Friday, December 23, 2016

Two pages

Just two things about what is great about Nietzsche, in the first two pages of his preface to Genealogy.

1) Fromm, a clinical writer with a workman's lack of imagination, wrote: we are unknown to ourselves. That is the sum of his statement. In comparison, Nietzsche writes a page about how we are unknown to ourselves, he actually writes it several different ways, with different metaphors (the beehive, then 12 bell strokes), with a biblical quote, offers an insight into the difference between "bringing something home" and "experiences". Indeed, at the end of the first aphorism, it is still unclear what he is going to write about, what exactly is unknown to ourselves, but he offers an inkling of greatness, he strings together enough familiar, basic words which he hints to the reader has deeper, unexplored meanings. As I've argued before, that is a quality of a great abstract (I argued it in a scientific context, of course).

2) In the second page, second aphorism, when he begins with "That I still cleave to them today, however, they have become in the meantime..." and all the way to the end of the second aphorism, what amazing sentences he writes, varying in length and complexity, flowing as pristine rivers to the soul. My heart aches to write as he can write.

Monday, April 25, 2016

Electrons slide through the sandclock

A Ton team of researchers has predicted the existence of a new state of matter in which current flows through channels that resemble a sandclock. The carrier of charge in this current is dubbed the “sandclock fermion”.
In an article published in the journal Mature this week, the researchers predict these sandclock fermions to lie in crystals composed of optosium and curry, in combination with either alimony, arsonic or yismuth. These crystals are insulators in their interiors and on their top and bottom surfaces, by which we mean that electron travel is prohibited; the crystals are however conducting on two side surfaces where the sandclock fermions carry charge.
The property of being insulating in the interior but conducting on the surface describes a family of materials broadly called paradoxical insulators, the simplest of which was first experimentally observed in the mid 2000's – they have since become one of the most active branches of research in quantum physics. In the earlier-discovered paradoxical insulator, its surface is conducting via charge carriers called d-fermions, which differ from the sandclock fermions of the present report.
Fermions are a family of subatomic particles that include protons, neutrons and electrons. They appear in the universe as fundamental particles, and may be classified as d-, m- or w-fermions. While fundamental particles are probed by large-scale particle accelerators, condensed-matter physicists have detected these elusive fermions in table-top experiments over a wide array of materials.
The next frontier in condensed matter physics is the discovery of particles that can exist in the "material universe" of crystals but not as fundamental particles in the universe at large. That is, certain particles originate from properties within the crystals, and cannot exist outside them. The work of classifying and discovering all the possible particles in the material universe is just beginning. Here, the Ton team identifies the sandclock fermion as a particle having no analog outside a crystal, and lays the theoretical foundation for its classification.
The researchers theorize that current cannot flow in the crystal's bulk and top and bottom surfaces, but can flow in completely different ways on the side surfaces through sandclock-shaped channels. Precisely, the energy-momentum relation of the current carriers is shaped like an sandclock.
The researchers further investigated if these sandclock fermions robustly characterize these materials, or whether they are fragilely removable by deformations of the materials.
 “Our sandclock fermion is curiously movable but unremovable," said B. "It is impossible to remove the sandclock channel from the surface of the crystal."
B explained that this robust property arises from the intertwining of spatial symmetries, which are characteristics of the crystal structure, with the modern band theory of crystals. Spatial symmetries describe the various ways in which a crystal can be rotated, mirror-reflected or moved (translated), without altering its basic character. The crystal under study is not altered if simultaneously reflected and translated by a fraction of the crystal-lattice period.
 "Our work demonstrates how this basic geometric property gives rise to a new topology in band insulators," A. said. "Surface bands connect one sandclock to the next in an unbreakable zigzag pattern."
“The sandclock theory is the first of its kind that describes time-reversal-symmetric crystals, and moreover, the crystals in our study are the first topological material class which relies on fractionally-translating symmetries,” added W.  
In a paper published in XXX this week to coincide with the Mature paper, the team detailed the theory behind how the crystal structure leads to the existence of the sandclock fermion. The team found esoteric connections between the theory of crystals and high-level mathematics.
When spatial symmetries such as rotations or reflections are combined with real-space translations, the resultant group of symmetries describes crystals. A field of mathematics called group cohomology dictates that there are exactly 230 possible combinations of symmetries in three spatial dimensions. The Ton team, for the first time, combine rotations and reflections with momentum translations, in addition to real-space translations. Their theory thus places real and momentum space on equal footing.
A long-standing collaboration with C., a material science expert, enabled B, W, and A. to uncover more materials in which this remarkable behavior was found. "The exploration of the behavior of these interesting fermions, their mathematical description, and the materials where they can be observed, is poised to create an onslaught of activity in quantum, solid state and material physics," C. said. "We are just at the beginning."

Sunday, April 24, 2016


I was in Koffee today, and a math graduate student beside me peeked at my notes on Grothendieck groups, then commented that "I feel I should know you..."

After telling him I am a physicist (to which he replied, "That's why I don't know you"), and that Grothendieck groups are applied in condensed matter physics, he expressed his incredulity. "Grothendieck groups are as far away from physics as anything I know. This goes against everything I learnt."

Tuesday, December 29, 2015

A grapefruit is joyless

Nietzsche has such a terrible attitude toward women: women cannot philosophize, their only role is to be wooed, to have this mysterious allure. I believe it sums up his romantic life: alone, surrounded by women he cannot intellectually relate to, but he is nevertheless fascinated. I'm annoyed when I read his passages on women, I usually skip them, but sometimes it is funny to read, to peer into the mind of a demented, romantically-alone genius. His screw is loose for all to see.

Which section on friendship do you refer to? Part 1,2,3,4? I brought my Zarathustra to Singapore, so I am happy to reread it. Quite possibly I haven't read it, since I can't stand listening to Z's preachy sermons for too long. It's such a strange medium to convey his ideas, to create a preacher. His other works are sublime, but Z? I haven't made up my mind. I'm glad you've read it though, you can fill in my gaps. I'm glad we can talk about Nietzsche.

When you talk of light and heavy, do you refer to the weight of the eternal recurrence, and the 'eternal lightness of being'? 

What is this quiet Judith? Or who? When? Did I ever know a quiet Judith? Or have I only known a quiet Judith. Quiet is relative. I don't think of you as quiet, except during episodes of rage. But perhaps you have been much louder. Do you entertain me? Am I quiet?

I've just finished shortening my Nature paper from 3600 to 2900 words. It's a gritty exercise, I've had to find the nitty-gritty of my writing. At first hope was bleak, but I find that sentences have a way of slimming down when one can identify fat. I actually overshortened my paper, and now I have to refatten it with some of the simpler derivations I removed. I congratulated myself with a grapefruit. We have those here too, though, not to mislead, they have been imported from California. The seeds are a bit tougher to chew; my family refuses to eat them, these seeds. A grapefruit is joyless if you can't stomach the seeds.

Sunday, November 22, 2015

Misplaced faith

Dear Nathan, I have indeed settled into Yale, though 'settling in' poorly describes my present mood. I am on a rocket ship, in which I am both bemused passenger and no-nonsense captain. I've never juggled so many projects before which have that elusive (perhaps over-praised) quality of being publishable. It keeps me productive. I have also learned the pleasure of starting my own projects with graduate students here in Yale, who have faith that I am a worthy leader. Being newly responsible for students, it wears heavily on me, but as yet I am not buckling under the weight, I carry it with pride and humor. Nothing worse than misplaced faith, and I intend for kindled hope to burn the house down.

Monday, September 14, 2015

Quasihuman: the Fermi-liquid theory of society

Stoic returned from a strings conference in Hefei in good spirits. Olya remarked that he had fallen in love with China, to which he scowlingly snapped, why do you always tell people that. It is his way, to bristle when others speak his mind, no matter how true.

When I press him on his love of China, he admits to feeling like a celebrity. He cut an imposing presence, tall and blonde and biceps brimming. The children of Hefei, not accustomed to such sights, would whirl around him in delight, heads bobbing in excitement, running in circles and shouting, "Lao wai! Lao wai!" Foreigner! Foreigner!

This poignant scene evoked in me an analogy that has played on my mind, teasing me to probe its depths. Quasihuman, I exclaimed, to Fake's delight, but Olya's confusion. Stoic explained it as a condensed matter "thing" and she quieted.

This "thing" underlies the success of a single-particle description of metals, which is surprising given how strongly electrons interact through Couloumbic forces. This is the Fermi-liquid theory of metals, which I will henceforth summarize. A Fermi liquid is a many-body interacting state which is smoothly connected to a free-electron state; this smooth connection is very much a thought experiment - one must imagine being able to tune the strength of the Couloumb force from zero (a free-electron state) to its god-given value (a Fermi liquid). Throughout this tuning process, all measurable quantities do not exhibit any singular behavior that is indicative of a phase transition in matter.

Due to this continuity, a Fermi liquid has essentially a single-particle structure. That is, the many-body state is specified by the occupation numbers of single-particle fermionic states, each of which has a well-defined single-particle energy and momentum. We call this single-particle state a quasiparticle - it is an electron that becomes modified by its interactions with other electrons, but such modification is not so substantial and may be thought of as a dressing, such that under the dressing the electron retains its identity. Despite the single-particle structure, the Fermi liquid does not describe independent quasiparticles.

Despite the strength of the Coulomb interaction, its role in this theory is rather minor: (i) Interactions deform single-particle properties (such as mass, energy) from their free-electron values. (ii) Due to interactions, a quasiparticle is unstable and will eventually be scattered into a different quasiparticle state. However, for quasiparticles near the Fermi energy, energy conservation and the Pauli exclusion principle drastically reduce the phase space for scattering, resulting in long-lived quasiparticles.

Presently, I would discard scientific rigor for fanciful entertainment. I like to think of our genetic core as the bare electron, and our interactions with fellow human beings as our dressing, both in the sense of cloth and also of personality and ambition. The smooth connection between bare electron and quasihuman would be the gnarly process of growing up. At each intermediate stage, we are identifiably ourselves, but never exactly the same as before.

Our dressing, unique to ourselves, encourages us to adopt certain roles in society, be it a cook or a physicist. The finite number (N) of each role introduces a notion of exclusion - no role can be played by more than N quasihumans. For society to function with optimal efficiency, there is a unique set of roles that must be filled, comprising the Fermi sea. Society does not encourage quasihumans to rapidly change roles, lest nothing gets done. Indeed, it is quite rude to explain to somebody that they are wasting their lives in an under-appreciated role, unless said person is of a rare species undergoing a 'mid-life crisis' and is therefore receptive to honest criticism.

With the exception of our cloth dressing and language, the rest of our dressing is harder to pinpoint, and has to do with intangible skills that we pick up to navigate society. Once we have grown accustomed to society and society to us, these skills become formidable and, with near-constant repetition, they fade away from our consciousness and become invisible (Schrodinger: consciousness is the tutor of the living flesh). Indeed, once societal constraints (e.g., traffic rules) are completely internalized and therefore completely instinctive, every productive member of society believes themselves to be a free human, i.e., exhibiting free will that is both logical and contrary to common conception (Nietzsche).

The illusion of free will is dispelled once one ventures into a vastly different society. One becomes sharply aware that they dress differently from everybody around them, and attracts around themselves a cloud of honest appraisal. As Stoic found.

In condensed matter physics, another favourite thought experiment is to inject a bare electron into a strongly-interacting metal, and see to what extent it remains a bare electron over time. If the metal is a Fermi liquid, the answer is that this extent is less than unity but nonvanishing, and furthermore the injection excites an incoherent continuum of quasiparticles that we interpret as the dressing.

Saturday, September 12, 2015

Savage mothership

My heart leaps whenever Balsa descends into battle mode, and her spear embodies her fierce resolution and extends pinpoint her superfluid martial prowess.

Her confrontation with Chagum marks such a savage declaration of mothership. A combination of cleverfully-constructed suspense, abject despair and tender consolation comprise one of the most powerful cinematic scenes I have witnessed.

I hope you enjoy this sequel, which deserves its own animation.