The shortest math paper ever reminds us why mathematicians think that P doesn’t equal NP, even if they can’t yet prove it. It’s much easier to check solutions to problems (P) than it is to actually solve them (NP).
Below you can see how a CDC 600 computer looks like around 1964-1969.
New model predicts that we’re probably the only advanced civilization in the observable universe. Via Universe Today.
Well, playing with the Drake equation and the Fermi paradox is always fun and educative, as long as you assume that you are on a purely speculative ground. We actually don’t know, and the “probably” adverb in the title is central.
[…] The expectation that the universe should be teeming with intelligent life is linked to models like the Drake equation, which suggest that even if the probability of intelligent life developing at a given site is small, the sheer multitude of possible sites should nonetheless yield a large number of potentially observable civilizations. We show that this conflict arises from the use of Drake-like equations, which implicitly assume certainty regarding highly uncertain parameters. We examine these parameters, incorporating models of chemical and genetic transitions on paths to the origin of life, and show that extant scientific knowledge corresponds to uncertainties that span multiple orders of magnitude. This makes a stark difference.
My first code in Mathematica goes back to V2 (1991) for the first reliable graphical environment from Microsoft (Windows 3.0, 3.1), lab reports improved instantly. Many things have changed in three decades in the world of computer algebra systems, even to the point to be of (irremediably) minority use, mostly because there are plenty alternatives both for high (Matlab, Octave, Sage) and low level (C, C++, Fortran…), or both (Python, Java, R…). But for people of a couple of generations (those born in the 60s and 70s or so) coming from an almost purely analogical world, seeing a pioneer (back then and now) of that generation as Stephen Wolfram (1959), posting this about the software that he himself had developed from the scratch before his 30 birthday, well, it makes us… happily nostalgic.
Interesting interview with theorist Brian Greene, I liked his concept of personalized education, I think he could be quite right on this.
“[…] I think in some number of years we’ll have a far more personalized approach to education. Kids are different. They come at things completely differently, different DNA, different experiences. If we could allow them to drive the right way to learn for their particular biochemical and neurophysiological make-up, how much more powerful would that be than a one-size-fits-all approach, which is what we do now?”