Posted in History & Literature

Stigler’s Law

In 1980, statistician Stephen Stigler suggested that in the history of science, no scientific discovery is really ever named after its original discoverer. This is because eponymous laws and discoveries tend to be named after the person that made it widely known.

Take the example of the famous Pythagorean theorem, which was known to Babylonians before Pythagoras was even born. Halley’s comet had been documented by astronomers since 240 BC. Fibonacci numbers were well-known to Indian mathematicians since 200 BC – 1400 years before being described by Fibonacci.

You could make the argument that these discoveries could not be traced to the original discoverer as it was too long ago and the discoverer’s name was never documented. This is certainly one reason for Stigler’s law being true. Usually, scientific discoveries tend to be popularised and named after the discoverer has already died, meaning that there is a chance they could be forgotten already.

There are plenty of examples where the original discoverer is known, thanks to historians of science, but it is too late to reverse the eponym as the name has firmly rooted itself into people’s vocabulary.

Take Alzheimer’s disease, which was discovered by Beljahow in 1887, but named after Alois Alzheimer in 1901. The bacteria Salmonella was identified by Theobald Smith in 1885, but as he was a junior inspector, his boss Daniel E. Salmon took the credit instead.

It is also worth noting that throughout history, there have been many cases of discoveries being made simultaneously by independent scientists.

Sometimes, the scientists credit each other and share the fame, such as Charles Darwin who decided to co-present his theory of natural selection with Alfred Russel Wallace, another scientist who came to similar conclusions at the same time.

Other times, scientists may fight aggressively to assert their credit, such as Isaac Newton and Gottfried Leibniz, who both discovered calculus around a similar time, but fought to claim that they were first.

An important lesson to learn here is that as much as we love stories where a brilliant individual changed the course of history, most advancements in human history happen thanks to collaboration and inherited knowledge over time. Things rarely happen in a vacuum and we all rely on each other’s experiences and knowledge, building on our predecessors to achieve greatness.

Ironically, Stigler’s law follows its own law, as Stigler identified sociologist Robert K. Merton as the original discoverer of this law.

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Posted in Science & Nature

The Dangerous Number

Everyone has learned of the Pythagorean theorem in maths class:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).

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A lesser known fact is that Pythagoras, the Greek mathematician who came up with the theorem, had a school where numbers were essentially worshipped. The school of Pythagoras were obsessed with whole numbers and their ratios, believing the universe was built around whole numbers. Their motto was “All is number”.

In 520BC, a mathematician named Hippasus was murdered by members of the school of Pythagoras, by being thrown off the side of a ship. Why did a group of scholars go as far as killing a fellow mathematician? The reason lies in a special number.

Hippasus raised an interesting question regarding the Pythagorean theorem. Imagine a square where each side is 1 unit long. What is the length of the diagonal?

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Using the theorem a² + b² = c²: 1² + 1² = 2 = c². Ergo, c = √2. This does not appear to be so controversial. The Pythagoreans would reason that it was simply a ratio between two whole numbers, much like ½ or ¾.

But as they tried to quantify what this ratio was, a horrifying truth emerged – no ratio between whole numbers could produce √2. It is what we now call an irrational number.

This was heresy – how can such a number exist in a universe built around whole numbers? The Pythagoreans would not allow this. Hippasus tried to argue that √2 was just as real a number as any other, but his attempts to propagate the knowledge of irrational numbers was quashed through murder.

Knowledge is power, but knowledge can also lead to tragedy.

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Posted in Science & Nature

Euclidean Geometry

In 300BC, a Greek mathematician called Euclid wrote a series of texts called Elements. The Elements was a textbook that outlined many principles of mathematics (especially geometry) and it would become one of the most influential works in the history of mathematics. It is composed of a series of axioms (the axiomatic approach) from which many deductions and theorems can be made. Although many of these axioms sound extremely simple and like common sense, the implications are staggering.

The following is Euclid’s Five Postulates of Plane Geometry:

  1. Two points determine a line. 
  2. Any line segment can be extended in a straight line as far as desired, in either direction. 
  3. Given any length and any point, a circle can be drawn having the length as radius and that point as centre. 
  4. All right angles are congruent (can be superimposed). 
  5. Parallel postulate: If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side, if extended far enough. 

Using these postulates, mathematicians are able to deduce more advanced theories. For example, the Elements also describes the famous Pythagorean theorem, which states that “in any right triangle, the area of the square of the hypotenuse (the diagonal) is equal to the sum of the areas of the squares of the other two sides” (a² + b² = c²).

Thanks to Euclid’s works, we are now able to accurately model and measure the three-dimensional space around us. Not only did Euclid set the foundations for mathematics, his works were also instrumental in the development of logic and modern science.

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