Sunday, August 31, 2014

The ordinary weirdness of quantum mechanics

Raymond Laflamme's qubit.
Photo: Christina Reed.
I’m just back from our 2014 Workshop for Science Writers, this year on the topic “Quantum Theory”. The meeting was both inspiring and great fun - the lab visit wasn’t as disorganized as last time, the muffins appeared before the breaks and not after, and amazingly enough we had no beamer fails. We even managed to find a video camera, so hopefully you’ll be able to watch the lectures on your own once uploaded, provided I pushed the right buttons.

Due to popular demand, we included a discussion session this year. You know that I’m not exactly a big fan of discussion sessions, but then I didn’t organize this meeting for myself. Michael Schirber volunteered to moderate the discussion. He started with posing the question why quantum mechanics is almost always portrayed as spooky, strange or weird. Why do we continue to do this and is beneficial for communicating the science behind the spook?

We could just blame Einstein for this, since he famously complained that quantum mechanics seemed to imply a spooky (“spukhafte”) action at a distance, but that was a century ago and we learned something since. Or some of us anyway.

Stockholm's quantum optics lab,
Photo: Christina Reed.
We could just discard it as headline making, a way to generate interest, but that doesn’t really explain why quantum mechanics is described as weirder or stranger as other new and often surprising effects. How is time-dilatation in a gravitational field less strange than entanglement? And it’s not that quantum mechanics is particularly difficult either. As Chad pointed out during the discussion, much of quantum mechanics is technically much simpler than general relativity.

We could argue it is due to our daily life being dominated by classical physics, so that quantum effects must appear unintuitive. Intuition however is based on experience and exposure. Spend some time calculating quantum effects, spend some time listening to lectures about quantum mechanics, and you can get that experience. This does not gain you the ability to perceive quantum effects without a suitable measuring device, but that is true for almost everything in science.

The explanation that came up during the discussion that made the most sense to me is that it’s simply a way to replace technical vocabulary, and these placeholders have become vocabulary on their own right.

The spook and the weirdness, they stand in for non-locality and contextuality, they replace correlations and entanglement, pure and mixed states, non-commutativity, error correction, path integrals or post-selection. Unfortunately, all too often the technical vocabulary is entirely absent rather than briefly introduced. This makes it very difficult for interested readers to dig deeper into the topic. It is basically a guarantee that the unintuitive quantum behavior will remain unintuitive for most people. And for the researchers themselves, the lack of technical terms makes it impossible to figure out what is going on. The most common reaction to supposed “quantum weirdness” that I see among my colleagues is “What’s new about this?”

The NYT had a recent opinion piece titled “Why We Love What We Don’t Understand” in which Anna North argued that we like that what isn’t understood because we want to keep the wonder alive:
“Many of us may crave that tug, the thrill of something as-yet-unexplained… We may want to get to the bottom of it, but in another way, we may not — as long as we haven’t quite figured everything out, we can keep the wonder alive.”
This made me think because I recall browsing through my mother’s collection of (the German version of) Scientific American as a teenager, always looking to learn what the scientists, the big brains, did not know. Yeah, it was kinda predictable I would end up in some sort of institution. At least it’s one where I have a key to the doors.

Anyway, I didn’t so much want to keep the mystery alive as that I wanted to know where the boundary between knowledge and mystery was currently at. Assume for a moment I’m not all that weird but most likely average. It is surprising then that the headline-grabbing quantum weirdness, instead of helping the reader, misleads them about where this boundary between knowledge and mystery is? Is it surprising then that everybody and their dog has solved some problem with quantum mechanics without knowing what problem?

And is it surprising, as I couldn’t help noticing, that the lecturers at this year’s workshop were all well practiced in forward-defense, and repeatedly emphasized that most of the theory is extremely well understood. It’s just that the focus on new technics and recent developments highlights exactly that what isn’t (yet) well understood, thereby giving more weight to the still mysterious in the news than there is in the practice.

I myself do not mind the attention-grabbing headlines, and that news focus on that what’s new rather than that what’s been understood for decades is the nature of the business. As several science writers, at this workshop and also at the previous one, told me, it is often not them inventing the non-technical terms, but it is vocabulary that the scientists themselves use to describe their research. I suspect though the scientists use it trying to adapt their explanations to the technical level they find in the popular science literature. So who is to blame really and how do we get out of this loop?

A first step might be to stop assuming all other parties are more stupid than the own. Most science writers have some degree in science, and they are typically more up to date on what is going on in research than the researchers themselves. The “interested public” is perfectly able to deal with some technical vocabulary as long as it comes with an explanation. And researchers are not generally unwilling or unable to communicate science, they just often have no experience what is the right level of detail in situations they do not face every day.

When I talk to some journalist, I typically ask them first to tell me roughly what they already know. From their reply I can estimate what background they bring, and then I build on that until I notice I lose them. Maybe that’s not a good procedure, but it’s the best I’ve come up with so far.

We all can benefit from better science communication, and a lot has changed within the last decades. Most notably, there are many more voices to hear now, and these voices aim at very different levels of knowledge. What is still not working very well though is the connection between different levels of technical detail. (Which we previously discussed here.)

At the end of the discussion I had the impression opinions were maximally entangled and pure states might turn into mixed ones. Does that sound strange?

Monday, August 25, 2014

Name that Þing

[Image credits Ria Novosti, source]
As teenager I switched between the fantasy and science fiction aisle of the local library, but in the end it was science fiction that won me over.

The main difference between the genres seemed the extent to which authors bothered to come up with explanations. The science fiction authors, they bent and broke the laws of Nature but did so consistently, or at least tried to. Fantasy writers on the other hand were just too lazy to work out the rules to begin with.

You could convert Harry Potter into a science fiction novel easily enough. Leaving aside gimmicks such as moving photos that are really yesterday’s future, call the floo network a transmitter, the truth serum a nanobot liquid, and the invisibility cloak a shield. Add some electric buzz, quantum vocabulary, and alien species to it. Make that wooden wand a light saber and that broom an X-wing starfighter, and the rest is a fairly standard story of the Other World, the Secret Clan, and the Chosen One learning the rules of the game and the laws of the trade, of good and evil, of friendship and love.

The one thing that most of the fantasy literature has which science fiction doesn’t have, and which has always fascinated me, is the idea of an Old Language, the idea that there is a true name for every thing and every place, and if you know the true name you have power over it. Speaking in the Old Language always tells the truth. If you speak the Old Language, you make it real.

This idea of the Old Language almost certainly goes back to our ancestor’s fights with an often hostile and unpredictable nature threatening their survival. The names, the stories, the gods and godzillas, they were their way of understanding and managing the environment. They were also the precursor to what would become science. And don’t we in physics today still try to find the true name of some thing so we have power over it?

Aren’t we still looking for the right words and the right language? Aren’t we still looking for the names to speak truth to power, to command that what threatens us and frightens us, to understand where we belong, where we came from, and where we go to? We call it dark energy and we call it dark matter, but these are not their true names. We call them waves and we call them particles, but these are not their true names. Some call the thing a string, some call it a graph, some call it a bit, but as Lee Smolin put it so nicely, none of these words quite has a “ring of truth” to it. These are not the real names.

Neil Gaiman’s recent fantasy novel “The Ocean at the End of the Road” also draws on the idea of an Old Language, of a truth below the surface, a theory of everything which the average human cannot fathom because they do not speak the right words. In Michael Ende’s “Neverending Story” that what does not have a true name dies and decays to nothing. (And of course Ende has a Chosen One saving the world from that no-thing.) It all starts and it all ends with our ability to name that what we are part of.

You don’t get a universe from nothing of course. You can get a universe from math, but the mathematical universe doesn’t come from nothing either, it comes from Max Tegmark, that is to say some human (for all I can tell) trying to find the right words to describe, well, everything - no point trying to be modest about it. Tegmark, incidentally, also seems to speak at least ten different languages or so, maybe that’s not a coincidence.

The evolution of language has long fascinated historians and neurologists alike. Language is more than assigning a sound to things and things you do with things. Language is a way to organize thought patterns and to classify relations, if in a way that is frequently inconsistent and often confusing. But the oldest language of all is neither Sindarin nor Old Norse, it is, for all we can tell, the language of math in which the universe was written. You can call it temperature anisostropy, or tropospheric ozone precursors, you can call it neurofibrillary tangle or reverse transcriptase, you can call them Bárðarbunga or Eyjafjallajökull - in the end their true names were written in math.

Friday, August 22, 2014

Hello from Iceland

So here I am on an island in the middle of the Atlantic ocean that's working on its next volcano eruption.


In case you missed yesterday's Google Hangout, FQXi just announced the winner's of this year's essay contest and - awesomeliness alert! - my essay "How to save the world in five simple steps" made it first prize!

I'm happy of course about the money, but what touches me much more is that this is vivid documentation I'm not the only one who thinks the topics I addressed in my essay are relevant. If you've been following this blog for some while then you know of course that I've been thinking back and forth about the problem of emerging social dynamics, in the scientific communities as well as in society by large, and our inability to foresee and react to the consequences of our actions.

Ten years ago I started out thinking the problem is the modeling of these systems, but over the years, as more and more research and data on these trends became available, I've become convinced the problem isn't understanding the system dynamics to begin with, but that nobody is paying attention to what we've learned.

I see this every time I sit in a committee meeting and try to tell them something about research dedicated to intelligent decision making in groups, cognitive biases, or the sociology of science. They'll not listen. They might be polite and let me finish, but it's not information they will take into account in their decision making. And the reason is basically that it takes them too much time and too much effort. They'll just continue the way it's always been done; they'll continue making the same mistakes over again. There's no feedback in this system, and no learning by trial and error.

The briefest of brief summaries of my essay is that we'll only be able to meet the challenges mankind is facing if our social systems are organized so that we can react to complex and emerging problems caused by our own interaction and that with our environment. That will only be possible if we have the relevant information and use it. And we'll only use this information if it's cheap, in the sense of it being simple, fast, and intuitive to use.

Most attempts to solve the problems that we are facing are based on an unrealistic and utopian image of the average human, the well-educated, intellectual and concerned citizen who will process all available information and come to smart decisions. That is never going to happen, and that's the issue I'm taking on in my essay.

I'll be happy to answer questions about my essay. I would prefer to do this here rather than at the FQXi forum. Note though that I'll be stuck in transit for the next day. If that volcano lets me off this island that is.

Monday, August 18, 2014

DAMA annual modulation explained without invoking dark matter

Annual modulation of DAMA data.
Image credits: DAMA Collaboration.
Physicists have plenty evidence for the existence of dark matter, matter much like the one we are made of but that does not emit any light. However, so far all this evidence comes from the gravitational pull of dark matter, which affects the motion of stars, the formation of structures, and acts as a gravitational lens to bend light, all of which has been observed. We still do not know however what the microscopic nature of dark matter is. What is the type of particle (particles?) that it is constituted of, and what are its interactions?

Few physicists today doubt that dark matter exists and is some type of particle which has just evaded detection so far. First, there is all the evidence for its gravitational interaction. Add to this that we don’t know any good reason why all matter should couple to photons, and on this ground we can actually expect the existence of dark matter. Moreover, we have various candidate theories for physics beyond the standard model that contain particles which fulfil the necessary properties for dark matter. Finally, alternative explanations, by modifying gravity rather than adding a new type of matter, are disfavored by the existing data.

Not so surprisingly thus, dark matter has come to dominate the search for physics beyond the standard model. We seem to be so very close!

Infuriatingly though, despite many experimental efforts, we still have no evidence for the interaction of dark matter particles, neither among each other nor with the matter that we are made of. Many experiments are searching for evidence of these interactions. It is the very nature of dark matter – it interacting so weakly with our normal matter and with itself – which makes finding evidence so difficult.

One observation being looked for is decay products of dark matter interactions in astrophysical processes. There are presently several observations, such as the Fermi γ-ray excess or the positron excess, whose astrophysical origin is not presently understood and so could be due to dark matter. But astrophysics combines a lot of processes at many energy and density scales, and it is hard to exclude that some signal was not caused by particles of the standard model alone.

Another type of evidence that is being sought after comes from experiments designed to be sensitive to the very rare interaction of dark matter with our normal matter when it passes through the planet. These experiments have the advantage that they happen in a known and controlled environment (as opposed to somewhere in the center of our galaxy). They experiments are typically located deep underground in old mines to filter out unwanted types of particles, collectively referred to as “background”. Whether or not an experiment can detect dark matter interactions within a certain amount of time depends on the density and coupling strength of dark matter, and so also on the type of detector material.

So far, none of the dark matter searches has resulted in a statistically significant positive signal. They have set constraints on the coupling and density of dark matter. Valuable, yes, but frustrating nevertheless.

One experiment that has instilled both hope as well as controversy among physicists is the DAMA experiment. The DAMA experiment sees an unexplained annual modulation in the event rate at high statistical significance. If the signal was caused by dark matter, we would expect an annual modulation due to our celestial motion around the Sun. The event rate depends on the orientation of the detector relative to our motion and should peak around June 2nd, consistent with the DAMA data.

There are of course other signals that have an annual modulation that cause reactions with the material in and around the detector. Notably there is the flux of muons which are produced when cosmic rays hit the upper atmosphere. The muon flux however depends on the temperature in the atmosphere and peaks approximately 30 days too late to explain the observations. The DAMA collaboration has taken into account all other kinds of backgrounds that they could think of, or that other physicists could think of, but dark matter remained the best way to explain the data.

The DAMA experiment has received much attention not primarily because of the presence of the signal, but because of the physicists’ failure to explain the signal with anything but dark matter. It adds to the controversy though that the DAMA signal, if due to dark matter, seems to lie in a parameter range already excluded by other dark matter searches. Then again, this may be due to differences in the detectors. The issue has been discussed back and forth for about a decade now.

All this may change now that Jonathan Davis from the University of Durham, UK, in a recent paper demonstrated that the DAMA signal can be fitted by combining the atmospheric muon flux with the flux of solar neutrinos:
    Fitting the annual modulation in DAMA with neutrons from muons and neutrinos
    Jonathan H. Davis
    arxiv:1407.1052
The neutrinos interact with the rock surrounding the detector, thereby creating secondary particles which contribute to the background. The strength of the neutrino signal depends on the Earth’s distance to the sun and peaks around January 2nd. In his paper, Davis demonstrates that for certain values of the amount of muons and neutrinos these two modulations combine to fit the DAMA data very well, as good as a dark matter explanation. And that is after he has corrected the goodness of the fit by taking into account the larger number of parameters.

Moreover, Davis discusses how the two possible explanations could be distinguished from each other, for example by analyzing the data for residual changes in the solar activity that should not be present if the signal was due to dark matter.

Tim Tait, Professor for theoretical particle physicist at the University of California, Irvine, commented that “[This] may be the first self-consistent explanation for DAMA.” Though of course one has to be cautious not to jump to conclusions since Davis’ argument is partly based on estimates for the reaction rate of neutrinos with the rock that has to be confirmed with more qualitative studies. Thomas Dent, a former particle cosmologist now working in gravitational wave data analysis, welcomed Davis’ explanation: “DAMA has been a distraction to theorists for too long.”

This post first appeared July 17, 2014, on Starts With A BANG with the title "How the experiment that claimed to detect dark matter fooled itself".

Thursday, August 14, 2014

Away note and Interna

Lara

I'll be traveling the next three weeks, so please be prepared for little or unsubstantial action on this blog. Next week I'm in Reykjavik for a network meeting on "Holographic Methods and Applications". August 27-29 I'm running the Science Writers Workshop in Stockholm together with George, this year on the topic "Quantum Theory." The first week of September then I'm in Trieste for the 2014 conference on Experimental Search for Quantum Gravity, where I'll be speaking about space-time defects.

Unfortunately, this traveling happens just during the time when our Kindergarten is closed, and so it's quite some stress-test for my dear husband. Since you last heard from Lara and Gloria, they have learned to count, use the swing, and are finally potty trained. They can dress themselves, have given up requesting being carried up the stairs, and we mostly get around without taking along the stroller. Yes, life has become much easier. Gloria however still gets motion sick in the car, so we either have to drug her or pull over every 5 minutes. By and large we try to avoid long road trips.

The girls have now more of a social life than me, and we basically can't leave the house without meeting other children that they know and that they have to discuss with whether Friday comes before or after Wednesday. That Lara and Gloria are twins apparently contributes greatly to their popularity. Every once in a while, when I drop off the kids at Kindergarten, some four foot dwarf will request to know if it's really true that they were together in mommy's tummy and inspect me with a skeptic view. The older children tell me that the sisters are so cute, and then try to pad Gloria's head, which she hates.
Gloria

Gloria is still a little ahead of Lara when it comes to developing new skills. She learned to speak a little earlier, to count a little earlier, was potty trained a little earlier and learned to dress herself a little earlier. Then she goes on to explain Lara what to do. She also "reads" books to Lara, basically by memorizing the stories.

Lara on the other hand is still a little ahead in her physical development. She is still a bit taller and more often than not, when I come to pick them up at Kindergarten, Lara will be kicking or throwing some ball while Gloria plays in the sandbox - and afterwards Gloria will insist on taking off her shoes, pouring out the sand and cleaning her socks before she gets into the car. Lara takes off the shoes in the car and pours the sand into the seat pocket. Lara uses her physical advantage over Gloria greatly to take away toys. Gloria takes revenge by telling everybody what Lara did wrong again, like putting her shoe on the wrong foot.

The best recent development is that the girls have finally, after a quite difficult phase, stopped kicking and hitting me and telling me to go away. They now call me "my little mommy" and want me to bake cookies for them. Yes, my popularity has greatly increased with them figuring out that I'm not too bad with cakes and cookies. They don't particularly like my cooking but that's okay, because I don't like it either.

On an entirely different note, as some of you have noticed already, I agreed to write for Ethan Siegel at Starts With A Bang. So far there's two pieces from me over there: How the experiment that claimed to detect dark matter fooled itself and The Smallest Possible Scale in the Universe. The deal is that I can repost what gets published there on this blog after 30 days, which I will do. So if you're only interested in my writing, you're well off here, but check out his site because it's full with interesting physics writing.


Tuesday, August 12, 2014

Do we write too many papers?

Every Tuesday, when the weekend submissions appear on the arXiv, I think we’re all writing too many papers. Not to mention that we work too often on weekends. Every Friday, when another week has passed in which nobody solved my problems for me, I think we’re not writing enough papers.

The Guardian recently published an essay by Timo Hannay, titled “Stop the deluge of science research”, though the URL suggests the original title was “Why we should publish less Scientific Research.” Hannay argues that the literature has become unmanageable and that we need better tools to structure and filter it so that researchers can find what they are looking for. Ie, he doesn’t actually say we should publish less. Of course we all want better boats to stay afloat on the information ocean, but there are other aspects to the question whether we publish too many papers that Hannay didn’t touch upon.

Here, I use “too much” to mean that the amount of papers hinders scientific progress and no longer benefits it. The actual number depends very much on the field and its scientific culture and doesn’t matter all that much. Below I’ve collected some arguments that speak for or against the “too much papers” hypothesis.

Yes, we publish too many papers!
  • Too much to read, even with the best filter. The world doesn’t need to know about all these incremental steps, most of which never lead anywhere anyway.
  • Wastes the time of scientists who could be doing research instead. Publishing several short papers instead of one long one adds the time necessary to write several introductions and conclusions, adapt the paper to different journals styles, fight with various sets of referees, just to then submit the paper to another journal and start all over again.
  • Just not reading them isn’t an option because one needs to know what’s going on. That creates a lot of headache, especially for newcomers. Better only publish what’s really essential knowledge.
  • Wastes the time of editors and referees. Editors and referees typically don’t have access to reports on manuscripts that follow-up works are based on.
No, we don’t publish too many papers!
  • If you think it’s too much, then just don’t read it.
  • If you think it’s too much, you’re doing it wrong. It’s all a matter of tagging, keywords, and search tools.
  • It’s good to know what everybody is doing and to always be up to date.
  • Journals make money with publishing our papers, so don’t worry about wasting their time.
  • Who really wants to write a referee report for one of these 30 pages manuscripts anyway?
Possible reasons that push researchers to publish more than is good for progress:
  • Results pressure. Scientists need published papers to demonstrate outcome of research they received grants for.
  • CV boosting. Lots of papers looks like lots of ideas, at least if one doesn’t look too closely. (Especially young postdocs often believe they don’t have enough papers, so let me add a word of caution. Having too many papers can also work against you because it creates the appearance that your work is superficial. Aim at quality, not quantity.)
  • Scooping angst. In fields which are overpopulated, like for example hep-th, researchers publish anything that might go through just to have a time-stamp that documents they were first.
  • Culture. Researchers adapt the publishing norms of their peers and want to live up to their expectations. (That however might also have the result that they publish less than is good for progress, depending on the prevailing culture of the field.)  
  • PhD production machinery. It’s becoming the norm at least in physics that PhD students already have several publications, typically with their PhD supervisor. Much of this is to make it easier for the students to find a good postdoc position, which again falls back positively on the supervisor. This all makes the hamster wheel turn faster and faster.
All together I don’t have a strong opinion on whether we’re publishing too much or not. What I do find worrisome though is that all these measures for scientific success reduce our tolerance for individuality. Some people write a lot, some less so. Some pay a lot of attention to detail, some rely more on intuition. Some like to discuss and get feedback early to sort out their thoughts, some like to keep their thoughts private until they’ve sorted them out themselves. I think everybody should do their research the way it suits them best, but unfortunately we’re all increasingly forced to publish at rates close to the field average. And who said that the average is the ideal?

Monday, August 11, 2014

When the day comes [video]

Because I know you couldn't dream of anything better than starting your week with one of my awesome music videos. This one is for you, who you just missed another deadline, and for you who you still haven't done what you said you would, and for you, yes you, who you still haven't sent title and abstract.


I'm getting somewhat frustrated with the reverb tails, I think I have to make something less complicated. The background choir is really hard to get in the right place without creating a mush. And as always the video making was quite frustrating. I can't get the cuts in the video being properly in synch with the audio, mainly because I can't see the audio in my video editor. I'm using the Corel Videostudio Pro X, can anybody recommend a software better suited to the task?

Monday, August 04, 2014

What is a singularity?

Not Von Neumann's urinal, but a
model of an essential singularity.
[Source: Wikipedia Commons.]
I recently read a bit around about the technological singularity, but it’s hard. It’s hard because I have to endure sentences like this:
“Singularity is a term derived from physics, where it means the point at the unknowable centre of a black hole where the laws of physics break down.”
Ouch. Or this:
“[W]e cannot see beyond the [technological] singularity, just as we cannot see beyond a black hole's event horizon.”
Aargh. Then I thought certainly they must have looked up the word in a dictionary, how difficult can it be? In the dictionary, I found this:
sin-gu-lar-i-ty
noun, plural sin-gu-lar-i-ties for 2–4.

1. the state, fact, or quality of being singular.
2. a singular, unusual, or unique quality; peculiarity.
3. Mathematics, singular point.
4. Astronomy (in general relativity) the mathematical representation of a black hole.”
I don’t even know where to start complaining. Yes, I did realize that black holes and event horizons made it into pop culture, but little did I realize that something as seemingly simple as the word “singularity” is surrounded by such misunderstanding.

Von Neumann.

Let me start with some history. Contrary to what you read in many places, it was not Vernor Vinge who first used the word “singularity” to describe a possible breakdown of predictability in technological development, it was von Neumann.

Von Neumann may be known to you as the man behind the Von Neumann entropy. He was a multiple talented genius, one of a now almost extinct breed, who contributed to many disciplines in math and physics, and what are now interdisciplinary fields like game theory or quantum information.

In Chapter 16 (p 157) of Stanislav Ulam’s biography of Von Neumann, published in 1958, one reads:
“One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.”
The term “singularity” was then picked up in 1993 by Vinge who coined the expression “technological singularity”. But let us dwell for a moment on the above Von Neumann quote. Ulam speaks of an “essential singularity”. You may be forgiven mistaking the adjective “essential” as a filler, but “essential singularity” is a technical expression, typically found in the field of complex analysis.

A singularity in mathematics is basically a point in which a function is undefined. Now it might be undefined just because you didn’t define it, but it is possible to continue the function through that point. In this case the singularity is said to be removable and, in some sense, just isn’t an interesting singularity, so let us leave this aside.

What one typically means with a singularity is a point where a function behaves badly, so that one or several of its derivatives diverge, that is they go to infinity. The ubiquitous example in school math is the poles of inverse powers of x, which diverge with x to zero.

However, such poles are not malign, you can remove them easily enough by multiplying the function with the respective positive power. Of course this gives you a different function, but this function still carries much of the information of the original function, notably all the coefficients in a series expansion. This procedure of removing poles (or creating poles) is very important in complex analysis where it is necessary to obtain the “residuals” of a function.

Some singularities however cannot be removed by multiplication with any positive power. These are those cases in which the function contains an infinite number of negative powers, the most commonly used example is exp(-1/x) at x=0. Such a singularity is said to be “essential”. Please appreciate the remarkable fact that the function itself does not diverge for x to zero, but neatly goes to zero! So do all its derivatives!!

So what did von Neumann mean with referring to an essential singularity?

From the context it seems he referred to the breakdown of predictability at this point. If all derivatives of a function are zero, you cannot make a series expansion (neither Taylor nor Laurent) around that point. If you hit that point, you don’t know what happens next, basically. This is a characteristic feature of essential singularities. (The radius of convergence cannot be pushed through the singular point.)

However, predictability of the laws of nature that we have (so far) never breaks down in this very sense. It breaks down because the measurement in quantum theory is non-deterministic, but that has for all we know nothing to do with essential singularites. (Yes, I’ve tried to make this connection. I’ve always been fond of essential singularities. Alas, not even the Templeton Foundation wanted anything to do with my great idea. So much about the reality of research.)

Geodesic incompleteness.
Artist's impression.
The other breakdown of predictability that we know of are singularities in general relativity. These are not technically essential singularities if you ask for the behavior of certain observables – they are typically poles or conical singularities. But they bear a resemblance to essential singularities by a concept known as “geodesic incompleteness”. It basically means that there are curves in space-time which end at finite proper time and cannot be continued. It’s like hitting the wall at 32km.

The reason for the continuation being impossible is that a singularity is a singularity is a singularity, no matter how you got there. You lose all information about your past when you hit it. (This is why, incidentally, the Maldacena-Horowitz proposal to resolve the black hole information loss by putting initial conditions on the singularity makes a lot of sense to me. Imho a totally under-appreciated idea.)

A common confusion about black holes concerns the nature of the event horizon. You can construct certain quantities of the black hole spacetime that diverge at the event horizon. In the mathematical sense they are singular, and that did confuse many people after the black hole space-time was first derived, in the middle of the last century. But it was quickly understood that these quantities do not correspond to physical observables. The physically relevant singularity is where geodesics end, at the center of the black hole. It corresponds to an infinitely large curvature. (This is an observer independent statement.) Nothing special happens upon horizon crossing, except that one can never get out again.

The singularity inside black holes is widely believed not to exist though, exactly because it implies a breakdown of predictability and causes the so paradoxical loss of information. The singularity is expected to be removed by quantum gravitational effects. The defining property of the black hole is the horizon, not the singularity. A black hole with the singularity removed is still a black hole. A singularity with the horizon removed is a naked singularity, no longer a black hole.

What has all of this to do with the technological singularity?

Nothing, really.

To begin with, there are like 17 different definitions for the technological singularity (no kidding). None of them has anything to do with an actual singularity, neither in the mathematical nor in the physical sense, and we have absolutely no reason to believe that the laws of physics or predictability in general breaks down within the next decades or so. In principle.

In practice, on some emergent level of an effective theory, I can see predictability becoming impossible. How do you want to predict what an artificial intelligence will do without having something more powerful than that artificial intelligence already? Not that anybody has been able to predict what averagely intelligent humans will do. Indeed one could say that predictability becomes more difficult with absence of intelligence, not the other way round, but I digress.

Having said all that, let us go back to these scary quotes from the beginning:
“Singularity is a term derived from physics, where it means the point at the unknowable centre of a black hole where the laws of physics break down.”
The term singularity comes from mathematics. It does not mean “at the center of the black hole”, but it can be “like the center of a black hole”. Provided you are talking about the classical black hole solution, which is however believed to not be realized in nature.
“[W]e cannot see beyond the [technological] singularity, just as we cannot see beyond a black hole's event horizon.”
There is no singularity at the black hole horizon, and predictability does not break down at the black hole horizon. You cannot see beyond a black hole horizon as long as you stay outside the black hole. If you jump in, you will see - and then die. But I don’t know what this has to do with technological development, or maybe I just didn’t read the facebook fineprint closely enough.

And finally there’s this amazing piece of nonsense:
“Singularity: Astronomy. (in general relativity) the mathematical representation of a black hole.”
To begin with General Relativity is not a field of astronomy. But worse, the “mathematical representation of a black hole” is certainly not a singularity. The mathematical representation of a (classical) black hole is the black hole spacetime and it contains a singularity.

And just in case you wondered, singularities have absolutely nothing to do with singing, except that you find both on my blog.

Tuesday, July 29, 2014

Can you touch your nose?

Yeah, but can you? Believe it or not, it’s a question philosophers have plagued themselves with for thousands of years, and it keeps reappearing in my feeds!

Best source I could find for this image: IFLS.



My first reaction was of course: It’s nonsense – a superficial play on the words “you” and “touch”. “You touch” whatever triggers the nerves in your skin. There, look, I’ve solved a thousand year’s old problem in a matter of 3 seconds.

Then it occurred to me that with this notion of “touch” my shoes never touch the ground. Maybe I’m not a genius after all. Let me get back to that cartoon then. Certainly deep thoughts went into it that I must unravel.

The average size of an atom is an Angstrom, 10-10 m. The typical interatomar distance in molecules is a nanometer, 10-9 meter, or let that be a few nanometers if you wish. At room temperature and normal atmospheric pressure, electrostatic repulsion prevents you from pushing atoms any closer together. So the 10-8 meter in the cartoon seem about correct.

But it’s not so simple...

To begin with it isn’t just electrostatic repulsion that prevents atoms from getting close, it is more importantly the Pauli exclusion principle which forces the electrons and quarks that make up the atom to arrange in shells rather than to sit on top of each other.

If you could turn off the Pauli exclusion principle, all electrons from the higher shells would drop into the ground state, releasing energy. The same would happen with the quarks in the nucleus which arrange in similar levels. Since nuclear energy scales are higher than atomic scales by several orders of magnitude, the nuclear collapse causes the bulk of the emitted energy. How much is it?

The typical nuclear level splitting is some 100 keV, that is a few 10-14 Joule. Most of the Earth is made up of silicon, iron and oxygen, ie atomic numbers of the order of 15 or so on the average. This gives about 10-12 Joule per atom, that is 1011 Joule per mol, or 1kTon TNT per kg.

This back-of-the envelope gives pretty much exactly the maximal yield of a nuclear weapon. The difference is though that turning off the Pauli exclusion principle would convert every kg of Earthly matter into a nuclear bomb. Since our home planet has a relatively small gravitational pull, I guess it would just blast apart. I saw everybody die, again, see that’s how it happens. But I digress; let me get back to the question of touch.

So it’s not just electrostatics but also the Pauli exclusion principle that prevents you from falling through the cracks. Not only do the electrons in your shoes don’t want to touch the ground, the electrons in your shoes don’t want to touch the other electrons in your shoes either. Electrons, or fermions generally, just don’t like each other.

The 10-8 meter actually seem quite optimistic because surfaces are not perfectly even, they have a roughness to them, which means that the average distance between two solids is typically much larger than the interatomic spacing that one has in crystals. Moreover, the human body is not a solid and the skin normally covered by a thin layer of fluids. So you never touch anything just because you’re separated by a layer of grease from the world.

To be fair, grease isn’t why the Greeks were scratching their heads back then, but a guy called Zeno. Zeno’s most famous paradox divides a distance into halves indefinitely to then conclude then that because it consists of an infinite number of steps, the full distance can never be crossed. You cannot, thus, touch your nose, spoke Zeno, or ram an arrow into it respectively. The paradox resolved once it was established that infinite series can converge to finite values; the nose was in the business again, but Zeno would come back to haunt the thinkers of the day centuries later.

The issue reappeared with the advance of the mathematical field of topology in the 19th century. Back then, math, physics, and philosophy had not yet split apart, and the bright minds of the times, Descarte, Euler, Bolzano and the like, they wanted to know, using their new methods, what does it mean for any two objects to touch? And their objects were as abstract as it gets. Any object was supposed to occupy space and cover a topological set in that space. So far so good, but what kind of set?

In the space of the real numbers, sets can be open or closed or a combination thereof. Roughly speaking, if the boundary of the set is part of the set, the set is closed. If the boundary is missing the set is open. Zeno constructed an infinite series of steps that converges to a finite value and we meet these series again in topology. Iff the limiting value (of any such series) is part of the set, the set is closed. (It’s the same as the open and closed intervals you’ve been dealing with in school, just generalized to more dimensions.) The topologists then went on to reason that objects can either occupy open sets or closed sets, and at any point in space there can be only one object.

Sounds simple enough, but here’s the conundrum. If you have two open sets that do not overlap, they will always be separated by the boundary that isn’t part of either of them. And if you have two closed sets that touch, the boundary is part of both, meaning they also overlap. In neither case can the objects touch without overlapping. Now what? This puzzle was so important to them that Bolzano went on to suggest that objects may occupy sets that are partially open and partially closed. While technically possible, it’s hard to see why they would, in more than 1 spatial dimension, always arrange so as to make sure one’s object closed surface touches the other’s open patches.

More time went by and on the stage of science appeared the notion of fields that mediate interactions between things. Now objects could interact without touching, awesome. But if they don’t repel what happens when they get closer? Do or don’t they touch eventually? Or does interacting via a field means they touch already? Before anybody started worrying about this, science moved on and we learned that the field is quantized and the interaction really just mediated by the particles that make up the field. So how do we even phrase now the question whether two objects touch?

We can approach this by specifying that we mean with an “object” a bound state of many atoms. The short distance interaction of these objects will (at room temperature, normal atmospheric pressure, non-relativistically, etc) take place primarily by exchanging (virtual) photons. The photons do in no sensible way belong to any one of the objects, so it seems fair to say that the objects don’t touch. They don’t touch, in one sentence, because there is no four-fermion interaction in the standard model of particle physics.

Alas, tying touch to photon exchange in general doesn’t make much sense when we think about the way we normally use the word. It does for example not have any qualifier about the distance. A more sensible definition would make use of the probability of an interaction. Two objects touch (in some region) if their probability of interaction (in that region) is large, whether or not it was mediated by a messenger particle. This neatly solves the topologists’ problem because in quantum mechanics two objects can indeed overlap.

What one means with “large probability” of interaction is somewhat arbitrary of course, but quantum mechanics being as awkward as it is there’s always the possibility that your finger tunnels through your brain when you try to hit your nose, so we need a quantifier because nothing is ever absolutely certain. And then, after all, you can touch your nose! You already knew that, right?

But if you think this settles it, let me add...

Yes, no, maybe, wtf.
There is a non-vanishing probability that when you touch (attempt to touch?) something you actually exchange electrons with it. This opens a new can of worms because now we have to ask what is “you”? Are “you” the collection of fermions that you are made up of and do “you” change if I remove one electron and replace it with an identical electron? Or should we in that case better say that you just touched something else? Or are “you” instead the information contained in a certain arrangement of elementary particles, irrespective of the particles themselves? But in this case, “you” can never touch anything just because you are not material to begin with. I will leave that to you to ponder.

And so, after having spent an hour staring at that cartoon in my facebook feed, I came to the conclusion that the question isn’t whether we can touch something, but what we mean with “some thing”. I think I had been looking for some thing else though…

Friday, July 25, 2014

Can black holes bounce to white holes?

Fast track to wisdom: Sure, but who cares if they can? We want to know if they do.

Black holes are defined by the presence of an event horizon which is the boundary of a region from which nothing can escape, ever. The word black hole is also often used to mean something that looks for a long time very similar to a black hole and that traps light, not eternally but only temporarily. Such space-times are said to have an “apparent horizon.” That they are not strictly speaking black holes was origin of the recent Stephen Hawking quote according to which black holes may not exist, by which he meant they might have only an apparent horizon instead of an eternal event horizon.

A white hole is an upside-down version of a black hole; it has an event horizon that is a boundary to a region in which nothing can ever enter. Static black hole solutions, describing unrealistic black holes that have existed forever and continue to exist forever, are actually a combination of a black hole and a white hole.

The horizon itself is a global construct, it is locally entirely unremarkable and regular. You would not note crossing the horizon, but the classical black hole solution contains a singularity in the center. This singularity is usually interpreted as the breakdown of classical general relativity and is expected to be removed by the yet-to-be-found theory of quantum gravity. 

You do however not need quantum gravity to construct singularity-free black hole space-times. Hawking and Ellis’ singularity theorems prove that singularities must form from certain matter configurations, provided the matter is normal matter and cannot develop negative pressure and/or density. All you have to do to get rid of the singularity is invent some funny type of matter that refuses to be squeezed arbitrarily. This is not possible with any type of matter we know, and so just pushes around the bump under the carpet: Now rather than having to explain quantum effects of gravity you have to explain where the funny matter comes from. It is normally interpreted not as matter but as a quantum gravitational contribution to the stress-energy tensor, but either way it’s basically the physicist’s way of using a kitten photo to cover the hole in wall.

Singularity-free black hole solutions have been constructed almost for as long as the black hole solution has been known – people have always been disturbed by the singularity. Using matter other than normal ones allowed constructing both wormhole solutions as well as black holes that turn into white holes and allow an exit into a second space-time region. Now if a black hole is really a black hole with an event horizon, then the second space-time region is causally disconnected from the first. If the black hole has only an apparent horizon, then this does not have to be so, and also the white hole then is not really a white hole, it just looks like one.

The latter solution is quite popular in quantum gravity. It basically describes matter collapsing, forming an apparent horizon and a strong quantum gravity region inside but no singularity, then evaporating and returning to an almost flat space-time. There are various ways to construct these space-times. The details differ, but the corresponding causal diagrams all look basically the same.

This recent paper for example used a collapsing shell turning into an expanding shell. The title “Singularity free gravitational collapse in an effective dynamical quantum spacetime” basically says it all. Note how the resulting causal diagram (left in figure below) looks pretty much the same as the one Lee and I constructed based on general considerations in our 2009 paper (middle in figure below), which again looks pretty much the same as the one that Ashtekar and Bojowald discussed in 2005 (right in figure below), and I could go on and add a dozen more papers discussing similar causal diagrams. (Note that the shaded regions do not mean the same in each figure.)



One needs a concrete ansatz for the matter of course to be able to calculate anything. The general structure of the causal diagram is good for classification purposes, but not useful for quantitative reasoning, for example about the evaporation.

Haggard and Rovelli and recently added to this discussion with a new paper about black holes bouncing to white holes.

    Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
    Hal M. Haggard, Carlo Rovelli
    arXiv: 1407.0989

Ron Cowen at Nature News announced this as a new idea, and while the paper does contain new ideas, that black holes may turn into white holes is in and by itself not new. And so it follows some clarification.

Haggard and Rovelli’s paper contains two ideas that are connected by an argument, but not by a calculation, so I want to discuss them separately. Before we start it is important to note that their argument does not take into account Hawking radiation. The whole process is supposed to happen already without outgoing radiation. For this reason the situation is completely time-reversal invariant, which makes it significantly easier to construct a metric. It is also easier to arrive at a result that has nothing to do with reality.

So, the one thing that is new in the Haggard and Rovelli paper is that they construct a space-time diagram, describing a black hole turning into a white hole, both with apparent horizons, and do so by a cutting-procedure rather than altering the equation of state of the matter. As source they use a collapsing shell that is supposed to bounce. This cutting procedure is fine in principle, even though it is not often used. The problem is that you end up with a metric that exists as solution to some source, but you then have to calculate what the source has to do in order to give you the metric. This however is not done in the paper. I want to offer you a guess though as to what source would be necessary to create their metric.

The cutting that is done in the paper takes a part of the black hole metric (describing the inside of the shell) with an arm extending into the horizon region, then squeezes this arm together so that it shrinks in radial extension no longer extends into the regime below the Schwarzschild radius, which is normally behind the horizon. This squeezed part of the black hole metric is then matched to empty space, describing the inside of the shell. See image below

Figure 4 from arXiv: 1407.0989

They do not specify what happens to the shell after it has reached the end of the region that was cut, explaining one would need quantum gravity for this. The result is glued together with the time-reversed case, and so they get a metric that forms an apparent horizon and bounces at a radius where one normally would not expect quantum gravitational effects. (Working towards making more concrete the so far quite vague idea of Planck stars that we discussed here.)

The cutting and squeezing basically means that the high curvature region from inside the horizon was moved to a larger radius, and the only way this makes sense is if it happens together with the shell. So I think effectively they take the shell from a small radius and match the small radius to a large radius while keeping the density fixed (they keep the curvature). This looks to me like they blow up the total mass of the shell, but keep in mind this is my interpretation, not theirs. If that was so however, then makes sense that the horizon forms at a larger radius if the shell collapses while its mass increases. This raises the question though why the heck the mass of the shell should increase and where that energy is supposed to come from.

This brings me to the second argument in the paper, which is supposed to explain why it is plausible to expect this kind of behavior. Let me first point out that it is a bold claim that quantum gravity effects kick in outside the horizon of a (large) black hole. Standard lore has it that quantum gravity only leads to large corrections to the classical metric if the curvature is large (in the Planckian regime). This happens always after horizon crossing (as long as the mass of the black hole is larger than the Planck mass). But once the horizon is formed, the only way to make matter bounce so that it can come out of the horizon necessitates violations of causality and/or locality (keep in mind their black hole is not evaporating!) that extend into small curvature regions. This is inherently troublesome because now one has to explain why we don’t see quantum gravity effects all over the place.

The way they argue this could happen is that small, Planck size, higher-order correction to the metric can build up over time. In this case it is not solely the curvature that is relevant for an estimate of the effect, but also the duration of the buildup. So far, so good. My first problem is that I can’t see what their estimate of the long-term effects of such a small correction has to do with quantum gravity. I could read the whole estimate as being one for black hole solutions in higher-order gravity, quantum not required. If it was a quantum fluctuation I would expect the average solution to remain the classical one and the cases in which the fluctuations build up to be possible but highly improbable. In fact they seem to have something like this in mind, just that they for some reason come to the conclusion that the transition to the solution in which the initially small fluctuation builds up becomes more likely over time rather than less likely.

What one would need to do to estimate the transition probability is to work out some product of wave-functions describing the background metric close by and far away from the classical average, but nothing like this is contained in the paper. (Carlo told me though, it’s in the making.) It remains to be shown that the process of all the matter of the shell suddenly tunneling outside the horizon and expanding again is more likely to happen than the slow evaporation due to Hawking radiation which is essentially also a tunnel process (though not one of the metric, just of the matter moving in the metric background). And all this leaves aside that the state should decohere and not just happily build up quantum fluctuations for the lifetime of the universe or so.

By now I’ve probably lost most readers so let me just sum up. The space-time that Haggard and Rovelli have constructed exists as a mathematical possibility, and I do not actually doubt that the tunnel process is possible in principle, provided that they get rid of the additional energy that has appeared from somewhere (this is taken care of automatically by the time-reversal). But this alone does not tell us whether this space-time can exist as a real possibility in the sense that we do not know if this process can happen with large probability (close to one) in the time before the shell reaches the Schwarzschild radius (of the classical solution).

I have remained skeptical, despite Carlo’s infinitely patience in explaining their argument to me. But if they are right and what they claim is correct, then this would indeed solve both the black hole information loss problem and the firewall conundrum. So stay tuned...

Sunday, July 20, 2014

I saw the future [Video] Making of.

You wanted me to smile. I did my best :p



With all the cropping and overlays my computer worked on the video mixdown for a full 12 hours and that in a miserable resolution. Amazingly, the video looks better after uploading it to YouTube. Whatever compression YouTube is using, it has nicely smoothened out some ugly pixelations that I couldn't get rid of.

The worst part of the video making is that my software screws up the audio timing upon export. Try as I might, the lip movements never quite seem to be in sync, even if they look perfectly fine before export. I am not sure exactly what causes the problem. One issue is that the timing of my camera seems to be slightly inaccurate. If I record a video with the audio running in the background and later add the same audio on a second track, the video runs too fast by about 100 ms over 3 minutes. That's already enough to note the delay and makes the editing really cumbersome. Another contributing factor seems to be simple errors in the data processing. The audio sometimes runs behind and then, with an ugly click, jumps back into place.

Another issue with the video is that, well, I don't have a video camera. I have a DSLR photo camera with a video option, but that has its limits. It does not for example automatically refocus during recording and it doesn't have a movable display either. That's a major problem since it means I can't focus the camera on myself. So I use a mop that I place in front of the blue screen, focus the camera on that, hit record, and then try to put myself in place of the mop. Needless to say, that doesn't always work, especially if I move around. This means my videos are crappy to begin with. They don't exactly get better with several imports and exports and rescalings and background removals and so on.

Oh yeah, and then the blue screen. After I noticed last time that pink is really a bad color for a background removal because skin tones are pink, not to mention lipstick, I asked Google. The internet in its eternal wisdom recommended a saturated blue rather than turquoise, which I had though of, and so I got myself a few meters of the cheapest royal blue fabric I could find online. When I replaced the background I turned into a zombie, and thus I was reminded I have blue eyes. For this reason I have replaced the background with something similar to the original color. And my eyes look bluer than they actually are.

This brings me to the audio. After I had to admit that my so-called songs sound plainly crappy, I bought and read a very recommendable book called "Mixing Audio" by Roey Izhaki. Since then I know words like multiband compressor and reverb tail. The audio mix still isn't particularly good, but at least it's better and since nobody else will do it, I'll go and congratulate myself on this awesomely punchy bass-kick loop which you'll only really appreciate if you download the mp3 and turn the volume up to max. Also note how the high frequency plings come out crystal clear after I figured out what an equalizer is good for.

My vocal recording and processing has reached its limits. There's only so much one can do without a studio environment. My microphone picks up all kinds of noise, from the cars passing by over the computer fan and the neighbor's washing machine to the church bells. I basically can't do recordings in one stretch, I have to repeat everything a few times and pick the best pieces. I've tried noise-removal tools, but the results sound terrible to me and, worse, they are not reproducible, which is a problem since I have to patch pieces together. So instead I push the vocals through several high-pass filters to get rid of the background noise. This leaves my voice sounding thinner than it is, so then I add some low-frequency reverb and a little chorus and it comes out sounding mostly fine.

I have given up on de-essing presets, they always leave me with a lisp on top of my German accent. Since I don't actually have a lot of vocals to deal with, I just treat all the 's' by hand in the final clip, and that sounds okay, at least to my ears.

Oh yeah, and I promise I'll not attempt again to hit a F#3, that was not a good idea. My voicebox clearly wasn't meant to support anything below B3. Which is strange as I evidently speak mostly in a frequency range so low that it is plainly unstable on my vocal cords. I do fairly well with everything between the middle and high C and have developed the rather strange habit of singing second and 3rd voices to myself when I get stuck on some calculation. I had the decency to remove the whole choir in the final version though ;)

Hope you enjoy this little excursion into the future. Altogether it was fun to make. And see, I even managed a smile, especially for you :o)

Saturday, July 19, 2014

What is a theory, What is a model?

During my first semester I coincidentally found out that the guy who often sat next to me, one of the better students, believed the Earth was only 15,000 years old. Once on the topic, he produced stacks of colorful leaflets which featured lots of names, decorated by academic titles, claiming that scientific evidence supports the scripture. I laughed at him, initially thinking he was joking, but he turned out to be dead serious and I was clearly going to roast in hell until future eternity.

If it hadn’t been for that strange encounter, I would summarily dismiss the US debates about creationism as a bizarre cultural reaction to lack of intellectual stimulation. But seeing that indoctrination can survive a physics and math education, and knowing the amount of time one can waste using reason against belief, I have a lot of sympathy for the fight of my US colleagues.

One of the main educational efforts I have seen is to explain what the word “theory” means to scientists. We are told that a “theory” isn’t just any odd story that somebody made up and told to his 12 friends, but that scientists use the word “theory” to mean an empirically well-established framework to describe observations.

That’s nice, but unfortunately not true. Maybe that is how scientist should use the word “theory”, but language doesn’t follow definitions: Cashews aren’t nuts, avocados aren’t vegetables, black isn’t a color. And a theory sometimes isn’t a theory.

The word “theory” has a common root with “theater” and originally seems to have meant “contemplation” or generally a “way to look at something,” which is quite close to the use of the word in today’s common language. Scientists adopted the word, but not in any regular way. It’s not like we vote on what gets called a theory and what doesn’t. So I’ll not attempt to give you a definition that nobody uses in practice, but just try an explanation that I think comes close to practice.

Physicists use the word theory for a well worked-out framework to describe the real world. The theory is basically a map between a model, that is a simplified stand-in for a real-world system, and reality. In physics, models are mathematical, and the theory is the dictionary to translate mathematical structures into observable quantities.


Exactly what counts as “well worked-out” is somewhat subjective, but as I said one doesn’t start with the definition. Instead, a framework that gets adapted by a big part of the community slowly lives up to deserve the title of a “theory”. Most importantly that means that the theory has to fulfil the scientific standards of the field. If something is called a theory it basically means scientists trust its quality.

One should not confuse the theory with the model. The model is what actually describes whatever part of the world you want to study by help of your theory.

General Relativity for example is a theory. It does not in and by itself describe anything we observe. For this, we have to first make several assumptions for symmetries and matter content to then arrive at model, the metric that describes space-time, from which observables can be calculated. Quantum field theory, to use another example, is a general calculation tool. To use it to describe the real world, you first have to specify what type of particles you have and what symmetries, and what process you want to look at; this gives you for example the standard model of particle physics. Quantum mechanics is a theory that doesn’t carry the name theory. A concrete model would for example be that of the Hydrogen atom, and so on. String theory has been such a convincing framework for so many that it has risen to the status of a “theory” without there being any empirical evidence.

A model doesn't necessarily have to be about describing the real world. To get a better understanding of a theory, it is often helpful to examine very simplified models even though one knows these do not describe reality. Such models are called “toy-models”. Examples are e.g. neutrino oscillations with only two flavors (even though we know there are at least three), gravity in 2 spatial dimensions (even though we know there are at least three), and the φ4 theory - where we reach the limits of my language theory, because according to what I said previously it should be a φ4 model (it falls into the domain of quantum field theory).

Phenomenological models (the things I work with) are models explicitly constructed to describe a certain property or observation (the “phenomenon”). They often use a theory that is known not to be fundamental. One never talks about phenomenological theories because the whole point of doing phenomenology is the model that makes contact to the real world. A phenomenological model serves usually one of two purposes: It is either a preliminary description of existing data or a preliminary prediction for not-yet existing data, both with the purpose to lead the way to a fully-fledged theory.

One does not necessarily need a model together with the theory to make predictions. Some theories have consequences that are true for all models and are said to be “model-independent”. Though if one wants to test them experimentally, one has to use a concrete model again. Tests of violations of Bell’s inequality maybe be an example. Entanglement is a general property of quantum mechanics, straight from the axioms of the theory, yet to test it in a certain setting one has to specify a model again. The existence of extra-dimensions in string theory may serve as another example of a model-independent prediction.

One doesn’t have to tell this to physicists, but the value of having a model defined in the language of mathematics is that one uses calculation, logical conclusions, to arrive at numerical values for observables (typically dependent on some parameters) from the basic assumptions of the model. Ie, it’s a way to limit the risk of fooling oneself and get lost in verbal acrobatics. I recently read an interesting and occasionally amusing essay from a mathematician-turned-biologist who tries to explain his colleagues what’s the point of constructing models:
“Any mathematical model, no matter how complicated, consists of a set of assumptions, from whichj are deduced a set of conclusions. The technical machinery specific to each flavor of model is concerned with deducing the latter from the former. This deduction comes with a guarantee, which, unlike other guarantees, can never be invalidated. Provided the model is correct, if you accept its assumptions, you must as a matter of logic also accept its conclusions.”
Well said.

After I realized the guy next to me in physics class wasn’t joking about his creationist beliefs, he went to length explaining that carbon-dating is a conspiracy. I went to length making sure to henceforth place my butt safely far away from him. It is beyond me how one can study a natural science and still interpret the Bible literally. Though I have a theory about this…

Saturday, July 12, 2014

Post-empirical science is an oxymoron.

Image illustrating a phenomenologist after
reading a philosopher go on about
empiricism.

3:AM has an interview with philosopher Richard Dawid who argues that physics, or at least parts of it, are about to enter an era of post-empirical science. By this he means that “theory confirmation” in physics will increasingly be sought by means other than observational evidence because it has become very hard to experimentally test new theories. He argues that the scientific method must be updated to adapt to this development.

The interview is a mixture of statements that everybody must agree on, followed by subtle linguistic shifts that turn these statements into much stronger claims. The most obvious of these shifts is that Dawid flips repeatedly between “theory confirmation” and “theory assessment”.

Theoretical physicists do of course assess their theories by means other than fitting data. Mathematical consistency clearly leads the list, followed by semi-objective criteria like simplicity or naturalness, and other mostly subjective criteria like elegance, beauty, and the popularity of people working on the topic. These criteria are used for assessment because some of them have proven useful to arrive at theories that are empirically successful. Other criteria are used because they have proven useful to arrive on a tenured position.

Theory confirmation on the other hand doesn’t exist. The expression is sometimes used in a sloppy way to mean that a theory has been useful to explain many observations. But you never confirm a theory. You just have theories that are more, and others that are less useful. The whole purpose of the natural sciences is to find those theories that are maximally useful to describe the world around us.

This brings me to the other shift that Dawid makes in his string (ha-ha-ha) of words, which is that he alters the meaning of “science” as he goes. To see what I mean we have to make a short linguistic excursion.

The German word for science (“Wissenschaft”) is much closer to the original Latin meaning, “scientia” as “knowledge”. Science, in German, includes the social and the natural sciences, computer science, mathematics, and even the arts and humanities. There is for example the science of religion (Religionswissenschaft), the science of art (Kunstwissenschaft), science of literature, and so on. Science in German is basically everything you can study at a university and for what I am concerned mathematics is of course a science. However, in stark contrast to this, the common English use of the word “science” refers exclusively to the natural sciences and does typically not even include mathematics. To avoid conflating these two different meanings, I will explicitly refer to the natural sciences as such.

Dawid sets out talking about the natural sciences, but then strings (ha-ha-ha) his argument along on the “insights” that string theory has lead to and the internal consistency that gives string theorists confidence their theory is a correct description of nature. This “non-empirical theory assessment”, while important, can however only be means to the end of an eventual empirical assessment. Without making contact to observation a theory isn’t useful to describe the natural world, not part of the natural sciences, and not physics. These “insights” that Dawid speaks of are thus not assessments that can ever validate an idea as being good to describe nature, and a theory based only on non-empirical assessment does not belong into the natural sciences.

Did that hurt? I hope it did. Because I am pretty sick and tired of people selling semi-mathematical speculations as theoretical physics and blocking jobs with their so-called theories of nothing specifically that lead nowhere in particular. And that while looking down on those who work on phenomenological models because those phenomenologists, they’re not speaking Real Truth, they’re not among the believers, and their models are, as one string theorist once so charmingly explained to me “way out there”.

Yeah, phenomenology is out there where science is done. To many of those who call themselves theoretical physicists today seem to have forgotten physics is all about building models. It’s not about proving convergence criteria in some Hilbert-space or classifying the topology of solutions of some equation in an arbitrary number of dimensions. Physics is not about finding Real Truth. Physics is about describing the world. That’s why I became a physicist – because I want to understand the world that we live in. And Dawid is certainly not helping to prevent more theoretical physicists get lost in math and philosophy when he attempts to validate their behavior claiming the scientific method has to be updated.

The scientific method is a misnomer. There really isn’t such a thing as a scientific method. Science operates as an adaptive system, much like natural selection. Ideas are produced, their usefulness is assessed, and the result of this assessment is fed back into the system, leading to selection and gradual improvement of these ideas.

What is normally referred to as “scientific method” are certain institutionalized procedures that scientists use because they have shown to be efficient to find the most promising ideas quickly. That includes peer review, double-blind studies, criteria for statistical significance, mathematical rigor, etc. The procedures and how stringent (ha-ha-ha) they are is somewhat field-dependent. Non-empirical theory assessment has been used in theoretical physics for a long time. But these procedures are not set in stone, they’re there as long as they seem to work and the scientific method certainly does not have to be changed. (I would even argue it can’t be changed.)

The question that we should ask instead, the question I think Dawid should have asked, is whether more non-empirical assessment is useful at the present moment. This is a relevant question because it requires one to ask “useful for what”? As I clarified above, I myself mean “useful to describe the real world”. I don’t know what “use” Dawid is after. Maybe he just wants to sell his book, that’s some use indeed.

It is not a simple question to answer how much theory assessment is good and how much is too much, or for how long one should pursue a theory trying to make contact to observation before giving up. I don’t have answers to this, and I don’t see that Dawid has.

Some argue that string theory has been assessed too much already, and that more than enough money has been invested into it. Maybe that is so, but I think the problem is not that too much effort has been put into non-empirical assessment, but that too little effort has been put into pursuing the possibility of empirical test. It’s not a question of absolute weight on any side, it’s a question of balance.

And yes, of course this is related to it becoming increasingly more difficult to experimentally test new theories. That together with self-supporting community dynamics that Lee so nicely called out as group-think. Not that loop quantum gravity is any better than string theory.

In summary, there’s no such thing as post-empirical physics. If it doesn’t describe nature, if it has nothing to say about any observation, if it doesn’t even aspire to this, it’s not physics. This leaves us with a nomenclature problem. How do you call a theory that has only non-empirical facts speaking for it and one that the mathematical physicists apparently don’t want either? How about mathematical philosophy, or philosophical mathematics? Or maybe we should call it Post-empirical Dawidism.

[Peter Woit also had a comment on the 3:AM interview with Richard Dawid.]

Sunday, July 06, 2014

You’re not a donut. And not a mug either.

A topologist, as the joke goes, is somebody who can’t tell a mug from a donut.

Topology is a field of mathematics concerned with the properties of spaces and their invariants. One of these invariants is the number of ways you can cut out slices of an object without it falling apart, known as the “genus”. You can cut a donut and it becomes an open ring, yet it is still one piece, and you can cut the handle of a mug and it won’t fall off. Thus, they’re topologically the same.

The genus counts essentially the number of holes though that can be slightly misleading. A representative survey among our household members for example revealed that the majority of people count four holes in a T-shirt, while its genus is actually 3. (Make it a tank top, cut open shoulders and down the front. If you cut any more, it will fall apart.)

Every now and then I read that humans are topologically donuts, with anus, excuse me, genus one. Yes, that is obviously wrong, and I know you’ve all been waiting for me to count the holes in your body.

To begin with the surface of the human body, as any other non-mathematical surface, is not impenetrable, and how many holes it has is a matter of resolution. For a neutrino for example you’re pretty much all holes.

Leaving aside subatomic physics and marching on to the molecular level, the human body possesses an intricate network of transport routes for essential nutrients, proteins, bacteria and cells, and what went in one location can leave pretty much anywhere else. You can for example absorb some things through your lungs and get rid of them in your sweat, and you can absorb some medications through your skin. Not to mention that the fluid you ingest passes through some cellular layers and eventually leaves though yet another hole.

But even above the molecular level, the human body has more than one hole. One of the most unfortunate evolutionary heritage we have is that our airways are conjoined with the foodways. As you might have figured out when you were 4 years old, you can drink through your nose, and since you have two nostrils that brings you up to genus three.

Next, the human eyes sit pretty loosely in their sockets and the nasal cavities are connected to the eye sockets in various ways. I can blow out air through my eyes, so I count up to genus 5 then. Alas, people tend to find this a rather strange skill, so I’ll leave it to you whether you want to count your eyes to uppen your holyness. And while we are speaking of personal oddities, should you have any body piercings, these will pimp up your genus further. I have piercings in my ears, so that brings my counting to genus 7.

Finally, for the ladies, the fallopian tubes are not sealed off by the ovaries. The egg that is released during ovulation has to first make it to the tube. It is known to happen occasionally that an egg travels to the fallopian tube on the other side, meaning the tubes are connected through the abdominal cavity, forming a loop that adds one to the genus.

This brings my counting to 5 for the guys, 6 for the ladies, plus any piercings that you may have.

And if you have trouble imagining a genus 6 surface, below some visual aid.

Genus 0.

Genus 1.

Genus 2.

Genus 3.

Genus 4.

Genus 5.

Genus 6.

Homework.