For mathematical typesetting, especially on slides, it’s hard to beat LaTeX.

Clearly my essay blogging is geared ever more towards the general population.

Funny thing: while making some diagrams for this post, I needed a table of Riemann zeta function values. My CRC Mathematical Tables and Formulas didn’t have it, so I reached for Billingsley’s Probability and Measure, but before I opened it I googled “Riemann zeta function table,” and found what I needed.

This Internet thing is worth saving, really.

Mathematician’s Dice

MAA Found Math for the week of July 11, 2011 (by MAA Found Math).

Some modal logic as I take a break from mildly irritating econometrics. That’s from a preprint of Johan van Benthem’s Modal Logic for Open Minds.

Pepper…and Salt - WSJ.com

Via bookofjoe: Bayesian Truth Serum. A tip of the actuarial green eyeshade to Ilkka.

This Saturday Morning Breakfast Cereal shows the importance of being precise: what Lambert proved was that pi cannot be expressed as a ratio of two integers.

As a annoying stickler for precision in mathematical references in daily life, I answer “pick a number” with “e to the cube root of pi.” Always a conversation changer.

Sure, they all require effort, dedication, discipline, focus; but that is true for doing anything well.

In these activities there’s a clear, inarguable standard of achievement: the program compiled and worked, the proof was valid, the barbell went from touching the chest to elbow lock-out, the finish line was crossed at 1h07m.

In many other activities there’s a lot of leeway for arguing merit and opportunities for feel-good talk. Not so with programming, math, strength training, or running. No amount of pleading will make an invalid-syntax program compile, a singular matrix invertible, elbows lock, or time stop.

(You can have bad form in strength training, of course; but it catches up with you, fast, with hilarious results. Once you get into the lift-multiples-of-bodyweight territory, bad form makes for spectacular accidents. Videos courtesy of Gym Idiots.)

When I taught computer science, I never had a student argue that their program failure to compile is “just the compiler’s opinion.” But I’ve had [a very small number of] students try to argue — unsuccessfully — for their wrong solutions to business problems as just differences of opinion. Since my classes are generally quantitative, there’s not much space for opinions or interpretation.

I guess I’m an old-style academic; and an overwhelming number of my students like that, according to the fast-food-like customer satisfaction measures administered at the end of my courses. They understand that for a successful education, reality must trump self-esteem, for the business world cannot be fooled. Well, not by just-minted MBAs.

Making people feel good about themselves at the cost of their learning doesn’t make sense to me. I’m all for deserved praise, but vehemently opposed to undeserved credit.

Just like a recent one-rep-max bench press attempt, where the weight didn’t care for my self-esteem: it went 98% of the way up, but the spotter had to help me lock-out, or as we say in the gym, no lift. 98% = No Lift. 100% = Good Lift.

No lift. No argument.

Line 27: invalid command sequence; compilation aborted. No argument, either.

MY CHILDHOOD INTERESTS AND THEIR INTERRELATIONS

My first, my last, my everything (yes, I grew up during the age of disco) was, is, and will be mathematics: order, structure, logic, truth. Gödel kind of threw a spanner into the whole machinery, but I only learned that in my teens. By then I had learned to deal with adversity from my interactions with the females of the species.

Math feeds into all my intellectual interests; even music: in its purest form, music is the construction of patterns of sound to stimulate patterns in our brains. (I don’t like much of modern serious music because it fails to fit this description.)

Music and electronics, separately, were my most observable interests: I played piano and built electronic circuits. Most of my early English learning was from reading Elektor Electronics (and later Byte); only much later did I start to read science fiction in the original language.

Interest in music and electronics led me to build synthesizers (analog synths, with VCO, VCF, VCA, ADSR… if you know what these things are, you’re old). And my interest in the synthesizers led me to an interest in old-style Electronica: Vangelis, Kraftwerk, Tangerine Dream, and Jean-Michel Jarre.

From analog electronics I graduated to digital (TTL first, CMOS later) circuits, where the beauty of their clean logic (instead of the analog’s calculus) trapped me. From these to computer hardware design (in theory) and programming (in practice) was a simple step. (I did publish a paper on fault-tolerant hardware design in Microprocessors and Microsystems at the end of my undergraduate degree.)

Propelled by Scientific American’s Metamagical Themas, I used computers to play around with puzzle-solving and simulated worlds (with different physical laws). Eventually this led to an interest in Artificial Intelligence and a change of major (EE to CS) in my undergraduate degree. I still have a more-than-professionally-required interest in machine learning due to this.

Physics was another early childhood interest. It was great to understand how the world worked; and physics allowed me to solve real-world puzzles that were at least as interesting as the mathematical puzzles I used to solve as a child. Huge intellectual debt to my Godmother, then the librarian of the Physics Department of University of Coimbra; a smaller one to Carl Sagan and his Cosmos series. (By the time I saw Cosmos, I was irrevocably an Engineer.) It also led to an interest in science fiction, mostly books and comic books.* 

Physics also got a leg up from my interest in the workings of acoustic musical instruments. I play piano, which is as far from having to understand the acoustics of the production of sound as any instrument can get (just hit the keys and the sound comes out), but the creation of sound fascinated me. (Which helps explain the interest in synthesizers by a Bach-and-Liszt player — uncommon, that.)

Quantum computation is not a childhood interest; it’s a recently acquired interest, but since it builds on these childhood interests, I included it in the graph.

Most people relax by watching TV or practicing sports. I like to make slides, and since I can’t (for various reasons) share professional or work slides, I make these just for fun.

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* I watched the original Battlestar Galactica and Buck Rogers in the 25th Century on TV, but they were about space cowboys, with zero science (or military) content; I had a crush on Erin Gray, though.

Inequality ≠ Poverty.

Suppose there’s a town with 1000 people, whose income follows a uniform distribution (meaning that the probability of a person having any of the possible income levels between the maximum and the minimum is the same for each level of income, not that every person has the same income as other people).

Let us also assume that there is no capital accumulation so that all wealth is created by income and is not wealth-generating on its own (meaning that there’s no income from savings that will accrue to those who made more money in previous terms). 

So, how does this affect inequality and wealth? The results for the lower and upper quintiles are in the table above. Notice how the middle quintile always has 1/5 of the wealth; this is a mathematical implication of the uniform distribution and serves as a validity check on the calculations (so if you decide to check those numbers, your formulas will be wrong if you don’t get those 20% in the middle).

What does this tell us?

Comparing scenarios 2, 3, and 4 with the base scenario 1: when a society gets richer by expanding its ability to generate wealth (and notice that everyone in that society except the lowest paid person does become more wealthy), inequality increases.

Mathematics makes no moral judgments. But it tells us to be careful when assuming that inequality is an indicator of poverty.*

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* Once, at a choice modeling conference where several american economists were talking about poverty, my PhD thesis discussant, a famous Indian economist, told me that “clearly these guys have never seen what real poverty looks like.”

Math notes: 1. The number of people in the town doesn’t matter, as long as it’s large enough to use a continuous approximation. 2. I picked uniform because it’s easy to integrate and get analytical rather than numerical solutions. 3. Not allowing for wealth accumulation makes the case stronger, since it’s all about income.

Pendulum Waves - A funny demonstration of the effects of multiple signals with different (but close) frequencies. The “beat” of this system is approximately 60 seconds, and we can see some noise in the third-to-furthest pendulum, probably caused by the release “mechanism.”