“Gaussian distributions give the standard model for share prices and underlie the Black-Scholes price of contracts based on them,” says Johnson. This means that the central limit theorem can be applied, giving the familiar 3% ‘margin of error’ attached to polls of 1,000 voters.”īut not every scenario is so straightforward. “For example, opinion polls average individual preferences and, if the country is sampled correctly, these preferences are independent of each other. “The central limit theorem justifies the statistical models used in many disciplines,” says Johnson. As a result, whenever observed data is formed as this type of average of random effects, a histogram of many data points will be close in shape to the Gaussian curve.” And the bell-shaped curve, it seems, crops up all over the place.
“One answer comes from the central limit theorem, which tells us that averages of many random terms have a roughly Gaussian distribution, provided the terms don’t depend too much on one another and aren’t too large (don’t have heavy tails). “The bell-shaped Gaussian (normal) curve appears ubiquitously in scientific data, and it is natural to wonder why,” says Oliver Johnson, reader in information theory at the University of Bristol. “The black hole is not consuming space-time, however, it is consuming mass-energy and the increase in the density of mass-energy leads to a change in the space-time curvature.” Why does a probability distribution eventually make the shape of a predictable Gaussian probability function, rather than a random scattering shape? asks Yusef Ahmad “As this happens, the mass and rotation rate of the black hole will tend to go up and the space-time curvature outside the black hole changes correspondingly,” he adds. This affects the curvature of space-time. Most astrophysical black holes are not isolated though and matter in their vicinity will fall into them over time,” Gair revealed. “Black holes can exist in isolation, in which case there is no change in anything over time the space-time curvature remains unchanged. “Space-time is strongly warped in their vicinity but saying that they warp it is a tautology – a black hole is, by definition, a region where space-time is so strongly curved that light cannot escape.”īut this is not, typically, a static situation. Again, a black hole is a property of space-time – they do not consume space-time. “Black holes are parts of space-time that have such great curvature that light can no longer escape them. “We talk in terms of curvature rather than density, but where mass-energy is more densely concentrated in space it will create greater curvature of space-time and hence stronger gravity.” And black holes, it seems, are in a league of their own. “Where the curvature of space-time is greater, gravity is stronger,” Gair explains. Other objects moving in the space-time follow these warps, which makes them appear to move on curved paths.”īut not every lump of stuff causes the same curvature. “Matter and energy cause space-time to curve (or warp) and this is what we call gravity.
“In Einstein’s theory of general relativity, gravity is warping of space-time,” points out Dr Jonathan Gair from the University of Cambridge. Gravity can warp space-time but can it make it more dense? (As a magnetic field is more dense round the pole of a magnet.) Also, do black holes consume space-time or merely warp it?” asks Alastair McKeown While other approaches, such as the use of polymers called “dye transfer inhibitors” in laundry detergents can also be used to sweep up stray dyes, colour catchers do boast a strangely appealing feature: at the end of the wash, the captured dyes can clearly be seen on the sheet. “The charge attracts it first and then you have a chemical reaction, so basically the dye cannot actually come off the sheet, it is stuck on to the sheet then so it can’t roam in the wash to transfer or to cross stain into your garments,” says McNamee.Īs a result, you can sling crimson jumpers in with snowy shirts without encountering a pink problem.
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