Zipf's law arose out of an analysis of language by linguist George Kingsley Zipf, who theorised that given a large body of language (that is, a long book — or every word uttered by Plus employees during the day), the frequency of each word is close to inversely proportional to its rank in the frequency table. We thought we
would test this out on Plus. What does this imply about how we use language and how it evolved?
Is it really a mystery? I have at least one idea off the top of my head.
Since one of the ways you can construct power law distributed networks (competitive scale networks) is through growth/decay rules (e.g. the next added link will have the highest probability of connecting to the node with the higher degree or existing connections) and thinking a little about how language evolves by adopting and abandoning words, it seems likely that words frequency could follow a
power law because they are added to and removed from over time with a similar set of rules (at some level).
The only question is what exactly do such network nodes and their degrees map to?
Nodes seems map to words or perhaps the idea represented by the word or word-sound or word-ideas. If the nodes map to ideas then there is also a link to memes and various mind-external scale-free structures.
Nodal degree seems to related to usage of the word - either simply the frequency of usage or something deeper that results in that frequency.
Mathematics is often used to study evolution, whether that be the evolution of animal species, the evolution of viruses or the evolution of language. A recent study has taken this one step further by modelling the evolution of national cuisine, and it was found that even though there are wall-to-wall celebrity chefs on television these days trying to broaden our culinary horizons, our cultural
cuisines are largely the same as they were almost 100 years ago.
After every Olympics, there is speculation about which country performed best. Should we really be surprised when China, with its huge population, and the US, with its combination of high GDP and population, top the medal table? Can we take a look at the medal tables and see which countries did indeed perform better than expected?
The model provided by the fancy pants bureau thingy is stupid.
it has A(Log[X])+B(Log[Y/X]), which is the same as A(Log[X])+B(Log[Y])-B(Log[X]), which is the same as (A-B)(Log[X])+B(Log[Y), and as A and B are just constants, A-B can be anything. say C. They've added in a completely unneccesary element.
WELL statistics and dam statistics. The problem is your raw data is wrong and as with all statistics the way you look at is partial. Is there a relation between GDP and medals, should there be? Difficult to say, I would have thought it is about social structure and expectations as well. GB did well in various areas because there was an expectation, resources and talent coming together and it
did badly in others because one or more of these was missing.
Disney Pixar have just released the movie, WALL-E. A bleak, post-apocalyptic tour-de-force, the movie depicts the gentle romance between two robots of the future: WALL-E, the not-so-bright and not-so-attractive "guy" with the big heart and sweet personality, and EVE, the sleek, sexy, totally
Pixar designed these robots so that we see them as human. But what exactly is WALL-E? Is he pure fantasy and speculative fiction? Or is he — is artificial intelligence — simply the way of the future?
"Instead of programming a computer to abide by the traditional step-by-step rules approach, we model it like the neurons in the human brain where the results of the program depend on the "strengths" of each particular neuron."
Neural computing runs on a computer...it too is algorithmic.
It seems to me that people are algorithmic as well but that each of our internal programs can achieve intuitive leaps, insights and creative ideas by accepting as input, data in many different forms...eg a certain spreadsheet of numerical data can be interpreted, from across the room as a portrait of Einstein.
The reason why computers will never be 'human', is because human reasoning, morality and intellect is not optimal. If a machine should have the computational power to rival human thinking, pressing it into the mold of a human brain will be diametrically opposed to the aims of such a machine. We like to consider ourselves to be the pinnacle of evolution, but we are forgetting that i) evolution
is an on-going process, and ii) humans are not as clever as all that. In fact, looking around you, from Big Brother to the Iraq war, would a computer with a vast intelligence feel nothing but derision for our species?
I agree with many of the comments left by Patrick Andrews.
It seems to me that the advancement of artificial intelligence is handicapped to a considerable extent by the intellectual capacity of the computer technocrat.
Using a trivial example to illustrate, while working for the now-defunct computer manufacturer Sperry Univac, I asked a visiting VP what the company's position was following IBM's introduction of its (then) 'Personal Computer'. He replied that the company regarded the PC as a fad and the future was in mainframe computers! It is this level of intellect that presents the handicap mentioned
Some years later, I was to have discussions with Professor Donald Michie of Edinburgh University about what he considered to be a problem in "pattern matching". Basically, the problem was to take a large amount of information about daily trading in a retail environement and establish through analysis what represented 'normal' trading. By this means, what repesented 'abnormal' trading could be
established. It was abnormal trading that was the holy grail being sought in this particular excercise. Sadly, we did not get very much further than stating the problem. The overall solution, though, was believed to lie in the computer's ability to learn from key factors in the environment of the problem. It was this ability, residing in the human counterpart (given the right degrees of
application, intellect and experience), that could provide answers for discrete cases, albeit at the expense of considerable time and effort.
On 30th August this year, London will be playing host to the inaugural science blogging conference, Science Blogging 2008: London, hosted by Nature Network, in collaboration with the Royal Institution.
Plus, being a very active science blogger, will be attending, so come and say hi (or leave a comment if you prefer).
The aim of the conference is to bring together science bloggers from around the world to discuss the pressing issues in science, science communication, publishing and education. What role does blogging play? If you are interested in coming along, registration is free although places are filling up.
Other favourite blogs of Plus in attendance will be the Cambridge-based blogs Understanding Uncertainty and Sciencebase. There aren't many mathematically focused blogs out there, so Plus will be happy to meet with anyone else who is blogging about maths!
We all have favourite movie characters, but who is your favourite fictional mathematician?
It is quite difficult to compile a list of fictional mathematicians. Scientists are often portrayed in films — usually as mad — but there are very few who are specialised mathematicians. Here at Plus, we have come up with a list that we think covers most well-known fictional mathematicians, although it is debatable whether some are even mathematicians at all! We are asking for your
opinion — who is your favourite?
Have we missed yours off the list? Please leave a comment and let us know. We will write a biography of the character who wins the poll.
If you're thinking about fictional mathematicians in print, there are quite a few others who might make the list. How about the title character from Uncle Petros and the Goldbach Conjecture by Apostolos Doxiadis (you can read a MAA review by Keith Devlin at http://www.maa.org/reviews/petros.html)? Or Daisy Love from Jeff Noon's Nymphomation? Hobbs Baranov from William Gibson's
Pattern Recognition? Or the narrator from The Oxford Murders, recently also made into a film?....
It was written that: 'He is a man of good birth and excellent education, endowed by nature
with a phenomenal mathematical faculty. At the age of twenty-one he wrote a treatise upon the binomial theorem, which has had a European vogue. On the strength of it he won the mathematical chair at one of our smaller universities, and had, to all appearances, a most brilliant career before him.
But the man had hereditary tendencies of the most diabolical kind. A criminal strain ran in his blood, which, instead of being modified, was increased and rendered infinitely more dangerous by his extraordinary mental powers. Dark rumours gathered round him in the University town, and eventually he was compelled to resign his chair and come down to London....'
'Is he not the celebrated author of The Dynamics of an Asteroid, a book
which ascends to such rarefied heights of pure mathematics that it is said that there was no man in the scientific press capable of criticizing it?'
Please may we have a simple .cgi voting page for this poll? I hate having to install plugins, particularly those which take up a lot of cycles like flash.
He's not fictional (prof. Comeau, the Stellan Starsgard character, is) but I like Matt whoever's question "who's the most famous living American pure mathematician?" in Good Will Hunting. The answer is Ted Kaczynski, the Unabomber.
My initial inclination is to vote for Yakima, the hero of Greg Egan's Diaspora, but that's because I really like the book as a whole. Another candidate, a great contrast with the former, would be Myron Aub who rediscovers mental arithmetic in Asimov's The Feeling of Power. More reflection is required.
There's also Kate Gunzinger from the film 'It's My Turn' (see here) - this film is in fact given by Weibel in his Introduction to Homological Algebra as a reference for the Snake Lemma, a proof of which opens the film.
I wouldn't call here my favourite character but Barbara Sabich - Harrison Ford's wife in Presumed Innocent - is a mathematician (I think we hear this in the scene where she complains about how long it has taken her to get tenure).
A minor, behind the scenes character, but one without whom there would be no story.
The list is definitely too "english-centered". You are missing many fictional mathematicians in non-English spoken movies. So, the question of the poll should be: "Who is your favourite English-speaking fictional mathematician"?
E.g.: have you seen the Argentinian movie "Il treno di Moebius" ("The Moebius train")?
One of the mathematicians on your list is Max Cohen from the film 'Pi' (played by Sean Gullette), but I'd prefer to nominate Cohen's mentor in the same film, Sol Robeson (played by Mark Margolis). When Cohen becomes obsessed with finding patterns in the digits of pi (π), Robeson quite rightly rebukes him, saying that he's no longer a mathematician but rather a numerologist.
There is at least another mathematician in another Michael Crichton's novel: Harry Adams in Sphere (also a movie) and his character is important in the plot.
Other side comments:
a) I concur that this list looks very english literature-centered but it is likely to evolve as more comments and references are made.
Two recent examples of novels with mathematician characters:
- Hans Singer in "Villa des Hommes" by Denis Guedj (closely copied from Cantor's character)
- Arthur Seldom in "Crímenes imperceptibles" (aka "The Oxford Murders")
b) John Nash is of course a real person, but his image in the Holywood dramatization of Silvia Nasar's pseudo biography A Beautiful Mind is a complete fiction who never existed except in the script of the film.
There are numerous references to fictional mathematicians and mathematical fiction at http://math.cofc.edu/kasman/MATHFICT/. I would vote for Professor James Darnley McCorkle in "The Chair of Philanthromathematics" by O Henry.
To the anonymous commenter who said "have you seen the Argentinian movie "Il treno di Moebius" ("The Moebius train")?" The answer is that we have tried and tried to see this film but cannot get a copy for public screening in the UK. It would have been part of the Edinburgh Maths at the Movies Festival last April if it had been possible. I can't speak for the USA but it's been seen by very few
people in the UK because it's only ever been screened at few film festivals shortly after release.
This film, however, is based on one of my all time favourite short stories "A Subway named Mobius" by Prof. A.J. Deutsch at Harvard. It was actually written about the New York subway system. Tupelo, the topologist who solved the problem, should be on the voting list but I'm afraid he was originally an English speaking New Yorker.
Rudy Rucker's work is stuffed full of fictional mathematicians! His 2006 book "Mathematicians in love" features Bela Kis and Paul Bridge, postgrads at Berkeley and a higher world of mathematician cockroaches!
My favourite is a much earlier work "White Light" whose hero, Feliz Raymond, stays in Hilbert's Hotel and visits Cantor's Continum. If he was on the list he'd have got my vote.
See www.rudyrucker.com to find out more