Put your hand on a hot stove for a minute, and it seems like an hour.
Sit with a pretty girl for an hour, and it seems like a minute.
That’s Relativity

”

—

Albert Einstein

P.S: sebenernya sih saya ga percaya Einstein bilang gini, kalo Richard Feynman masih lah percaya. Tapi, percaya gak percaya yang penting frasenya menarik haha

Proof: isomorphismes: A beautiful depiction of a 1-form by Robert Ghrist. You... »

isomorphismes:

A beautiful depiction of a 1-form by Robert Ghrist. You never thought understanding a 1→1-dimensional ODE would be so easy!

What his drawing makes obvious, is that images of Phase Space wear a totally different meaning than “up”, “down”, “left”, “right”. In this…

(Source: math.upenn.edu)

[T]he point of introducing L^p spaces in the first place is … to exploit … Banach space. For instance, if one has |ƒ − g| = 0, one would like to conclude that ƒ = g. But because of the equivalence class in the way, one can only conclude that ƒ is equal to g almost everywhere.

The Lebesgue philosophy is analogous to the “noise-tolerant” philosophy in modern signal progressing. If one is receiving a signal (e.g. a television signal) from a noisy source (e.g. a television station in the presence of electrical interference), then any individual component of that signal (e.g. a pixel of the television image) may be corrupted. But as long as the total number of corrupted data points is negligible, one can still get a good enough idea of the image to do things like distinguish foreground from background, compute the area of an object, or the mean intensity, etc.

”

—

Terence Tao

If you’re thinking about points in Euclidean space, then yes — if the distance between them is nil, they are in the exact same spot and therefore the same point.

But abstract mathematics opens up more possibilities.

• Like TV signals. Like 2-D images or 2-D × time video clips.
• Like crime patterns, dinosaur paw prints, neuronal spike-trains, forged signatures, songs (1-D × time), trajectories, landscapes.
• Like, any complete, normed, vector space. (= it’s thick + distance exists + addition exists + everything’s included = it’s a Banach space)

(Source: terrytao.wordpress.com, via proofmathisbeautiful)

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