Upvote for anything math related!

Meh - the multiplication trick looks less impressive if you're working with both numbers in binary to begin with. When you double the number, you're just shifting it one place to the left - if you write this down, it looks like this:

100
*11
---
100
1000
----
1100

That should look familiar. You end up doing it exactly like a regular third grader would do multiplication - just in binary. So saying that computers work this way is a bit misleading. And, yes, there is implicit multiplication tables involved. It just might not seem that way because the binary multiplication table is (naturally) very short.

"The ancient Indian mathematician Pingala presented the first known description of a binary numeral system around 800 BC." -Wikipedia

"Sciences and arts seem to have been in place at the very beginnings of Egypt." -The dude in the beginning of that video

"Ancient Egypt developed over at least three and a half millennia. It began with the incipient unification of Nile Valley polities around 3150 BC." -Wikipedia

jmerzo, I thought the cool thing was that the world doesn't present us with binary numbers to begin with, and that this system is conversion process to a binary system that allows for fairly simple calculation that doesn't require memorisation of a times table. Maybe I don't understand your criticism.

I agree Engels, I can't say I agree with jmerzo, multiplication is based on more visual means rather than memorization.

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>> ^Engels: the world doesn't present us with binary numbers to begin with

The world presents us with no numbers. If we grossly categorize things we can use unary(base 1, think counting on your fingers). All bases are pure and arbitrary abstractions.

While many argue "using base ten follows from having ten fingers", that would technically give us base-11(0-10 fingers). Also consider that, since we are using an arbitrary base anyway, we could use 64(the number you can count to on your fingers of one hand in binary).

One of the nice things about being multi-base conversant, is that it's easy to see how arbitrary and unnatural any of these decisions are. base 60 (think sec/min min/hr) or base 12(think mo/yr hr/day) are used regularly with analog devices, because these bases work better for these purposes. The fact that we label these devices with digital numbers does not effect their non-base-10 function.

We just think of everything in base-10 by default and assume that the world works that way, even though we regularly and unknowingly use systems and technology which rely on other bases.