ontolog-forum
[Top] [All Lists]

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

 To: "'[ontolog-forum] '" "Rich Cooper" Thu, 20 Feb 2014 16:16:08 -0800 <00D22E6AC6AF44FC8F93AFEEE1C6236B@Gateway>
 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 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."   _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J   ``` _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (01) ```
 Current Thread [ontolog-forum] Beauty in mathematics -- detected in brain scans, John F Sowa Re: [ontolog-forum] Beauty in mathematics -- detected in brain scans, Rich Cooper <=