The Mystics and Realists of Quantum Physics

It is said that when the 20th century is long gone, it will be remembered for two revolutionary theories – those of relativity and quantum physics. While both have led to a deeper understanding of our world, quantum physics stands alone in its profound weirdness – the ability to accurately predict totally counter-intuitive aspects of the physical world. From the simple indisputable oddity of the double slit experiment to the philosophical implications of Schrodinger’s cat, it becomes clear that we still understand very little of the actual mechanics of our world.

When explanations are lacking, the mystical is often brought up to fill the void. This has degenerated today into complete pop-psychology crap such as The Secret or What the Bleep Do We Know, but the role that human consciousness plays as an “observer”, if any, was considered very early by the founders of these theories. These arguments brought forth by some of the finest thinkers of our time echo to this day.

Niels Bohr


Winner of the Nobel Prize in Physics in 1922, employed by the Manhattan Project, and father of the Bohr model familiar to every high school student, Niels Bohr was first accused by Einstein of introducing “mystic” elements in his explanation of quantum physics – mystic elements which in Einstein’s view had no place in science.

This was part of the famous Bohr-Einstein debates, and was perhaps not a fair criticism. Bohr appeared to not worry excessively about the “reality” underpinning the equations of quantum theory, and was simply more concerned about the equations of quantum theory rather than their implications. He rejected the hypothesis that the wave function collapse requires a conscious observer, insisting that “It still makes no difference whether the observer is a man, an animal, or a piece of apparatus”.

His view is perhaps best summarized in the following quote recalled by Heisenberg:

This argument looks highly convincing at first sight. We can admittedly find nothing in physics or chemistry that has even a remote bearing on consciousness. Yet all of us know that there is such a thing as consciousness, simply because we have it ourselves. Hence consciousness must be part of nature, or, more generally, of reality, which means that, quite apart from the laws of physics and chemistry, as laid down in quantum theory, we must also consider laws of quite a different kind. But even here I do not really know whether we need greater freedom than we already enjoy thanks to the concept of complementarity.

In short, if the numbers work out, don’t worry too much.

Wolfgang Pauli


But some did worry. Pauli was a skeptic’s skeptic – a man so dedicated to rationality it led him down a strange path. In 1927 the Solvay Conference was busy reaching consensus that Bohr’s approach was the best way to regard quantum physics (the Cophenhagen Interpretation), but Pauli was equally confident in a different interpretation. He tried to trace out just what part of consciousness it is that seems to prevent an in-depth, rational understanding. Deeply influenced by Schopenhauer’s The World as Will and Representation, Pauli appropriated his concept of a will “which breaks through space and time”.

He viewed that the acquisition of knowledge in mathematics or quantum physics “gives rise, however, to a situation transcending natural science” that can even acquire a “religious function” in human experience. This is not a belief in the religions of old, but as Pauli states “I do not believe in the possible future of mysticism in the old form. However, I do believe that the natural sciences will out of themselves bring forth a counter pole in their adherents, which connects to the old mystic elements.”

Perhaps the most interesting viewpoint on Pauli was that of Heisenberg, who viewed Pauli’s paradigm as even more rational than Bohr’s equation-focused approach because only he acknowledged that the scientific evidence pointed to something pre-rational or ‘mystical’. Pauli claimed that consciousness was presented philosophically by mystics and studied scientifically by psychologists. With the advent of quantum mechanics, physicists should then be able to unify both approaches. Unfortunately, we continue to wait.

Albert Einstein

Einstein 1921

Einstein was a scientific superstar, with fame not equalled to this day. One day, a quote was making the round in British newspapers that Einstein subscribed to the theory that “the outer world is a derivative of consciousness”. His response was swift and critical.

No physicist believes that. Otherwise he wouldn’t be a physicist. Neither do [Eddington and Jeans]. . . . These men are genuine scientists and their literary formulations must not be taken as expressive of their scientific convictions. Why should anybody go to the trouble of gazing at the stars if he did not believe that the stars were really there?

Einstein’s opposition to Bohr’s view or more “mystical” approaches is often cast as the great divide between the philisophies of idealism and those philosophies based on realism. Pauli often referred to Einstein’s “philosophical prejudice” assuming that reality is independent of any mind. In fact, his approach and objections were far more subtle. His major concern was the incredibly subjective aspect of consciousness introducing an unmeasurable “geist”, and this clash with the precise and well defined philosophical principles of physics such as locality or determinism.

This led to Einstein’s famous attempt at “breaking” quantum physics, the EPR paradox. At first a thought experiment which appeared to demonstrate quantum physics violating the seemingly well established principle of locality, later experiments showed that quantum physics instead proved locality false.

Violations of locality and determinism seemed to bother Einstein greatly, and this can be seen in his famous quote objecting to the randomness involved in wave function collapse under Bohr’s interpretation, that “God does not play dice”.

Bohr, summing up the debate perfectly, replied “Einstein, stop telling God what to do with his dice.”

John von Neumann


The “last of the great mathematicians”, von Neumann solved one of the great problems of quantum theory. While the theory itself was established and experimentally verified, it lacked a “deep” mathematical understanding based on an axiomatic approach. He treated the world as a Hilbert space, an infinite dimensional structure.

While classical mechanics approached the world as a collection of points with six different characteristics (position and momentum along the x, y, and z axis), von Neumann’s approach considers a quantum system as a point in infinite dimensional space, corresponding to the infinite amount of possible outcomes. This led to very interesting implications in terms of “measurement”. While the “measurement” of a classical system simply involved finding one or more of those six values, the “measurement” of a quantum system involved mathematical operators acting on an infinite amount of values to produce a finite measurement.

The interesting conclusion arises when we consider the “real” interpretation of these mathematical operators. While we may say that an scientific instrument has caused wave function collapse, we run into the problem that no physical system (and a scientific instrument is a physical system completely described by quantum mechanics) can cause wave function collapse. We can describe the entire ensemble perfectly as a Hilbert space. But we do not experience this Hilbert space – we measure and experience only finite values.

The conclusion von Neumann reached is that consciousness, whatever it is, appears to be the only thing in physics that can ultimately cause this collapse or observation. This does not mean that consciousness is “required” for the universe to work, but that wave function collapse appears to be caused by consciousness and we observe only a tiny slice. We are therefore an “abstract ego” acting as a measurement device on the infinite values of true reality.


Today, the argument has largely died down, a combination of practicality and lack of any suitably shocking experimental results. The majority of physicists today take the approach of “it works”, namely that quantum physics produces accurate predictions of the real world and that the mathematical formalism is just that – a mathematical formalism that produces accurate results.

It may not reflect the true reality of the world (whatever it is), but it is suitably accurate to any level of precision that we are physically able to obtain. One may stay awake at night wondering “why”, but one will not get much work done with this approach. Perhaps more clarity lies in the future, but in the meantime – we will have to tolerate crap that tells us we can “will” our way to riches with quantum mechanics (and coincidentally make the authors rather rich, will indeed) instead of a rational approach dedicated to the pursuit of truth.

Human Evolution and Frameshift Mutations

How did humans evolve from early primates? How did “human like” traits such as a smaller jaw relative to apes and hairlessness pop up when they don’t appear in the wild in any real frequency? The typical explanation for why humans have smaller jaws than early primates is that our diets changed and our brains got bigger, pressures that caused a smaller jaw. But there’s another way to look at this – what if our diets changed and our brains got bigger due to proto-human society dealing and adapting to an increasingly frequent and nearly catastrophic mutation of the jaw?

Myosin Heavy Chain 16

The human and chimpanzee genomes have both been mapped, so we are able to make comparisons between them. This is extremely useful, as chimpanzees and humans shared a common ancestor, but genetic lines split apart approximately 7 million years ago. So examining the differences may tell us something about how humans evolved.


There is a protein called myosin heavy chain 16 (aka MYH16) which in chimpanzees and other non-human primates is expressed almost exclusively in their powerful jaw muscles. These strong jaws are an adult trait – a logically complex one that would be more sensitive to random mutations.

And that’s exactly what seems to have happened. Non-human primates have DNA that codes for the complete MYH16 protein. The corresponding part of human DNA is missing a random chunk – which causes a frameshift mutation.

Frameshift Mutations

What is a frameshift mutation? Well, first let’s find out how we build proteins. We have a strand of messenger RNA (imagine a long tape with letters on it) which a ribosome (hell, imagine a tiny elf) uses to produce proteins. The critical thing to consider is that a ribosome builds a protein by reading three nucleotides at a time, and these three nucleotides code for a certain amino acid. These amino acids are chained together to produce proteins. Some combinations of three nucleotides can also act as “punctuation marks”.

"Wait, did you say there's three million more pages after this?"

So our wee elf looks closely at the long tape of letters, and starts off with the first three. His “frame”, the little chunk he works on, is three letters long. This frame is an instruction to build a certain amino acid, which he makes. He then goes along the tape, three letters at a time, making an amino acid each time that he sticks onto the last. This will eventually create a long chain of amino acids that we call a protein. But each frame doesn’t need to code for just an amino acid – it can also code for other instructions (those “punctuation marks”) starting or stopping this chaining process.

Now you may have guessed what a frameshift mutation is by now – it’s where a single letter in our tape disappears, or a new random one gets thrown in, causing our frame to get shifted slightly. This means that the resulting triplets after this error will be horribly wrong. It’s like the difference between


if one were to speak in sentences containing only three letter words. The first sentence makes sense if we parse three letters at a time. The two others have a random letter removed, and a random letter added in. If we parse them three letters at a time, the sentence turns into garbage halfway through! The resulting nonsense (or malformed protein) is a result of a random insertion or deletion of information (nucleotides) and our “frame”, the manner in which we interpret it.


So a frameshift mutation occured in early humans that affected the production of the protein MYH16. This protein is involved in the strong powerful jaws that primates have, but not humans. We often think of mutations as a simple little “blip” in the genetic code, but the way our bodies parse this code can cause cascading effects. Instead of MYH16 having a slightly different amino acid in a random spot from a random mutation, the specified amino acids after the mutation will change completely!

So you might think that we’ll have some odd protein that’s mostly normal, and the parts after the mutation affected by the frameshift will be wonky. But – and this is an important but – the triplets code for “punctuation marks” too, remember? In this MYH16 mutation, it turns out that this frameshift caused a punctuation mark (aka a stop codon) to just pop up – so the protein is cut off far sooner than it should be! Not too good for any traits relying on that protein.

Look at the differences between these gorilla and human skulls below. The large bony ridges on the gorilla skull on the left are where the larger jaw muscles attach – otherwise they would literally tear off of the skull. You can also see how the gorilla skull seems “empty” on the sides – that’s because it is filled with large jaw muscles, reducing space available for the brain. The red tinted parts are where the jaw muscles attach – you can see how much more “anchoring” a gorilla’s jaw muscle requires.


And this is where it gets interesting. This mutation in our human ancestors happened approximately 2.4 million years ago. Right before our ancestors stopped looking like primates and started looking like us. If you lacked the protein that operated a powerful jaw muscle, you could not carry a large jawbone around and use it effectively. If you can’t carry a large jawbone around, there is strong selection pressure for those with smaller jaws to survive. If your jaw gets smaller, then the loading of the jaw on the skull decreases – bony ridges disappear, and the skull can get larger and lighter since it doesn’t need to be as strong. A larger and lighter skull can accommodate a bigger brain.

It appears that a random mutation, flipping a single bit of genetic information, has beautifully complex cascading results. Viewing the world as a hostile agent of noise and fury, winding down to an eventual death by entropy is wrong. You can fold a piece of paper, give it to a child, and have them cut crude holes in it with cheap scissors – and when you unfold it, the snowflake is beautiful.

So too can randomness be folded and twisted by logical structures in biology and physics – and the result is our amazing world.

Chimpanzees and Neoteny

One of the biggest “human” questions is “where did we come from?”. While the mechanisms of evolution are well established, the route humanity took to get to its present state is not as well detemined. It’s the difference between knowing the rules of chess and being able to figure out the personality and play style of a grandmaster from a few snapshots of a very long game in progress.

One proposed mechanism for the evolution of humans from primates is neoteny, where juvenile traits are retained and adult adaptations lost. This has been observed in foxes subject to behavioural selection. For instance, look at this young chimpanzee.


This picture is from a 1926 study by the German anthropologist Adolf Naef. He describes it as “the the most human-like picture of an animal, of any that is known to me.” The little guy does seem to have a rather regal and refined air about him, but we can’t just wave our hands and call it case closed at this point. Can we look at the development of a chimpanzee and see if there are any quantifiable parallels?

Bone structure is a great place to start. Chimpanzees, like humans, have a skeleton that changes shape and size as the organism matures.


The two skulls on the far left are those of an infant chimpanzee (top) and an infant human (bottom). Bone structure and shape are very similar, with the classic huge head and tiny cute face we seem programmed to love. The two skulls in the middle are of a adolescent chimpanzee (top) and an adult human (bottom). We can see the jaw start to lengthen in both, and their overall similarity. The final picture on the top right is of an adult chimpanzee, who has a significantly larger and more powerful bite than any adult human.

So what does this show us? Well, humans and chimpanzees appear to have very similar development in terms of bone structure as they grow up, except that humans just seem to… stop at a certain point. There are a multitude of theories as to why this happens, but they all seem to follow the pattern of certain behaviours being selected for which affect the balance of hormones in the body that control the development of adult features. This is called neoteny.

Now neoteny doesn’t mean that every single part of the entire animal becomes more juvenile, or that the animal becomes less complex overall. It’s a selective reduction in complexity – traits that appear later in the animals development (ie adolescence) become less likely to appear.

So how did humans get their unique features? It’s very difficult to select for traits like a bigger brain or hairlessness when those traits don’t appear in the wild in any real frequency to begin with. Viewing human evolution through this lens seems to indicate that change would be very slow, and very hard to do.


But what if instead of selecting for a simple trait, we (or the species as a whole) selects for a behaviour? The neat thing about selecting for this is that hormones have a strong influence on behaviour. So we are partly selecting for certain hormone levels or actions. These hormones also share logical relationships with other hormones, and act in many different parts of the body, not just the parts of the brain influencing behaviour.

If we put significant selection pressure on a species, we are effectively increasing the mutation rate (ie “mutant” creatures tend to be selected more). Increases in mutation rates would be more likely to affect more logically complex proteins arising later in life involved in the development of adolescent features (due to more references to more parts of the mutating DNA) rather than less logically complex proteins that would be involved in juvenile features.

As a result, we now have a mechanism for how these bizarre traits that we simply don’t see in the wild can become so common, so quickly, and also a predicted side effect – neoteny.

But how could this end up as an advantage? It seems that mutations are destroying those adult adaptations that made the organism successful in the first place. But what if the world changes simply because you and others like you live in it? We like to think of physical strength as the be all and end all of “dominance”, but I think this is only true if you’re “one chimp against the world”. A chimp who can more accurately figure out social structure and how to manipulate his place in it could be far more successful in breeding than a chimp who is simply stronger than average.

A chimpanzee’s ability to learn is drastically reduced upon reaching maturity. But baby chimps…


Baby chimps will eagerly mimic a human caretaker – sticking out their tongues, opening their mouth wide, or making their best effort at a kissy face. Not only is the basic mechanism of learning there (imitation), it appears to be very focused on social relationship. And this ability decreases with age! It seems that the retention of juvenile traits is not the burden it appears at first.

So the origin of humanity? Well, it’s still up in the air. But I think it’s incredibly likely that we literally changed ourselves – that living together created environmental pressures (namely social ones) that selected for behaviour in an incredibly complex manner, where the ability to learn and social skills were valued and led to reproductive success. All too often we look for outside pressures in evolution, when some of the most magnificent examples (like the plumage and mating rituals of birds of paradise) are simply a result of everyone agreeing to play an elaborate game.

Clever as a Fox

Sometimes we see things so often that we simply forget to ask “why are they like that?” For instance, let’s take a closer look at domestic animals. Dogs, cats, horses, cows, pigs – animals that we live with, and who couldn’t live without us.

Common Traits

What do all these domestic animals have in common?

pb_pup pb_cat pb_dog
pb_cow pb_horse pb_pig

Now this isn’t a particularly subtle example, but that’s kind of the point. You can see that all of these domestic animals have large white patches – they’ve lost pigment in their coats in some areas. Why do we care? Well, this is something that is extremely common among domesticated animals, but very rare among wild animals. I hear you saying “but what about zebras, or any other wild animal with white patches?”. What we’re referring to here is slightly different. A zebra will always have that patterning, whereas what we’re looking at here is depigmentation – the loss of color in certain areas in an animal that is “normally” colored.

What else is common among domestic animals but rare in the wild? Well, things like dwarf and giant varieties, floppy ears, and non-seasonal mating. Charles Darwin, in Chapter One of Origin of the Species noted that “not a single domestic animal can be named which has not in some country drooping ears”. A very significant observation when you consider that there is only a single wild animal with drooping ears – the elephant.

So perhaps something weird is going on here. Why do animals as different as cats and dogs have these common traits? It seems to arise simply from being around humans!

The Hypothesis


The Russian geneticist Dmitri Belyaev provided a very interesting potential explanation. Genetics at the time was preoccupied with easily measurable traits that could be passed on – if you bred dogs, you could pick the biggest puppies, breed them, and they would produce bigger dogs on average. Fine. But that is selection of a single simple trait, something that likely did not require that many genes to “switch” in order for the puppies to be bigger.

But what if you were selecting for something more complicated? What if, instead of selecting for a simple trait like size or eye color, you selected for something more vague like behaviour – in this case, the very behaviour that made these animals more likely to be around humans. We can call it tamability, or lack of aggressiveness, or whatever – the point is, we are selecting for those animals who will behave in a manner we want around us. A wolf who does not display aggressive behaviour might be able to grab a few scraps of food from the garbage pile of a early human settlement, rather than being driven off.

And if we were selecting a complicated behaviour, rather than a simple trait, it seems likely that it will require more change in the animals genetic code. And since the genetic code is a tangled web where a small bit of DNA can be referenced in many areas of the body – perhaps selecting for a common behaviour would also cause other common traits to arise in animals that are otherwise different.

It’s like giving your car a paint job versus trying to make it go faster – the paint job is easy, but trying to make it faster could lead to your car exhibiting other traits you didn’t directly request, like consuming more gas during regular driving. This could be common across all your project cars. One is a low level trait (the paint, the size of puppy) that can be encompassed in a tiny bit of information (color, size), the other is a high level trait (speed, tamability) that must involve a wide variety of sub-systems changing as well.

The Experiment

Now if you were a Soviet scientist in the late 1950s, you probably worked on something awesome like a giant robot that shot nuclear missles, or a flying submarine. Not Dmitri Belyaev. No, he lost his job as head of the Department of Fur Animal Breeding at the Central Research Laboratory of Fur Breeding in Moscow in 1948 because he was committed to the theories of classical genetics rather than the very fashionable (and totally wrong) theories of Lysenkoism.

So instead, he started breeding foxes. Well, it was technically an experiment to study animal physiology, but that was more of a ruse to get his Lysenkoism-loving bosses off his back while he could study genetics and his theories of selecting for behaviour.


He started out with 130 silver foxes. Like foxes in the wild, their ears are erect, the tail is low slung, and the fur is silver-black with a white tip on the tail. Tameness was selected for rigorously – only about 5% of males and 20% of females were allowed to breed each generation.


At first, all foxes bred were classified as Class III foxes. They are tamer than the calmest farm-bred foxes, but flee from humans and will bite if stroked or handled.


The next generation of foxes were deemed Class II foxes. Class II foxes will allow humans to pet them and pick them up, but do not show any emotionally friendly response to people. If you are a cat owner, you would call the experiment a success at this point.


Later generations produced Class I foxes. They are eager to establish human contact, and will wag their tails and whine. Domesticated features were noted to occur with increasing frequency.


Forty years after the start of the experiment, 70 to 80 percent of the foxes are now Class IE – the “domesticated elite”. When raised with humans, they are affectionate devoted animals, capable of forming strong bonds with their owner.

These “elite” foxes also exhibit domestic features such as depigmentation (1,646% increase in frequency), floppy ears (35% increase in frequency), short tails (6,900% increase in frequency), and other traits also seen frequently in domesticated animals.

The Results

Belyaevn passed away in 1985, but he was able to witness the early success of his hypothesis, that selecting for behaviour can cause cascading changes throughout the entire organism. For instance, the current explanation for the loss of pigment is that melanin (a compound that acts to color the coat of the animal) shares a common pathway with adrenaline (a compound that increases the “fight or flight” instinct of an animal). Reduction of adrenaline (by selecting for tame animals) inadvertently reduces melanin (causing the observed depigmentation effects).

So if Belyaevn is right, genetics is not just a low slow process that works on tiny incremental tweaks. Complicated environmental pressures can result in complicated genetic results, in a stunningly quick period of time. Where do I think we’re going with this?

Well, designer pets for one. Following the collapse of the Soviet Union, the project ran into serious financial trouble in the late 1990s. They had to cut down the amount of foxes drastically, and the project survived primarily on funding obtained from selling the tame foxes as exotic pets. Imagine a menagerie of dwarf exotic animals, who crave human attention and form bonds with people. It would be obscenely profitable.

And the out there thought for the day? We’re doing this to ourselves. We don’t encourage people to act aggressively all day to everyone they meet. We reward certain behaviours more than other behaviours. My unprovable conjecture? Humanity is selecting itself for certain behaviours, and the traits we think of as fundamentally human (loss of hair, retention of juvenile characteristics relative to primates) are a side effect of this self-selection.


Here are some great videos with footage of the tame foxes.

From NOVA – Dogs and More Dogs (starts at about 17:30)

“Suddenly, it all started to make sense. As Belyaev bred his foxes for tameness, over the generations their bodies began producing different levels of a whole range of hormones. These hormones, in turn, set off a cascade of changes that somehow triggered a surprising degree of genetic variation.

Just the simple act of selecting for tameness destabilized the genetic make up of these animals in such a way that all sorts of stuff that you would never normally see in a wild population suddenly appeared.” (Full transcript)

Great Moments in Bat Science

Space Shuttle Discovery was launched this Sunday. If you look at a picture of liftoff, there appears to be something on the side of the external fuel tank.


Upon closer inspection, we find the most adventurous bat in the history of bats.


All photo evidence so far indicates that he clung on during liftoff and the ascent above the Kennedy Space Center. I like to think he sacrificed himself for the advancement of bat science.

Koide’s Formula

Finding a beautiful and simple equation for something in the natural world is fascinating to me – it’s like picking at a corner of loose wallpaper in your room and suddenly seeing the scrolling green text of the Matrix on the wall behind it. Often these relations lead to a deeper understanding, but sometimes an indisputably true and simple relation will remain maddeningly confounding.

In 1981 Yoshio Koide was researching leptons, a family of fundamental particles that includes the familiar electron. There are three leptons which are “charge carriers” (they have mass) – the electron, the muon, and the tauon.

Koide was wondering if there was a way to relate the masses of these three particles with one another. He developed the following equation (related to the eigenvectors of the democratic matrix, here’s a review paper if you want more detail):


Nothing too wild mathematically here. If we assume our three lepton masses are positive (pretty reasonable) then the value of Q can range from 1/3 (all the masses are the same) to 1 (the masses vary wildly from each other). So what is the value of Q? Well, when Koide first proposed this equation, the masses of the leptons were thought to be as follows:

  • Electron: 0.511 MeV/c2
  • Muon: 105.658 MeV/c2
  • Tauon: 1,784.2 MeV/c2

If we plug these values into Koide’s equation, we get a value of 0.667074 – incredibly close to 2/3, which would be precisely halfway between our upper (1) and lower (1/3) bounds we figured out before! This seems like a ridiculous coincidence.

Things like this make you wonder… well, is it exactly 2/3? Or is it just “kind of” close? The mass of the electron and the muon had been measured to a rather high level of accuracy, but the accuracy of the tauon measurements had been lagging behind due to the higher energies required. Perhaps the measurement of the tauon was wrong! It’s a hell of a hunch – but let’s go with it. Assume that the tauon mass has been measured incorrectly, we can set Q = 2/3, input the masses of the electron and muon, and see what the tauon mass “should” be. It turns out that Koide’s equation says the mass of the tauon “should” be 1777 MeV/c2.

Well that’s wonderful, but nature doesn’t seem to care how you think it “should” behave. The only test was to wait for more accurate measurements of the tauon mass and see if this was a neat coincidence based on measurement error or whether there may be something more interesting going on. The mass of the tauon was later revised with better measurements, and… drumroll…

Old Measurement Koide’s Prediction New Measurement
1,784.2 MeV/c2 1,777 MeV/c2 1,776.9 MeV/c2

Whoa. Our simple little equation, using nothing more than grade school arithmetic, has accurately predicted the mass of a fundamental physical particle years in advance of having this measurement confirmed by the best research labs on earth.

And now the question becomes why – why does this work at all? We have three seemingly random lepton masses, measurements of the most complicated physical system we know – our universe. We then input them into a ridiculously simple equation, and the most ridiculously simple answer pops out.

We can gain a tiny bit of insight by figuring out what exactly this equation is telling us.


Basically, we can calculate Q for a given set of three lepton masses. This Q will tell us where a three-dimensional vector specified by the square roots of our three lepton masses will end up.

Q = 1/3 The set of all vectors that form an angle of zero with the unit vector (multiples of the unit vector).
Q = 2/3 The cone seen above which fits perfectly into the “corner” created by our three axes. The set of all vectors that form an angle of pi/4 with the unit vector.
Q = 1 The set of vectors that form an angle of zero with our basis vectors. These vectors lie along one of our three axes.

So it appears that our lepton masses have been chosen in some magical manner as to fall perfectly in the middle of these two extremes. The concept appeals to our perception of the universe as a finely tuned apparatus, but gets us nowhere closer to an interpretation based in physical reality.

It’s a maddening equation. Beautiful. Simple. True. And no one knows what the hell to do with it.

The Trees of Mars

Science is a far more dynamic process than many realize. The constant upheaval of new measurements and new data forces us to constantly reassess our theories and our very view of how well we know the world.

In 2001, a very interesting image began circulating around the internet. It was of a narrow strip of Mars, captured by the Mars Global Surveyor’s MOC (Mars Orbital Camera, great originality there). It was stored in a large database open to the public, but this image had sat unnoticed next to thousands of others until now.


What did we see? These dark blobs were almost a kilometer across. Well, no one really wanted to say. It kind of looked like lichen:


Or a bacterial colony:


Sir Arthur C. Clarke even suggested that they were some sort of Martian banyan tree. “I’m quite serious when I say have a really good look at these new Mars images,” he said. “Something is actually moving and changing with the seasons that suggests, at least, vegetation.”

There’s only one problem with that, and any schoolchild can point it out to you – Mars is supposed to be a dead planet. No life has been found there, at least not that the unwashed masses have been made aware of. The conspiracy theories soon flew fast and thick – that this was one of many images NASA had suppressed that indicated life on Mars.

In short, we were being manipulated by some sort of New World Order that kept knowledge of Martian life silent in order to… well, no one was really clear on that point. Thankfully, the file clerk of this powerful cabal was so incompetent as to leave these blockbuster images on a public server.

But what could it be if it wasn’t life? There are other processes that can produce similar structures:


such as diffusion limited aggregation. So perhaps imminent takeover of the world via suppressed satellite images wasn’t the first thing we should worry about. Maybe there was a less elaborate explanation.

If all we had to base our assumptions on was that single picture, the debate could rage on for a while. Thankfully a new satellite, the Mars Reconissance Orbiter (MRO), entered the skies of Mars in 2006. On the MRO was one crucial piece of equipment – the High Resolution Imaging Science Experiment (HiRISE) camera. This camera was the largest camera ever carried on a deep space mission – to give you an idea of its capabilities, it could see a beachball on the surface of Mars from orbit.

So what did the new pictures look like? Well…


they certainly weren’t lichen, or bacteria, or banyan trees. These long tortured cracks hundreds of meters long were like nothing ever seen on Earth. What could have caused them? Conventional geologic processes on Earth simply didn’t do things like this.

So what was the alternative? Were we back to thinking it may be life again? Well, perhaps there was an unconventional geologic explanation.

Hypothesis: The [carbon dioxide] seasonal ice in the cryptic terrain is translucent, allowing sunlight to penetrate through the ice to the surface below. The ice then sublimates from the bottom of the slab, eroding channels in the surface below. (H. Kieffer, 2000)

Here’s the idea. Mars is cold. So cold in fact, that in it’s “winter” carbon dioxide will actually freeze into transparent sheets over certain regions of the planet. The key thing here is that the ice is transparent, like black ice on asphalt.

Now, think what happens when bright sun shines on black ice. Where does it start melting from? Well, it doesn’t start from the top like you’d think. The sun shines through the clear ice, heats up the asphalt, and the asphalt melts the ice from the bottom. It might even make tiny river-like channels of water between the ice and asphalt, as the liquid water needs somewhere to go.

But what if you ice isn’t made of water, and instead is made of a gas like carbon dioxide? Suppose the sun shines through the ice, heats up the Martian soil, and starts melting the ice from the bottom. Enormous amounts of gas are produced – but where can it go? Well, first it might start to make little channels under the ice like we thought of before to escape. But if there’s no where to go to, eventually, something has to give.


And so, screaming with pressure, the ice fractures. Gas rushes out of these many cracks, carrying dust and soil with it. So what do we end up with? A giant circular region with fractures, darkened relative to the rest of Mars by freshly spit up soil and dust.

So a deep dark conspiracy theory? Perhaps not. It may not be Martian trees, but it is an amazing geologic process that has never been observed on Earth.

Elementary Cellular Automata

Simple rules can often give rise to very complex behaviour.


Applet built using Processing, Wolfram CA code example used as base. Source code available upon request. If this applet fails to load or screws up in any other way, please leave a comment with your browser version and operating system – thanks!

What is this?

Imagine we have a line running left to right made up of squares, and these squares can be either white or black. We then want to draw another line directly below this – but how do we do it? What rules should we use?

Well, we could use a very simple rule and just copy it directly.


But that gets pretty boring. Maybe we could use a slightly more complicated rule and say if a cell used to be black, it’s now white, and vice versa.


Well, it’s a bit more interesting, but not by much. What is a simple set of rules we can use that will produce more interesting behaviour? Perhaps instead of having a square rely just on the previous one, let’s have the rules depend on the previous square and its neighbors.


This means we’re looking at three squares that can either be black or white. There are eight total possible combinations, shown below.


And we can decide what we want to happen when any of these situations occur. Lets try this set of rules:


And see what happens when we start with a single black cell.


Could be interesting! It’d be a lot easier if we had more lines and squares for us to see a bigger picture of the structure produced by these rules though…

So that’s exactly what the application at the top of the post does. You can select whatever rules you want for the eight possible states, and toggle between a single point and random data to start by clicking on the circle in the top right.

Some Interesting Rule Sets

Since there are eight possible combinations that we can choose to either result in a black or a white square, there are a total of 28 = 256 possible rule combinations. A lot of these rules end up producing patterns that become very similar, and it was found that there are 88 unique rules, depending on your definition of unique. Here are a few interesting ones.

Rule 110

random initial conditions
How complex can the behaviour be from these simple rules? Well, you can use this ruleset to simulate a computer. You’ve got to set up the initial line of black and white squares very carefully, and it’s equally hard to read the results, but the logic ends up being exactly the same. If you had a lot of time, you could do some interesting things…

Rule 90

single point initial condition
This ruleset produces a fractal – the Sierpinski Triangle – when a single point is used to start.

Rule 30

single point initial condition
If you’re wondering if these things have any real world application, this rule set displays chaotic properties and is used as the random number generator for large integers in Mathematica, used by millions worldwide.

Rule 169

random initial conditions
I couldn’t find any information online about this, but it certainly stands out visually.

Rule 184

random initial conditions
This rule set can be used to model traffic flow, or deposition of particles onto an irregular surface.

TED Talks – Mushrooms Can Save the World

I enjoy TED greatly. The multidisciplinary approach is a perfect way to introduce yourself to new ways of thinking – and thinking in unconventional ways is something Paul Stamets has spent a lifetime doing. Paul loves mushrooms – or more correctly, he loves fungi.

You can also download the MP4, or add the video to iTunes. I’m not going to repeat the content of the video (because you should watch it!) but I am going to highlight a few amazing thing I learned.

Paul Stamets

We are intimately related to fungi. Animals and fungi are part of a larger group called Opisthokonta, that is, we share a common ancestor. The same pathogens that attack fungi attack us – and some of the most promising and effective antibiotics come from fungi. Unlike plants (and like us) fungi inhale oxygen and produce carbon dioxide.

Prototaxite Landscape

Fungi used to rule the earth. There’s a common misconception that first there was life in the oceans, then plants grew around the oceans, and eventually basic animals wandered out somehow. Not true. Fungi were the first organisms to arrive on land, and plants followed several hundred million years later.

Why? Fungi can produce oxalic acid along with many other acids and enzymes in order to grab minerals they need to grow. Where do they get these minerals? Well, as they moved out of the ocean they obtained them from rocks. This slow process of calcium oxalate formation causes rocks to slowly crumble, and is the first step in producing the soil conditions necessary for plant growth.

So what, you may say – just more slime around a very old pond. Well, not true! This is the absolutely mindblowing part, and I was surprised that I’ve never even heard of it before. There are organisms called prototaxites which could reach sizes of up to 1 m (3 feet) across and 8 m (24 feet) high – all during a time when the largest plants were 2 feet tall.

The landscape of this early Earth must have been breathtaking.

Remediation Experiment

The industrial potential of fungi has not yet been realized. Not even close. I think in this part of the talk he starts to run out of time, but what he manages to state is stunning.

Paul was involved in an experiment to gauge the effectiveness of various methods to remove petroleum waste. Four piles of dirt were saturated with hydrocarbons. One was left alone, one was treated with bacteria, the other with enzymes, and Paul’s used fungi (of course). Fast forward six weeks – three of the piles remain “dead, dark, and stinky”, while the fungi-treated pile was covered in hundreds of pounds of oyster mushrooms. Fast forward to eight weeks, polycyclic aromatic hydrocarbon levels (a measure of the level of contamination of the soil) went from 10,000 parts per million to 200. Not to mention that by the end of the experiment the fungi treated pile was the only one covered in grass…

There are more great examples in the talk itself. I strongly recommend giving it a listen or three – it’s about as far from my line of work as you could get, and I found myself absolutely fascinated.

The Fracture Modes of Spaghetti

Basile Audoly and Sebastien Neukirch at the Université Pierre et Marie Curie in Paris, France have written a wonderful little paper on the fracture mechanics of thin rods. It’s beautiful science – we’ve all seen that spaghetti will break into multiple pieces when you bend it enough, and tends to not break nicely in half like you’d expect. What most of us then don’t do is wonder precisely why this happens – and it turns out that if delve a bit deeper, we gain some very interesting insights.

First let’s go over simple fracture that we’re all familar with. A rod is bent more and more, and soon the curvature becomes too much. The rod then breaks along a weak point, the free end falls off, and the fixed end returns to where it was before. This is what we typically expect.

The critical thing to realize here is the curvature of the rod around the time of break. Immediately before the break, it has a defined, positive curvature. After the beam breaks, the end is free, and structural mechanics tells us that a free end must have zero curvature. We can then deduce that there’s a small period of time where the end of the rod must transition from some defined curvature to zero curvature.

The clever thing that Audoly and Neukirch did was ignore the first break in the spaghetti. Basically, they decided to model spaghetti not from the first break, but from the instant that break happens, and see how the spaghetti then behaves. How can you do this? Well, you can bend the spaghetti very close to the point where it would break, hold it there (with curvature defined at the end) and then let it go (where curvature must then become zero, like the above example). From the paper, “the release of a rod mimics the initial breaking event“.

Well, this all seems very well and good in theory, but what actually happens? Well, it turns out that if you bend spaghetti to a point where it doesn’t break, then let it go, it breaks into a bunch of pieces! This seems totally counterintuitive – if we didn’t curve it enough initially to break it, how can the curvature increase afterwards enough to cause it to break into multiple pieces?

It turns out that the transition from a certain defined curvature to zero curvature causes “waves” of curvature to ring through the spaghetti like waves in a waterbed when you sit on it. This doesn’t typically happen in large beams like we’re familiar with, only thin brittle rods like spaghetti. One would assume that it would be impossible for these curvature waves to have any value beyond the initial curvature – however, this is not the case! This is the critical finding.

We can see the numerical analysis above – demonstrating that for the case of initial semicircular curvature, the peak curvature wave amplitude generated is 1.428 times as great as the initial curvature.

As the spaghetti breaks along a weak point, it send out these waves of higher curvature – which then cause the spaghetti to break along another weak point, and the cycle continues. This breaking process is eventually slowed (or else we’d end up with spaghetti dust) by forces which reduce these waves over time such as energy dissipation in transverse cracks and viscoelastic effects.

So there you have it! Every time you make dinner, you can witness a highly nonintuitive example of structural dynamics. You can see some movies the authors have made here.