What’s your number?

Another maths curiosity from the Futility Closet:

Fortuitous numbers
In American usage, 84,672 is said EIGHTY FOUR THOUSAND SIX HUNDRED SEVENTY TWO. Count the letters in each of those words, multiply the counts, and you get 6 × 4 × 8 × 3 × 7 × 7 × 3 = 84,672.

Here’s something I’ve (pointlessly) struggled with for a long time, now. Can you complete this sentence?

Written as words, there are _____________ letters in this sentence.

Use Excel’s LEN() function and AutoSum and try it like this, writing it out one word at a time.

number-1

So, forty three letters so far, with those two empty boxes. If you were to write forty three into those boxes, the total would obviously be more than forty three. A little trial-and-error, and we get

number-2

the answer fifty three. Well, that was fairly straightforward. Let’s try a slightly different sentence.

number-3

Maybe this isn’t so difficult, after all. One more?

number-4

That’s not right, there are forty nine letters in that sentence, not forty eight.

number-5

But now there are forty eight. Is it not possible to accurately complete that sentence, then?

Communication tied up in knots

I think I might have remembered that the Inkas never invented the wheel, but I didn’t know they hadn’t invented writing. It seems so fundamental to civilisation development. Apparently ‘knot’.

The khipu code: the knotty mystery of the Inkas’ 3D records
But, after more than a century of study, we remain unable to fully crack the code of the khipus. The challenge rests not in a lack of artifacts – over 1,000 khipus are known to us today – but in their variety and complexity. We confront tens of thousands of knots tied by different people, for different purposes and in different regions of the empire. Cracking the code amounts to finding a pattern in history’s knotted haystack.

Ok, I can just about understand the like-an-abacus-but-made-of-string category of these strange artefacts, but those types only accounts for two thirds of the ones remaining today.

The remaining third of these devices – the so-called narrative khipus – appear to contain encoded non-numerical, narrative information, including names, stories and even ancient philosophies. For those who love puzzles, the narrative khipus are a godsend.

tied-up-in-knots-3

tied-up-in-knots-2

tied-up-in-knots-4

The Internet Archive

Still can’t get my head around the scale of these things, the numbers involved.

Internet Archive
Internet Archive is a documentary focused on the future of long-term digital storage, the history of the Internet and attempts to preserve its contents on a massive scale.

Via Webmonkey. Don’t know why it makes me think of this though…