Once upon a time, the world only had numbers, but creative
and brilliant mathematicians then discovered several types of numbers, each
with its own distinct and remarkable name. So we have irrational numbers,
negative numbers, and imaginary numbers, and their counterparts. At some point
mathematicians realized that fractions are also numbers, so non fractions were
named whole numbers. While all these numbers exist in nature, animals and
plants and fungi ignore them, and mathematicians have to make special efforts
to persuade people to take notice of them. And share their joy with those swimming
in apathy about theoretical classes of numbers. So they named the numbers people
use as Natural Numbers, and flooded textbooks in schools and colleges with the
delights and joys of unnatural numbers, all in the name of education.
In Europe several of these people who taught mathematics
early were Christian priests or their trainees. In India, higher mathematics
were the field of jyotishas or ganakas, technically astronomers but usually
astrologers, substantially a large number of whom were brahmins. Indian
jyotishas either cruelly and haughtily withheld the mathematics of unnatural
numbers from the teeming masses or were so kind that they spared them horrors
of sums and homeworks and entrance exams, until the benevolent British decided
that all children should suffer equally, a principle they borrowed either from the
Prussian inventors of elementary schools or the American inventors of equality.
To add to the merry
confusion, around the seventeenth century, non religious Europeans, still often
funded by various churches, started learning mathematics with a vengeance, and
formed societies where they shared their discoveries. They invented new categories
of numbers like transcendental numbers (without the advantage of Vedanta! Before
Osho! Horrors!), sets, fields, quarternions, boolean numbers, and so on. They
also discovered friendly numbers and perfect numbers. Shockingly they never
bothered to invent moral numbers. Whether this is a failure of Christianity, of
atheism or sadists, it is not clear. What is astounding is that Indian
mathematicians or philosophers didn’t
discover moral numbers either.
A Mystery
How could Punyabhumi, Jambudvipa, the mother of history and
the grandmother of religion, as Mark Twain described her, with such a long history
of mathematics (and morality), not have discovered, or at least invented, Moral
Numbers? We put morality in everything. Our panchatantras effused the animal
kingdom with morality. Our philosophers moralized the living daylights out of
everything from death to drinking, to brushing teeth and revering palm leaves.
Today Indian intellectuals are compensating for some of these absurd traditions,
by disrespecting almost everything that our ancestors venerated. Never mind. Varahamihira wrote half a book simply on the morals
to be observed about combs and couches, while the planets and stars oversaw
their fortunes. And thanks to the printing press, high taxes, a socialist
constitution, a massive population, and a desperate desire to get certificates
that we are at least as educated as the next person, everyone is taught all
kinds of mathematics! So many types of numbers – except Moral numbers.
An objection may be raised. Why do we need morality in numbers?
We have them in our laws, judgments, customs, in habits, food, drink, dress, entertainment,
sports, cinema, music, literature, application forms, other forms, tax
policies, goods and services, loans, write offs, grants, donations, fees, fines,
in construction, inauguration, economics, economic opinions, in newspaper
editorials, social media essays and tweets, public speeches, private speeches, outrage,
occasionally even in religion. The sciences we learn or teach are free of
morals, at least they are amoral, rather than immoral, but we compensate by
loading our scientific institutions with morals. So much so, that we value
their moral standing and probity more than any scientific output. Only our
mathematics, sadly lacks morals, and that I think because we havent invented
moral numbers. We can forgive Aryabhata and Bhaskara for this lapse, but our
future generations will not forgive us if we don’t create a new system of
morality among numbers, and propagate them for the benefit of Mankind.
After all if some numbers can be perfect, some irrational,
and some even imaginary, surely some numbers can be moral?
But how do can we separate numbers into moral and immoral
(and perhaps some amoral or doubtfully moral). What if some numbers prefer to
be moral in public and immoral in private? We will then have a whole class of
hypocritical numbers. A property so far confined to people and words. But since
we have had centuries of experience with these, we can perhaps deal with
numbers which are hypocritical too. But we may be jumping the gun.
Beauty
Isnt morality subjective? Like truth, justice, fairness,
even honesty etc which are all subjective. Unless of course you believe in
particular set of truths and consider everyone who doesn’t accept these as
immoral by choice? Eureka! Why would this principle not apply to numbers also?
And consider the possibilities of academic research in mathematics, which so
far has been unfairly confined to people who are excellent in mathematics! How
exclusionary – to leave our journalists, politicians, preachers, philosophers,
writers, artists, who all usually avoid any mathematics that isnt financial?
That is the beauty of it, a beauty GH Hardy and Paul Dirac and S Chandrasekhar would
have appreciated. The case for moral numbers is that they will not only help us
understand morality, they will help humanity achieve equality. We live in a
terribly unequal world, where rewards frequently go to competent or hard
working people. This must be rectified as soon as possible. Why confine equality to equations?
But how would a mathematician discover which numbers are
moral? Is there something inherently moral about some numbers, but not others
(a dangerous possibility of inequality, which is immoral, but we must
theoretically consider this)? We must also consider that the morality of
numbers may be independent of the mathematicians who investigate them or even
the areas of mathematics where they could prove to be useful (or useless). We
may discover that morality is not binary – or discrete as mathematicians like
to call them – but has many shades of grey. There may a Fuzzy Arithmetic, a
counterpart of Fuzzy Logic, just waiting to be discovered. Fuzzy Logic was
first propounded by an Aryan called Lofti Zadeh, and it would be fitting if
Fuzzy Arithmetic came from our beloved Dravidian land. It would be so poetic, if
our beloved Madras aka Chennai which gave the world three language families,
could also give the world several new number families. And even our omnipresent
Malthusians and Ehrlichians wouldn’t object on the grounds that this doesn’t come
under family planning.
I have drowned you, dear reader, in words, in an essay
purporting to be about numbers. Wrong, I know. But I am merely trying to drench
my ankles as I wade into a sea that may not even exist, and I will only know if
the sea is watery when my ankles become wet. Sadly, until now, my ankles like
this essay, are dry. Now, Tamilnadu is hardly a dry state – but so many of our
fellow citizens have parched throats in this never ending Corona Virus
Lockdown.
Possibilities
The Lockdown, similar to what Isaac Newton suffered in his
early twenties, has inspired this flow of thought. Unlike I Newton, owing
perhaps to a lack of apple trees in Madras, I have not discovered a single law
of physics in these forty days. I thought I must at least explore the
possibilities of mathematics. A notable Indian author wrote a famous book
called the Algebra of Infinite Justice, which was sadly lacking in algebra, but
compensated by being finite. Is it not our duty then to explore such other
topics as the Calculus of Limited Economics, the Geometry of Tangential Discussions,
the Statistics of Sesquipedalian Solipsistic Sophomoric Soliloquies, the
Probability of Profoundly Perfidious Perspicacity, the Differential Equations
of Indifferent Inequalities, and so on? Some mute inglorious Milton in
Meenambakkam, some Cromwell in Coimbatore, surely is working on these. Will
moral numbers help them or the current mathematics suffice?
So moral numbers may not be merely theoretical mathematics,
but applied to. This would have disappointed Hardy and Dirac. But the word application
is music to the ears of lawyers, bureaucrats, and software developers, so let
us not worry too much. In fact there may be some basic Pythagorean theorem of
morality, whereby the happiness of some people may be equal to the sum of the
discontent of the neighbors on two sides of their houses. It may be
quantifiable as a number. Happiness and discontent are currently not measured
with numbers but only by vague notions, but once we assign numbers to them, we
can compute them, develop a quantitative economics about them, securitize and
monetize them, tax them, collect distribute them based on other principles, and
so on. Surely this will lead to greater happiness and contentment. What a
marvelous similarity this would be to the world’s central banks, which simply
print more currency notes whenever economies start floundering, and thus
increase the world’s overall wealth. One of these days we will all be
billionaires. Perhaps, Happionaires too.
I will wait for reader’s suggestions before revealing some
of my other ideas on moral numbers. I have visualized a small set of
operations, equivalent to arithmetic operations, but I still haven't figured out
how to determine which numbers are moral and which aren't.
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