What led to the first computer? │ The History of Mathematics with Luc de Brabandère
What happened when George Boole tried to merge mathematics and logic?
He discovered the binary system of zeros and ones a whole century before the first computer.
Join Luc de Brabandère, in the latest episode of his remarkable series The History of Maths, to discover more about the amazing equations that led to the birth of the binary system.
Find out more:
George Boole invented the world of zeros and ones, a century before the first computer.
Find out why and how. And subscribe to our series ‘The History of Maths’ on the YouTube channel ‘What makes it tick?’
We have seen in video number 1 how Arab mathematicians started this field of algebra. And we have seen in video 5 the birth of logic. You remember A is B, B is C, hence A is C? Many people have tried to merge the two disciplines. Probably the last one was George Boole.
Here is how he did it. Let's take a set X, and as a definition it's the set of all Xs. Then you take another set. Let's call it Y, the set of all Ys. Let's also define if we overlap, if we put the two sets like this, we can define the hatched area in this drawing as the sum X+Y. On this drawing now the hatched area can be defined as the product XY.
If you accept those assumptions, you can do some interesting things. For example, a proposition coming from the logic: some X are Y, can be translated into a mathematical formula: XY≠0. This gives you a flavour of how George Boole tried to merge mathematics and logic.
He also came up with very strange equations. For example, one of his formulas was X^2=X. This formula is amazing. Why? Because you only have 2 solutions, 0 and 1. This can be considered as the birth of the binary system.
Today, we all use the decimal system, and the computer counts. So, it's interesting to see how you move from one to the other. It's not too difficult. Let's take for example 43. 43 is the sum of 32 + 8 + 2 + 1. So, it's 4 times ‘the power of 2’. Then if you cut the 43 into pieces like using only power of 2 you have here, you can see the binary translation of 43.
Of course, it goes backwards as well.
So, it's interesting to realise that a theory of computer started a century before the computer itself.
Join us next time to find out how the system to measure data was devised.
Subscribe now to follow our series on ‘The History of Maths’ on the YouTube channel ‘What makes it tick?’
