Today’s Google Doodle celebrates the birthday of Claude Shannon in 1916 (died 2001), called the “father of information theory,” but also the father of digital circuitry, which uses binary zeroes and ones (he’s juggling them above) to design electrical switching circuits. (As the New Yorker notes in a profile, “Claude Shannon, the father of the Information Age, turns 1100100.”) If you click on the Doodle, you’ll go to a list of links about Shannon. As the New Yorker article notes:
First and foremost, he introduced the notion that information could be quantified at all. In “A Mathematical Theory of Communication,” his legendary paper from 1948, Shannon proposed that data should be measured in bits—discrete values of zero or one. (He gave credit for the word’s invention to his colleague John Tukey, at what was then Bell Telephone Laboratories, who coined it as a contraction of the phrase “binary digit.”)
I hadn’t noticed, but a reader let me know, that yesterday Google also had a Doodle marking the birthday of engineer, mathematician, and physicist Hertha Marks Ayrton (1854-1923):
Time Magazine describes her achievements, which includes breaking (or at least butting up against) a scientific ceiling:
Hertha Marks Ayrton became the first woman to present her own work to the U.K.’s Royal Society when she stood in front of the scientific academy in 1904 and read “The Origin and Growth of Ripple Marks.” Until then, scientists were baffled by the creation of ridges in sand when a wave washes over a beach.
To celebrate Ayrton’s scientific discoveries and victories over discrimination, Google has honored the British engineer, mathematician, physicist and inventor with a Doodle, on the 162nd anniversary of her birth. In addition to unlocking the mystery of ripples, Ayrton also became and expert on electric arcs, widely used in lighting at the time.
In 1906, the Royal Society awarded Ayrton with its prestigious Hughes Medal for her contributions to physical sciences. But the academy denied her the honor of becoming a fellow, because she was married. Addressing this kind of gender discrimination in science, Ayrton wrote: “An error that ascribes to a man what was actually the work of a woman has more lives than a cat.”
Speaking of cats, it’s time for our weekly Felid Lineup.
Gleick’s The Information was a fantastic book ( as was his older Chaos).
As a Briton the Hertha Marks Ayrton doodle didn’t have a wide distribution so it wouldn’t have been visible in the USA.
It was visible in California…
… and Maryland. Can’t speak to all those blank parts in between.
Yes it was, because I checked later yesterday when a reader emailed me about it. You can check a Doodle’s geographic reach by going to the page where Google collects all the Doodles.
Claude Shannon is waaay up there in the list of people who Changed Our World, along with several others (Edison, Haber + Bosch…). Funny how some of them are household names and others are not.
The Shannon index (=pi*ln pi , where pi is the proportion of individuals in the sample belonging to species i) is commonly used in ecology as a measure of species diversity. Frequent commenter here Lou Jost has shown that the exponential of this measure has superior properties.
Hmmm, seemingly I fail at html tags. The i in pi should be a subscript.
Thanks for remembering that!
In fact Shannon used the exponential version in the reasoning that led to his famous formula.
While biologists usually think that they are borrowing Shannon’s formula from information theory, in fact it can be derived from scratch within biology by careful thinking about diversity. Lo and behold, out comes (the exponential of) Shannon entropy! That was first shown by Mark Hill in 1973, with others filling in the details later. Unfortunately for biology, this was several decades after Shannon’s alternative route to the same formula. But anyway there is a deep connection between the biological concept of diversity and Shannon information.
Yes, when I learned that many of the diversity indices are just variants of each other related by simple transformations as shown by Hill, it really made me regret my lack of numeracy. Also makes it hard to fully understand and analyze your papers, or anything else requiring a quantitative understanding of biology. Fascinating, though. When I taught, I made certain to introduce the “Jost transformation” even though it’s not in the text.
There’s some news on this front: Anne Chao just last year discovered the formula for the entropy the probability distribution of alleles at a neutral locus in equilibrium, in terms of the demographic and genetic parameters of the population. Even though this seems like it would be a messy and complicated problem, she proved that the solution is an elegant mathematical function called the digamma function, plus Euler’s constant. To me this is one of the most remarkable formulas in all of population genetics, connecting a messy stochastic biological process to an elegant mathematical formula:
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0125471
Thanks for the link, I’ll take a look. I started your paper with Chao and some of your solo papers, but have never made it through because more immediate and pertinent papers had to be prioritized, despite my interest.
The paper I linked to is particularly dense. But that simple result near the beginning is enough. Maybe we should have ended the paper there and saved the rest for another paper. As it is, very few people will ever notice the shocking main result.
I should point out that though Hertha Ayrton was denied membership of the Royal Society on the grounds that as a married woman she had no separate legal existence; they actually hadn’t ever admitted any women, single or married, as fellows (Queen Victoria as monarch had been a patron of the society) and wouldn’t do so until 1945 (Marjory Stephenson and Kathleen Lonsdale). They certainly didn’t reconsider their decision after 1908 when her husband (who was a member of the Royal Society in his own right) died (she lived on until 1923).
Claude Shannon turns 1100100 reminds me of an old joke.
It is said there are 10 kinds of people in the world–those who understand binary and those who don’t.
Ripple marks – fascinating! I was walking across the beach last week and I noticed that a little rivulet running across the sand had become braided, like a South Island river but on a 1/1000th scale, with sand grains subtsituting for the shingle of a river. What made the braiding more visible was the mix of ‘black sand’ and regular off-white sand, which the flow had sorted into streaks. Further up, left by the shallow stream at high tide, were ripple marks and I idly wondered if anyone had ever explained their origin (some form of wave motion, obviously, but I wouldn’t care to try and work out any equations!).
While I’m at it, a shallow stream flowing across a gentle flat sandy bed (ripple free) has an unstable flow, little waves or surges build up such that, at the bottom end of a 50-yard reach, the flow which started out absolutely uniform at the top arrives at the bottom in surges of two or three times the minimum flow.
And the sea waves on a flat beach pile up in a chaotic fashion – the extent to which a wave surges up the beach depends not only on the size of the sea wave which generated it, but also the extent to which previous waves, washing back, hold the water back and allow following waves to pile up and generate a massive surge.
There’s a lot of incredibly sophisticated processes going on on a simple flat beach (preferably with a stream running across it). And it’s all non-linear which (as I think James Gleick would say) is a recipe for chaos.
I can watch it for hours.
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