Friday, 2 December 2011

The Deterministic Universe

“There is a theory which states that if ever for any reason anyone discovers what exactly the Universe is for and why it is here it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another that states that this has already happened.”
Douglas Adams
The creation of the universe is a mysterious thing (from our viewpoint within its boundaries at least). We can theorize and think ourselves closer and closer to the beginning of time and come up with theories for that beginning that correlate with observations done today. The beginning itself though, and how something could come out of nothing (if it did), could very well be impossible to grasp.

Let us, for discussions sake, create a universe in a state at the start of its time. We will also assume that this state could be exactly described, and that if we knew every underlying parameter we could from it derive the next moment in time. This would mean that the universe was deterministic.

In a deterministic universe we could, assuming that we knew all the input parameters (not worrying about computational limitations) exactly calculate another state that is further along in time. A complication would probably be that if we tried to predict a future state, that state would look different because of us being part of it and thus changing it. Since this is a thought experiment, we will just assume that an observer is able to see the state from the outside without affecting the universe. If this was true then, in a deterministic universe, any passage of time would be a surjective function, where every input state maps to exactly one outcome.

The above version of a universe would not fit very well into the more popular theories of today. In fact everything points to uncertainty being a core principle of the universe. This could very well be true, although it could also be true that the randomness we see is based on some pattern that would only be obvious if we extended our viewpoint to outside the current realm. If there was no way for us to see that pattern, to us the universe would always be uncertain even if the rules controlling it were deterministic.

So let us imagine that the universe has these properties of being entirely predictable from a given initial state. Would that mean that if we started a new universe, the same events would happen and a version of me would end up writing this article again? Well, if we go one step back there is no state before the creation (once again, as far as we know). This could mean that even though the universe would behave the same way from a certain state, it could start from different states (and laws) and such even the deterministic universe is not deterministic if we do not have an initial state.

Time to sum this up. If the universe is deterministic it means that if we have the configuration for a universe at a certain time, all that follows can be inferred from it. If it is not deterministic, then the exact same state could yield something different the second time around. Whichever one it is, from where we stand, it will probably always be unpredictable. Just like the amount of time between these articles some things will always be shrouded in uncertainty.

Sunday, 7 August 2011

Evolutionary Noise

“Most species do their own evolving, making it up as they go along, which is the way Nature intended. And this is all very natural and organic and in tune with mysterious cycles of the cosmos, which believes that there’s nothing like millions of years of really frustrating trial and error to give a species moral fiber and, in some cases, backbone.”
Terry Pratchett
It is time for a thought experiment. Imagine a world where all possible variations of life exist already. In that world we have not yet created any obstacles or limitations. Life just exists and every part of it gets exactly what it needs to survive. This would result in a world where no part of life is more favoured than any other, and all combinations are as likely to survive. We would have what can be compared to a white noise, where every part of the life spectrum exists and is equally strong.

Noise will normally get shaped by different environmental properties. When it bounces somewhere or passes through something, certain frequencies are weakened or die out. The noise is filtered into something. Taking the idea of life as a noise a bit further, we can add filters to our constructed world as well. We can add constraints and obstacles that weaken or kill certain parts of life, thus forming it into a non-uniform shape.

Of course, real-world limitations are not as simple as having one filter shaping all life. For one, the filters will be changing between different geographical locations. There is also the fact that we do not have a static world, so the filters in each location will be changing constantly. An example of a short-term filter transition is the difference between night and day, while a long-term example could be continents drifting apart. Now if, in our sound analogy with an ever-lasting white noise, we would keep changing the filters for the sound, at some point all the frequencies would have been reduced to zero in strength. The same thing would of course happen with life, unless we introduce mutations.

Let us first change our one-dimensional life noise into a two-dimensional landscape, which has hills and valleys corresponding to where life is strong or weak (or even non-existing). There would be areas in this landscape void of life because of environmental filters. If a filter for such a region is lifted, the effect would still be visible afterwards. Now, because of possible mutations in life around the region, life from the outside can sporadically take root in the void area. When we remove a filter, life could slowly grow into that part of the landscape and cover it. There is of course the possibility of a big mutation skipping over a void region. Larger moves have a potential to end up in parts of the landscape where life did not exist yet, but can exist, but if these areas are very small it will be unlikely. This means that we will probably find islands of possible life that never get covered because there is no easy path through the filtered regions.

In the evolutionary approach, we would not have all combinations of life to start with. Instead we would start off with a very narrow peak in the landscape. Because there are already filters in place when life is started, it means that certain parts will be filtered already before anything exists there. Life will only be able to expand using certain open paths (or very unlikely jumps), and those paths can close or open again depending on the changing filters of the world. A region can be open for a while, letting life spread through it to another region, just to close and leave an island of life behind.

One can add more and more dimensions and add interaction between different parts of life (e.g. predator-prey relationships), to make this model more and more complex, but the simple case is enough to give us another viewpoint on evolution. What is the conclusion of all this? Not much. Sometimes looking at things from other angles can give you helpful insights. In other cases it does not, but at least gives you something to occupy your brain with for a while. Just as with life, human thoughts will keep spreading, sometimes mutating into blog posts like this one!