Tales from the Evil Empire : Science

Metrics in software and physics

Bertrand Le Roy — Sat, 14 Nov 2009 07:32:00 GMT

Every so often, somebody points out how bad of a metric code coverage is. And of course, on its own, it doesn’t tell you much: after all, it’s a single number. How could it possibly reflect all the subtlety (or lack thereof) of your designs and of your testing artillery? Of course, within all the various *DD approaches, some better than others enable you to know whether or not your code conforms to its requirements, but I thought I’d take a moment to reflect on the general idea of a software metric and how it relates to the mothers of all metrics: physical ones, cause you know, I used to be a scientist. Proof: the lab coat on the picture.

The theory of measurement is at the center of all experimental physics. This comes from the realization that any observation of the natural world is ultimately indirect.

For example, when you look at a red ball, you don’t directly perceive it. Rather, photons hit it, some of them are absorbed by the surface of the ball (violet, blue, green and yellow ones, but not red ones) and some of them bounce back (the red ones if you’ve been following). Those red photons that bounced back then hit your eyes, where a lens distorts their paths so that all those photons that came from a specific point on the ball converge to roughly the same spot on your retina. Then, the photoreceptor cells on the retina transform the light signal into electric impulses in your optic nerve, which conveys all that information into your brain and then, only then the complex mechanisms of conscience give you the wonderful illusion of seeing a red ball in front of your eyes.

The brain reconstructs a model of the universe, but what it really ever perceives is a pattern of electric impulses. Everything in between is a rather elaborate Rube-Goldberg contraption that can be trusted most of the time but that is actually rather easy to fool. That it can be fooled at all is the simple consequence that what you observe is an indirect and partial measure of reality rather than reality itself.

When we measure anything in physics, we build our own devices that transform objective reality into perceivable quantities. For example, when physicists say they have “seen” a planet around a faraway sun, they don’t (always) mean that they put their eyes on the smaller end of a telescope and perceived the shape of that planet with their own eyes like I saw the red ball of the previous paragraph. No, what they saw is something like this on a computer monitor:This shows the very small (1.5%) variation of the light coming from the star as the planet transits in front of it. All this really tells them is that something dark that takes about 1.5% of the area of the star passed in front of it. By repeating that observation, they can see that it happens every 3.5 days. That’s it. No image, just measures of the amount of light coming out of a powerful telescope aimed at a star against time.

But just from that minimal data and our centuries old knowledge of celestial mechanics, researchers were able to deduce that a planet 1.27 times the size of Jupiter but 0.63 times its mass and a surface gravity about the same as Earth’s was orbiting that star. That’s an impressively precise description of a big ball of gas that is 150 light years away (that’s 1.4 million billion kilometers in case you’re wondering or 880 thousand billion miles if you insist on using an archaic unit system).

The Rube Goldberg device that enables us to see that big ball of gas from so far away is a mix of optics, electronics and knowledge, the latter being the really awesome part. Science is awesome. The bottom line of all this is that although it seems less “direct” than seeing the red ball with our own eyes, it does just as well deserve to be described as “seeing” it. The only difference is that we’re not seeing with our eyes but more with our brains. How awesome is that?

Where was I?

Yes, you might be wondering what this has to do with software. Well, all that long digression was to show that little data is necessary to infer a lot about the object you’re observing. So code coverage? Sure, it’s just a number, but combined with a few other numbers, it can help get a reliable picture of software quality.

Another point I’d like to make is that a lot of resistance to software metrics comes from the illusion that we know a lot more about our own code than any tool can tell us. But as anyone who has ever tried to read code he wrote only five years ago knows, that is delusional. What you know about your code is a combination of what you remember and what you intended to write, neither of which is particularly reliably representative of what your code is doing. Tools give us a much more reliable picture. Sure, it’s a narrow projection of the code and it doesn’t capture its full reality, but that is exactly the point of a measure: to project a complex object along a scale of our choosing. What set of projections you choose to make is what determines their relevance.

The conclusion of all this is that we should assume that our code is an unknown object that needs to be measured, like that big ball of gas 150 light years away, if we want to get an objective idea of its quality without having our judgment clouded by our own assumptions.

And probably the best tool you can use to do exactly this by the way is NDepend by Patrick Smacchia.

The symmetrical universe

Bertrand Le Roy — Mon, 17 Aug 2009 08:01:21 GMT

Warning: this post is devoid of contents.

During one of the very first classes of my Bachelor of Science in Physics, I got struck with a particular piece of information that sounded like a revelation to me:

If a problem exhibits a certain symmetry, the solutions to this problem do not necessarily exhibit that same symmetry, but the set of solutions always does.

The example my professor was using to illustrate this is the following. Imagine you have the four summits of a square and you want to find how to connect each point to all of the others using lines, but the total length of those lines must be as small as possible.

The problem itself has mirror symmetry, central symmetry and rotational symmetry with an angle of 90 degrees. In other words, the four summits are perfectly equivalent and can be exchanged without changing the problem in any way.

Now here’s the weird thing. There are two solutions, which are themselves less symmetrical than the problem itself and that look something like this:

Notice how rotating any one of those by an angle of 90 degrees doesn’t keep it unchanged, but instead gives the other solution. In other words the set of solutions (those two solutions together) has exactly the same symmetries as the problem itself although each one of them separately doesn’t.

This is more far reaching than it seems and is nothing else than the phenomenon called spontaneous symmetry breaking that has been keeping a good number of physicists busy during the 20th century and the beginning of the 21st. Because there is only one universe that we can observe, whenever a physical process has the same characteristics as the above problem, the physical world has to choose one of the solutions and “break” the symmetry of the problem.

Now in any physical process, the experimental conditions are never perfect and small perturbations are likely to push the system to this or that particular solution so there is nothing super-weird about what’s happening here.

But there are phenomena where an external nudge to the system can’t explain the symmetry breaking: the ones that are at the origin of the universe. Cosmologists are actually still debating explanations to why the universe is so dissymmetrical (the arrow of time, the four fundamental forces, the inhomogeneity of matter, etc.) whereas the equations that seem to describe it are so symmetrical.

Many plausible explanations do exist, such as that our observable universe is part of a bigger “multiverse”. The weaker versions of this idea still consider a connected symmetrical universe that is one big multidimensional space-time continuum with different local regions where symmetry is broken in all possible ways. But why do we need the connectedness at all? Is it even an option? If you look at the square problem above, those two solutions are entirely disconnected and you couldn’t find a connected symmetrical solution if you tried. Why would the multiverse then need to be connected?

This leads us to the strongest version of the multiverse concept, the Mathematical Universe Hypothesis. The idea behind this is to attribute reality to all mathematical structures and to postulate that our observable universe is just one of this infinite number of structures (in an interesting case of taking the map for the territory).

Mathematical structures have this interesting property that they exist independently of culture, the human mind and even physics. Group theory for example could be discovered in any universe and would yield the exact same list of finite groups. In other words, they have lots of the qualities we associate with the reality of our own physical universe. Going from that to the idea that our physical world is just emerging from that primordial mathematical soup is quite tempting.

Now of course, it has been objected that such an idea is not testable or falsifiable and thus cannot be called scientific. That is absolutely true. But it does have that Occam’s razor quality of simplifying some of the apparent complexity of our universe. It also has the advantage of being an entirely naturalistic hypothesis to the origin of the universe if you’re into that sort of thing.

All this to give you an idea of the rush of ideas that went through my 20 year old brain at the precise moment when that professor showed us those two simple diagrams that you see above, oblivious at the time that those ideas that seemed so new and original to me had actually already been invented and debated a couple of years earlier. I felt at this instant the raw explanatory power of science and also its ability to extend its influence way beyond its self-imposed limits of testability. It is without a doubt the most powerful instrument of thinking and the best catalyst of ideas that the human mind has invented.

Quantum computing done right

Bertrand Le Roy — Wed, 01 Apr 2009 23:44:00 GMT

I know as a good microsoftee I should be supportive of what my employer does no matter what it is, and I might get fired for this post, but Eilon’s latest article is wrong on so many levels I have to step up with whatever integrity I have left and fix this mess.

In his post, he exposes the new ShrödingOr<TDead, TAlive> type that will be introduced in .NET 5.0 as part of the System.QuantumEntanglement namespace. Well, let’s face it, the current implementation has nothing quantum about it.

Here’s how I would have written it:

namespace System.QuantumEntanglement {
    public class SchrödingOr<TDead, TAlive> {
        private Complex _howDead;
        private Complex _howAlive;

        public SchrödingOr(Complex howDead, Complex howAlive) {
            _howDead = howDead;
            _howAlive = howAlive;
        }

        public Type Measure() {
            double howAliveSquareModulus =
                _howAlive.Real * _howAlive.Real +
                _howAlive.Imaginary * _howAlive.Imaginary;
            double howDeadSquareModulus =
                _howDead.Real * _howDead.Real +
                _howDead.Imaginary * _howDead.Imaginary;
            double probabilityOfBeingAlive = howAliveSquareModulus /
                (howAliveSquareModulus + howDeadSquareModulus);

            if ((new Random()).NextDouble() < probabilityOfBeingAlive) {
                _howAlive = new Complex(1, 0);
                _howDead = new Complex(0, 0);
                return typeof(TAlive);
            } else {
                _howAlive = new Complex(0, 0);
                _howDead = new Complex(1, 0);
                return typeof(TDead);
            }
        }
    }
}

This way, the state really is a (complex) linear combination of the dead and alive types, which are the eigenstates of the system. Once you’ve created the state, you can never get it back unless you do a measurement. When you do that, the object collapses its state to one of the eigenstates based on probabilities determined by the actual quantum state of the system.

The first measurement is random but once you’ve measured it, the cat remains alive or dead forever (the entanglement is destroyed by the measure).

Here’s a little console app that creates a cat, puts it in the box and then opens the box:

static void Main(string[] args) {
    // put the cat in the box
    var cat = new SchrödingOr<DeadCat, LiveCat>(
        new Complex(1, 0), new Complex(1, 0));
    // Open the box
    Console.Write(cat.Measure() == typeof(DeadCat) ?
        "Cat is dead." : "Cat is alive");
    Console.ReadKey();
}

This, I believe, is a much more realistic and useful implementation of SchrödingOr.

The code: http://weblogs.asp.net/blogs/bleroy/Samples/Quantum.zip

Eilon’s original article: http://weblogs.asp.net/leftslipper/archive/2009/04/01/the-string-or-the-cat-a-new-net-framework-library.aspx

Deep thoughts on scientific research

Bertrand Le Roy — Fri, 29 Sep 2006 22:22:00 GMT

Heard on France Inter the other day about scientific research funding (didn't catch the names of the authors of these quotes though):

"Ignorance will always be more expensive than research."

"Electricity wasn't discovered by trying to improve the candle."

The duck's wake

Bertrand Le Roy — Wed, 01 Mar 2006 08:31:00 GMT

This is the first translation I'm doing of one of my French science popularization blog posts.

When I was preparing my PhD thesis a few years ago, I was also doing weekly hour-long preparation sessions for groups of three students to train them for the engineering schools contests. In these sessions, each student is given a problem that he must solve on a chalkboard.

The students were often brilliant and showed a great physical sense.

One of my favorite problems was the following: "the duck's wake". The student was supposed to figure out both the questions and the answers. Great exercise if you ask me and very revealing of the student's qualities or lack thereof. Here are some of the things you could say on this subject...

Let's simplify and suppose that the duck is a dimensionless point. When it moves on the water surface, it casts waves. Let's imagine these circular waves travel at an approximately constant speed (in reality they don't, more on that later). There are two possibilities: the duck can move slower than the waves, in which case the first wave will always be ahead of all the others, or the duck is "supersonic" and the waves will form a triangular wake. The first question you can ask yourself is to determine the relation between the angle of the wake and the speed of the duck. As could be expected, the faster the duck, the sharper the angle. The angle would be 180 degrees if the duck had the exact speed of the waves: the wavefront would be a line perpendicular to the direction of the duck and it would move with it.

The triangle that the wave's enveloppe creates is really a shockwave similar to the one that a supersonic plane emits. The supersonic bang is just the shockwave. Contrary to popular belief, the bang is not emitted by the plane as it passes the speed of sound but is continually emitted as long as it travels faster than sound. The thing is that the places where the bang can be heard move at the speed of sound. What you hear when a supersonic plane flies by is thus, to summarize: silence as long as you're outside the sound cone, a bang as you enter it, and the noise of the plane after that.

The second question you could ask is the repartition of energy in the shockwave. The result of the calculation is really surprising: the energy diverges and becomes infinite at the tip of the cone. This means that you would need infinite energy to go above the speed of sound. I suppose that's one reason why people used to think it was impossible. Of course, it's not really infinite in practice, just very expensive because no plane or duck is a point.

So now we know that any object that travels faster than the waves it emits emits these waves as a shockwave that packs most of its energy in its enveloppe. This phenomenon is commonly observed for surface waves (a duck's or a boat's wake) as well as for sound (supersonic planes). Now can it be observed for lightwaves?

A priori, no physical object can travel faster than the speed of light in a vacuum, so this phenomenon looks like something that would be out of the question. Nevertheless, light doesn't always travel in a vacuum. In any medium, light travels slower than the speed of light in a vacuum. It is thus possible to travel faster than light in a medium. The shockwave that the theory predicts does exist and is a commonly observed phenomenon called Cerenkov radiation. It is this radiation that is used in some neutrino detection devices.

Neutrinos are subtle particles. They have a very low mass (it's only recently that we've discovered thay have one), they don't have an electrical charge, don't participate in the strong force and the only way they interact with anything is through improbable weak interactions (gravitation can be neglected for detection purposes, the neutrino masses being so small). Despite their being very common particles in the universe (billions of neutrinos go through us every second), as they rarely interact with ordinary matter that is made from electrons, protons and neutrons, their detection is very difficult. Some detectors use the Cerenkov effect. When a neutrino interacts inside the detector, a particle such as an electron can be emitted with a faster than light speed. This particle emits light while decelerating (any charged particle accelerating emits electromagnetic waves). The resulting shockwave is then measured by detectors, from which we can deduce the trajectory of the charged particle, which gives us the direction of the neutrino that created it.

This is how you can start from the duck's wake and end up discussing the detection of neutrinos. That's just one illustration of the extraordinary explicative power of physics...

UPDATE: comments pointed out that the angle of the wake of the duck (or of a boat, or of whatever moves fast enough) does not depend on the speed of the object, as the good Lord Kelvin showed. It is constant at approximately 39 degrees. This is because the speed of the waves depends on the wavelength in such a subtle way as to cancel the dispersion that a single wavelength wave would show. Our simplistic calculation is still perfectly valid for cases where such dispersion doesn't exist, such as Çerenkov radiation.

Black hole evaporation paradox?

Bertrand Le Roy — Wed, 15 Dec 2004 00:45:00 GMT

I just sent this letter to Scientific American. I'd be interested to have any informed opinion on the matter.

I’ve read the article about black hole computers with great interest, but there are still a few questions that I think remain unanswered.

The article makes it quite clear how black holes could be memory devices with unique properties, but I didn’t quite understand what kind of logical operations they could perform on the data.

But another, more fundamental question is bugging me ever since I read the article. From what I remember learning about black holes, if you are an observer outside the black hole, you will see objects falling into the black hole in asymptotically slow motion. The light coming from them will have to overcome a greater and greater gravitational potential as the object approaches the horizon, losing energy along the way and shifting to the red end of the spectrum. From our vantage point, it seems like the object does not reach the horizon in a finite time.

From a frame that moves with the object, though, it takes finite time to cross the horizon.

This is all very well and consistent so far. Enter black hole evaporation.

From our external vantage point, a sufficiently small black hole would evaporate over a finite period of time. So how do we reconcile this with the perception that objects never actually enter the horizon?

It seems like what would really happen is that as the horizon would actually become smaller over time, the incoming particles would actually never enter it.

If this is true, and no matter ever enters it, would the black hole and the horizon exist at all?

From the point of view of an incoming object, wouldn’t the horizon seem to recess exponentially fast and disappear before it is reached?

If nothing ever enters the horizon, is it really a surprise that black hole evaporation conserves the amount of information?

Does the rate of incoming matter modify the destiny of the black hole? If it grows faster than it evaporates, I suppose the scenario is modified, but how so?

I know it is quite naïve to think in these terms and that a real response could only come from actual calculations, but still, I hope that you can give me an answer to what looks like a paradox to me. I don’t see how you can reconcile the perceptions of an external and a free-falling frame of reference if the black hole evaporates except if nothing ever enters the horizon.

UPDATE: a recent paper presents a similar theory to solve the information paradox:

http://arxiv.org/abs/gr-qc/0609024v3
http://arstechnica.com/news.ars/post/20070622-apotential-solution-to-the-black-hole-information-loss-paradox.html