# Radiometric dating controversy

However, this got the least amount of attention from the naysayers, as Tyson mentions Giordano Bruno, a Catholic who dared to challenge the church’s geocentric theory of the cosmos and proposed that the earth actually revolved around the sun.

Bruno was jailed, charged with heresy and eventually burned at the stake.

The station later claimed this was a complete accident, but many remain skeptical.

Cleverest student : That doesn’t work either, because if then is so your third step also involves dividing by zero which isn’t allowed! Hence, That is, as x gets arbitrarily close to (but remains positive), stays at .

The size of the sample then required, however, was ~500cm, which would clearly have resulted in an unacceptable amount of damage, and it was not until the development in the 1970s of small gas-counters and accelerator-mass-spectrometry techniques (AMS), requiring samples of only a few square centimetres, that radiocarbon dating of the shroud became a real possibility. The shroud was separated from the backing cloth along its bottom left-hand edge and a strip (~10 mm x 70 mm) was cut from just above the place where a sample was previously removed in 1973 for examination.

Roman poet Lucretius, intellectual heir to the Greek atomists, believed its formation must have been relatively recent, given that there were no records going back beyond the Trojan War.

So which of these two definitions (if either of them) is right? But when x=0 and y=0, the formula doesn’t have an obvious meaning.

The value of is going to depend on our preferred choice of definition for what we mean by that statement, and our intuition about what means for positive values is not enough to conclude what it means for zero values.

One of the most anticipated shows of 2014 was Fox’s “Cosmos: A Spacetime Odyssey,” hosted by notable astrophysicist Neil de Grasse Tyson and produced by Seth Mc Farlane and Ann Druyan, the widow of Carl Sagan, the host of the original “Cosmos” series.

In that case, when x is one, the y is repeated just one time, so we get = . Interestingly, using this definition, we would have = = = Hence, we would find that rather than .

However, this definition extends quite naturally from the positive integers to the non-negative integers, so that when x is zero, y is repeated zero times, giving = which holds for any y. Granted, this definition we’ve just used feels rather unnatural, but it does agree with the common sense notion of what means for all positive real numbers x and y, and it does preserve continuity of the function as we approach x=0 and y=0 along a certain line.

But if this is the case, then how can mathematicians claim that ? Some very important formulas become less elegant to write down if we instead use or if we say that is undefined.

1 - Department of Geosciences, 2 - Department of Physics, University of Arizona, Tucson, Arizona 85721, USA 3 - Research Laboratory for Archaeology and History of Art, University of Oxford, Oxford, OX1 3QJ, UK 4 - Institut für Mittelenergiephysik, ETH-Hönggerberg, CH-8093 Zürich, Switzerland 5 - Lamont-Doherty Geological Observatory, Columbia University, Palisades, New York 10964, USA 6 - Research Laboratory, British Museum, London WC1B 3DG, UK Very small samples from the Shroud of Turin have been dated by accelerator mass spectrometry in laboratories at Arizona, Oxford and Zurich.