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Math/Maths 89: Remark on a Theorem of Hilbert

A new episode of the Math/Maths Podcast has been released.

A conversation about mathematics between the UK and USA from Pulse-Project.org. This week Samuel and Peter spoke about: Pi day; US judge rules that you can’t copyright pi; Drug Data Reveals Sneaky Side Effect; Researchers Send “Wireless” Message Using Elusive Particles; Computing Power Speeds Safer CT Scans; Mathematics Matters UK Parliament meeting; Mario is NP-hard; ERC rejects ‘impact agenda’; Article Titles Make a Difference; Half of children find science and maths too difficult or too boring; Careers advice cuts could be putting kids off science; and more.

Get this episode: Math/Maths 89: Remark on a Theorem of Hilbert

Dispute over mathematical music dismissed

New Scientist reports on a lawsuit that was dismissed by a US district court this week, a decision apparently “intentionally released” on pi day. The case, “a claim of copyright infringement brought by one mathematical musician against another”, centred around a piece of music and YouTube video which went viral last pi day. Michael Blake, this says, created an “original musical composition, “What pi sounds like”, translating the constant’s first few dozen digits into musical notes”. The article explains:

That afternoon, jazz musician Lars Erickson from Omaha, Nebraska, cried foul. Erickson thought Blake’s work sounded suspiciously similar to his own 1992 piece “Pi Symphony,” also based on the digits of pi, which is registered with the US copyright office. He contacted YouTube, and Blake’s video vanished.

They had “both assigned each of the digits 0 to 9 to a musical note and then treated the digits of pi as a musical score”. Erickson calls the two melodies “identical”, but the court disagreed. The article reports the ruling:

the two pieces differed enough in areas like tempo, musical phrasing, and harmonies to be considered distinct. Plus, US law doesn’t protect every aspect of the piece, like underlying facts and ideas.

What’s more, Simon, who intentionally released his decision on Pi Day, noted that Erickson’s copyright registration only protects musical flourishes – and his are markedly different from Blake’s.

The legal opinion reads:

Pi is a non-copyrightable fact, and the transcription of pi to music is a non-copyrightable idea. The resulting pattern of notes is an expression that merges with the non-copyrightable idea of putting pi to music.

Read the full story at New Scientist: US judge rules that you can’t copyright pi.

Mockus, mathematician-king

Charlotte Bouckaert shared this story on Google+. It’s about Antanas Mockus, a mathematician and philosopher who was elected mayor of Bogotá twice. It’s a fascinating read.

People were desperate for a change, for a moral leader of some sort. The eccentric Mockus, who communicates through symbols, humor, and metaphors, filled the role. When many hated the disordered and disorderly city of Bogotá, he wore a Superman costume and acted as a superhero called “Supercitizen.” People laughed at Mockus’ antics, but the laughter began to break the ice of their extreme skepticism.

I think I’d heard about Mockus before on an episode of From Our Own Correspondent, but it’s good to read more about his exploits, and that he seems to be genuinely popular with the citizens of Bogotá even after his term has ended.

via Charlotte Bouckaert.

Deriving dynamical equations is NP-Hard

This paper has just been accepted by Physical Review Letters:

The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this work, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP-hard), both for classical and quantum mechanical systems. As a by-product of this work, we give complexity-theoretic answers to both the quantum and classical embedding problems, two long-standing open problems in mathematics (the classical problem, in particular, dating back over 70 years).

This paper has been accepted, so I can’t see why I shouldn’t be able to read it yet. Possibly something to do with money. The preprint is on the ArXiv, anyway.

via ScienceNOW via Slashdot, who reported it as “It’s Official: Physics is Hard”. That’s exactly the kind of unhelpful attention-grabbing headline we’re hoping to avoid here at The Aperiodical.

A commenter on Slashdot raises an interesting point:

Could we then map NP-HARD computation problems onto real world physics systems to find solutions?

Experimental evidence for Turing’s morphogensis mechanism

Alan Turing’s research in the latter part of his life focused, among other things, on morphogensis – particularly of animal pattern formation.  According to a King’s College London press release, Turing “put forward the idea that regular repeating patterns in biological systems are generated by a pair of morphogens that work together as an ‘activator’ and ‘inhibitor'”. Now researchers at Kings have provided experimental evidence to confirm this theory. This study:

not only demonstrates a mechanism which is likely to be widely relevant in vertebrate development, but also provides confidence that chemicals called morphogens, which control these patterns, can be used in regenerative medicine to differentiate stem cells into tissue.

The press release quotes Dr Jeremy Green from the Department of Craniofacial Development at King’s Dental Institute saying:

“Regularly spaced structures, from vertebrae and hair follicles to the stripes on a tiger or zebrafish, are a fundamental motif in biology. There are several theories about how patterns in nature are formed, but until now there was only circumstantial evidence for Turing’s mechanism. Our study provides the first experimental identification of an activator-inhibitor system at work in the generation of stripes – in this case, in the ridges of the mouth palate.
“Although important in feeling and tasting food, ridges in the mouth are not of great medical significance. However, they have proven extremely valuable here in validating an old theory of the activator-inhibitor model first put forward by Alan Turing in the 50s.
“Not only does this show us how patterns such as stripes are formed, but it provides confidence that these morphogens (chemicals) can be used in future regenerative medicine to regenerate structure and pattern when differentiating stem cells into other tissues.”

Source: Scientists prove Turing’s tiger stripe theory.

Why maths, Dara O’Briain?

Dara O’Briain has written a piece for the Telegraph’s numeracy campaign. Dara, as he explains, has “a deep passion for maths and physics”, having studied mathematical physics at University College, Dublin prior to starting his career in comedy.

Dara writes about maths and “cool”.

I’m often asked to speak about science, in the vain hope that the perceived “cool” of entertainment will somehow rub off onto the science and make it more alluring. Nothing like a heavy, bald 40-year-old to make something “cool”.
Listen. Maths is never going to be “cool”, other than to the sizeable rump of destined-to-love-it-no-matter-how-it’s-presented kids who are like I was at 15.

He argues that maths should be compulsory in schools, like PE, because it is good for pupils, giving both pragmatic – “exercise for the brain” – arguments and philosophical ones. The latter is likely to more attractive here:

Maths is one of the greatest achievements of humanity. It is the common language of science; it has allowed us to drag ourselves from ignorance by creating communal knowledge, which in turn enables us to master our world and to understand our universe. Maths teaches us to spot patterns, to predict behaviour and the steps of an argument. Maths is, above all, a way of approaching problems – stripping things down, extracting the relevant information, and then solving them.

Improving numeracy, Dara says, is more than just enabling people “to be faster at calculating the cost of the weekly shop”, citing the use of statistics in “a world of claim and counterclaim”.

Maths reform campaign: Sum up: you’ll hang on to your knighthood.

Ian Stewart on Black-Scholes

Ian Stewart gives us a taste of his new book Seventeen Equations That Changed the World in a Guardian article about the Black-Scholes equation. This, he says:

provided a rational way to price a financial contract when it still had time to run… It opened up a new world of ever more complex investments, blossoming into a gigantic global industry. But when the sub-prime mortgage market turned sour, the darling of the financial markets became the Black Hole equation, sucking money out of the universe in an unending stream.

So what went wrong? Stewart explains that “the equation itself wasn’t the real problem”, going into some detail about how the equation was derived, how it works and what assumptions are included. He concludes:

Was an equation to blame for the financial crash, then? Yes and no. Black-Scholes may have contributed to the crash, but only because it was abused. In any case, the equation was just one ingredient in a rich stew of financial irresponsibility, political ineptitude, perverse incentives and lax regulation.

Ultimately, Stewart argues, “the financial sector performs no better than random guesswork”, with the system “too complex to be run on error-strewn hunches and gut feelings, but current mathematical models don’t represent reality adequately”, a situation that requires “requires more mathematics, not less”.

Guardian: The mathematical equation that caused the banks to crash.