Monday, June 03, 2013

MoAR: assorted bits.

maths follows art.

i've heard the claim before that for some phenomena, physicists "knew" them long before mathematicians did.

that choice of wording has always bothered me, because it suggests that (experimental) physicists are somehow "smarter" than mathematicians .. as if the disciplines can really be compared. it's a difference in methodology, or for that matter, epistemology:

scientific conclusions are only as accurate as the data you can physically observe and measure within the scope of the problem. on the other hand, if a mathematician proves that something is true then (s)he is simultaneously asserting that a countless number of pathologies are impossible.

at any rate .. with respect to the same abuse of language, sometimes artists are "smarter" than mathematicians:
" The same is true in visual arts. Vincent van Gogh’s later paintings had all sorts of swirling, churning patterns in the sky — clouds and stars that he painted as if they were whirlpools of air and light. And, it turns out, that’s what they were! In 2006, physicists compared van Gogh’s patterns of turbulence with the mathematical formula for turbulence in liquids. The paintings date to the 1880s. The mathematical formula dates to the 1930s. Yet van Gogh’s turbulence in the sky provided an almost identical match for turbulence in liquid.

Art sometimes precedes scientific analysis, and the relationship can go the other way too: Scientists can use art to understand math.

Even the seemingly random splashes of paint that Jackson Pollock dripped onto his canvases show that he had an intuitive sense of patterns in nature. In the 1990s, an Australian physicist, Richard Taylor, found that the paintings followed the mathematics of fractal geometry — a series of identical patterns at different scales, like nesting Russian dolls. The paintings date from the 1940s and 1950s. Fractal geometry dates from the 1970s. That same physicist discovered that he could even tell the difference between a genuine Pollock and a forgery by examining the work for fractal patterns.

~ from "How an Entirely New, Autistic Way of Thinking Powers Silicon Valley" @wired
the last paragraph gives me pause: to what extent is this phenomenon unique, really? the only way to check this if most drip paintings do not obey a self-similar pattern; otherwise pollock wouldn't really be unique in this sense, would he?

so i'm not alone in my confirmation bias.

this reminds me of something from a previous roundup, but better stated and not just about the job search.
" Survivorship bias also flash-freezes your brain into a state of ignorance from which you believe success is more common than it truly is and therefore you leap to the conclusion that it also must be easier to obtain. You develop a completely inaccurate assessment of reality thanks to a prejudice that grants the tiny number of survivors the privilege of representing the much larger group to which they originally belonged."

~ from "Survivorship Bias"

(this excerpt is a lot more interesting, once you learn the title of the article.)

i like this article, if only because it hints at why we mathematicians study things that "don't really exist" .. at least in everyday physical reality.
" What these theories do share is a certain level of rigor. Rather than being arbitrary, they involve precisely defined conditions that collectively give rise to interesting properties. While a theory in the theoretical physics sense isn't “true” in that it doesn’t describe the real world, it is “true” in that two researchers will agree on the theory’s properties. This allows interested parties to build off each other’s work. "

~ from "Earning a PhD by studying a theory that we know is wrong" @arstechnica

lastly, some cool links!

first, some time-dependent distortion and translation on a space that is close to a sphere:

secondly, the geometric consequence of a harmonic series:

" With no wind, a lot of time, and a ridiculous amount of patience, it’s possible to make a tower like the one [below].

(Vertical axis not to scale).

The overhang for 52 cards is approximately 2.269 times the width of one card. Not bad.

~ from "How far can you overhang blocks?" @datagenetics

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