Rosalind Franklin's centenary

Today is the 100 year anniversary of the birth of Rosalind Franklin, and I have something to say about Nobel Prizes and scientific reputations.

I think we can agree, from the start, that prizes for science suck.  In particular, the Nobel Prize sucks.  Some prizes have been given to yahoos.  Other prizes have been given to mentors but not to the juniors who actually did the work, and in some of those cases the juniors had the great ideas.  See Enders, John for a counter-example.

Some prizes were limited because more people deserved them than just the maximum of 3.

Bob Gallo should have been awarded the Nobel Prize, he invented every tool for studing HIV that anyone ever used.  But he was an asshole, and the Swedes decided to make a point.

Rosalind Franklin arguably deserved the Nobel Prize.  Her major problem was that she died of cancer several years before the prize for DNA was awarded, and there is a rule against posthumous awards.

One often sees (now more frequently) the claim that Watson and Crick "stole" Franklin's data and received recognition for discovery of the double helix when it was rightfully hers.  It's feminist dogma.

It's also revisionist nonsense.

It is false that Franklin discovered the double-helix.  What she did was to take a beautiful X-ray picture of DNA that Crick knew immediately implied the double helix.  Franklin herself was unsure.  She wrote "if a helix..."  Furthermore, this would be her only contribution, seminal to be sure, but her only one.

Franklin was in some respects in competition with Watson and Crick, and she was definitely unhappy when it became known that her boss Wilkins (she disputed his authority), and Max Perutz, had made her picture available to Watson and Crick.  It had already been shown in local seminars.  Perutz, as straight an arrow who ever lived, was not bothered about how things went down.

Beyond that, the discovery of the double helix relied on deep crystallographic and structural knowledge of Crick, as well as the enormous luck of Watson.  He had no idea what the picture meant, but he knew about Chargaff's ratios, and he knew the correct structures for the bases in solution.  This was crucial.  The ultimate aha moment was Watson's, much as I would wish otherwise.  (Because he is also an asshole).

Franklin was, in years shortly following the events, friendly enough with Crick and his wife that they vacationed together.  There was no animosity between them about DNA.  She died 5 years later, in 1958.

If you dispute any of this, go re-read Judson's book and Perutz's writing about this and get back to me.

The idea that Watson and Crick stole the double helix from Franklin is complete nonsense.

[Update: re-reading Judson after 40 years, there is a long discussion of who knew what, when, mainly informed by interviews with Perutz. In particular, the crucial inference from Franklin's photos was not that the structure is a helix, she recognized that, but that the symmetry is "monoclinic". This has as the consequence that a 180 rotation is symmetric, which then has as a consequence that a two-chain model must have the chains going in opposite directions. ]

Sum of angles, revisited

I've run into a number of different derivations for the "sum of angles" formulas over the years.  These are 

cos s + t = cos s cos t - sin s sin t

sin s + t = sin s cos t + cos s sin t

For example, here is one using Euler's formula, and here is a derivation of the difference version of the cosine that I encountered in Gil Strang's Calculus textbook.  As I've said, I find it only necessary to memorize one:

cos s - t = cos s cos t + sin s sin t

which is easily checked for the case where s = t.

Recently I ran into a couple more.  Probably the simplest is this one:

Two stacked right triangles with a surrounding rectangle.  The upper triangle is sized so that the hypotenuse is 1 and the sine and cosine are obvious.  For the triangle with angle phi, we need an extra term in the sine and cosine so that when dividing, say, opposite/hypotenuse, the result is correct.

The angle theta + phi is known by the alternate interior angles theorem, and the small triangle with angle phi is known by a combination of the complementary and supplementary angles theorems.

Now, just read the result.  One diagram gives both formulas!  

There is also a simple derivation for the sine formula based on area calculations.  We calculate the area of this triangle in two ways:

On the left, we have that

A = (1/2) a sin (theta + phi) b

On the right (h = a cos phi = b cos theta) and

A = (1/2) h a sin phi + 1/2 h b sin theta 

  = (1/2) (b cos theta a sin phi + a cos phi b sin theta)

Equating the two and factoring out (1/2)ab, we obtain the addition formula for sine.  (Unfortunately, I've lost the links where I saw these).

Here is a link to a rather comprehensive chapter on the subject from my geometry book (Github).