Sometimes, one wonders why Google offers so many amazing services for free. There is a saying in Silicon Valley: “If you don’t know what the product is, then YOU are the product.” In this case, Google collects millions upon millions of text queries, each one providing a little bit more data about what people are interested in. According to the book In the Plex, the short-lived free telephone directory service GOOG411 service allowed Google to collect voice samples to create the voice-recognition engine in the Android smart phone operating system. By running the Universe’s most popular search engine, Google collects samples of queries that allow it to build better and better algorithms for predicting what you are looking for, even before you finish typing. The most direct examples are Google Autocomplete and Spell-Check, but the Andriod keyboard can use your typing history, along with its database of what letters come next in queries, to make very good guesses about what you are trying to say.

A Pioneer in the this field, Claude Shannon, is probably the most important computer scientist (almost) no one has heard of. In addition to his work on artificial intelligence, Shannon came up with the definition of information.

Claude Shannon’s robotic mouse Theseus. The original maze is on display at the MIT museum in Boston

The essential idea is that not all signals will carry the same amount of information. The redundancies in a message contains that could be excised without loss of meaning do not convey any extra information. In a sense, information is the same as the surprise the receive experiences by reading it. For example, if you see me throw a fair coin and ask me which way it landed, by saying “heads,” I am conveying one bit of information – the anwser to a single “yes/no” or “1/0” binary question. Now imagine that you ask me who won the Stanley Cup this year.

Continue reading “Redundant”

Science Tourism

I just got back from Copenhagen, a city with a lot of science history. For example, next month marks the 100th birthday of the Bohr model for the structure of atoms. This was developed primarily by Niels Bohr at the University of Copenhagen as was way to better explain how the electrons and protons are arranged in matter. The Bohr model is almost a requirement in most introductory physics and chemistry classes, despite the fact that its has several important shortcomings that can only be fixed using a completely quantum mechanical treatment, as opposed to the “semi-classical” approach taken by Bohr. I think the reason is that it is “mostly right,” (especially compared to previous attempts like the “plum pudding model“)  in the sense that the electrons in atoms are confined to specific orbits around a positively charged nucleus, and more accurate models require quantum mechanics that is much more mathematically taxing and difficult to visualize.



The city itself is also the namesake for the “Copenhagen Interpretation” of quantum mechanics. This was developed by Bohr and Heisenberg and attempts to explain the weirdness of quantum mechanics by saying that it does not refer to an objective reality, rather, QM is a mathematical tool that allows us to calculate the probability of any event. A few, somewhat unsettling consequence are the concept of “wavefunction collapse,” in which the probability function of a particle instantly changes everywhere in the universe when we make a measurement on that particle. In addition, the Copenhagen Interpretation holds that questions like “where was the electron before the measurement?” are not meaningful. All we can say is there is a function that indicates the likelihood of finding the electron at a particular location if we look. Again, this is the way virtually all introductory classes are taught, despite the shortcomings that may be fixed in more complicated interpretations, including Quantum Bayesianism.

The Tycho Brahe made astronomical observations from the “Round Tower,” the oldest such tower in continuous use.




Seeing and Believing

We live in an exciting time for science. Experimentally techniques have advanced to the point that some fundamental concepts, long predicted but never before seen directly, can be visualized. Three examples come to light recently:

As you can find in any quantum mechanics textbook, the way electrons orbit around an atomic nucleus is not (as sometimes explained) like a planet circling a star, in the sense that the electron does not have a definite position at any specific point in time. Rather, the electron exists in an orbital, which indicates the probability of finding the electron at each point. Such an abstract and counter-intuitive concept might seem beyond any attempt to demonstrate directly. Some have even claimed that orbitals are just a kind of mathematical slight of hand, useful for calculation but not corresponding to anything “real.” But recently, the electron orbitals of a hydrogen atoms have been visualized, using a clever technique that takes advantage of the interference pattern of the electron with “itself” when it is ejected from the atom by a strong laser.

The First Image Ever of a Hydrogen Atom's Orbital Structure

The First Image Ever of a Hydrogen Atom's Orbital Structure

Another surprising prediction of quantum mechanics is the possibility of “entanglement,” in which the state of two particles cannot be expressed by describing each independently. Instead, information about one is entangled with the other, and making a single measurement gives you information about both simultaneously. For example, imagine a photonic crystal that emits two photons, but always in such a way that the polarizations are the different (if one photon is polarized up and down, the other is polarized at a 45 degree angle, or vice versa). Measuring one photons will instantly change the state of the other in something that Einstein called “Spooky action at a distance.” Entanglement has been shown many times before, but a new video has been made showing the effects in real time. Sean Carroll has a good explanation.


Lastly, but probably most amazingly, scientists have been able to directly observe the atomic bonds inside a molecule using an atomic force microscope.

In order to obtain such sharp resolution, a single carbon monoxide atom was attached to the end of the cantilever tip, and the deflection created by the electron density of the chemical bonds was measured by shining a laser on the tip.

What is amazing is that all of these experiments agree with predictions made decades ago, although if you asked scientists then, they would likely have been very skeptical that these predictions could have been confirmed so vividly.

Poison Seed

An important finding from studies in evolutionary psychology regards the instinct to avoid “contamination.”  Humans avoid touching a object, and even more so, ingesting food, that is thought to be “contaminated” without regard to the ratio of “good” to “bad.” This might be considered a hard-wired version of a naive biology, which protects from dangerous pathogens in the form of replicating bacteria or parasites. The main difference between a threat of replicators as opposed to something toxic like a poisonous chemical, is that final population of replicators is not limited by their initial numbers. Rather, they will, as is their want, replicate until they reach some natural limit or resources, etc. That is why they are called “germs” (literally “seeds”). Like weeds, once one is in the garden, no part is safe. While the germ theory is disease is centuries old, more recent threats have been intensified  in which the poisonous seeds are not alive in the conventionally sense. Mad Cow Disease, which is called Creutzfeldt–Jakob disease in humans, was so terrifying since it seemed to be contagious although no previously known pathogen could be identified as the cause. It turned out that a single misfolded protein called a prion was what was being passed in CJD. The misfolded protein served as a template that caused normal proteins to also misfold in the same way, creating a contagion no less real than one caused by multiplying bacteria.

Crystals can often be coaxed to form in a solution if a seed crystal is added to the mix. This helps overcome the “nucleation barrier” that causes small crystals to dissolve. However, once the crystal is large enough, the addition of new units is spontaneous. The same process causes the bubbles to float out of carbonated drinks – at least one bar advertises that their beer glasses are laser etched to help encourage the bubbles to become “nucleated.”

Kurt Vonnegut’s “Cat’s Cradle” explores a similar theme, in which the dangerous germ is a seed crystal for a more stable configuration of ice that would be solid at room temperature. If a crystal would come in contact with normal water, the whole thing would freeze solid, based on the action of the tiny seed. In real life, Tin pest is an autocatalytic form of tin that can lead to metal slowly turning to dust after being contaminated.

An important new paper shows how another condition, Alzhimer’s disease, is the result of a misfolded protein that conscripts normal proteins into its deadly game. In this case, a single misfolded protein serves as a template that grows as new proteins are added, forming a fibril. The authors of the new study were able to show that even the sides of this fibril contribute to the “secondary nucleation” of additional fibrils. In this one, a single seed of malignant protein can wreak havoc. Insights like this are crucial to efforts to stem the tide of the disease.


On the Skeptics Guide to the Universe, the hosts noted that the plural of “glass” is “glasses,” not to be confused with a term that refers exclusively to corrective lenses (or many sets of Google’s latest invention).

The news story under discussion was a recent study on the physical properties of a 20 million year old piece of amber. The findings highlight the fact that, even given such a long time period, the amber, which is dried tree resin, hardly flowed at all. This shows the pitfalls in thinking about glasses as “frozen liquids,” as this can lead to some severe misconceptions. For example, as discussed in the same SGU segment, there used to be an urban legend that the “flow” of glass could be observed in the stained-glass windows of old cathedrals, which are supposedly thicker at the bottom than the top. However, this is due to the limitations of Medieval glass-making technology, which could only produce nonuniform slabs, which were logically installed with the thicker end down. (Another good example of accurate observation coupled with a totally off-base interpretation) Glass is a frozen liquid in the sense that if you could take a snapshot of its molecules, they are arranged in a disordered noncrystalline configuration, compared to the regular repeating lattice a solid. You can imagine taking a liquid and instantly freezing all of the molecules in place, and it would look like a glass. However, if you actually try to freeze an ordinary liquid by cooling it, the molecules will try to arrange themselves into their preferred lattice configuration and create a solid. This liquid-solid phase transition is essentially reversible and not path dependent. That is, the system always tries to minimize its free energy, which sets up an epic struggle between the chemical energy (which is minimized by the formation of many regular bonds), vs entropy, which wants to have as much freedom as possible. The key parameter, not surprisingly, is temperature, so there is a well-defined “melting point,” above which entropy wins (liquids are free to flow) and below which chemical energy wins (in a crystalline solid, there are many regular bonds).  With glasses, the situation is much more complicated. Instead of a melting point, there is a “glass transition temperature,” which changes the hard glass into a liquid.

As the molten glass is cooled below the glass transition temperature, the molecules try to arrange themselves into a regular lattice, but they move slower and slower and never quite make it. They just get stuck, but the degree to which they remain disordered depends greatly on how quickly the glass was cooled. If it was cooled too fast, it might have to be annealed afterwards in a process that reheats the glass so that the molecules will have enough energy to escape local minima and find more stable configurations. A quick analogy might be the carpentry dictum “don’t tighten the screws too soon” you should keep in mind when assembling furniture from IKEA. You want to allow enough play for the pieces to shift slightly into the “right” positions, then progressively tighten the constraints so they remain there.


One Family

While often conflated with the Theory of Evolution, the idea that all living organisms surviving to the present day are descended from a single common ancestor is a separate notion (although there is overwhelming evidence for both). Given the common characteristics of all known forms of life, especially the mechanism by which DNA is encoded and translated into proteins, it is very probably that a single instance of abiogenesis is responsible for all life, although we cannot rule out the possibility that other replicators – with a completely different genetic system – that we would still readily classify as “alive” existed at some time but died out. We tend to think that the development of “life” from “nonlife” would be so rare as to happen only once, but it may be that just one of several survived. In any case, the “frozen accident” of the existing DNA code created such a deep “local minimum” in the adaptation landscape that it was not possible for an organism to go back and change it, whether it is the best conceivable system or not.

We can make some interesting suppositions about the lifestyle of the universal common ancestor based on characteristics common to all life. In a certain sense, multicellular organisms expend at lot of effort to RECREATE this environment. Our bodies are almost like reverse scuba suits (as in The Far Side cartoon, in which a fish could walk outside its bowl) providing a salty, aqueous mileu akin to the “warm little pond” that Darwin envisioned as the birthplace of life. The blood and intersititial fluid provide a high sodium, low potassium environment (compared to the interior of cells) that UCA would find comfortable. As discussed in The Spark of Life by Frances Ashcroft, these needs are so engrained in the way our cells function that they require special ion channels to keep the Na+ and K+ ions out and in, respectively, and many neurotoxins exploit this universal need as molecules that block or prop open the channel, with very deleterious effects.

Thinking about all life as related causes some unsettling philosophical conclusions. For example, every act of predation is, in a sense, fratricidal. Perhaps an unconcious unease with thinking about Man and louse as being in any way comparable led to notions like spontaneous generation. The death of which was the slaying of a beautiful theory by an ugly fact according to Thomas Henry Huxley. In any case, by applying moden bioinfomatic methods to patterns in human DNA code allow us to recreate migration patterns, or establish that we are all part Neanderthal. The latter conclusion was apparently confirmed in the most direct way possible when the remains of the child of a such a union were discovered.

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Ship of Theseus

Sadly, Futurama is ending, again. Since the entire series is available on Netflix, I’m trying to catch up on any episodes I may have missed. What I love about the show, in addition to the trenchant parodies of sci-fi, are some of the most advanced math ever to appear on mainstream TV. For example, the main plot of the episode Prisoner of Benda hinges on an new mathematical theorem created by the writer Ken Keeler, who has a Ph.D. in applied mathematics from Harvard.

In fact, many of the show’s writers have math and science backgrounds, and sprinkle in references liberally. Sometimes, classic philosophical puzzles also feature prominently. For example, in the Six Million Dollar Mon, Hermes incrementally upgrades his body with cybernetic implants, while Zoidberg keeps the discarded human parts for a ventriloquist’s dummy. The writers cleverly bring up the logical paradox usually called the Ship of Theseus: If you take a single plank from a boat and replace it with an identical one, almost everyone would agree that it is the “same” boat as before. But if you keep repeating this process, you can end up with a boat that consists of none of the “original” planks. Even worse, if you take all the discarded planks and build a second, identical boat, which of the two is the “real” one? Far from being a game of semantics, this process really occurs during biological processes like DNA replication, prion diseases,  and the ability of amoebae to move by breaking down and rebuilding actin filaments in their cytoskeleton.


In our digital world, computer files are copied and the originals overwritten almost constantly. We readily say that the file is the same, referring to the information as opposed to the physical bits. More speculatively, the transporter in Star Trek essentially obliterates the person being transported and recreates him or her somewhere else. Yes, very few people in the Star Trek universe refuse to use the transporter for this reason (see also the duplicating machine in the film “The Prestige“).

Perhaps this is the way we should think about life, or replicating crystals, in general. We should focus on the self-replicating information, as opposed to the particular physical realization.