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This week’s project is a molecular dynamics simulation. Don’t get too excited, it’s not using any of the state-of-art algorithms nor is assembling 3-dimensional structures of complex proteins. I began with a simple carbon chain using only coulomb’s law in a spring-mass system.

The molecule I’m using is this:

The drawing program is quite simple and wont work for most molecules, but for the 2-dimensional simple molecules (max. of 3 connections per atom) it kinda works.

Later on, putting the program to run, each atom “pushes” all others electrically and the spring “pulls” them back. A good way to solve that is to say that q1 . q2 / x² = - k . x = m . d²x/dx² (where x is a vector) and integrate numerically using Runge-Kutta.

But that’s my first openGL program, so I decided to go easy on the model and actually see it pseudo-working with an iterative-based simulation following the same equations above. This picture is a frame after a few iterations.

Quoting its page: “As this simulation is not using any differential solution, the forces grow and grow until the atom becomes unstable and break apart. Some Runge-Kutta is required to push the realism further.”

UPDATE:

The webpage of the fully-functional prototype is HERE.

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The first time I read this book was during my special relativity course at university. I couldn’t understand a thing the teacher was saying (probably because his explanations were always: “you won’t be able to understand that”) and I needed to replace a 35% grade I got in the first exam to complete the course.

Well, hopeless as I was, headed to the library in search of a magical book (other classmates were helpless as well) and found this one. The magic in it is that, instead of trying to force the Lorentz transformations down the throat first and then explain the basic principles of relativity, it does it by simply showing the topology of the space and assuming that the speed of light is constant (pretty much the same path Einstein took in the first place).

So, the first chapter has no equations whatsoever, only graphics with light waves going back and forth and he derives the light-cones automagically from it, what happens to the “world” at high speeds and how does it affect our senses of reality. It goes on for all kinematic principles only using Newton equations and gamma. Lorentz transformations only appear in the fourth chapter.

After that, not only I could understand relativity as a whole, but I also got 90% grade on the final exam! It’s an old (88) book but time has no meaning for a very good book, especially for a subject that hasn’t changed that much in the last decades.

I recommend it to physics-wannabe as well as lay people with little background in math, and if your teacher is as hopeless as mine was, ignore him and read this book.

Click here for the US version.

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I wonder why the human race is so tied up with serial thinking… We are so limited that even when we think in parallel, each parallel line is serial!

What?

Take the universe. Every single particle in the universe know all the rules (not many) that they need to follow. On themselves, the rules are dumb: you have weight, charge and can move freely round the empty space. But join several particles together and they form a complex atom with much more rules (combined from the first ones) that, if combined again form molecules that form macro-molecules that form cells that form organs that form organisms that form societies etc. Each level makes an exponential leap on the number of rules from the previous one.

Than, the stupid humanoid looks at reality and says: “That’s too complex, I’ll do one thing at a time”. That’s complete rubbish! His zillions of cells are doing zillions of different things each, his brain is interconnecting everything at the same time and that’s the only reason he can breathe wee and whistle at the same time.

Now take machines. The industrialization revolutionized the world by putting one thing after the other, Alan Turing revolutionized the world again by putting one cell after the other in the Turing tape. Today’s processors can only think of one thing after the other because of that.

Today you have multi-core processors doing different things but still each one is doing things in serial (Intel’s HyperThreading is inefficiently working in serial). Vector processors like graphic cards and big machines like the old Crays were doing exactly the same thing over a list of different values and Quantum computers will do the same operation over an entangled bunch of qbits (which is quite impressive) but still, all of it is serial thinking!

Optimization of code is to reduce the number of serial steps, parallelization of code is to put smaller sets of serial instructions to work at the same time, even message passing is serial on each node, the same with functional programming, asynchronous communications, everything is serial at some point.

Trying to map today’s programming languages or machines to work at the holographic level (such as the universe) is not only difficult, it’s impossible. The Turing machine is serial by concept, so everything built on top of it will be serial at one point. There must be a new concept of holographic (or fractal) machine, where each part knows all rules but only with volume you can create meaningful results, where code is not done by organizing the high-level rules but by creating a dynamic for the simple rules that will lead to the expected result.

How then?

Such holographic machine would have a few very simple “machine instruction” like “weight of photon is 0×000″ or “charge of electron is 1.60217646 × 10^-19″ and time will define the dynamics. Functions would be a pre-defined arrangement of basic rules that must be stable, otherwise it’d blow up (like too many protons in the nucleus), but it wouldn’t blow up the universe (as in throw exceptions), it would blow up the group itself and it would become lots of smaller groups, up to the indivisible particle.

The operating system of such machine should take care of the smaller groups and try to keep the groups as big as possible by rearranging them in a stable manner, pretty much as a God would do to it’s universe when it goes crazy. Programs running on this operating system would be able to use God’s power (GodOS libraries) to manipulate the groups at their own discretion, creating higher beings, able to interact, think and create new things… maybe another machine… maybe another machine able to answer the ultimate question of Life, the Universe and Everything.

I know letting the machine live would be the proper way of doing it but that could take a few billion years or I’ll be quite tired of engineering the machine and it’s OS and I’ll just want to the the job done quickly after that…

Why?

There is a big fuzz about Non-Polynomial time problems (NP-complete), those that can’t be solved in a reasonable (polynomial) time. The classic example is the travelling salesman problem where a salesman has to go to each one of a number of cities. Which is the best path to follow to visit all of them in the smallest distance possible? With 3 or 4 it’s quite simple but when you have lots like 300 it becomes impossible for normal (serial) computers to solve.

Another problem quite fancy is the Steiner tree problem, where you have some points and you want to connect them using the least amount of strings. This is as complex as the problem above, can take forever (longer than the age of the universe) for relatively small sets of points, but if you use water and soap the problem is solved almost instantly.

Of course, soap films cannot calculate the last digit of PI but because every part of it know a small list of basic rules (surface tension increased by the soap molecules derived from opposite charges between atoms) every particle of the machine works together at the same time and the result is only achieved because the dynamic of the system has it’s least energy (least amount of strings) in that state.

It’s true that today’s computers are very efficient on working on a wide range of problems (thanks to Turing proving the classes of problems his tape could solve) but there are some that it can’t, given that we only have a few billion years yet of universe to spare. Such problems could be solved if there was a holographic machine.

UPDATE:

More or less what I said was practically applied here. Thanks André for the link, this video is great!

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In September, Sunny Bains wrote Why Nano still macro? and since then I’m thinking about it once in a while.

Recently, a study in the University of California showed how to create a demodulator using nanotubes. So far there were advances in memory containers such as this and that and also batteries but all of them, as Sunny remembers, trying to build small structures following the design of big things.

Quantum computation nowadays have exactly the same problem, quantum effects in a classic assembly, big, clumsy and very expensive. If it was required a quantum effect (the transistor) to make classical computational cheap and available what will be required to make quantum computers cheap? A SuperString effect? Something messing around with the Calabi–Yau shape of the 6 additional dimensions?

Anyway, back to nanotech, building a nano-battery is cool but using ATPs as the primary source for energy would be much cooler! Using the available nano-gears and nanotubes to make a machine is also cool but creating a single 2,3 Turing machine (recently proven to be universal) would be way better!

Once you have the extremely simple processor like that, a nano-modem, some storage and ATP as food you can do whatever you want for how long you like inside any living being on Earth. Add a few gears to make a propeller and you’re mobile!

Of course it’s not that simple, but most of the time to state that something is viable means exactly the same as to say that it’s classic as in boring and clumsy and expensive and brute force… well, you got the idea…

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