Keith Devlin, head of maths at Standford University had some very interesting ideas on the theories of Ancient Greeks. He said theorists such as Aristotle, 300/400 BC, Develop crude and simplistic rules of logic. Their theories on logic are not the logic people use today when making complex deductions. Devlin believes logic is important not because you use the rules to do reasoning, but thinking about those rules makes you reflect on the rules you do use. Most reasoning today is so complex; you have to use a holistic approach using all kinds of methods. The Greeks didn’t really value logic in itself; they were interested in politics and democracy and thought it was all about convincing people.
Devlin had a very interesting idea of probability. The year following 9/11 found that death rates increased in America. I’ve never took the time to dwell on this and his ideas have made me think more about it. Less people wanted to fly after 9/11 because they were too afraid of the same incident happening again so death rates increased because more people were deciding to drive and travel by car. This meant there was more traffic on the roads and so more traffic accidents were happening. These accidents killed more people in America the following year than were killed in 9/11.
Devlin said after 9/11 it was actually the safest time to fly as there were fewer planes in the air and crews were more cautious and had more time. People were frightened by the odds. The odds of being killed in a terrorist attack on a plane are zero. If you’re worried about dying on a plane, don’t get a taxi to the airport because that’s where the danger lies. Once you’re on a plane and it takes off, the chances of there being a terrorist on that plane are essentially zero. This completely makes sense and I have never actually considered it before. If you think about it more carefully you are able to realise, terrorists are after a new story, airplane crashes are dramatic and they make news and have an impact but there’s only been one 9/11 incident in the entire history of America yet people are dying from various other things everyday for example, a car accident, but to the majority they don’t see that as a likely to occur to them and continue to drive their cars everyday.
Devlin also had interesting views on scientific method. It is a Universal myth that science is all about finding the truth. Science cannot possibly do that. Science is about getting the best rational explanation grounded in the evidence we have and it changes over time. If you go back to Newton’s time, Newton has the idea that gravity is an unseen force that keeps the planetary system together, now called the Newtonian theory of gravity, and it still works today. Einstein overturns that in a sense as he says that there was some things wrong with it and we have a new theory. When we send space equipment into the outer reaches of the solar system, we know that Newton’s theory is not accurate enough; we have to make allowances for Einstein’s corrections. So our knowledge changes and we now have masses of evidence about human illnesses and the human body from human research. Whereas going back to the 50’s we didn’t know as much as we know now. Theories have developed and they’re better theories than before but there is no such thing as the truth. Today’s truth is tomorrow’s approximation. Science is about making better approximations to this mythical thing called the truth. Any scientific statement is capable of being tested and therefore could be overturned, the longer something which could be overturned isn’t, the more confident we feel about these statements. Science doesn’t go by the majority; it only takes one person to prove your explanation wrong in order for it to be abolished. That’s why we have such faith in science.
He also discussed probably and justice. When a crime is committed and there’s evidence containing DNA, the FBI immediately looks through the database to find a match. Your profile data on an FBI database if you have one is a sequence of 13 numbers. The question is to prove identity, how likely is it that 2 people randomly chosen from the population will have those same 13 numbers? It is pretty likely. The classic case that shows you often do get accidental matches is that you only need 23 people in a room to have the better than 50% chance that two of them share the same birthday. The fact is when you have populations of any size, and 23 is large for this to happen, random coincidences occur. So with DNA identification, the issue comes down to what s the likelihood of two people chosen at random, share the same 13 numbers. It’s quite high and Devlin says that proving innocence is like a scientific method, you only have to show the DNA doesn’t match and the person is innocent because there’s no evidence and the DNA has no value. If the DNA does match then there’s the issue, is it matched because you were there at the crime scene and you committed the crime or did the DNA get there through some other means or is it just a random occurrence? The courts need to have a calculation for how likely is it that the DNA match is just an accident so that’s a statistical issue and calculations have to be made.
The Invention of Google at Standford University was a piece of mathematics. One of the powers of mathematics is that you don’t need a huge laboratory to do mathematics, you need a paper and pencil and you could come up with an idea anywhere and within a year or so, that idea could change the entire world. I myself have never enjoyed mathematics and often, as many pupils at high school, found myself saying I didn’t see any point to it because there’s not much mathematics can get you. However, I began to learn that we do actually use the subject every day and mathematics is the key to a lot of great inventions. It is fascinating to think, as Devlin said, that one day you could be in the bath, jogging through the hills, having a bike ride, or on the beach abroad and you think of a brilliant new idea, for example, a new web creation, that makes you a billionaire the following year. It makes a fantastic dream!
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