The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful, the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test; there is no permanent place in the world for ugly mathematics… It may be very hard to define mathematical beauty, but that is just as true of beauty of any kind—we may not know quite what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it.
 — G. H. Hardy(A Mathematician’s Apology)

Should Science Majors Pay Less for College Than Art Majors?

Down in Florida, a task force commissioned by Governor Rick Scott is putting the finishing touches on a proposal that would allow the state’s public universities to start charging undergraduates different tuition rates depending on their major. Students would get discounts for studying topics thought to be in high demand among Florida employers. Those would likely include science, technology, engineering, and math (aka, the STEM fields), among others.

But Art History? Gender Studies? Classics? Sorry, but the fates are cruel. Unless a university could show that local companies were clamoring to hire humanities students, those undergrads would have to pay more for their diploma.

No.

This is ridiculously dumb. Colleges aren’t employment factories, they’re institutions of higher learning.

This is the kind of stuff that I like to spend time thinking about. I know I’m weird, but I’m OK with it. This is some cool ish, and if it doesn’t mess with your head a bit, you’re not thinking hard enough.

Just playing with z² / z² + 2z + 2

$g(z)=\frac{z^2}{z^2+2z+2}$

on WolframAlpha. That’s Wikipedia’s example of a function with two poles (= two singularities = two infinities). Notice how “boring” line-only pictures are compared to the the 3-D ℂ→>ℝ picture of the mapping (the one with the poles=holes). That’s why mathematicians say ℂ uncovers more of “what’s really going on”.

As opposed to normal differentiability, ℂ-differentiability of a function implies:

• infinite descent into derivatives is possible (no chain of C¹ ⊂ C² ⊂ C³ ... Cω like usual)

• nice Green’s-theorem type shortcuts make many, many ways of doing something equivalent. (So you can take a complicated real-world situation and validly do easy computations to understand it, because a squibbledy path computes the same as a straight path.)

Pretty interesting to just change things around and see how the parts work.

• The roots of the denominator are 1+i and 1−i (of course the conjugate of a root is always a root since i and −i are indistinguishable)
• you can see how the denominator twists
• a fraction in ℂ space maps lines to circles, because lines and circles are turned inside out (they are just flips of each other: see also projective geometry)
• if you change the z^2/ to a z/ or a 1/ you can see that.
• then the Wikipedia picture shows the poles (infinities)

Complex ℂ→ℂ maps can be split into four parts: the input “real”⊎”imaginary”, and the output “real“⊎”imaginary”. Of course splitting them up like that hides the holistic truth of what’s going on, which comes from the perspective of a “twisted” plane where the elements z are mod z • exp(i • arg z).

ℂ→ℂ mappings mess with my head…and I like it.

It takes ~20 observations to verify your first significant digit of the mean with confidence.

Do you know how many observations it takes to verify your first sig-fig of the variance? More like 1000. And that’s just to get one digit of accuracy! Higher moments (skew, kurtosis) are even worse.

That’s why I often laugh out loud when I read in the newspaper claims that rely on a certain value of the variance. Even in serious, published papers!—I often see tables with estimates of standard deviation that go out to three decimal places, just because the software spat the numbers out that way. It gives a false sense of accuracy. It’s ridiculous.
Why yes, I will spend the rest of the weekend day-dreaming about a Levon Helm/MCA collaboration…

I just can’t help it.

truth. now get on your bikes and ride.

“Ooooooohhhh, won’t you take me home tonight?” Rock on forever, Freddie!

In American today, anti-evolutionism matters because it has become the vanguard of a genuine anti-science movement. To be sure, opposition to evolution isn’t new. State laws against the teaching of evolution actually go back nearly a century, and the famous Scopes trial took place 87 years ago. However, if you thought such things were behind us, guess again. Laws designed to encourage the teaching of non-scientific “alternative” theories to evolution were introduced in 11 state legislatures last year. This year, Darwin’s 203rd birthday, on February 12th, saw an anti-evolution bill, already passed by the Indiana State House of Representatives, awaiting action in the State Senate. Its fate there is uncertain, but there are plenty of reasons to be concerned.

Our Darwin problem is really a science problem. The easier it becomes to depict the scientific enterprise as a special interest immersed in the culture wars, the easier it becomes to reject scientific findings. We see this everywhere in American culture and politics today, from the anti-vaccine movement to the repeated assertion that global warming is a deliberate “hoax” rather than a straightforward conclusion driven by reams of scientific data. Sometimes this is done for deliberate political reasons, to secure advantage for a particular industry or financial group, but just as often it is motivated by fear of the implications of what science has discovered or might discover in the future.

Our Darwin problem matters for two reasons. First, it threatens the future of American scientific leadership in an increasingly competitive world. Convince enough young Americans that science is a close-minded system with a particular cultural and political agenda, and we will cede leadership to emerging countries that don’t share our Darwin hang-ups, and see science as the wave of the future. If you doubt this is happening today, look at the graduate programs of America’s research universities, still the greatest in the world. Increasingly, they are filled with bright, eager, creative students from around the world, taking places that American students just don’t seem interested in filling. Once trained, they will become the scientists of the future, while more and more of our own students have been persuaded that science has nothing to offer them. If this doesn’t change, scientific discovery will increasingly become something that happens elsewhere.

Second, and in my view just as important, our problem with science constrains and narrows our views and vision of the world. My personal concern for those who hold that view isn’t just that they are wrong on science, wrong about the nature of the evidence, and mistaken on a fundamental point of biology. It’s that they are missing something grand and beautiful and personally enriching.

Evolution isn’t just a story about where we came from. It’s an epic at the center of life itself. Far from robbing our lives of meaning, it instills an appreciation for the beautiful, enduring, and ultimately triumphant fabric of life that covers our planet. Understanding that doesn’t demean human life — it enhances it. We may be animals, but we are not just animals. We are the only ones who can truly appreciate, as Darwin put it, that there is “grandeur in this view of life,” and indeed there is. To accept evolution isn’t just to acknowledge the obvious — that the evidence behind it is overwhelming — it is to open one’s eyes to the endless beauty that life has generated and continues to produce. It is to become a knowing participant, in the truest sense, in the living world of which we are all a part.

 — Everything about this essay. (via dennymayo) What Denny said, with the additional thought that so very much of the extends into mathematics as well.

CLUE 1:
“went to short dogs house,
they was watching Yo MTV
RAPS”
Yo MTV RAPS first aired:
Aug 6th 1988
CLUE 2:
Ice Cubes single “today was a good day” released on:
Feb 23 1993
CLUE 3:
”The Lakers beat the Super
Sonics”
Dates between Yo MTV Raps air date AUGUST 6 1988 and the release…

One reason polynomials are interesting is that you can use them to encode sequences.

$\large \dpi{150} \bg_white \begin{matrix} 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + \cdots \\ \\ 5 + 2 \, x + 13 \, x^2 + 87.1 \, x^3 - x^4 + x^5 - 3 x^6 \cdots \\ \\ (\ 5, \ \ 2, \ \ 13, \ \; 87.1, \ -1, \ \ 1, \ -3, \ \ldots\ ) \\ \\ a + b \, x + c \, x^2 + d \, x^3 + e \, x^4 + f \, x^5 + g \, x^6 + \cdots \\ \\ \sum_0^N \mathrm{const}_i \cdot x^i \end{matrix}$

In fact some of the theory of abstract algebra (the theory of rings) deals specifically with how your perspective changes when you erase all of the x^297 and x^16 terms and think instead about a sequence…

Things that probably aren’t all that interesting to most of my followers, but insanely interesting to me, part 9,432