13 February 2014

Brain scans and beauty in mathematics

Hot off the press:
Brain scans show a complex string of numbers and letters in mathematical formulae can evoke the same sense of beauty as artistic masterpieces and music from the greatest composers. The same emotional brain centres used to appreciate art were being activated by "beautiful" maths. The researchers, from University College London, suggest there may be a neurobiological basis to beauty and their study was published in the journal Frontiers in Human Neuroscience.

Of course, this is not news to people doing mathematics. But it is nice to know that it can be confirmed independently, or that methods are slowly arising for evaluating such things as "beauty", "elegance", etc. Perhaps, one day, we will have some criteria for other kinds of states which belong to the emotional domain, and, perhaps, we will even be able to quantify such things like morality.

Marcus du Sautoy, mathematician and professor for the public understanding of science [Dawkins' successor in this],  said he "absolutely" found beauty in maths and it "motivates every mathematician". [He is almost right. He should remove the pronoun `every' or define the term `mathematician', for there certainly exist `mathematicians' who are not motivated by beauty but, rather, for example, how much money they can raise or how many papers they can publish (regardless where), and other factors.]

Again, we should be careful in generalizing and cautious in interpreting what the news article linked above says, as it concludes by stating that, "in the study, mathematicians rated Srinivasa Ramanujan's infinite series and Riemann's functional equation as the ugliest of the formulae." At the very minimum, most of us know when something is beautiful or not and also know that beauty may not be apparent from the very beginning, and that it may take a lot of ugly, hard, persistent work, frequently by more than one person, in order that this beauty be revealed and finally be written down so that others may admire [or ignore].


  1. I have not read the article, but it is testing brain areas the light up during music. Is it "beauty", I doubt it. Imagine that you do the brain scan on a person listening to their favorite rap or watching their favorite stripper or petting their dear dog or cat.

    People get pleasures from lots of things and this varies from person to person. Heck, if their standards are low, they may even enjoy Riemann's Functional Equation.

    And just as a I don't thing "Beauty" is a Platonic real item, so "Morality" is not. There is no "morality" waiting to be discovered. There are people's preferences which match their constitution, environment, training and much more.

    The study shows people get kicks out of Math -- that is not surprising. But I am sure mathematicians want it to say much more.

    (Maybe I should read the article, but that is my suspicion)

    Suggestion Takis: put your comments in-line with your post -- don't open on a separate page.

    1. Sabio,

      That's why I'm saying we should be cautious... I won't deny the beauty in mathematics, but I can also see a lot of ugliness. So you say that neither beauty nor morality are "platonic items"?

      As for the suggestion, thanks. I think I managed to change the settings. I think.

  2. Nice fix -- why is everything bold font.

    I did not understand your question.
    But I like putting operational definitions on things like beauty and morality to make clear that they are convention.
    Is that clear?

    1. Oh, it's just a semantics question. You said:

      And just as a I don't thin[k] "Beauty" is a Platonic real item, so "Morality" is not.

      Is this supposed to mean that, according to you,

      Neither "Beauty", nor "Morality" is a Platonic real item.

      As for bold fonts, I noticed it too, but there is no obvious way to fix it.

    2. Oh.
      First, I take a nominalist approach -- Platonic ideals are mistaken ideas. They don't exist.
      These are abstractions which trick us into thinking there is something real behind them that is very different from all the on-the-ground activities that the abstraction is actually addressing.

      Is that more clear?



What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant