Here you will find material about Ioannis Souldatos’ teaching and material from other instructors or from the web that I found interesting.
See the full article at https://doi.org/10.3389/fnhum.2014.00068
Original Research ARTICLE
Front. Hum. Neurosci., 13 February 2014 |
The experience of mathematical beauty and its neural correlates
- 1Wellcome Laboratory of Neurobiology, University College London, London, UK
- 2Department of Physics, Imperial College London, London, UK
- 3School of Mathematics, University of Edinburgh, Edinburgh, UK
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.
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty”
The beauty of mathematical formulations lies in abstracting, in simple equations, truths that have universal validity. Many—among them the mathematicians Bertrand Russell (1919) and Hermann Weyl (Dyson, 1956; Atiyah, 2002), the physicist Paul Dirac (1939) and the art critic Clive Bell (1914)—have written of the importance of beauty in mathematical formulations and have compared the experience of mathematical beauty to that derived from the greatest art (Atiyah, 1973). Their descriptions suggest that the experience of mathematical beauty has much in common with that derived from other sources, even though mathematical beauty has a much deeper intellectual source than visual or musical beauty, which are more “sensible” and perceptually based. Past brain imaging studies exploring the neurobiology of beauty have shown that the experience of visual (Kawabata and Zeki, 2004), musical (Blood et al., 1999; Ishizu and Zeki, 2011), and moral (Tsukiura and Cabeza, 2011) beauty all correlate with activity in a specific part of the emotional brain, field A1 of the medial orbito-frontal cortex, which probably includes segments of Brodmann Areas (BA) 10, 12 and 32 (see Ishizu and Zeki, 2011 for a review). Our hypothesis in this study was that the experience of beauty derived from so abstract an intellectual source as mathematics will correlate with activity in the same part of the emotional brain as that of beauty derived from other sources.
Plato (1929) thought that “nothing without understanding would ever be more beauteous than with understanding,” making mathematical beauty, for him, the highest form of beauty. The premium thus placed on the faculty of understanding when experiencing beauty creates both a problem and an opportunity for studying the neurobiology of beauty. Unlike our previous studies of the neurobiology of musical or visual beauty, in which participating subjects were neither experts nor trained in these domains, in the present study we had, of necessity, to recruit subjects with a fairly advanced knowledge of mathematics and a comprehension of the formulae that they viewed and rated. It is relatively easy to separate out the faculty of understanding from the experience of beauty in mathematics, but much more difficult to do so for the experience of visual or musical beauty; hence a study of the neurobiology of mathematical beauty carried with it the promise of addressing a broader issue with implications for future studies of the neurobiology of beauty, namely the extent to which the experience of beauty is bound to that of “understanding.”
See the full article at https://doi.org/10.3389/fnhum.2014.00068
September 20, 2017 by Andy Thomason
Laura Kipnis Says She Faced Another Title IX Investigation, This Time for Her Book
Laura Kipnis, the Northwestern University professor whose Chronicle article titled “Sexual Paranoia Strikes Academe” sparked a chain of events that led to a Title IX investigation of her, faced another inquiry, The New Yorker reports. That one was prompted by the publication of her book Unwanted Advances: Sexual Paranoia Comes to Campus, she said.
In her initial essay in The Chronicle, Ms. Kipnis argued that a culture of protection rather than empowerment around sexual issues on campuses was wrongheaded. The response to that essay included the filing of a Title IX complaint against Ms. Kipnis, alleging, in part, that the essay had had a chilling effect on complaints, and an investigation was opened. She chronicled the proceedings in another Chronicle essay, “My Title IX Inquisition,” and was cleared of wrongdoing.
But over the summer, The New Yorker reports, Ms. Kipnis faced another university investigation, prompted by the publication of her new book. The allegations, according to the magazine, were similar to those of the first complaint. In a statement to the university, Ms. Kipnis wrote that “these complaints seem like an attempt to bend the campus judicial system to punish someone whose work involves questioning the campus judicial system, just as bringing Title IX complaints over my first Chronicle essay attempted to do two years ago.”
She was cleared of violating university policy, the magazine says. Northwestern did not respond immediately to The New Yorker’s request for comment.
See full article at: http://www.bbc.com/news/uk-england-oxfordshire-41265057
Carbon dating reveals earliest origins of zero symbol
- 15 September 2017
Carbon dating shows an ancient Indian manuscript has the earliest recorded origin of the zero symbol.
The Bakhshali manuscript is now believed to date from the 3rd or 4th Century, making it hundreds of years older than previously thought.
It means the document, held in Oxford, has an earlier zero symbol than a temple in Gwailor, India.
The finding is of “vital importance” to the history of mathematics, Richard Ovenden from Bodleian Libraries said.
The zero symbol evolved from a dot used in ancient India and can be seen throughout the Bakhshali manuscript.
Other ancient cultures like the Mayans and Babylonians also used zero symbols, but the dot the Bakhshali manuscript developed a hollow centre to become the symbol we use today.
It was also only in India where the zero developed into a number in its own right, the Bodleian Libraries added.
Earlier research had dated the Bakhshali manuscript to the 8th and 12th century, but now carbon dating has shown it to be centuries older.
Bodleian Libraries said scholars had previously struggled to date it because it is made of 70 leaves of birch bark and composed of material from three different periods.
The manuscript was found by a farmer in a village called Bakhshali, in what is now Pakistan, in 1881 before being acquired by the indologist Rudolf Hoernle, who presented it to the Bodleian Libraries in 1902.
The creation of zero was one of the “greatest breakthroughs” in mathematics, Prof Marcus Du Sautoy of the University of Oxford said.
Cryptography sets the tone… A story of string instrument making in the 19th century
1 February 2017
Pierrick Gaudry, CNRS researcher in the Caramba team has broken the codes in the accounting registers of major Parisian instrument makers from the 19th century. This deciphering reveals the value of string instruments and provides more knowledge of the history of the instrument-making business.
Jean-Philippe Echard, the curator of the music museum in Paris, found three accounting registers covering a period of nearly 150 years in some archives. These had been kept by the various successors of the great Parisian string instrument maker Nicolas Lupot who founded his workshop in 1795.
These accounts have become yellowed by time but have references to nearly 250 instruments. These were mainly violins bought by the instrument makers with a view to selling them on to their clientele of musicians.
For each instrument, 4 prices were entered – the violin’s purchase price, the desired selling price, the reserve price (the minimum price the instrument maker would accept) and the actual sale price.
The instrument makers coded the purchase price and the reserve price to keep them confidential by replacing numbers with letters. The coding enabled the instrument maker to have the book open in front of clients without the latter knowing his profit margins.
Jean-Philippe Echard therefore contacted Pierrick to ask him to decipher these codes. “In that era, communications were multiplying and coding messages had become fashionable”, explains Pierrick.
Pierrick usually uses powerful calculators for his research but in this case to decipher the codes he just needed a sheet of paper and a pencil. It turned out to be a monoalphabetic substitution cipher. The instrument maker replaced a figure by a letter basing this on a ten-letter word. After trying out a few hypotheses, Pierrick discovered that this code was based on the French word “harmonieux” (harmonious), with the “h” standing for 1 and the “x” for 0 (this was sometimes replaced by “z” as the figure 0 was often used).
Why was the word “harmonieux” chosen? The soundboard – ‘table d’harmonie‘ in French – is the front surface of a violin or any string instrument. It receives the vibration to be amplified, usually via the bridge of the instrument.
Following this discovery, an article was submitted to and accepted by the journal “Cryptologia” which features the historical aspects of cryptography.
This deciphering work revealed numerous secrets about the value of string instruments and more generally on the history of the instrument-making business but also showed that cryptography is not just based on working with computers. It existed long before computers in fact and even involves many other disciplines. The main thing is to make them work together in harmony.
See the video (copyright – CNRS Images)
Articles from http://www.sciencesquared.eu/who-wants-live-forever
Who wants to live forever?
We are living longer. How can we live better?
Your mother’s diet, your immune system and air pollution are among the many factors affecting how long you live and whether you develop Alzheimer’s or cancer. ERC researchers are unravelling the secrets of longevity, exploring ways of adding ‘life to years’ as well as ‘years to life’. (Hint: It helps to be a monk.)
Story by Gary Finnegan
Video by Sabina Brennan
Design by Ben Newton.
Let’s start with the good news: most Europeans born today will live long lives – on average, 78 years for men and 83 years for women.
Now the bad news: although they will live longer, they will not live better. Men born today will spend 17 of their years in poor health, and women will be ill 22 years. Hence the adage: ‘women are sicker but men die quicker’.
Nor is this un-healthy ageing problem a European issue only. In rapidly developing nations such as China and India, life expectancy is also on the up – but so too are chronic conditions, including cancer, heart disease, diabetes and dementia. It seems we have added quantity of life without making much progress on quality.
How to Spot Visualization Lies
Keep your eyes open.
It used to be that we’d see a poorly made graph or a data design goof, laugh it up a bit, and then carry on. At some point though — during this past year especially — it grew more difficult to distinguish a visualization snafu from bias and deliberate misinformation.
Of course, lying with statistics has been a thing for a long time, but charts tend to spread far and wide these days. There’s a lot of them. Some don’t tell the truth. Maybe you glance at it and that’s it, but a simple message sticks and builds. Before you know it, Leonardo DiCaprio spins a top on a table and no one cares if it falls or continues to rotate.
So it’s all the more important now to quickly decide if a graph is telling the truth. This a guide to help you spot the visualization lies.