Reductio ad absurdum

abeilles Reductionism is the idea that all known phenomena are the simple sum of simpler, more fundamental ones.

It has worked really well in science, and it could even be argued that reduction is a good part of what science is.

Chemistry is well explained by the interactions of atoms, atoms are well understood as a quantum assemblage of protons, neutrons and electrons, and protons and neutrons are quarks bound by their strong interaction mediated by gluons.

Another example of very successful reduction is thermodynamics. Thermodynamics provide a set of consistent and successful laws that rule the behavior of macroscopic quantities such as temperature, pressure or volume. You do not need to understand the microscopic dynamics of atoms and molecules in a gas to use it and understand how a fridge or a thermal engine work. Still it’s true that using only statistics and some simple dynamics, you can derive all the laws of thermodynamics. Reductionism win!

Now take higher-level phenomena such as sociology or psychology. It would seem absurd to claim that these can be reduced to the quantum interaction of subatomic particles. More importantly, it would be sterile and counter-productive to attempt it. Not to mention impossible in practice.

A second way in which reductionism can fail besides practical irrelevance is in the assumption that you can effectively separate reality in distinct layers that don’t interact with one another. In particular with non-linear or chaotic phenomena, small uncertainties in the state of lower layers can translate into very large differences in the higher layers (the so-called and much misunderstood butterfly effect). This also means that in turn, higher layers can affect the lower ones in inextricable ways.

Take evolution for example. Biology is reducible in principle to chemistry (and biochemistry is a triumphant discipline that has probably done more for the betterment of humankind than most), but the interactions of living bodies run so deep and are so tied to environmental factors (even though those are also reducible in principle), and they do in turn affect their own environment in such important ways that it is impossible to give a complete picture of evolution based only on chemistry.

But in principle, each layer does strictly depend on the underlying, more fundamental layer. To this day, there are no phenomena that expose demonstrable contradictions with lower layers. Such a contradiction could come for example in the form of a macroscopic phenomenon not conserving energy. Here you would have a quantity that is valid at both levels but that would behave differently at the higher level than it does at the lower one. This never happened so far.

In other words, the failures of reductionism are not failures of the principle, they are failures of practical applicability and relevance.

Reductionism is not sufficient anymore in the scientific arsenal. It does however remain extremely useful and we do still rely in many cases on its theoretical validity.


More fundie fun

snakeThere is an article on stupid Conservapædia (that I won't grace with a link) that rants about the theory of Relativity because apparently it contradicts the Bible. Well, what doesn't? Even the Bible contradicts the Bible...
Anyways, here is how that fantastic piece of entertainment begins:

"The theory of relativity is a mathematical system that allows no exceptions."

Well, wrong. This just shows how much these clowns understand about science: nothing at all.
The theories of Relativity are *using* mathematical tools, but they are not about the tools, they are about the physics of high energy phenomena and strong gravitational fields. So they got the most basic definitions wrong. But of course they did it on purpose you see, because mathematical theorems suffer no exceptions (which is precisely why math is not science) whereas physics is perfectly fine with limiting its own theories to a specific experimental range.
It's worth repeating: if science knew everything, it would be over and nobody would do it. Only engineering would remain. Contrast that with religion, which was done once and for all thousands of years ago and that people are still doing today.
This being said, I think the authors of the silly piece in question should stop using their GPS right now, cause you know, of being an insult to God and all.


When failure is a feature

I was reading an article in SciAm this morning about the possibility of a robot uprising. Don’t laugh yet, this is a very real, if still quite remote possibility.

The main idea that was described was that AI could rise one day to self-awareness and to an ability to improve itself through self-replication beyond human abilities to control it.

Sure, that’s one possibility, and some people are actually arguing that if that’s the case, maybe it’s just the march of evolution and humankind is just destined to one day become obsolete and be replaced by something fitter, whether from good old evolution or by artificially creating its own replacement.

I would tend to agree but I do have an objection. There is a distinction in this kind of speculation that is not often pointed out: self-replication and evolution are not the same thing.

We don’t know exactly how a self-replicating pre-biotic device emerged out of inanimate matter a few billion years ago, but that it did and that it managed to evolve to the variety of life that we observe today was only possible because of one crucial little feature of the whole system: failure.

Because they arose naturally, the first pre-biotic replicators probably were clunky little things that were only working within specific conditions and that were failing often. In particular, such an imperfect replication mechanism could fail in lots of different ways under the influence of a varying environment.

And this is precisely what enabled them to mutate into something a lot more interesting. That ability to create imperfect copies of themselves is what made it possible for early organisms to adapt to an environment that is sure to change (from external causes as well as under the influence of the organisms themselves on their own environment).

Guess what? This “strategy” has been so successful that it is still a feature of all living organisms today. You’d think that organisms could have evolved to remove the imperfections and to ensure perfectly faithful self-replication. But that in the long run would be a losing strategy because the next time the environment changes in a way that is no longer compatible with your perfection, you die and leave no successor.

In fact, modern organisms did evolve such perfecting mechanisms that suppress mutations from expressing themselves, but the amazing thing is that this suppression can fail under stress, which might be part of what you observe at times of mass extinctions, which are also fertile events in that they trigger the appearance of a large number of new species that are fit to the new conditions in a geologically short amount of time.

Sex on the other hand is another evolved way of introducing variation into the genes of a population. In other words, sex is the greatest invention of all times after failure.

What I’m getting at is that we may be able in the not so remote future to create self-replicating machines and when we do, we might make the mistake of making the replication perfect. It may actually be a lot simpler to do so: the easiest to build self-replicating structure probably is a lot simpler than the messy stuff nature came up with through random processes and selection.

And if the replication is perfect, this leaves no room for anything new, ever. What it could allow on the other hand is a reproduction mechanism that is much more efficient than anything life has been able to invent yet, the sort of manufactured efficiency that could take over the planet.

Self-awareness is clearly not necessary for self-replication and might even impair it so why they are packed together so often is kind of a mystery to me.

So why am I talking about this today? To make the larger point that failure can be an essential creative force and that without it the world would be a cold and sterile place where creativity has no role to play.

I often tell my 6-year-old that if she never fails, she will never learn. Failed ideas for example are at the heart of the concept of brainstorming: failure is the path to success.


Wild non-scientific musings: extra dimensions and parallel universes

fig. 8Amy was asking me some questions on "alternate dimensions" and "parallel universes". Here's my answer, which is entirely non-scientific although it is based on a few things I know (or think I know) about physics. I'm suspecting for example that the string theory stuff is a little shaky as I never really studied the math in there.

Alternate dimension doesn’t mean much in itself: alternate to what, and how? A dimension is a direction in space-time. We experience the four known ones every day: width, height, length and time. But there are many physical theories such as string theories that postulate additional dimensions. Why we don’t experience them has different explanations. One is that some of those dimensions may be closed on themselves (think circle vs. open line) with a very small radius. Such an additional dimension would be hard but not impossible to detect. We may actually know in the next few years as there are experiments being built right now to test that hypothesis (negative results wouldn’t entirely rule out the possibility but would put a limit to the radius of space along those dimensions). By the way, there is an interesting theory from the 20th century that was able to unify gravitation and electromagnetism through an additional closed dimension. It suffered from a number of problems and was more or less proven wrong but it was an interesting idea that all forces would somehow come from the geometry of a larger space-time.

Now a parallel universe is a completely different idea. It’s the idea that what we perceive as our universe is only a fraction of physical reality, and that other similar or entirely different universes may exist somewhere else. You then have the idea of a metaverse that contains all of those, which should be what we really call Universe if we used words appropriately.

As to where those universes might be, there are several possibilities, not necessarily exclusive of one another. First, according to string theories, we live on a kind of multi-dimensional “brane” which is like a slice of a bigger space-time (read with more dimensions) to which the particles we’re made of cling. There would be more open dimensions in this view that we don’t see because the particles we’re made of are inherently bound to a particular brane: they only exist as part of it, they are a property of that particular brane if you want. In that view, there are other branes with other universes that may be as big as ours. Sometimes, actually, these branes can get close to one another or even collide, which gives us a possibility of confirming their existence by observing the effects of cross-brane interaction (for example, matter from one brane might gravitationally affect matter on another, and the closer branes are, the bigger the effect, which is interesting as branes are not flat and distance between them is not fixed).

Another idea that is also realized in string theory is that there is a multi-dimensional landscape of universes, and that one universe can experience a local instability that turns into a completely new baby universe that expands on its own, with physical laws that are a variation of the ones in the parent universe. It’s an interesting concept because it gives rise to the idea that a large number of universes might evolve from a larger cosmos. Here the word “evolution” is not used lightly: it would really be the case that there would be a form of survival of the fittest where the most common universes would survive and give birth to more and more stable baby universes. In both versions of parallel universes, the smaller universes are still connected within a larger Universe

But there is yet another possibility which I think is quite interesting, although completely untestable.

The idea would be that parallel universes don’t have to be connected to one another at all: why should there be one single connected universe, all in one piece? You could actually postulate that any universe that is self-consistent would just exist by virtue of being possible. For example, the group Z2, which is a mathematical structure described by: 1 x 1 = 1, 1 x -1 = -1, -1 x 1 = -1 and -1 x -1 = 1 just exists, and it exists outside of any universe we may be in. It’s just universal, it doesn’t need a creator god or to be observed to exist. It just is. How about our universe just is one of those mathematical structures, only much more complex, that just exists by virtue of being consistent? Am I confusing the map for the territory? Am I? I mean, if we discover one day that the world’s natural laws can be reduced to a relatively simple mathematical structure (and we have lots of indication that it could from looking at elementary particles), how much of a stretch would it be to say that the universe actually *is* that mathematical structure? I mean, if it’s indistinguishable from it, isn’t it just the same?

We could then talk about how consciousness fits into all this but that’s a whole ‘nother discussion.


News from the gym: oh the hypocrisy!

Davy safety lampUh oh, I've been watching Fox at the gym again...

The big thing they were talking about was Harry Knox, a White House advisor, having said the Catholic Church was "hurting people in the name of Jesus" by forbidding the use of condoms. Fox pundits of course were outraged, their arguments being that scientific consensus was agreeing with the Pope that condoms weren't preventing the spread of AIDS and that the Catholic Church was saving a lot more lives through its charities than Knox's organization, HRC.

Let's look at these claims.

The claim that science agrees with the Pope probably comes from here: But Green says "I believe condoms should be made available to everyone. It should be, and as you say, the ABC strategy: Abstain, Be faithful, use a Condom." If his findings are correct, they only show that condom distribution pushes people to more risky behavior, but condom usage is perfectly efficient. As often, there is no silver bullet and a multi-pronged approach is often preferable. But this kind of subtlety totally escapes Fox and the Catholic Church, which promotes abstinence as the only acceptable contraception. What they forget is that abstinence has been demonstrated time and again to be terribly inefficient and counter-productive: that case as well, the distribution of the contraceptive method is harmful, although the usage obviously works. Except that using the pill or a condom is much easier to achieve than abstinence.

And of course, there is the motivation. The reason why the Church prohibits contraception methods is not disinterested, nor is it to apply good science or to limit the spread of diseases. They couldn't care less about that. The subtext is that extramarital sex and of course homosexuality are considered by them as sin, and they don't really mind sinners dying from their sins. When they don't explicitly wish for it to happen.

Then there is the claim that the Church saves more lives through its charities than Knox's organization. That is probably true and clearly something that should be praised, but how the hell is it relevant? If you are a brain surgeon AND a serial killer, does the surgery excuse the killing if you save more lives than you take? This is just irrelevant.

On other news, I heard some tea party idiot on NPR saying that "people who can't spell 'vote' elected Barack Hussein Obama" (emphasis on Hussein of course). This is wrong on so many levels. So wasn't what triggered the original Boston tea party "no taxation without representation"? That implies that immigrants should have a right to vote where they pay their taxes.

Oh, and I also heard Bill O'Reilly ask why Obama's birth certificate had never been produced. Seriously. Wow. Incredible that a channel that claims to be a news channel couldn't do the very basic fact checking that I just did in less than ten seconds:

People, when you are proven wrong, it's OK to say "I was wrong". It will actually make you more credible the next time you're right (whenever that may be).


How to build 2D glasses

My two pairs of 2D glasses It’s the week-end, which is the perfect time for a slightly off-topic post. It’s still engineering of sorts though in that it provides what I think is an original and cheap solution to a real problem.

3D movies are all the rage recently. But they are not comfortable for everyone. A friend of mine recently went with her family to see Avatar in 3D and instead of enjoying this rather good movie experience, she had to leave the theater after 20 minutes, suffering from a terrible headache. Of course, removing the glasses is not a solution because you then see both of the images –the ones destined for your left and right eyes– at the same time, blurring most of the screen.

Before I explain my solution to this problem, let me explain how modern 3D movies work.

Most 3D viewing technologies rely on providing a different image to the right and left eye. They are not reproducing an actual 3D structure like holography does. Rather, they feed later into the series of events that end up with perceived volumes. It works fine for movies, but you will never be able to walk into or around a scene with any of these techniques. Holodeck they are not.

The problem is to project both images on the same screen but still allow goggles to separate them. Several approaches exist, the most simple being the infamous red and blue glasses that use the plasticity of the brain when perceiving colors. Another interesting approach is to re-use retinal persistence not just to make what is a series of static images look like something that moves, but to multiplex two versions of the same movie into one. In other words, slice time, alternate left and right images and synchronize that with shutters on each eye. This has the advantage that it can work without special screens or projectors, only special glasses and a feed into the sync signal of the screen or of its video source.

What is used in movie theaters is quite different though and relies on a subtle quality of light that our eyes are completely blind to. Our visual sensors (a.k.a. eyes) are fantastic devices but are quite limited in a number of ways: they only perceive three color ranges out of the infinitely fine light spectrum, they frequently go out of tune and require correction and surgical intervention, and they do not see polarization at all. That last quality opens a uniquely neat way of creating stereoscopic vision.

Polarization is a quality of all transverse waves (of which light waves are one example and sound waves are not). Transverse waves are the propagation of a displacement that is orthogonal to the direction of propagation. Because we live in a three-dimensional space, that leaves two directions for the wave to wiggle in addition to the propagation direction. A light ray aimed directly at you may vibrate horizontally or vertically, or in a combination of both, but you won’t see the difference because the eye only sees the amplitude and some frequency information, not that directionality. This means that you can have two completely independent signals at any given frequency (which for light means color) simultaneously propagating in the same direction. You can see where this is leading: you can have the left and right images coexist in the same beam. All you need is to separate those images with glasses that see only one direction to create the illusion of volume.

Early polarized movies were using the linear polarization that I just described in a technique that is older than you may realize. For example, when I was a kid, I saw Hitchcock’s Dial M for Murder in 3D using linearly polarized glasses.

Modern 3D movies use a variation of polarization called circular polarization where light is split not in horizontal and vertical components but in clockwise and counter-clockwise rotating components. This has the advantage of better maintaining the illusion when you rotate your head. It’s not perfect because the images are still shot with a horizontal offset but it definitely helps.

In both cases, the left and right images travel on the two polarized components of light and they are split by the glasses before they reach the eye. As you can see, it’s a good thing for all this to work that we only have two eyes…

So what do we do for my poor friend who can’t watch those movies for any prolonged period of time? Well, that’s fairly easy, we suppress the 3D effect by feeding her only one of the two images. We do that by building her a pair of 2D glasses that filter out and send the same image to both eyes.

To build that pair of glasses, I bought two pairs of circularly polarized glasses from e-Bay (they are quite easy to find and go for a dollar or two) and broke them open to extract a left filter out of the first pair and a right filter out of the second pair. I then exchanged these filters and glued the frames back together. The result is two pairs of glasses, one of which will see only the right image, the other seeing the left image. In effect, my friend can now enjoy the same movie as the rest of her family in the same theater, except that to her and to her only it just looks like a plain old 2D movie. It’s just as comfortable as seeing the movie in a regular movie theater except for the weight of the glasses. No movement of the head affects the experience.

A small note on polarized sunglasses and why they wouldn’t work here. First, wearing sunglasses in a movie theater would further obscure even David Lynch’s Inland Empire. More importantly, polarized sunglasses use linear polarization because they are designed to eliminate specular reflection from the sun off water or ice and to eliminate part of the sunlight scattered by the atmosphere, both of which are linearly polarized.

Understanding polarization:

The RealD Cinema technology:

Note: feel free to build your own 2D glasses for your own personal use, but please contact me for any bigger-scale use of the idea.


News from the gym

I don't watch the news and to be honest I don't understand why anyone with half a brain would. That is, I don't watch except when they put a screen in my face with the captions on like it's the case at the gym. I didn't think I would ever regret being able to read. A TV screen is a terrible thing: it's very hard not to look at it. And I had forgotten the Zune.
So I watched the news.
Here's what I learned...

  1. Some random woman got condemned for murder. Not sure how this is newsworthy but that's all they talked about on CNN while I was there.
  2. Some famous golf player did something apparently not very nice. Not sure who or what, I think I my brain might have gone to sleep at that point.
  3. We might have to reconsider all the scientific results for the last five centuries, because apparently a bunch of scientists are vicious assholes.
  4. There is a segment on Fox News called "the dumbest thing of the week" that surprisingly isn't a best of what they said during the week. That's when I noticed the blood coming out of my eyes.
  5. Surprisingly, the dumbest thing I heard this week wasn't on Fox, it was on NPR in the car on my way back home. They were interviewing a guy who had raped 11 of the children that he was coaching, and he was saying that it was all right now because God had forgiven him. So apparently what's important is not that the people you hurt forgive you, what's important is that some hypothetical deity does.

Must think of taking the Zune next time...


Metrics in software and physics

A Horrible experiment 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:What a beautiful planet!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

(c) Bertrand Le Roy 2005 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:How to minimally connect the summits of a square

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.


Deep thoughts on scientific research

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."