Monday, December 14, 2009

Combinatorial explosions

I'm reading, next to "Consciousness explained", a book from one of my favourite writers Steven Pinker. This one is called "A blank slate", otherwise known as tabula rasa, where this blank slate refers to the idea as the brain being a type of blackboard that is written to by experiences, or whether certain capabilities and intricacies are preprogrammed, otherwise called innate. Pinker's writing is everything from an exploration, to various explanations, but not in the least a (strong) argument about how we should interpret this "blank slate" and how, in the search for an explanation about intelligence and consciousness. Probably it's best to see his presentation over at TED talks. But be aware that this presentation doesn't cover the topic of the book entirely and that there are many more little facts and explorations that the presentation certainly doesn't cover. Other than that, it provides a good insight into his kind of thinking and scientific approaches and validations.

The combinatorial explosion comes into effect when the number of variables increases by such an amount, that a true understanding of every state and how states influence each other becomes an impossible task. In two examples given, there's the case where the human genome was analyzed and in some reports counted as the number 30,000. The total DNA is a bit more than that, but 1.5% of this are these 30,000 genes, the rest is considered "junk DNA" (apparently and allegedly). Well, looking up the numbers on different sources, you get different numbers here as well. Some sources say 35,000, others 30,000 and Wikipedia claims 23,000. Which one is the true number, we'll never know :).

There's a kind of worm though that has roughly about 18,000 genes (or 20,000 as in other claims?). This worm has 203 neurons or so exactly, avoids certain smells and crawls around looking for food. How come such a worm with 18,000 genes is so strikingly different in behaviour and intelligence from us humans, where we have "only" 35,000 genes? Are we so much like worms?

If you consider the numbers as a linear base, then this must indeed be shocking. But genes amongst themselves interact and may then inhibit or activate other genes that create different proteins, which in turn influences the way an organism develops and grows and at which time-scale in life.

Here we go... The combinations of 18,000 genes interacting amongst themselves is already staggering, but 35,000 genes is a factor 2^17,000 larger. Whoops! That has the potential to be substantially more complex than anything we've ever seen before :). This doesn't mean that all these genes do interact, but the amount of information in this sense cannot easily be captured by just listing the numbers of genes. The actual information is contextually determined by the numbers that actually do interact together, and whether there are also combinations of 3-4-5 genes that form some kind of composition together. In those cases, the complexities go up to 3^x or 4^x even (we assumed interacting genes together before).

Now, it is interesting to find out how these genes interact and how influence these genes really have on our thinking and behaviour. We generally consider the environment a very important element in the analysis of behaviour and growing up, sometimes to such an extent that the entire evaluation is attributed to how some environment determined a person's actions and behaviour. But if we find out that general behaviour, personality twists, general motives and so on aren't necessarily determined by the environment, but hardcoded in genes. It's just our experience that allows us to exhibit this behaviour or not, then the picture severely changes. I'm starting here with my own thoughts by the way, this is not necessarily what was written in the book.

In that case, experience is more of a method to determine probabilities, elements of chance and other things that either inhibit our motives or stimulate them. In this view, our personality and things we do are genetically determined, while our dynamic interaction and behaviour choices are mostly governed by experiences from the environment. The general observations that one can draw from this is that personality twists, likes and dislikes probably come out as characteristic features of a person, but they are genetic. Whereas specific choices not to do something or go for it all the way are potentially given by variables in the environment. This sheds a totally new light on behaviour and how we perceive it in general.

Another thing that I found interesting is the way how it interlinks with computer science books about modularity and compositions of specific system parts with a particular purpose. Rather than thinking of a computer as a single thing, you can divide it into multiple elements like the CPU, the harddrive, graphics card, etc. But if you look closer, than the CPU is a large number of transistors with a number of pins plugging into the motherboard somewhere, such that it is linked with memory and buses on the motherboard to give it the power it has. The CPU is often called the central part and other parts are ancillary to that (well, you might also argue that the motherboard is the main part, because that's what everything is slotted into).

In this way, you can look at the entire computer from totally different views, each explaining very different purposes and levels of abstraction. Looking at the transistors of the CPU, there is no point in discussing why a word processor does all the things that it is told to do, the level of detail is too high to consider it. A more appropriate level is to consider the functions of the computer as a whole and then to explain how people interact with it, why a computer reacts and acts the way it does (it's been told to do that by its designers) and so on. There is also the level of how devices interact that is interesting. To handle keystrokes for example, you could consider yourself part of this system, the input provider. The keyboard is a transducer that converts a small burst of electricity into a scancode, which is read from the USB port of the computer. This scancode, a byte, is then processed by the CPU and sent to the OS and program, which determine if the scancode should be discarded or accepted. The program may then decide to attach the scancode to some array of bytes it has in memory, completing a long line of character strings. For feedback into this entire cycle, the graphics card gets a pointer into this array and repaints the screen when needed.... PHEW!

For each of these things, you can go down to the signal level even, but also further than that on the physics level of electrons. Explaining this process through electrons is going to be a long sit-in, so let's not do that here. At the highest level, it just seems to make sense. You press a key on the keyboard and that makes the character appear there on screen where the cursor is... Is that so hard to understand? :).

Similarly in the understanding of our thought processes, there surely seems to be good room for finding out how networks interact and process or store information. I don't think the sciences in neural networks can be called complete, in the sense that we know everything about them and what they do. One idea for example is that neural networks are very good at processing signals and outputting another. Basically directly responding to signals. But the way how we compose neural networks in amateuristic ways doesn't yet provide handholds for doing more things with them. Biological networks may have a lot of "failover cells" in them that are not strictly necessary to make something function. Also, the human brain consists of 100,000,000 neurons, but 60,000,000 of those are necessary for direct, muscular responses, instinct and movement (the reptilian brain). That leaves "only" 40,000,000 cells for human reasoning, visual perception, auditory perception, speech and other functions. Hmmm... that does shed a different light on things.

Basically, numbers by themselves don't give you information about actual complexity. It's about the interactions between these components, what they can do together in unison that's yielding the most power.

1 comment:

zubehör said...

Assembling objects from building blocks by means of predefined combination rules leads to combinatorial explosions. Indeed, it does not matter how many classes of building blocks or alternatives of combination rules are given, provided one of both is two or larger, because then the number of possible objects commonly increases exponentially with the number of elements and soon exceeds the realizations that can be sustained by taking together all available resources.