Science  Write  Now

WHAT YOU ALWAYS WANTED TO KNOW ABOUT MATHEMATICIANS  BUT WERE AFRAID TO ASK 

Abstract: A paper in which we enter the Mathematics Tea Room at Cookie Time to see  what there is to see, take copious notes, then pre-enumerate them for the story to  follow. Please feel free to read the story in any order you like. 

† Max Zorn was a famous Modernist-era Mathematician who lived and worked into something like the early 21st century to the delight of absolutely everyone.  

‡ Once, before the Modernist era, the State Senate of Indiana enacted a law requiring that π = 22/7. This is why the Statehouse in Indianapolis, designed to be round, has no discernible shape whatsoever.  

§ Topologists study things like cowlicks or how to count the number of holes in something like a whiffle ball, as well as the possibility of the existence of meaning with respect to cowlicks or the number of holes in a whiffle ball. They say stuff like “You can’t comb the hairy ball” with a straight face. By the way, if you have noticed Every Single Little Boy in the World Has a Cowlick, it’s because of the “You Can’t Comb the Hairy Ball Theorem” from Topology. I swear I am not making this up. 

**Analysts study a special kind of box where you drop stuff in through a chute on one side of the box, and something or other comes flying out of the other side. Watch out for bats.

†† This story might well have been an early-new-millennium piece. At that time, it was well-known that the permanent voting members in the UN Security Council had these exact rights. That particular UN Security Council, whose permanent voting members we shall not name, gave rise to  an inconceivable insecurity in the world, particularly for those who pay attention to that kind of  thing. We pretend not to know any people like that. 

‡‡ Either one of The Fruits of the Knowledge of Good or Evil. 

§§ Mathematicians are notoriously bad with numbers. Time? Time is a number of things. 

ß All self-respecting Math departments have Afternoon Tea at 3:30 every day, for cookies, conversation, collegiality, and the New York Times crossword. There is a large sum budgeted by the department for excellent cookies, so Tea is simply not to be missed. 

A Definition: An axiom is a law one accepts as true in order to get on with one’s Creation. A well-known example of an axiom is the axiom of Free Willµ which God accepted for us at the beginning of Creation. An axiom is that kind of law. All the other rules for any world are derived from its axioms.  

∝Please note here that ten seconds after God had decided yes to the Axiom of Free Will, Adam and Eve had already committed two acts of extraordinarily bad judgement; two counts  of refusal to take responsibility for anything; and one count of a man blaming God for the  man's own shortcomingsη (Gen. 3:12). Coincidentally, this was also the first jokeη. 

***The Axiom of Choice says that no matter how many trees you have in a Garden, you can pick a  piece of fruit from every single tree. Finite, infinite, doesn’t matter. The presence or absence of the fruit of the Tree of the Knowledge of Good & Evil here is irrelevant. ℵ,Ω

ℵ Genesis once contained several verses right after Adam names the animals, in which God says to Adam: You must decide whether to acceptℵor rejectΩ the Axiom of Choice**** in the  beginning of Your Creation/Discovery of My Mathematics.  

ℵ God continued: Accepting the Axiom of Choice will lead to a rich and beautiful field of study. And baskets of fruit. 

Ω Further, God said: Rejecting the Axiom of Choice*** is likely, though I can’t be sure, to lead to  questions like, “What if there were no mathematics?” These questions are simply not to be asked.  

Ω Since even God did not know for sure what rejecting the Axiom of Choice**, Ω would lead  to, the Axiom of Choice**,ℵ is generally accepted. SO, you may indeed ***,ℵ pick a piece of  fruit from every single tree in the Garden. Eating any given piece? Entirely up to you. 

††† Logicians say things like “Schrödinger’s bat is either alive or dead but not both.” They think this  only applies to Schrödinger’s bat. 

‡‡‡ Algebraists say things like, Let’s suppose we have a group of three bats, and the three bats have to live  by only these three simple rules: a) Each bat must sleep hanging upside down from a branch like a piece of  fruit; and b) That’s right, bat. Bat the animal. c) No-one is to leave the Statehouse grounds for any reason  whatsoever. Now, let’s see who dresses up as what for Halloween! 

§§§ Induction says that if something starts out being true, and keeps on being true, then it’s true, for  Christ’s SAKE. 

**** No-one is exactly sure what Transfinite Induction is, though there is the possibility that it involves  picking pieces of fruit from many, many, oh-so-many trees, and one of those fruits may be a bat, so.

†††† The Hahn-Banach Theorem is the only theorem in the world powerful enough to get all the mathematicians described in this paper and any other to tea every afternoon at the same time. For  this reason, Hahn-Banach simply cannot fail. 

‡‡‡‡ Functional Analysis is a branch of mathematics that could conceivably be tied to any other, though only an analyst would ever think such a thing, while knowing it is true, besides. 

§§§§ While hanging out with e.e. cummings one Modernist-type evening, Max Zorn proved his amazing Zorn’s Lemmaδ, which is just as cool£ as cummings’ as is the sea marvelousΨ. 

δ Zorn’s lemma has to do with fruitφ choice, cookieφ varieties, and whether or not you can choose a favorite, if you can manage to put the fruit or is it the cookies in some kind of  order.  

φ Why both cookies and fruit, you may ask? Because it is important that no-one ever  eats the cookies with the cherry goop in them. Toddler rules! They must never touch! Are the fruit and the cookies touching here? *** 

£ Because, after all, Zorn’s Lemma is equivalent& to the Axiom of Choice***! 

***** For an example of a Set Theory question, I will ask you to name a set which is not contained in  the set of all sets. You will look at me with a righteous rage saying, Just fuck me! And I will say, No, fuck you! Then we will laugh our heads off because we love that old joke. 

††††† Since I am writing this for writers and other readers, I don’t even want to get into the whole Just fuck me thing again. 

‡‡‡‡‡ No fruit appears in this story, or any other. Fruit may appear in the cookies, though this is discouraged by toddlers and analysts. 

§§§§§ Before the galoshes incident, Professor Russell was a fine mathematician of some type.

Max Zorn† was still doing mathematics at Indiana University when I started grad school there.  

The Eternal Ad-Hoc Committee for Democratic Mathematics‡ mysteriously appeared in the minutes of a departmental meeting soon thereafter, along with rules giving all the topologists§ and all the analysts** permanent voting rights with veto powers.†† I could pass for either one‡‡, so I was happy. Professor Zorn could pass for anything, because he had proven seven wonderful theorems before  logic or mathematics were even invented, and he was always happy. 

The first 3:00 meeting was called to order promptly at 3:17§§. A motion was made and seconded, by  Professor Zorn himself, that we accept the Axiom of Choice***,ℵ,Ω without further ado so that we might adjourn in time to get to Afternoon Teaß before the logicians††† and algebraists‡‡‡ ate all the damn cookies.  

During the ensuing ado, it was noted that Transfinite Induction§§§,***, is reason enough to reject the  Axiom of Choice*. A permanent member pointed out that Ωwithout the Axiom of Choice**, there  IS no Hahn-Banach Theorem††††, which means there IS no functional analysis‡‡‡‡, in which case every single one of us might as well just call it a dayΩ .  

because it had already been proven that Max Zorn is equivalent to the Axiom of Choice,§§§§ and there was no denying that even though he was at least 114 years old, Max Zorn was standing right there, leaning on his cane, saying he wanted cookies. And he wanted a choice! A choice from an infinite  variety of cookies! OK, he didn’t really say that, but of course I knew what he meant. 

In new business, a motion was made and seconded that we continue to live in Abject Denial of All Paradoxes Arising from the Modernist-era Mathematics the logicians called Set Theory,***** and the analysts called Language Poetry.††††† Since the permanent members were required to veto anything that did not exist, a motion was made, seconded, and passed unanimously that no vote be taken. 

The meeting adjourned, at which time the Committee took its Abject Denial to Tea, without, finally, any further ado.  

Surprisingly, everyone was able to choose at least one cookieφ at tea, though they were completely out-of-order, and no-one could be sure he or she had gotten the best cookie from any given plate.‡‡‡‡‡. No matter how many cookies we ate, there were still infinitely many left to choose from, but that was only because all the logicians and algebraists were trapped in a subset of themselves, located somewhere in either one of Bertrand Russell's§§§§§ abandoned galoshes.

Feature image via IIIF