Math in the Media: Arguing on Pi-Day

I cannot say that we, as mathematicians, do not have our fair share of math-arguments and inside jokes and math puns and such.  You know, stuff that the "outside" world would either groan at or simply walk away from in a head-shaking fashion.  But Pi-Day, March 14, or 3/14, does seem to bring things like this to the surface....

Here are two articles that have leaked out into the "real" world.  The first is not a real debate or controversy, really..., but it is kinda fun in a strange sort of way.  It is an argument for a better way to generally represent the constant that arises from comparing the diameter or radius of a circle to its circumference.  Since pi radians represents only half a turn around a circle, why not have the universal constant simply be 2pi, representing a full turn around the circle.  Call this number tau = 2pi.  The article, in the Verge, is kind of a rant on pi's fame:

Stop Celebrating Pi Day and embrace Tau as the true circle constant

I am not sure about this one, but the accompanying "Tau Manifesto" is a pretty good read. 

The other is really more of a comedy routine, designed to educate and highlight some real math.  The sort of sweetened medicine you were forced to take as a child.  Broadcast via Mother Jones, the interview/debate

What is the greatest number of all time?

is an argument between two mathematicians Tom Garrity and Colin Adams.  Clever....

Enjoy Pi-Day!!!

Math in the Media: Homer vs. Pierre?

I just had the pleasure of watching a neat 8 minute video detailing some of the mathematics injected in to the Simpsons animations.  Apparently, there are mathematicians among the creative staff who cannot help themselves throwing in a little math humor into the background every so often. 

The video, listed here on YouTube by Numberphile is titled

Homer Simpson vs Pierre de Fermat

 Do give it a watch.  It is always good to know where the subliminal messages about how cool math really is are lurking, no?

Math in the Media: Prime Gaps....

I am always amazed at how some of the most vexing, curious and fascinating puzzles in mathematics can be stated so simply, even as they evade solution or even complete understanding for centuries.  It is one of the more alluring aspects of this trade. 

Here's one:  Just how big can the gaps between consecutive pairs of prime numbers get as one traverses the natural numbers out toward infinity? 

One would expect the gaps to get larger and larger and also tend toward infinity in the long run, no?  But showing this, and providing some sort of measure of the growth of the size of the gaps as one goes "out there" has been remarkably elusive. 

I'll let you read this nice article by Erica Klarreich in Quanta Magazine, to "see" that progress has recently been made, and there is promise of more progress coming. 

Mathematicians Make a Major Discovery About Prime Numbers

Will math ever cease to amaze....

Playfully Serious Math: A glimpse at Vi Hart and Fibonacci

I am often struck by just how repulsive mathematics is to some people when, in my eyes, it is all an absolute kaleidoscope of color, art and logical splendor.  But it is not always easy to get someone else to see what you see.  This is what education is all about, I guess.  One step at a time....

I was recently turned on to an absolutely wonderful math and science educator whose videos would do well to provide the backbone of the next generation of the Common Core, at least in math education.  Vi Hart is a videographer (is that what one would call someone who makes videos) who specializes in a playful, though very serious approach to expose and illustrate complicated science concepts and techniques.  One of her series, entitled Doodling in Math Class, exposes the rich, playful and beautiful structure inherent in every math class but lost in the tedium of sterile, and solely utile function.  Below is a three part video explaining why and how the Fibonacci Sequence (not a series, really) shows up so often in nature.  It is mind-boggingly well done, IMHO:

Doodling in Math: Spirals, Fibonacci, and Being a Plant

The other two parts follow immediately from this one.  Give them a look!

BTW, THIS is what mathematics is really about.  Vi's money quote (at the end of the third part):

This is why science and math are so much fun.  You discover things that seem impossible to be true, and then you get to figure out why it is impossible for them not to be true.

Math in the Media - Perhaps the Matrix is....

Here is an article filed under the category "Thoughts to Ponder":  Edward Frenkel, a mathematician from Berkeley, posits that the university perhaps is just a giant simulation and we are simply participants.  How would we know?  Can we detect if we were?  The article is an OpEd in the New York Times, and can be found here:

Is the Universe a Simulation?

Frenkel gives some sense to this idea by differentiating (no pun intended) mathematical ideas (manuscripts, really) from literary ones in the following way:  Mathematical ideas are somewhat universal.  The laws and constructions of Pythagorus, Euclid, Newton, etc., would surely have been created (discovered?) even if these greats had never existed.  It may have taken longer for someone else to develop them.  But the structure of mathematics (its logical framework) exists as it is whether we discover it or not.  Try that with a sonnet sans Shakespeare....

It is a very nice read, this article, and again, gives a sense for how mathematics seems different from other disciplines of study.  Frenkel mentions that many mathematicians consider themselves Platonists, believers that everything exists in the ideal, and what we perceive in this world is simply real versions of that ideal.  It works for me.  I would believe that it would work for most all mathematicians, really.

Frenkel even goes so far as to say that the giant computer simulation that we exist in is, like all computer simulations, not entirely without anomalies, coding inaccuracies that render the coding conspicuous.  Perhaps all of our logic in mathematics is simply facets of the coding that can be detected "from within"?

Certainly a "thought to ponder"....     

Math in the Media: Math Food?

One of the more basic and interesting shapes (spaces) in mathematics is the torus.  We typically describe is as the surface of a doughnut or bagel.  That it is mathematically different from the surface of a ball is a good entry point for a lay explanation of some fun higher mathematics. 

Speaking of a bagel, here is an interesting video on a way to mathematically play with your food:

A Mathematically Correct Breakfast

Buon appetito!!!

Math in the Media: Eating Mathematics?

Alright..., just for fun.

If you are not yet convinced that mathematics is not a subject to study as much as it is the underlying logical framework for all that exists both in reality and in imagination, I give you another example.

The New York Times' Kenneth Chang has written a piece on the mathematics of pasta:

Pasta Graduates From Alphabet Soup to Advanced Geometry.

Those seemingly random and crazy shapes, designed specifically for texture, even cooking, and the ability to meld well with sauces and such, can be quite beautiful and subtle. This article exposes those who look for the mathematical structure behind the designs and the playful aspects of the shapes.

Take a look. But beware. You may never view a plate of spaghetti in the same way again!

Math Play: Every Natural Number is Interesting.

I just read this in the first chapter of the text we use for our senior class Advanced Algebra. The book is Introduction to Advanced Algebra by W. Keith Nicholson. I like it, so I will pass it on.

If you study math, you have probably heard of the Well-Ordering Axiom, a property of the integers which is equivalent to the Principle of Induction. The Axiom states: Every non-empty set of non-negative integers has a smallest member.

Intuitively clear, no? Here's how it works in practice:

I claim that every positive integer is interesting. To show this, let's assume it is false (this is a proof technique known as proof by contradiction, in which one assumes the claim is false, then works by deduction until something absurd follows, a clear contradiction. If the logic is solid, only the assumption can be flawed. Thus your original statement must be true. )

Since the statement is assumed false, there must be a non-empty set of uninteresting positive numbers. But by the Well-Ordering Principle, there then must be a smallest uninteresting number. But an extreme element of any ordered set is automatically interesting (in that it is special)! Hence we arrive at the contradiction, making our assumption false and the original statement true.

Silly, yes?

Playful Math: Doodling to Aleph_null

I believe most people who really get mathematics are the ones who see the frivolity in much mathematical construction not as a flaw, but as a strength ( I am teasing my profession here). And sometimes presenting mathematics in playful ways is precisely the best way to expose deep meaning.

With a hat-tip to Engineering Innovation (@JHU_EI), a high school summer program in the Whiting School of Engineering here at Hopkins, I am reposting a video from one of their recent tweets.

Doodling in Math Class: Infinite Elephants

Have fun!

Oh, and BTW, we mathematicians tend to associate letters from other alphabets to important constants and concepts in our work. Aleph (the first Hebrew letter) is commonly used for measures of infinity. Aleph_null, or Aleph with the subscript zero, is used to denote a kind of infinity called countable infinity, and denotes the size of a set of objects that can be placed in a one-to-one correspondence with the natural numbers 1,2,3,... Jus'sayin'....