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Brain scans: mathematical beauty acts just like artistic beauty

The concept of beauty in physics or mathematics has been discussed dozens of times on this blog. You may also find things like a two-hour debate about beauty in mathematics – this one features Barry Mazur, Brian Greene, Elaine Scarry, Mario Livio, and Eva Brann.

If it is supposed to be helpful at all, the concept of "beauty" is a problematic one because one must have the "right sense of beauty" which is usually inseparable from some talent as well as education in mathematics and physics in order to really "feel" the beauty of the beautiful laws and mathematical structures and to preserve the beauty's correlation with the truth. For other people, beauty and intuition may be as misleading as helpful.\[

{\Large e^{i\pi} + 1= 0}

\] This identity has been identified as the ultimate beautiful equation by the mathematicians interviewed by the BBC. I like it, too.

However, some neuroscientists have shown that there is one aspect in which the beauty of mathematics looks indistinguishable from the beauty of arts: brain scans:

The experience of mathematical beauty and its neural correlates by Zeki, Romaya, Benincasa, Atiyah (yes, THE Sir Atiyah, Frontiers in Human Neuroscience)

Mathematics: Why the brain sees maths as beauty (BBC)
Euler's identity above induces a similar activity in the (mathematicians') brain as the best works by Mozart, Shakespeare, and van Gogh. On the other hand, e.g. equations from papers about loop quantum gravity manifest themselves just like a painting of Joseph Stalin's buttocks created by Trofim Lysenko using cattle feces or a concert by Pussy Riot.




15 mathematicians and 60 equations were used for the brain scans. To perceive the beauty of an equation, lots of regions of the brain have to become active. More beautiful equations generally increased the overall activity in the fMRI (functional magnetic resonance imaging) scans.




Beauty is said to be a source of inspiration for mathematicians (well, I guess that this largely applies to theoretical physicists, too). Sometimes the true potential or beauty starts to be unmasked only gradually, when various pieces start to fit together.

Missing galaxy matter found

The quantum fluctuations of the geometry imprinted to the cosmic microwave background may be used to calculate the density of galactic matter etc. However, the Planck telescope indicated that the actual density was 1.4 times lower. Now, some folks use a more robust weak-lensing analysis to claim that the discrepancy isn't there, so no new physics is needed to explain it: Nature (popular), Planck paper (2013), Weak-Lensing Fix (2014).

Runaway pulsar with a strange jet

One more astronomical gospel. NASA's Chandra has seen a runaway pulsar that is firing a very unusual jet, IGR J11014-6103: Phys.ORG (2014), Lighthouse Nebula Long Helical Jet (2014, arXiv).

Flat Earth Society and climate alarmism

Alabama-based atmospheric scientists Richard McNider and John Christy wrote a wonderful reply in the Wall Street Journal to John Kerry's insulting remarks. In an Asian theater play that turned the climate alarmists into their own cartoons, the secretary of state would label the climate skeptics as "shoddy scientists who shouldn't be allowed" and "extreme ideologues" or "members of the Flat Earth Society".

McNider and Christy point out that the actual relationship was upside down. It was the "consensus builders" who would defend the Flat Earth concept before skeptics like Pythagoras would buck the consensus and focused on empirically-rooted arguments that allowed him to see that the Earth was spherical. The two atmospheric scientists review the points in which the skeptics and some or all alarmists agree as well as the discrepancies between the alarmists' predictions and the observations. They also coin a wonderful new euphemism for the alarmist shitheads, "the climate-change-consensus community". ;-)

(Their always mild-mannered colleague in Alabama, Roy Spencer, decided to start to use another diplomatic phrase for the climate alarmists, as long as they call him a denier: the global warming Nazis. Maybe we should agree that we will use this term at all times.)

They urge this community to become as modest and open-minded as the lousy results of verifications of their beliefs seems to require and summarize the likely negative implications of a hypothetically continuing arrogance by this "climate-change-consensus community".

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reader Dilaton said...

Sorry for the off topic Lumo, but have you seen this :-/?

http://www.preposterousuniverse.com/blog/2014/02/19/dept-of-energy-support-for-particle-theory-a-calamity/

The responsible retarded anti-scientific, anti-civilisation trolls in too powerful positions should be sacked immediately ...!

Have to put my nose now into my Ziebach book to calm down and then enjoy this TRF article to cheer me up ...


reader Luboš Motl said...

Dilaton, were you upset by the trolls behind the counterproductive funding decisions, or commenter-trolls like "AI" in the thread? I would understand your dissatisfaction in both cases. ;-)


Good luck with Zwiebach.


reader Dilaton said...

Yep, on Sean Caroll's blog, the omnipresent comment trolls can be dealt with by downvoting them until their comments collapse :-)

The trolls behind the destructive funding decisions are much more annoying and damaging. The only efficient way to deal with them is to revert their biological development back to an early state such that they can savely be aborted ...!

Haha, some of the comments in this article make me feel like googling for an image that properly represents the beauty of the relevant equations of LQG :-D
I will update my comment when I have found one ...


reader curmudgeon said...

Haven't read the original article, but I hope it points out that there's a strong question of causation here. Does the fact that mathematicians find math beautiful imply that there's an intrinsic beauty that they're smart and well-educated enough to perceive? Or does it imply instead that there's some subset of people who naturally find math beautiful just like some people find abstract art beautiful, and mathematicians are drawn from the mathematically talented members of that subset? Put another way, do they do math because they think it's beautiful (a $10 term for "they like it") or do they think it's beautiful because it really is and only they have the right organ of perception to feel it (their talented and trained brains)? fMRI doesn't let us distinguish the two possibilities. My strong bias is that math is intrinsically beautiful, but this is more of a non-disproof than a proof..,


reader Tom said...

Anna, recall the rush to war a century ago, in a civilization arguably at its apogee. It seems just possible to me that had those people had the Internet they might not have been so keen to march off to the front. Or, suppose, masses of people started not paying their income tax. Would the authorities crush such revolt? If it were extensive enough, maybe not, as they would have nothing to rule afterwards. No doubt war has written our maps to this point, but maybe the amazing communication revolution we are living through gives a non-trivial probability of change for the better.


reader Tom said...

lucretius, globalization is surely the face of today’s capitalism, but for me “capitalism” means something more fundamental that never occurs in practice. I borrow terminology from Hayek, but I define “pure” capitalism as a random walk in an information field leading to a spontaneous order (or, equilibrium points in game theory if that’s to your taste), where people execute exchanges freely when both perceive advantage. If the laws of land are transparent and such that contract and private property are respected, some version of capitalism will appear. I guess you and I agree that England around 1875 probably came closest to pure capitalism.

What I see happening today is crony capitalism growing to the point were it crowds out free exchanges. The green energy “capitalists” perhaps providing the vilest example. A big business a decade or so out, after the global warmers go back to wailing about the next ice age, will be dismantling their stupid wind mills.


reader NikFromNYC said...

The myth that normal sophisticated city folks rejected Van Gogh when really it was only the local rural peasants, has been used in Emperor's New Clothes fashion to discourage whole generations of talented kids from pursuing their gifts competently instead of participating in an aesthetic scam. Tom Wolfe wrote a short book (The Painted Word) spilling the beans on just how preposterously silly the resulting Modern Art movement became through the artistic versions of Mike Mann or Ancel Keys (dietary lipid theory of heart disease) in which painting became merely concerned with “the flat picture plane” but later some naughty Modernists found flat objects themselves as a loophole to once again paint real things like the American flag or comic strips. The height of this tulip craze was Helen Frankenthaler's rejection of paint itself in favor of ugly smears of dye in order to stain the canvas instead of paint on top of it, a real art historical *revolution*, as our local Guggenheim museum still prominently displays, some of her splashed crap being seen here:

http://hommemaker.com/2011/12/27/rip-hommegirl-helen-frankenthaler/

“Cézanne is the finest expressions of this decadence. He was truly unable to imitate the masterpieces and all of his admired technique is merely proof of his inability. His apples are made of cement. The paradox is that what is least admirable is most admired: nullity! What a symbol for a period! On the pretext of the academic being detestable, the worst in the class was made a hero! He opens the door to the ethics of shit! Newness at whatever costs and art becomes just a latrine! The logic of this search for newness leads to the gratification of total shit of which Cézanne is the high priest.” – Salvador Dali (Dali on Modern Art, 1957)

Recently the Nobel Prize winner concerning mirror neurons have a talk at Columbia's odd Casa Italiana building, a sort of campus embassy, and in soft science manner he suggested that the brain could distinguish real art from random patterns but the real art he tested were “paintings” with no paint, just blank canvases that had been boringly slashed once or twice with a box cutter, resulting in photographs of them that looked symbolically like either female anatomy or a gash wound indeed worthy of a confused brain searching for the meaning of it that it wouldn't search for in a photo of a few scribbles. And that was the *only* “art” his study used. The chattering class then loudly chattered, gleefully, as the noble Nobelist was off to a very expensive dinner.


reader Gerry said...

Dept. of Energy Support for Particle Theory: A “Calamity”

http://www.preposterousuniverse.com/blog/2014/02/19/dept-of-energy-support-for-particle-theory-a-calamity/

"Now that support is crumbling — drastically. In the last couple of years, the DOE has radically changed how it carries out reviews of different university theory groups, to decide how much grant support each will get. All for ostensibly good reasons — leveling the playing field and all that."
BS!


Just go to the DOE home page and you will see where the money is going. Hint...Consensus
http://energy.gov/


reader Gordon said...

"On the other hand, e.g. equations from papers about loop quantum gravity manifest themselves just like a painting of Joseph Stalin's buttocks created by Trofim Lysenko using cattle feces or a concert by Pussy Riot."


---or else they can use any photo of Lee S. as the control.


reader Gordon said...

Speaking of Pussy Riot, the little minx have been busy at Sochi, haven't they? Putin should give them a free holiday in Siberia with all the trimmings.


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I'll see your air traffic map, and raise you an ocean traffic map.
https://www.marinetraffic.com/en/


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