Dylan on Letterman

This is not a retrospective on all of Bob Dylan’s appearances on David Letterman’s shows. In keeping with the personal reminiscences of my recent Letterman post, and given that it’s Bob’s birthday, it seems appropriate to post the three songs Dylan did on his first appearance on Late Night on March 22, 1984.

This was a show I saw on the night it first aired. In a post I wrote last year when Letterman first announced his retirement (a post I’d completely forgotten by the time I wrote the more recent one), I mentioned one distinct memory I have of that show:

It’s funny how certain things stay with you. In 1984, Bob Dylan appeared on the show (playing, if I remember correctly, a Stratocaster borrowed from Keith Richards). It was a Thursday, so there was a Viewer Mail segment after the monologue. One of the letters was from a guy named Eric Anderson. When Paul Shaffer heard the name, he butted in. “Eric Andersen? Wow, it’s a big night for The Bitter End.” The joke died because no one in the audience understood the reference. But Dave did, and he delighted in how Paul’s joke fell flat. “Too hip for the room, Paul.”

Unless you’re middle-aged, a folk music fan, or both, you’ll have to do some Googling to get the joke. And then it won’t be funny.

Here are the three songs Dylan did on the show:

Don’t Start Me Talkin’

License to Kill


Depot followup

Things have been busy here, and I forgot to post this brief followup to my customer service and security trouble with Office Depot.

When we left the story, I had arranged for payment on the bill my company had never received, and the customer service rep at Office Depot (actually at OD’s credit card provider) told me that the order that had been put on hold would be released. A couple of days went by with no delivery, but I didn’t expect things to work out that quickly. Then there was a weekend and a business trip, and before I knew it, a week had gone by since the problem was “resolved.” I set a reminder to call Office Depot the next day.

The next morning started with an email from Office Depot, saying that the order had been canceled because the problem with our account had not been fixed. I checked with our bank to confirm that payment on the problem invoice had gone through (it had), got together my notes from the previous week’s conversations,1 and called customer service.

After working my way through a couple of departments, I got to the representative who could tell me what was wrong with our account.

“There’s a note in your file saying ‘Mail Returned.’”

“What does that mean?”

“I’m not sure how to say it any other way.”

“Does that mean that you sent us a bill and the post office returned it to you?”


“Well, that explains why we didn’t pay that bill. We never got it.”

“Yes, and since we couldn’t confirm your address, that put a hold on your account.”

“When I talked to one of your representatives last week, he told me the hold was there because we had an unpaid bill and that once it was paid the hold would come off. You do have a record of us paying that bill, don’t you?”

“Oh, yes. Your account has a zero balance.”

“When was this ‘Mail Returned’ note put in our file?”

“Let’s see… February 24.”

“And you waited until May to try to contact us?”

“Yes, I’m sorry for the inconvenience, sir.”

“Any idea why the guy I talked to last week didn’t say anything about the problem with our address?”

“No, sir. I’m very sorry about that.”

There was some more about how they had temporarily confirmed our address but couldn’t permanently confirm it. I didn’t understand any of that and decided it wasn’t worth trying. I also didn’t bother telling her that the delivery of goods to our office should be sufficient confirmation of our address. By this time I knew that the credit people and the store people were completely separate—the credit people would have no record that the store had sucessfully delivered to us the order that was on that February invoice.

“So is our account straightened out now?”

“Yes, sir.”

“And will the order go through?”

“No, sir. Because it was canceled, it’ll have to be placed again. Let me put you through to that department.”

I really should have hung up at this point. I knew our account was up to date and that they knew we didn’t owe them any money. The likelihood of an error-free order was low. But I stuck with it for the same reason people can’t turn their heads away from a car accident.

When the order rep came on the line, I gave her the order number. She confirmed the items in the order—which I took to be a good sign—and then asked, “And how would you like to pay for that, sir?”

“With the same credit card I used on the original order.”

“Is that your personal card, sir?”

“No, it’s our company Office Depot credit card.”

“All right. Can I have the credit card number, sir?”

“You don’t have it?”

“No, sir, it’s not on my screen.”

“It’s saved with our account information. It comes up automatically when I make an order on the website.”

“Yes, sir, but it’s not on my screen.”

“Well, I’m sorry, but this has gone on too long. We’re done. Good-bye.”

After hanging up, I went to Amazon and placed the order in a couple of minutes. I won’t be going back to Office Depot.

To be clear, it didn’t bother me that she couldn’t see our Office Depot credit card number. I see that as a decent security feature. But she should have been able to see that we had one on file and that it was in good standing. She should have been able to place the order on that card without knowing its number.

The postscript to this story came the next morning. I pulled into the parking lot and saw two boxes by our front door. They were, of course, the items in the canceled order from Office Depot.

  1. And I opened ANIAT to the post, which was a pretty good summary. The only thing it lacked was the amount of the previously unpaid invoice. 

Time to stand

Thirty years ago, in the “1984” Macintosh commercial directed by Ridley Scott, a young woman smashed the big screen her fellow citizens were forced to watch and obey. You imagine them standing up and rebelling afterwards.

Today, in the “Up” Apple Watch commercial seemingly directed by Stanley Milgram, a young woman docilely stands when a little screen strapped to her wrist tells her to.

Bamboo, cicadas, and integers

I enjoyed this article, “Bamboo Mathematicians,” by Carl Zimmer over at the National Geographic website, but I am skeptical of some of what it says. In particular, the math seems fishy.

The gist of the article is that there are species of bamboo that flower and spread their seeds very rarely—once every 120 years for one species. Weirder still is that these bamboo are in sync with one another. No matter where they are in the world, no matter what conditions they’ve been subjected to, every member of that species flowers and seeds the same year. Other bamboo species are also synced, but to shorter periods: 60 years in one case, and 32 years in another.

The accepted reason for the synchronicity, developed in the 70s by biologist Daniel Janzen, is that the masses of seeds generated in those special years overwhelm the animals that feed on them. A larger percentage of seeds survive and germinate than otherwise would because the animals simply can’t eat them all.

Zimmer’s article was prompted by a recent paper that tries to extend the theory by explaining how the particular periods of 32, 60, and 120 years arose. They believe the periods, which are multiples of small numbers only, not only convey a survival benefit, but are the easiest to mutate to. As Zimmer says,

Veller and his colleagues realized that they could test this model. Over millions of years, they reasoned, species should have multiplied their flowering cycles. It’s likely that they could only multiply the cycles by a small number rather than a big one. Shifting from a two-year cycle to a two-thousand-year cycle would require some drastic changes to a bamboo plant’s biology. Therefore, the years in a bamboo’s cycle should be the product of small numbers multiplied together.

The mathematics of bamboo offers some promising support. Phyllostachys bambusoides has a cycle of 120 years, for example, which equals 5×3×2×2×2. Phyllostachys nigra f. henonis takes 60 years, which is 5×3×2×2. And the 32 year cycle of Bambusa bambos equals 2×2×2×2×2.

But could this just be a kind of meaningless bamboo numerology? Is it just a coincidence that these species display such elegant multiplications? Veller and his colleagues carried out a statistical test on bamboo species with well-documented flowering cycles. They found that the cycles are tightly clustered around numbers that can be factored into small prime numbers. It’s a pattern that you would not expect from chance. In fact, they argue, this test offers very strong evidence for multiplication (for stat junkies: p=0.0041).

I’m certainly no biologist, and the paper apparently includes compelling genetic evidence that traces the branching of bamboo’s evolutionary tree, but the purely mathematical explanation strikes me as odd for a couple of reasons.

First, there are the cicadas. Periodic cicadas use the same strategy as the bamboo to overwhelm their predators and increase the odds of survival. But their periods are prime numbers, 13 and 17 years, and the reason for that, we’re told, is that prime numbers are the best bet for survival. Stephen Jay Gould gave exactly that explanation in his essay “Of Bamboo, Cicadas, and the Economy of Adam Smith.” You can find the essay in his collection Ever Since Darwin, and as you can probably guess from the title, he also talks about the synchronized flowering of bamboo.1

So on the one hand, we have an older mathematical explanation that says prime numbers are the key to long-period survival adaptations; and on the other hand, we have a new mathematical explanation that says multiples of small numbers are the key to long-period survival adaptations. While this does not necessarily mean that one of the explanations is wrong—evolution can lead to different paths being taken to achieve the same end—it’s surprising to me that Zimmer didn’t mention the apparent contradiction. He’s generally considered one of the best science journalists, and I’m sure he knows the cicada story.

The second reason I thought the multiples-of-small-numbers hypothesis was odd was my sense that it was pretty common for integers in the range of interest (dozens to hundreds) to factor into just a few small primes. To test this, I fired up IPython and started playing around.

I started with this function for getting a list of prime factors:

def prime_factors(n):
  f = []   
  d = 2
  while n > 1:
    while n % d == 0:
      n /= d
    d += 1
  return f

I stole it from this discussion at Stack Overflow. It works like this:

In [2]: prime_factors(150)
Out[2]: [2, 3, 5, 5]

To get the prime factors of all the integers from 2 through 200, I made this list comprehension:

all = [ (n, prime_factors(n)) for n in range(2, 201) ]

Following the ideas in Zimmer’s article, I made a list of all the integers whose largest prime factor is 5:

max_fives = [ x[0] for x in all if max(x[1]) <= 5 and x[1] > 5 ]

As you can see, I also eliminated 2, 3, and 5 from this list, as I didn’t want to include such short periods. Here are the 41 integers in max_fives:

[6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36,
40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 90, 96, 100,
108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192, 200]

So if we’re talking about periods on the scale of Phyllostachys bambusoides, values that are multiples of 2, 3, and 5 only aren’t especially rare. For comparison, there are 43 prime numbers in that range.

And apparently there’s some fuzziness to the periods of these bamboo species. Note that Zimmer says “the cycles are tightly clustered around numbers that can be factored into small prime numbers” (emphasis mine). Let’s expand our results to integers that are within one of the numbers in max_fives.

clustered = set()
for n in max_fives:

There are 105 integers in clustered, which is over half of the integers in question. This makes me suspicious of that p value of 0.0041 quoted in Zimmer’s article.

You may argue that by restricting the sample space to integers up through 200, I’ve cooked the books to make these small integer multiples more common than they would be if we looked at a larger range. I thought it was reasonable to stop at 200, since the longest cycle we know of is 120 years. But you’re right that multiples of small numbers become less common as the range gets larger. If we’d defined all to go up to 500, for example, then max_five would have only 62 integers and clustered would have only 168. This is a distinctly lower proportion of the total, but it’s still substantial.

I could, of course, buy the original paper if I really wanted to know how the authors came up with that p value, but scholarship isn’t a hallmark of blog posts. Plus, I mainly just wanted to play around in IPython.

Update 5/23/15 10:04 AM
OK, fine. Aaron Meyer tweeted me a link to a PDF that describes the statistical work. It’s 37 pages long, and I certainly haven’t dug into it properly, but the gist seems to be that although numbers that factorize into small primes (NFSP) are relatively common, what’s uncommon (and leads to the low p value) is that so many bamboo species that have long-period synchronized flowering have cycles that match NFSPs. This is analogous to coin flipping: flipping a coin and getting heads is no big deal, but flipping ten coins and having them all come up heads is. Zimmer’s article didn’t say how many species of bamboo were studied, but I supposed I should have guessed that it was more than just the three he mentioned.

Update 5/23/15 5:42 PM
More biology enthusiasts here than I’d’ve guessed. Reader Bror Jonsson emailed me a link to the original paper, thus screwing Wiley out of tens of dollars.2 If you look through it, you’ll see that the authors do discuss periodical cicadas, which was also pointed out to me on Twitter by Pete Carlton.

  1. Gould’s essay was written in the 70s, shortly after Janzen’s work, and includes no theories on why bamboo would have periods of 32, 60, and 120 years. 

  2. Extra points to Bror for having a Bob Dylan quote in his email signature.