## How not to be wrong

I recently finished listening to Jordan’s book “how not to be wrong,” and thought that I would record some of the notes I made. Unlike other reviews, Persiflage will cut through to the key aspects of the book which perhaps non-specialists may have missed.

Unfortunately, my first few notes did not record the specific time in the recording where the relevant passage occurred, so some of the earlier comments are a little more vague, because I couldn’t go back and check them more carefully.

Title: How Now to Be Wrong: The Power of Mathematical Thinking.
Author: Jordan Ellenberg.
Book Format: Pirated audio copy.

• OK, Penguin, what have you done to Jordan? It sounds as though before the recording session began, Jordan was force fed him a greasy pizza with a couple of prozac stuffed in the crust. I was expecting a hyperactive delivery style, but instead there is a relatively calm and measured tone you might expect on any professionally made audio book.
• Did he just say yoked? Yes, my friends, we have here a student of Barry Mazur.
• 2377. This is all it says in my notes. I think this was used as a number which was supposed to sound random. But I did wonder whether it had any other significance. A brief web search indicates the full phrase may have been: Moving over to complicated/shallow, you have the problem of …[computing]… the trace of Frobenius on a modular form of conductor 2377. I checked — there are no elliptic curves of conductor 2377. I think there was an opportunity missed to say 5077 instead, thus alluding to the Gross-Zagier plus Goldfeld solution to the class number problem.   Although if there was such an allusion, it may have ruined the implication of being shallow, so never mind.
• Some reference to galois representations being deep; unfortunately I didn’t write any further notes here. They are indeed complicated and deep.
• The claim is made that if you cut a tuna fish sandwich you will be left with two right-angle isoceles triangles. Is this so clear? I mean, does everyone cut their tuna fish sandwiches along the diagonal?
• Rounding Errors: the range for (I guess?) one standard deviation for some normal distribution with mean 50 is given as 46.2 and 53.7, but these numbers are not symmetric around 50.
• Infinity of my profit comes from pastry. I liked this line.
• 4, 21, 23, 34, 39. Repeated strings of numbers on the page are easy to read, but even Jordan is getting a little bored reading out 4, 21, 23, 34, 39 for the n-th time.
• if your kid drew Jesus on the cross… See two comments up.
• At this point, I should probably point out to the readers of the book that they are missing out on all the extra fancy technological gizmos that Penguin took advantage of when transferring the book from the page to audio. And by this, I mean that, in approximately 13 and half hours of reading, we not only have Jordan reading out the text of the book, we are also treated to exactly one such extra, namely, the first 9 notes of Beethoven’s Ode to Joy as played on what appears to be an 8-key child’s keyboard.
• Ouroboric? Is that really how you pronounce that? It doesn’t seem consistent with the OED’s pronunciation of Ouroboros. Hmmm, but on the other hand, http://en.wiktionary.org/wiki/ouroboric gives someting similar to what Jordan says…
• How Many States should one have expected Nate Silver to get wrong? This might have been another opportunity to mention how the expectation is not the “expected” answer. Presumably, one would expect a high correlation between getting one (close) state wrong and getting another wrong (I’m imagining here that swings undetected by polls would be nationwide rather than statewide). So I have several questions here. Was there anything in Silver’s model which could allow one to predict not only the expected number of states he would get wrong but the expected *distribution* of the number of states he would get wrong? Because of the stickiness of states, I suppose that the expectation that he would get all the states correct is higher than what one might guess from the fact that the expected number of states one expected he would get wrong (from his model) was approximately 3. I’m sure I’ve heard Jordan mention elsewhere that Nate Silver claimed that one should not have expected Silver to get all 50 states right. However, it’s completely consistent to believe that a well designed model could both predict that the expected number of states that Silver would get wrong is 3, but also that there is a high probability (at least > 50%) that he really would get all the states correct. So it’s not clear that a criticism of Silver for getting too many states correct is necessarily valid.
• The problems you meet freshman year are the deepest… Is this true? Matt and I wondered which $p$-adic modular functions were expressible as convergent sums of finite slope eigenforms, and I still don’t know, but I’m not sure that’s the deepest question ever.
• Did the student of the introduction listen to the entire book? I think I kind of missed that this was a preface (I think?) and kept expecting her to return.

Summary: Was I convinced at the end that the girl’s time spending doing those 30 definite integrals was worthwhile? I’m not so sure. In fact, I could almost have been convinced that we should slash all the public math departments in half and replace them by statistics departments. On the other hand, by every other measure, the book was a complete success — as a piece of prose, as a source of interesting yet thematically linked historical anecdotes, and as both an exposition and celebration of a certain way of thinking (“mathematical thinking”) which we all aspire to. It was worth every cent.

Audio: On a scale from “Jordan’s talking to you quite loudly on a train in Germany and someone tells you to shut up” to “Ambient waterfall sounds for Ultimate Bedtime Relaxation,” I rate it a 4, which is about where you would wish it to be. (For an inside look at the recording session, see this post.)

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### 7 Responses to How not to be wrong

1. JSE says:

It was worth every cent.

I see what you did there.

• Is there any reason behind the choice of 2377, BTW?

• JSE says:

Dunno. I wrote “a modular form of conductor 2377” and I don’t remember whether I had a particular one in mind.

• Having just checked, it seems that $J^{+}_0(2377)$ and $J^{-}_0(2377)$ are simple abelian varieties of dimensions 95 and 102 respectively.

• JSE says:

Must have just made up a number, then, since I don’t have any brief for any particular totally real number field of either of those degrees.

2. JSE says:

Re my subdued speed and affect: not greasy pizza but a producer in my earphone yelling “PACING!” every time I started to approach normal JSE speech rate.

Re tuna fish sandwich: in the book there’s a picture, making it clear that yes, I meant diagonal slicing, the only correct way to slice a tuna fish sandwich.

Re the student in the introduction: I tried to call back to the opening lines in the last line of the book, but I do think in the end it’s a bit of a structural flaw; the intro gives the impression the book will be more about “school math” than it actually is.

Re “how many states”: excellent point. Without knowing more about correlation between states you can’t compute the distribution of the error, just its expected value. I doubt he’d have given himself a 50-50 chance of getting all 50 right, but he hasn’t revealed enough of his internals for me to know. But they did post this info for the UK election that just happened. http://fivethirtyeight.com/features/are-we-right-about-the-uk-general-election/

3. JSE says:

And thanks for the kind words overall! I hope I don’t actually convince our state governments the public math departments are useless. That’s Michael Harris’s job!