The asymmetrical universe

I'm currently reading the 2006 book Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions, by the brilliant theoretical physicist Lisa Randall.  As you might imagine from the title, it's a provocative and mind-blowing read.  And although it's written for laypeople, with most of the abstruse mathematics removed -- theoretical physics is, honestly, 99% math -- I must admit that a good chunk of it is going so far over my head that it doesn't even ruffle my hair.

The rest, though, is way cool.

The heart of the book is the consideration of superstring theory as a model for the way the universe is built.  The idea -- at least at the level I understand it -- is that the fundamental building block of matter and energy is the string, a one-dimensional structure that can either be open-ended or a closed loop, and the various manifestations we see (particles, for instance) are the different vibrational modes of those strings.  But deeply embedded in this model is the idea that the universe has fundamental symmetries, which unify seemingly disparate forces and allow you to make predictions about what exists but is as yet undiscovered based upon what might be necessary to complete the symmetry of the theory.

This search for underlying patterns in what we see around us drives a lot of theoretical physics.  And certainly there are times the approach pays off.  It was that mode of inquiry that allowed Sheldon Glashow, Abdus Salam, and Steven Weinberg to come up with electroweak theory, which showed that at high enough energy the electromagnetic and weak nuclear forces act as a single force.  (It was later experimentally confirmed, and the three won the Nobel Prize in Physics in 1979 for the discovery.)  Carrying this approach to its extreme are people like Garrett Lisi, whose eight-dimensional model of particle physics (based upon a mathematical structure called a Lie group) tries to unify everything we know from experimental results into a symmetrical whole based upon it seeming to fit into a pattern that is "too beautiful not to be true."

The superstring model, too, makes predictions of particles and forces, largely based upon arguments of symmetry and symmetry breaking.  Each of the particles in the Standard Model should, the math tells us, have a "supersymmetric partner" -- each known fermion paired with a boson with the same charge and similar interactions, but a higher mass, and vice versa.

Experimental confirmation, of course, is the hill on which scientific theories live or die, and what the theorists need is hard evidence that these predicted particles exist.  Randall's book is peppered with optimistic statements such as the following:

In a few years, CERN will be the nexus of some of the most exciting physics results.  The Large Hadron Collider, which will be able to reach seven times the present energy of the Tevatron, will be located there, and any discoveries made at the LHC will almost inevitably be something qualitatively new.  Experiments at the LHC will seek -- and very likely find -- the as yet unknown physics that underlies the Standard Model.

Randall's book was published in 2006; the LHC came online in 2008.

And in the sixteen years since then, not a single particle has been found confirming superstring theory -- no superpartners, no Kaluza-Klein particles, nothing.  It did find the Higgs boson, which was a coup, but that was already predicted by the Standard Model, and didn't explain anything about the fundamental messiness of particle physics; why particles have the masses they do, forces have the strength they do, and (most vexing) why the extremely weak gravitational force seems to be irreconcilable with the other three.

This understandably bothers the absolute hell out of a lot of particle physicists.  It just seems like the most fundamental theory of everything should be a lot more elegant than it is, and that there should be some underlying beautiful mathematical logic to it all.  Instead, we have a model that works, but has a lot of what seem like arbitrary parameters.

But the fact is, every one of the efforts to get the Standard Model to fit into a more beautiful and elegant theoretical framework has failed.  Physicist Sabine Hossenfelder, in a brilliant but stinging takedown of the current approach that you really should watch in its entirety, puts it this way: "If you follow news about particle physics, then you know that it comes in three types.  It's either that they haven't found that thing they were looking for, or they've come up with something new to look for which they'll later report not having found, or it's something so boring you don't even finish reading the headline."  Her opinion is that the entire driving force behind it -- research to try to find a theory based on beautiful mathematics -- is misguided.  Maybe the actual universe simply is messy.  Maybe a lot of the parameters of physics, such as particle masses and the values of constants, truly are arbitrary (i.e., they don't arise from any deeper theoretical reason; they simply are what they're measured to be, and that's that).  In her wonderful book Lost in Math: How Beauty Leads Physics Astray, she describes how this century-long quest to unify physics with some ultra-elegant model has generated very close to nothing in the way of results, and maybe we should accept that the untidy Standard Model is just the way things are.

Because there's one thing that's undeniable: the Standard Model works.  Just to give one recent example, a paper last year in Physical Review Letters described a set of experiments showing that a test of the Standard Model passed with a precision that beggars belief -- in this case, a measurement of the electron's magnetic moment that agreed with the predicted value to within 0.1 billionths of a percent.

This puts the Standard Model in the category of being one of the most thoroughly-tested and stunningly accurate models not only in all of physics, but in all of science.  As mind-blowingly bizarre as quantum mechanics is, there's no doubt that it has passed enough tests that in just about any other field, the experimenters and the theoreticians would be high-fiving each other and heading off to the pub for a celebratory pint of beer.  Instead, they keep at it, because so many of them feel that despite the unqualified successes of the Standard Model, there's something deeply unsatisfactory about it.  Hossenfelder explains that this is a completely wrong-headed approach; that real discoveries in the field were made when there was some necessary modification of the model that needed to be made, not just because you think the model isn't pretty enough:

If you look at past predictions in the foundations of physics which turned out to be correct, and which did not simply confirm an existing theory, you find it was those that made a necessary change to the theory.  The Higgs boson, for example, is necessary to make the Standard Model work.  Antiparticles, predicted by Dirac, are necessary to make quantum mechanics compatible with special relativity.  Neutrinos were necessary to explain observation [of beta radioactive decay].  Three generations of quarks were necessary to explain C-P violation.  And so on...  A good strategy is to focus on those changes that resolve an inconsistency with data, or an internal inconsistency.

And the truth is, when the model you already have is predicting with an accuracy of 0.1 billionths of a percent, there just aren't a lot of inconsistencies there to resolve.

I have to admit that I get the particle physicists' yearning for something deeper.  John Keats's famous line, "Beauty is truth, and truth beauty; that is all ye know on Earth, and all ye need to know" has a real resonance for me.  But at the same time, it's hard to argue Hossenfelder's logic.

Maybe the cosmos really is kind of a mess, with lots of arbitrary parameters and empirically-determined constants.  We may not like it, but as I've observed before, the universe is under no obligation to be structured in such a way as to make us comfortable.  Or, as my grandma put it -- more simply, but no less accurately -- "I've found that wishin' don't make it so."

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The conservation conundrum

A major underpinning of our understanding of physics has to do with symmetry and conservation laws.

Both have to do with order, balance, and the concept that you can't get something for nothing.  A lot of the most basic research in theoretical physics is driven by the assumption that despite the seeming complexity and chaos in the universe, at its heart is a deep simplicity, harmony, and beauty. 

The mathematical expression of this concept reaches its pinnacle in the laws of conservation.

You undoubtedly ran into conservation laws in your high school science classes.  The law of the conservation of matter and energy (you can move matter and energy around and change its form, but the total amount stays the same).  Conservation of charge (the total charge present at the beginning of a reaction is equal to the total charge present at the end; this one is one of the fundamental rules governing chemistry).  Conservation of momentum, conservation of spin, conservation of parity.

All of these are fairly well understood, and physicists use them constantly to make predictions about how interactions in the real world will occur.  Add to them the mathematical models of quantum physics, and you have what might well be the single most precise system ever devised by human minds.  The predictions of this system match the actual experimental measurements to a staggering accuracy of ten decimal places.  (This is analogous to your taking a tape measure to figure out the length of a two-by-four, and your answer being correct to the nearest billionth of a meter.)

So far, so good.  But there's only one problem with this.

Symmetry and conservation laws provide no explanation of how there's something instead of nothing.

We know that photons (zero charge, zero mass) can produce pairs of particles -- one matter, one antimatter, which (by definition) have opposite charges.  These particles usually crash back together and mutually annihilate within a fraction of a second, resulting in a photon with the same energy as the original one had, as per the relevant conservation laws.  Immediately after the Big Bang, the universe (such as it was) was filled with extremely high energy photons, so this pair production was going at a furious rate, with such a roiling sea of particles flying about that some of them survived being annihilated.  This, it's thought, is the origin of the matter we see around us, the matter we and everything else are made of.

But what we know about symmetry and conservation suggests that there should have been exactly equal amounts of matter and antimatter created, so very quickly, there shouldn't have been anything left but photons.  Instead, we see an imbalance -- an asymmetry -- favoring matter.  Fortunately for us, of course.

So there was some matter left over after everything calmed down.  But why?

One possibility is that when we look out at the distant stars and galaxies, some of them are actually antimatter.  On the surface, it seems like there'd be no way to tell; except for the fact that every particle that makes it up would have the opposite properties (i.e. protons would have a negative charge, electrons a positive charge, and so on), antimatter would have identical properties to matter.  (In fact, experimentally-produced antihydrogen was shown in 2016 to have the same energy levels, and therefore exactly the same spectrum, as ordinary hydrogen.)  From a distance, therefore, it should look exactly like matter does.

So could there be antimatter planets, stars, and galaxies out there?  Maybe even with Evil Major Don West With A Beard?

The answer is almost certainly no.  The reason is that if there was a galaxy out there made of antimatter, then between it and the nearest ordinary matter galaxy, there'd be a boundary where the antimatter thrown off by the antimatter galaxy would be constantly running into the matter thrown off by the ordinary galaxy.  So we'd see a sheet dividing the two, radiating x-rays and gamma rays, where the matter and antimatter were colliding and mutually annihilating.  Nothing of the sort has ever been observed, so the conclusion is that what we see out in space, out to the farthest quasars, is all made of matter.

This, though, leaves us with the conundrum of how this happened.  What generated the asymmetry between matter and antimatter during the Big Bang?

One possibility, physicists thought, could be that the particles of matter themselves are asymmetrical.  If the shape or charge distribution of (say) an electron has a slight asymmetry, this would point to there being a hitherto-unknown asymmetry in the laws of physics that might favor matter over antimatter.  This conjecture is, in fact, why the topic comes up today; a paper last week in Science described an experiment at the University of Colorado - Boulder to measure an electron's dipole moment, the offset of charges within an electron.  Lots of molecules have a nonzero dipole moment; it's water's high dipole moment that results in water molecules having a positive end and a negative end, so they stick together like little magnets.  A lot of water's odd properties come from the fact that it's highly polar, including why it hurts like a sonofabitch when you do a belly flop off a diving board -- you're using your body to break simultaneously all of those linked molecules.

What the team did was to create a strong magnetic field around an extremely pure collection of hafnium fluoride molecules.  If electrons did have a nonzero dipole moment -- i.e., they were slightly egg-shaped -- the magnetic field would cause them to pivot so they were aligned with the field, and the resulting torque on the molecules would be measurable.

They found that to the limit of their considerable measuring ability, electrons are perfectly spherical and have an exactly zero dipole moment.

"I don’t think Guinness tracks this, but if they did, we’d have a new world record," said Tanya Roussy, who led the study.  "The new measurement is so precise that, if an electron were the size of Earth, any asymmetry in its shape would have to be on a scale smaller than an atom."

That's what I call accuracy.

On the other hand, it means we're back to the drawing board with respect to why there's something instead of nothing, which as a scientific question, is kind of a big deal.  At the moment, there don't seem to be any other particularly good candidates out there for an explanation, which is an uncomfortable position to be in.  Either there's something major we're missing in the laws of physics -- which, as I said, otherwise give stunningly accurate predictions of real-world experimental results -- or we're left with the even less satisfying answer of "it just happened that way."

But that's the wonderful thing about science, isn't it?  Scientists never write the last word on a subject and assume nothing will ever change thereafter.  There will always be new information, new perspectives, and new models, refining what we know and gradually aligning better and better with this weird, chaotic universe we live in.

So I'm not writing off the physicists yet.  They have a damn good track record of solving what appear to be intractable problems -- my guess is that sooner or later, they'll figure out the answer to this one.

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Beauty, truth, and the Standard Model

A couple of days ago, I was talking with my son about the Standard Model of Particle Physics (as one does).

The Standard Model is a theoretical framework that explains what is known about the (extremely) submicroscopic world, including three of the four fundamental forces (electromagnetism, the weak nuclear force, and the strong nuclear force), and classifies all known subatomic particles.

Many particle physicists, however, are strongly of the opinion that the model is flawed.  One issue is that one of the four fundamental forces -- gravitation -- has never been successfully incorporated into the model, despite eighty years of the best minds in science trying to do that.  The discovery of dark matter and dark energy -- or at least the effects thereof -- is also unaccounted for by the model.  Neither does it explain baryon asymmetry, the fact that there is so much more matter than antimatter in the observable universe.  Worst of all is that it leaves a lot of the quantities involved -- such as particle masses, relative strengths of forces, and so on -- as empirically-determined rather than proceeding organically from the theoretical underpinnings.

This bothers the absolute hell out of a lot of particle physicists.  They have come up with modification after modification to try to introduce new symmetries that would make it seem not quite so... well, arbitrary.  It just seems like the most fundamental theory of everything should be a lot more elegant than it is, and that there should be some underlying beautiful mathematical logic to it all.  The truth is, the Standard Model is messy.

Every one of those efforts to create a more beautiful and elegant model has failed.  Physicist Sabine Hossenfelder, in a brilliant but stinging takedown of the current approach that you really should watch in its entirety, puts it this way: "If you follow news about particle physics, then you know that it comes in three types.  It's either that they haven't found that thing they were looking for, or they've come up with something new to look for which they'll later report not having found, or it's something so boring you don't even finish reading the headline."  Her opinion is that the entire driving force behind it -- research to try to find a theory based on beautiful mathematics -- is misguided.  Maybe the actual universe simply is messy.  Maybe a lot of the parameters of physics, such as particle masses and the values of constants, truly are arbitrary (i.e., they don't arise from any deeper theoretical reason; they simply are what they're measured to be, and that's that).  In her wonderful book Lost in Math: How Beauty Leads Physics Astray, she describes how this century-long quest to unify physics with some ultra-elegant model has generated very close to nothing in the way of results, and maybe we should accept that the untidy Standard Model is just the way things are.

Because there's one thing that's undeniable: the Standard Model works.  In fact, what generated this post (besides the conversation with my science-loving son) is a paper that appeared last week in Physical Review Letters about a set of experiments showing that the most recent tests of the Standard Model passed with a precision that beggars belief -- in this case, a measurement of the electron's magnetic moment which agreed with the predicted value to within 0.1 billionths of a percent.

This puts the Standard Model in the category of being one of the most thoroughly-tested and stunningly accurate models not only in all of physics, but in all of science.  As mind-blowingly bizarre as quantum mechanics is, there's no doubt that it has passed enough tests that in just about any other field, the experimenters and the theoreticians would be high-fiving each other and heading off to the pub for a celebratory pint of beer.  Instead, they keep at it, because so many of them feel that despite the unqualified successes of the Standard Model, there's something deeply unsatisfactory about it.  Hossenfelder explains that this is a completely wrong-headed approach; that real discoveries in the field were made when there was some necessary modification of the model that needed to be made, not just because you think the model isn't pretty enough:

If you look at past predictions in the foundations of physics which turned out to be correct, and which did not simply confirm an existing theory, you find it was those that made a necessary change to the theory.  The Higgs boson, for example, is necessary to make the Standard Model work.  Antiparticles, predicted by Dirac, are necessary to make quantum mechanics compatible with special relativity.  Neutrinos were necessary to explain observation [of beta radioactive decay].  Three generations of quarks were necessary to explain C-P violation.  And so on...  A good strategy is to focus on those changes that resolve an inconsistency with data, or an internal inconsistency.  

And the truth is, when the model you already have is predicting with an accuracy of 0.1 billionths of a percent, there just aren't a lot of inconsistencies there to resolve.

I have to admit that I get the particle physicists' yearning for something deeper.  John Keats's famous line, "Beauty is truth, and truth beauty; that is all ye know on Earth, and all ye need to know" has a real resonance for me.  But at the same time, it's hard to argue Hossenfelder's logic.

Maybe the cosmos really is kind of a mess, with lots of arbitrary parameters and empirically-determined constants.  We may not like it, but as I've observed before, the universe is under no obligation to be structured in such a way as to make us comfortable.  Or, as my grandma put it -- more simply, but no less accurately -- "I've found that wishin' don't make it so."

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Strange attractors

A couple of months ago, I read Paul J. Steinhardt's wonderful book The Second Kind of Impossible, about his (and others') search for quasicrystals -- a bizarre form of matter that is crystalline but aperiodic (meaning it fills the entire space in a regular fashion, but doesn't have translational symmetry).  Here's an artificial quasicrystal made of aluminum, palladium, and manganese:

[Image is in the Public Domain courtesy of the United States Department of Energy]

As the above photograph shows, they can be created in the lab, but Steinhardt believed they could occur naturally -- and he finally proved it, in a meteorite sample he and his team found in a remote region of Siberia.

I was immediately reminded of Steinhardt's aperiodic crystals when I read a paper in Chaos: An Interdisciplinary Journal of Nonlinear Science, by Francesca Bertacchini, Pietro Pantano, and Eleanora Bilotta, of the University of Calabria, who were experimenting with another nonrandom but chaotic shape -- a "strange attractor."

A strange attractor is a concept from fractals and chaos theory, and represents a value toward which a perturbed system tends to evolve.  Chaos theory has been around for a while, but came to most people's attention from Jurassic Park, when the character Ian Malcolm (portrayed in memorable fashion by Jeff Goldblum) is explaining the unpredictability of complex systems using the direction a drop of water rolls on a relatively (but not perfectly) flat surface, in this case, the back of someone's hand.  Systems like that one tend to rush far out of equilibrium -- once the drop starts to move, it keeps going -- but some systems settle into a set of loops or spirals, as if something in the middle was drawing them in.

Thus the name strange attractor.

These systems, when mapped out, create some beautiful patterns -- like Steinhardt's quasicrystals, with the superficial appearance of regularity, but without any repeats or obvious symmetries.  Bertacchini et al. used the mathematical functions describing the system to drive a 3-D printer and actually create models of what strange attractors look like.  The team was struck with how beautiful the shapes were, and had a goldsmith fashion them as jewelry.  Here are a few of their creations:

They look a little like Spirograph patterns gone off the rails, but they have a striking, almost-but-not-quite-symmetrical shape that keeps drawing the eye back.

The authors write:

[We used] a chaotic design approach used to develop jewels from chaotic design.  After presenting some of the most important physical systems that generate chaotic attractors, we introduced the basic steps of this approach.  This approach exploits a number of fundamental characteristics of chaotic systems.  In particular, the parametric design approach exploits the concept of extreme sensitivity to the initial data that leads to evolutionary transformations of dynamic systems, not only along the traditional routes to chaos and through qualitative changes in the starting chaotic system, but also through changes in the basic parameters of the system, which create infinite chaotic forms.  Such phase spaces, therefore, represent an enormous potential to be exploited in the design of artistic objects, whether they are jewelry pieces or other objects of abstract art. In the computational approach used, each shape is unique and it is identified by a set of parameters that almost constitute its precise value.  This leads to the creation of unique artistic forms and, thus, to the customization of products in the case of jewelry pieces, which exploits chaotic design as a methodology.

The whole thing brings up for me the mysterious question of what we find beautiful -- and how so often, it's a balance between predictability and unpredictability, between symmetry and randomness.  It reminds me of the quote from the brilliant electronic music pioneer Wendy Carlos: "What is full of redundancy is predictable and boring.  What is free from all structure is random and boring.  In between lies art."

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Thy fearful symmetry

Everyone knows that most living things are symmetrical, and the vast majority of them bilaterally symmetrical (i.e. a single line down the midsection divides the organism into two mirror-image pieces).  A few are radial -- where any line through the center point divides it in half -- such as jellyfish and sea anemones.  Even symmetrical organisms like ourselves aren't perfectly so; our hearts and spleens are displaced from the midline toward the left, the appendix to the right, and so forth.  But by and large, we -- and the vast majority of living things -- have some kind of overall symmetry.

True asymmetry is so unusual that when you see it, it really stands out as weird.  Consider the bizarre-looking flounder:

[Image licensed under the Creative Commons Peter van der Sluijs, Large flounder caught in Holland on a white background, CC BY-SA 3.0]

Flounders start out their lives as ordinary little fish, upright with symmetrically-placed eyes, fins, and so on.  But as they mature, their skulls twist and flatten, and they end up with both eyes on the same side of the head -- a great adaptation for a fish that spends its life lying flat on the seabed, and who otherwise would constantly have one eye pointing downward into the mud.

A question I've asked here before has to do with the constraints on evolution; which of the features of life on Earth are so powerfully selected for that we might expect to see them in life on other planets?  (An example of one that I suspect is strongly constrained is the placement of the sensory organs and brain near the front end of the animal, pointing in the direction it's probably moving.)  But what about symmetry?  There's no obvious reason why bilateral symmetry would be constrained, and it seems as if it might just be a holdover from the fact that our earliest ancestors happened to be bilateral, so we (with a few stand-out exceptions) have inherited it down through the eons from them.

What about symmetry in general, however?  If we went to another life-bearing planet, would we find symmetrical organisms, even if they differ in the type of symmetry from ours?

The answer, judging from a paper that appeared this week in Proceedings of the National Academy of Sciences, by a team led by Iain Johnston of the University of Bergen, appears to be yes.

What Johnston and his team did was analyze the concept of symmetry from the perspective of information theory -- not looking at functional advantages of symmetry, but how much information it takes to encode it.  There are certainly some advantages -- one that comes to mind is symmetrically-placed eyes allows for depth perception and binocular vision -- but it's hard to imagine that's a powerful enough evolutionary driver to account for symmetry in general.  The Johnston et al. research, however, takes a different approach; what if the ubiquity of symmetry is caused by the fact that it's much easier to program into the genetics?

The authors write:

Engineers routinely design systems to be modular and symmetric in order to increase robustness to perturbations and to facilitate alterations at a later date.  Biological structures also frequently exhibit modularity and symmetry, but the origin of such trends is much less well understood.  It can be tempting to assume—by analogy to engineering design—that symmetry and modularity arise from natural selection.  However, evolution, unlike engineers, cannot plan ahead, and so these traits must also afford some immediate selective advantage which is hard to reconcile with the breadth of systems where symmetry is observed.  Here we introduce an alternative nonadaptive hypothesis based on an algorithmic picture of evolution.  It suggests that symmetric structures preferentially arise not just due to natural selection but also because they require less specific information to encode and are therefore much more likely to appear as phenotypic variation through random mutations.  Arguments from algorithmic information theory can formalize this intuition, leading to the prediction that many genotype–phenotype maps are exponentially biased toward phenotypes with low descriptional complexity.

Which is a fascinating idea.  It's also one with some analogous features in other realms of physiology.  Why, for example, do men have nipples?  They're completely non-functional other than as chest adornments.  If you buy intelligent design, it's hard to see what an intelligent designer was thinking here.  But it makes perfect sense from the standpoint of coding simplicity.  It's far easier to have a genetic code that takes the same embryonic tissue, regardless of gender, and modifies it in one direction (toward functional breasts and nipples) in females and another (toward non-functional nipples) in males.  It would take a great deal more information-containing code to have a completely separate set of instructions for males and females.  (The same is true for the reproductive organs -- males and females start out with identical tissue, which under the influence of hormones diverges as development proceeds, resulting in pairs of very different organs that came from the same original tissue -- clitoris and penis, ovaries and testicles, labia and scrotum, and so on.)

So symmetry in general seems to have a significant enough advantage that we'd be likely to find it on other worlds.  Now, whether our own bilateral symmetry has some advantage of its own isn't clear; if we landed on the planets orbiting Proxima Centauri, would we find human-ish creatures like the aliens on Star Trek, who all looked like people wearing rubber masks (because they were)?  Or is it possible that we'd find something like H. P. Lovecraft's "Elder Things," which had five-way symmetry?

And note that even though the rest of its body has five-way symmetry, the artist drew it with bilateral wings. We're so used to bilateral symmetry that it's hard to imagine an animal with a different sort. [Image licensed under the Creative Commons Українська: Представник_Старців (фанатський малюнок)]

So that's our fascinating bit of research for today; coding simplicity as an evolutionary driver.  It's a compelling idea, isn't it?  Perhaps life out there in the universe is way more similar to living things down here on Earth than we might have thought.  Think of that next time you're looking up at the stars -- maybe someone not so very different from you is looking back in this direction and thinking, "I wonder who might live on the planets orbiting that little star."

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Thy fearful symmetry

For some of the most fundamental aspects of life, it's uncertain whether or not evolution was constrained.

This has huge implications for the search for extraterrestrial life, and whether or not we'd recognize it if we saw it.  One I've dealt with here before is the fact that terrestrial life is based on carbon -- but is that necessarily true everywhere?  Sure, carbon's pretty cool stuff, with its four snazzy valence electrons and all, but maybe there are other ways to build functional organic molecules.

What about oxygen?  Even here on Earth, we have living things that get by just fine without it; they're the anaerobes, and include such familiar fermenters as yeast and Lactobacillus acidophilus (the bacteria responsible for yogurt), and such bad guys as the causative agents of tetanus, botulism, and gangrene.  Being aerobic certainly seems like a great innovation -- it increases the efficiency of a cell's energy utilization by a factor of 18 -- but it certainly isn't a requirement.  In fact, probably the most common life form on Earth, individual for individual, are methanogens -- deep sea-floor bacteria that metabolize anaerobically and produce methane as a waste product.  By some estimates, methanogens may outnumber all other living things on Earth put together.

So maybe anaerobic respiration isn't as efficient as aerobic respiration, but apparently it works well enough.

There are other features that deserve consideration, too.  How many of the things we take for granted about animal life are ubiquitous not because they were the result of strong natural selection, but simply because one of our ancestors had those features and happened to be the one that survived?  I'm guessing that having the sensory organs, central processing unit (brain), and the mouth clustered together at the anterior end of the animal will turn out to be common; it makes sense to have your perceptive equipment and your feeding apparatus pointing basically in the direction you're most likely to move.  And speaking of movement, that's probably going to turn out to be fairly uniform everywhere, because there aren't that many ways to fashion an appendage for walking, flying, or swimming.

But what about symmetry?  The vast majority of animals are bilaterally symmetric, meaning that there's only one axis of symmetry that divides the animal into mirror-image halves.  (A few have radial symmetry, where any line through the center works -- jellyfish being the most obvious example.)  Even animals like starfish, that seem to have some weird five-way symmetry, are actually bilateral, which is obvious if you look at starfish larva, and in fact is given away by the position of the sieve plate (the opening through which they draw in water), which is off-center.

True multiple-line symmetry doesn't seem to exist in the animal world, and even in science fiction most aliens are depicted as being nicely bilateral.  An exception are the Antarctic Elder Things, an invention of H. P. Lovecraft, which have pentaradial symmetry, if you don't count the wings -- further illustrating that as unpleasant a person as Lovecraft evidently was, he had a hell of an imagination.

[Image licensed under GNU Free Documentation; original available at http://vixis24m.deviantart.com/art/The-Elder-Thing-39576904]

So are most animals bilateral because it's got some kind of selective advantage, or simply because we descend from bilateral creatures who survived well for other reasons?  In other words, is it selected for, or an accidental neutral mutation?

The reason all this comes up is because of a discovery in South Australia described in a paper that came out this week in Proceedings of the National Academy of Sciences.  Paleontologists have discovered a fossil half the size of a grain of rice that is over half a billion years old, and is the oldest truly bilateral animal ever found -- meaning what we're looking at may be a very close cousin to the ancestor of all the current bilateral animals on Earth.

In "Discovery of the Oldest Bilaterian from the Ediacaran of South Australia," by Scott D. Evans and Mary L. Droser (of the University of California-Riverside), Ian V. Hughes (of the University of California-San Diego), and James G. Gehling (of the South Australia Museum Department of Paleontology), we read about Ikaria wariootia, a teardrop-shaped critter whose unprepossessing appearance belies its significance.  This tiny little proto-worm might actually be our great-great-great (etc. etc. etc.) grandparent.

Not only was it bilateral, it had a throughput digestive system (two openings, one-way flow of material), another innovation that has turned out to be pretty important.  "One major difference with a grain of rice is that Ikaria had a large and small end," said study lead author Scott Evans, in an interview with The Guardian.  "This may seem trivial but that means it had a distinct front and back end, which is the kind of organization that leads to the variety of things with heads and tails that are around today."

Of course, this doesn't solve the question of whether bilateral symmetry is constrained or not.  My guess is that if it turns out to be, it will be because mirror-symmetry is easier to produce genetically.  A lot of the homeotic genes (genes that guide the development of overall body plan) work by creating a gradient of some protein or another, so the polarity of structures is established (head here, butt there, and so forth).  It might simply be easier to establish a one-way gradient, with a high on one end and a low on the other, than one with multiple highs and lows arranged symmetrically.

Although we do manage to do a five-point gradient in the development of our fingers and toes, so it's doable, it just may not be common.

In any case, here we have a creature that may be the reason we're arranged bilaterally, whether or not it gives us any sort of advantage.  Kind of humbling that we might come from a millimeter-wide burrowing scavenger.  I guess that's okay, though, if it'll keep humanity from getting any more uppity than it already is.

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Any guesses as to what was the deadliest natural disaster in United States history?

I'd speculate that if a poll was taken on the street, the odds-on favorites would be Hurricane Katrina, Hurricane Camille, and the Great San Francisco Earthquake.  None of these are correct, though -- the answer is the 1900 Galveston hurricane, that killed an estimated nine thousand people and basically wiped the city of Galveston off the map.  (Galveston was on its way to becoming the busiest and fastest-growing city in Texas; the hurricane was instrumental in switching this hub to Houston, a move that was never undone.)

In the wonderful book Isaac's Storm, we read about Galveston Weather Bureau director Isaac Cline, who tried unsuccessfully to warn people about the approaching hurricane -- a failure which led to a massive overhaul of how weather information was distributed around the United States, and also spurred an effort toward more accurate forecasting.  But author Erik Larson doesn't make this simply about meteorology; it's a story about people, and brings into sharp focus how personalities can play a huge role in determining the outcome of natural events.

It's a gripping read, about a catastrophe that remarkably few people know about.  If you have any interest in weather, climate, or history, read Isaac's Storm -- you won't be able to put it down.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Unexpected asymmetry

The question "why are we here?" has vexed scientists and philosophers alike.

The philosophical answers to this are beyond the purview of this blog, and, frankly, beyond my expertise.  I've got a decent background in a lot of areas -- one of the unforeseen benefits of changing one's major over and over -- but philosophy is a subject on which I am unqualified to weigh in.

The scientific twist on this question, however, is equally thorny.  Why is there something rather than nothing?  The current model of the Big Bang Theory predicts with considerable certainty that when the universe formed, there should have been equal amounts of matter and antimatter.  The two are (in a physics sense) symmetrical; every property that matter has, with the exception of mass, antimatter has the opposite.  Positrons (anti-electrons) are positively charges; anti-protons are negative.

The rub is that if you look around the universe, you don't see antimatter.  At all.  Which is, on one level, unsurprising; when matter and antimatter meet, the result is mutual annihilation (and the release of tremendous energy, as per E = mc^2), as any aficionado of Star Trek knows.

In another way, however, this is puzzling.  If matter and antimatter were created in equal amounts during the Big Bang, in the intervening years it should all have mutually annihilated, leaving behind nothing but gamma rays.  If the symmetrical production of matter and antimatter is correct, then our universe should be devoid of anything but energy -- and we wouldn't be here to consider the question.

[image courtesy of NASA/JPL]

So physicists have been refining their techniques to study antimatter, to see if there's something to account for the imbalance.  Just three days ago, a paper appeared in the journal Nature, by Mostafa Ahmadi of the University of Liverpool et al., called, "Characterization of the 1S-2S Transition in Antihydrogen," in which the team created molecules of antihydrogen -- made of an antiproton and a positron -- to see if it exhibited different properties than ordinary hydrogen.  They did this by creating 90,000 antiprotons, mixing them with five million positrons, and allowing them to form atoms -- then trapping a small number of these in a "magnetic bottle."  (Remember that antimatter violently explodes if it comes into contact with ordinary matter.)

The outcome: antihydrogen seems to behave exactly like ordinary hydrogen.  It emits the same spectral lines (the particular property Ahmadi et al. were studying).  As Aylin Woodward wrote in LiveScience:

As expected, hydrogen and antihydrogen ­— matter and antimatter — behave identically. Now, we just know that they're identical at a measurement of parts per trillion.  However, [coauthor Stefan] Ulmer said the 2-parts-per-trillion measurement does not rule out the possibility that something is deviating between the two types of matter at an even greater level of precision that has thus far defied measurement. 

As for [coauthor Jeffrey] Hangst, he's less concerned with answering the question of why our universe of matter exists as it does without antimatter — what he calls "the elephant in the room."  Instead, he and his group want to focus on making even more precise measurements, and exploring how antimatter reacts with gravity.

The results of this study don't rule out one possibility -- which is that some distant galaxies may actually be composed of antimatter.  As the Ahmadi et al. study shows, it's increasingly unlikely we'd be able to tell that from a distance.  The spectral lines of antihydrogen in an "antisun" would look the same as those of hydrogen from an ordinary star, so there'd be no way to tell unless you went there (which would be unfortunate for you, because you'd explode in a burst of gamma rays).

Whether such an antimatter galaxy would have all of the same people in it, only the good guys would be evil and would have beards, is a matter of conjecture.

But if, as many scientists believe, there really is an imbalance between the amount of matter and antimatter -- if unequal amounts were created during the Big Bang, so during the mutual annihilation that followed, some ordinary matter was left over -- it points to some physics that we haven't even begun to understand.

Which is pretty exciting.  As I pointed out in yesterday's post, unanswered questions are the bread-and-butter of scientific research.  The team is hoping to have even more precise measurements made by the end of 2018, at which point CERN is shutting down for two years for upgrades.  As Jeffrey Hangst put it, "We have other tricks up our sleeve.  Stay tuned."

Which even Evil Spock would have approved of, I think.

Euler's identity, and seeing the divine in mathematics

Yesterday I ran into a "proof of the existence of god" I'd never seen before; the idea that there are mathematical patterns that suggest the hand of a deity.

One of the most popular patterns that religiously-inclined mathematicians point to is "Euler's identity:"

And on the surface of it, it does seem kind of odd.  "e" is the base of the natural logarithms; "i," the square root of -1, and thus the fundamental unit of imaginary numbers; pi, the ratio between the circumference of a circle and its diameter.  That they exist in this relationship is certainly non-intuitive, and the non-intuitive often makes us sit back, and go, "Wow."

Euler's identity isn't the only such set of patterns, though.  A gentleman named Vasilios Gardiakos goes through a good many mathematical gyrations to show that god wrote his signature in number patterns, including the presence of "Pythagorean triplets" in the decimal expansion of pi.  (A "Pythagorean triplet" is a set of three integers that solve the Pythagorean theorem, that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.  The most famous one is 3, 4, and 5.)

Gardiakos's messing about seems to me to stray a little too close to numerology for my comfort.  If you've already have decided that number patterns Mean Something, and you're willing to use any pattern you find, you're already off to a good start.  Add to that the fact that he was searching for patterns in decimal expansions that are infinite (pi, e, and √2), and it's a sure bet that given enough time, you'll come across whatever you need.

The use of the Euler identity, though, is a little harder to answer.  It certainly seems... well, perfect.  It relates five fundamental constants in mathematics -- e, pi, i, 1 and 0 -- in one simple, elegant equation.  And the mathematicians themselves have waxed rhapsodic over it.  Mathematician and writer Paul Nahin calls it "the gold standard for mathematical beauty."  Mathematician Keith Devlin of Stanford University states, "Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

Which is all well and good, but does it prove anything beyond a fascinating and complex mathematical relationship?  First of all, the fact that it's true might be non-intuitive, but it is hardly a coincidence.  For a lucid explanation of why Euler's identity works, you have to go no further than the Wikipedia page on the subject, which leads us step-by-step through a proof of how it was constructed.

And honestly, all of the theologizing over beautiful theorems in mathematics seems to me to turn on one rather awkward question; if you are claiming that Euler's identity, or any other mathematical pattern, proves the existence of god, you are implying that had god wanted, he could have made the math work differently.  God exists -- we get Euler's identity and various patterns of numbers in the decimal expansion of pi.  God doesn't exist -- we don't.

So then, can you conceive of a mathematical system in which Euler's identity is a false statement?  Because if not, then god (should he exist) was apparently constrained to creating a universe where Euler's identity was true, and the god/no god models end up looking exactly the same.

Kind of a poor proof, honestly.

What this sort of thing seems like, to me, is an extension of the Argument from Incredulity: "I don't really understand how this could be true, so it must be god."  Understanding Euler's identity does require that you know a good bit of mathematics; easier, maybe, just to marvel at its beauty, and attribute that beauty to a deity.

For me, I'd rather just try to understand the reality, which is marvelous enough as it is, and worth reveling in a little.  It might be time to break out Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid and K. C. Cole's The Universe and the Teacup again.