|To:||"'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>|
|From:||"Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>|
|Date:||Thu, 20 Feb 2014 16:16:08 -0800|
It seems this shows that different places in the brain are activated for perceived beauty and ugliness. That’s not too surprising, is it? Every time we’ve isolated one experience class in the brain from another experience class, by definition, it has to be something we can detect in our toolkit for viewing the brain, e.g., fMRI.
fMRI and magnetic stuff can distinguish among pretty small brain areas, growing smaller as technology improves. That is the way mechanical structure software evolved also, as speed and memory improved historically. Ultimately we should be able to simulate the brain to some feeble degree, after which we may learn something and iterate the improvements.
Use data mining to aggregate the evidence and learn the spectrum of projections, decompositions, and alternatives. It should work, unless I’ve missed something in that chain of reasoning.
By the way, Euler’s identity is new to me, many thanks. That old geezer was up to a lot in his leisure time, but that equation is truly beautiful:
e^iπ + 1 = 0
and since π is defined as the circumference over the diameter:
e^(i*π) + 1 = 0
e^(i*(Circumference/Diameter)) + 1 = 0
e^(i*(Circumference/Diameter)) = -1
i*(Circumference/Diameter) = ln(-1)
Whoops! Ln(-1) is awkward. I suppose extending the curve for ln(x) to the –x axis (verboten!) could lead you to hypothesize that ln(-1) = - infinity, but that would be intuitive, and would ruin the next step.
i = (ln(-1)*Diameter)/Circumference
that is of the form
i = a/π
which is truly weird, whatever you use for a.
But there should be an informative picture of the unit circle in complex arithmetic somewhere on the web.
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
Beauty is one of the most "subjective" experiences, but evidence
from fMRI scans has a high correlation with subjective reports
-- even in a subject as abstract and "objective" as mathematics.
From BBC science news:
> Mathematicians were shown "ugly" and "beautiful" equations while
> in a brain scanner at University College London. The same emotional
> brain centres used to appreciate art were being activated by
> "beautiful" maths. The researchers suggest there may be a
> neurobiological basis to beauty...
Excerpts below from the original publication and the BBC summary.
Frontiers in Human Neuroscience, 13 February 2014
The experience of mathematical beauty and its neural correlates
by Semir Zeki, John Paul Romaya, Dionigi M. T. Benincasa, and
Michael F. Atiyah
Many have written of the experience of mathematical beauty as being
comparable to that derived from the greatest art. This makes it
interesting to learn whether the experience of beauty derived from such
a highly intellectual and abstract source as mathematics correlates with
activity in the same part of the emotional brain as that derived from
more sensory, perceptually based, sources. To determine this, we used
functional magnetic resonance imaging (fMRI) to image the activity in
the brains of 15 mathematicians when they viewed mathematical formulae
which they had individually rated as beautiful, indifferent or ugly.
Results showed that the experience of mathematical beauty correlates
parametrically with activity in the same part of the emotional brain,
namely field A1 of the medial orbito-frontal cortex (mOFC), as the
experience of beauty derived from other sources.
One of the researchers, Prof Semir Zeki, told the BBC: "A large number
of areas of the brain are involved when viewing equations, but when one
looks at a formula rated as beautiful it activates the emotional brain -
the medial orbito-frontal cortex - like looking at a great painting or
listening to a piece of music."
The more beautiful they rated the formula, the greater the surge in
activity detected during the fMRI (functional magnetic resonance
"Neuroscience can't tell you what beauty is, but if you find it
beautiful the medial orbito-frontal cortex is likely to be involved, you
can find beauty in anything," he said...
To the untrained eye there may not be much beauty in Euler's identity,
but in the study it was the formula of choice for mathematicians. It is
a personal favourite of Prof David Percy from the Institute of
Mathematics and its Applications.
e^iπ + 1 = 0
He told the BBC: "It is a real classic and you can do no better than
that. It is simple to look at and yet incredibly profound, it comprises
the five most important mathematical constants - zero (additive
identity), one (multiplicative identity), e and pi (the two most common
transcendental numbers) and i (fundamental imaginary number).
"It also comprises the three most basic arithmetic operations -
addition, multiplication and exponentiation.
"Given that e, pi and i are incredibly complicated and seemingly
unrelated numbers, it is amazing that they are linked by this concise
At first you don't realise the implications -- it's a gradual impact,
perhaps as you would with a piece of music and then suddenly it becomes
amazing as you realise its full potential."
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