December 2010

A Puzzling Year

Ever since I can remember I've enjoyed putting together jigsaw puzzles. Even as an adult it's a fun diversion for me; of course there have been lots of opportunities to do simple ones with the kids over the years. Every once in a while, since we've been married, Shelly and I would get out one of the tougher ones and do it together - ones with 3000 pieces, or unusual shapes, or other challenges. Each is different, to some degree unique: dominant colors may greatly help find the right piece with one puzzle, while textures, element size and focus help with another, or sometimes you just have to go by piece shape.

Blinding them with math

There exists a widely quoted story about [18th century philosopher/mathematicians] [Denis] Diderot and [Leonhard] Euler according to which Euler, in a public debate in St. Petersburg, succeeded in embarrassing the freethinking Diderot by claiming to possess an algebraic demonstration of the existence of God: "Sir, (a+b^n)/n = x; hence God exists, answer please!"

This story turns out to be (at least in detail) false, but it was likely invented and resonated because it embodies an underlying truth almost any of us in the sciences have seen: once a mathematical equation comes out, it tends to blind the naive, and even the experienced will often skip over the equations on a first reading of any complex argument. A minor error in a mathematical expression (a forgotten minus-sign being the most common example!) can completely change its meaning, and reasoning about such things requires detailed understanding, it's something that's intellectually demanding, requiring time and mental effort. Sometimes we are willing to put that time in, but more often than not we just don't have the time, or the requisite background, and just skip over the math, hoping that it makes sense to somebody else.

Of course, there is an equation that's proof of amazingly beautiful self-consistency in mathematics, that some have taken as evidence for God:

ei π + 1 = 0

but the beauty of that expression isn't something I intend to get into right now.

What brought to my mind the apocryphal story about Euler and Diderot was a pair of recent posts by Dr. Judith Curry, who I've criticized here before. The first post seemed in some ways to finally be a response to my earlier queries about the no-feedbacks question - about which more below. But in the second she oddly chose to highlight 3 comments which claimed the whole thing was ill-defined, with one of them chock-full of equations that seems to have blinded her and others to the fact it made no more sense than Euler's apocryphal equation, ending with a claim that it's all nonsense:

... it is impossible to evaluate these 2 integrals because they necessitate the knowledge of the surface temperature field which is precisely the unknown we want to identify.
The parameter dTa/dFa is a nonsense

which is the sort of language that should remind my few regular readers of our friends Gerlich and Tscheuschner...

5 year planning

APS Staff were recently asked about our thoughts on the future, to help with a planning exercise for coming years. The following are somewhat frank comments I submitted in response to two of the questions, on biggest challenges and opportunities for the future. I doubt they represent the average views of APS staff right now, but they do capture a number of my concerns and ideas at the present so I thought I'd share a bit more widely... I'd certainly be interested in others' thoughts on these and other ideas for what the relatively near future may hold.

Five biggest (but perhaps not most likely) challenges:

1. Retaining the trust of the physics community as a filter and enabler of physics communication (journals, meetings, new media). Trust is fragile; mistakes that drain that trust could come from any front; openness and honesty in all dealings with the community and society at large are paramount.