Black Holes, Quantum Information, and the Structure of Spacetime:

**Readings.**

Educational
Learning resources for teachers and students

More Mole Day facts for you!!

If you covered the Earth in a mole of donuts, how thick would that layer be?

8 km!

Happy Mole Day!From the TED-Ed Lesson How big is a mole? (Not the animal, the other one.) – Daniel Dulek

Animation by Augenblick Studios

Happy Mole Day!

Not every number is cool enough to have its own nickname, let alone two.Way to go 6.02 x 10^23 (aka Avogadro’s number aka the mole)!How big is a mole? (Not the animal, the other one.) – Daniel Dulek

Animation by Augenblick Studios

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Cauchy-Lorentz: “Something alarmingly mathematical is happening, and you should probably pause to Google my name and check what field I originally worked in.”

** Stanford-news five-part series** on the *String Theory Landscape*, by Ker Than (illustrations by Eric Nyquist).

Long and Winding Road: A Conversation with String Theory Pioneer | Caltech:

Cool interview with **John Schwarz** pioneer and co-father of the *first superstring revolution*.

“After the 1984 to 1985 breakthroughs in our understanding of superstring theory, the subject no longer could be ignored. At that time it acquired some prominent critics, including Richard Feynman and Stephen Hawking. Feynman’s skepticism of superstring theory was based mostly on the concern that it could not be tested experimentally. This was a valid concern, which my collaborators and I shared. However, Feynman did want to learn more, so I spent several hours explaining the essential ideas to him. Thirty years later, it is still true that there is no smoking-gun experimental confirmation of superstring theory, though it has proved its value in other ways. The most likely possibility for experimental support in the foreseeable future would be the discovery of supersymmetry particles. So far, they have not shown up.”

The shortest-known paper published in a serious math journal: 2 Succinct Sentences. (Via **Open Culture**) – PDF

As Sean Carroll says in his FB page:

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.

[Image credit: Jitze Couperus, Supercomputer – The Beginnings – Flickr]

*New model predicts that we’re probably the only advanced civilization in the observable universe*. Via

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.

From the original paper’s abstract (**Dissolving the Fermi Paradox** – PDF):

[…] 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.