Imagine if being shortsighted, a bit shy and socially awkward, not
much handsome or strong, would still end up being a great boost to
your chances of making babies and passing on your genes?
That’s what
arguing for a genetic ability for ‘mathiness’ may entail, as the
qualities above are pretty common among ‘mathy’ people (I know, I
live among them). I can get why at least ‘mathy’ people would
very much like to believe that :-)
As I see it, if
anything, genes for “mathiness” would be more of an evolutionary
burden than a gift. At least up to the last three decades, when being
a ‘nerd’ shifted to being acceptable or even a positive trait –
though in social circles where they also have lower than replacement
reproductive rates, not helping much with the evolutionary part.
Yet, as Bret may be arguing, it is undeniable the influence of Jewish
heritage, particularly of the Ashkenazi sort, in the mathematical
sciences of the last 2 centuries. The disproportinate presence of
Jews in modern Academia has been a source of envy with fateful
consequences, such as Nazi Germany banning a sizable part of their
own academic elite - handing their enemies a most valuable resource,
as those same minds led America to the ultimate weapon (and the best
proof that “karma is a b****” you may ever find).
Is it possible that
Ashkenazi “mathiness” is a genetic trait, as Bret poses? We know
intelligence is heritable, and there is even a (reasonable?) case on
Ashkenazi IQ being above average. Yet geneticists have been looking –
very unsuccesfully – for “gay genes” for half a century now. I
wonder, if a nearly primal thing as love for humans can’t easily be
represented by a set of genes, what to say about love for numbers?
But if we are to
invoke history, we must go all the way through. After all,
notwithstanding the cultural hallmarks of Israel, it is not there that
you’ll find the great pyramids, Giza (c. 2500 BC) being built way
before Abraham or the Kingdom of Judah (c. 900 BC) were around.
The mathematical
acumen of the Egyptians was probably acquired by the Babylonians
before 1600 BC. Though also a semitic people, they enslaved their
Hebrew cousins a thousand years later, and we can conjecture the
captives must have learned some math too – the Torah/Old Testament
does present the number ‘pi’ as 3 (though Babylonians knew it
with a few more decimal places). By the time Judeans were getting
back their land (c. 540 BC), the torch of ancient Math was being
passed on to another people of no semitic kinship: the Greek.
By then Thales of
Miletus had already invented the fundamental stone of proper
Mathematics, the Axiomatic method. He used it to prove the first
theorems in geometry we know of – though he probably got them from
the Egyptians who ‘knew’ it without formal proof. A generation
later Pythagoras (or whatever group of people under that name) would
initiate that famed school of thought, after traveling around Egypt
and Persia, drinking from those mathematical sources too.
In the next 300
years the Greek would advance Math beyond anything seen previously,
reaching their highest point with Euclid’s Elements (in Alexandria)
and, a generation later, the greatest mathematician of the ancient
world: Archimedes (288-212 BC) of Syracuse, though he did study in
Alexandria too. This man will be responsible, nearly 17 centuries
later, for the resurrection of the Heliocentric system (Copernicus
got the idea from an Archimedes’ book, though Archimedes himself
built on another Greek, Aristharcus of Samos); and the birth of
integro-differential calculus by Fermat-Newton-Leibniz, both
hallmarks of the modern scientific revolution.
At this point, maybe
a keen observer back then would be justified at wondering about a
Hellenistic gene for mathematics, except they had no idea about genes
and so far Egyptians, Babylonians, Persians and Greek had not too
many genetic connections. They did have cultural bridges built along
history though. ‘Nature 0’ X ‘Nurture 1’ so far.
Archimedes will die
by the hands of the new up and coming Empire - the Romans - in the
second punic war, because his king (and cousin) made the mistake to
betray the Romans for Carthago, a city of Phoenician background (so
another cousin of the Judeans) trying their hand in the great
geopolitical game. The relevant mathematicians of the next few
centuries will mostly be around the Library of Alexandria (in Egypt,
at some point Roman possession too). For all their mastering of
engineering techniques, the Romans themselves won’t contribute
much else to fundamental mathematics. We also know that Hellenistic
cities of this ancient period had more literacy rates than Israeli ones, for example. So
apparently, having a good Library was of much greater value than any
genetic consideration back then. ‘Nature 0’ X ‘Nurture 2’.
A bit over 600 years
later, the (western) Romans will fall to “barbarians” with no
mathematical knowledge whatsoever, taking down also anything
resembling an “education system”, with libraries (and whole
cities) burnt, no more tutoring paths to Roman citizens, no more
engineering corps and orderly societies under Roman pax and law.
Western Europe will forget most of the Greek-Roman former ‘high
culture’, Greek mathematics very much included. They will take more
than 700 years to rediscover it, by translating it from Arab back to
Latin after expelling the Muslims from Toledo (Spain) and taking the
great Library the Arabs built therein – igniting a process that
will lead to the European Renascence a couple of centuries later.
There again, ‘Nature 0’ X ‘Nurture 3’.
By the time the
Romans fell, they had expelled the Jews out of Judea for nearly 400
years. Though literacy rate of Jews before diaspora was probably
below 3%, post-diaspora Jews were mainly influenced by their more
nerdy faction, the Pharisees, who placed great emphasis on teaching
male Jews from a young age to read their sacred texts. Yet, after six
hundred years of diaspora the worldwide Jew population fell from 5 to
merely 1 million, if much. A good deal of those lost Jews were not
dead, but probably gave up on being Jews, for it was too taxing to
keep the strict Pharisaic laws.
It is possible that
this ‘selective pressure’ among Jews themselves drove the
“strongest/smartest” to stay? Is it possible that continued
formal education throughout centuries of father-to-son (or
Rabbi-to-students) led to (be it ‘evolutive’ and/or
‘Lamarck-like’ – mind you, epigenetics is in fashion again) a
sort of smarter people?
I don’t know, but
in what refers strictly to Mathematics that was hardly the case: the
new hot point was the Arab world, who greatly developed our
computational capability by the introduction of a more intelligent
notation (algarisms) and upon incorporating a grossly underestimated
invention from the Indians: the zero. They also had libraries full
of that old Greek wonderful math.
You will first hear
of Jewish mathematicians along history in Spain circa 1100, back
in the intersection among Muslims, Jews and Christians, where the
last two are trying to cacht up with the first one.
Even allowing that
capacity for language may lead to mathematical skills (since math is
a kind of language too), there is still the point that literacy here
isn’t a very well defined concept. A sizable proportion of male
Jews were exposed to reading from an early age, but how efficient was
that? Up to the 1600s (previous to Gutemberg), the best case
scenarios would be the most devot (or connected to Rabbinic service)
would read much of a very limited literature (few books around); the
most common scenario is the one of a majority that would scarcely read
any literature in their everyday life. Many probably even forgot what
they’ve learned when kids. To drive home this point, even in
relatively modern Tsarist empire of 1897, one third of Jewish male population was illiterate. I doubt
pre-1600s was even half as good as that.
But let us suppose
that a good number (say, at least 50% of males) of Ashkenazi in
post-1600 Europe were not only literate, but actually used letters in
their everyday life in meaningful ways. They certainly had a head
start compared to the rest of the European population. Let us also say that at least 20% of these (hence 10% of total male population)
used mathematics – four operations basic stuff at least– in their
everyday life in meaningful ways. It remains the question: would 2 or
3 hundred years (give or take a few more if you wish) be enough for
selection pressure to act on this group?
Just for comparison,
lactose tolerance was developed among European populations in a
timeframe considered real quick: a few (3 to 5, give or take) thousand years. And
that’s for a genetic variation that depends on far, far less genes
than a trait like ‘intelligence’.
I don’t know about
you, but I am willing to bet that whatever points “nature” scores
on this matter, “nurture” will be far off in the scoreboard.