100 Essential Things You Didn't Know You Didn't Know by John D. Barrow Read Free Book Online Page B

most likely use a technique that has been found effective in all other simulations of complex systems: the use of error-correcting codes to put things back on track.
    Take our genetic code, for example. If it were left to its own devices we would not last very long. Errors would accumulate and death and mutation would quickly ensue. We are protected from this by the existence of a mechanism for error correction that identifies and corrects mistakes in genetic coding. Many of our complex computer systems possess the same type of internal immune system to guard against error accumulation.
    If the simulators used error-correcting computer codes to guard against the fallibility of their simulations as a whole (as well as simulating them on a smaller scale in our genetic code), then every so often a correction would take place to the state or the laws governing the simulation. Mysterious changes would occur that would appear to contravene the very laws of Nature that the simulated scientists were in the habit of observing and predicting.
    So it seems enticing to conclude that, if we live in a simulated reality, we should expect to come across occasional ‘glitches’ or experimental results that we can’t repeat or even very slow drifts in the supposed constants and laws of Nature that we can’t explain.

20
    Emergence
    A politician needs the ability to foretell what is going to happen tomorrow, next week, next month, and next year. And to have the ability afterwards to explain why it didn’t happen.
    Winston Churchill
    One of the buzz words in the sciences that study complicated things is ‘emergence’. As you build up a complex situation step by step, it appears that thresholds of complexity can be reached that herald the appearance of new structures and new types of behaviour which were not present in the building blocks of that complexity. The world-wide web or the stock market or human consciousness seem to be phenomena of this sort. They exhibit collective behaviour which is more than the sum of their parts. If you reduce them to their elementary components, then the essence of the complex behaviour disappears. Such phenomena are common in physics too. A collective property of a liquid, like viscosity, which describes its resistance to flowing, emerges when a large number of molecules combine. It is real but you won’t find a little bit of viscosity on each atom of hydrogen and oxygen in your cup of tea.
    Emergence is itself a complex, and occasionally controversial, subject. Philosophers and scientists attempt to define and distinguish between different types of emergence, while a few even dispute whether it really exists. One of the problems is that the most interesting scientific examples, like consciousness or ‘life’, are not understood and so there is an unfortunate extra layer of uncertainty attached to the cases used as exemplars. Here, mathematics can help. It gives rise to many interesting emergent structures that are well defined and suggest ways in which to create whole families of new examples.
    Take finite collections of positive numbers like [1,2,3,6,7,9]. Then, no matter how large they are, they will not possess the properties that ‘emerge’ when a collection of numbers becomes infinite. As Georg Cantor first showed clearly in the nineteenth century, in finite collections of numbers possess properties not shared by any finite subset of them, no matter how large they are. Infinity is
not
just a big number. Add one to it and it stays the same; subtract infinity from it and it stays the same. The whole is not only bigger than its parts, it also possesses qualitatively different ‘emergent’ features from any of its parts.

    A Möbius strip
    Many other examples can be found in topology, where the overall structure of an object can be strikingly different from its local structure. The most familiar is the Möbius strip. We make one by taking a thin rectangular strip of paper and gluing the ends