Physicist Amok

Someone recently pointed out to me a new show on the History Channel called Human Weapon. I don’t have a television, so my response comes from poking around the website and watching the short videos there. The show consists of two guys, one a mixed martial artist, one a football player, going around the world importuning various local martial artists and then ending the show by fighting with them. I was sufficiently annoyed by it and the level of idiocy in the comments that I had to write something in response.

Before anyone asks, I’m not going to discuss whether or not I study martial arts.

1. Which is more ludicrous:
American marines and Chinese tai chi,
or American tai chi and Chinese marines?
What is either ludicrous?
In the end we have the same form.
Why the preoccupation with karate vs. capoeira?
A style is a codification by a master.
The codex matters, but not its name.
The codex lost, the name has no meaning.
A line of masters can build great things,
one generation can lose them all.
Study with a present master,
or the skilled student of a previous master.
Beyond that the line is broken.

2. The fool says, this attack can’t be blocked.
The master says,
     angle your elbow so or it will be broken
     you lose your balance in the step
     don’t neglect your other hand
     you’re putting a weird twist in your spine; stop it
     remember your elbow!
     what is it you’re trying to hit? hit it
     you locked your elbow straight. why?
     your opponent dodged. what’s your followup?

3. It’s a different mind to play in the ring
or react at once to the unexpected
or premeditatedly kill a man.
The last I’ll gladly leave to soldiers
the second we call self defense
does the first prepare us for the other two?

4. Watching a master, you see his limbs move,
     you don’t see the motions of his spine
you see where he hits, but you don’t perceive
     the nerves and bones he strikes
you see his stance
     but what muscles bear the weight?
you see him move
     do you know why he does?
how will you know unless you can ask him?

I am appalled at the editions of John Donne’s ‘Ecstasy’ available on the Internet.  Donne was among the most precise minds to write in English.  Moving commas around can destroy his poems.  This isn’t the case with Shakespeare or Chaucer.  Their language is robust, meant to be broadly spoken.  Donne’s is for careful reading.

Here are the offenders: the Oxford Book of English Verse (at Bartleby) is properly punctuated, but prints only the first five strophes.  Luminarium has a rendering. It has semicolons everywhere for no good reason besides straitjacketing a freer English into modern use, and lots of punctuation with grates on the ear:

He—though he knew not which soul spake,
Because both meant, both spake the same—

What is that dash there to break up the line?  The pause here goes at the end of the first line.  That’s why it was put there. Incompetech’s version has somewhat better punctuation, but has entirely abandoned the strophic structure. Poetry X has both abandoned the strophic structure and egregiously punctuated.

But this is nothing compared to the essays I found. This one from some graduate student is merely trite, and occupies itself either with telling us what is said more clearly in the poem or with things totally irrelevant to it. This one doesn’t even understand the first strophe! Then it goes on to give a PowerPoint presentation of the rest of the poem.

So, in the interests of western civilization, I am putting the text of the poem (in the version due to Ezra Pound, found in his ABC of Reading) online.  It doesn’t have the original spelling, but I think it’s otherwise unexceptionable.

Where like a pillow on a bed
A pregnant bank swell’d up to rest
The violet’s reclining head
Sat we two, one another’s best.

Our hands were firmly cémented
By a fast balm which thence did spring,
Our eye-beams twisted and did thread
Our eyes upon one double string

So to engraft our hands, as yet
Was all the means to make us one,
And pictures in our eyes to get
Was all our propogation.

As twixt two equal armies Fate
Suspends uncertain victory,
Our souls, which to advance their state
Were gone out, hung twixt her and me.

And whilst our souls negotiate there,
We like sepulchral statues lay.
All day the same our postures were
And we said nothing all the day.

If any, so by love refined
That he soul’s language understood
And by good love were grown all mind,
Within convenient distance stood,

He, though he knew not which soul spake
(Because both meant, both spoke the same),
Might thence a new concoction take
And part far purer than he came.

This ecstasy doth unperplex,
We said, and tell us what we love,
We see by this it was not sex
We see, we saw not what did move,

But as alll several souls contain
Mixture of things they know not what,
Love these mixed souls doth mix again
And make both one, each this to that.

A single violet transplant,
The strength, the colour and the size,
All, which before was poor and scant,
Redoubles still and multiplies,

When love with one another so
Interinanimates two souls
That abler soul which thence doth flow
Defects of loneliness controls,

We then, who are this new soul, know
Of what we are composed and made,
For th’anatomies of which we grow
Are souls whom no change can invade.

But O alas, so long, so far
Our bodies why do we forbear?
They are ours though they’re not we. We are
Th’intelligences, they the spheres.

We owe them thanks because the thus
Did us to us at first convey;
Yielded their foces to us
Nor are dross to us, but allay.*

On man heaven’s influence works no so
But that it first imprints the air,
So soul into soul may flow
Though it to body first repair.

As our blood labours to beget
Spirits as like souls as it can
Because such fingers need to knit
That subtle knot which makes us man.

So must pure lovers’ souls descend
To affections and to faculties
Which sense may reach and apprehend
Else a great prince in prison lies.

To our bodies turn we then that so
Weak men on love reveal’d may look,
Love’s mysteries in souls do grow
But yet the body is his book.

And if some lover such as we
Have heard this dialogue of one,
Let him still make us, he shall see
Small change when we’re to bodies gone.

*alloy, i.e., that which makes metal fit for a given purpose

The only thing that might need any comment is that the second two lines of the fifteenth strophe are a single sentence with the four lines of the sixteenth: “So soul into soul may flow…because such fingers need to knit the subtle knot…” Pound wants to say that “bodies” in the last strophe is a technical term for atoms. I think that’s unnecessarily deep, and that it can refer perfectly well to when their souls return to their bodies from hanging between them.

Consider some population in its environment. The environment has some set of properties, and each member of the population likewise as some set of properties. Epidemiology concerns itself with the following problem: given some environment and population, predict the evolution over time of the properties of some individual placed in that environment, usually with respect to some disease or chemical. The issue is to select an appropriate set of properties for environment and population, and to construct empirically verifiable relationships among the values of these properties.

But first, what do we mean by a property? Hatsopoulos and Keenan have articulated a clearer definition than I can hope to:

A primitive property of a body is specified by describing an operation or test to which the body can be subjected. The value of the property at any time is the result of the operation performed at that time. Not all operations can be used in defining primitive properties of a body — only those whose result is uniquely related to the condition of the body at a particular time. Specifically, an operation defines a primitive property at time if the values obtained by successively repeating the operation on the body, beginning at and extending over decreasing intervals of time previous to , approach a limit as the interval approaches zero. (Hatsopoulous and Keenan, Principles of General Thermodynamics, 1981, p.7)

Then they go on to define properties as all functions of primitive properties. When we are concerned with populations, we have to extend this a little bit. We can measure an individual’s eye color, but what is a population’s eye color? For populations the relevant primitive properties generally take the form of probability distributions, and our measurement becomes some kind of sampling algorithm or time averaging. For the abstract object, the population, such a thing is a primitive property, but our actual measurement is on individuals.

Almost all epidemiological models use the rate of infectious doses being delivered to an individual, which we’ll call the infectivity . In general this is a property. Consider a model for tuberculosis in a hospital. Tuberculosis is carried by small droplets which are expelled into the air when an actively tuberculous patient coughs. We can construct a device which gathers droplets which come into contact with some area of its surface, and then checks for the presence of the bacillus in the droplets (for instance, by chemically extracting the DNA and amplifying genes specific to TB). Then we install this device in the hospital’s air handling units and record for some period of time. We can calibrate the device by sending a known quantity of bacilli containing droplets at it in the laboratory. In this case is a well posed, primitive property.

Unfortunately, usually shows up in combination with another factor, , the probability that an individual with specified properties will contract the disease in question when exposed to an infectious dose. is far more difficult to measure (in an ethical way), and probably depends on the properties associated with individuals.

To make matters worse, in many epidemiological problems, mechanical measurements of the infectivity aren’t available, much less of . If we are dealing with a relatively homogeneous population, a group of medical students in Denmark, say, then we can estimate the combination from the rate at which they are infected.

If we assume that infectious doses arrive independently, then the fraction of the population infected after some time is given by a Poisson distribution with parameter . We can’t tell how many of these people received multiple doses, so the only reliable number we get is those who are still healthy. The probability of zero infectious doses actually causing disease in time is given by . So if we have healthy individuals out of total, then . is a constant, so after some rearrangement we get . This method is due to RG Ferguson.

The sadist in me cackles with glee when groups of people who make “reasonable” assumptions in their calculations get walloped.  An example of just such a reasonable assumption can be found in predicting binding affinities of transcription factors to DNA sequences: the additivity assumption.

Say that we have a stretch of DNA and some protein we wish to bind to it.  How tightly will the protein bind to various possible nucleic acid sequences?  To put it symbolically, we have a set representing the four possible base pairs.  The space of sequences of bases is , the set of ordered sequences of length of elements in .

Our task is to construct a function which maps a sequence into the free energy difference between the protein and DNA bound and unbound.  The additivity assumption says that any given base contributes independently of whatever bases adjoin it.  This makes the problem wonderfully simple mathematically.  We can say where the give the free energy difference for each base.  Note that all the are not identical.  Some bases matter more than others, and matter in different ways. But if the additivity assumption holds, then we only have to make measurements at each base, and we’re done.

Unfortunately, it doesn’t work.  There were some preliminary studies that seemed to say it wasn’t alright, but they were still small enough where with sufficiently blind application of statistics, you could eventually find a method saying that it was approximately true.  Sebastian Maerkl and Steve Quake, in a results rich paper, produced the following graph of the change in binding free energy for changes in sequence as predicted by the additivity assumption and as measured in their experiments:

And that about wraps it up for the additivity assumption.  This is the problem with techniques which are (as Eric Siggia likes to put it) socially acceptable.  Unless you have nailed down the assumptions under the math and gone out and tested them, your mathematics doesn’t mean anything.  I explain this to biologists by comparing it to running a Western blot without controls.

As an aside, Sebastian Maerkl is coming to visit this week, as there’s talk of him taking up a faculty position here at EPFL.