Patterns

Patterns: Why do they appear in some random things? Out of some easy rules there emerge somehow complex structure. Bird swarms or fish swarms, flowers, aliasing in pictures, clouds, crystals, snowflakes and much more. This list is only here ending because I know too little. I’m sure in every natural or engineering science there are these effects. I know some more in mathematics. Aliasing is one example in IT. And the mathematics is the correct keyword for that. These easy rules all can be formulated with mathematics. Most of the time with a grammar (Formal grammar, L-system) or a state-machine(finite-state machine) which is then recorded over some time. And the thing that is created is then a big pattern. But what is a big pattern? It is also something mathematical that we recognize. Maybe a symmetry, maybe a number, maybe a shape. Something that is rather simple for its size. But I think this is not so special at all. Isn’t it clear that when you do something structured and not random you create a structure. I think it is way more difficult that no such pattern emerges. In information security there is the concept of pseudo-random numbers. These are numbers, that are generated by some deterministic algorithm. So an algorithm without randomness. But not any numbers. These numbers should behave random. So there should not appear any pattern. And to show, that the algorithm produces good pseudo-random numbers we need to prove that there is no ‘efficient’(P, Turing-machine, Probabilistic Turing-machine) algorithm that can predict the number or parts of the number. And do you think this is easy or hard to achieve? It is hard. There are only a few pseudo-rand number generators (PRNG) for which no one found an algorithm which can predict some bits of it. What does this mean? It is pretty hard to come with some simple rules that do something which has no pattern. If you know enough about PRNGs (Link 1, Link 2) you can even argue that this is not possible. (If you prove that this isn’t possible or that it is possible. Please come to me. The answer to that question is equivalent to the question (P=NP?). And when you solve this you get a million US$ (Millennium Goals). 😉 ) This is just how things are. Let’s register that small rules most often result in bigger patterns. And these bigger patterns have itself some attributes like a swarm that doesn’t get attacked by it’s individuals enemies. A flower having spacial efficient ordering of its seeds. Crystals that are very hard and so on. But for me interesting is that I think even more complex phenomenons appear because of some simple rule. Like our society. It is not obvious that this is the case but it is also not so difficult to imagine that. Rules like Tit for Tat and effects like shame and empathy enable a quite complex community. What I want to say is that from patterns that emerge from small rules can emerge again even bigger patterns. Because the big patterns like the spiking behavior of a neuron is again mathematical pretty simple. Maybe you don’t think this is so interesting but the proposal I am aiming for is hopefully more exciting. Research has shown, that only the wiring of the spinal cord of a salamander enables complex movement(Video[download], EPFL-Article, TED-Talk). They have rebuilt it in a robot without encoding any movement explicitly and the robot had the same movements like the salamander. Many suggest that this is also the case in human movement, even though we make conscious decisions to walk or not, and where to put the foot. (I know that the conscious decision are not in the spinal cord but it is still remarkable that we can trigger the movement, alter it. But still mainly use the movement patterns encoded in the spinal cord.) And this is the case for most of our conscious decisions. They are encoded in well known and understood networks in the nervous system(Visual Cortex). The next step that comes very naturally from here is, that consciousness itself emerges from the simple rules in neurons and in neuronal networks. For me it is very likely that such a big compound of cells, that all have an impact on their surrounding form an interesting pattern. That this pattern is the “me” is of course not clear but also not that abstract.

Let’s appreciate that the world is such mathematical and consisting of simple rules, this is the reason for nearly if not all the beautiful behavior of the world. What we regard for beautiful is nearly always patterns we see. This drive for patterns has led us to find more and more patterns. And we sense beauty most easily with our ears and our eyes. This is also the reason why mathematics isn’t universally seen as beautiful, because you have to understand it. You can’t sense it. But maybe beauty is another blog for itself. (Ugliest Music Video)

Summary: Patterns are everywhere, All patterns are mathematical, They build bigger patterns which is beautiful but not surprising, it is hard to find an easy mathematical description without bigger patterns emerging, the bigger patterns can build even bigger patterns, maybe consciousness emerges from neuronal behavior; beauty are mostly patterns.

Remarks: When I say easy mathematical rules I mean not that you will understand it fast. I mean, when you understand it, you see that this wasn’t such a difficult thing.