The majority of the e-mail I’ve gotten about the bounded gaps piece concerns two questions of this kind:  I’ll answer them both here, in case other readers are following the link from Slate to the blog.

Q:  You say that the number of primes less than X is about X/log(X), but don’t you mean X/ln(X)?

A:  When mathematicians say “log” we mean the natural log, the thing which in some other contexts (e.g. Google’s search bar calculator) is denoted “ln.”  But mathematicians never say “ln.”  (To be honest, we kind of think the base-10 logarithm should be called “lu.”)

Q:  You say that every positive number is the product of primes, but this is not true for prime numbers themselves, which can’t be expressed as products.

A:  A prime number is indeed the product of prime numbers!  It is the product of just one prime number, itself.

What about 1?  It’s the product of zero prime numbers.

And a lot of twin primes is exactly what number theorists expect to find no matter how big the numbers get—not because we think there’s a deep, miraculous structure hidden in the primes, but precisely because we don’t think so. We expect the primes to be tossed around at random like dirt. If the twin primes conjecture were false, that would be a miracle, requiring that some hitherto unknown force be pushing the primes apart.

Here is what Harvard alums name their kids.  These are chosen by alphabetical order of surname from one segment of the book.  Most of these children are born between 2003 and the present.  They are grouped by family.

Molly, Danielle

Zachary, Zoe, Alex

Elias, Ella, Irena

Sawyer, Luke

Peyton, Aiden

Richard, Sonya

Grayson, Parker, Saya

Yoomi, Dae-il

Io, Pico, Daphne

Lucine, Mayri

Matthew, Christopher

Richard, Annalise, Ryan

Jackson

Christopher, Sarah, Zachary, Claire

Shaiann, Zaccary

Alexandra, Victoria, Arianna, Madeline

Samara

Grace, Luke, Anna

William, Cecilia, Maya

Bode, Tyler

Daniel, Catherine

Alex, Gretchen

Nathan, Spencer, Benjamin

Ezekiel, Jesse

Matthew, Lauren, Ava, Nathan

Samuel, Katherine, Peter, Sophia

Ameri, Charles

Sebastian

Andrew, Zachary, Nathan

Alexander, Gabriella

Liam

Andrew, Nadia

Caroline, Elizabeth

Paul, Andrew

Shania, Tell, Delia

Saxon, Beatrix

Benjamin

Nathan, Lukas, Jacob

Noah, Haydn, Ellyson

Freddie

Leonidas, Cyrus

Isabelle, Emma

Joseph, Theodore

Asha, Sophie, Tejas

Gabriela, Carlos, Sebastian

Brendan, Katherine

Rayne

James, Seeger, Arden

Helena, Freya

Alexandra, Matthew

George

If you saw these names, would you be able to guess roughly what part of the culture they were drawn from?  Are there ways in which the distribution is plainly different from “standard” US naming practice?

To get this out of the way first — yes, the food was good.  Very, very good.  But I don’t actually want to talk about the food!  Lots of restaurants have good food.  What’s really interesting about EL Ideas is the way it merges the idea of “restaurant” with the idea of “theater.”

There’s no menu — each of the 24 diners eats the same thing at the same time, so that, as in a play, everyone in the room is having the same experience.  Before the meal begins, the chef/impresario/director/producer pops out from the kitchen to tell you that this isn’t going to be the usual stuffy expensive restaurant deal — he wants you to wander into the kitchen and ask what’s going on, he wants you to really get into it.  He warns that you should summon an Uber car rather than trying to walk home through the somewhat desolate neighborhood because if you did the latter “you might die.”  In other words:  we are the ones hip enough to be in this neighborhood, to feel a  little frisson of danger, though nothing you can’t dispel with an app!  (In fact, I cannot say the crowd looked notably hip — my dinner companions were younger than me, but most other people looked old and rich, one more thing EL Ideas has in common with the theater.)

Before each dish is presented, the chef gives a little introduction, during which you are supposed to be quiet — if you talk while the he’s talking, the chef warns, you might get thrown out.  Just like the theater.

You don’t exactly get a reservation here; you purchase the meal in advance, as with a ticket to a show.

And at the end everyone claps!

When I was younger, I used to go to plays a lot.  OK, not a lot.  But I probably saw three to five plays a year, and even then I think most people I knew weren’t going.  Now I never go to plays; for all I know, I may never see a play again.

But EL Ideas makes me think that there are things people want from plays, and these are things that people who never go to plays sense, consciously or not, that they still want, and so something wonderful happens — the theater, seemingly made extinct by other, nimbler forms of entertainment, spores out into the atmosphere and embeds itself in another cultural host.

But I think this fun-making is somewhat misplaced!  We should instead be jeering at the conventional dichotomy that a result significant at p < .05 is “a real effect” and one that scores at p = .06 is “no effect.”

The lexically twisted scientists are on the side of the angels here, insisting that a statistically insignificant finding is usually much better described as “not enough evidence” than “no evidence,” and should be mentioned, in whatever language the journal allows, not mulched.

This is precisely to look for rational points on the modular surface S parametrizing pairs (E,E’,C,C’,φ), where E and E’ are elliptic curves, C and C’ are cyclic 13-subgroups, and φ is an isomorphism between C and C’.

S is a quotient of X_1(13) x X_1(13) by the diagonal in the natural (Z/13Z)^* x (Z/13Z)^* action.

Is S general type, rational, what?

Six bucks a ticket, kids get in free.  There were at least 500 fans cheering the Radicals, most of whom clearly know the rules of ultimate much better than I do.

It was extremely wholesome and I highly recommend it.

The game also featured a truly great halftime contest, in which spectators competed to see who could throw a Roman Candle pizza, frisbee-style, farthest down the field.  Now that was already great, but then, at the end of the contest, the contestants scooped the pizzas up off the turf and  tossed them to clamoring fans in the stands, who picked the grass off them and ate them.  I felt honored to be present.

Other notes:

• Ultimate is traditionally played without a referee, but they’ve added refs for the pro game.  To maintain the spirit of the game, he AUDL has instituted the “integrity rule:”  if both teams agree that a call on the field is wrong, the referee is overruled.  I can’t think of any reason this isn’t the rule in every sport.
• Apparently, one of the players (“the guy with the goatee,” according to a nearby fan) is the owner of the team.
• Almost forgot to say — the Radicals battled back from a 12-8 deficit but eventually lost 16-15 to the Windy City Wildfire.

In 1926, age 22, living in his parents’ attic, he writes an essay in his notebook called “WHAT I ACHIEVE I DESPISE,” which includes this:

Nothing is worth doing.  But we have the instinct to do, and we should be wise enough to do the thing which is most nearly worth doing.

The world considers me lazy because I do not earn bread.  The world expects of me that I should measure up to its standard of strength, which means that if I “got a job” for eight hours of office work (minus the time spent in being friendly to the other employees, in arranging for a party for the evening, in arguing the merits of a baseball scandal, etc.) [if it] constituted a day and paid me respectable money, I should be a man.  It’s not so much my “being a man” that people desire, it is my being one of them.

I see clearly now that the only thing left for me to do in life is to justify myself for doing nothing.

Pace Tolstoy, unhappy 22-year-olds are all alike.

Now he works for Echo Nest, the Greater Boston music startup that sponsored the Music Hack Day I participated in a couple of years ago.  And his latest project, Every Noise At Once, is a map of all music.  Seriously!  A map of all music!  By which I mean: an embedding of the set of genres tracked by EN into the Euclidean plane, and, for each genre, an embedding of bands tagged in that genre.

Play with it here.