About a year ago, I finished the last semester of my Physics degree at Tel Aviv University. A few scary exams and written projects later, and I had completed my requirements. Two days ago, they announced a Higgs-like particle observed at the LHC. Yesterday, I received notice that my university user is about to expire. And so I feel the time has come for me to write a little about my own experiences. (Also inspired by a friend, turning 26, who wrote a few words to mark the occasion.)

For many people, and for me especially, a university degree is a voluntary act. My reasons had nothing to do with finding a job or getting “ahead”, because I had already been a professional programmer. Extremely confident with my capabilities, I chose Physics because it drew me more than any other exact science. I also thought it might help with “breaking into” the games “industry”. Because of my high matriculation grades, the thought of failure was quite far from my mind. I didn’t even take the first semester seriously, remaining to work part-time at my job (hastily remedied by second semester, when I quit). I also hesitantly add that while I was not pressured into higher learning, my family’s culture surrounded me with a sense that it is The Right Thing to Do. At the very least, people close to me who I respect greatly also have backgrounds in physics.

Israelis begin university relatively late in life due to mandatory military service. I started even later still (at 25), making me among the oldest studying for their bachelor’s. Being older didn’t make it much easier. I certainly wasn’t any smarter than my classmates, some of whom are shining examples of the brightest minds I have had the pleasure of meeting. This was, eventually, a great experience for me, and a step outside of being surrounded by programmer types all day long. There were programmers in our group, but plenty of others had different backgrounds and had been steeped in various professional (and non-professional) cultures.

Physics, science, and thought

When studying physics with others, one begins to notice two types of thought.

• The intuitive: An intuitive physics student will study a problem by “feeling” for the answer. For this student, equations and formulae may be more of a chore or a hindrance than a tool, something to be left for the engineers to work out later. Qualitative answers are always better than quantitative ones, and theories become more of an abstract, cloud-like entity in their minds, rather than a concrete set of relations.
• The methodological: This student has organized his or her previously-learned knowledge in a thoughtful manner. This organization may be either inside the student’s mind, or held in an external structure (like meticulously-taken notes and photocopies of all important material). In either case, when solving a problem, this student starts with the known values and carefully works their way towards a solution, walking from node to node of their organized network of information.

The obvious statement is that to be successful at physics, one needs to have a balance between these two types of thought. The not-quite-so-obvious statement is that if one has to choose between one and the other, the methodological type is far, far more important. (At least for this stage of learning.)

Intuition is extremely important, because only intuition can see beyond the myopia of our rulebooks and theoretical frameworks. However, intuition is also often wrong.

Studying physics typically begins with the most basic of concepts: Newtonian mechanics. While not simple or easy, it is not too challenging to understand that the symbols on the blackboard actually relate to things we experience in our day-to-day. Especially in our age of 2D physics-based games, I doubt anyone could look at a diagram of two weights on an inclined plane without immediately “running the tape forward” in their head. This miracle of human thought is remarkable and wondrous — but to rely on it is a mistake. Professors often talk of “developing your intuition” in each subject, but I think they really mean “understand the material better”. Having a system is worth much more than being able to visualize problems, because physics rapidly gets to a point where visualization is extremely difficult (for example: thermodynamics, special relativity, or quantum mechanics).

While we’re on preconceived notions, I’d like to mention religion and science for a moment. For both Quantum I and II, we had two different professors who were [apparently] extremely observant of the Jewish faith. How can someone hold religion in such a central part of their life, while teaching about quantum mechanics? Does god “play dice”? How does one reconcile these two seemingly opposite notions? This puzzled me for quite a while, and it wasn’t until I read Alan Watts’s The Wisdom of Insecurity (thanks to Wolfgang for recommending it) that I began to understand:

The clash between science and religion has not shown that religion is false and science is true. It has shown that all systems of definition are relative to various purposes and that none of them actually “grasp” reality. And because religion was being misused as a means for actually grasping and possessing the mystery of life a certain measure of “debunking” was highly necessary.

There are religious rituals and moralities and they can form a kind of answer in response to certain questions. Science offers insight into the mechanics of the world, answering entirely different questions. As the quote hints, there are overlapping areas, but for the most part, both of these disciplines entirely fail to bring a complete understanding of all there is to know. This rejection of the absolute struck a chord, and it made studying science easier. It suddenly wasn’t so important to try and find the ultimate abstraction, or the most general solution, because there may not be one. And it seemed possible that a person could pursue both science and religion without living in conflict.

Unexpected turns of events

Before my time at the university, I don’t know if I ever considered the concept of failure. Sure, things went wrong in my daily life, none of which could be termed an absolute failure. But subscribing to a three-year cram of fast-paced studies, graded by an uncaring staff with absolute finality produced a new option of true self-failure. Having to retake courses, having to extend studies beyond the basic six semesters, dropping out entirely — these are all modes of failure that I was suddenly exposed to. Furthermore, my own abilities started being called into question. I left the safe haven of being, in what was my opinion, among the best at my field. Instead of being humbled or spurred to greatness, I started experiencing stress-related health symptoms (which I won’t go into here).

Time has passed since then, and I am much better now. And maybe a little wiser for my troubles.

Pacing of studies

Three years is too short a time for this amount of material. If I have one criticism or suggestion for the university, it would be to shorten the curriculum or add another semester or two. The smartest students got extremely good grades consistently, that much is true. But we are not all geniuses, and I feel that I was always one step behind the material. If I had taken my time (and some students did this purposefully), I would take an extra year to complete my B.Sc. and learn each subject more thoroughly.

The feeling of being behind was emphasized by the way professors and TAs push through the material. There is a constant feeling of “let’s get through this rudimentary subject matter and get to the Real Stuff.” The problem is, even in your Master’s degree, you don’t really get to the Real Stuff. Maybe for your doctorate or post-doc. Good luck!

(Although I suppose this is a symptom of any educational system — constantly “preparing” the student for “real life”, forgetting that Real Life is actually happening right now, no matter where you are in your studies.)

The legacy

Most of my colleagues stayed to begin their Master’s degrees, or to re-take failed courses. I took indefinite leave of higher learning for the time being, turning my attention to creative endeavors such as game programming and drawing.

So what did I get out of my degree?

Everything they say about “new modes of thought” are correct. I can see things a little differently, I can analyze problems from a new viewpoint. I can read technical documents easier. It’s more natural for me to stop and come up with a plan before diving into making or fixing something. Maybe even some improvements to self-discipline.

I also can appreciate the academic bureaucracies better (something I don’t feel I will ever want to be a part of). What it means to research something, what it means to have to work with professors — even if I didn’t have to do much of either.

Furthermore, there was a strong feeling of knowing less and less the more you know. The close you get to understanding a subject, the more it shows you the true vastness of what lies beyond your knowledge (and human knowledge in general, as well). Similarly, I discovered subjects in physics that I really, really didn’t care for (Solid State physics comes to mind).

That said, I did learn new things. It’s saddening to say, but I’ve already forgotten many of them, though I’m sure that if I had to pick them up again it would be possible (with a lot of hard work, of course). I have a list hanging around of special subjects I grew especially fond of that I’d like to put here:

• Harmonic analysis: one of the central themes in physics and engineering. Fourier is the simplest kind, but it pops up everywhere. Similar constructs include spherical harmonics and Bessel functions. Harmonic decomposition is beautiful, elegant, and incredibly useful. Learning how to build and use each kind was one of the most satisfying parts of my degree. Also related:
• Self-adjoint differential operators.
• Waves in general (linear waves, plane waves, spherical waves ….).
• Analytical mechanics: one of the most eye-opening courses. An entirely new way to look at problems, all the while paving the way towards more advanced subjects (like quantum physics).
• The seeming magic of the Lagrangian and Hamiltonian formalisms. Solving unthinkably difficult problems often with the greatest of ease.
• Principle of stationary action, the quantum-mechanical interpretation, relation to Fermat’s principle of shortest time, Euler-Lagrange, etc., etc., etc….
• Understanding the Hamiltonian as an operator, specifically the energy operator and the generator of the time-evolution operator (!!!!!!!!!!!).
• Vector calculus: some of these tools were pretty nice (Stokes, Green, Gradient, Divergence theorems, etc.).
• Special Relativity: About the least intuitive subject, and one of the most interesting. Extremely hard to really visualize. If you don’t believe me, see this video of a relativistic speed simulation. (General Relativity is even more bizarre, but I didn’t take that course.)
• Maxwell’s Equations: concise, elegant, and the incredible inspiration for Einstein’s special relativity. There is even a covariant form that turns all four of these into one single equation.
• Schrodinger’s Equation: Instead of providing deterministic laws of motion, this equation explains how a system is distributed statistically over time and space. Perfectly solvable for only a few special cases, and thus there are tons of approximation methods for “real life” systems. These aren’t much fun, but it helps to show the sheer depth and how much we don’t know about this quantum world.
• Astrophysics: I really hated this course, yet it (and other lectures I attended) tickled a deep feeling of wonder at the scale of the universe. Dark matter, dark energy, exoplanets and strange objects, and uncountable stars. All sorts of things to discover there. If I were to continue studies, I would probably go in this direction.
• EDIT — more things I liked!!
• Complex numbers and contour integrals!! This bit of Cauchy magic is too cool for words.
• Let’s not forget dimensional analysis and other approximation techniques. This skill might be trivial in some cases, but this is the kind of thing I literally use in the supermarket.

I also took an extra-curricular course in 19th Century Russian Literature, which was excellent. During my last year I used the central library extensively, reading books by Dostoevsky, Hesse, Joyce, Tolstoy, and Watts, among others. I also got pretty good at using Matlab and LyX/LaTeX.

“Academic” stuff I’ve done

• End-of-studies project: Gravitational Microlensing and the Search for Extrasolar Planets
• A software project demonstrating a genetic algorithm, using quadrupedal creatures simulated in 3D

As an elective course taken in order to fulfill requirements to complete my B.Sc., I took the course Introduction to Computational Physics, taught by Professor Karliner at Tel Aviv University. The course was a mash-up of many interesting computational techniques, most of which are used to perform approximations of physical systems.

The course included a short practical project chosen by the student. I decided to use a genetic algorithm to “breed” a kind of simulated life-form. The plan was elaborate, and I considered many complex ideas, but eventually stayed with the simplest creature I could come up with. It took form as a 3D box with four boxy “paddle” appendages. I used the Bullet physics engine, and I made the rest with C++ in Visual Studio.

Videos of the wild creatures in action after the jump.

Here is Generation Zero of a random batch:

After many unsuccessful attempts at tweaking the breeding algorithm, damping was added to the simulation, and the populations began to converge after only a few generations…

Afterwards, to up the ante, I changed the plane to accept different inclines. This demanded that the creatures climb up, instead of just in any arbitrary direction.

Finally, here is a video of the creatures reacting and adapting to an erroneous fitness function. This function mistakenly demands that the creatures go as far as possible to their right (roughly in the direction of the camera). This leads to some strange and lopsided behavior.

All the code and some binaries are available for download. You can also find a more formal writeup in .PDF format.

Entropy and time

To illustrate entropy, we use the classic example: a bottle full of gas, suddenly opened. The laws of thermodynamics dictate that the gas will expand to fill the new volume available to it. Conversely, placing an empty bottle inside a room full of gas would never collect every molecule inside it. This tendency towards disorder is quantified as entropy — but entropy is only a property of the entirety of the gas cloud as a very large collection of microscopic molecules.

Gravity affects all particles, even a single particle alone in a vacuum. Each particle of that gas “feels” the acceleration of gravity, but no single particle can “feel” entropy.

Entropy is more fickle than that, even. In closed systems, the total entropy can never be lowered — but nothing is guaranteed when it comes to local or open systems. Entropy can easily be lowered in many cases at the expense of total entropy, which can only rise. It’s safe to say that nothing on a human scale is truly a closed system, being as we are only a minuscule speck in the infinite expanse of the universe. We don’t even know if the universe itself is open or closed.

And so the question: how do we “feel” time passing? Even while staring at a wall, we have a sense of movement, that we traverse time like a fourth dimension. We certainly have no need of observing a thermodynamic process like a bottle of gas being opened in order to feel time moving by. We don’t need to observe our own body processes responding to entropy (such as hunger). Holding your breath and closing your eyes, you still feel time passing, even between heart beats.

Organic reduction of entropy through emergence

As I said before, it is possible to reduce local entropy at the expense of global entropy. Nature performs this miracle all the time in a process known as emergence. This occurs when many, many tiny components are exposed to huge influxes of energy. These tiny components tend to spontaneously organize themselves into larger structures, capable of reducing or even reversing their own entropy. A simple example is a desert full of many grains of sand, exposed to the terrific energy of endless winds. The sand grains tend to organize themselves into sand dunes, thus reducing their entropy.

Taken further, this describes life-forms very well. As living beings, made up of countless cells, animals are structures that minimize or reverse their own entropy.

Does consciousness reverse entropy?

And what of consciousness? Obviously this is a field that nobody currently understands very well, but we can still make observations of this strange phenomenon. I’ll use a very primitive model of the consciousness, which is probably wildly simplistic and inaccurate.

Our senses provide input, and translate events as they happen into signals.  These signals are consumed by the consciousness and stored in “memory”. Thus, the disparate signals reaching us from the outside world become organized spontaneously into what we can access later as memories. The brain, which has something to do with all this, consumes a huge amount of energy. I believe that this mimics the emergence phenomenon mentioned earlier: a huge influx of energy and information that organizes itself. In a word, the consciousness exists in an entropic minimum — or even in a realm of negative entropy, consistently.

To answer our question, maybe entropy does tell us which way is “future”. The world may be decaying, but our consciousnesses are busy organizing and reducing entropy. And thus, we “feel” time flow towards the lowest internal entropy of our consciousness, just as our bodies feel we are being accelerated “down” towards the center of the Earth.

The concept stems from my experiences studying physics, specifically the schism between the real world and the representation of the real world in theory. As a larger concept, there is much more to explore here, and it may be fuel for projects in the future.

Play Rocket Research in your browser

or:

• Download for Windows
• Download for Mac OS

Although not a long game, Rocket Research boasts its own soundtrack, graciously provided by Daniel Zoran.

All sounds were recorded by me from household items (except the Geiger counter; that came from the university lab).