English pronunciation is notoriously underdetermined. Here’s an example. I guess we all know how to pronounce

    A tear in the eye.

Well, I would have thought so anyway, but last weekend I had an ophthalmic scare that introduced another possibility. It seemed I had

    A tear in the retina.

[27 March 2014]

Is mathematics about numbers?

Is the law about money?

I think the two situations are much the same.  In principle, mathematics is concerned with all kinds of logical relationships, not just numerical ones.*  Yet many of the most powerful things we do with logic involve numbers, and mathematicians are the experts in their use.

As for the law, in principle, it is concerned with all kinds of human relationships, not just financial ones.  Yet so much of human relationships is regulated by money that inevitably lawyers have a special interest in this area.

*The Independent reassures Sudoku players: “There’s no maths involved.  You solve the puzzle with reasoning and logic.”

[30 December 2013]

Why did the Lord send his son to earth?  I was embarrassed to realize last night that it took me to age 58 to notice how I’d been hoodwinked by the standard narrative.

The line we’re fed is that he did it to help us sinners out, since we can be redeemed through Christ.

And yet if you look at it from God’s point of view, well, let’s face it, in the BC years he was nobody, with just a few Jewish believers.  Sending Jesus down changed that completely, a brilliantly successful advertising ploy.  Jesus made God go viral.

[22 February 2014]

It’s October, start of a new year.  Having purchased my blue Oxford diary for 2013-2014, I’ve just put 2012-2013 on the shelf.  The stack is 16 high now, beginning with 1997-1998.

Life has its rhythms, on different time scales.  You get a cup of coffee every few hours, go to bed once a day, put the trash out each Friday… and put the old diary on the stack each October.  The top of my stack is rising around one centimeter per year, so its velocity is slightly less than that of your average tectonic plate.

As a youngster I used to imagine with fascination the plateau of adulthood, that unending time of regular habits, one day after another, year stretching on year.  Who could comprehend such an infinity?  Here at age 58, I think I’ve reached it.

[25 October 2013]

Slowly, over the generations, cultures adapt to the conditions they face, but year on year we mostly do what we’re used to.

And so it is that among the hundreds of mathematicians here in Oxford’s Andrew Wiles building, there are two who habitually wear short trousers, even in the winter.  Both of these young men get plenty of good-natured kidding on the subject of their dress habits.  Maybe you guess that Cameron and Anthony are from Iceland or northern Russia, finding Britain balmy in comparison?  Of course the truth is just the opposite.  One of them is from sun-baked Queensland, and the other from steamy Texas.

[10 December 2013]

The two most important things I’ve worked on in the past seven years are Chebfun, a software package that people are using around the world, and Approximation Theory and Approximation Practice, a bestselling SIAM book that is changing perceptions of the mathematical properties of polynomials.  It’s a safe bet that among my “outputs” of the past seven years, these two will have the greatest impact.

Not according to the UK’s assessment scheme known as the Research Excellence Framework, however.  Our department has just sent in its REF submission, reporting for each of 147 researchers their four best outputs from the past seven years.  In theory, the REF welcomes nonstandard outputs, including software.  In practice, everybody is scared to death of deviating from the safe pattern of specialist papers in specialist journals.  Luckily I’ve produced enough of those too.

So neither Chebfun nor ATAP has been included in our REF submission.  Among the more than 500 outputs of Oxford Mathematics for the period 2007-2013, they do not appear.

[13 December 2013]

My cycling safety jacket exploits two different technologies to be visible.  I can’t resist wondering, are the two analogous?  What I find is that no, in a sense they are opposite.

One technology is directionality, which makes the silver strips on the vest shine bright in headlights. The trick here is that the fabric reflects light in the same direction it came from, making the strips appear magically bright to oncoming drivers.  (Traffic signs have used this technology for years.  I remember once as a kid being amazed when my father said, look, I can turn off all those signs up ahead on the highway just by switching off our car’s headlights!  My mother wasn’t pleased with this experiment.)

The other is fluorescence, which gives the fabric of the jacket its unnatural brightness.  The physics here is that ultraviolet light hitting the fabric is converted by quantum mechanical effects to a visible wavelength and radiated out again.   So my jacket emits more yellow light than it receives.  Our eyes see the magic in this, and in the last year or two people have started wearing “neon” shirts and shoelaces.

Here is what I mean by saying that the two technologies are opposites.  Fluorescent fabrics work by bending incident light from one wavelength to another.  Reflective strips work by preventing the bending of incident light from one direction to another.

[21 October 2013]

As we know, the heart has two atria, of unequal sizes, with a barrier between them.  The smaller right atrium is involved with pumping blood through the lungs, while the larger left atrium handles the rest of the body.

This is pretty much the setup in our new Andrew Wiles mathematics building at Oxford, which will open officially next week.  The pure mathematicians have offices in the right atrium, and the applied ones on the left.  I guess this means pure maths is the lungs, bringing in the oxygen of new ideas, and applied maths is the body, applying the oxygen to do some work?  With a cafeteria in-between.

[30 September 2013]

In recent years the US Federal government has pretty much ceased to legislate.  It can no longer make decisions about budgets, taxes, judicial confirmations, drugs policy, gun control, immigration, or much of anything else.

A symbol of the paralysis can be found at the Republican National Committee web site this week.  Three years ago the “ObamaCare” bill was passed.  It’s complicated, but it is the law.  Nevertheless, the Republicans have decided to block the law and have threatened to shut down the government unless funding for it is eliminated.  At the RNC website just now I found this digital display:

          COUNTDOWN TO OBAMACARE TRAIN WRECK

          8 days, 7 hours, 50 minutes, 53 seconds

Welcome to the world’s greatest democracy.

Politicians have always had to balance rewards for getting things done against rewards for beating the other team.  Somehow it would seem that in recent years, the incentives have moved out of balance.  Republicans would rather have Obama fail (and the country with him) than have the country succeed (and Obama with it).  The Democrats are not blameless either.  How can we get the debate to focus on readjusting the nonlinear dynamical system of government to make it work again?

[22 September 2013]

Everybody thinks Manhattan’s avenues run north-south and the streets east-west, but it isn’t true.  The whole grid is actually titled 29 degrees to the northeast.  29 degrees!  This is why the Empire State Building looks so nice when seen from the “south” on a sunny afternoon—you’re actually viewing it from the southwest.  In fact Broadway, which we think of as running diagonally, is the road that approximates north-south; and even Broadway actually tilts slightly to the east.

It fascinates me how few people are aware of this situation.  Most NYU mathematics professors don’t know about it (I’ve asked them), nor does the man on the street (just one of the three I sampled).  Maps depict avenues vertically, often without an arrow to indicate north.  The NYU maps posted all around Greenwich Village compound the deception with an outright lie, including an arrow for North that points straight up.

Does it matter?  What is truth?  My feeling is that we get through life with all kinds of useful approximations, and until better data comes along, I’m going to take the view that their alignment with the truth, on average, is around 29 degrees.

[21 September 2013]