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).


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?


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.

Posted in Science & Nature

Mitochondrial Eve

We were all born from our parents. Our parents were all born from our grandparents. Everyone has a family tree and a root. If so, is it possible to find the beginning of mankind – our true “root”?

Our cells have an organelle (a part of the cell) called mitochondria. Mitochondria act as the cell’s engine and allow the cell to generate energy through respiration. An interesting fact about them is that they are not originally “ours”. About 1.5 billion years ago, there was an event where a prokaryote (cells without a nucleus, like a bacteria) invaded (or was eaten by) a eukaryote (cells with nuclei, like our cells). The prokaryote and the cell began a symbiosis and the prokaryote became a part of the cell.

Due to the external origin of mitochondria, they have a different genome to us. This is called mitochondrial DNA, shortened to mtDNA, which allows mitochondria to divide and synthesise proteins without the help of the host cell. It used to be a completely independent organism, but it has lost some of its functions to the cell.

mtDNA is inherited in a different way to normal DNA. Normally we receive half of our mother’s and half of our father’s genes, but we only inherit our mother’s mtDNA. This is because sperm keeps mitochondria in the tail which is lost during fertilisation, meaning our father’s mitochondria cannot be inherited. The only way to gain mitochondria is from those in the cytoplasm (the material that fills cells) of our mother’s egg. This is known as maternal inheritance.

Using this information, scientists compared a large sample of people’s mtDNA to turn back the clock. Knowing that a child and its mother share the same mtDNA and the mother and grandmother share the same mtDNA, we can analyse mtDNA to find the origin of mankind, or our first common female ancestor – also called Mitochondrial Eve.

Mitochondrial Eve is estimated to have lived 200,000 years ago in Africa, thus she is also known as African Eve. Her mtDNA is an ancient heirloom passed along generation after generation to us, as evidence of evolution. Every living person on the face of the Earth is a descendant of her. So in some ways, it could be said that we truly are one big family.