I left EPFL at 11AM this morning. The beautiful train trip to Zurich seems routine, so I read a math book. The beautiful train trip from Zurich to Landquart I spent half the time reading a math book. On the unbelievably gorgeous train trip from Landquart to Davos I just gawked.

From Zurich, the trains were full of other people going to the ELMI conference. At the station in Davos, most stood around looking at bus schedules or being lost. But not me, no! I seized a map from the tourist information desk, and set forth on foot to find my hotel, the Arabella Sheraton Hotel Waldhuus (that’s Waldhaus, but with a quaint, Swiss misspelling).

Davos, the hotel, and the conference center are succinctly described “out of my price range.” The town sprawls over a long valley, with luxury hotels every block. My room is a two room suite, with a two section bathroom, a marble shower, and two balconies looking out on the alps. I am admiring the clouds racing over the snow-capped peaks in the last light of day as I write. I must add: there is a Gideon Bible on one nightstand, and “The Teaching of Buddha” on the other.

The conference center specializes in events like the World Economic Forum. Our conference has the feel of the gardeners who have convinced the household servants to serve them high tea in the parlor while the master’s away.

Axelrod from Michigan gave a talk on TIRF, including a couple of fun new ideas about measuring membrane orientation next to coverslips, then we all gorged ourselves on hors d’oeuvres. I was sociable and met four people, then took a long walk west along the valley through Davos.

28 May 2008, Davos

The Waldhuus has a splendid breakfast buffet, at which I fortified myself for two and a half hours of talks, followed by a coffee break with croissants, followed by more talks, followed by lunch. This morning’s talks were on thick specimen imaging and fluorescent labeling methods.

What should a talk for this conference be? Enough detail of optics, label chemistry, or application area to be more than a waste of time is impossible since the most of the audience lacks the necessary background for any of the three. Of course, most of the speakers haven’t even thought about this, and are giving the same talk they always give.

I went to one workshop, where a man soberly told me and a few others what a point-spread function is. I skipped the rest and took a hike up one of the mountains. A poster session — which is approximately the worst environment to discuss science possible — and dinner filled the rest of the day.

And after dinner, two men started playing alpenhorns, those long, straight things everyone sees in Swiss stereotypes. And then one of them played bugle calls on it while standing on his head. After this, I retreated to reading a paper on Galois connections, then headed back to the hotel.

29 May 2008, Davos

This morning’s talks focused on assorted new microscopy techniques, and were very good, particularly the final one by Tony Wilson from Oxford. He has figured out an extremely clever way to focus microscopes really, really fast. It turns out that you can only achieve 1.5x magnification and still optically image a volume perfectly.

So he takes the output of a microscope objective, images it backwards through another microscope and onto a mirror, then from the mirror back through the objective and onto a detector. The mirror is about the same size as the specimen — a few microns — so it can be moved extremely quickly and accurately. Viola: high speed focusing.

After lunch I attended a workshop by Definiens, who have turned image analysis around. Classically, you massage your image until you can segment it perfectly in one fell swoop. Instead, they oversegment horribly, and then merge regions until they achieve good segmentation. This turns out to be a much better way to do things.

I wasn’t interested in the other workshops in the afternoon, so I went hiking again. Davos lies in Grunewald, the easternmest, newest, largest, and least developed of Switzerland’s cantons. The canton consists of mountains striated with rich valleys. The woods are remnants from glaciation, which means they greatly resemble those of the high Appalachains.

Davos, in keeping with the Swiss obsession with outdoor sports, is laced with hiking trails. They stay in the woods up on the slopes in the main valley, but come down into the pastures in the side valleys, and wind past stone barns banked with dirt and sod uphill against the winter snow.

At junctures as I climbed towards the ridge I stopped and looked across the valley at fingers of white creeping down the mountains. Some were streams; others were still snow. Even in May, the landscape is dotted with snow packs several feet thick. In winter, this place must be impassible without snowshoes.

A gala dinner at a sanatorium-turned-ski hotel on one of the peaks filled the evening. We rode up by cablecar, and stood around on the terrace overlooking the valley sipping glasses of wine (or water in my case) until the black flies started bothering people. Then we trooped in for dinner.

From the Tiffany-esque stained glass, I think that the building has been maintained in its grand state of the 1920s. The walls are muralled. The fireplace is lined with sculpted ceramic tiles. We filled the grand dining room with its enormous mirrors, and I pontificated at my neighbors over a dinner of perfectly normal roast chicken masquerading under some pretentious and singularly unappetizing name. After dinner I skipped the disco and caught the first cable car down to the city.

30 May 2008, Davos

Those who made it to the first talk this morning coincided exactly with those to take the first tram home with me last night. The highlight of the morning was a talk by a lady from McGill which showed that fluorescence recovery after photobleaching measurements require an additional set of controls: in the range that causes bleaching, the photons can also reversibly dissociate protein complexes.

The only workshop of any interest after lunch was an open session about the Open Microscopy Environment project by Jason Swedlow, but I wasn’t feeling sadistic enough to go ask mean questions about a project I’m already acquainted with. I took the bagged lunch the conference center provided, tossed in a couple extra croissant which I hoarded from the coffee break, and caught the train home.

CERN had an open day for the Large Hadron Collider before they turned it on. A group of us, biologists all except for me, headed out bright and early on Sunday morning from Lausanne to see the great machine, along with 15,000 other people.

The primary attractions were of course the detectors and a tour of the tunnels, but by the time we arrived at the Meyrin site at about 11:00, there was at least a four hour wait to get a ticket, assuming there were any tickets left at that point. This didn’t stop us: CERN had arranged many other attractions. There were demos of superconductivity and superfluidity, the requisite freezing of things in liquid nitrogen and shattering them for the children, and a display of artwork inspired by the LHC. I didn’t see any of this.

I dragged the unfortunate biologists who accompanied me to the magnet factory, to the magnet testing center, and to the prototype of the linear collider that will succeed LHC. They were good sports, even as I quizzed them on the discoveries of the famous physicists whose names the streets bear.

One thing that astonished them was the amount of prefabricated construction. The buildings aren’t pretty. I explained that this is a working lab: the buildings have to go up fast, and if you need a hole in the wall, you can’t wait for approval. You just grab a drill. Under these conditions, prefab is the best option.

CERN put an enormous amount of effort into this open day. The magnet factory had magnets in various stages of construction set up throughout the room, and the engineers of the facility giving tours in English, French, and German. We were lucky enough to get a tour by one of the head engineers of the division, who gave us a wonderfully detailed description of the construction process.

In any circular accelerator, you have to bend the beam, accomplished with magnetic dipoles, and you have to focus it, using quadrupoles. The LHC ring consists of a series of 50m long dipoles with smaller quadrupoles of 6m interspersed. Protons traverse narrow tubes through the length of these magnets. The magnets look almost straight, but the accelerator is a circle. They must be curved. But if you do the calculation for an accelerator 27km in diameter, a proton only has to shift 7mm to the side in a 50m tube.

Actually, the quadrupoles are straight. The dipoles are ever so slightly curved: the physicists insisted that the beam could deviate no more than 1mm, not 7mm, from the center of its containing tube all the way along the accelerator. Our guide recounted a scene anyone who has dealt with physicists will find familiar:

“We need 1mm precision the whole way.”

“Impossible.”

“1mm.”

“Alright, it’s possible, but it will be enormously expensive.”

“1mm.”

To curve them, they string the plates that form the magnets on the beam tube, put the whole thing in an enormous press, forcefully bend it, then weld it in that shape.

How do they know they have met their required precision? They transfer the magnet to a sealed room where they use a laser/reflector system to measure the geometry to a fraction of a millimeter precision.

Once it has passed that test, the magnet is transferred to the testing facility, which we also visited. Here they seal the magnet into its insulating jacket, insert the tubes that carry liquid helium to cool the coils of the magnet, and check that it’s air tight.

The coils are superconducting. This is one of the most important facts about LHC: it’s what makes the machine possible. A superconducting wire can carry seven hundred times the current of a copper wire of the same cross section. A comparable magnet made with superconducting wire is 25 times smaller than its copper counterpart. LHC’s coils are a few cm across. In copper they would be almost a meter. In the tight spaces of LHC’s underground tunnels, this is a vital concern.

The superconductors carry a price though: NbTi, the only one commercially viable when LHC’s development began, isn’t superconducting above a couple degrees above absolute zero. The only practical coolant at these temperatures is liquid helium. Making and distributing that much liquid helium demands cryogen facilities as expansive as the magnets themselves.

The test facility has a direct link to the tunnels. When a magnet is declared complete, it is lowered 100m to the tunnels and slowly, carefully dragged to its final position. The pit was closed to prevent anyone falling in it, but they had a movie of the magnets being hauled at 2km/h through the tunnels, with a selection of charmingly incongruous background music along the lines of ‘Carmina Burana’ or the closing march from ‘Star Wars.’

All of this occupied our afternoon, after we had eaten lunch at a nearby Indian restaurant, and half our party (including a nine and ten year old boy) had departed. Before lunch was the hilight of the day: CLIC, the Compact Linear Collider, or rather its prototype. LHC smashes protons together. Protons are heavy, which makes it easy to reach high energies, but they consist of three particles. Making sense what happened when two protons, six particles, smashing into each other is difficult. LHC gets us to high energies to see what’s there. Then we need a collider that uses truly elementary particles — in this case electrons and positrons.

The day of circular electron collider is over. Electron radiate their energy as X-rays when dragged in a circle, and it swiftly becomes impractical to push energy in faster than it radiates. Modern facilities using electrons are straight, but unlike in circular accelerators where you can increase the energy just a bit with every circuit, all the energy must be given in one pass. As the energy grows, the distance you need to do this gets longer and longer.

CERN’s cost constraints dictate an accelerator no longer than 50km, but you can’t get close to the target energy of 3TeV in this distance. CLIC’s designers have found an incredibly clever solution.

Instead of accelerating one electron to 3 TeV, accelerate a thousand in a bunch to 3 GeV, which is perfectly possible in a reasonably sized linear collider. How does this get us closer to 3 TeV? It’s only the energy of individual particles that count, not the combined energy of all of them.

Someone person figured out how to build a device, two specially shaped metal chambers connected by a mass of fiber optic cable, that saps 96% of the energy from those thousand electrons as they fly into one chamber, and transfers it all to one electron just entering the other chamber. That single electron goes flying out at the required 3 TeV. The technical difficulties are enormous, but suddenly a sub-50km, 3 TeV collider seems possible.

It was a lovely day. My biological colleagues learned something about smashing very small things, and I relived my childhood dreams of building particle accelerators. And I bought a t-shirt with the Lagrangian of the standard model on the front.

According to the relativistic theory of the electron, an electron has energy . This equation permits negative energy values.

In Dirac’s theory, practically all negative states are filled at all points in space. A vacuum is then a sea of electrons in negative energy states. The presence of this charge is not observed because it is uniformly distributed.

A photon of sufficiently high energy may lift an electron from a negative energy state. The energy threshold for the photon is , since for a free electron there are no states between and . Physically, this means that the photon must supply enough energy to create two particles of mass . Momentum must be conserved and this requires either that the negative energy electron be near a nuclear or an electron, i.e., not free, or that two photons coming from different directions coalesce and lift an electron from a negative energy state. If the electron is near a nucleus it may occupy discrete states just below . These are within a few eV of 510,000eV. Strictly, then, the threshold for pair formation near a nucleus is . This is of no importance because binding energy and because transitions from negative energy states to the discrete part of the spectrum are improbable and not yet observed.

Treat values of a sequence as values of a random variable with uniform probability density. Then if has an accumulation point at , . To see this, when you’re close to , you get enormous denominators. Since you get arbitrarily close to arbitrarily often, you have infinitely many denominators as large as you like. These completely swamp any contribution of points of the sequence away from .

I suspect that there is a “fundamental theorem of analysis” which says that a statement about a space is true is equivalent to the statement being true at the accumulation points of all accumulating sequences in that space. But I don’t know how to define the above expectation except as a limit of finite sequences, so this doesn’t advance the program at all.

(Before people misunderstand, I like limits. I use them constantly. Some of my best friends are limits. This is a mathematical diversion.)

Among the things that came to light while reading people’s response to this occasion was the font Euler. Add the following code to your LaTeX preamble, and suddenly your mathematics goes from slick, standard, LaTeX, to a gorgeous idealization of the best mathematical handwriting:

\usepackage{ccfonts,eulervm}
\usepackage[T1]{fontenc}

A little more digging found this wonderful post discussing the font, and its sibling Alcuin Light. Alcuin Light is not included in TeX distributions, and must be bought separately and converted by hand, unfortunately. Knuth paired Euler with Concrete Roman. In isolation I prefer the default Computer Modern, but Concrete Roman does fit better with Euler.

But I admit I’m tempted to drop the $20 for Alcuin.

A data model is a set of data structures plus all the operators on them. I don’t mean the implementation of these, I mean the abstract mathematical definition. Relational databases are a mathematical definition distinct from any given implementation, and include both the underlying structure (the relation and a set of projectors on the tuples which constitute the relation), and all the operations to manipulate relations.

Given a particular data model, how much code is required to ensure that an implementation of that particular data model is sufficiently close to the mathematical ideal that the programmer can treat it as such in all further work? The only difficulty is saying when an implementation is sufficiently iron-clad to be so treated. This can be done experimentally.

We are comparing languages A and B. We take a group of subjects who all know both languages. Each produces an implementation of the same data model in both languages.

Different programmers may have different tolerances for abstraction leakage. To fix this, take each implementation and mark all the testing code (unit tests, run-time checks, etc.). Partition it randomly into equal subsets. Sequentially remove subsets of testing code. This gives a sequence of monotonically less assured mutilations of the original implementation.

Give each programmer who submitted an implementation a randomly chosen mutilation of each implementation he didn’t write. He marks each of them as iron-clad or leaky.

When we have all the marks, we find the level of mutilations for each implementation which gives some fixed fraction marking it as iron-clad, say 95%. This gives us a distribution of amount of code for each language, controlled for how faithfully it implements a data model, and we turn to standard statistical techniques to ask if they are different, and how different.

This presupposes that a shorter program that truly does the same thing than a longer one is better.

Biology is autonomous from physics. Any change to quantum mechanics will have at most cosmetic implications for biology. Quantum mechanics contributes nothing more than the existence of atoms and molecules, which are necessary for the lossless transmission of information. However, anything that replaces present day quantum mechanics must also predict atoms and molecules. The interactions between the two subjects a minimized because their interface is pinned by experiment.

Within physics, thermodynamics, fluid mechanics, elasticity, and the other macroscopic theories bear the same relation to quantum mechanics. The interfaces between the subjects are experimentally pinned.

A similar pattern appears within biology. Population genetics is built on molecular biology, but their interface is pinned by the existence of genes. We can replace our understanding of an allele’s molecular character, but that allele’s propagation in a population isn’t going to dramatically change.

This pinning is a form of damage control. All fields of science depend on other fields to be able to bootstrap themselves. The only way to keep the structure from falling to shreds is to pin the interfaces. A particle physicist uses macroscopic equipment, which experimentally obeys classical mechanics and electromagnetism. If the relation between his equipment and what he studies weren’t experimentally fixed in the intervening scales, his experiments would be impossible.

It is worth keeping your field as self contained as possible. Black boxes that reach into the heart of entirely different fields are a recipe for disaster.

This is why I dislike the Copenhagen interpretation of quantum mechanics. It posits an observer, whose observation collapses the wave function to an eigenstate of the observation in question. In so doing, it reaches directly to the heart of neuroscience, and builds quantum mechanics on the hardest, most central questions of an even larger area of science.

If the neuroscientists come up with the answer that consciousness isn’t anything special, just a pattern of spikes in neurons, then we have an insoluble problem. Further, there isn’t likely to be a physically robust structure of these firings which is consciousness, so what’s to stop other random patterns of particles from observing and collapsing wave functions? These difficulties are so great, that any interpretation — that is, a connection of the undisputed mathematical structure to reality — which is properly pinned at its boundaries are immediately preferable.

Yet most physicists aren’t willing to accept a new interpretation which requires conceptual gimmicks. Visualizations are tools with local use, not integral parts of theories. Since Heisenberg, we want our theories only to relate observable quantities, not enforce a particular picture. This was the great downfall of the Bohm-de Broglie pilot wave mechanics.

Thankfully, there is an interpretation which is both properly pinned and satisfies the Heisenberg aesthetic. There’s a beautifully written, absolutely simple book on it (Consistent Quantum Mechanics by Robert Griffiths). The book is available for free online.

Some gems: “The most refined expression of the rational intelligibility of the cosmos is found in the laws of physics.” (Paul Davies) No, the most refined expression of rational intelligibility is a properly randomized experiment. Theoretical physics is not king of the sciences, and most of science won’t change one whit if the entire forefront of theoretical physics reaches a dead end.

“Over the years I have often asked my physicist colleagues why the laws of physics are what they are.” (Paul Davies again) He gives various naive answers. The proper answer is, “I don’t know, and I can’t think of a good way to answer such a question, so I’m going to keep it in the back of my mind in case I do, and get on with questions I can answer.”

“The only problem is that inductive reasoning is not sound.” (first comment on the first blog post I linked to above) Here is someone with little exposure to logic, who doesn’t realize that deductive reasoning isn’t sound either. You can choose any of an infinite number of rules for manipulating sets of well defined strings of symbols. The applicability of any of them is an empirical question. Classical deduction occupies no privileged place. It’s just old.

Then Davies rambles about how the emergence of life is sensitive to the details of the universe. We don’t know this, and no one has thought of any way of finding this out, hallucinations of a few experimentally-challenged string theorists aside, and they have no idea how to construct a science from the ground up. I might even use the word parasite.

Aside from all this, everyone seems to agree that they’re arguing over the proposition “The universe behaves in an orderly and rational manner.” I have no idea what that actually means, and I think there’s a better statement of the required proposition: “There exists some finite level of detail which guarantees the outcome of a protocol/algorithm/recipe.” (I don’t think we have a word for what I have offered three to convey.)

That statement is much weaker, and can be considered in an even weaker form: “For a GIVEN protocol/algorithm/recipe, there is a finite level of detail which guarantees the outcome.”

If we assume that tomorrow will be much like yesterday, then this statement’s converse is falsifiable, though it may not be finitely so. This isn’t perfect, but it’s a long way from a leap of faith.

If we don’t assume that tomorrow will be much like today, we can’t get anywhere. Christians don’t assume this (they expect a Judgement Day, when tomorrow will decidedly not be like yesterday), but fail to realize that you could just as strongly assert that tomorrow there just wouldn’t be a god anymore. So, although I don’t know how to demonstrate the axiom, I don’t have demonstrate it in an argument between science and faith. I would need to demonstrate it in an argument between science and skepticism.

I have tried for a conservative estimate. The real cost may be anywhere from a third again as large to twice as large.

I have left out airfares for professors to attend study sections, paychecks of the bureaucrats, panels to assign grants to institutes, heads of study sections, time spent in study sections, and a wealth of other costs. Some of these are absorbed in the total award cost NIH reports for grants, since half of most grants disappears into overhead, both for the NIH and the institution which receives it.

How long does writing and reviewing take? How much does it cost? I assume $150/h as the going rate. This is what my mother, a professional science writer, charges. MDs and PhDs on the same projects regularly bill $200-$300 an hour. She estimates producing a document takes 2.5h/page and costs $375/page. Reviewing or editing a document takes 0.2h/page and costs $30/page.

An NIH R01 grant — the backbone of the funding system — is 25 pages long. In 2006, the average success rate (counting all repeat submissions as a single grant) was 0.128 (weighting new and continued grants by the number of each). The average award size with the same weighting was $363,731.08.

Each grant gets four reviewers. 25 pages takes 5h and costs $750. Writing it takes 62.5h and costs $9,375. The total cost for a single grant is 4*$750 + $9375 = $12,375. The time for a single grant is 82.5h. We can assign the reviewing cost without worrying about where in detail it should be counted: the reviewers are grant-seeking scientists as well, and someone must review their grants, so this is a shared cost in the community.

A success rate of 0.128 means we need to submit 7.81 grants in order to get one funded. Each R01 gets three resubmissions (which are still counted as one submission in the NIH statistics). Anecdotally, nothing is getting funded right now on first submission, so we have to multiply the expected number of grants by three, or 23.44 grant equivalents.

The mean cost of a successful grant is $290,039.06. The mean time for a successful grant is 1,933.8h. A full time job of 40h a week, 52 weeks a year is 2080h. Getting a grant is 0.93 of a full time job. It is 0.8 of the first year of the average grant size mentioned above, and remember that most of that money doesn’t make it to the professor at all. A full professor can reasonably ask for $220,000 a year. The first year and a third of the grant is eaten by the costs of getting the grant.

The final summary:
Cost of a grant: $290,039.06
Annual award of a grant: $220,000
Time to get a grant: 1,933.8h
Full time job: 2080h/year

Before we wade in to fix this, let’s set a target for what constitutes “fixed.” I say reduce cost and time to a tenth of their current value. Then we should develop a set of possible systems, and run controlled, randomized experiments to compare them.

‘Story’ is the concept that should underlie the structure of the entire paper. The clearer and simpler, the more engrossing it is. On that basis, think about relegating technical details — essential to the science but not the narrative — to a Methods section or to Supplementary Information (the latter published online). Similarly, figures should be designed to enhance the telling of the story and each accompanied by a caption that is as short as possible; to an expert reader, the information conveyed in a figure should be clear without needing to consult the main text.

Do exactly the opposite and you have begun well.

Shun captions. When layout was hard and expensive, pictures and graphs were excised from their surrounding text and typeset on their own pages. This time is behind us. Restore your figures to their natural environment. Dismiss the captions you set to watch over them.

Leave your scaffolding in place. When you have jailed your technical information in ‘Materials and Methods’ or exiled it entirely, what is left but verbiage, citations, and graphs taken on faith? The details of your analysis are shunted elsewhere. Even the measurement technique is banished from its point of use.

Supplemental information has one use: source code, analogous to plasmids and strains in genetics. We would attach our plasmids, too, if only we knew how.

Most damning of all, science isn’t stories. We reason about the world from hypotheses we have justified by stringent test. A mixing angle in quantum field theory is not a story, nor the Gibbs distribution, nor template directed synthesis of DNA. Their value is independent of any story around them. They have value as they provide traction for testing other hypotheses. Wrapping them in a story merely imposes on your reader to unwrap them.