Friday, April 29, 2016

Friday Fabulosity: Gravitational Ripples

From 5:45 - 6:00, watch two of Saturn's shepherd moons herd ring particles:
If you watch the ring, not the moons, you can see the "ripple" in the ring as the moons pass.

If you love space, this entire Crash Course Astronomy video series is well worth watching.  It's free on youtube, with the inimitable Phil Plait of the always interesting and informative Bad Astronomy blog as narrator.  

Wednesday, April 27, 2016

Babylonian Algebra and an Uzbekistanian Tangent

Everyday Life in Babylonia and Assyria, by H.W.F. Saggs, is probably rather outdated at this point.  However, I found it an interesting and very readable overview.  And it has a math problem.  An actual Babylonian math problem, with solution, from a clay tablet.  The problem goes as follows:

I have added the surface of my two squares: 28;20.[The text uses sexagesimal numbers.  In our usual decimal system, \(28;20 = 20\cdot 1 + 28 \cdot 60 = 1700\).]
(The side of) one square is a quarter (the side of) the (other) square.
You put down 4 and 1.
You multiply 4 by 4: 16.
You multiply 1 by 1: 1.
You add 1 and 16: 17.
The reciprocal of 17 cannot be solved.
What must I put to 17 [i.e. What must I multiply 17 by] which will give me 28;20 [1700]? 1;40 [100].
This is the square of 10.
You raise 10 by 4 and 40 is (the side of) one square.
You raise 10 by I and 10 is (the side of) the second square.

A modern symbolic solution: Let x and y be the side lengths of the squares.  We know that

\[x^2 + y^2 = 1700 \] and (without loss of generality assume \(y < x\) ) \[ x = 4y \]

Substitute \(x = 4y\) into \(x^2 + y^2 = 1700\) and get
 16y^2 + y^2 & =& 1700 \\
17y^2 &=& 1700\\
y^2 &=& 100\\
y &=& \pm 10

Since the problem is talking about physical squares, we discard the negative solution and get \(y = 10\), \(x=4y=40\).

You can find problems exactly like this in any present day basic algebra textbook, right down to the use of nice integers which tempt natural arithmeticians to not show their work and thus receive only partial credit on graded homework and tests. 

My number theory textbook says that the mathematician whose book Kitab al-jabr introduced Europe to algebra, Abu Ja'far Mohammed Ibn Musa Al-Khwarizmi, was from the town of Khiva (Kowarzizm) in modern day Uzbekistan.  I tried to do a short research report on Khiva my first year of college, and could (at the time) put my hands on almost zero substantive material.  The most anyone could seem to say about the town was that it (a) wasn't quite as notorious a slave-trading center as its neighbor town, Merv, and (b) has a lovely, though relatively recent, half-finished minaret:
image from Wikipedia

Saturday, April 23, 2016

Caturday Post: Scaramouche Is A Measurable Set*

But he might chew on the measuring instrument.
*That is, we can apply to him a non-negative real function m such that
   1) m(empty set) = 0
   2) for any finite or countable collection of pairwise disjoint sets A_n in Scaramouche with the union of the A_n's = A also in Scaramouche, the sum over n of the m(A_n) = m(A). (i.e., measuring all the little pieces and adding is the same as adding all the little pieces and then measuring, since we are assuming that none of the pieces overlap: that's the pairwise disjoint bit). 

For further reading on measures, Wolfram Mathworld is always helpful.  

Thursday, April 21, 2016

History Tidbit: The Language of the Law

While reading at Matthew Ferguson's blog I came across the following thought-provoking detail quoted from W.E.H. Cockle.  In State Archives in Graeco-Roman Egypt from 30 BC to the Reign of Septimius Severus, Cockle says

“In legal contracts or documents the language of the contract determined the law which would apply. In case of disagreement a Greek contract was judged by Greek law, an Egyptian Demotic contract by Egyptian native law, and a Latin contract by Roman law.”

 I must now see if I can get JPASS register and read to work for me so I can read Cockle's whole article.  I dearly miss having university access to JSTOR.  

Friday, April 15, 2016

Enthusiastic Consent for Everyone, Real Life Edition

Recently someone asked me if they could give me a hug.  They ASKED me.  They asked ME.  And they waited to hear my answer before making a single move towards me.  It was amazing and wonderful.

More of that for everyone, please. 

Thursday, April 14, 2016

A Moment of Fan-Personing*

I got to meet Richard Carrier!!!  He signed two of his books for me!!!!!

*In what I hope was/is a very polite and non-creepy way.

Tuesday, April 12, 2016

What Good Is Math?

From Kiery King, who was deprived of a basic education, the reason why they need math:

and how being denied an education based on sex is still very much alive and well in the United States of America:

If you know someone who wants to do (math, science, sewing, whatever) don't tell them they can't because they are (female, black, male, whatever).  Don't stand there and let that person's parents tell them they don't need to/are not allowed to learn.  Deliberately sabotaging someone else's choices because of arbitrary and nonsensical gender restrictions is a vile thing to do.

Saturday, April 9, 2016

No Food Weekend

A good friend of mine is a teacher in a low income area.  Not only does she teach kids, a feat I find remarkable, this weekend she is going without food just so that she can understand her kids better. She will be discussing the experience here.

Caturday Post: Scaramouche In a Large Box With Paper

Sunday, April 3, 2016

In Which Conan the Engineer Takes a Nap

The story thus far.

After cleaving in twain the coffee-belching toad, Conan sank to the ground, his mighty thews at the last weary from his travails.  Stretching out his taut and muscular frame, glistening with sweat, upon the sward next to the tarn of coffee spewed by the monstrous toad which he had just hewn in twain, Conan sank into slumber.

While he lay there, like a panther on a high branch, ready to become alert at the slightest disturbance, he dreamt.  In his mighty warrior's dream he found himself in an ancient and massy datacenter.  Even the smallest of universal serial bus cables had the girth of Conan's great arm, and the power cables were large enough to crush a man in their coils even as a great boa constrictor crushes a cayman. 

Greatly wondering, yet undaunted ,for nothing of heaven above nor hell beneath could daunt the mighty engineer, Conan approached the server nearest him, leaving light sandal prints in the untracked dust.  With the fearless resolve of a follower of the great god of the Cimmerians, Cron, he ascended 99 steps to a great platform upon which rested a keyboard and monitor, and entered a keystroke.  Immediately the monitor screen filled with these dread characters, repeated over and over:
"ERROR:  requested WAL segment 00000001000051E200000053 has already been removed"

Then Conan awoke, disquieted. 

Saturday, April 2, 2016