Sunday, June 23, 2013

Mathematics- the new beginning?

In the waning days of the First Gulf War, a marauding US Army unit came across a treasure trove of five thousand years old Egyptian scrolls discussing the decimal number system. One particular document resembling a government circular and affixed with several high level endorsements puzzled historians. In a semi-literal translation it said:
"Counteth the children of all your numbers and for each of their children giveth a dinar to the pharaoh."
Historians had problems understanding the exact meaning, and the document lingered in the Pentagon archives for several years. Enter NSA cryptologist and amateur egyptologist hiding under the code name Pink Squirrel. After quick glance at the document she posited that this is a patent claim for decimals and the document establishing the double logarithmic taxation system. More precisely, for ancient Egyptians, digits in the decimal notation were "children" of a number. Thus the number of children is a logarithm of a number and the number of grand-children is a double log. The idea that the mathematical community owns the decimal system and can exact a modest charge (log(log(x)) is a nearly constant function) for using it was very exciting and prompted a great deal more research. It turned out that the number crunching capacity of early societies was quite significant and the level of tax evasion was low. Consequently the revenue stream from the Double Log Tax in the five hundred years since its introduction created the pharaonic surplus that comfortably funded  the pyramids and various melioration projects. The Double Log Tax was applied for the next two thousand years, leading to unprecedented scientific developments and the creation of the Seven Wonders of Antiquity . All historians agree that until the stoning of Hypathia and the burning of the  Library of Alexandria, science was doing quite well. Afterward things turned sour and it was a big lesson for the mathematical community that perhaps they had tried to collect too much too early.

Fast forward a decade to  the Second Gulf War  - US Army units plundering the Baghdad's historical sites came across an arabic document from 513 AD which copyrights the sine function! The document allows for free use of the sine function for the first 1500 years, after which there is a sliding scale fee for each use. Clearly the mathematical community decided to give a moratorium for early adopters of the technology and to hook generations of teenagers on the art of triangle solving. Now the trigonometric holiday is over, time is running out and as of January 1, 2014, the mathematical fiscal cliff is looming large. School districts are worried and so is the  general population. Of course the document is being contested and attacked from many sides. Opponents of Sine Function Usage Fee bring up faded signatures on the original document and Saddam Hussein's human rights abuses, questioning the right of Islamic mathematicians to the ownership of the sine function. The Taliban's sudden affection for mathematics and the pledge to abandon opium trade for sine function revenue does not seem to be helping anybody. And there is much more: further historical studies show that the only commonly used mathematical objects that are free to use forever are zero and TeX. Everything else, such as +, -, =, square root and other standard functions have varying user licenses. None of this is completely unexpected, even if it is widely unknown. School districts have argued for years that studying polynomials of a degree higher than two is not worth the effort and educators have been suppressing the multiplication sign in their anticipated cost cutting efforts.
Suddenly mathematicians are facing a possibility of cashing in on their inventions. Re-enacting the Double Log Tax and enforcing the Sine Function Usage Fee and all of its cousins would be a tremendous source of income.  Just to illustrate consider the following: It is widely known that there are at most six degrees of separation between any two individuals on the planet. What is less known is that there are two degrees of separation between a person and a criminal. Consequently, even though criminals account for only a small percentage of the society, the high level of connectivity of this community makes it necessary to put entire population under surveillance, and that was how NSA's Prism program was born.   With an appetite for numbers which is that big, the Double Log Tax bill for NSA alone would fund the development of modern mathematics and bring the leadership in this area back to the US. 

 The latest news
So this is where we are. In a close vote, the Supreme Court ruled that the Double Log Tax and Sine Function Usage Fee and such are constitutional and cleared the way for the Congress to act. Furthermore, during a brief lull in fighting, a US Army  unit operating alongside the Syrian rebels  came across an ancient papyrus from 5000BC that describes executive orders concerning the Double Log Tax. Although the pharaoh is listed as a nominal recipient of the proceeds, the executive order specifies the "counters" as the caretakers of the funds. Consequently, just like most things in this world, numbers have a legitimate owner and it is the mathematical community. For the first time in history, mathematicians have a chance to free themselves from the government handouts and caprices of the modern day sponsors, and simply cash-in  on the contributions to Humanity that they were making for the last several thousand years.
The American Mathematical Society, which has always had a rocky relationship with the government funding agencies, took the lead in lobbying for the legislative action. Politically this is a very slippery ground. On one hand, proposed laws represent new taxes, an intolerable course of action for many members of Congress. On the other hand, the issue represents the recognition of intellectual property rights at the dawn of human civilization - something that the Founding Fathers would have respected deeply. In the end, the bill H.R 666 proposes to recognize intellectual rights of the mathematical community to its inventions such as numbers, functions and formulas and to compensate them according to the law of the land. There is a great deal of discussion in the society about these proposed laws. Mathematicians are also energized, and many conflicting views are being presented.  Superficially, enacting the Double Log tax has more than a passing resemblance to a retirement - an annuity after a long and productive life. Many younger colleagues do not quite feel ready, even if they are neither appreciated nor respected. Others argue that this is the dawn of a golden age of mathematics. Free from the bondage of interdisciplinary research and the need to reach outside own community, mathematicians will pursue their own interests in the yeshiva-style environment. Classical geometry, point-set topology, and finite group theory will came back roaring and infuse the discipline with the unprecedented level of abstraction and irrelevance.  Applied and computational mathematicians are quite pragmatic, they plan to collect whatever they can and find something useful to do in the aftermath. Statistics community is most nervous. For years they insisted that statistics is not mathematics and now they are out of the loop. At the same time the Double Log Tax is likely to ruin the entire community, and it is not certain whether the  societal importance of this discipline warrants the government bailout.
Needless to say, to push this through Congress is not a trivial task and many compromises have to be made. As with every major piece of legislation, unusual alliances and back-room deals shore up the votes. It is not different this time. The American Mathematical Society needed to strengthen its hand and its alliance with National Rifle Association came both as a surprise and a big gamble. Details are sketchy, but math meetings will be combined with gun shows and mathematicians will be encouraged to get concealed weapon permits and carry sidearms. AMS members will get a complimentary subscription to Guns and Ammo while NRA members will enjoy Bulletin of the AMS. A few thousands of AMS members dropped out immediately, but the influx of five million new souls from NRA compensated it thousand-fold. This union is a big challenge for the mathematical community, and we are encouraged to welcome our gun-toting friends with open arms. So far so good, we are doing our best, even though seeing ads for a Bushmaster M4 semi-automatic in the Bulletin of AMS takes some getting used to.
Other amendments are piling up as well, given the size of the revenue stream going towards math, from subsidizing Obamacare and Social Security to new subway lines in several cities and a zoo in North Dakota.
Neverthless, it looks like math has enough of the  votes. If all goes well, math will begin a new millennium as the first science that is sustained entirely by its past contributions to Humanity, and no real expectation to keep on giving.  Indeed, 7000 years old tools that just keep on getting better and carry a lifetime warranty - unbeatable!