Folded Corners

I was recently reminded of a Richard Feynman anecdote I once read in James Gleick’s biography, Genius: The Life and Science of Richard Feynman. I had given the book to my Dad as a gift almost 20 years ago, and — as is tradition for me when I give books to family — I borrowed and read the book immediately.

Yesterday, I borrowed the book from my Dad again to see if I could find the passage. I vaguely knew where the anecdote was, but it was going to require some flipping and scanning, as the book is over 500 pages long with dense type.

To my delight, the corner of the page I was seeking was folded over! It was the only corner folded in the whole book. Apparently, I had been so struck by that very anecdote when I first read the book 20 years ago, and I had folded the corner to hold the place.

I stopped folding corners years ago (reverting instead to Post-Its), and I barely even read paper books anymore, thanks to my Kindle. This discovery was a nice, visceral reminder of the joys of paper artifacts that you can touch and feel and fold.

For those of you curious about the anecdote that has stuck with me all these years, it was about an informal lecture Feynman gave to his peers while he was at Los Alamos working on the Manhattan Project. Here’s the passage, from pages 181-182 of the original hardback edition:

Meanwhile, under the influence of this primal dissection of mathematics, Feynman retreated from pragmatic engineering long enough to put together a public lecture on “Some Interesting Properties of Numbers.” It was a stunning exercise in arithmetic, logic, and — though he would never have used the word — philosophy. He invited his distinguished audience (“all the might minds,” he wrote his mother a few days later) to discard all knowledge of mathematics and begin from first principles — specifically, from a child’s knowledge of counting in units. He defined addition, a + b, as the operation of counting b units from a starting point, a. He defined multiplication (counting b times). He defined exponentiation (multiplying b times). He derived the simple laws of the kind a + b = b + a and (a + b) + c = a + (b + c), laws that were usually assumed unconsciously, though quantum mechanics itself had shown how crucially some mathematical operations did depend on their ordering. Still taking nothing for granted, Feynman showed how pure logic made it necessary to conceive of inverse operations: subtraction, division, and the taking of logarithms. He could always ask a new question that perforce required a new arithmetical invention. Thus he broadened the class of objects represented by his letters a, b, and c and the class of rules by which he was manipulating them. By his original definition, negative numbers meant nothing. Fractions, fractional exponents, imaginary roots of negative numbers — these had no immediate connection to counting, but Feynman continued pulling them from his silvery logical engine. He turned to irrational numbers and complex numbers and complex powers of complex numbers — these came inexorably as soon as one from facing up to the question: What number, i, when multiplied by itself, equals negative one? He reminded his audience how to compute a logarithm from scratch and showed how the numbers converged as he took successive square roots of ten and thus, as an inevitable by-product, derived the “natural base” e, that ubiquitous fundamental constant. He was recapitulating centuries of mathematical history — yet not quite recapitulating, because only a modern shift of perspective made it possible to see the fabric whole. Having conceived of complex powers, he began to compute complex powers. He made a table of his results and showed how they oscillated, swinging from one to zero to negative one and back again in a wave that he drew for his audience, though they knew perfectly well what a sine wave looked like. He had arrived at trigonometric functions. Now he posed one more question, as fundamental as all the others, yet encompassing them all in the round recursive net he had been spinning for a mere hour: To what power must e be raised to reach i? (They already knew the answer, that e and i and π were conjoined as if by an invisible membrane, but as he told his mother, “I went pretty fast & didn’t give them a hell of a lot of time to work out the reason for one fact before I was showing them another still more amazing.”) He now repeated the assertion he had written elatedly in his notebook at the age of fourteen, that the oddly polyglot statement eπi + 1 = 0 was the most remarkable formula in mathematics. Algebra and geometry, their distinct languages notwithstanding, were one and the same, a bit of child’s arithmetic abstracted and generalized by a few minutes of the purest logic. “Well,” he wrote, “all the mighty minds were mightily impressed by my little feats of arithmetic.”

Sports and Collaboration

My friend, Andrew, recently gave me the book, Scorecasting. Just started reading it (thank you, Kindle), and I came across this excerpt:

Exploring the hidden side of sports reveals the following:

  • That which is recognizable or apparent is often given too much credit, whereas the real answer often lies concealed.
  • Incentives are powerful motivators and predictors of how athletes, coaches, owners, and fans behave — sometimes with undesirable consequences.
  • Human biases and behavior play a pivotal role in almost every aspect of life, and sports are no exception.
  • The role of luck is underappreciated and often misunderstood.

As with most things having to do with sports, these principles also apply to anything related to collaboration. If only we had as much data about our work lives as we do about our favorite sports teams.

Off to watch the Lakers….

Borders and the New Age of Books

Borders declared bankruptcy this past week, and it’s closing a number of stores in the Bay Area. I was running errands yesterday and was near the San Mateo store, so I decided to drop by and prowl about for deals.

It was an absolute madhouse. Parking was just about impossible, and the purchasing line snaked around the entire store. It was nice in a way to see that so many people still valued books.

Which is a good thing, because even at 20-40 percent discounts throughout the store, I couldn’t find a single good deal. I found a bunch of books that I wanted to read, scanned their barcodes on my phone, and saw that was selling all of them for cheaper, even with the Borders discount.

Frankly, that’s old news. The real game changer is’s distribution model and the Kindle.

I love traditional books — the feel, the smell, the timelessness. I remember visiting the Lincoln Museum years ago and staring in wonderment at his Bible, the actual, physical book that he had lovingly thumbed through as a child. I have a huge collection of my own books, and the thought of getting rid of any of them pains me.

That said, my parents got me a Kindle for Christmas last year, and I am absolutely in love with it. As much as my sentiment lies with traditional books, the reality is that the Kindle has got me reading books again. The screen is a marvel, it’s lighter and more comfortable to read than most of my real books, and I can carry a whole slew of books on it. The companion case is worth the extra price for the built-in book light alone.

Here’s how dramatically has changed the book industry. While scanning for books on my phone, I could easily have purchased one immediately with one click and had it sent to my Kindle automatically. Much easier than waiting in that monstrous line, and much more portable.

If I had wanted to, I could even have read the book on my phone. This sounds painful to me, but I’ve heard from others that they often read books this way, and that — as with my experience with the Kindle — they’re reading more as a result.

Barnes and Nobles might be late to the game, but it’s adapted, and it has a chance. Borders is done. It has not proven an ability to adapt with the times.

The real question continues to be, what’s the future of the local, independent book store?

I don’t think the death knell is a sure thing. I viewed the Borders discounts with scorn, but the reality is, I often pay more for books at Green Apple Books, even though I know I can get them cheaper at It may be irrational, but I’m not alone. I like going there, even if books are more expensive. The opportunity is for local bookstores to leverage what’s magical and important about them — namely, the customer experience — and adapt it to the times.