Futurama's Math Jokes

Those that love math will probably get a kick out of Futurama and their blink and you miss it math jokes.

Aleph-Null Plex as a theater name instead of a "multiplex." Now that's good. For those that don't know, Aleph-Null is a part of Set Theory, a mathematical concept described in the 1870s by Georg Cantor, a concept that is taught even at simple levels by the use of Venn diagrams (remember those?). According to him there are various types of infinities, and because Cantor was Jewish, he described by the Hebrew letter Aleph.

Aleph-Null (or Aleph-Zero) is used to describe the set with the smallest cardinality (or size of the elements in a set). It measures an infinity according to natural, ordinary counting numbers (excluding zero, negative numbers, and irrational numbers). Cantor made a distinction between transfinite and absolute infinity, in the sense that transfinite numbers are sets bigger than any finite set, yet they fall far short of absolute infinity. In fact, it's been demonstrated at least in classical cardinal mathematics that the sum of all ordinal numbers can't possibly exist, something called the Burali-Forti Paradox.

Think of the Burali-Forti Paradox like this. Take something that is meant to represent the sum of all ordinal numbers. Cantor was partial to the Omega symbol for religious reasons. Now, the concept you just created has all the properties of a number that can be listed in a set! There are some interesting ways to resolve this paradox, notably through use of different principles of set theory.

Upcoming movie about the real Hypatia

Hypatia is my hero and it's not hard to see why. In the world of Hellenistic Greece, she stood out as a great thinker and teacher, a pagan in a time of mostly Christians, one of history's greatest mathematicians.

Rachel Weisz is going to be playing Hypatia, the single most obvious and appropriate casting choice in the history of Hollywood. I wait with eager anticipation to see "Agora," a movie about the life and challenges of Hypatia and the Library of Alexandria. It's not very often that Hollywood does a movie about a mathematician...the last one I can think of is A Beautiful Mind. It doesn't hurt that Hypatia was supposedly one of the world's most beautiful women, or is at least romanticized as being that way by poets. Carl Freidrich Gauss and Paul Erdos may be great mathematicians, but they definitely don't have much in the way of sex appeal.

I have no idea how it is that I didn't hear about this movie until today. It totally blindsided me, and I usually keep my pulse on movies about math and my hero, Hypatia.

Feast your eyes on the trailer, spuds:



By the way, after several years of text flying at the screen and quick cuts passed as movie trailers, isn't it great to hear an old-fashioned Voice of Doom trailer again? "In a world of conflict and torment...one woman will rise to lead a nation..." It's like the movie trailer was made in 1994!

Altitude map of the planet Mars

Now for some good stuff - a topographical map of the planet Mars arranged by altitude. Notice the southern hemisphere is so much higher!

There are some points that go way, way higher than 8km on Mars, but that's because this picture is what the scientist Gauss calls a Geoid - a crucial concept in planetary mapping and geodesy, a sort of surface model/figure of the earth (or other planets) that smooths out extremes by surface gravity. However, the use of 8km as a base shows it goes by earth gravity - which may result in a less useful model.

A geoid is very different from say, a reference ellipsoid, which is a smoothed out, idealized diagram of the earth. These two are used together in the field of Geodesy, which is scientific surveying, how maps are constructed and GPS works. It is the use of mathematics to determine altitudes and points on a map.

If you're like me, you're the sort that gets curious and asks questions, and one for me is this: how exactly is that they KNOW that Mt. Everest is the highest mountain on Earth? The answer is that it wasn't known. Until 1849, it was commonly believed that Kangchenjunga in North India was the highest mountain in the world (today, it is believed to be the 3rd tallest).

Check out this document out from the National Geospacial Intelligence Unit that introduces interested laymen to how Geodesics is done.

Lord Kelvin's less famous brother Jimmy

What I find amazing about James Thomson is that he was no shoe salesman, yet he was totally overshadowed by his older brother William...a guy you might have heard of by the name of Lord Kelvin.

Lord Kelvin's less famous brother Jimmy was the president of the Scottish Society of Shipbuilders and Engineers from 1884-1886. He was a true scientific Renaissance man, who did research into glacier motion and the flow of rivers, and who also invented a type of accelerated turbine used for underwater vehicles. He was also the first person to invent the term "interface," a word to this day. He was the closest thing in reality to one of those TV scientists like Dr. Benton Quest that can do Nuclear Physics one day and anthropology and linguistics the next.

James Thomson's best contributions by far were to the field of mathematics. Based on the work of the Bavarian engineer J.H. Hermann, Jimmy created an improved version of the polar planimeter - an instrument that allows area to be determined on a flat surface of any arbitrary and irregular shape.

What's more, he was the first to coin the term "radian" for the single most useful angle of measurement in calculus, the length of an arc of a sliced of subtended angle that is equal to the radius of a circle. Radians are useful because they allow derivative and integral identities to be expressed in very short time-saving terms. What's more, in trigonometry, the relationship between sine and cosine angles can only really be expressed in radians and it's extremely awkward to represent in any other way.

Among other things, radians are useful in determining the speed of rotation (something physicists call angular velocity). The radian is also used in (God help us) Quantum Mechanics, where it is necessary to describe the functions of Planck's Constant. According to Max Planck, the flow of energy is determined by fundamental "bits" in the universe, Quantum. Energy can't assume any given variable range, but only on a finite set of ranges determined by grouping Quanta. It's possible to make something move a "little bit faster" or making something "a little bit brighter" because the amount of Quanta involved are very, very tiny so they're invisible to the everyday scale. Planck's Constant is used to describe the scale of quanta as the smallest amount of energy a quanta can have, and it is necessary to use radians to understand it because when applying Planck's constant to energy, you need to figure out the relationship between quanta and frequency, which comes in waves as in trigonometry.

This was the guy that was Lord Kelvin's "less famous" brother! Amazing! Why would a guy like this be known as the lesser of the two brothers, anyway?

Because Lord Kelvin did nothing short of create the unifying principles of physics, almost like Darwin created the unifying principles of the biological sciences. He codified the Laws of Thermodynamics, and connected how heat functioned in a way similar to that of electric charges, a unifying idea that was one of the most crucial in the history of science. Though Faraday discovered that electromagnetism needs a medium to flow, it was Lord Kelvin that put forth the mathematical models for how that could be. It was also Lord Kelvin who speculated on the idea of a possible "absolute zero," and the idea that heat is actually a form of motion.

All that said, why is it that Lord Kelvin is better remembered than his engineer brother? Scientists are often called impractical Ivory Tower people, especially in the face of "doers" like engineers and industrial scientists. Scientists that work with "theory" (a term misunderstood by people outside of science) are viewed as less crucial to the world than inventors and practical people. Alas, in the end, it is the theorists that end up being ultimately more important because theories in science are not half-baked guesses, but grand, unifying ideas that explain facts and make predictions. More is ultimately learned, and more ultimately comes out of a theory. Lord Kelvin tried his hand at being an engineer, too, like his famous brother, but more people remember his formulation of the laws of thermodynamics than his efforts at telegraphing and his building a newer and better galvanometer.

God thinks he's a mathematician

There's an old joke that ecologists think they're biologists, biologists think they're organic chemists, organic chemists think they're physicists, physicists think they're God, and God thinks he's a mathematician.

I may be heading into Gosporn territory here, but that's always been my attitude to theology. At the end of the day, the only decent field of metaphysics is mathematics.

Here's a great yarn from one of my college physics textbooks:

The temperature of Heaven can be rather accurately computed. Our authority is Isaiah 30:26, "Moreover, the light of the Moon shall be as the light of the Sun and the light of the Sun shall be sevenfold, as the light of seven days." Thus Heaven receives from the Moon as much radiation as we do from the Sun, and in addition 7*7 (49) times as much as the Earth does from the Sun, or 50 times in all. The light we receive from the Moon is one 1/10,000 of the light we receive from the Sun, so we can ignore that.... The radiation falling on Heaven will heat it to the point where the heat lost by radiation is just equal to the heat received by radiation, i.e., Heaven loses 50 times as much heat as the Earth by radiation. Using the Stefan-Boltzmann law for radiation, (H/E) temperature of the earth (-300K), gives H as 798K (525C). The exact temperature of Hell cannot be computed.... [However] Revelations 21:8 says "But the fearful, and unbelieving...shall have their part in the lake which burneth with fire and brimstone." A lake of molten brimstone means that its temperature must be at or below the boiling point, 444.6C. We have, then, that Heaven, at 525C is hotter than Hell at 445C. ~From Applied Optics

Happy Pi Day!

"Mathematics is just the sex urge sublimated."

- M.C. Reed

"If people find mathematics complicated, it is only because they do not understand how complicated the real world is."

- John von Neumann

You know, there was a time as a college undergraduate that I could actually rattle off Pi to the 50th digit by memory, and compared to some other people I knew in the Mathematics program, I was a downright underachiever. Mathematics is a fundamentally humbling field because there are occasions where you feel that your pencil is smarter than you are.

Nonetheless, Pi is a miraculous number, an elegant mathematical constant that expresses the ratio of a circumference of a circle to its diameter. Like the properties of water (see below!) pi is one of those wonderful things that show a comprehensible, symmetrical universe. It's great to dedicate a day to celebrating it.

Yes, you will need to know this in your life

There's no such thing as a useless field of math.

As someone that loves mathematics enough to get an undergraduate degree in it, I am often frustrated by a world of people that are oddly math-illiterate and strangely, shamelessly proud of this! I don't have statistics on hand, but I wonder how connected this math illiteracy is to the current financial and banking crisis, where part of the problem was people took out loans they couldn't understand.

Part of this seems to be the weird belief there are two jobs out there: math track jobs and non-math track jobs. In reality, everyone benefits from math and it opens doors to new careers. Here's a solid expectation for American education: it's a failure if every kid can't speak a second language or at least do calculus.

I expect this kind of attitude from smartassed kids that wonder what it means to their lives, and politicians, but it's a little surprising at times to hear from math teachers too! I grew up at the start of the era of "New Math" instruction, and one thing that we learned was matrix mathematics, a key tool of linear algebra and linear transformations which involves a rectangular array of numbers, each of which are called "elements." This is occasionally pointed to as the

epitome of useless experimentalism on the part of educational psychologists.

I'm gobsmacked to hear this from educators because this is actually a skill I use in my life!

Here's just one area where you may need to know matrix modelling in your life: electronics. One of my hobbies is electronics. Nothing beats a lazy afternoon tinkering on a breadboard with a multimeter and logic probe in hand!

In circuit design, determining resistance to current comes from figuring out either the sum of resistor component values (expressed in Ohms, not to be confused with Watts, a unit of power) as in series circuits (those arranged in a straight line) or in the case of parallel resistors, where the current splits between the impedance elements and flows on the path of least resistance.

Since many circuits use various kinds of resistance elements, figuring out total equivalent resistance can get pretty hairy, because voltage is a relative factor. It can be different at various points along a circuit.

Enter matrix models! A simple way to determine it at various points in a circuit is to create two 2 x 2 matrix models, one with input voltage, input current, output voltage and output current as elements, and another matrix model with four elements: impedance, admittance, and two dimensionless qualities.

Did you get all that? Okay, even if the vocab is a little intimidating, there's no reason to be nervous about them since how they work is relatively simple: all you have to do is multiply the two matrixes together! This is one example where math is the universal language. Even if you don't know your impedance from your admittance, you can actually still figure out how it works if you know the process!

In fact, come to think of it, in a hobby as entertaining as electronics, math is everywhere! When working with alternating current, some trigonometry is necessary, for instance, because you're handling a sine wave, as current strength changes and switches many times per second, so a single value just can't be given.

Hey, Esperanto Grrl, what can I do with a degree in pure Mathematics?

The truth is, I went into Mathematics because I was good at it and I loved it. I especially loved the "pure" kind of mathematics, and to this day, I'm involved with GIMPS, the search for Marsenne prime numbers. And while prime numbers have applications today in modern cryptography, it's basically pure math. Likewise, topology (geometry on a non-flat plane) always intrigued me most of all.

But the truth is, as I've discovered, a Mathematics degree is a stepping stone to graduate school.

What I'm saying is, don't listen to the people that tell you an undergrad degree in Mathematics is useless. Good math skills are useful wherever you go. Who do you think designs IQ tests, eh? Psych PhDs with skills that are better than the average bear, that's who!

And if you've got a lower division mathematics degree, try going into physics or engineering. The problem with the mathematics used by those two groups is, their use of math is extremely heuristic. Math, to them, is almost magical, like a kind of voodoo. A math background gives you the ability to actually reason and work with numbers.

If you're in the process of getting your mathematics degree, try to concentrate on linear algebra, as it is at the heart of ordinary and partial differential equations. Don't forget numerical analysis and linear programming (as well as optimization theory) as that may be helpful to a computer-centered field.