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

two diameters of the convoys of area A/2 that don’t overlap in the field of view is bigger by a factor of √2, and so the divided convoy is 41% more likely to be detected by the attacking submarine than is the single one.

18
    VAT in Eternity
    In this world nothing is certain but death and taxes.
    Benjamin Franklin
    If you live in the United Kingdom you will know that the sales tax added on to many purchases is called ‘Value Added Tax’ or VAT. In continental Europe it is often called IVA. In the UK it amounts to an additional 17.5% on the price of a range of goods and services and is the government’s biggest source of tax revenue. If we suppose that the 17.5% rate of VAT was devised to allow it to be easily calculated by mental arithmetic what do you expect the next increase in the rate of VAT to be? And what will the VAT rate be in the infinite future?
    The current value of the VAT rate sounds arcane – why pick 17.5%? But if you have to prepare quarterly VAT accounts for a small business you ought soon to recognise the niceness of this funny number. It allows for very simple mental calculation because 17.5% = 10% + 5% + 2.5%, so you know what 10% is immediately (just shift the decimal point one place to the left), then just halve the 10%, and then halve the 5% that remains and add the three numbers together. Hence, for example, the VAT on an £80 purchase is just £8 + £4 + £2 = £14.
    If the same convenient ‘halving’ structure for mental arithmetic is maintained, then the next VAT increase will be by an amount equal to half of 2.5%, or 1.25%, giving a new total of 18.75% and the new VAT on £80 would be £8 + £4 + £2 + £1 = £15.
    We would then have a tax rate that looked like 10% + 5% + 2.5% + 1.25%. To the mathematician this looks like the beginnings of a never-ending series in which the next term in the sum is always half of its predecessor. The current VAT rate is just
    10% × (1 + ½ + ¼)
    If we continue this series forever we can predict that the VAT rate in the infinite future will be equal to
    10% × (1 + ½ + ¼ + ⅛ +++ . . . ) = 10% × 2
    where, as we see here , the same series except for the first term is shown to sum to 1, so the sum of the infinite series in brackets is 2. The VAT rate after infinite time is therefore expected to be 20% !

19
    Living in a Simulation
    Nothing is real.
    The Beatles, ‘Strawberry Fields Forever’
    Is cosmology on a slippery slope towards science fiction? New satellite observations of the cosmic microwave background radiation, the echo of the Big Bang, have backed most physicists’ favourite theory of how the Universe developed. This may not be entirely good news.
    The favoured model contains many apparent ‘coincidences’ that allow the Universe to support complexity and life. If we were to consider the ‘multiverse’ of all possible universes, then ours is special in many ways. Modern quantum physics even provides ways in which these possible universes that make up the multiverse of all possibilities can actually exist.
    Once you take seriously the suggestion that all possible universes can (or do) exist then you also have to deal with another, rather strange consequence. In this infinite array of universes there will exist technical civilisations, far more advanced than ourselves, that have the capability to simulate universes. Instead of merely simulating their weather or the formation of galaxies, as we do, they would be able to go further and study the formation of stars and planetary systems. Then, having added the rules of biochemistry to their astronomical simulations, they would be able to watch the evolution of life and consciousness within their computer simulations (all speeded up to occur on whatever timescale was convenient for them). Just as we watch the life cycles of fruit flies, they would be able to follow the evolution of life, watch civilisations grow and communicate with each other, even watch them argue about whether there