What can drew one to think is the
idea that ‘Is all a tautology?’ i.e. A implies B, B implies C to C implies A.
If it's all logic, there really shouldn't be anything to understand. The early
one figures out that it's not logic, the better it is. What keeps one from
understanding it and that one couldn't follow the logic is that these ideas are
so different and new. One can finally realize that it wasn't all about logic
but rather about the creative process. Sometimes it gives a feeling of ‘writing
a book’ or ‘providing piece of music’ as one solves a math problem, because
it's not about the tools, everyone knows about the tools, it's about how one
put them together. There's a little bit artistry involved and that's what drew
one to it. One gets drawn into geometry just because it really emphasizes the
‘visual’ aspect as well as the ‘aesthetic’ aspect. One honestly can find a kind
of beauty in thinking creatively about problems because somehow something
doesn't click until two dollars. There's a little bit of mystery to the
creative process. What exactly clicks in your brain that takes you from not being
able to solve problem to solving it. One really enjoys their thinking about
beautiful problems. Mathematics is known for the use of aesthetic terms in
describing their way of work. Nobody can deny the fact that beauty lies in the
eyes of beholders. A lot of people, irrespective of whether they are from a
mathematical background or not, they seem to appreciate the state of art that
mathematics provide. Vi Hart, a self described ‘recreational mathemusician’
from National Museum of Mathematics performed dance with music by representing
each figure as a digit. She represented a series of numbers using the powers of
2. She also danced for the value of pi in binary. Finally, she made a painting
out of that hand dance by having different color for her different fingers.
Scott Kim is an artist and use mathematics as his language. He is the author of
many American puzzles and has also designed many computer games. He describes
his work as the relationship of mathematics with various shapes and sizes.
Mathematics is as valid a form of
art, as any other. Now it's difficult to put into words, exactly what it is
that makes numbers and symbols so appealing - but according to scientists, it
boils down to simple brain chemistry. In a recent study at University College
in London, researchers showed a group of mathematicians 60 different
mathematical equations, and asked them to rate those equations on a scale of
"ugly” to "beautiful," while inside an fMRI scanner. The results
showed that the more "beautiful" an equation was - according to the
test subject - the more likely it was to elicit activity in the A1 field of the
medial orbitofrontal cortex. This is the part of your brain that's typically
associated with emotional responses to visual and musical beauty. Thus, people like
us respond to numbers and equations, the same way other people do to music or
art. But even people with no musical talent can still appreciate good music -
so what constitutes beauty in math? And does the appreciation of it require
some understanding of its meaning? Well, not necessarily. To test that idea, researchers
performed the same study on a control group - with no special appreciation of
math. And while those subjects did show a significantly lower emotional
response to the equations - a handful of them were still capable of finding
their beauty - even with no understanding of what they actually mean. So what
makes an equation "objectively beautiful"? Is it just a formula of
curves and shapes, maybe symmetry that makes it pleasing to the eye? It's
difficult to quantify the exact reasons, but there is one equation consistently
rated to be the most attractive - and that's Euler's identity (1+eiπ=0)
– perhaps because it contains the 3 most fundamental numbers in the
mathematical universe, e, π, and i. It's a pretty hot equation. What's the
ugliest, if one asks, according to the mathematicians in this study, it's the Srinivasa
Ramanujan's rapidly converging infinite series of π.
Figure 1 Figure
2
Data visualization is a way of
representing information and an artistic and interesting way. Scientists might
be happy with scatter plots in black-on-white laps, but if one wants to
communicate information and data to the public, he or she would want it to be enjoyable
as well as colorful. To quote one of the chief icons of such form is Martine Kaminsky.
It is quite interesting to look at his artistic work, finding beautiful
artistry in the randomness of pi. His painting as seen in Figure 1 is pi in a
beautiful colorful way. What make it so special is that, it is done in the simplest
way one could have think off. He takes the digits of pi and gives each digit a
different color to start with three. Three is an orange color there, then one is
a red, four is a yellow, one again is red and then five is green, nine is
purple and so on. it makes a really beautiful poster, one can kind of see the
randomness of it, but one can’t see it as any particular pattern to the colors;
which is which reflects the randomness of the digits of pi is well. To take
that further, he started to kind of make the center of the circle using the
color of the next digit. Probably he did so, just to make it a bit prettier at
produced. He might have found it interesting because he had to join up digits
that had the same colors in them. In a research like this, they care to go a
bit further and in this art, she connects digits adjacent digits in his poster that
have same color, so actually they are the same number, which makes the
disconnected networks. One doesn’t need to use any great mathematical truth
defined underneath this. This is a thought and Martine is very clear about himself
that this is less about the mathematics and more about the beauty of it. But it
is intriguing as well. The other way one could do this is if he put the digits
of pi in a spiral as seen in the Figure 2. This looks similar to tiling in a
Roman bath house. Something that makes one happy, maybe that's because of the
colors she used. But to take this a step further is one of Brady's Patriots. It
makes us think that we should just appreciate the beauty of that before we
describe it and not merely bringing the beauty of it by describing it and not
doing the justice to appreciate it. Now what he's done there is connected the
digits together as you go through the digits of pi. So he started at three and he
has connected three to one and then connected one to four and so on. He has
also given each digit a color as well to a psychopath. He's made a package by
putting numbers in a circle zero one two three four five up to nine and one
have made a path and makes this beautiful piece of art. About data
visualizations, which is hugely important, it goes way back! Florence Nightingale
once had to represent the statistics that she had in Crimean War, where she was
a nurse and the deaths that she was suffering on the wards. It was because they
weren’t clear enough and she had to represent it to the state. She was a
mathematician herself and she used diagrams for representing the data in a
visual way. A simpler example is a pi graph representing data in a visual way. What
these guys know and has become quite a thing recently is to make it beautiful
as well. This is important because to communicate especially to the general
public, one should be able to look at the information, understand it and enjoy
looking at it and then only one appreciates it better. While talking about
serious mathematics subjects like combinatorics, which is very visual as well
and one can and do the maths through pictures, diagrams, networks, graphs and
things like that. In the present example, we saw how pi is pretty random. Martine
actually compared pi with a few randomly generated numbers. She generated all sorts
of ways to randomly generated numbers and did the same sort of artistry and one
can see the similar sorts of patterns coming from pi has the appearance of any
of the randomly generated number. Another piece of art by Martine is the same idea
again i.e. circular paths, but here there is little dots on the outside just to
show that where the lines are coming from and where they going to. If it's 3.141,
then above the three, is shown in with a little dot that it's going to the
number one; and above the number one shows that it is coming from the number
three. It's basically showing where it is going to and where it is coming from.
So the size of the dots means that it occurs more often. There is a big
purple-topped in the piece. Purple means nine and what it is showing is that
there's a sequence in pie where there is just 9999, called the Feynman point,
which is eighty six consecutive nine's, which is 762nd digit in pi. One
can see it right there in the piece which are just six consecutive nines and it
makes a big blob because it's coming from 9 repeatedly. Martine has done this
with other numbers as well. He has done it for the golden ratio, another famous
mathematical number, also e, another famous mathematical number and what he was
interested in was to find out where they coincide. When he did this, he lined
up these three special mathematical numbers and looked at where they had the
same digit. Now, because these numbers are kind of random, he wanted to find
out when they have the same digit. So, for all three numbers to have the same digit
that happens with the probability of one in a hundred, when one line them up he
got something, which he called the accidental similarity number and he
discovered that yes they do lined up with the same digit about one in a hundred
which is what probability tells us. So the average gap between linings up is
about 100. He started to experiment with his accidental similarity number and
made some piece of art based on that as well especially circular ones which
look pretty.
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