l33tminion | Entries tagged with math

Erica is away with Julie's parents this week, on a road-trip to the Grand Canyon.

On Thursday, I had a birthday dinner with Julie at Bogie's Place which is a tiny steakhouse tucked between jm Curley and The Wig Shop in downtown Boston.

I went to a concert with Julie on Friday at Sonia , one of the music venues at the Middle East in Central Square. Hadn't been there before, though I'd been to some of their other stages. Was EDM, the headliner was Shingo Nakamura, the openers were a B2B (collab set) with Cloudcage and rshand, followed by OTR. Been a while since I caught live music, and also a long while since I was out late in Central. Lively place, was a good time.

I watched a bunch of the runs from SGDQ this week, but I still feel like I want to catch some of the replays. Not as much stood out to me this year of the things I caught. The Super Metroid race is still always a good time.

Yesterday, managed to get out to Ingress coffee get-together in Arlington for the first time in a while. Saturday evening, we had dinner at Black Ruby, which was pretty cool. This evening, I got together with gaming group at Xave's to play more of The Far Roofs.

Random favorite thing from the last few weeks: This video titled What is PLUS times PLUS? about the Lambda Calculus. The visualization for that used in the video (Tromp's Lambda Diagrams) are a really striking way to look at that mathematical system. I was familiar with the concepts in the video before, but it's still a mind-blowing foundational piece of computer science that all you need to do literally any computation is just the simplest sort of function definition and function application, nothing more, that's it.

Current Mood: awake

Reposting this riddle from Tanya Khovanova's Math Blog, so that I can put the solution behind a link:

Four wizards, A, B, C, and D, were given three cards each. They were told that the cards had numbers from 1 to 12 written without repeats. The wizards only knew their own three numbers and had the following exchange.

A: "I have number 8 on one of my cards."
B: "All my numbers are prime."
C: "All my numbers are composite. Moreover, they all have a common prime factor."
D: "Then I know the cards of each of you."

Given that every wizard told the truth, what cards does A have?

( Solution )

Current Mood: thoughtful

Needless to say, I should post about interesting things I find more frequently instead of fishing through my backlog for an entire year.

Technology and Mathematics

The new way of passing the Turing test is to have humans pretend to be AI.

Who Was Ramanujan - Stephen Wolfram (of Mathematica and Wolfram Alpha fame) tells the story of one of an unlikely mathematician (and the subject of a recent biopic). Really interesting stuff.

Urbanism and Transit

How Japanese zoning laws avoid many of the problems of US zoning.

Navigating NYC with a guidebook from 1899.

How to save the MBTA $100M a year: Fix paratransit, subcontract bus maintenance, cut administration.

On state-level funding of urban mass-transit, and why this is about rural-urban political conflict.

An old post with an interesting idea for modifying urban development proposal contests.

"Nations aren't the proper unit of macroeconomic analysis; cities are."

The king of the frequent fliers.

Food and Medicine

Why almost all eggnog sold in the US violates FDA regulations, and why that's not technically illegal.

Why the cure for scurvy was widely known in Europe in the 1700s, but not known by polar explorers in the early 1900s.

An amusing post on pharma company sneakiness, with a great post title.

More Recent Politics

Why Sanders Trails Clinton Among Minority Voters: It has a lot to do with Obama.

Why didn't Bernie Sanders raise any money for the DNC? Short version: Clinton is there to do it for him.

What Would a Trump Victory Tell Us About the Republican Party? The article proposes several possibilities about what pundits and politicians may have gotten wrong in underestimating the chances of a Trump victory. Very interesting to look back at this January post a few months later.

The Smug Style in American Liberalism: Accurately characterized on Reddit as Vox Voxsplains Itself.

Current Mood: tired

A StackOverflow poster asked if auto-currying functions could be implemented in Lisp dialects, and I decided to take a crack at it in Common Lisp.

Currying is easy enough to implement in Common Lisp, as shown here:

(defun curry (function &rest args)
  (lambda (&rest more-args)
    (apply function (append args more-args))))

But I found my (hopefully correct) implementation of auto-currying rather amusingly self-referential:

(defun auto-curry (function num-args)
  (lambda (&rest args)
    (if (>= (length args) num-args)
        (apply function args)
        (auto-curry (apply (curry #'curry function) args)
                    (- num-args (length args))))))

Current Mood: amused

Anime: Japanator's top 50 for the decade. An interesting selection. I've watched all of 22 of those and touched on 6 more.

Clothes: Ties! Also, the other kind of ties! umbrellas! Blue shoes! Double monks!

It occurs to me that I've gone from two pairs of shoes (running shoes, black oxford dress shoes; three if you include beach sandals) to seven (running shoes (which I still wear at least 95% of the time), black oxford dress shoes, cheap old wingtips, moar better wingtips, thrifted fringe loafer, cheap blue canvas sneakers (CVOs), casual slip-ons (I like the idea of using those as beach shoes much, much more than sandals, which I hate)). Basically, if I ever win the lottery I'm in danger of becoming this guy. (Not really. I hope.)

Education: Here's a method of learning phonetic alphabets (like Japanese kana): transliterate random things.

An interview with the Olin College president. I find the answers both interesting and disappointingly moderate.

A Wellesley student discusses Wellesley's admissions office's discrimination against transgendered students. Yet another "the writing is on the wall for Wellesley as women-only" story, there were several others during my Olin days. A good example of how overt, allegedly acceptable discrimination leads to covert, obviously shady discrimination.

An MIT researcher turns his house into a (self-directed) panopticon, with interesting results. I discussed this at length on my other blog.

A discussion of the World Peace Game, an educational game of global politics played by fourth graders.

Random Interesting: Broken lottery scratch-off games and their relation to security, math, and crime.'

Overthinking It analyzes Rebecca Black's "Friday", which must be the most successful vanity video of all time.

Playing video games while blind.

A bit of randomly interesting math: What is the highest value of n for which the decimal representation of 2^n has no 0s?

An article on a handbook for overthrowing dictators, which has evidently been quite influential this year.

An article on the psychology of (media) overabundance.

Better libertarian rhetoric with regard to "anti-privilege" liberals. Good stuff.

Dinosaur Comic's take on polyamory. Read the extra title text. I love that brand of subtle snark.

Current Mood: amused

Been ages since I did a links post, so here's some of the best of the web since last time:

A bunch of Overthinking It essays: One on Starship Troopers (on why critics got it wrong), one on Fantastic Mr. Fox (a Freudian analysis), one on Avatar (the James Cameron sci-fi movie; starts off slow but then gets brilliant at the end). For those of you who don't read Overthinking It, it's a great site for those who like literary criticism applied to things that often aren't looked at through that lens.

A comic, Mysteries of Public Transit, mainly because I identify far to much with point 3. Subnormality is a great comic (for those who like their comics to be WALLS OF TEXT).

An 18-minute video essay on the world's most important six-second drum loop. Actually rather fascinating.

Every two years, Robert Jensen writes an essay on how much he hates Thanksgiving. Here's his offering for this year.

Here's an essay titled Can Videogames Be Our Friends. Yeah, it's about Japan.

Here's a post explaining why only an infinitesimal subset of all numbers can be described. Speaking of things which can't be counted, here's some crazy's argument that the real numbers are countable, and a rather entertaining takedown of that essay.

Finally, here's a news piece on one of my favorite charities, Kiva.org. Evidently, there's some confusion about how the site actually works, some people were surprised to learn that money can be loaned out before a loan is marked as "funded". To be clear, it's not necessarily your money that goes out to the entrepreneur in question. Rather, your funds secure the loan in question, if the loan is not paid back, you take the loss, rather than the microlending institution. That spreads their risk, so they can keep on lending. As long as every loan funded through Kiva is actually disbursed to the entrepreneurs by someone, and as long as Kiva lenders are repaid when the loan they agreed to secure is repaid, Kiva is living up to their end of the bargain.

A few brief bonus links for those of you not yet put to sleep:

Japanese people mortified by crazy US media.
Don't use regular expressions to parse HTML or Cthulu will devour your soul.
One of the most dramatic examples of missing the point I have ever seen.
"Thinking about your own beliefs" and "thinking about God's beliefs" look suspiciously similar on an MRI.

Current Mood: working

SIPB talk today by Keith Winstein about "The Non-Conflict Between Bayesians and Frequentists" was interesting.

Basically, the two approaches to probability are as follows: Bayesians use prior probability (which may involve assumptions) to calculate the probability of a result given a new piece of data. Frequentists determine what answer they can give that will be right a given percentage of the time.

There's no real conflict, mathematically, it's just a matter of looking at different things. Bayesians look at the error rate among positive results, Frequentists look at the rate of false positives. Alternately, Bayesians focus on giving the best answer for every possible input, Frequentists focus on being most reliable overall for every possible output.

Less flatteringly: Bayesians use all of the information they have, but also some of the information they don't. Frequentists are reliable overall, but are willing to tell you manifestly untrue things so long as they only do so a small percentage of the time.

Frequentist vs. Bayesian is far from the only issue, which specific statistical test you use matters. Then again, the difference between reasonable statistical tests (even ones overly permissive for some values) might not be that significant in numerical terms, even if the difference can be quite substantial in financial terms.

Still, the conflict has some relevance to science. If you assume that people are studying a wide variety of hypotheses, only a tiny portion of which is likely to actually reflect the real world, then you might only have to admit a small percentage of false positives before the false positives overwhelm the true results.

Current Mood: thoughtful

The Case for Separated Bike Lanes in NY: Good short documentary essay.
The Filled Pause Research Center: Um...
Absurdly Long Key Lengths in Crypto are Silly: Includes an interesting argument about computer science based on physics.
The Conservative Bible Project: Wonder what they'll do about Jonah.
Quine Relay in 11 Languages: I am in awe.
An Anecdote About Health Insurance: Yet another reason why paying for health insurance doesn't necessarily help if you actually get sick.
Avego Shared Transport: Interesting idea, but won't it run afoul of laws on commercial vehicles, cab licenses, and so on?
Drinking Age of 21 Doesn't Work: I agree.
The Story of the Gömböc: An odd tale of geometrical modeling.
EVAL-WHEN Considered Harmful to Your Mental Health: Read if you're a Lisp programmer.
On Overdraft Fees and Usury: $38.5 billion / year in the US alone.
On the Overton Window, Columbine, and Healthcare: An interesting essay.
An Interview With Patrick Galbraith: Mainly, I like the guy's wholehearted rejection of critical distance in ethnographic study.

Current Mood: awake

Here's an interesting graphic, the map of changes in voting patterns between 2004 and 2008 by county. Almost all of the country went more Democratic, which is hardly a surprise when you compare Obama and Kerry (world of difference) versus McCain and Bush (basically clones). Except for that one infected-looking patch, for which the usual metaphor applies quite a bit more visually than usual. Other 2008 election maps and cartograms are also interesting.

The rest of the stories I have to share are largely unrelated to eachother, so hang on a moment while I break out the bullet points:

It looks like Obama might squeak out one more electoral vote by carrying Omaha (Nebraska divides it's electoral votes by district).
Here's part one of the post-election GOP asplosion watch. Prepare for many popcorn-worthy moments in the weeks ahead.
There's something really fishy going on in the Alaskan election (a native on the ballot and unprecedented registration and turnout is much lower?), which matters because the senate race has still not been called. If the convicted felon Ted Stevens wins, it would be a spectacular failure of polling.
The website for Obama's transition office is up, so share your vision. Meanwhile, the ACLU calls out Obama with a detailed and demanding transition plan. There's also a reddit-style website for political policy suggestions; no idea who's running that, though.
Obama was quite the candidate, but his campaign-level strategy was also quite something, especially in Pennsylvania , where McCain committed vast resources to lose by double digits. The Obama campaigners were apparently masters of the political rope-a-dope.
Hey, the high-speed rail ballot initiative passed in California! This is very good news, I hope it's a trend-setter. High-speed passenger rail is one of the best investments we can make now. Provides jobs and gets people where they need to go when the airline industry is failing, lowers fuel consumption, takes pressure off overtaxed highway infrastructure. Good for the economy, gas prices, and the environment.

Current Mood: excited

Programming:

I've been seeing quite a lot of discussions of web design style lately. Compare the emerging style of early web design with the polished Web2.0 Style. Even newer styles, such as Grunge and Hand-Drawn use the techniques of modern web design while breaking from the Web 2.0 aesthetic.
Rich Programmer Food: On compilers and the most important class for computer scientists.
An article on "Turing Tar Pits" and how programmers make things hard for themselves.
How to teach yourself programming in ten years.
10 Python Quirks: Read this if you're a Python programmer. Did you know all of those? (I didn't.)
An anecdote about teaching children programming.
Big Red Angry Text: On CSS styles for debugging

Other:

Post-It Note Art: Completely amazing!
On why "don't talk to strangers" is "just about the worst possible advice you can give a child".
An article on the Naked Rambler, who in January was free for several steps before being arrested again for his persistent nudity. *facepalm* How should society deal with such people? And should (yes, I mean that in the moral sense) the Naked Rambler just wrap / shut up and conform?
An anecdote on parenting, food, and vegetarianism.
The website for Urville, a fictional city created by a savant who now makes a living by imagining / drawing / writing about / talking about said fictional city. Also a particularly good example of (what I'd refer to as) 90's Crazy web design style.
A recipe for Pan Seared Salmon with Avocado Remoulade
A video on turning a sphere inside-out. Nifty. Watch if you're interested in topology / are wondering what the heck "topology" means.
On creating a warning marker to last for 10,000 years.
Why Starbucks actually helps local coffee shops.

Current Mood: chipper

Here's the answer to that homework problem I mentioned earlier. To restate the problem:

A ball is sewn together from pentagonal and hexagonal pieces of material. Each edge of each polygon lines up exactly with an edge of another polygon. Three polygons meet at each corner of each polygon. Prove that the ball must contain exactly 12 pentagons.

( The answer to this problem is simple... )

Current Mood: thoughtful

The following problem was on my homework (paraphrased):

A ball is sewn together from pentagonal and hexagonal pieces of material. Each edge of each polygon lines up exactly with an edge of another polygon. Three polygons meet at each corner of each polygon. Prove that the ball must contain exactly 12 pentagons.

It's quite the beautiful proof.

( Hint )

Current Mood: contemplative
Current Music: This Week in Tech #73

L33tminion: To work! ... Oh, sorry, I though you were proposing a toast...

Sam: *shakes head*

I didn't have any classes this morning (although I did get some work done), but the afternoon was very busy. After software design, which was unexceptional, was the cohort, where we split into teams and began work on our project for the quarter, bottle rockets. We're going to use this as a center point for our curriculum, allowing us to apply to what we learned (physics, calculus, Matlab, mathematical modeling, experimental design, the scientific method, teamwork, design, etc.).

Afterwords, I attended a guest lecture given by Dr. Arthur Benjamin, a professor of Applied Mathematics from Harvey Mudd University (and a mathematical genius and exceptional human calculator).

( More on the lecture (interesting, but long)... )

Current Mood: busy

Yesterday's lecture on chaos theory was interesting, but today's lecture, which was on the physical properties of soap films, was by far the best lecture this session. The lecture showed how properties of soap bubbles can be used to demonstrate solutions to minimization problems.

( More Details on the Lecture )

The professor also gave the following problem. How can you construct a square of side length a given two points a units apart using only a compass (no straight edge)? I've thought about this for a little, but so far I haven't figured it out. I might work on it a little later.

Today in lab, I finished working on the first draft for our final report. Tomorrow we will finish the report and begin work on our presentation.

Current Mood: happy

Today was pretty relaxing. I got my kit of stuff, which includes a map and a really nice hat.

The group spent the morning attending lectures on the different research projects, and the afternoon interviewing with the project coordinators who will make the project assignments.

I interviewed with the Mathematics and Computer Science Coordinator. My top 5 project choices were:
1. Image Completion Using Multiscale Interpolation (Computer Vision)
2. Using Genetic Algorithms to Solve a Simplified Version of the Protein Folding Problem (Genetic Algorithms)
3. Reconstructing Motions from Data Recorded from a Sensor Glove (Data Recording)
4. Identifying Objects in a Database from an Image Despite Arbitrary Lighting (Computer Vision)
5. Proving that a Simplified Version of a Game of Minesweeper is NP-Complete (Complexity Theory)

The interviewer seemed impressed by my ComSci knowledge (I think I am the only serious Computer Science person in the program, or at least one of a few) and offered me number 3 as I was telling him my choices (It wasn't mentioned in the lectures, and I only had four projects chosen at the time).

After my interview, I took a walk to get my glasses fixed (I lost a nosepiece). The walk was long, and I wasn't sure of the directions, but I was finally sucessful. The walk would have been really nice, except that it is so hot and humid here (remember: hat, water bottle, sunscreen). At least the buildings are all air-conditioned.

( Extended Weather Forcast )

Tonight, a party. And project assignments will be revealed.

Current Mood: energetic

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Sam

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Canyon Week
A Math Riddle
L33t Links: Unbacklog Edition
Math With More Curry
L33t Links: Too Many Shoes Edition
L33t Links: WALL OF TEXT Edition
I'd Still Rather Have Bayesians Running Nuclear Reactors
L33t Links: Long List, Short Summaries
What, You Thought I Was Going to Stop with the Election Talk?
More of the Best, Programming and Otherwise
Soccer Ball Theorem Proof
The Soccer Ball Theorem
To Work
Soap Bubble Science
Calm Before the Research

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Sam's L33t Journal

(Secret Master Plan Draft v0.2)

Entries tagged with math

Canyon Week

A Math Riddle

L33t Links: Unbacklog Edition

Math With More Curry

L33t Links: Too Many Shoes Edition

L33t Links: WALL OF TEXT Edition

I'd Still Rather Have Bayesians Running Nuclear Reactors

L33t Links: Long List, Short Summaries

What, You Thought I Was Going to Stop with the Election Talk?

More of the Best, Programming and Otherwise

Soccer Ball Theorem Proof

The Soccer Ball Theorem

To Work

Soap Bubble Science

Calm Before the Research