Found a Wikipedia page on it:

http://en.wikipedia.org/wiki/Euler%27s_identity

-Rich

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

**From:**
ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] **On Behalf Of **Rich Cooper

**Sent:** Thursday, February 20, 2014
4:16 PM

**To:** '[ontolog-forum]
'

**Subject:** Re: [ontolog-forum] Beauty in mathematics -- detected in
brain scans

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

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

-----Original Message-----

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx]
On Behalf Of John F Sowa

Sent: Tuesday, February 18, 2014 9:08 AM

To: '[ontolog-forum] '

Subject: [ontolog-forum] Beauty in
mathematics -- detected in brain scans

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.

John

_____________________________________________________________________

http://www.frontiersin.org/Journal/10.3389/fnhum.2014.00068/abstract

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.

_______________________________________________________________________

http://www.bbc.co.uk/news/science-environment-26151062

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

imaging) scans.

"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

formula.

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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