Below is a snapshot of a computation I was working on earlier this Summer. Will explain later. Spoke about it at the Southern California Strings Seminar.
I’m curious about what a physicist’s scribblings look like to others, regardless of field (science or non-science). So, non-specialists: What does this all look like, to you? What impressions do you get, if any? Do tell.
There’s no wrong answer here.
-cvj
Cosmic Variance is a group blog by people who, coincidentally or not, all happen to be physicists and astrophysicists:
Our day (and night) jobs notwithstanding, the blog is about whatever we find interesting — science, to be sure, but also arts, politics, culture, technology, academia, and miscellaneous trivia. We have similar outlooks on many things, widely disparate opinions about others, and will do our best to keep the discourse reasonably elevated.
October 3rd, 2005 at 1:34 pm
Hey Clifford, it looks cool to me. I like writing on blackboards.
That was my non-student view on the thing.
My student view: Looks scary as hell. Guesses on what it is comes later!
Cheers, Helge
October 3rd, 2005 at 1:42 pm
It looks like someone really ought to sell some kind of stretchy snap-together topology toys.
October 3rd, 2005 at 1:57 pm
Something is definetly merging there. Perhaps there is a flow, but more likely the computations have something to do with the pipes themselves.
One theory is that since there are strings involved, the pipes are some kind of a 3d extension of strings.
This might not make sense to you; then again, most of theoretical and high-energy physics does not make sense to me. Let’s call it a draw!
October 3rd, 2005 at 2:06 pm
body part assembly plant. Looks like engineers scribbling.
October 3rd, 2005 at 2:22 pm
I think the interesting thing here Clifford is that you would even ask:) You have taken bloggery to new heights.
But if you follow the subject, this is part of the developement that I had been trying, in my self motivated wisdom to try and comprehend.
While later life provides ample time to have a look at what mathematicains are doing, it is equally nice to understand these relations with the normal world? Is there “theoretically” such a thing?:)
I think so and such relevance in relation to the toy models of feynman diagrams, are these not readily available for introspection among such a blackboard as this?
So prepare our young minds then Clifford in a history so that we might say on second look, “ah I now know what Clifford is doing.”
Even Sean plays his roles in this one. So here is the case then for a “string theorist” to make their claim?
October 3rd, 2005 at 2:24 pm
Though intriguing it’s not art, sorry: you forgot a “Do not wipe out” or your signature.
October 3rd, 2005 at 2:25 pm
Plato said: “You have taken bloggery to new heights.”
Oooh, you flatterer you!
-cvj
October 3rd, 2005 at 2:32 pm
Something this blackboard reminds me of, is the trouble with the alphabet. It has like 26 letters, but only a few are usuable. Like x, lamba, and the big Gamma. And here you are even using the greek one too!
Or are that kappas and not x?
Cheers, from just another freak knowing the greek alphabet, but not a single word.
October 3rd, 2005 at 2:36 pm
The things down the left side look like failed designs for clothing patterns. The top one looks like trousers which can be worn either way up. On the next one, the pants are OK, but there’s no hole in the top for a head. And the third looks like two pairs of trousers mating.
Lots of xs and lamdas. I suppose I expected far more variable names.
October 3rd, 2005 at 2:48 pm
Looks like plumbing.
Rube Goldberg does not need another toilet.
As for the equations – we could call them flow calcs, I guess. Maybe it’s a toilet drainage array for the Kingdome. With control levers.
Or maybe I need more than two hours’ sleep.
CS
October 3rd, 2005 at 2:49 pm
plumbing parts
October 3rd, 2005 at 2:53 pm
My first thought was macaroni, but the clothing designs also occurred to me, especially the ones on the left that look sort of like pairs of trousers; but then in the middle there’s something that looks like a crude robot.
Actually, what it looks like is a New Yorker cartoon, but I can’t think of a good caption.
October 3rd, 2005 at 3:19 pm
I think you made a sign error and missed a factor of 2.
October 3rd, 2005 at 3:32 pm
Clifford,
This looks cooked up, surely nobody’s blackboard is that clean and organized, with such beautiful figures. On second thought though, I do remember the blackboards in Aspen were unusually attractive some afternoons.
October 3rd, 2005 at 3:33 pm
Planning for a heart, liver, kidney and gall-bladder transplant. The drawings show the woven-Teflon fittings that will be used to splice blood vessels. The equations are there to make the surgeons feel less like plumbers and more like real scientists, e.g. M-theorists.
October 3rd, 2005 at 3:37 pm
Looks like you are working out the topology of strings as they evolve through time.
While I do not understand the content, I think I recognize the mode of thinking. It is the same thing mathematicians do: sketch an argument or explore lines of reasoning using a combination of diagrams and formulas that are sensible only to someone trained in that field.
This is the perspective of a mathematician, though I have not looked at topology since I took my qualifying exams in grad school several years ago.
October 3rd, 2005 at 3:53 pm
Speaking as a true expert on this topic, I’d say that this looks like evidence that either you are tall, or the board is quite short. At 5′4″, I never get to use that oh-so-enticing top quarter of the board…
October 3rd, 2005 at 3:54 pm
It could be closed strings separating and merging, with an operator ‘x’ that (cuts and) pastes. It preserves Gamma which could be string tension. Which seem to allow for some calculations. But perhaps this is all a pipe dream.
October 3rd, 2005 at 3:55 pm
I’m familiar at least with the common notations if not with their usage in advanced Math and Physics. But this sure looks strange. I suspect your calculations have to do with string theory. Or maybe the loops are some aggregations of quantum foam? Usually x is used to denote points in spacetime and lambda is some kind of parameter, so it was kind of unnerving to see you adding powers of x to lambda terms and taking derivatives or doing some operation denoted by ‘ (?)
It is also interesting to see that you have not used any of the usual physical (and numerical) constants such as c, pi, e, G, hbar etc. Or all they all set to 1?
How come you don’t have any integrals or bra-kets?
Or did you add some … ahem .. unusual nutrition to your vegetable plots at home and decided to develop a whole new branch of topology to describe the geometry of the harvest?
October 3rd, 2005 at 4:03 pm
It can be done! Putting the tomatoes and and beef INSIDE the macaroni is genius. We will surely win the race to achieve the first sauceless goulash!
October 3rd, 2005 at 4:04 pm
Laundry management meets football coach.
October 3rd, 2005 at 4:09 pm
jfaberuiuc on Oct 3rd, 2005 at 3:53 pm
Speaking as a true expert on this topic, I’d say that this looks like evidence that either you are tall, or the board is quite short. At 5′4″, I never get to use that oh-so-enticing top quarter of the board…
**************************************************
I agree … sigh. I HATE it when I hold a LONG piece of chalk from the tips of my fingers and rise up on my toes to write all crooked, with the chalk dust falling in my eyes just so that I can keep as many equations as possible on the chalkboard. (I’m 5′3″, for the record.)
October 3rd, 2005 at 4:11 pm
A highly scientific deconstruction of the method to depants someone.
October 3rd, 2005 at 4:15 pm
As had long been speculated, Clifford did not put his pants on like everyone else, one leg at a time.
October 3rd, 2005 at 4:33 pm
A plan for some kind of vascular surgery …
October 3rd, 2005 at 4:40 pm
It looks like a fairly typical math filled blackboard but with an unusual large number of diagrams.
The diagrams seem to have something to do with topology and the symbols look like some kind of asymptotic expansion.
Not that it MEANS anything to me…
Now, let me see what others thought…
October 3rd, 2005 at 4:43 pm
Looks like some loop amplitude calculations.
October 3rd, 2005 at 5:03 pm
This image reminded me of a favorite photograph of a blackboard. It is of an important letter in physics, the letter “h” and is underlined three times, strongly underlined. It is found in Arthur Miller’s splendid study, “Imagery in Scientific Thought: Creating 20th Centrury Physics (MIT Press 1986). Niels Bohr had done the underlining while makiing a point about physics. There is part of me that wishes it were never erased and a part of me that also believes this is what should be done. Still, I’m glad for the photograph.
I want to thank you for letting us take a peek, this result of you at work. It gives me an insight into the tools you use as you think, perhaps how you think (although I lack the mathematical/visual skills to really know much about this), stuff many of us don’t often see or know much about, part of that record of science that doesn’t get published. Such traces are filled with delight.
Do I dare quote Lumo who recently wrote on blackboards? why not?! You can’t give me a boot where it counts from there! A few weeks ago, Czech president Vaclav Klaus was at Harvard’s Center for European Studies (CES). In his comments on this occasion, Professor Motl noted that “Klaus became the first person in the CES who used the so-called blackboard. The CES is not like our physics department where we fill all the blackboards on the walls with physics five times a day; in the CES, the blackfboard is apparently only used as a background for a CES poster” (followed by Professor Motl’s trademark, a smily). So, maybe some of my pleasure is the expectation that this is what you do when not at the farmer’s market.
I thought,too, of another blackboard I never tire of seeing. Japanese teachers, at least many in elementary school when teaching science, make use of blackboards as records of the day’s lesson from beginning to end. The few I’ve seen are remarkable, data rich for researchers whom I don’t think have ever used them; extraordinary summaries and aids in keeping the class and themselves on task. They could be very useful and helpful to students, too. They are a remarkable tool. I suspect before they are erased that they are used to think about the lesson to follow.
This blog is richer for this posting but it is never deficient in calories; this a dessert course.
Cheers.
October 3rd, 2005 at 5:08 pm
What I don’t quite get is, since it looks like space-time paths of strings (or something like that; my knowledge comes only from lay-books like Brian Greene’s), why draw them as loops at all, rather than just branching lines, a la Feynman? I see that one half of each initial loop (assuming time goes left to right) has a little x, to orient the loop or something, but since the other end of the piping has no x’s, it doesn’t seem like there’s any twisting or anything going on, and so I don’t see how the diagrams contain any more info than branching/reconnecting lines would have. Maybe the the equations contain all sorts of twistiness though, and the pictures are just frameworks to help the mind’s eye. I guess there’s also those little circles pointing to sections of the surface of the space-time piping, which presumably say something about what is going on on that 2D surface. Pretty stuff though.
October 3rd, 2005 at 5:18 pm
Clifford,
You fellows really stretch the imagination.
Graviton emission can occur when open strings collide and form closed strings that are free to go into the bulk.
http://physicsweb.org/articles/world/13/11/9/1
I couldn’t help envisioning Steinhardt’s model of colliding branes.
Why can we not see in this way? Why do People not like to entertain such theoretical models. If it helps us see your drawing as a pair of pants, why not include, Smolins idealization in Glast determination as relevant.
Are you not both working to the same ends?
Calorimetric views, of what existed in the beginning, as this action?
Am I way off base here?
October 3rd, 2005 at 5:24 pm
It’s a M-Theory tube diagram.
October 3rd, 2005 at 5:32 pm
sorta looks like a pantyhose assembly line design analysis
October 3rd, 2005 at 5:34 pm
Blackboards are like Buddhist sand mandalas — meant to be enjoyed for a brief period and then destroyed, as a reminder of the impermanence of life.
But I’m with Moshe; this one looks a little too pretty to be true. Perhaps the art was influencing the artist?
October 3rd, 2005 at 5:59 pm
Speaking of non-physicists intepreting physics (or at least physicists), here’s a round-up of the reviews of the new opera about Robert Oppenheimer, Doctor Atomic, which just premiered in San Francisco:
http://irontongue.blogspot.com/2005/10/fallout.html
October 3rd, 2005 at 6:03 pm
I also thought it too good to be true – a physicist with handwriting that remains neat all the way down the board?! Though to be fair, a closer look revealed that there are several places where parts of diagrams have been rubbed out with the fingers, which gave it a little more authenticity.
Looking forward to the explanation though!
October 3rd, 2005 at 6:08 pm
Let me decode your diagram for you, Clifford.
It is a story and it says:
Yesterday, I punctured the tires on my Rolls Royce. I’ve created two big holes in it. We will see how much (x) it will cost to fix it. If I will count the damage “x” including the sales tax lambda, we will save -1/2 on income taxes. But if we don’t include lambda, we will save the same thing. My friend pays 4 times as much (-4/2) anyway.
Maybe I could fix the tire myself. Let’s take my pants, attach them to the first hole on the tire, and cut the tire on the other side. The piece of the rubber will look like a disk, and the cost will be just like before. It’s always calculated from x and lambda to some power.
A better idea could be to throw away the tire completely, and replace it by two pairs of pants. We may obtain a new tire for the Rolls Royce by sewing the bottom holes on the pants. It we don’t sew it properly, there will be (2,1,0) holes left at various places. That’s too bad. We will still have to attach two disk-shaped patches on it.
It may be better to ignore the whole inside the tire. What about just taking a cylinder and …
Clifford combines and recombines his pants and tires and patches for three more hours, and the cost is always the same, except for the derivatives in the last expression. Eventually he gives up, having filled the whole blackboard, and buys a new Rolls Royce.
October 3rd, 2005 at 6:16 pm
For those who like visualizations and the undertanding that universe are cyclical in nature, this leaves one with ideas about the bulk perceptions and receding elements in the universe. What is empty sapce really made of then?
The interesting thing about “mandalas” though, is the structure with which it comes into existance. While the three dimensional attribute of sand mandalas are destroyed, there always understood as to what they were building, even on the surface and with which colors of sand. For the buddhists it is a temple with allegorical relations in evlutionary psychology? Archetectually such symbology modelling has it’s place?
So that structure never really leaves you, even those you look on the blackboard and erase. The “blank slate” or “white board” provides opportunities for expressing these new ideas, and this is the understanding that they issue from some place. While we work on the “screen” computerization really lets us know that we are definitiely working in new terrain. Much closer to probable realites in a fifth dimesional sense even to see it might represent “light” in a flash. The brain might recognize this as a idea?
October 3rd, 2005 at 6:48 pm
It looks to me like some equations that have very few “identities of one” left in them, and probably concern topography. To your mind, a pinnacle, to mine, a Grand Canyon in which I am careful not to venture without an experienced guide. And a bottle of aspirin.
October 3rd, 2005 at 8:19 pm
Clifford, blackboards are so dated. Using glass or clear perspex panels, with colored fibre pens, is so much cooler:) I would say you are carefully figuring out the optimum way to cut up and cook the veggies you grew this year.
October 3rd, 2005 at 8:39 pm
(I’m a pure mathematician, or at least I was several years ago. I don’t know a thing about string theory beyond what I’ve gleaned from a couple of very popular accounts. I hope that’s sufficiently non-specialist.)
Strings. Something akin to knot polynomials, where topological operations on surfaces correspond to algebraic operations on (Laurent) polynomials. Looks like the top-level question is something along the lines of “consider something with an S^1 at each end and genus-1 stuff in the middle; how can that come about?” That corresponds to something like photon -> e + anti-e -> photon, right? I guess the Gamma is just a label for one component of the boundary. It feels a bit weird to see something that I’d expect to mean “cartesian product” used to mean something more akin to “concatenation”, but maybe it makes sense category-theoretically if you look at it right. The bits where you seem to be joining cones onto things look particularly strange. (Do they somehow correspond to events where a particle loses some energy and emits a photon, or the reverse?) Much repetition; you’re clearly less lazy than I am. I suspect that an hour’s hard thinking might condense what’s on the blackboard into about a quarter of the space
.
October 3rd, 2005 at 9:09 pm
But there are no square roots! In the movies, there must always be a big square root sign on the blackboard of a scientist, to show that it is scientific. And preferably some nonsensical equations. By the way, about “do not erase”-signs: when I was at Ecole Polytechnique, we had these ingenious little signs that you could put by your blackboard saying “Ne pas effacer” (do not erase). Then, if you wanted the cleaners to wipe your board you could turn it over, and the next time they cleaned, you’d get a fresh start! (Not that anybody ever turned their signs over…)
October 3rd, 2005 at 9:13 pm
It is a very artistic board. Remarkably few smudges.
Also, you were writing out expressions and then taking a square root, I see x^(-4/2) s and perhaps a x^(-2/2) (that had better not be a z in the denominator).
October 3rd, 2005 at 9:23 pm
g,
Lubos, was giving us a “Lewis Carroll” discription above.But instead of Alice and Mirrors, he likes talking about tires and holes:)
Do all mathematicians think alike, in disemminating from the center, pure mathematics arise, to general concepts of “fiction” further out?:)
With skeptic valuation of what god might be to some, this idea of buddhist recognition might be more palatable. Maybe Sean could apply his skepticism and could give us a course in this as well?:)
See that’s the point. What will materialize from this center, in that flash?
October 3rd, 2005 at 9:40 pm
Synchronicitously, today i was looking through some of the print collections of the LeRoy Neiman Center for Print Studies at Columbia. In and amongst them are some with which your blackboard could easily be associated. Intaglio is an interesting medium when the plates are left more to the random chemical reactions that occur as the acid works its way through various “tints” and lifts. Sometimes they begin to look a great deal like images from the linear accelerators and colliders. This blackboard image of yours could stand up in such a collection. Either that or Mattel is working on developing a new transformer toy.
October 3rd, 2005 at 9:42 pm
Immediately reminded me of this classic Einstein quote:
http://en.wikipedia.org/wiki/Plumber
(others too, I think).
October 3rd, 2005 at 10:54 pm
The diagrams bring to mind manifolds.
Intake and exhaust manifolds. and the accompanying pipes.
October 3rd, 2005 at 11:23 pm
As a cartoonist… my first thought was severed body parts (of a very cartoony person, I mean).
As the mother of a toddler…. pasta shapes.
October 4th, 2005 at 1:11 am
Hello all. Well, what can I say? Some of your suggestons are way more interesting than what I see when I look at them. I’ll try to begin an explanation soon, answering the questions asked a long time ago about what I’m actually working on. Yes, my version of the story involves strings, but there is no need for yours to!
And no Lubos, I don’t drive a Rolls Royce. That would be a very odd choice of car for me…but thanks, I guess. On the other hand, I could well see myself taking that long and roundabout way of solving such a problem! (Fingers crossed that I don’t ever have to solve that problem……)
Moshe, Sean, erc: It is a real working board from an afternoon at Aspen. It began as a list of things figured out elsewhere (with James Carlisle at Durham), written neatly to see if I could see a pattern in the summary, but then further computations and speculations followed in real time. The board is small so it encourages neatness in order to use the space well.
Then I was moving away form the office and so I took a snapshot to allow me to record my thougths. Always present on my laptop for later reference.
Later….
-cvj
October 4th, 2005 at 2:56 am
Excuse me… Will this be on the end of term exam?
October 4th, 2005 at 3:38 am
topology, manifolds, string theory… and some maths thrown in for good fun.
i like the way that you can ‘add’ and ‘multiply’ the tubes and that the ‘equal’ something.
are the quotation marks around the ‘x’ on the lower right eqn, becuase you didn’t know it was valid? or its not really a multiplication sign?
on the blackboard theme… in high school my advanced calculus class figured out that a trig class used our room after us.
so some cruel soul thought that instead of having the good ol’ “SOHCAHTOA” as a method of remembering the trig relationships, he put up “SAHCAOTOH”.
m
October 4th, 2005 at 7:21 am
I now see that we have different x’s here. citrine and Lubos refer to the expressions, I was refering to Michaels ‘multiply’ operation in the images.
And I also missed that it was all about pants, as some suggested. One can even see ( in (3,1,0) ) a man’s pants!
October 4th, 2005 at 7:51 am
mmm
Makes me think of school, going back, and the days when Calculus still made me happy.
And who said blackboards are outdated? It’s the best way to work out thoughts. White backgrounds don’t offer the best nuetrality; in my world, black grounds the mind.
Thanks for sharing.
October 4th, 2005 at 8:04 am
If I would be a young man again and had to decide how to make my living, I would not try to become a scientist or scholar or teacher. I would rather choose to be a plumber or a peddler in the hope to find that modest degree of independence still available under present circumstances.” — Albert Einstein, The Reporter, 18 November 1954
Dissident’s link above.
Maybe it was the “freedom” he was referring too, and the simple life, that allowed for such freedoms?:)
Imagine getting paid to draw on blackboards, and about things that are so abstract. It would take a quantum leap?
Plumbers are real people too, with their ingenuities on awards ( I can see Einsteins humour to being awarded such a title). I mean “imagine” Mark Sean, Clifford and the Group describing for us issues about energy and flows, using pipe references.
As part of Cosmic Variance, they are really now offering their plumbing franchise links to Cosmic Plumber Incorporated. I knew they had a plan.
October 4th, 2005 at 9:33 am
Just like a scene from a TV movie:
Police Detective: Dr. Johnson was murdered last night. Here’s what we found on his blackboard. We think there’s a connection.
Belizean: It looks like he was trying to systematically sum the contributions from various closed string topologies that would…, OH MY GOD!
Detective: What!? What?!!
Belizean: He was trying to calculate an OBSERVABLE! A string theory OBSERVABLE!!
Detective: Could that have gotten him killed?
Belizean: Good God, man. Don’ t you understand! Had he succeeded it would have been the end of everything! A multi-billion dollar global industry of speculative calculation divorced from experimental confirmation could have been destroyed! The elimination of brane world scenarios alone would have caused so much unemployment that…
Detective: Sounds like a motive to me.
October 4th, 2005 at 1:43 pm
basquiat paintings.
http://static.flickr.com/5/9028007_b1e093dc16.jpg
October 4th, 2005 at 1:54 pm
john sadowski…wow! Thanks for the link.
-cvj
October 4th, 2005 at 5:33 pm
Looks like… The parts, of a Super Nova, once you’ve put them all together, it’ll come at you so fast. You will have to slap a sticker on it’s butt, that says; “You’ve been Nova taken”.
October 4th, 2005 at 5:51 pm
it reminded me of my first topology lecturer’s joke: topology is the study of how to take your underpants off without first taking off your pants. (You could tell it was a joke by the way his beard bristled up – there was a smile in there somewhere..)
October 4th, 2005 at 6:54 pm
Looks to me like Clifford has a possibly unhealthy fascination with bicycle shorts. Your design for a new bicycle saddle may save thousands from sexual disfunction though.
Has anyone come up with a Maple program that has a palette of clickable surfaces of appropriate genus coupled to the appropriate calculational factors?
October 5th, 2005 at 3:55 am
I figured it out Clifford, and by providing such a nice environment for ideas to spring forth, we have certainly seen “the humourous” as well as indicators, as to how different portions of society might see this blackboard.
So to be fair, I though I would share link for extra thinking that I had incurred by way of “conversation” and recognition of your article.
May I use your picture( of course remembering your photographic talents) and directly link it back to this blog entry?
Thanks,
October 5th, 2005 at 6:57 am
The topology joke probably stems from that you can, if I remember correctly, remove your shirt from under your jacket, which is provable by topology. This fact is illustrated by a rather funny contortionist series of photos.
CIP, I would also wish for a palette chooser for genius (or IQ) coupled to the appropriate palettes. That would help immensely!:-)
October 5th, 2005 at 12:53 pm
Here’s a update version of article, “Trademarks of the Geometer,” near completion.
October 5th, 2005 at 1:53 pm
Is it topologically provable that you can remove your bra without taking off your shirt?
October 5th, 2005 at 7:20 pm
Sure janet, I do it all the time….
-cvj
Yes, comment was deliberately left ambiguous.
October 31st, 2005 at 6:45 pm
[...] It is hard to start without setting the scene with motivating remarks, so what I am going to do is steal some of my own words from the introduction to the paper I’m writing with my young collaborators James Carlisle (graduating soon with a Ph.D. from Durham, UK) and Jeff Pennington (an undergradaute at USC), and sprinkle in some comments for those who don’t work in this area. Then I’ll do a part III, and maybe even a part IV, to which the mysterious scribblings on the board will be connected. It is safe to say that, at this point in time, we do not understand string (or M-) theory as well as we would like. While we have understood and appreciated that there is a rich bounty of physical phenomena contained in the theory, this has mostly been uncovered in perturbation theory, occasionally sweetened by a glimpse into the non–perturbative realm afforded by special sectors of the theory such as soliton solutions (including branes of various sorts) or various topological reductions. [...]