isomorphismes

David Uy by Mary Borgman

Tue, 18 Jun 2013 17:00:20 -0600

David Uy by Mary Borgman

Here’s a physically intuitive reason that rotations ↺ (which seem circular) are in fact...

Tue, 18 Jun 2013 15:21:00 -0600

Here’s a physically intuitive reason that rotations ↺

(which seem circular) are in fact linear maps.

If you have two independent wheels that can only roll straight forward and straight back, it is possible to turn the luggage. By doing both linear maps at once (which is what a matrix

or Lie action does) and opposite each other, two straights ↓↑ make a twist ↺.

Or if you could get a car | luggage | segway with split (= independent = disconnected) axles

to roll the right wheel(s) independently and opposite to the left wheel(s)

, then you would spin around in place.

Still Life with Cat (I don’t know the title or the artist...

Mon, 17 Jun 2013 16:00:24 -0600

Still Life with Cat

(I don’t know the title or the artist of this image. If you know/are the artist, please isomorphismes.tumblr.com/ask with the correct attributions!)

This morning I had another talk with the German Chancellor,...

Sun, 16 Jun 2013 16:00:20 -0600

This morning I had another talk with the German Chancellor, Herr Hitler, and here is the paper which bears his name upon it as well as mine. (cheers) Some of you, perhaps, have already heard what it contains but I would just like to read it to you: “We, the German Fuhrer and Chancellor, and the British Prime Minister, have had a further meeting today, and are agreed in recognising that the question of Anglo-German relations is of the first importance for the two countries, and for Europe. (mutters of approval) We regard the agreement signed last night and the Anglo-German Naval Agreement as symbolic of the desire of our two peoples never to go to war with one another again.”

(wild cheering)

—Neville Chamberlain, 30th September 1938

I wish I could meet a super-smart lawyer from the early Middle...

Sat, 15 Jun 2013 16:00:31 -0600

I wish I could meet a super-smart lawyer from the early Middle Ages who would persuasively argue me the divine right of kings, primogeniture, appanage, the distinction between movable and immovable property.

(That’s Just) The Way My Dick Is by My Dick

Fri, 14 Jun 2013 14:52:35 -0600

(That’s Just) The Way My Dick Is by My Dick

"Quality Time"

Fri, 14 Jun 2013 13:06:00 -0600

Words that seem innocuous to me can set other people into anger mode. (I too, of course, have my own buttons that can be pushed—mostly economics-related.)

One woman who has raised more children than I can even fathom doing (9) will launch off if she hears the phrase “quality time”.

She says “Quality time” is short for “I don’t really know my kids—but I’ll make up for it by going to their sports games and dance recitals.”

To her, ∄ such thing as “quality time”—time spent with your kids that’s significantly better than, or can make up for, other, less important, time. For her you really get to know your kids during all the unimportant, mundane, pedestrian moments of life.

Balwant Singh’s Elephant Clawed by a Lion by Nainsukh of Guler,...

Thu, 13 Jun 2013 19:00:16 -0600

Balwant Singh’s Elephant Clawed by a Lion by Nainsukh of Guler, 1752

Conversation topics on Facebook by age.

Wed, 12 Jun 2013 19:00:21 -0600

Conversation topics on Facebook by age.

"Although partial least squares regression was not designed for classification and discrimination, it..."

Tue, 11 Jun 2013 19:00:00 -0600

“

Although partial least squares regression was not designed for classification and discrimination, it is … used for these purposes. For example, PLS has been used to:

distinguish Alzheimer’s, senile dementia of the Alzheimer’s type, and vascular dementia
discriminate between Arabica and Robusta coffee beans
classify waste water pollution
separate active and inactive compounds in a quantitative structure-activity relationship study
differentiate two types of hard red wheat using near-infrared analysis
distinguish transsexualism, borderline personality disorder and controls using a standard instrument
determine the year of vintage port wine
classify soy sauce by geographic region
determine emission sources in ambient aerosol studies

”

- Matthew Barker and William Rayens

"I do not believe that financial markets make the economy more efficient. The analogy I use is Earth...."

Mon, 10 Jun 2013 19:00:00 -0600

“I do not believe that financial markets make the economy more efficient. The analogy I use is Earth. If it were reduced to the size of a basketball, it would be smoother than a billiard ball. However, at a human scale, there are mountains and oceans we can exploit….

The guy talking about making markets more efficient is thinking of something like rolling rocks down a mountain to power useful work. This indeed makes the Earth smoother, wearing down mountains and filling in oceans. But … [that] bears no resemblance to what people really do. They’re more likely to build a hydroelectric dam that holds water back, that is it keeps the system farther from equilibrium, not moves it closer.”

- Aaron Brown, Red-Blooded Risk

(I rearranged his words a little bit.)

Yuichi Yokoyama via untilasinglesolitonsurvives

Sun, 09 Jun 2013 19:00:31 -0600

Yuichi Yokoyama

via untilasinglesolitonsurvives

"The word “statistics” was a coinage of German and Italian enthusiasts for state action..."

Sat, 08 Jun 2013 19:00:00 -0600

“

The word “statistics” was a coinage of German and Italian enthusiasts for state action in the early eighteenth century…..

It became a sort of insanity….[tourists]…Samuel Johnson…. By the 1850’s the conservative critics of capitalism, such as Charles Dickens, were becoming very cross about statistics….

Counting can surely be a nitwit’s, or the Devil’s, tool. Among the more unnerving exhibits in the extermination camp at Auschwitz are the books in which Hitler’s willing executioners kept records on every person they killed.

The formal and mathematical theory of statistics was largely invented in the 1880’s by eugenicists (those clever racists at the origin of so much in the social sciences) and pefected in the twentieth century by agronomists (…Iowa State…). The newly mathematised statistics became a fetish in the wannabe sciences. During the 1920’s…sociology…quantification was a way of claiming status, as it became also in economics…(political economy), and in psychology, fresh[ly] separated from philosophy. In the 1920’s and 1930’s…social anthropologists…counted coconuts.

”

- Deirdre McCloskey

HT @AClassicLiberal

Oblivion by Grimes (por GrimesVEVO)

Fri, 07 Jun 2013 19:00:15 -0600

Oblivion by Grimes (por GrimesVEVO)

Why is the slope of perpendicular lines flipped over and switched signs?

Thu, 06 Jun 2013 19:00:00 -0600

Oh! This one only took me 17 years or so to figure out. This was a “fact” I had committed to memory in school but never thought about why.

From The Symplectization of Science by Mark Gotay and James Isenberg:

There are some connections to circles and homogeneous coordinates (v/‖v‖) but let’s leave those for another time.

Gotay & Isenberg’s exposition using the metric makes it clear that the
/‖v‖ part of the definition of cosine isn’t where the right-angle concept comes from. It comes from the v₁ w₁ + v₂ w₂ .

So if the slope of my starting line is m, why is the slope of its perpendicular line −1/m?

First I could draw some examples.

I drew these with http://www.garrettbartley.com/graphpaper.html which is a good place to count out the “rise over run” and “negative run over rise” Δx & Δy distances to make sure they really do look perpendicular.

The length and the (affine or “shift”) positioning of perpendicular line segments doesn’t matter to their perpendicularity. So to make life easier on myself I’ll centre everything on zero and make the segments equal length.

The metric formula is going to work if let’s say my first vector v is (+1,+1) (one to the right and one up) and my second vector goes one down and one to the right. Then the metric would do:

+1 • +1 (horizontal) + +1 • −1 (vertical)

which cancels.

What if it were a slope of 9.18723 or something I don’t want to think about inverting?

This is a case where it’s probably easier to think in terms of abstractions and deduce, rather than using imagination in the conventional way.

If I went over +a steps to the right and +b steps to the up (slope=b/a), then the metric would do:

a•? + b•¿

What is that missing? If I plugged in (?←−b, ¿←a) or (?←b, ¿←−a), the metric would definitely always cancel.

And in either of those cases, the slope of the question marks (second line) would be −a/b.

So the multiplicative inverse (flipping) corresponds to swapping terms in the metric so that the two parts anti-match. And the additive inverse (sign change) means the anti-matched pairs will “fold in” to zero each other (rather than amplifying=doubling one another).

in-the-sky-and-rising by memoryradio via sfmoma

Wed, 05 Jun 2013 19:00:00 -0600

in-the-sky-and-rising by memoryradio

via sfmoma

In harmonic analysis and PDE, one often wants to place a...

Tue, 04 Jun 2013 19:00:00 -0600

In harmonic analysis and PDE, one often wants to place a function ƒ:ℝᵈ→ℂ on some domain (let’s take a Euclidean space ℝᵈ for simplicity) in one or more function spaces in order to quantify its “size”….

[T]here is an entire zoo of function spaces one could consider, and it can be difficult at first to see how they are organised with respect to each other.

…

For function spaces X on Euclidean space, two such exponents are the regularity s of the space, and the integrability p of the space.

…

…

—Terence Tao

Hat tip: @AnalysisFact

Paul Klee, Monument, 1929 via workman, vitabrevisarts

Mon, 03 Jun 2013 19:00:28 -0600

Paul Klee, Monument, 1929

via workman, vitabrevisarts

‘The Descent of the Modernists’, cartoon by E. J. Pace, first...

Sun, 02 Jun 2013 19:00:00 -0600

‘The Descent of the Modernists’, cartoon by E. J. Pace, first published in Seven Questions in Dispute by William Jennings Bryan (1924).

with some nice autobiographical details, via cmnotes

What if every Olympic sport was photographed like beach...

Sat, 01 Jun 2013 19:00:22 -0600

What if every Olympic sport was photographed like beach volleyball?

via ineedmymorningtea:, s-m-i