Tag Archives: mathematics

Mathematical Proof that Aliens Do Not Exist (Sorry to Burst your Bubble)

Every now and then random people in the world go bat-guana crazy about something, whether it’s about a Big Foot sighting, or believing that a trust-fund billionaire troll-bot will govern for anyone other than other billionaires, or evidence of extraterrestrials. This latter went big in 2016, moving from cow-probing theory-spinning abductees to legitimate astronomers and physicists who tried really, really hard not to sound like they were talking about E.T.

However they tried to dress it up, it was ridiculous. A star, KIC 8462852 (now known as Tabby’s Star), was showing behaviour they didn’t recognise, and the cry of “ALIENS” reverberated around the internet. Sound like a familiar argument?

In fact, the probability of contact with extraterrestrial intelligence is so tiny that there is literally no evidence compelling enough to refute the maths. I explain this here.

Source: NASA

The Irrelevancy of Logical Fallacies in Mathematics

Scientific American is focusing on Einstein in September, it being 100 years since he came up with the general theory of relativity. It briefly describes how he came up with the theory, which makes it a lot easier to understand and is interesting to me because it contains a logical fallacy.

Einstein claimed that the happiest thought in his life was: “If a person falls freely, he will not feel his own weight.” To be honest, this sounds like his personal troubles were causing depressive episodes. However, he noted that if a man was in an enclosed chamber in free fall, he would feel weightless. He would not be able to tell if he was in free fall or if he was floating in zero gravity. Likewise, if the chamber was in zero gravity and a constant force was pulling the chamber up at an accelerated rate he would feel his feet pressed to the floor, and would have no way of telling if he were in a stationary chamber under gravity or was being accelerated in zero gravity.

Einstein dubbed this “the equivalence principle.” The local effects of gravity and of acceleration are equivalent. Therefore, they must be manifestations of the same phenomenon, some cosmic field that accounts for both acceleration and gravity.

This seems to be an invalid argument. It takes the form:

If A, then C.
If B, then C.
Therefore, A = B.

Just because two things have the same effect doesn’t mean they are the same thing. For example, saying “if an elephant sat on me I would die, and if a rhinoceros sat on me I would die, therefore an elephant is a rhinoceros” is clearly incorrect.

Of course, this insight of Einstein’s allowed a theory that is very good at explaining the universe that we observe. That could be because it got translated into mathematics, and in mathematical logic it is actually true. If A=C and B=C, then A=B must be true.

This might indicate something very profound about mathematics and its relation to the universe, but I’m not sure what.