(N.B. IBM Research is also well along on various aspects of AI, such as Watson, and a new generation of cognitive computing chips and other frontiers of neuroscience, supercomputing and nanotechnology)

John Markoff of the New York Times reports, “Inside Google’s secretive X laboratory, known for inventing self-driving cars and augmented reality glasses, a small group of researchers began working several years ago on a simulation of the human brain. There Google scientists created one of the largest neural networks for machine learning by connecting 16,000 computer processors, which they turned loose on the Internet to learn on its own. Presented with 10 million digital images found in YouTube videos, what did Google’s brain do? What millions of humans do with YouTube: looked for cats.”
He continues, “The neural network taught itself to recognize cats, which is actually no frivolous activity. This week the researchers will present the results of their work at a conference in Edinburgh, Scotland. The Google scientists and programmers will note that while it is hardly news that the Internet is full of cat videos, the simulation nevertheless surprised them. It performed far better than any previous effort by roughly doubling its accuracy in recognizing objects in a challenging list of 20,000 distinct items. The research is representative of a new generation of computer science that is exploiting the falling cost of computing and the availability of huge clusters of computers in giant data centers. It is leading to significant advances in areas as diverse as machine vision and perception, speech recognition and language translation.”
July 2012
June 2012
Take for example, topology, one of the 3 “main” branches of abstract, pure math (along with algebra and analysis). Note the definition of a topology: for some set/space X, it contains ∅ and both ∅ and X itself are open, as well as the arbitrary intersection and union both being open.
Note that this means, under union, topologies for monoids: basically groups without an inverse element. Union with empty gives an identity, and it’s very obviously associative; the only thing missing is inverse (this means including the set minus operation \ forms a ring, though). This means that the set of all topologies is a monoid.
Now, let’s look at something on the very far end of math — formal languages. Formal languages form the basis for computer programming languages and are a large traditional tenet of discrete math, a branch of applied math most consider fundamentally different from pure math, about as opposite as you could get from topics like algebra or topology.
Well, formal languages, like topologies, also form monoids under concatenation: a formal language is all the strings over an alphabet of characters with the empty string ε/λ (depending on who’s talking it’ll be epsilon or lambda), and when concatenated with another (put together in a manner such that the strings ‘aba’ and ‘bbaab’ would be ‘ababbaab’) is still in the formal language. The empty string forms the identity and the union of formal languages is associative (and a formal language).
Pretty interesting, huh? Both topologies and formal languages form the same type of abstract structure. Well, since the proof is a little dense, I’m going to outright say it: you can write an isomorphism to show that all topologies with the discrete topology (in which all subsets of the space X are open) can be written as a formal language. Likewise, you can write formal languages as a discrete topology. That is to say, even topology and formal languages are the same structure.
There’s loads of other examples, but this is one of the more opposite ones.
