Wikipedia page on vorticity has some awesome GIF animations. Also, I should know this stuff already…

Working on a Fuzzy Cognitive Mapping prototype for Thicket. You can really easily get limit cycles with a couple negative edge weights. Jagged lines are due to testing some time-lag implementation techniques after reading this paper by Park & Kim.

Almost 8 months after the initial idea, I brought mathematician/sculptor/professor George Hart to Brown University and orchestrated the installation of a sculpture in the entrance hall of the engineering building!

Couldn’t have done it without RISD+Brown STEAM, the Division of Applied Math, the Brown Design Workshop, and the Departments of Engineering and Physics. Thank you! Now I gotta make a plaque.

## STEAM lecture examines connection between math, arts - Brown Daily Herald

When people picture a “rhombic dodecahedron,” they might see a 12-faced geometric object. George Hart sees a sculpture.

Had dinner with one of my math idols this past Wednesday ^^

In a little less than a month, we will be bringing George Hart, professor at Stony Brook University, to Brown. He is a mathematician and freelance sculptor, bringing inspiration from geometry and topology.

On March 5th he will give a presentation on his life, work, process, and inspiration. This should get everyone excited about a workshop the following day during which 20 participants will collaboratively build a hanging geometric orb sculpture for installation in Barus-Holley.

To reserve a spot at the workshop, please email brown@steamwith.us and plan to attend the lecture as well—those who attend both events will get preference!

(Source: brownsteam)

Trying my hand at a poster design. I have no clue what i’m doing! Illustrator is fun.

In other news, George Hart is coming to Brown University in March and installing a sculpture! The Applied Math department is sponsoring.

## What virtues does studying mathematics inculcate, besides logical thinking?

Mike Kayser’s answer:

Patience. Math is hard. It takes time. Try to make progress today, but also know it will be there for you tomorrow.

Humility. Related to the above. Math will surpass your abilities on some days. That’s fine. It does that to everyone sometimes.

Intellectual honesty. You won’t get anywhere until you admit to yourself what you don’t know.

Zenlike mental calm. It is impossible to do math if you are feeling overly emotional. To study math is thus in some sense to rehearse inner stillness.

An aesthetic appreciation for rationality. This is harder to explain. For me, math can be an almost spiritual experience, like an interaction with pure abstract beauty. One could almost compare it to “talking to God.” You know that in some sense it will always be beyond you, but the slow, steady accretive work of understanding one piece at a time has its deep, life-long satisfactions.

Willingness to tolerate bad explanations. Changing gears, a lot of pedagogy in math is terrible, perhaps because people generally don’t understand math all that well, or just don’t know how to talk about it clearly. By wading through bad explanations, you can learn how to mentally translate something complex into something that makes sense to you. This is a useful skill in other domains too.

An appreciation for complexityand for the limits of our ability to understand things. I guess this is the same as humility above, but doing math makes you realize that most people, most of the time, probably don’t know what they are talking about. Math, like programming, chess, or most complex pursuits, is an antidote to human BS because BS doesn’t get you anywhere in trying to figure out something mathematical.

Some inspiration going forwards with my education.

Also, a favorite: Quora: What is it like to understand advanced mathematics?

On Monday I finished up a semester-long independent study I called “Tactile Math”. In it, I made 4 pieces to explore visual and tangible understanding of math concepts and math thinking, in addition to doing some research into pedagogical practices. I’ll update my website over winter break to include process and details!

Thank you to friends who gave me sketches to complete one of the pieces.

I love this!

## Math As Craft

I had a late-night snack with a few friends Wednesday night while in the middle of some problem sets due today.

I brought down with me a particular problem on streamfunctions that had been giving me hell all day. My buddy Dan asked what was keeping me from solving it. Did I have all the necessary tools and techniques? I was pretty sure I did. Was I misreading the question? I didn’t think so. My answer was then simply, “I haven’t spent enough time staring at it.”

The next thing he asked was, “what’s the application?” To this I had no real response. The problem had already been solved and the uses had been worked out; I was just following in the footsteps of some long-dead mathematician or physicist. I was just deriving an expression.

On one hand, this is a bit sad. For much of mathematics, understanding the problem means you are 90% of the way to answering it, but I was struggling so much with just the boring mechanics of it—the last 10%. Algebra. Indicial notation. Variable substitution.

As I’ve been mulling it over since however, I feel more comfortable with this. My friends down the road at RISD spend hours in physical labor: throwing pottery, working the loom, blowing the glass, mixing the paint. Their arts education begins from the ground-up mechanics. Their schoolwork for the first 2 years is mostly gruntwork: project after project that seem irrelevant and annoying and tiring. (I am generalizing here from a few conversations with friends.) Yet at the end of their foundations period, they have a diverse skillset, a nimbleness in their medium of choice, and have often developed philosophical ideas integrated in their craft. This is a very Zen in the Art of Archery idea.

I think that this is the same in math. Math students like myself spend years doing fairly mindless work do develop a dexterity with our medium (scribbles on paper). After all this, we find we can express grand ideas in math language once we graduate to a high enough level. The mechanics become second nature so that you can look beyond them, play with them more flexibly, and begin making more meaningful work. It’s a “you have to know the rules before you can break ‘em” mentality.

So I’ll stare a little bit more at the problem and not worry about any application… I like to think my brain is making the necessary connections and my mastery of medium will come.

This is an image of a Montessori Binomial Cube, one of their slew of “sensorial materials.” It illustrates how (a+b)^3 = a^3 + 3•ab^2 + 3•ba^2 + b^3. A friend of mine introduced me to this as he worked in a Montessori school for a short time.

These kinds of toys are *really* fascinating to me because I’ve been thinking a lot about how to represent mathematical ideas in ways other than the weird, abstruse language we use nowadays (abstract symbols whose shapes have almost no relation to their use). Instead, how can we convey these ideas in other visual ways (or, in this case, tactile ways too!).

Would love to see these kinds of things expanded upon, outside of just blocks.

To roughly quote my applied math professor today: “Mathematics is a game of twisting problems we don’t know how to solve until they look like easy ones we can solve. Then we prove or pretend they’re the same thing.”

Also, Eric Harshbarger makes his own dice! I’m curious as to what the process is. (also, he does professional lego sculpting, though I don’t believe he’s lego certified)

I like the math constants one…

Also, I’ve been a bit torn between studying applied or pure mathematics; I continue to hope my degree will be in applied but I enjoy studying pure quite a bit too. This is because I believe theoretical math to be the more noble, beautiful science…. but this quote, again from A Mathematician’s Apology, while ragging on applied math, is the reason it excites me so much.

It is plain that [a physicist or applied mathematician] is trying to correlate the incoherent body of crude fact [i.e. the real world] confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics.

This kind of approximation and shooting in the dark, is exciting to me. Almost everything in applied math is *new* and warrants exploration; everything is dark.