Monday, March 28, 2011


Lara and Gloria are now almost three months old. They have doubled their birth weight and grown in and out of the newborn cloths. Gloria is smiling generously at all and everybody while Lara's smiles are reserved for special occasions. Stefan and I are glad they now make some sounds other than crying; their "ouee" and "agooh" are music to my tinnitus.

The girls can now almost hold their head, and they have begun to take note of the mobiles above their beds. Gloria spends hours waving around with her arms and kicking into the air, hoping to hit something. Lara happily talks to the wooden bees and butterflies above her head. Interestingly enough, the babies hardly take note of each other. When we put them both in the playpen, they completely ignore their sibling. They pay more attention to about everything else than they pay to their sister.

Responsibility hits you in funny ways. The other day it occurred to me with some months delay I should probably wash the babies behind their ears. If I don't do it, who will? And then there was the day when I misplaced the baby. I went to see if they're all right and found one bed empty. Since it was unlikely the baby had learned to walk while I wasn't looking, I probably took her someplace and then forgot. I checked the big bed and the babyseat and the playpen before I remembered I put her on the couch, where she was still sleeping peacefully. (But don't tell my husband.)

Stefan and I, we have meanwhile organized our lives with the babies pretty well, though we are still short on sleep. It didn't help that Europe switched to summer time yesterday. Today, Lara and Gloria seem a little confused that breakfast is so early. And I have learned to type two-handed while balancing a baby on my forearms.

Thursday, March 24, 2011

What is mathematics good for?

Some weeks ago I asked my midwife what made her chose her job. She told me she had actually wanted to study medicine, but didn't meet the numerus clausus. Rspt she ranked place thirtythousandsomething. With an apologetic look at the shelves full with physics and maths books behind me, she added maths was her problem. She couldn't figure out what is was supposed to be good for.

She has a point there, I thought through endless repetitions of my pelvis floor exercises, and though it's hardly the first time I've heard this remark I started to wonder what role mathematics does really play in every day life. (Okay, I admit, what I really thought was it would make a good topic for a blog post.) Arguably, I need a lot of maths in my life because otherwise I'd be unemployed. But how much maths does the average person really need? And what do they need? And does school teach it?

You don't need to learn maths to survive. Otherwise mankind would have gone extinct long ago. Amazingly enough though, your brain performs some basic mathematics all the time, such as extrapolating the motion of moving objects. In an interesting experiment measuring the activity of neurons in rhesus monkeys, researchers from the University of Tübingen have found that different sets of neurons fire in response to the monkey seeing sets with different numbers of elements. Basically, there's neurons that are (primarily) activated by specific numbers. (See Bongard and Nieder, PNAS 107, 2277 (2010)). And it is known that people with certain brain injuries lose the ability to understand, compare, and deal with numbers, a disability known as acalculia. It does seem plausible then that dyscalculia, difficulties in learning and comprehending mathematics, is so some extend due to wiring instead of motivational problems. However, that's estimated to affect only a small percentage of the population. Most people who don't understand maths don't understand it because they've never really made an effort. Which brings us back to the question what's it good for?

Basic arithmetics is so universally useful that it benefits your selective advantage. Whether you want to know if you've enough money to fill up the tank, are worried that the baby didn't drink enough, or need to know how many bottles of sparkling wine to order for your graduation party, it haunts you everywhere. Beyond that, if you want to understand your average magazine or newspaper, you better know how to read a graph. And unless you want to blindly trust your financial adviser, percent calculation should be on your list.

Having come to this point, I Googled for "mathematics in every day life." The first hit was a long deserted blog with a handful of entries that, next to percent calculation, discusses symmetries in car logos and flowers. However, one doesn't need to know the mathematical definition of a group to plant a flower. Google further brought up a document I couldn't open, a file not found, a power point representation on photoshopping, and a Tutorvista question "How is maths used in everyday life?" with the reply "Math is used in time calculation, shopping, traveling, cooking, and all other important activities." All together not an impressive result. What is maths good for if not even Google knows?

School mathematics tends to drown pupils in 'real life' examples that no normal person will ever use in their real life. Yes, I sometimes add up the prices of items in the supermarket just for distraction, but it's arguably a pretty pointless exercise. Yes, it helps to know some trigonometry to figure out if the new furniture will actually fit through the door, but then you can rent furnished. And who really cares what's the volume of that piece of cake.

The real value of mathematics isn't that you can calculate what 500 sq ft is in international units, because Google does that for you. That, incidentally doesn't have much to do with maths anyway. Sadly, school doesn't teach children much about the beauty of maths, the value of logic, and the power of proofs. You don't need mathematics to live, but you need it to understand - for example Google's PageRank. What is mathematics good for? Mathematics is at the basics of science, including physics, computer science, and economics, examples are omnipresent in your every day life. Without mathematics, you're left in the fuzzy realm of storytelling. How can one understand the world without knowing what a differential equation is, without knowing what optimization is?

No, you don't need to know maths to plant a flower, to admire a night sky, or to like a crystal. But as in the arts, getting to know the artist and his techniques add to the appreciation and understanding of her work - may that be the Fermat's principle, data compression, self-organization, Noether's theorems or chaos. Mathematics is the language of Nature and learning it is your connection to the universe. No more and no less.

Since I acknowledge that the selection of maths taught at school is, sadly, suboptimal to this end, I set out to explain to my midwife that statistics is essential to understand the studies she's been telling me about and a doctor should indeed know what a standard deviation is. And being familiar with the exponential function might explain the funny face I made when she recommended some homeopathic remedy in D10. Things went downhill from there.

Wednesday, March 16, 2011

This and That

Friday, March 11, 2011

Causes of women's underrepresentation in science

I always feel awkward if somebody brings up the topic of women's underrepresentation in physics. Though I'm one of these underrepresented women, I don't actually have a lot to say about the possible causes that hasn't been said a million times already. I'm not a social scientist and I'm not a neurologist and I don't follow the relevant literature. That leaves me with my own experience to talk about, but I generally dislike talking about myself. Also, exactly by virtue of being one of the aberrations I'm not the right person to ask why there aren't more girls studying physics.

I'm generally supportive of all these women's networks, especially those aiming at providing the all-important much talked about 'role models' for young girls - something that in today's overconnected world can be done without much effort - and groups dedicated to helping with issues that women are more likely to want to discuss (Breastfeeding in my office - do or don't?). I've on occasion participated in on or the other meeting and such, and I think most of these initiatives serve a good purpose in providing encouragement and connections to others in similar situations and can be very helpful indeed.

But thing is I get along well with my male colleagues and I have no reason to suspect any sort of systematic bias has conspired against me at any point. Of course one or the other guy is an asshole, but nothing surprising about that. Just that I know many of my female colleagues have made bad experiences and I don't want to do a disservice to them by saying I think much more important than gender bias is that the typical academic career is simply incompatible with many women's priorities. Do I have to spell it out? If you're lucky enough to get tenure, you'll on the average get there in the late thirties or early forties. If you're a man, you can then go marry a younger woman and start thinking about reproduction. If you're a woman, you better freeze some eggs in time if you want to wait that long.

Interestingly, I yesterday came across a paper examining the question if it's a bias against women causing their underrepresentation in science

In their paper the authors surveyed studies past the mid 80s on bias against women in manuscript and grant reviews and in hiring. They basically found that while there's the occasional outlying study claiming to have found a bias against women, these outlying results haven't been reproduced, and most studies found very little or no bias in either direction. (That is, one should add, after productivity has been corrected for by available resources since women are more likely to work in positions with limited resources which by itself is correlated with lower productivity.)

Now, as I said, I'm not an expert on these questions so it's hard for me to tell if their survey of available data is complete. But if it is, one should pay attention to their conclusions. They argue that looking at the evidence, or lack thereof, efforts to reduce gender bias are misdirected since there is already little or no bias to find. Instead, one should focus on making career options more friendly towards women's life plans so one doesn't unnecessarily lose them early. Quoting from a report on gender issues by the General Accounting Office and referring to the UC-Berkeley's "Family Friendly Edge" program, they suggest measures such as
"stopping tenure clocks for family formation and tenure-track positions seguing from part-time to full-time [...], adjusting the length of time to work on grants to accommodate child-rearing, no-cost grant extensions, supplements to hire postdocs to maintain momentum during family leave, reduction in teaching responsibilities for women with newborns, grants for retooling after leaves of absence, couples-hiring, and childcare to attend professional meetings [...], [Employer providing] high-quality childcare and emergency backup care, summer camps and school break care, [...] instruct[ions for] committees to ignore family-related gaps in CVs."

They kind of forgot to say that maybe most important is a decent maternity and parental leave to begin with, Sweden tells you how to.

Of course one should add it's not just women affected by this. Men who don't want to wait with having a family till they have job security and/or who have a partner not in the mood moving with them around the globe are in the present system also likely to drop out early. That's got nothing to do with hitting a glass ceiling. It's more like following the arrow that points to the open door.

Monday, March 07, 2011

Evolving Dimensions

That the space-time of Einstein's Special and General Relativity might not be fundamental plays a central rôle in our quest for quantum gravity. There are many possibilities how the fundamental structure of space-time may be different from the four-dimensional continuum; discretization and additional space-like dimensions are among those that have received the bulk of attention. No matter what the modification though, one has to make sure that deviations from the experimentally extremely well confirmed Standard Model of particle physics and General Relativity become important only at scales that we have not yet tested, typically at high energies or short distances.

The idea that space-time might not be higher-dimensional on short distances but instead be lower-dimensional has been around for some while, inspired by results from causal dynamical triangulation. In a paper last year, Anchordoqui et al proposed to examine the possibility of lower dimensionality at small distances for its phenomenology in their paper
    Vanishing Dimensions and Planar Events at the LHC
    Luis Anchordoqui, De Chang Dai, Malcolm Fairbairn, Greg Landsberg, Dejan Stojkovic
    arXiv:1003.5914v2 [hep-ph]

Greg Landsberg gave a talk about this work on our last year's workshop on Experimental Search for Quantum Gravity (recording of the talk here). The basic idea is that the dimensionality of space changes with distance in such a way that it is 3-dimensional on scales we have tested it, lower dimensional on distances shorter than we have probed yet (about 1/1000 of a femtometer) and possibly higher-dimensional on distances larger than we can observe. The picture suggested is that of a (one-dimensional) string being knitted, and the knitted sheet (2-dimensional) being crumpled to a ball (3-dimensional). The authors dubbed this "evolving dimensionality." The merit of having a smaller number of space-like dimensions at small distances or high energies is that it improves the renormalizability of quantum field theories and esp. that of quantum gravity. (In contrast to additional dimensions which actually make the problem worse.)

The above paper as well as two recent follow-up papers, arXiv:1012.1870 [hep-ph] and arXiv:1102.3434 [gr-qc], looked at the phenomenological consequences of the evolving dimensions. Most interesting, they predict that at high energies the outgoing particles in scattering events should have an increased probability of being aligned in a plane. And the latest paper investigates the modification of the gravitational wave background. This modification is due to the early universe having been lower-dimensional if the idea is true, which would prohibit the propagation of gravitational waves. Both predictions are for all I know unique to this particular model.

But the question that springs to mind immediately is: What about Lorentz invariance? If one has a lower number of dimensions at short distances, these dimensions need to be oriented somehow relative to the four-dimensional continuum that must be reproduced at large distances. This orientation necessarily breaks Lorentz invariance. The problem is then that violations of Lorenz invariance are extremely tightly constrained already. I was thus curious to see how the model of evolving dimensions avoids these constraints.

The way this is achieved is that there is no model. Instead, it's in the authors words "not a concrete model, but rather a conceptual new paradigm." The papers offer pictures and analogies instead of a mathematical description of the new fundamental structure of space-time and the dynamics of quantum fields in it. The most recent paper addresses the issue of Lorenz invariance as follows:
"For random orientation of lower-dimensional planes/lines (see e.g. Fig. 2 ), violations of Lorentz invariance induced by the lattice become non-systematic, and thus evade strong limits put on theories with systematic violation of Lorentz invariance."

Unfortunately, this claim is not backed up by any argument and the figure does not represent a Lorentz-invariant random orientation. (The average spacings are approximately of the same size which is not boost invariant). From Causal Sets we know there are Lorentz-invariant 'sprinklings,' but these are sets of points and not distributions of planes. I also don't see from the picture if and how these planes end when they meet and it remains unclear how the length scales on which the dimensionality changes, supposedly a property of the space-time structure, is defined Lorenz-invariantly. Most problematic however is that the previous paper (arXiv:1012.1870) talked about the loss of energy into the background. This necessitates an interaction and that interaction should be described by an operator coupling the fields to the, oriented, background. I would then suspect this interaction falls among the already highly constrained Lorenz-invariance violations. It doesn't matter if these orientations average out on large distances if the effect that one looks for necessitates one is in a regime where one is sensitive to the distance it is not averaged out. This is very difficult to say though without a model.

However, in the recent paper on gravitational waves, one doesn't actually need Lorenz-invariance since one is concerned with cosmology and has a preferred frame - the restframe of the CMB - at hand anyway. So I wrote to one of the authors of the paper, Dejan Stojkovic from the University of Buffalo, who explained that they consider the model to be breaking boost-invariance but not rotational invariance. With that, the length scales on which dimensionality changes can be well defined without much effort. The question of Lorentz invariance violating operators however remains open. Dejan also readily admits that their new paradigm still needs work and explains how the first paper came about:
"I had this idea since 2003 while intensively working on higher dimensional theories. It crossed my mind that instead of making things more complicated at high energy (and hoping that the problems will miraculously disappear) we could instead make things less complicated - thus evolving dimensions (at short distances we have less dimensions, while at large distances we have more). However, I could not come up with a Lagrangian and would not dare to make it public.

Then at the meeting in Heidelberg, after diner and several beers, I told our friends, who intensively worked on extra dimensions, that the LHC is much more likely to find less rather than more dimensions, and after first 10 minutes of disbelief, they liked the idea and convinced me that in order to make a prediction rather than post-diction, the paper must go out NOW."

In summary: The idea of evolving dimensions is very interesting and makes predictions that are, for all I know, unique to this particular setting. At present it however lacks a mathematical model for the new fundamental structure and the dynamics of quantum fields in it.

Friday, March 04, 2011

This and That

Tuesday, March 01, 2011

Societal Fixed Points

The extend to which one can construct a model for human society is a matter of dispute. Among the most common arguments why it might not be possible to build a testable model of the behavior of large groups of humans is that the elements of this model are conscious and self-aware and in contrast to, say, electrons, able to react to the proposed model. In the social sciences, this feedback into the system is called reflexivity.

There are many examples for this feedback indeed spoiling the predictions of a model. One of the best known is maybe the experiment conducted at Hawthorne Works from 1924 to 1932, where it was studied (among other things) how monetary incentives affect workers' productivity. Surprisingly, the productivity decreased. It has been suspected that this happened because the workers had heard of the study and were afraid an increase in their productivity would later result in lay-offs or a lowering of the base rate. Another example is Nobel-prize winners or other experts and authorities commenting on the economy. It is well known that consumer behavior is influenced by whether the outlook is pessimistic or optimistic, though in this case it's of course more difficult to identify the causes.

In any case, the argument that feedback necessarily spoils any model and thus such efforts are in vain has never made much sense to me. While this may be for some models, there's no reason a model can't remain unmodified under the feedback or that the feedback must be such to necessarily spoil the accuracy of the model. Take the previous example about a prediction affecting consumer behavior. If it's an optimistic outlook it (ideally) causes people to spend more. This doesn't spoil the prediction. On the contrary: it may turn it into a self-fulfilling prophecy. Or take the model of supply and demand. Most people know it, yet they don't go and buy the most expensive crap just to prove economists wrong. And why is that? Because they have no reason to. Instead, they believe everything is working in their favor as long as they continue to do what the model says they'll do anyway.

This of course lead me to wonder if there's fixed points in the set of models. There is arguably a trivial fixed point. That's the one when nobody knows of a model or nobody believes it, thus there's no feedback. But one could say it's not an attractive fixed point in the sense that it's unstable: The more successful a model is the more people will know of it and believe it. So, I'm posing the question to you: is there an attractive fixed-point? Because if there is one, that might be where we're going.