Revelations from Edmund Slowdown concerning collateral benefit (reported here) took many by surprise. I started wondering if various scientific communities were aware that collateral benefit, an explicit goal for many of them, was a great impediment to their well being. I contacted Edmund and lo and behold he came up with documents (summarized below) that show that the mathematical community, perhaps one of the strongest generators of collateral benefit, was very much aware of the risks literally from Day One.
Brief history of mathematics
The universe as we know it was created about six thousand years ago and the need for mathematics was evident from the moment that first people showed up, that is 5774 years ago. Thus mathematics was made by the Troglodyte family: Troglodite the Wise, his wife the Wiser, and their daughter Gozka. It may come as a surprise that all of mathematical knowledge was conjured by just three people but this is one of the miracles of creation.
Numbers - natural, real, complex and quaternions, plus some that have not yet been revealed - were all thought up by Troglodyte the Wise. All of geometry was done by the Wiser, and Gozka unified the work of her parents and created the entirety of modern mathematics from Descartes onward. If you think that it is improbable, you are not alone. In fact, nearly 60 centuries later Kronecker, rather than give all due credit to the Troglodyte family, said that "God made natural numbers; all else is the work of man.” This is inaccurate, and for the record: a man made natural numbers; all else is the work of women.
The Troglodyte family had the good sense to realize that releasing all mathematics at once was not a good idea. Instead they created a secret society - Famiglia Mathematica as it was later called - that was endowed with all the knowledge and charged with releasing it for the benefit of humanity and support of their members. And this is where the wrath of collateral benefit raised its ugly head. To meet both goals, the release of mathematics had to be done very, very slowly. Every time Familia Mathematica tried to quicken the pace there were dead bodies, mayhem, and operational loss. Pythagoras, Hypathia, Abel, and Galois are the best known examples of members of the Famiglia who tried to outpace the agreed upon schedule and suffered terribly.
It is not only Fortune 500 companies who found collateral benefit to be a threat to their business; Abraham and Moses would have agreed with them as well. Evidence of this attitude towards collateral benefit is all over the Old Testament.
The Bible contains excruciating minutia from the life of prophets and other one-percenters, but you will be hard pressed to find explicit references to the Troglodyte family and to the Famiglia Mathematica. The Bible only obliquely speaks of the creation of mathematics and the establishment of a society charged with the release of mathematical knowledge. Still, a solid confirmation can be found and it deserves a closer look.
There is much doubt whether Koheleth was indeed the king of Jerusalem, but it is clear that he was a member of the Famiglia. In the Book of Ecclesiastes he described the purpose of the Famiglia and chronicled his thoughts on their efforts.
On the creation of mathematics by the Troglodyte family he tweets "All things continue the way they have been since the beginning. What has happened will happen again; there is nothing new here on earth.” Quite appropriately he ties mathematics with wisdom and explains the purpose of the Famiglia: "Wisdom is better when it comes with money. They both help those who are alive.”
He predicts that mathematicians will have tough times ahead when he tweets "All of their lives their work is full of pain and sorrow, and even at night their minds don't rest. This is also useless.”
He does not offer ideas to cheer oneself up other than "Put on nice clothes and make yourself look good,” an advice often scorned by members of the Famiglia.
Overall, the Book of Ecclesiastes earned the reputation of being one of the most depressing parts of the Old Testament, and sadly the reasons might be mathematical. More than ten times Koheleth tweets complaining about “chasing the wind”. It is reasonable to assume that within the Famiglia his charge, perhaps assigned by error, had to do with fluid dynamics and turbulence. This would more than explain a cloud of depression hanging over his tweets. Dealing with Navier-Stokes equations two millennia before the release of calculus? Ouch!
So what is known about the Famiglia Mathematica? It is a secret society whose members recognize each other with great ease. There are no particular induction procedures, and most members know that they belong, while others are nurtured and encouraged early on. Since most of mathematics was created by two women, the Wiser and Gozka, society tries to encourage diversity and gender balance by directing their recruitment efforts predominantly to men. The operation - that is the release of knowledge - is unchanged since Troglodyte's times. The motto of the Famiglia Mathematica is Prohibe et obscure - hold back and obfuscate - and this says it all.
Some members of the Famiglia did a splendid job, the release was timely, the membership soared and the society welcomed the gifts with the share of the profits. These include Descartes, Newton, von Neumann, Wiles and even a bit hyperactive Euler.
Others became black sheep and gave the Famiglia a lot of grief. Ramanujan was the worst offender who did not bother to read the sources beyond the executive summary. It took close to a hundred years to reconstruct the original work of Troglodyte the Wise after this rascal destroyed the original scripts and replaced them with his notebooks. Riemann is not much better, substandard exposition based on mediocre efforts resulting in diluted impact and tremendous amount of unnecessary work for others. Not to mention the snafu with the Riemann Hypothesis, a simple corollary that Gozka thought would nicely connect to various applications. Riemann got the sources by accident, glanced at them overnight, slapped together a paper to pass the exam that required a presentation on some obscure topic, and promptly forgot about the whole episode. The Famiglia is dealing with the fallout to this very day as sloppy Riemann hardly included any proofs, particularly of the Riemann Hypothesis, and did not bother to pass the sources to someone with more gumption.
Over the centuries members of the Famiglia often quarreled about the timing of the knowledge release. The basic mantra was to follow the ebb and flow of the societal indifference towards mathematics. The Famiglia flourished in the 1600's but did not do well during the Dark Ages or at the beginning of XXI century. In time, many members were willing to accept subsistence level jobs that would give them a little time each day to release some mathematics which they claimed would make a lot of difference. Others were pointing to the consequences of holding back and keeping society in the dark. Indeed, the price of dividing by zero, a practice responsible for most human disasters, could have been in check if a better algebra package was available a few millennia earlier. The wheel, the invention of the Wiser, who released it right away, was very helpful. But the ball bearing, a close mathematical cousin, had to wait 57 centuries to be released. For all this time the most common road accident was nicknamed “wheels coming off” and the very thought that a small royalty payment to the Famiglia could have prevented all these senseless deaths and injuries makes one’s heart bleed.
Famiglia Mathematica is mum on the subject of how much more mathematics is still left to be released. Off the record, many members indicate that there is “quite a bit” and it is “really good stuff." As Koheleth tweeted millennia ago "There is a time for everything, and everything on earth has its special season.” Well, there is consensus within the Famiglia that time for mathematics is now, that we ought to quicken the pace of release and that the Famiglia really has a chance to capitalize on the fact that no scientist was burned on a stake for quite some time. In fact, the fear of collateral benefit on the part of political and industrial leaders has put the humanity in a corner. Science, with mathematics in particular, might be the only way forward and out of this predicament as going back to the time of creation would be a considerable hardship. Ever pessimistic Koheleth tweets "Everything is boring, so boring that you don't even want to talk about it” but perhaps this one issue deserves a second thought.
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