Hello, my name is QUANTUM MASTER EQUATION

“Why does it have that name?”

I’ve asked in seminars, in lectures, in offices, and at group meetings. I’ve asked about physical conjectures, about theorems, and about mathematical properties.

“I don’t know.” Lecturers have shrugged. “It’s just a name.”

https://en.wikipedia.org/wiki/Name_tag

This spring, I asked about master equations. I thought of them as tools used in statistical mechanics, the study of vast numbers of particles. We can’t measure vast numbers of particles, so we can’t learn about stat-mech systems everything one might want to know. The magma beneath Santorini, for example, consists of about 1024 molecules. Good luck measuring every one.

http://thewatchers.adorraeli.com/2012/04/18/the-santorini-volcano-caldera-is-awake-again-and-rapidly-deforming/

Imagine, as another example, using a quantum computer to solve a problem. We load information by initializing the computer to a certain state: We orient the computer’s particles in certain directions. We run a program, then read out the output.

Suppose the computer sits on a tabletop, exposed to the air like leftover casserole no one wants to save for tomorrow. Air molecules bounce off the computer, becoming entangled with the hardware. This entanglement, or quantum correlation, alters the computer’s state, just as flies alter a casserole.* To understand the computer’s output—which depends on the state, which depends on the air—we must have a description of the air. But we can’t measure all those air molecules, just as we can’t measure all the molecules in Santorini’s magma.

http://www.savingyoudinero.com/2012/06/05/chicken-fajita-casserole/

We can package our knowledge about the computer’s state into a mathematical object, called a density operator, labeled by ρ(t). A quantum master equation describes how ρ(t) changes. I had no idea, till this spring, why we call master equations “master equations.” Had someone named “John Master” invented them? Had the inspiration for the Russell Crowe movie Master and Commander? Or the Igor who lisps, “Yeth, mathter” in adaptations of Frankenstein?

http://www.wallcoo.net/movie/master_and_commander/html/image4.html

Jenia Mozgunov, a fellow student and Preskillite, proposed an answer: Using master equations, we can calculate how averages of observable properties change. Imagine describing a laser, a cavity that spews out light. A master equation reveals how the average number of photons (particles of light) in the cavity changes. We want to predict these averages because experimentalists measure them. Because master equations spawn many predictions—many equations—they merit the label “master.”

Jenia’s hypothesis appealed to me, but I wanted certainty. I wanted Truth. I opened my laptop and navigated to Facebook.

“Does anyone know,” I wrote in my status, “why master equations are called ‘master equations’?”

Ian Durham, a physicist at St. Anselm College, cited Tom Moore’s Six Ideas that Shaped Physics. Most physics problems, Ian wrote, involve “some overarching principle.” Example principles include energy conservation and invariance under discrete translations (the system looks the same after you step in some direction). A master equation encapsulates this principle.

Ian’s explanation sounded sensible. But fewer people “liked” his reply on Facebook than “liked” a quip by a college friend: Master equations deserve their name because “[t]hey didn’t complete all the requirements for the doctorate.”

My advisor, John Preskill, dug through two to three books, one set of lecture notes, one German Wikipedia page, one to two articles, and Google Scholar. He concluded that Nordsieck, Lamb, and Uhlenbeck coined “master equation.” According to a 1940 paper of theirs,** “When the probabilities of the elementary processes are known, one can write down a continuity equation for W [a set of probabilities], from which all other equations can be derived and which we will call therefore the ‘master’ equation.”

“Are you sure you were meant to be a physicist,” I asked John, “rather than a historian?”

“Procrastination is a powerful motivator,” he replied.

Lecturers have shrugged at questions about names. Then they’ve paused, pondered, and begun, “I guess because…” Theorems and identities derive their names from symmetries, proof techniques, geometric illustrations, and applications to problems I’d thought unrelated. A name taught me about uses for master equations. Names reveal physics I wouldn’t learn without asking about names. Names aren’t just names. They’re lamps and guides.

Pity about the origin of “master equation,” though. I wish an Igor had invented them.

http://fashions-cloud.com/pages/y/young-frankenstein-igor-brain/

*Apologies if I’ve spoiled your appetite.

**A. Nordsieck, W. E. Lamb, and G. E. Uhlenbeck, “On the theory of cosmic-ray showers I,” Physica 7, 344-60 (1940), p. 353.

20 years of qubits: the arXiv data

Editor’s Note: The preceding post on Quantum Frontiers inspired the always curious Paul Ginsparg to do some homework on usage of the word “qubit” in papers posted on the arXiv. Rather than paraphrase Paul’s observations I will quote his email verbatim, so you can experience its Ginspargian style.qubit-data

fig has total # uses of qubit in arxiv (divided by 10) per month, and
total # docs per month:
an impressive 669394 total in 29587 docs.

the graph starts at 9412 (dec '94), but that is illusory since qubit
only shows up in v2 of hep-th/9412048, posted in 2004.
the actual first was quant-ph/9503016 by bennett/divicenzo/shor et al
(posted 23 Mar '95) where they carefully attribute the term to
schumacher ("PRA, to appear '95") and jozsa/schumacher ("J. Mod Optics
'94"), followed immediately by quant-ph/9503017 by deutsch/jozsa et al
(which no longer finds it necessary to attribute term)

[neither of schumacher's first two articles is on arxiv, but otherwise
probably have on arxiv near 100% coverage of its usage and growth, so
permits a viral epidemic analysis along the lines of kaiser's "drawing
theories apart"  of use of Feynman diagrams in post wwII period].

ever late to the party, the first use by j.preskill was
quant-ph/9602016, posted 21 Feb 1996

#articles by primary subject area as follows (hep-th is surprisingly
low given the firewall connection...):

quant-ph 22096
cond-mat.mes-hall 3350
cond-mat.supr-con 880
cond-mat.str-el 376
cond-mat.mtrl-sci 250
math-ph 244
hep-th 228
physics.atom-ph 224
cond-mat.stat-mech 213
cond-mat.other 200
physics.optics 177
cond-mat.quant-gas 152
physics.gen-ph 120
gr-qc 105
cond-mat 91
cs.CC 85
cs.IT 67
cond-mat.dis-nn 55
cs.LO 49
cs.CR 43
physics.chem-ph 33
cs.ET 25
physics.ins-det 21
math.CO,nlin.CD 20
physics.hist-ph,physics.bio-ph,math.OC 19
hep-ph 18
cond-mat.soft,cs.DS,math.OA 17
cs.NE,cs.PL,math.QA 13
cs.AR,cs.OH 12
physics.comp-ph 11
math.LO 10
physics.soc-ph,physics.ed-ph,cs.AI 9
math.ST,physics.pop-ph,cs.GT 8
nlin.AO,astro-ph,cs.DC,cs.FL,q-bio.GN 7
nlin.PS,math.FA,cs.NI,math.PR,q-bio.NC,physics.class-ph,math.GM,
physics.data-an 6
nlin.SI,math.CT,q-fin.GN,cs.LG,q-bio.BM,cs.DM,math.GT 5
math.DS,physics.atm-clus,q-bio.PE 4
math.DG,math.CA,nucl-th,q-bio.MN,math.HO,stat.ME,cs.MS,q-bio.QM,
math.RA,math.AG,astro-ph.IM,q-bio.OT 3
stat.AP,cs.CV,math.SG,cs.SI,cs.SE,cs.SC,cs.DB,stat.ML,physics.med-ph,
math.RT 2
cs.CL,cs.CE,q-fin.RM,chao-dyn,astro-ph.CO,q-fin.ST,math.NA,
cs.SY,math.MG,physics.plasm-ph,hep-lat,math.GR,cs.MM,cs.PF,math.AC,
nucl-ex 1

Who named the qubit?

Perhaps because my 40th wedding anniversary is just a few weeks away, I have been thinking about anniversaries lately, which reminded me that we are celebrating the 20th anniversary of a number of milestones in quantum information science. In 1995 Cirac and Zoller proposed, and Wineland’s group first demonstrated, the ion trap quantum computer. Quantum error-correcting codes were invented by Shor and Steane, entanglement concentration and purification were described by Bennett et al., and there were many other fast-breaking developments. It was an exciting year.

But the event that moved me to write a blog post is the 1995 appearance of the word “qubit” in an American Physical Society journal. When I was a boy, two-level quantum systems were called “two-level quantum systems.” Which is a descriptive name, but a mouthful and far from euphonious. Think of all the time I’ve saved in the past 20 years by saying “qubit” instead of “two-level quantum system.” And saying “qubit” not only saves time, it also conveys the powerful insight that a quantum state encodes a novel type of information. (Alas, the spelling was bound to stir controversy, with the estimable David Mermin a passionate holdout for “qbit”. Give it up, David, you lost.)

Ben Schumacher. Thanks for the qubits, Ben!

Ben Schumacher. Thanks for the qubits, Ben!

For the word “qubit” we know whom to thank: Ben Schumacher. He introduced the word in his paper “Quantum Coding” which appeared in the April 1995 issue of Physical Review A. (History is complicated, and in this case the paper was actually submitted in 1993, which allowed another paper by Jozsa and Schumacher to be published earlier even though it was written and submitted later. But I’m celebrating the 20th anniversary of the qubit now, because otherwise how will I justify this blog post?)

In the acknowledgments of the paper, Ben provided some helpful background on the origin of the word:

The term “qubit” was coined in jest during one of the author’s many intriguing and valuable conversations with W. K. Wootters, and became the initial impetus for this work.

I met Ben (and other luminaries of quantum information theory) for the first time at a summer school in Torino, Italy in 1996. After reading his papers my expectations were high, all the more so after Sam Braunstein warned me that I would be impressed: “Ben’s a good talker,” Sam assured me. I was not disappointed.

(I also met Asher Peres at that Torino meeting. When I introduced myself Asher asked, “Isn’t there someone with a similar name in particle theory?” I had no choice but to come clean. I particularly remember that conversation because Asher told me his secret motivation for studying quantum entanglement: it might be important in quantum gravity!)

A few years later Ben spent his sabbatical year at Caltech, which gave me an opportunity to compose a poem for the introduction to Ben’s (characteristically brilliant) talk at our physics colloquium. This poem does homage to that famous 1995 paper in which Ben not only introduced the word “qubit” but also explained how to compress a quantum state to the minimal number of qubits from which the original state can be recovered with a negligible loss of fidelity, thus formulating and proving the quantum version of Shannon’s famous source coding theorem, and laying the foundation for many subsequent developments in quantum information theory.

Sometimes when I recite a poem I can sense the audience’s appreciation. But in this case there were only a few nervous titters. I was going for edgy but might have crossed the line into bizarre.. Since then I’ve (usually) tried to be more careful.

(For reading the poem, it helps to know that the quantum state appears to be random when it has been compressed as much as possible.)

On Quantum Compression (in honor of Ben Schumacher)

Ben.
He rocks.
I remember
When
He showed me how to fit
A qubit
In a small box.

I wonder how it feels
To be compressed.
And then to pass
A fidelity test.

Or does it feel
At all, and if it does
Would I squeal
Or be just as I was?

If not undone
I’d become as I’d begun
And write a memorandum
On being random.
Had it felt like a belt
Of rum?

And might it be predicted
That I’d become addicted,
Longing for my session
Of compression?

I’d crawl
To Ben again.
And call,
“Put down your pen!
Don’t stall!
Make me small!”

Mingling stat mech with quantum info in Maryland

I felt like a yoyo.

I was standing in a hallway at the University of Maryland. On one side stood quantum-information theorists. On the other side stood statistical-mechanics scientists.* The groups eyed each other, like Jets and Sharks in West Side Story, except without fighting or dancing.

This March, the groups were generous enough to host me for a visit. I parked first at QuICS, the Joint Center for Quantum Information and Computer Science. Established in October 2014, QuICS had moved into renovated offices the previous month. QuICSland boasts bright colors, sprawling armchairs, and the scent of novelty. So recently had QuICS arrived that the restroom had not acquired toilet paper (as I learned later than I’d have preferred).

Interaction space

Photo credit: QuICS

From QuICS, I yoyo-ed to the chemistry building, where Chris Jarzynski’s group studies fluctuation relations. Fluctuation relations, introduced elsewhere on this blog, describe out-of-equilibrium systems. A system is out of equilibrium if large-scale properties of it change. Many systems operate out of equilibrium—boiling soup, combustion engines, hurricanes, and living creatures, for instance. Physicists want to describe nonequilibrium processes but have trouble: Living creatures are complicated. Hence the buzz about fluctuation relations.

My first Friday in Maryland, I presented a seminar about quantum voting for QuICS. The next Tuesday, I was to present about one-shot information theory for stat-mech enthusiasts. Each week, the stat-mech crowd invites its speaker to lunch. Chris Jarzynski recommended I invite QuICS. Hence the Jets-and-Sharks tableau.

“Have you interacted before?” I asked the hallway.

“No,” said a voice. QuICS hadn’t existed till last fall, and some QuICSers hadn’t had offices till the previous month.**

Silence.

“We’re QuICS,” volunteered Stephen Jordan, a quantum-computation theorist, “the Joint Center for Quantum Information and Computer Science.”

So began the mingling. It continued at lunch, which we shared at three circular tables we’d dragged into a chain. The mingling continued during the seminar, as QuICSers sat with chemists, materials scientists, and control theorists. The mingling continued the next day, when QuICSer Alexey Gorshkov joined my discussion with the Jarzynski group. Back and forth we yoyo-ed, between buildings and topics.

“Mingled,” said Yigit Subasi. Yigit, a postdoc of Chris’s, specialized in quantum physics as a PhD student. I’d asked how he thinks about quantum fluctuation relations. Since Chris and colleagues ignited fluctuation-relation research, theorems have proliferated like vines in a jungle. Everyone and his aunty seems to have invented a fluctuation theorem. I canvassed Marylanders for bushwhacking tips.

Imagine, said Yigit, a system whose state you know. Imagine a gas, whose temperature you’ve measured, at equilibrium in a box. Or imagine a trapped ion. Begin with a state about which you have information.

Imagine performing work on the system “violently.” Compress the gas quickly, so the particles roil. Shine light on the ion. The system will leave equilibrium. “The information,” said Yigit, “gets mingled.”

Imagine halting the compression. Imagine switching off the light. Combine your information about the initial state with assumptions and physical laws.*** Manipulate equations in the right way, and the information might “unmingle.” You might capture properties of the violence in a fluctuation relation.

2 photos - cut

With Zhiyue Lu and Andrew Maven Smith of Chris Jarzynski’s group (left) and with QuICSers (right)

I’m grateful to have exchanged information in Maryland, to have yoyo-ed between groups. We have work to perform together. I have transformations to undergo.**** Let the unmingling begin.

With gratitude to Alexey Gorshkov and QuICS, and to Chris Jarzynski and the University of Maryland Department of Chemistry, for their hospitality, conversation, and camaraderie.

*Statistical mechanics is the study of systems that contain vast numbers of particles, like the air we breathe and white dwarf stars. I harp on about statistical mechanics often.

**Before QuICS’s birth, a future QuICSer had collaborated with a postdoc of Chris’s on combining quantum information with fluctuation relations.

***Yes, physical laws are assumptions. But they’re glorified assumptions.

****Hopefully nonviolent transformations.

Paul Dirac and poetry

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite!

      – Paul Dirac

http://en.wikiquote.org/wiki/Paul_Dirac

Paul Dirac

I tacked Dirac’s quote onto the bulletin board above my desk, the summer before senior year of high school. I’d picked quotes by T.S. Elliot and Einstein, Catullus and Hatshepsut.* In a closet, I’d found amber-, peach-, and scarlet-colored paper. I’d printed the quotes and arranged them, starting senior year with inspiration that looked like a sunrise.

Not that I knew who Paul Dirac was. Nor did I evaluate his opinion. But I’d enrolled in Advanced Placement Physics C and taken the helm of my school’s literary magazine. The confluence of two passions of mine—science and literature—in Dirac’s quote tickled me.

A fiery lecturer began to alleviate my ignorance in college. Dirac, I learned, had co-invented quantum theory. The “Dee-rac Equa-shun,” my lecturer trilled in her Italian accent, describes relativistic quantum systems—tiny particles associated with high speeds. I developed a taste for spin, a quantum phenomenon encoded in Dirac’s equation. Spin serves quantum-information scientists as two-by-fours serve carpenters: Experimentalists have tried to build quantum computers from particles that have spins. Theorists keep the idea of electron spins in a mental car trunk, to tote out when illustrating abstract ideas with examples.

The next year, I learned that Dirac had predicted the existence of antimatter. Three years later, I learned to represent antimatter mathematically. I memorized the Dirac Equation, forgot it, and re-learned it.

One summer in grad school, visiting my parents, I glanced at my bulletin board.

The sun rises beyond a window across the room from the board. Had the light faded the papers’ colors? If so, I couldn’t tell.

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite!

Do poets try to obscure ideas everyone understands? Some poets express ideas that people intuit but feel unable, lack the attention, or don’t realize one should, articulate. Reading and hearing poetry helps me grasp the ideas. Some poets express ideas in forms that others haven’t imagined.

Did Dirac not represent physics in a form that others hadn’t imagined?

Dirac Eqn

The Dirac Equation

Would you have imagined that form? I didn’t imagine it until learning it. Do scientists not express ideas—about gravity, time, energy, and matter—that people feel unable, lack the attention, or don’t realize we should, articulate?

The U.S. and Canada have designated April as National Poetry Month. A hub for cousins of poets, Quantum Frontiers salutes. Carry a poem in your pocket this month. Or carry a copy of the Dirac Equation. Or tack either on a bulletin board; I doubt whether their colors will fade.

http://cdn.shopify.com/s/files/1/0377/1697/products/2011_poster_WEB_1024x1024.jpg?v=1410808396

*“Now my heart turns this way and that, as I think what the people will say. Those who see my monuments in years to come, and who shall speak of what I have done.” I expect to build no such monuments. But here’s to trying.

Putting back the pieces of a broken hologram

It is Monday afternoon and the day seems to be a productive one, if not yet quite memorable. As I revise some notes on my desk, Beni Yoshida walks into my office to remind me that the high-energy physics seminar is about to start. I hesitate, somewhat apprehensive of the near-certain frustration of being lost during the first few minutes of a talk in an unfamiliar field. I normally avoid such a situation, but in my email I find John’s forecast for an accessible talk by Daniel Harlow and a title with three words I can cling onto. “Quantum error correction” has driven my curiosity for the last seven years. The remaining acronyms in the title will become much more familiar in the four months to come.

Most of you are probably familiar with holograms, these shiny flat films representing a 3D object from essentially any desired angle. I find it quite remarkable how all the information of a 3D object can be printed on an essentially 2D film. True, the colors are not represented as faithfully as in a traditional photograph, but it looks as though we have taken a photograph from every possible angle! The speaker’s main message that day seemed even more provocative than the idea of holography itself. Even if the hologram is broken into pieces, and some of these are lost, we may still use the remaining pieces to recover parts of the 3D image or even the full thing given a sufficiently large portion of the hologram. The 3D object is not only recorded in 2D, it is recorded redundantly!

Left to right: Beni Yoshida, Aleksander Kubica, Aidan Chatwin-Davies and Fernando Pastawski discussing holographic codes.

Left to right: Beni Yoshida, Aleksander Kubica, Aidan Chatwin-Davies and Fernando Pastawski discussing holographic codes.

Half way through Daniel’s exposition, Beni and I exchange a knowing glance. We recognize a familiar pattern from our latest project. A pattern which has gained the moniker of “cleaning lemma” within the quantum information community which can be thought of as a quantitative analog of reconstructing the 3D image from pieces of the hologram. Daniel makes connections using a language that we are familiar with. Beni and I discuss what we have understood and how to make it more concrete as we stride back through campus. We scribble diagrams on the whiteboard and string words such as tensor, encoder, MERA and negative curvature into our discussion. An image from the web gives us some intuition on the latter. We are onto something. We have a model. It is simple. It is new. It is exciting.

Poincare projection of a regular pentagon tiling of negatively curved space.

Poincare projection of a regular pentagon tiling of negatively curved space.

Food has not come our way so we head to my apartment as we enthusiastically continue our discussion. I can only provide two avocados and some leftover pasta but that is not important, we are sharing the joy of insight. We arrange a meeting with Daniel to present our progress. By Wednesday Beni and I introduce the holographic pentagon code at the group meeting. A core for a new project is already there, but we need some help to navigate the high-energy waters. Who better to guide us in such an endeavor than our mentor, John Preskill, who recognized the importance of quantum information in Holography as early as 1999 and has repeatedly proven himself a master of both trades.

“I feel that the idea of holography has a strong whiff of entanglement—for we have seen that in a profoundly entangled state the amount of information stored locally in the microscopic degrees of freedom can be far less than we would naively expect. For example, in the case of the quantum error-correcting codes, the encoded information may occupy a small ‘global’ subspace of a much larger Hilbert space. Similarly, the distinct topological phases of a fractional quantum Hall system look alike locally in the bulk, but have distinguishable edge states at the boundary.”
-J. Preskill, 1999

As Beni puts it, the time for using modern quantum information tools in high-energy physics has come. By this he means quantum error correction and maybe tensor networks. First privately, then more openly, we continue to sharpen and shape our project. Through conferences, Skype calls and emails, we further our discussion and progressively shape ideas. Many speculations mature to conjectures and fall victim to counterexamples. Some stand the test of simulations or are even promoted to theorems by virtue of mathematical proofs.

Beni Yoshida presenting our work at a quantum entanglement conference in Puerto Rico.

Beni Yoshida presenting our work at a quantum entanglement conference in Puerto Rico.

I publicly present the project for the first time at a select quantum information conference in Australia. Two months later, after a particularly intense writing, revising and editing process, the article is almost complete. As we finalize the text and relabel the figures, Daniel and Beni unveil our work to quantum entanglement experts in Puerto Rico. The talks are a hit and it is time to let all our peers read about it.

You are invited to do so and Beni will even be serving a reader’s guide in an upcoming post.

Quantum Frontiers salutes Terry Pratchett.

I blame British novels for my love of physics. Philip Pullman introduced me to elementary particles; Jasper Fforde, to the possibility that multiple worlds exist; Diana Wynne Jones, to questions about space and time.

So began the personal statement in my application to Caltech’s PhD program. I didn’t mention Sir Terry Pratchett, but he belongs in the list. Pratchett wrote over 70 books, blending science fiction with fantasy, humor, and truths about humankind. Pratchett passed away last week, having completed several novels after doctors diagnosed him with early-onset Alzheimer’s. According to the San Francisco Chronicle, Pratchett “parodie[d] everything in sight.” Everything in sight included physics.

http://www.lookoutmountainbookstore.com/

Terry Pratchett continues to influence my trajectory through physics: This cover has a cameo in a seminar I’m presenting in Maryland this March.

Pratchett set many novels on the Discworld, a pancake of a land perched atop four elephants, which balance on the shell of a turtle that swims through space. Discworld wizards quantify magic in units called thaums. Units impressed their importance upon me in week one of my first high-school physics class. We define one meter as “the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.” Wizards define one thaum as “the amount of magic needed to create one small white pigeon or three normal-sized billiard balls.”

Wizards study the thaum in a High-Energy Magic Building reminiscent of Caltech’s Lauritsen-Downs Building. To split the thaum, the wizards built a Thaumatic Resonator. Particle physicists in our world have split atoms into constituent particles called mesons and baryons. Discworld wizards discovered that the thaum consists of resons. Mesons and baryons consist of quarks, seemingly elementary particles that we believe cannot be split. Quarks fall into six types, called flavors: up, down, charmed, strange, top (or truth), and bottom (or beauty). Resons, too, consist of quarks. The Discworld’s quarks have the flavors up, down, sideways, sex appeal, and peppermint.

Reading about the Discworld since high school, I’ve wanted to grasp Pratchett’s allusions. I’ve wanted to do more than laugh at them. In Pyramids, Pratchett describes “ideas that would make even a quantum mechanic give in and hand back his toolbox.” Pratchett’s ideas have given me a hankering for that toolbox. Pratchett nudged me toward training as a quantum mechanic.

Pratchett hasn’t only piqued my curiosity about his allusions. He’s piqued my desire to create as he did, to do physics as he wrote. While reading or writing, we build worlds in our imaginations. We visualize settings; we grow acquainted with characters; we sense a plot’s consistency or the consistency of a system of magic. We build worlds in our imaginations also when doing and studying physics and math. The Standard Model is a system that encapsulates the consistency of our knowledge about particles. We tell stories about electrons’ behaviors in magnetic fields. Theorems’ proofs have logical structures like plots’. Pratchett and other authors trained me to build worlds in my imagination. Little wonder I’m training to build worlds as a physicist.

Around the time I graduated from college, Diana Wynne Jones passed away. So did Brian Jacques (another British novelist) and Madeleine L’Engle. L’Engle wasn’t British, but I forgave her because her Time Quartet introduced me to dimensions beyond three. As I completed one stage of intellectual growth, creators who’d led me there left.

Terry Pratchett has joined Jones, Jacques, and L’Engle. I will probably create nothing as valuable as his Discworld, let alone a character in the Standard Model toward which the Discworld steered me.

But, because of Terry Pratchett, I have to try.