Tags: latex math
Tags: clojure

A little project I did to make it more convenient to use Apache Commons Math

### I have an interesting idea

but it involves simulating thousands of points interconnected by thousands^2 springs until the points positions converge.

I have no idea how computationally expensive that is.

Is it for this:
http://en.wikipedia.org/wiki/Force-directed_graph_drawing
?

Pretty much. Now I know what the technique is called! Thanks!

There’s this magic way of doing it that is really fast:

### I have an interesting idea

but it involves simulating thousands of points interconnected by thousands^2 springs until the points positions converge.

I have no idea how computationally expensive that is.

Is it for this:
http://en.wikipedia.org/wiki/Force-directed_graph_drawing
?

You and Your Research — Richard Hamming

Richard Hamming gets to the heart on what differentiates a prolific scientist from an ordinary one.

"If you do not work on an important problem, it’s unlikely you’ll do important work. It’s perfectly obvious. "

Another key idea is that of an attack. These problems are hard because they are not amenable to brute force. You need to find a trick to make the problem approachable.

By important I mean guaranteed a Nobel Prize and any sum of money you want to mention. We didn’t work on (1) time travel, (2) teleportation, and (3) antigravity. They are not important problems because we do not have an attack. It’s not the consequence that makes a problem important, it is that you have a reasonable attack. That is what makes a problem important.

Although watching this may induce an existential crisis in grad students, understanding the ideas presented here is the key to making a difference with the work you pursue.

A silly experiment of mine that lets you write math in Clojure using Unicode symbols:

(defn binet-fib [n]
(/ (- (ⁿ φ n)
(ⁿ (- φ) (- n)))
(√ 5)))

(assert (∀ [p [true false] q [true false]]
(= (¬ (∧ p q))
(∨ (¬ p) (¬ q)))))

(assert (= (count (∪ A B))
(+ (count A)
(count B)
(- (count (∩ A B))))))

Tags: clojure math

An awesome animation of a rotating 4D cube (tesseract)…and it’s transparent! Source. Learn about tesseracts here.

(via barrelshifter)

An animation showing that in a Pythagorean triple, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Source.

(via mattlehrer)

Bianca’s new New Balances have the Spaceship Operator on them

"When in very good spirits he would jest in a delightful manner. This took the form of deliberately absurd or extravagant remarks uttered in a tone, and with a mien, of affected seriousness. On one walk he ‘gave’ to me each tree that we passed, with the reservation that I was not to cut it down or do anything to it, or prevent the previous owners from doing anything to it: with those reservations it was henceforth mine. Once when we were walking across Jesus Green at night, he pointed at Cassiopeia and said that it was a ‘W’ and that it meant Wittgenstein. I said that I thought it was an ‘M’ written upside down and that it meant Malcolm. He gravely assured me that I was wrong."

— Norman Malcolm, Ludwig Wittgenstein: A Memoir, 1958

Robot Runs Like a Cat

Thanks to its legs, whose design faithfully reproduces feline morphology, EPFL’s four-legged “cheetah-cub robot” has the same advantages as its model: it is small, light and fast. Still in its experimental stage, the robot will serve as a platform for research in locomotion and biomechanics.

Even though it doesn’t have a head, you can still tell what kind of animal it is: the robot is definitely modeled upon a cat. Developed by EPFL’s Biorobotics Laboratory (Biorob), the “cheetah-cub robot,” a small-size quadruped prototype robot, is described in an article appearing today in the International Journal of Robotics Research. The purpose of the platform is to encourage research in biomechanics; its particularity is the design of its legs, which make it very fast and stable. Robots developed from this concept could eventually be used in search and rescue missions or for exploration.