Physicist Amok

I formulated a principle at a conference I just attended: ignore talks and posters with protein names in their title or the first sentence of their introduction.

It’s an issue of relevance. Each major discipline has its own concept of relevance. Roughly, a problem gains relevance as it constrains swathes of a field. Alain Aspect’s experimental tests of Bell’s inequalities was eminently relevant to physics because of the amount of speculation in quantum mechanics which they ended. Integrable models in statistical mechanics are less physically relevant because they only point out directions of interest in the limited corners where they were formulated.

Biology has its own relevance, largely dictated by evolution. Results are less relevant the more narrowly they apply to specific genera, species, or strains. Results on specific organisms are relevant only insofar as they can be combined with results in other organisms to produce a larger picture.

Chemistry has its own relevance, largely based on the fact that a carbon is always a carbon, a hydrogen is always a hydrogen.

Much of molecular biology, cell biology, and immunology is almost chemical in its aesthetic. Immunoglobulins share so much structure throughout vertebrates that studying them with an eye only to chemical relevance, as if an IgB were always and IgB, still has biologically relevance. DNA, that ubiquitous molecule, invites a chemical approach. Type III secretion systems vary enough among species to doom the purely chemical aesthetic.

As a rule of thumb, any molecule familiar to a random biologist from a random field is fair game for a chemical approach. DNA is justified. IgB is justified. A particular Rac GTPase or kinase involved in synthesizing a particular phosphoinositol are not.

If it is not, you must provide the biological context. What organisms, and what variation among them? What phenomenon caused this protein to rear its head? If the protein’s name has already appeared in the title, then relevance has been squeezed out.

madhadron :: Sep.27.2008 :: biology :: No Comments »

My laboratory does a lot of microscopy, and the image analysis tools available to us are largely inadequate. ImageJ is much more a viewing and processing environment, and the code base is sufficiently crufty and Java sufficiently inflexible to make extending it an exercise in futility. The academic libraries encoding many of the interesting algorithms are in C++, a language which I cannot decide is more atrocious for its design failure or the artificial walls it erects around any code written in it. Commercial packages such as Metamorph provide a fraction of ImageJ’s functionality with cuter artwork and a hefty pricetag. So when I find a new package, I don’t harbor much hope.

Definiens seemed different. The ideas were good: most of what you actually want to measure are properties of regions, and what you need are tools to operate on labelled image partitions, not just individual pixels.

The second stumbling block was the price tag: €3500 per license, plus an annual charge for updates and upgrades, and a few hundred more for training. But it’s science, and taxpayer money is wasted by the sheer inefficiency of the supplier market. If it were really a first class analysis environment, we could live with one license on a powerful machine and running a custom batch processing system next to it. Thankfully they expose enough of their APIs to write your own batch system which can run at the same time as the program itself. Given how little effort a batch processing system is, I wonder that anyone pays the €8,750 for their eCognition Server (functionally the same thing, with Perl bindings).

So I requested a trial license to play with, and play with it I did. I read their manuals. I read their API documentation and tested it. I spent several days, all day, working with the program, trying to make it do my bidding. In the process I lost all interest in the software.

First, the manuals are lamentable. The company operates in English, does not even have a German version of their website despite being based in Munich, all quite normal for a small scientific supplier, yet they could not hire a native speaker of English to make sure their manuals were grammatically correct. I could overlook that if they were insightful and taught you to use the software, but they are not. They define an enormous number of words informally, so many that I felt compelled to convert them into a set of mathematical statements to keep track of them, yet embedded in useless verbiage. They tell you a lot about handling the very complicated interface, but very little about actually doing anything with it, and that is when they are coherent.

For example, the introductory tutorial purports to take you step by step through a simple analysis, yet it jumps back and forth, refers to layers you create five sections later, and gets so bogged down in the intricacies of handling Definiens that it hasn’t time for any real instruction. I would not have completed it at all if I didn’t already largely understand what it was trying to say. It was useful for figuring out where they had stashed various functions I needed.

And that is the most damning flaw of the program. Its interface is so complicated, so ill designed and unsorted, that using it requires endless searching for a basic feature that you are sure must be there, but it is anyone’s conjecture what it will be called, where it will be, and what strange vocabulary will surround its use. If the underlying concepts really were this complicated, that would be one thing, but they are not. Half the complexity comes from mathematical naïveté — using trees of objects where lattices of partitions are called for, insisting on fuzzy logic as a foundation rather than extension to standard propositional calculus — and half from trying to wrap all the necessary mathematics in little graphical wizards instead of providing some kind of programming language. If you want to set a threshold to anything but a hard coded value, your must jump through a rather absurd number of hoops.

And to add insult to injury, it’s slow. When I handed it an 800 frame time series of 2D frames, it took forever to load — perhaps 100x longer than ImageJ — forever to redraw, and when I actually tried to perform operations on it, basic things like a quadtree segmentation, it took minutes to accomplish it. And then it crashed after three or four hours of poking at it.

I also took a moment to look at Definiens’s patent portfolio. Aside from some nonsense about using distributed algorithms for flow optimization on graphs for traffic control, they had the gall to patent semantic region growing in 2001, despite all the materials being publicly available in Ballard and Brown in 1982, and the technique described in language an undergraduate could implement in Sonka, Hlavac, and Boyle in 1999! They also have similar patents, from similar dates, out on basic motion tracking and other staples that have been well known in computer vision for fifteen to twenty years.

In summary, it’s not worth its exorbitant price tag, and the company has a rapacity for patents that should make the rest of us uncomfortable. Maybe it’s finally time to roll up my sleeves and write something that’s actually good.

madhadron :: Aug.31.2008 :: computers :: No Comments »

27 May 2008, Davos

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.

madhadron :: Jun.06.2008 :: Uncategorized :: No Comments »

(I’m posting a lot of things that fell through the cracks, beginning with this. )

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.

madhadron :: Jun.06.2008 :: physics :: No Comments »

I found myself in need of a rough form for the -decay spectrum, so I went and fetched Fermi’s Nuclear Physics from the library. I thought I would share a passage which suddenly made a lot of things go click for me:

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.

madhadron :: Apr.24.2008 :: physics :: No Comments »

Everyone is familiar with the derivative of a function in terms of limits: for a sequence converging to , . I spent a couple days playing with sequences which accumulate but do not converge, seeing if I could do calculus without limits. I came to my senses and realized I’m a biologist, but not before I stumbled across this:

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.)

madhadron :: Jan.15.2008 :: Uncategorized :: 1 Comment »

First off, happy birthday to Don Knuth. If you don’t know who that is, just crawl back under your rock.

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.

madhadron :: Jan.11.2008 :: Uncategorized :: No Comments »

Most metrics to compare programming languages — lines of code, number of symbols, compressed lines of code — hover between useless and harmful. Most of these metrics have one fundamental problem: they compare apples and oranges. Here’s a way to get past that hurdle. The resulting metric still seems broken and unjustified, but it’s an improvement.

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.

madhadron :: Dec.01.2007 :: Uncategorized :: No Comments »

I’ll get around to quantum mechanics eventually. Bear with me.

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.

madhadron :: Nov.28.2007 :: physics, teaching :: 1 Comment »

There’s been a hullabaloo about a New York Times op-ed by one Paul Davies which claims that rational ordering of the universe is an article of faith. Blog posts followed.

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.

madhadron :: Nov.26.2007 :: Uncategorized :: No Comments »