The Allusionist: Num8er5

The Allusionist is a podcast focusing on language, and this episode, Num8er5, is all about, well, numbers. You can listen to it in the player below, or read more information (including a link to its page at the Allusionist) underneath that.

The episode compares the development and use of numbers as expressed verbally with numeral systems for writing them down. It provides an interesting thread through aspects of history that are relevant to both language and mathematics, and touches upon number use across different societies, cultures and civilisations throughout history. Click the link below to listen to the episode on The Allusionist's website, where there is further information and links to related resources including other episodes.

The Allusionist: Num8er5

A Partition Enigma

Colin answers a question on partitioning numbers, prompted by an aspect of Enigma codebreaking discussed in Dermot Turing's book, X, Y & Z: The Real Story of How Enigma Was Broken.

Ask Uncle Colin: A Partition Enigma: https://www.flyingcoloursmaths.co.uk/auc_enigma-md/

Life Stats

Enter your date of birth and read some interesting statistics about the world since you came into it. Plenty of discussion starters here!

Life Stats:

https://neal.fun/life-stats/

What is a quadrillion?

The word 'quadrillion' comes from the same family of number names as 'ten', 'hundred', 'million' and 'googol'. It's just a name for a particular number.

But which number?

Another way of saying 'one quadrillion' would be 'one thousand million million'. What's that in digits? Let's work it out:

We know that 'one thousand' is written like this: 1,000 (a one with three zeroes, or 10³),

and 'one million' is written like this: 1,000,000 (a one with six zeroes or 10⁶).

So 'one thousand million' is just the 'million' bit with the 'one' replaced with 'one thousand', like this: 1,000,000,000.

So 'one thousand million million' should just be the 'million' bit with the 'one' replaced with 'one thousand million', like this: 1,000,000,000,000,000.

So 'one quadrillion' is 1,000,000,000,000,000 (a one with fifteen zeroes, or 10¹⁵).


Facts* about the word 'quadrillion'

• The SI prefix for a quadrillion is 'peta-'. This means that a 'petabyte' is one quadrillion bytes, or a 'petametre' would be a quadrillion metres.
• 'Quadrillion' can also refer to the number 'one million million million million', or 1,000,000,000,000,000,000,000,000, or 10²⁴, in the 'long scale' system of number naming. This definition is, however, falling out of use in the English language, which is why I have demonstrated the first definition in more detail (which uses the 'short scale' number naming conventions).
• The SI prefix for the long scale definition of a quadrillion is 'yotta-'. In the short scale system, 'yotta-' is the prefix for a 'septillion'.

*Whether they're interesting or not is entirely down to personal preference and circumstances.

What is a google / googol?

The famous web search engine Google took its name from the maths word 'googol'. But what does it mean? Well, just like words such as 'four,' 'pi,' 'six thousand' and 'one hundred and thirty billion,' 'one googol' is a number. Specifically, the word 'googol' belongs in the same family as hundred, thousand, million, billion and so on: it is a power of ten. What's a power of 10? That's a bigger question for another post (please ask us to get going on it if you really want to know!), but a quick recap: Powers tell you how many times to multiply a number by itself (for example, 5³ means 5 x 5 x 5). A power of 10 is just the number ten 'raised to a power' (for example, 10⁴ is read as "ten to the power of 4," and means 10 x 10 x 10 x 10, which is ten thousand (10,000)). So what's a googol? A googol is

• "ten to the power of one hundred," or
• 10¹⁰⁰, which means:

10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10

• Which equals:

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 That's quite big.