It’s that time of year again

 Altered from NPR source.

Faadosly Polir is back in contact with us. We have encountered him before, but this time he has company. He has teamed up with two well-known radio personalities to launch a quiz show about mathematics.

Today Ken and I wish to talk about material for the show that Faadosly has sent us.

The draft he sent has the subtitle, “Strange Facts About Mathematics.” The material is not only about strange facts, but is strange in itself. Many of the “facts” are false. Everyone’s name is replaced by an anagram. Decoding the name to a true person helps you, but the fact can still be false. His co-authors on the scripts are named Pearl Gates and Slack Laser.

Apparently the idea is that the quiz contestant hears three “facts” and has to say which one is true. The problem is that their math items are not arranged that way, but rather jumbled all together. The proportion of true ones seems to be more like 1/2 than 1/3. Perhaps it is harder to generate true ones that seem false than false ones that are plausible, so they figure they can do more of the latter later? Anyway, they are allowing us to share some with you.

Some Strange Facts?

Here is a sampler from their draft—a mix of true stories and “fools.” Count a “fool” if either the personal description or the mathematical “fact” is false, or both.

${\bullet }$ Hydra Dye Frog, while well known for his brilliant mathematics in number theory and analysis, once wrote a seminal paper on genetics. The issue was whether a dominant character should show a tendency to spread over a whole population; or put another way would all recessive characters tend to die out. Assuming a reasonable random model of mating, he showed that dominant genes would not force out recessive ones.

${\bullet }$ Gail Kali is a mathematician from Chennai, India. Like her countryman Srinivasa Ramanujan, she credits a Hindu goddess for her mathematical insights—of course in her case the goddess Kali. In a dream Kali told her that every generalized Platonic solid with central symmetry in ${N}$-dimensional space has at least ${3^N - 1}$ lower-dimensional faces, including its vertices. Unfortunately, Gail woke up before Kali got beyond the all-triangles cases in the proof.

${\bullet }$ Rich-Cal Fried Sugars was another great mathematician known for many results in number theory. But in his lifetime he was famous for helping solve one of the great mysteries of his time. Astronomers were tracking the position of Ceres, a huge asteroid, and they lost it owing to the glare of the sun. He famously predicted the path of where it would be, and on New Year’s Eve astronomers found it.

${\bullet}$ One-Ale Hurdler proved that there was no way to route one-way traffic touring his whole city without causing a snarl. Even before his rule that T-junctions were bad news, he discovered that the bridges made it impossible. This problem founded an entire big branch of mathematics.

${\bullet}$ One-Cat Tree proved that a relativistic smoothing of the Navier-Stokes equations allows infinite concentration of energy in finite time, because of its ability to simulate universal computation. Running this in reverse, it follows from the quantum complementarity of energy and time that the Big Bang did a lot of computation in its brief timespan. The computational results can now be read off from the pattern of gravity waves in the cosmic microwave background. At over a trillion times the concentrated power of the Large Hadron Collider, the Big Bang Computer represents almost a billion times the processing capacity of Google, whose data-mining efforts to read off long numerical calculations from it are underway. Thus we have it: the digits of ${\pi}$ in the sky.

${\bullet }$ Wes Gromit is not related to the famous British star of animated films, but his father has composed many movie scores. In disjoint work with One-Cat Tree and Gene Bern, he proved the existence of an infinite arithmetical progression with exactly two prime numbers in it. Although married with five children, he was declared a bachelor by Queen Elizabeth II in 2012.

${\bullet }$ Annual Trig was a mathematician who along with a colleague introduced modulo wrap-around computation to cryptography. They actually used it modulo six, but the ability to wrap was essential to make their system work. They were working on an analog system to scramble telephone calls. In their system there were six bands that had to be moved around, and they found that by doing certain arithmetic operations modulo six they had more security.

${\bullet }$ Town Falconer proved that there is a language in ${\mathsf{NP}}$ whose complement does not have an interactive protocol. This flies in the face of there being an oracle constructed by Amish Raid that gives every language in ${\mathsf{PSPACE}}$ such a protocol, so that Falconer and Semi Spiker are credited with proving the only truly natural non-relativizing result in complexity.

${\bullet }$ Joint Who Tolled was a mathematician famous for work in analysis and related areas. He was a doubter of the Riemann Hypothesis (RH) throughout his life. There are claims—but who can tell—that he might have changed his mind if he knew some of the modern computations that show RH holding for a huge number of zeroes.

${\bullet }$ Glacial Warmish is a complexity theorist who is interested in Kolmogorov Complexity, among other things. One of his main results is a proof that this theory gives a natural construction of a set that is undecidable, but is weaker than the Halting problem.

${\bullet }$ Glib Tales co-wrote a paper proving what until recently was the fastest known way to flip pancakes in a stack so that the larger ones end up below smaller ones. Instead of opening a pancake business he founded a company which became rich enough to sponsor him in a match against the world chess champion. However, he got checkmated in nine moves. The paper still earned him an Erdős Number of 4.

${\bullet}$ Sonata Consort proved that quantum computers can solve ${\mathsf{NP}}$-complete problems. Although his algorithm is “galactic” in worst case, his ideas inspired a Vancouver startup company to build a quantum computer that solves ${\mathsf{NP}}$-complete problems in many cases, perhaps even without needing anything “quantum” at all. As this company’s most valuable consultant, he is paid in a quantum-money scheme of his own devising.

Open Problems

Which ones are the “fools”? Try not to be fooled today. As a hint, the fools have something in common…

5 Comments leave one →
1. April 2, 2014 11:59 pm

hey RJL one of my fave days of the whole year & you did not disappoint. cs is full of weird & wonderful characters & hope this show catches on. it seems there are so few shows about CS and thats ridiculous considering how much it permeates our culture.

in honor of today, there is an old saying in software engr…

its impossible to make anything foolproof…
because fools are so ingenious ❗