By way of Slate, we can read John F. Kennedy’s Harvard application, sent in 1935. Things must have gotten (much) harder. Would this application get you in these days, even as a legacy candidate? I’d be surprised. Competition in admissions arises from scarcity of education opportunities. Is education necessarily a scarce resource? Perhaps not, but as an abstract enabling opportunity, that scarcity cannot be eliminated, I don’t think, even with the likes of OpenCourseWare, etc. This is by definition: the scarcity is what makes a thing (e.g. an elite education) an enabling opportunity.

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“Joey Crawford (the referee) fouls Damon Jones yet calls it against Chauncy Billups”

There is something disturbing about electric heating, especially if the electricity used is generated by thermodynamic processes, such as burning coal or natural gas. Lots of heat is sacrificed at the power plant to be able to turn a fraction of the input energy into this superb high-quality electricity that can do mechanical work. Then at the other end, an electric heater just turns it right back into waste heat without doing anything else useful.

But something useful can be done. Instead of straight heating elements, I suggest a server farm. Maybe box it up like an electric heater, sell the CPU cycles back while still getting the same heat out.

Should pandas be extinct? There is a lot to be said for the panda’s maladaptation to nature, but this comment is interesting:

Panda’s evolutionary path has lead them down a very narrow cul de sac from which there is no escape. By all Darwinian rights they should become extinct.

But I like pandas, as do many others. Pandas have the one survival trait that is very important in today’s environment – they have value to human beings.

And on that note,

How about DOGS people? I mean come on, those little dogs do not serve any purpose in this life!! Billions of dollars go to them for food and cleaning, drugs etc.

chivava or something, why waste resources on DOGS? esecially little one with nothing to do but look pretty!?

Indeed, looked at in this way, pandas and dogs are very well adapted — to humans, who determine their survival. It’s an increasingly singular niche that likely all animals will fall into. In a million years, if humans are still around, probably all animals will look like stuffed toys.

The Kinect hardware seems to be in high demand at the moment, perhaps for a good reason. Smart input devices such as beamforming microphone arrays, vision-algorithmic 3d scanners, and the like are finally moving out of research labs. Given the right software, these can do quite sophisticated things… even an ordinary webcam can acquire 3d models, so these can only be better.

The nice thing about these input devices is that they don’t require anything special in terms of hardware — maybe a duplicity of some parts, but not expensive ones — all the smarts are in software. This can only mean two things: the devices will get smarter and smarter as time goes on, and, they will (soon) become standard parts of computers (and indeed, all devices), enabling a new field of naturally human-interactive applications. Definitely something to look forward to.

Something in the news here today, referring also to Penrose’s paper from several years ago.

In my limited understanding, Penrose suggests that the universe goes through these cycles of what can be interpreted as infinite expansions “followed by” big bangs, where the cycle renewal “happens” in a mathematical sense: in the way spacetime is metrized. He says that in the infinite future, when all massive particles will have evaporated, we will be returned to a situation without a notion of space or time (since all things are lightlike, I suppose). From this, the very large scale of the given final universe can be reinterpreted as the very small beginning of the next universe. It’s an interesting thought.

The latest problem from fakalin. Took some wrong turns and hints to solve it…

Given a polynomial \(f: \mathbb{Z}\to \mathbb{Z}\) with positive integer coefficients, how many evaluations of \(f\) does it take to obtain the polynomial?

(An \(f: \mathbb{R}\to \mathbb{R}\) polynomial with real coefficients would take the number of degrees plus 1 to specify, which, if it held in this case, would render the answer unbounded. But the correct answer in this case is surprisingly small.)
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Stephen Boyd quips about a power allocation algorithm:

Oh by the way, this is used now, for example, in DSL and it’s used actually everywhere. Okay, and I’m not talking about used by …professors… I’m talking about, it’s used when you use DSL.

Sometimes engineers forget that to a mathematician, an “application” is another theoretical problem … only maybe in physics.

How do escalators work? I’ve wondered for years how escalators recycled their step blocks internally. At one point I thought they slid past each other on all four faces to save on turning radius (because I thought the blocks locked along grooves). Today I see an escalator under repair. Now the answer is clear. It’s much simpler than that: the blocks just turn along a track in the most obvious way imaginable.

(Read the article)

In a fully informative world with continuous elections between two competing parties, the equilibrium, if it exists, should be an even split.