math is fun, not gross

April 21, 2013

I’m finishing my evening, reflecting on my math brains.  This morning I took the GRE Subject test in Mathematics [PDF] (on the chance that I want to apply to any post-graduate programs in the next 5 years), and I prepared by taking one Math GRE a day for the last week.  What I found was that everyone must think that math is boring and gross.  I believe that this couldn’t be farther from the truth.  This is probably more a comment on standardized tests, but out of all of the disciplines, I would hope that the mathematicians could make word problems interesting.

I am probably not allowed to comment on what was and wasn’t on today’s exam, but I can say that it was practically the same material as the practice exams I took: there were people in committees, students waiting in line for lunch, dice being cast (although of the two problems, at least one involved a dodecahedron), coins being flipped–there was a differential equation, but none of the group theory questions had any context, and definitely not the set theory or topology.  Linear algebra and complex analysis were context free as well, and even the geometric questions were as bland as “here is an object, apply divergence theorem” or “here is a circle, compute some chords”.

During the week that I was studying / practicing / drilling / training* I accumulated the following (amazing) sample of material in my feedly, which is wholly opposite that material I was working on: These are engaging, interesting, and intellectually challenging accounts instead of numbing drills:

What a roundup!  What if the material generated _just_this_week_ was the kind of stuff that the GRE tested people on?  What if we could ask people how to think _creatively_ about _new_ problems?  Write programs instead of deciphering them?  How many times will students be asked to identify the programmatic output of a Collatz Sequence or Euclid’s Algorithm?  Obviously, it’s hard to standardize good problems, but we’ve had over 150 years of Residue Calculus–can’t someone come up with a complex function with poles that means something?

Anyway, I’m not really ranting.  I thoroughly enjoyed brushing up on my math.  Wronskian?  Adjugate?  L’Hôpital’s Rule (to the max)?  These are things I don’t use in my day job.  Lie groups and matrix invertibility, FFTs and signal processing, and, every once in a while, some Fundamental Theorem (of Algebra, Invertible Matrices, Calculus, &c), but not much, and not in very wide company.  But diving into the tips and tricks was actually a joy for me–and that’s because of where I come from.  My personal (Math Nerd**) and educational (Math Mudder) backgrounds get me excited about what are, truly, “Math Tips and Tricks”.  But wouldn’t it be great if we didn’t test our future mathematicians on those, but instead on exciting, engaging material?  What if people learned something from standardized tests, and what they learned was that they _want_ to answer hard problems with interesting techniques?  I know that should be happening in the classroom (in person), but why can’t we manage to make it happen on paper, too?  Don’t mind the rhetoric too much, and let me know if I’m way off base here.  I hope, in either case, that either the Tips and Trick become interesting on their own to everyone, or we all work very hard to make questions about thinking, and not about Tips and Tricks.

* I was actually doing these tests on my train commute to work, half on the way there and half on the way home.  Happily, everyone was very considerate and didn’t bother me with book, paper, pencils, and countdown timer spread across the tables.  Sadly, no one engaged me about what I was doing so I couldn’t teach any lay-residue theory or integration by parts.

** This is the book I did an independent study with in High School to continued my jump-started career in math (kicked off in earnest by Mr. Sisley’s introduction to Spivak and Mr. Robinson’s introduction to Chaos and Dynamical Systems in 11th and 12th grades, respectively).

ideal vs. real – wikipedia weighs in on pants

March 17, 2013

I’ve been reading up on this month’s announcement that the 3-body problem has 13 more solutions, and came across a wonderful little nugget of a wikipedia disambiguation:

Pair of pants

From Wikipedia, the free encyclopedia


This article is about an object in hyperbolic geometry. For the article of clothing, see trousers.

It’s usually the case that disambiguations favor primary topics by usage but, in same strange twist of fate, the following image is described with the awesomely gross sentence:

Six pairs of pants sewn together to form an open surface of genus two with four boundary components.

So think about that next time you’re at the sewing machine, trying to patch your punctured spheres.

[Edit: “Trousers” is now the front page of the “Pair of pants” redirect, accessed April 2013]

Links

[1] sciencemag.org article: physicists-discover-a-whopping.html
[2] wiki/Pair_of_pants
[3] wiki/Wikipedia:Disambiguation#Is_there_a_primary_topic.3F
[4] wiki/File:Worldsheet.png
[5] wiki/Riemann_surface#Punctured_spheres

pi-kus for pi day

March 14, 2013

I’ve been looking around the twitter-spheroid and blago-blogs and finding that lots of people are writing “pi-ku”s today, a haiku about pi, in honor of pi day:

you go around once
and make an infinity,
of digits that is

But what is a pi-ku, really?  Is a “haiku about pi” the best we can do?  What about my wife’s suggestion (which she came across from Powell’s Bookstore) , where the syllables pay homage to pi’s most well known digits?  Here’s the formula:

— First line: 3 syllables
— Second line: 1 syllable
— Third line: 4 syllables

and used in a sentence poem:

i know, of
pi,
pi squared digits

But we can get grosser than that.  What about longer pi-ku sequences, traversing the decimal-dance of pi’s digits:

(3) from where does
(1) pi
(4) originate?

(1) is
(5) it an integral
(9) half (neg why dee ex plus ex dee why)?

(2) maybe
(6) riemann zeta at 2,
(5) times six, square root is

But I digress.  How can you contort pi into your poetry?  Leave your poems in the comments, and don’t forget to enjoy your favorite kind of pi to celebrate the sweetness and the arbitrary transcendental numbers that permeate  our limited understanding of the universe.  Today I enjoyed smitten kitchen’s apple pie cookies.  Smaller size, same great ratio of circumference to diameter.

Links

[1] Powell’s Bookstore’s Facebook Conversation, Pi Day 2013
[2] my favorite approximations of pi, on github
[3] smitten kitchen’s apple pie cookies

gross contraptions

June 14, 2012

the whole “good things come in small packages” thing is relatively recent [1877], and it’s only in the last 40 years or so that we could really say the same thing about technology. i’ve been sitting on a few great blog posts for the last while now that really show off some of these bigger, and awesome machines that we (as humanity) came up with:

Punch Tape Programmable Metal Mill from 1952

The Machines That Made The Jet Age

Early Russian Hydraulic Computer

Analog Tide Computers and the D-Day Invasion


but then again, some machines haven’t gotten much smaller…

Gorgeous 1940s Lathe Restoration

bamf climbing

May 29, 2012

i’ve realized that i’ve found some RIDICULOUS links about some incredible climbers to share.  despite the frustratingly low frequency with which i utilize my membership at hangar 18, i have a developed a deep love and respect for climbing and those who do it well.  collected here are three generations of climbers that will make your jaw drop.  Hat tips to Eric, Yael, and my Grandpa.

Tiny Hand Over Hand:
Ashima Shiraishi, 11, Conquers Difficult Bouldering Climbs

more not-gross art in the gallery and a new toy

May 20, 2012

on this lazy-sunday-that-should-not-be-so-lazy i find myself, again, equating the high priority of my “starred” and “flagged” emails to my “starred” and “flagged” items in my google reader feed.  as such, i’ve added some more art to the gallery.

i also got a new toy to play with.  once i learn more about the circuit, i’m thinking of creative ways to make it wearable and fun.  thoughts are welcome!

you can also find an instructable on how to build it and the kit itself for purchase.

not-gross things for your eyes

April 25, 2012

so…i am really quite good at being anxious, procrastinating, feeling guilt, and just generally wallowing.  mind you, doing this well is actually a passion of mine; i can get quite a fair amount of enjoyment out of it.  i also enjoy a good watermelon-smashing or purring cat, but that’s neither here nor there.  that is a lie, as there is a purring cat right here “helping” me type this by being slumped over my hands.  digressing is also enjoyable.

the point is that–in addition to all this, i am a grade-A hoarder.  and i also love art.  the time has come, though, where i am learning that making good “engineering decisions” is the only way to move forward out of the analysis paralysis that i call home.

so, rather than never posting an all-encompassing collection of enjoyable art on the internet, i’ve made a new gallery page that can hold on to it for us.  mostly, they are just things i’ve seen on design milk that i’ve really enjoyed.  i hope you do to.

 
 

bounce

March 21, 2012

two very different bounce videos that i’d like to share with you all:

share your favorites in the comments.

in time – clock design

October 5, 2011

today was a good day for interesting time keeping design.  i came across these three different time keeping devices, which have a really interesting parallelism in their features:

we know the time
the tree tells the season
industry, the hour
and with robotic precision
an instant is born

a little musing on the wonderful juxtaposition of materials and fidelity that were used in all these clocks.  also, it’s the fault of Google+ that i didn’t just share the clocks and get on with my life, since you can’t share more than one fancy link in a post.  now i had to make a big deal out of it and waste a bunch of everybody’s time.

Wooden Perpetual Calendar

Roller Chain Clockworks

Robot-Readable Wall Clock

in your brain – you are not so smart

October 5, 2011

in the spirit of both “defeat[ing] procrastination now by giving the gift of humility to everyone you know” and entering in raffles, i’d like to present you with some beautiful kinetic type on the not so beautiful topic of procrastination.  not only is this a good watch, but the new book should be a good read, and the original content on the website is incredibly enlightening.

also, if you thought that I was ass-kissing there, then you are not so smart.  and neither am i.  On with the show…