual slaughters,
of deaths put on by cunning and forced cause,
and, in this upshot, purposes mistook
fallen on the inventor’s heads: all this can I
truly deliver.

This metatheater is what makes Rosencrantz and Guildenstern are Dead such an entertaining read.

The small jokes integrated into stage directions near the beginning of the play establish the mood. By including these witty remarks, Stoppard indicates that he won’t be taking the play too seriously; his wit and sarcasm signals that he intends to use the beginning of the play as a satire of Hamlet and theater in general, and does so quite successfully.

Rosencrantz and Guildenstern’s meta remarks create much of the same effect. For those familiar enough with legal rhetoric (Benjamin Lamb), shouting fire in a burning theater is absolutely hilarious. While I can’t speak for everyone, the subtle metatheatrical details like the “fill the theaters of Europe” comment, which I didn’t notice the first time reading R&G are Dead, give a sense of childish joy at finding an “easter egg” metatheatrical detail included in the play.

Finally, the references to the original text of Hamlet do even more to contribute to this feeling. If anything, the quotations of Hamlet give most readers the warm feeling of understanding the literary equivalent of an inside joke when one recognizes those quotes.

The end goal of course, though, is not humor. While they do create a lighthearted tone that makes reading the play enjoying and probably are largely responsible for the play’s popularity in this manner, they do first and foremost lend themselves to the play thematically. Intellectual discussion involving fate in Gardner’s Grendel, for example, draws from the fact that the work is based on Beowulf, and thus has an ending quite literally set in stone. Thus, similar discussion involving fate in Rosencrantz and Guildenstern are Dead also utilizes heavily its nature as a derivative work of Hamlet; however, the difference here is that R&G are Dead makes its primary focus the discussion of fate. Whereas Grendel saw little point in drawing additional attention to its composition, Stoppard draws as much attention to this fact as possible to ensure the audience understand that universe of the play is undoubtedly devoid of free will. In this manner, Stoppard constructs a thought experiment on the nature of free will. Other secondary themes also derive meaning from this obvious use of metatheater: exploration of the issue of absurdism, for example, is facilitated by metatheater in that disregarding reality lends itself to increasingly absurd actions and occurrences in the play.