Adding gravity to the nuclear liquid drop model: stabilizing the all-neutron atom.

The liquid drop model is a formula used to calculate the excess mass of an atomic nucleus based on the different factors that contribute to its total energy. It can tell us whether a given nucleus with a certain number of protons and neutrons will be stable or unstable, and informs us that an all-neutron nucleus is always unstable. However, if we modify the model slightly to include gravitational attraction, we can find how many neutrons are required to make a stable nucleus, and use this to estimate the minimum mass of a neutron star. I think it's a neat application of various physics concepts, so I'm sharing it with you, the readers of this blog.

Exactly like this.

The Liquid Drop Model

The liquid drop model, also known as the semi-empirical mass formula, is an equation used for predicting the binding energy of a nucleus, such that the total mass of the nucleus is the sum of the protons, the neutrons, and the mass due to the binding energy. If the total mass of the system is lower than just a pile of free protons and neutrons (e.g. the binding energy is negative), the nucleus will be bound, and if it is greater than the mass of the particles alone, it will not be bound*. It does a pretty good job at explaining nuclear masses, but is not perfect. The variables in the formula are the number of protons, Z, the number of neutrons, N, and their sum, A=N+Z. The nucleus is treated as a spherical "drop" with a volume proportional to the number of particles that make it up. Typically, there are five terms in the formula:

Each term has a unique scaling with the nucleon numbers, and the strength of each term is determined by the value of the individual Greek prefactors, with dimensions of energy (they are 15.4, 16.9, 0.7, 22.4, and 11.1 in mega electron volts, from alpha to epsilon). I'll briefly discuss what each term means and motivate its scaling. The first is the residual strong attraction**, which is the only term that is always binding (negative). The attraction is so short-range that it can be treated as an interaction between neighbouring protons or neutrons, and the number of neighbour-pairs is proportional to the number of particles, which is why it is linear. The second term has to do with surface-to-volume ratio (the number of particles at the surface scales as the 2/3 power of the volume), and the fact that particles at the surface of the nucleus will have less binding partners than interior particles. This term is most relevant for nuclei smaller than iron, that can increase their binding energy by undergoing fusion. The third term is the electrostatic repulsion between protons, and has the same form as the electric potential of a charged sphere: proportional to the two charges multiplied in Coulomb's force law, and inversely proportional to the radius which goes as the cube-root of volume. The fourth term, which will become more important later in this post, is minimized when the number of protons and neutrons is the same. This can be understood in terms of the Pauli exclusion principle: only two of each kind of particle can be in the same energy level, so each additional pair must have a higher energy. If there are more neutrons than protons, some of the higher energy neutrons can become lower energy protons and overall the excess energy decreases. Or vice versa, if there are more protons. An excess difference between the number of protons or neutrons can lead to either kind of beta decay (although the Coulomb term tends to bias nuclei towards having more neutrons than protons). The last term has to do with the fact that it's energetically favourable to have an even number of protons and an even number of neutrons so that the spins of the particles can align (sort of like a magnetic attraction between pairs, if you will), so an odd number of either will make the energy more positive (bad), while an even number will make it more negative (good).

From Wikipedia's article on the topic, demonstrating that extra neutrons mean extra energy.

So just to give a basic example, if we have iron-56, Z=26, N=30, A=56, and the formula gives us -490 MeV, about half the mass of a proton. The nuclear mass of iron-56 is 55.935 amu, the sum of the protons and neutrons is 56.429 amu, so the difference is 0.494 amu or 460 MeV, so the formula was pretty close, if I did the math right. It's not perfect, but it works. Another thing this model is good at, which is left as an exercise to the reader, is calculating the ideal proton:neutron ratio as a function of A.

The All-Neutron Atom

Neutrons are unstable, because they outweigh a proton by 2.5 electron masses, and will decay into a proton, an electron, and a neutrino after about 15 minutes if left alone. They are stable when part of a nucleus with protons. Could agglomerates of neutrons be stable? There has been some experimental evidence of unstable isotopes emitting correlated neutrons, indicating they perhaps transiently formed a "dineutron." What does the liquid drop model say about this?

If we substitute A=N, Z=0 into the equation, the Coulomb term goes away, but the symmetry term is always there. Now that the binding and symmetry terms are both linear functions of N, ignoring the surface and pairing terms, we have the binding energy going as $N\cdot(\delta-\alpha)$, and because the absolute value of delta is bigger than alpha, the total binding energy is always positive, meaning that bound states of neutrons cannot exist. A clump of ten neutrons would become ten clumps of one neutron and then would become ten protons.

Astute students of physics will realize that the above model does not take into account all the fundamental interactions: every particle exerts a gravitational attraction on every other particle. For charged protons, this is typically like 40 orders of magnitude weaker than the electrostatic repulsion and is totally irrelevant, but neutrons do not experience electrostatic repulsion. Perhaps if we had enough neutrons, the gravitational attraction would overcome the "symmetry"-induced instability of neutronium.

If we add a Newtonian gravitational term to the all-neutron liquid drop model, the negative binding energy scales as the square of the number of neutrons (divided by the cube-root), while the instability scales linearly. Thus, for a very very large number of neutrons, we might expect a stable state to be reached. Let's write down the new equation...

I'm going to go out on a limb and make the assumption that this will be a large number of neutrons, which lets us neglect the surface and pairing terms. I did make one slight change for the Newtonian term: I've explicitly included the mass and radius of the neutron (roughly a femtometer), whereas the charge and radius of the proton were embedded in the definition of gamma in the old Coulomb term. The Newtonian prefactor is on the order of $10^-{36}$ MeV. So, how many neutrons are required for an all-neutron nucleus to be gravitationally stable? We can set $E_B$ to zero and solve for N.

Lots of neutrons.

So by modifying an equation used to predict the mass of nuclei with 1 to 300 neutrons, we have derived a result of $10^{55}$ neutrons to be gravitationally stable. This gives a mass of about $10^{28}$ kg or about 1% the mass of the sun.

Now, stellar-sized gravitationally bound agglomerates of neutrons already sort of exist; they are called neutron stars. They are not 100% neutrons; they have a crust that is still full of protons. The interior structure and composition of a neutron star are also not fully known (it's not even known whether their radius gets bigger or smaller as a function of mass), and the core is basically the "here be dragons" of stellar astrophysics. What is known, however, is that a neutron star must be at least 1.44 times the mass of the sun (the Chandrasekhar limit), because below that it can still be supported by electron degeneracy pressure, and the star is a white dwarf.

The gravitational neutron drop model underpredicted the minimum neutron star size by two orders of magnitude. I still think it's impressive, however, that we extrapolated the model by 53 orders of magnitude beyond its intended use and were only off by another two orders.

Neutron Stars

At this point in the post I'll mention that this calculation was not my idea. I saw it in a talk by John Michael Pearson at McGill in 2014. It was a nuclear talk about stars, which is good because nuclear talks about nuclear physics and astrophysics talks about astrophysics are both too technical for a general physicist, but when someone has to talk to people outside their own speciality, the talks become more accessible. In his talk he introduced this calculation, and then went on to refine it to get a better answer. In particular, he was interested in using this type of reasoning and precise nuclear mass data to derive an upper-bound to the neutron star mass (before it collapses into a black hole), which could be compared to observations of very large neutron stars to verify their description of the nuclear physics. He mentioned in the talk that the recent discovery of a very large neutron star had already ruled out one of his models.

He has a paper on it here, and he got $10^{56}$ neutrons (not sure where our divergence lies, perhaps in a factor of 3/5 that I dropped, or maybe I have to take into account the surface terms), within one order of magnitude of the Chandrasekhar limit, before refining his calculation with nuclear physics that is far beyond what I have encountered.

The way neutron star models are typically derived is by constraining the internal density of the star to the pressure by assuming hydrostatic equilibrium, and further constraining the pressure to the density using nuclear physics***. Because gravitational fields in neutron stars are so intense it becomes necessary to make general relativistic corrections to the hydrostatic equilibrium, so it gets pretty complicated.

So, just to summarize, by adding a gravitational attraction to the liquid drop model, you can make a wild extrapolation and get logarithmically-almost the correct answer, which I think is cool.

*I have read mixed conventions of whether the binding energy is additive and negative, or subtractive and positive. The sentence "adding a negative binding energy reduces the mass and makes the nucleus stable, and a larger magnitude of this energy makes it more stable" describes my convention. If this doesn't quite make sense, imagine pulling the protons and neutrons out of the nucleus and considering how that increases the total energy, and then compare the bound energy to the energy of all the particles at infinity, sort of like gravitational potential.  If this still doesn't make sense...leave a comment.

**Sort of like the van der Waals version of the strong nuclear force. There's a misconception that the strong force holds nucleons together, but it actually holds quarks together inside nucleons, and the residual force holds nucleons together.

***I'm now talking about something I don't really understand so it sounds vague.

The Simpson-Hawking Donut Universe

Your idea of a donut shaped universe is intriguing, Homer. I may have to steal it.-Stephen Hawking, The Simpsons.

In a 1999 episode of The Simpsons, Stephen Hawking discusses a donut-shaped universe with Homer, before punching him in the face with his robotic boxing glove. Is this just a joke by the writers playing on Homer's love of donuts, or does it hint at something deeper? A donut-shaped universe does have physical implications, and observational searches for them neither confirm nor explicitly reject the Simpson-Hawking donut universe.

The mathematical structure resembling a donut is called a torus. It's the shape that is generated if you take a rectangle, attach two opposite sides together so that it forms a cylinder, and than attaching the two circular ends of the cylinder together.

A torus.

A torus is the geometry of the game Asteroids and many others, where going off the screen on one side makes you appear on the others. Solving physics problems on a toroidal geometry can be pretty useful, because you don't have to deal with boundary conditions (Onsager's solution to the square-lattice Ising model is such an example). Conceptually, this cosmic looparound is comforting, avoiding both the edges of the universe and the fact that there are none.

It looks like a rectangle but it's a donut.

Our universe apparently has three spatial dimensions, so if it were donut shaped it would have to be a 3-torus, which is beyond my ability to visualize as its enclosed volume is some kind of hyperdonut in four dimensional space. But what the physical implications of the universe being a 3-donut, and can we look for them?


Even before getting into cosmology, one might want to consider special relativity in a torus. Because two inertial observes can move with respect to one another and cross each others' path multiple times, the so-called twin paradox cannot be resolved by requiring that one of the twins has to change directions in order to compare the elapsed time. The resolution is that in a toroidal spacetime, there is a preferred reference frame, which is the one that makes a given side of the torus appear shortest. So, special relativity in the land of donuts is not the same as the version we are familiar with. This challenges our Copernican sensibilities, because there will be some place and frame from which the universe appears smallest.

Homer Simpson, you are accused of breaking half the Lorentz symmetry of the planet of the donuts.

Considering a cosmological torus, light that is emitted and travels far enough would reach the point where it was emitted, so if we looked far enough we might see another Earth. However, we live in a universe that used to be a hot opaque plasma, so light from that epoch reaches us in the form of the cosmic microwave background, which is seen in all directions, and we can't see beyond that. So even if we can't see another Milky Way, we could detect the donutness of the universe. Consider Earth in a toroidal universe. Light is emitted from some distant point in all directions. Instead of only one of those light rays reaching Earth, many of them take a different path, each arriving at Earth in a different direction. When we look up at the sky, we would see multiple versions of the same image, in a circle whose angular size depended on the relative size of the torus and distance to the source. This took me a while to figure out, so I drew a crappy MS Paint drawing to illustrate it.

Yellow, red, and green all go from the star thingy to Earth in different directions, arriving at different angles in the sky.

As was the case in the photon decay paper, the cosmic microwave background is the most distant light source we have, so this has the best chance of being duplicated by the topology of the universe. To see if this is the case we can look at measurements of the temperature anisotropy of the universe, such as those taken by the WMAP satellite. That's what these guys did, and by their non-observation of obvious cosmic circles (the analysis was considerably more detailed), they placed the bounds of the size of any potential torus at about 78 billion lightyears. I am not sure whether this should be compared with the radius (46 billion lightyears) or diameter (92 billion) of the observable universe. There are a number of independent analyses of this, and to my surprise they do not really rule out the donut universe, although they do not support it either.

If the size of the universe exceeds the size of the torus, the "intersection" will appear at multiple points on the sky.

So, the jury is still out on the Simpson-Hawking donut universe. Did Hawking himself every discuss this? In a 1992 paper on chronology projection, he did brush over it slightly:

"For example, if the initial surface is a three-torus, the Cauchy horizon will also be a three-torus, and the generators can be nonrational curves that do not close up on themselves. However, this kind of behavior is unstable."

However, this kind of behavior is unstable. 

A Living Ising Model: Bacterial Vortex Lattices

Today I read an interesting paper in Nature Physics by Hugo Wioland and friends, called "Ferromagnetic and antiferromagnetic order in bacterial vortex lattices." A lot of Nature Physics is devoted to solid state physics which I personally don't find too interesting, so I almost glossed over until I saw the "bacterial vortex" at the end of the title. In the paper, they grew bacterial colonies in circular cavities that spontaneously rotated, and showed that each colony vortex can behave the way atoms do in magnetic solids, and use it as a jumping-off point to model complex living systems with lattice physics.

A bacterial vortex, taken from the supplemental material of the paper. The graininess is due to me trying to convert from mov to gif and is not part of the paper. The colonies are 50 microns in diameter.

The bacteria, Bacillus subtilis, is covered in flagella which are constantly waving around. The bacteria cannot occupy the same space as one another and so organize themselves in such a way as to avoid that, and influence each other through hydrodynamic interactions of the beating flagella. When they are packed into these circular cavities, they fill the space, and when the flagella beat coherently the colonies start to rotate. One rotating colony they call a bacterial vortex, and they can rotate clockwise or counterclockwise with varying magnitude.

Four connected colonies. The top left and bottom right spin counterclockwise, and the top right and bottom left spin clockwise. (You can see this in the movies from the paper) 

The circular cavities are arranged in a lattice, either square or triangular, with a gap of a certain size connecting each one. Tuning the size of the gaps tunes the interactions between cavities, which are mediated by the row of bacteria on the edge of each circle next to the walls. If the gaps are narrow, the bacteria do not move through and they interact hydrodynamically through the flagella beats, and want to move in the same direction as their neighbour across the gap, which makes the vortices spin in opposite directions. If the gaps are wide, bacteria tend to line up along the walls of the gap, such that a row of bacteria will do a "180" going from one cavity to the next, meaning neighbours will move in opposite directions and thus the vortices will spin in the same direction.

Diagram from the paper of inter-vortex interactions. If the gaps are small, they bacteria at the gaps interact hydrodynamically and move in the same Cartesian direction. If the gaps are wide the bacteria move along the edges, making adjacent cavities rotate the same way. I can foresee my explanation being confusing and unsatisfactory.

This is cool and all, but at this point I should take a step back and actually explain why they are doing this experiment.

Physics is hard. There are very few complex problems that can be exactly solved, but there are computational methods that can get approximate solutions. One of these is called lattice field theory, where space and time are broken into finite-size steps (sites on a lattice), and interactions between adjacent lattice sites are considered and the system is simulated with a computer.

One of the simplest but most ubiquitous lattice models is called the Ising Model*, which is used to understand magnetic materials. In the Ising model, there is a lattice of "spins" that can either be "up" (+1) or "down" (-1), and the total energy of the system depends on whether each spin is pointing the same direction or the opposite direction as its neighbor**. (Imagine two adjacent wire loops with electrical current going around them, and consider the torques they exert on each other if the current is going in opposite directions. Then try to consider a thousand loops.)  Materials where the spins want to point in the same direction are ferromagnetic (like iron) and materials where the spins want to point in opposite directions as their neighbor are called antiferromagnetic (like chromium). Solving the Ising model can be complicated, but it's much simpler than considering the interactions of $10^{23}$ interacting atoms.

A two dimensional Ising lattice, showing ferromagnetic order (left) and antiferromagnetic order (right).

The authors wanted to see they could apply the Ising model to a living system, so the created these bacterial vortices to see if they obeyed Ising-like behaviour. From a thermodynamic standpoint, living matter is substantially more complicated than inert matter: it's constantly producing its own energy and is never in equilibrium. There is a whole relatively new branch of physics just dedicated to studying the thermodynamics of active matter. A network of colonies, each a network of bacteria, each a network of interacting proteins of incredible complexity, would be essentially impossible to model from a "bottom up" approach, but mapping it onto the Ising model would allow its large scale behaviour to be predicted and studied, and may open the door to more generally studying the physics of living systems.

Back to the results of the paper. You may recall that I said that for lattices with narrow gaps, the adjacent bacterial vortices spin oppositely, and for wide gaps adjacent vortices spin in the same direction. The former case corresponds to antiferromagnetism, and the latter to ferromagnetism. By changing the size of the gaps, they can ordain what kind of "magnet" these bacterial colonies will be. The critical size where the behaviour crosses over is about 8 microns.

Left: An antiferromagnetic bacterial vortex lattice, where adjacent cavities tend to spin in opposite directions (alternating green and purple). Right: A ferromagnetic lattice, where neighbors tend to spin in the same direction, with domains of green and purple.

To make the whole thing slightly cooler, they explain the spin-spin interactions between adjacent vortices in terms of an "edge current" of the outer layer bacteria moving along the walls in the opposite direction as all the bacteria in the middle. This is analogous to certain quantum materials such as a quantum hall state in a two dimensional electron gas (a "thin cold semiconductor" doesn't sound as neat), where the electrons propagate in the opposite direction along the outside of the material. Many-body quantum mechanics and bacterial fluid mechanics do not have much in common, but both can be described by this lattice model. I generally think it's neat that these colonies can be modelled as a lattice interacting spins the same way that atoms in a magnet can, even though the first kind of spin is the net motion of the bacteria and the second kind is the intrinsic angular momentum of an electron.

People invariably ask what the practical applications of a given paper are. I will quote the how-we-will-save-the-world-if-we-get-more-funding section from the last paragraph, where the authors state: "Improved prevention strategies for pathogenic biofilm formation, for example, will require detailed knowledge of how bacterial flows interact with complex porous surface structures to create the stagnation points at which biofilms can nucleate."

Overall, very cool paper.

*Named after Ernst Ising and also a good name for a physics hockey team.
**Still haven't decided to go with American or Canadian spelling on this one.

Article on PhysicsForums about Earth's gravity.

Read it here and learn!

Microcannons firing nanobullets

Sometimes I read papers that enhance my understanding of how the universe works, and sometimes I read papers about fundamental research leading to promising new technologies. Occasionally though, I read a paper that is just inherently cool. The paper by Fernando Soto, Aida Martin, and friends in ACS Nano, titled "Acoustic Microcannons: Toward Advanced Microballistics" is such a paper.

The grand scheme of this research is developing a tool that can selectively shoot drugs into cells at a microscopic level. This is hard because everything happens really slowly at the  microscopic scale in a liquid, in ways that meter-sized beings who live in air would not necessarily expect. For example, it is impossible for small organisms to move through a fluid using a repetitive motion that looks the same in reverse. For example, the way we move our feet back and forth to walk would not work for a tiny aquatic human, because the forward motion in the first phase of movement would be nullified by backwards motion in the second phase. This is why bacteria use things like rotating flagella to move*. Digressions aside, if you tried to shoot a tiny bullet through a cell wall, it would halt really quickly and diffuse away. Soto, Martin, and collaborators wanted to beat this.

They developed a "microcannon," starting with a thin layer of polycarbonate  plastic studded with small pores, which is a thing you can buy and don't have to make. They deposited graphene oxide onto the inside of pores in polycarbonate using electrochemistry, and then sputtering gold onto the inside of the graphene layer. The polycarbonate could be washed away with acid, leaving free-floating carbon and gold cannon barrels a few microns in size. While they were still in plastic membrane, the cannon pores were filled with a gel (literally gelatin from the supermarket) loaded with micron-sized plastic beads to act as bullets, and the "gunpowder."

The microcannons, loaded with nanobullets before and after firing.

Regular readers of my blog will remember that bubbles are somewhat of an exception to the small+water=slow rule, and that when they collapse it can lead to very fast motion on very small scales. So, the authors of the paper used perfluorocarbon (same structure as a hydrocarbon but with fluorine instead of hydrogen) droplets as a propellant, which they turned into bubbles with an ultrasound-induced phase transition. The bubbles collapse, leading to a pressure wave which drives the nanobullets out of the barrel towards their target**.

Composition and operation of the microcannons.

The authors wanted to characterize how powerful these things were, so they did two relevant tests. First, they embedded the cannons in an agar gel and loaded them with fluorescent beads. They looked at where the beads were before firing the ultrasound trigger at the cannon, and after. It was observed that they penetrated an average of 17 microns through the gel. I don't have much context to gauge whether this is a lot or a little.

The bullets were too fast to record with a microscope camera, so their second test involved recording the motion of the cannon after it fired the bullets. Naively one would expect to be able to calculate the bullet speed with conservation of momentum from knowing the cannon's speed, but momentum isn't conserved in a noisy viscous environment. They modeled the fluid dynamical forces acting on the system, measured that the terminal speed of the cannon was about 2 meters per second, and concluded that the initial speed of the bullets is 42 meters per second or 150 kilometers per hour. Pretty fast, especially for something so small in a draggy environment.

I don't know if this technology will succeed in the authors' goal of localized drug delivery to cells, but I think it's awesome that they made a functioning microscale cannon.

Oh the humanity.

*I recommend reading Life at Low Reynolds Number if this interests you.
**Or just in whatever direction it was pointing, I guess.

PhysicsForums article on the early history of relativity and the speed of light

https://www.physicsforums.com/insights/speed-light-galilean-relativity/

The most exciting thing I've written in a while!

An old teacher hacking life itself: Christian Bok's Xenotext at MIT

This morning, I was googling for seminars at MIT that would provide lunch for me so I could avoid eating my own food which would bring me closer to havingö to buy groceries. I was planning on going to a fairly boring looking talk at Harvard about cell mechanics for a pizza dinner. However, I found a link saying that Canadian poet Christian Bök (pronounced "book") was reading from his new book of poetry.

I met Christian Bök in 1998 when he was my sixth grade teacher at a small school called Fieldstone. At the time I thought he was a great teacher; he always had lots of really interesting knowledge to share and would answer any question in an enlightening way. I thought he was the smartest person I had ever met. My friends often accuse me of knowing everything, but they are wrong. I don't know everything. Christian Bök knows everything. This was also the year that I stopped hating school and everything associated with it, and started becoming excited about learning new things. It is also around the time I stopped being one massive walking behavioural problem and started being someone that teachers would want to teach. I think Dr. Bök had a big part in both these things.

Some years after he taught me, he released his then-magnum opus, Eunoia, a book of poetry where each chapter uses only one vowel. So, the A chapter has passages like "Catamarans as fast as narwhals dash past sandbars and make ballast at landfall," while the U chapter has the coarser "Ubu untucks Ruth's muumuu; thus Ruth must untruss Ubu's truss." Each chapter is a self-contained coherent story. Eunoia put him on the map of the poetry world.

So naturally I was excited that he was at MIT today. So excited that I decided to forgo free pizza at Harvard and go to his poetry reading*. I also emailed his host mentioning that I was his old student and asked if there was time to meet with him. There was, so I met with him in the early afternoon. Fieldstone was a very small school and I was the most eager student so he has a decent memory of me. I imagine teachers are happy to find out that their students stayed in school, and boy did I ever stay in school. We talked for a bit about what I was working on, and its broad applications. I was quickly reminded of how sharp he was, as he quickly grasped the overview of my work and started asking tough and insightful questions. I mentioned that in 1998 I thought he was really smart. For the past fifteen years, through highschool, university, and grad school I have been surrounded by people who have been pre-selected for intelligence. I have met a lot of smart people. In this 20 minute conversation I got the impression that he was still the smartest person I had ever met. I mentioned that I had listened to the CD of Eunoia and that I liked the A chapter the best; he said he prefers I but most people like U.

After work I went to his poetry reading. His current project, Xenotext, is even grander and crazier than Eunoia. He plans to encode a poem in the genetic sequence of a bacterium, and when that gene is transcribed into a protein, that protein also reads as another poem in response. He wants to put this in the genome of an extremely robust extremophile, so that his poem will survive the death of humanity. I'll talk a bit more about this in a bit.

The poems in his book (not all of which will make it into the genome) generally have an apocalyptic theme, and draw a lot upon the Greek myth of Orpheus and Eurydice, about a poet who travels to the underworld to reclaim his lost wife. The first reading was a description of the destruction of the Earth through various man-made and natural cataclysms, which seemed to draw upon a lot of astronomical research (he mentioned Gliese 710 and Wolf-Rayet stars). It reminded me of the book Seveneves by Neal Stephenson, the best novel I've read this year**, which details aftermath of the moon's destruction and its effect on the Earth. He also read a short love poem, which sounded normal but he said took him five months to write due to the constraints he imposed on the writing.

After his readings there was a Q&A session and somebody asked him about the constraints on his love poem. He listed them off one by one, and they started normal and quickly got more and more extreme. First of all, it was a sonnet of seventeen lines and each line needed to have twelve syllables. Each line also had its own internal rhyming. The dedication of the poem was written as an acrostic in both the first and last letters of each line, so the first letter of each line read "FOR THE MAIDEN IN" and the last letter of each line read "HER DARK PALE MEADOW." To make the last letters line up, each line needed to have 33 letters (in addition to twelve syllables), so that they'd all fit on a grid. Then, finally, all the letters of the poem are actually a re-arrangement of all the letters in another poem by John Keats. I am no poetry expert but I thought that was pretty impressive.

Then somebody asked about the relevant biochemistry of his encoding the poem into a genome and getting it to read out another poem. He went on to explain it, and even when you don't include biochemistry it sounds insane. He made the analogy of encoding a text using a two-way cyper, switching let's say A with N, B with O, C with P, etc, but when you encode your sentence with this cypher, it makes another sentence. To do this, you have to choose an appropriate mapping between letters. If you start with A, you have 25 choices of what to make it, and after that you have 23 choices for which letter to map to B (unless you already mapped it to A) etc, so the total number of possible ciphers is 25x23x21... which is known as the double-factorial of 25, which is 7,905,853,580,625. So, find one of these eight trillion possible ciphers that will allow you to cipher English words into other English words, which I imagine is a very small subset, and Bök had the additional constraint of having to have it sound nice.

Ok so he eventually found a cipher that let him encode a poem into another poem, which seems like a huge accomplishment to me, but then he had to encode this into the genome of a bacteria! The way genes work is that there is a DNA sequence written in the four letters of A, T, G, and C, and the DNA is copied into a complementary RNA strand. The RNA goes through this little cellular machine called a ribosome, that concatenates amino acids onto a protein chain. There are twenty-three amino acids and only four nucleobases, so  combination of three bases is required to tell the ribosome to add a given amino acid to the chain, which it does by following the genetic code (which is not the same as your genetic sequence). For example, if the DNA reads CAG then the amino acid glutamine gets added. Each gene codes for one protein (there is a combination that essentially acts as a period and stops the transcription), and one protein does one chemistry thing. He didn't go into the details, but in order for his project to make sense, he would need a mapping of three bases to one Latin letter (unless he restricts himself to a 16 letter alphabet), and then another mapping of amino acids back to Latin, either using a 23 letter alphabet or using pairs of adjacent acids to make 26 letters. He would have to choose his mappings between Latin, DNA, and proteins to work as a poem. THEN he would have to engineer this gene and implant it in the genome of a bacteria, not have it die, and have it actually produce this protein. This could be verified through genetic sequencing on one end, and protein sequencing on the other.

The central dogma of biology and poetry. Source.

It turns out he actually did succeed at doing this, implanting a poetic gene into E. coli which produces a poetic protein. They are called Orpheus and Eurydice respectively. The first poem, which he read at the reading, begins "any style of life / is prim..." and the second begins "the faery is rosy / of glow..." Apparently the Eurydice protein is also fluorescent (he used a supercomputer to see how each proemtein would fold),  so you can tell when it's expressed. His next step is to implant this in the extremophile.

I have a deep respect for ideas that seem too crazy to work but are attempted anyway. This is the craziest such idea that I have heard of. After the reading I bought his new book, which he signed. It also has a lot of biochemistry-themed poetry in its explanation of the project, for instance a poetic ode to each nucleobase and poems where the words end and start with complementary base letters. I look forward to reading it.

It was a nice surprise re-acquainting myself with Dr. Bök  today. He is a truly impressive human being, and had a big effect on who I am today.


*It's ok though because I found free pizza anyway.

**The worst is The Land of Painted Caves by Jean M. Auel. Do not read this book.