Three Types of Symmetry

Past 6 months brought a lot of travel, relocation to a new city & country, new job…  now let’s try to get back into good habits like writing.

From 101 Things I Learned in Architecture School I finally understood the appeal of asymmetrical architecture and why is it so beloved by modern architects. This appreciation resonated with a 900 year old echo when we visited Angkor Wat.

1. Static symmetry

The most basic type of symmetry is the one we all imagine when one mentions “symmetry”. Invariance of shapes (or systems) under certain transformations (rotation, reflection, scaling) is deeply appealing to us. Like the layout of the Angkor Wat complex.

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2. Symmetry, broken

The breaking of symmetry is however a quintessential physical mechanism that gives rise, among others, to replicating complex patterns balancing on the edge of chaos (aka “life”).

The breaking of symmetry between past and future gives rise to the arrow of time. And where is time there are stories – such as the The Battle of Kurukshetra. Static symmetry of the army formations is ultimately broken to be able to tell the story of the big battle.

angkor-bas-relief-23-s-banerjee1

3. Dynamic balance – the symmetry of asymetry

Finally, we arrive at the least obvious form of symmetry – the dynamical balance.

From 101 Things I Learned in Architecture School:

Balance is inherent in a symmetrical composition, but asymmetrical com-
positions can be either balanced or unbalanced. Consequently, asymmetry tends to
require a more complex and sophisticated understanding of wholeness.

An example – a dancer is in dynamic balance, yet the posture is not symmetrical in the static sense.

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A spinning dancer is in dynamical balance. To keep with the Angkor Wat theme I could have showed a picture of dancing Apsaras. I found this optical illusion however extra interesting, because in addition to dynamical balance it demonstrates a dynamical clockwise/anti-clockwise symmetry in rotation.

This concept too hasn’t been unknown to the builders of Angkor Wat in the 11th century. My favourite bas relief is The Churning of Ocean of Milk.

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It shows 92 gods and 88 demons fighting for the elixir of immortality and a snake caught up in the middle. The gods hold the tail, the demons hold the head, while the snake coils itself around Mt. Mandala. Each time the gods and demons pull from their sides, the mountain turns and the ocean churns.

There is a lot of static (translational) symmetry in the repeating figures. The symmetry is also broken (the head and tail of the world-snake, gods and demons, 92 vs. 88). But ultimately there is a dynamical balance, at least for the moment.

And to close the circle (another symmetry), my new “home” town is famous for its own version of a building in a dynamic equilibrium, that is inspired by dancers: The Dancing House.

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David MacKay passed away

Prof. David MacKay passed away yesterday. He was an excellent teacher, author and scientist. I’ve learned about his terminal cancer earlier this week. He chronicled his treatment on his blog.

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I’ve learned about Prof. MacKay’s work through his fantastic, free, book Information Theory, Inference, and Learning Algorithms – a book that is scientifically proven to be better than Harry Potter. The gist of the book is also captured in the series of lectures here.

But it was his second fantastic, free, book Sustainable Energy – without the hot air that made a personal impact on my life – I decided to work in the energy sector, because it seemed as a very important topic plagued by misguided incentives, wishful thinking, but also full of exciting opportunities for a better future. Prof. MacKay summarized my motivations wonderfully:

I love renewables, but I’m also pro-arithmetic.

I even mentioned the book during my interview (of course nobody heard about it, which puzzled me at that time…).

Two years later I was working on a project of optimizing home heating and I needed the some additional data from the book. I wrote to Prof. MacKay and he kindly sent me the data. Looking at the date of the email, it was less than 2 weeks after he learned his terminal diagnosis.

Prof. MacKay taught us a lot, not only about information processing, machine learning or energetics, but especially about scientific integrity, curiousness and independent thought. For all that I’m deeply thankful to him.

What I learned this week: 18/2015

This was a very busy week, co-organising a workshop, travelling and then an extended weekend.

Statistics, Probability, Machine Learning, Data Science

Xgboost

I played with Xgboost, a parallelized gradient boosting machine implementation. I managed to install it on both a Windows and a Linux machine and it really is fast. I didn’t test it yet directly against the standard GBM implementation so I can’t say if the advantage is purely speed (claim is up to 20x) or if you can get extra predictive power per computational cycle.

Kaggle

After following the fora since quite some time I decided to actually try it (made just 2 submissions on 1 competition). I don’t expect it to use it competitively, and it is definitely a bit of stylized/artificial approach to data analysis/machine learning, but I think it is an interesting endeavor.

It is a martial arts kata excercise to the dirty, non-linear street fighting of the day-to-day data science. Where, as you know, street fighting is 50% of knowing when to avoid fight, 10% actual fight and 40% administration and sitting in meeting. Wait, somehow my metaphor broke.

Kaggle Higgs boson search post-mortem

Read up mostly Motl’s point of view (1,2, and the xgboost solution 3) and the Kaggle forum. Turned out to be a bit less interesting and enlightening than I thought, but it fit with the xgboost theme of the week.

General Science / Misc.

ER = EPR? 

Quanta has a series on recent developments here: 1, 2, 3. Being a total dilettante, but this just feels so very right. God knows, I’ve been in the past excited about many results, that then just went away. But this time it is different (I always say that…). The firewall problem was just a precursor, this is the real deal.

The quantum entanglement wormhole octopus is my new favourite animal.

So you want to be a consultant…?

Excellent article. Focused on freelence IT, but it is interesting also for other areas. And even if you don’t want to be a freelance consultant. Or a consultant.

The days are long but the decades are short

Sam Altman turns 30. Here is the wisdom from the elder. (The article is alright, it just strikes funny to get a life advice from a 30 year old).

Prescriptions, Paradoxes, and Perversities

An alarming analysis by Scott Alexander on the state of pharmaceutical.

Management Myth

An entertaining piece on MBA education and management.

Or: we hope this article will compensate you with a smug feeling of superiority, because although you have the hard science doctorate, we’ll pay far more for the fresh MBA graduate manager :).

Videos / Lectures

The Knowledge – Lewis Dartnell | Authors at Google

  • have his book on my “to read” pile. The talk wants me to move it up in the queue.

Podcasts

Phil Rosenzweig on Leadership, Decisions, and Behavioral Economics

  • Strongly recommended – lot’s of new ways to look at familiar experimental results and their (non) implications in practice. Highlight of the week.

Triple H on Pre-Fight Rituals, Injury Avoidance, and Floyd Mayweather, Jr.

  • after enjoying the Schwarzenegger episode and even (gasp!) the Glen Beck one, I’m hardly surprised about a wrestler coming out as a very reasonable, driven and articulate man. Ferris is an excellent interviewer and his podcast is very good time filler when I’m too tired for other stuff.

Suspended in the immense vastness of space and time

Watching us at 4K resolution at ~1000 frames/s, we realize how increadibly lonely we are.

Any signal takes millenia of milliseconds, whole aeons of femtoseconds to reach us. Any communication is impossible through the chasm of time.

The nearest human being can be tousands of attoparsecs away. How could be a warm touch be possible through the deep abyss of space?

We are hopelessly suspended in the immense vastness of space and time.

We are hopless vastness of space and time.

No man is an island. That doesn’t even begin to describe it.

Anti-inductive environments and social fermions

Phatic and anti-inductive environments

Scott Alexander has an excellent article on phatic vs. anti-inductive environments. He contrasts content-free communication (phatic, “talk-for-talk’s sake”) used for social signalling [1] with anti-inductive communication – coming up with unusual insights, that have not yet demoted to clichés by overuse [2].

Epistemology and anti-inductivity

The archetypal example of an anti-inductive system is the stock market (especially under the strong version of efficient market hypothesis).

Let’s say two stock prices are historically anticorrelated – the variance in their returns moves in opposite directions.  As soon as everyone believes this, hedge-fund managers will leverage up and buy both stocks.  Everyone will do this, meaning that both stocks will rise.  As the stocks rise, their returns get more expensive.  The hedge-fund managers book profits, though, because their stocks are rising.  Eventually the stock prices rise to the point they can go down.  Once they do, hedge-fund managers who got in late will have to liquidate some of their assets to cover margin calls.  This means that both stock prices will go down – at the same time, even though they were originally anticorrelated.  Other hedge funds may lose money on the same two stocks and also sell or liquidate, driving the price down further, etcetera.  The correlative structure behaves anti-inductively, because other people can observe it too.

– Eliezer Yudkovsky, Markets are Anti-Inductive

Anti-inductive environments are fascinating, because it is here that the bread-and-butter of “standard epistemology” – inductive reasoning – breaks down. I put quotes around “standard epistemology” because obviously this is exactly what hard-line Popperianism warns against (currently its most vocal proponent being Nicolas Nassim Taleb of the Black Swan fame).

Nonetheless, we do use induction all the time, trading off robustness of predictions for efficiency. It is indeed a great tool – assuming you are in an inductive environment (so definitely not in stock markets). Induction also works better, if you are close to the right solution (a local optimum in the solution space) – say ordinary, regular day-to-day problems. It does not work well with not well mapped solution spaces – say the cutting edge of science. That’s why we should rely there on falsification rather than induction.

Utility vampirism

The second key point is that anti-induction drains out any information value, the more it is acted on or decreases the utility of a given resource the more it is utilized.

Besides stock market, Scott mentions job interviewing as anti-inductive. Can we come up with other examples?

restaurant and VACATION Recommendations

These are typical anti-inductive situations: say you find a perfect vacation spot. The more people know about it, the worse it gets due to overcrowding.

traffic recommendations

If the GPS recommends the same alternative route to avoid a traffic jam for everybody, it potentially creates a new traffic jam.

The hipster Dilemma

Hipsters have it though. Saying: “I liked X, before it was cool” (for X being an indie band, foreign movie, underground writer etc.) is needed to signal your superior aesthetic taste and intellect, but at the same time devalues the resource X, by making it less obscure.

Social circles

“I don’t want to belong to any club that would accept me as one of its members.”

— Groucho Marx

You want to join social circles so that they increase your status. That means that your status has to be lower than the average of the social circle. If they accept you, the average status of the group decreases. And vice versa, a group wants new members with status higher than its average status, but why would he/her want to join?

Shared resources and tragedy of Commons

Many shared resources have anti-inductive features. The experience of a great movie can be ruined by an overcrowded cinema etc. This all is closely related to the tragedy of commons.

Solving anti-induction with Fermi-Dirac statistics

Interestingly, “crowd-aversion” behavior has a parallel in physics. Fermions are elementary particles with half-integer spins that follow the Fermi-Dirac statistics. Examples are quarks, leptons (e.g. electrons) and any composite particle from odd-number of fermions (e.g. protons and neutrons) [3].

Fermions obey Pauli’s exclusion principle: two identical fermions cannot occupy the same quantum state simultaneously. That’s why electrons don’t just bunch up on the lowest orbit in an atom and give rise to all kinds of interesting chemistry, such as you and me.

Recommendation engines can meet the required degrees of crowd-avoidance by incorporating a fermionic replusion term in their objective function.  A vacation recommendation engine therefore will not recommend both you and me the top place (giving us both a miserable time), but splits us between the few top ranked locations maximizing our overall satisfaction.

So did we solve anti-induction? Not so fast grasshopper! Maybe there is a second order anti-inductivity? As the old zen master asks: if an algorithm finds a trend, is it still cool?

I will leave as an exercise to the reader to work out the principles of a fermionic-stock market (herd behaviour? No problem!) and a fermionic utilitarianism (repugnant conclusion? Not for us!).


[1] Key here is that this is not a judgment statement. Content-free signalling is in fact important in many circumstances, albeit makes nerd-y types like us uncomfortable.

[2] Being true to Robin Hanson, anti-inductive communication is not about insights, but it is too about signalling just as phatic communicaiton, except it signals high cognitive capability and creativity (and hence a good genetic fond) instead of social alignment.

[3] For completeness, the counterparts to fermions, the integer spin bosons, do not mind crowds and they too can serve as a metaphor (and maybe more) in socio-economic systems, such as modelling monopolies/winner-takes-all dynamics in social networks via a Bose-Einstein condensation.

Against beauty

I’ve come across a quote by the great Buckminster Fuller:

When I’m working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is beautiful, I know it is wrong.
-Richard Buckminster Fuller

I felt satisfied – I always thought that requiring beauty in our solutions (in mathematics, physics, design or elsewhere) is very parochial. If your solution is beautiful, it only means the problem was too easy.

This is not to diminish the aesthetic pleasure of a beautiful proof, particularly clever experiment setup or elegant line of reasoning. Even after so many years, I still remember when I first heard the Cantor’s diagonal argument [1] and I can re-live the sheer excitement of it.

Buckminsterfullerene, a particularly beautiful configuration of 60 Carbon atoms.

On the other end of the beauty spectrum we can put the proof of the Four-color theorem. It was derived in the 70s using a computer and because of that it was (and still is) considered inelegant and problematic. Similarly, in physics solutions derived based on simulations are often deemed intellectually unsatisfactory.

However, beauty is a just a heuristic criterion telling us that a description of the system was found, which not only has a high-compression factor (sign of a good theory), but that this compression is in fact high enough to make the model of the system conveniently mind-sized, i.e. that it fits into the very limited memory and processing capacity of a human brain.

This also means, that a more capable cogitor (presumably an artificial intelligence) would have an aesthetic sense that extends far beyond the reaches of human minds and most of its creations would be deemed ugly by our standards. For such a system the difference between the Cantor’s diagonal and the reduction to 1936 submaps in the Four Color Problem might be only a tiny step down in the “beauty” department.

In the general problem space, problem that have solution we deem beautiful occupy only a vanishingly small subvolume. What worries me is that for many of our most important problems (scientific, technological, societal, ecological) there might be no solutions that we will considered beautiful. If we’re looking for beauty we might miss the correct (or at least satisficing) solutions.

One final lesson too: to echo the original quote – if you think you found a citation that beautifully demonstrates your idea, you know it is wrong.

Why? It turns out, that originally I misread the quote and it should in fact read:

When I’m working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong.
-Richard Buckminster Fuller

Emphasis mine.

So while Fuller doesn’t calls for looking for beautiful solutions, he still does use it as a correctness criterion. Let’s just hope we are not dismissing a satisfactory solutions, by chasing a mirage of a (non-existing) beautiful solution.

[1] If you haven’t seen it yet, I almost envy you that you have the experience ahead of you. Do yourself a favor and check it out!