What We Cannot Know. Marcus du Sautoy

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СКАЧАТЬ produced species with eyes regardless of what is going on around them. Lots of other examples illustrate how some features, if they are advantageous, seem to rise to the top of the evolutionary swamp. This is illustrated every time you see the same feature appearing more than once in different parts of the animal kingdom. Echolocation, for example, is used by dolphins and bats, but they evolved this trait independently at very different points on the evolutionary tree.

      But it isn’t clear how far these outcomes are guaranteed by the model. If there is life on another planet, will it look anything like the life that has evolved here on Earth? This is one of the big open questions in evolutionary biology. As difficult as it may be to answer, I don’t believe it qualifies as something we can never know. It may remain something we will never know, but there is nothing by its nature that makes it unanswerable.

       WHERE DID WE COME FROM?

      Are there other great unsolved questions of evolutionary biology that might be contenders for things we can never know? For example, why, 542 million years ago, at the beginning of the Cambrian period, was there an explosion of diversity of life on Earth? Before this moment life consisted of single cells that collected into colonies. But over the next 25 million years, a relatively short period on the scale of evolution, there is a rapid diversification of multicellular life that ends up resembling the diversity that we see today. An explanation for this exceptionally fast pace of evolution is still missing. This is in part due to lack of data from that period. Can we ever recover that data, or could this always remain a mystery?

      Chaos theory is usually a limiting factor in what we can know about the future. But it can also imply limits on what we can know about the past. We see the results, but deducing the cause means running the equations backwards. Without complete data the same principle applies backwards as forwards. We might find ourselves at two very divergent starting points which can explain very similar outcomes. But we’ll never know which of those origins was ours.

      One of the big mysteries in evolutionary biology is how life got going in the first place. The game of life may favour runs of 6s on the roll of the evolutionary dice, but how did the game itself evolve? Estimates have been made for the chances of everything lining up to produce molecules that replicate themselves. In some models of the origins of life it is equivalent to nature having to throw 36 dice and get them all to land on 6. For some this is proof of needing a designer to rig the game. But this is to misunderstand the huge timescale that we are working on.

      Miracles do happen … given enough time. Indeed, it would be more striking if we didn’t get these strange anomalies happening. The point is that the anamolies often stick out. They get noticed, while the less exciting rolls of the dice get ignored.

      The lottery is a perfect test bed for the occurrence of miracles in a random process. On 6 September 2009 the following six numbers were the winning numbers in the Bulgarian state lottery:

      4, 15, 23, 24, 35, 42

      Four days later the same six numbers came up again. Incredible, you might think. The government in Bulgaria certainly thought so and ordered an immediate investigation into the possibility of corruption. But what the Bulgarian government failed to take into account is that each week, across the planet, different lotteries are being run. They have been running for decades. If you do the mathematics, it would be more surprising not to see such a seemingly anomalous result.

      The same principle applies to the conditions for producing self-replicating molecules in the primeval soup that made up the Earth before life emerged. Mix together plenty of hydrogen, water, carbon dioxide and some other organic gases and subject them to lightning strikes and electromagnetic radiation and already experiments in the lab show the emergence of organic material found only in living things. No one has managed to spontaneously generate anything as extraordinary as DNA in the lab. The chances of that are very small.

      But that’s the point, because given the billion billion or so possible planets available in the universe on which to try out this experiment, together with the billion or so years to let the experiment run, it would be more striking if that outside chance of creating something like DNA didn’t happen. Keep rolling 36 dice on a billion billion different planets for a billion years and you’d probably get one roll with all 36 dice showing 6. Once you have a self-replicating molecule it has the means to propagate itself, so you only need to get lucky once to kick off evolution.

      Our problem as humans, when it comes to appreciating the chance of a miracle such as life occurring, is that we have not evolved minds able to navigate very large numbers. Probability is therefore something we have little intuition for.

       THE FRACTAL TREE OF LIFE

      But it’s not only the mathematics of probability that is at work in evolution. The evolutionary tree itself has an interesting quality that is similar to the shapes that appear in chaos theory, a quality known as fractal.

      The fractal evolutionary tree.

      The evolutionary tree is a picture of the evolution of life on Earth. Making your way through the tree corresponds to a movement through time. Each time the tree branches, this represents the evolution of a new species. If a branch terminates, this means the extinction of that species. The nature of the tree is such that the overall shape seems to be repeated on smaller and smaller scales. This is the characteristic feature of a shape mathematicians call a fractal. If you zoom in on a small part of the tree it looks remarkably like the large-scale structure of the tree. This self-similarity means that it is very difficult to tell at what scale we are looking at the tree. This is the classic characteristic of a fractal.

      Fractals are generally the geometric signature of a chaotic system, so it is suggestive of chaotic dynamics at work in evolution: the small changes in the genetic code that can result in huge changes in the outcome of evolution. This model isn’t necessarily a challenge to the idea of convergence, as there can still be points in chaotic systems towards which the model tends to evolve. Such points are called attractors. But it certainly questions whether if you reran evolution it would look anything like what we’ve got on Earth today. The evolutionary biologist Stephen Jay Gould has contended that if you were to rerun the tape of life that you would get very different results. This is what you would expect from a chaotic system. Just as with the weather, very small changes in the initial conditions can result in a dramatically different outcome.

      Gould also introduced the idea of punctuated equilibria, which captures the fact that species seem to remain stable for long periods and then undergo what appears to be quite rapid evolutionary change. This has also been shown to be a feature of chaotic systems. The implications of chaos at work in evolution are that many of the questions of evolutionary biology could well fall under the umbrella of things we cannot know because of their connections to the mathematics of chaos.

      For example, will we ever know whether humans were destined to evolve from the current model of evolution? An analysis of DNA in different animals has given us exceptional insights into the way animals have evolved in the past. The fossil record, although incomplete in places, has also given us a way to know our origins. But given the time scales involved in evolution it is impossible to experiment and rerun the tape of life evolving on Earth and see if something different could have happened. As soon as we find life on other planets (if we do), this will give us new sample sets to analyse. But until then all is not lost. Just as the MET office doesn’t have to run real weather to make predictions, computer models can illustrate different possible outcomes of the mechanism of evolution, speeding up time. But the model will only be as good as the hypotheses we have made on the model. СКАЧАТЬ