

Modern math solves Ramanujan’s ‘vision’ - may clarify black holes - mrkuchbhi
http://www.futurity.org/science-technology/modern-math-solves-ramanujan%E2%80%99s-%E2%80%98vision%E2%80%99/

======
Xcelerate
I love articles like this. Ramanujan was a very interesting man and perhaps
had some of the deepest mathematical insights of anyone who existed. People
are still trying to figure out what the things he wrote down meant. If you
want to know more about his life, there's a great book called "The Man who
Knew Infinity" ([http://www.amazon.com/The-Man-Who-Knew-
Infinity/dp/067175061...](http://www.amazon.com/The-Man-Who-Knew-
Infinity/dp/0671750615/ref=sr_1_1?ie=UTF8&qid=1355776982&sr=8-1&keywords=the+man+who+knew+infinity))

~~~
jlgreco
I find this very interesting since, while I am positive it has a mundane
naturalistic explanation (like: the guy was really smart and had exceptional
intuition), revealing the answers to questions that perhaps cannot yet even be
formally asked is how I think I would go about proving that I was either from
the future or another world.

Somehow get sent back in time a couple dozen thousand years? Carve a bunch of
primes into the side of a cave somewhere, maybe throw in the Pythagorean
theorem and a suspicious number of digits of Pi too. Messages that perhaps
mean little to the contemporaries of the message.

Kind of fun to think about I think.

~~~
nsomaru
It gets even more interesting when you think about what 'intuition' really is,
and what it means to 'know' something. Words, words m'lord.

If you're willing to leave the standpoint of a 'reality' which is based in the
interactions between 'subject' and 'object' then things get really interesting
and you begin to question what such an apparently great man meant when he said
that what was revealed to him was done so by divinity.

To do so, of course, would mean you would have to understand the metaphysics
of Indian thought and culture, which may be (rather basically) summarised to
hold that the objective is merely a reflection of the absolute Subjective,
i.e. divinity.

This is especially important because it is from this cultural standpoint that
these visions were realised. I could go on if anyone is interested.

~~~
catshirt
please do. i'd contribute more in response to encourage you, but anything i
have to say on the topic is something i've drawn from my own processes and
probably not worth discussing until i've at least done Wikipedia on it. and
it's not really a topic i've heard discussed before, even in the context of
"genius". though that is the context in which i've pieced them together.
disclaimer IANAG

~~~
nsomaru
I think use of that acronym itself constitutes geekiness ;)

A bit of background: I've spent the last three years of my life studying
Indian metaphysics in India at a traditional academy known as an 'ashram'. The
environment was somewhat similar to the original Greek academies, I can
imagine, but that is speculation. I also have interests in tech, programming
and philosophy. Please note that I am not trying to 'prove anything' either
correct or incorrect -- indeed, this would not be the forum to do so. Rather,
an opportunity to be of service to another individual and present two
different views of this experience of the world and thus life itself.

For the western mind, indeed, for my mind -- it is ingrained to a point of
'truth' that there is a single objective world around us which presents itself
to various individuals via the senses. It literally took me 1.5 years of
serious mental deconstruction, analysis and questioning before I was able to
entertain the thought that my body, brain and indeed the world around me were
a _product_ of the mind, and did not produce the mind itself. Consider that.
It's your whole system of thinking about the world turned upside down.

In building a metaphysical system for the world and individual, the Indians
defined an individual as a 'body-mind-intellect' (BMI) experiencing
'perceptions-emotions-thoughts' (PET). The former they termed the 'relative
subject' and the latter the 'relative object'. It is easy to see that these
cover EVERY aspect of human experience.

I am taking a shortcut and would be happy to clarify further, but there is a
facet of the spiritual path in India known as bhakti yoga (the science of
union with the Divine through emotion) which targets the mind in its emotional
capacity. It is not uncommon, then, to use an IDOL (which is NOT the same as
the goal itself) to represent the goal of absolute subjectivity which one is
striving for and cannot be perceived, felt or conceived via the BMI and their
PET.

This representation, symbol, takes the form of a goddess/god whose strange and
crazy figures and ornamentation are intended to initially (1) evoke questions
in the seeker as t to their presence and (2) inspire more devotion once their
significance is intellectually understood.

Coming back to the genius mathematician. If one traces one's own moments of
lucidity or inspiration, one would find that they come at times when the mind
is relatively calm, composed and engaged in a subject. The extrapolation of
this is the state of bhakti yoga (complete absorption in the ideas represented
by the deity), and most adherents thereto ascribe the 'doing' of their
thoughts, words and deeds to the deity Itself, to efface their egos and move
closer to their ideal of transcending the world itself.

Now look at that simple statement: "These ideas were revealed to me by my God"
[paraphrase]. The simplistic notion that an apparition appeared before him or
in his mind to provide him with these incredible insights does not hold to a
scientifically-inclined mind. But the notion that he had trained his mind so
highly that he was able to become absorbed single-thoughtfully upon a subject
to the extent that he was able to perceive subtle nuances therein, indeed
subtle nuances that would seem 'magical' to a non-trained observer is not
unthinkable. That he then ascribed his discoveries to a deity is something
that happens daily in Indian life and as previously covered is intended as an
effacement and ultimate transcendence of the ego and the world it projects.

I can highly recommend A Parthasarathy's Vedanta Treatise if you are
interested further.

------
Tycho
This paragraph makes no sense to me:

 _They found that while the outputs of a mock modular form shoot off into
enormous numbers, the corresponding ordinary modular form expands at close to
the same rate. So when you add up the two outputs or, in some cases, subtract
them from one another, the result is a relatively small number, such as four,
in the simplest case._

~~~
rfurmani
You have two functions both of which grow to infinity, one of which is much
better understood than the other. It turns out that if you subtract the two
functions, they balance out perfectly so you end up with something converging
to 4 instead of going to infinity.

~~~
powertower
When you subtract any two functions that are exponential, the answer is 4?

~~~
Slickarango
Not quite. Take two exponentially growing functions, say e^x and e^2x over the
interval [0,infinity). as x-> infinity both grow without bound. So does the
difference of e^(2x)-e^x because the former is just so much larger than the
second. They both approach infinity, but at different rates! If the difference
between two functions (in the limit) converges, that means that the two
functions diverge at the same rate (i.e. both with the end behavior of e^(ax)
for some constant a) This is all a little hand wavy though but I hope that
clears things up.

------
whatshisface
I wish the article had talked more about what it had to do with black holes.
Can anyone here explain that to me?

~~~
Jun8
Here's a link to a paper on this: <http://arxiv.org/abs/1208.4074>. Explaining
it is _well_ beyond my capacity, though.

~~~
d0mine
For a layman the abstract sounds like a computer-generated hoax.

~~~
rfurmani
You could say that about any field that one is unfamiliar with. Heck, the most
basic art concepts could seem like so to a blind man. Mathematicians have
worked for ages on simplifying the concepts so every term is there because it
helps a trained mathematician understand what is going on.

------
scotty79
I hope we have handful of Ramanujan's DNA stashed somewhere so, once we accept
(and achieve) human cloning, we can clone thousands Ramanujans in hopes of
some of them developing such beautifully abnormal brain.

~~~
prewett
I think it would be poetic justice if in a triumph of naturalism we actually
cloned him and got only boring copies because the real Ramanujan actually got
his insights supernaturally, like he claimed...

~~~
scotty79
There might be additional factors like mitochondrial DNA or some epigenetic
factors or some accident during development of his brain. Getting 1000 boring
Ramanujan clones would prove that the our skill is lacking not that we
couldn't replicate a goddess.

