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Or like a computer. Or like an Egyptian computer.
December 9, 2010 6:37 AM   Subscribe

Multiply like an Egyptian. (SLYT)
posted by overeducated_alligator (24 comments total) 26 users marked this as a favorite

 
Translate Ancient Egyptian!
posted by The Whelk at 6:42 AM on December 9, 2010


I love math. I wish my early math teachers had also loved math.
posted by odinsdream at 6:47 AM on December 9, 2010 [1 favorite]


Don't be silly. The Egyptians didn't know math(s). Those buildings were built by aliens.
posted by clvrmnky at 6:51 AM on December 9, 2010


Multiply like an alien.
posted by overeducated_alligator at 6:52 AM on December 9, 2010 [1 favorite]


via chestbursters.
posted by The Whelk at 6:55 AM on December 9, 2010


All the old paintings on the tomb they do binary, donchaknow ...
posted by bwg at 7:04 AM on December 9, 2010


Cool, thank you!

And - the on/off icon comes from the state of electrical flow in early computer switches? - Neat!
posted by carter at 7:14 AM on December 9, 2010


Ancient Egyptian Science: A Source Book, Vol. Three Ancient Egyptian Mathematics

Egyptian numerals

Mathematics in Egyptian Papyri

History Topics: Ancient Egyptian mathematics

Also interesting is Assyro-Babylonian mathematics which uses a base 60 numeral system.

Babylonian Mathematics
posted by AElfwine Evenstar at 7:15 AM on December 9, 2010 [2 favorites]


Actually, I'm pretty sure most computers do this. Still a neat technique though.
posted by Chuckles at 7:33 AM on December 9, 2010


So, now I understand how binary works. thanks!
posted by oddman at 7:40 AM on December 9, 2010 [3 favorites]


No, no! Carry the ankh.
posted by TheWhiteSkull at 8:02 AM on December 9, 2010 [3 favorites]


2094 / 13 GO!
posted by From Bklyn at 8:05 AM on December 9, 2010


Math with a New Yawker.
posted by monospace at 8:06 AM on December 9, 2010


"No more tears for 3rd graders" yeah! Instead of memorizing 6x7=42 all they have to do is be able to double 347 in their heads (twice) while also remembering that 6 is 2+4! It's so simple!

Computers use binary because it's natural to the switch paradigm. The Egyptians used binary (I'm guessing) because doing math base 60 isn't too convenient in terms of the number of symbols you have to remember, not to mention an enormous multiplication table (3600 1 digit products!).

But if your numbers are already in base 10, it's much more natural to use this same algorithm in that same base.

17 x 25 is 10 x 25 + 7 x 25.

10 x 25 is easy: 250
7 x 25 is pretty easy, but if not keep in mind that 7 = 4 + 3.
4 x 25 = 100
3 x 25 = 75

So we have 250 + 100 + 75 = 425.

The is the exact same algorithm but you don't have to convert bases (double) before hand NOR do you have to remember the binary representation of the other number because the base 10 digits are sitting there right in front of you.
posted by DU at 8:15 AM on December 9, 2010 [3 favorites]


I learned about this in a great book about non-western science and math called "Lost Discoveries"- it's a great read if anyone is interested.
posted by rmless at 8:21 AM on December 9, 2010 [1 favorite]


Lacks Hoff.
posted by chavenet at 8:22 AM on December 9, 2010


Yeah, this should look familiar - it's exactly the long multiplication you learned in gradeschool, but performed in base-2 rather than base-10. Notice how clean everything looks in an alphabet of only two symbols.

If you're new to math and got a kick out of this, try proving to yourself that any natural number (counting numbers like 6,7,8, 365, 1001, and so on, as large as you can imagine) can be expressed by adding together nothing but powers of 2.

Take 365.
= 256 + 64 + 32 + 16 + 4 + 2 + 1.
= 2^8 + 2^6 + 2^5 + 2^4 + 2^2 + 2^1 + 2^0. (Remember that 2^0 = 1.) All powers of 2.

Try to conceive of a natural number that isn't expressible as a sum of powers of two. What would have to be true about this number?
posted by kid ichorous at 8:46 AM on December 9, 2010


I vote for DU's method. Doing base 2 in my head isn't as intuitive. For example, to write out 365 as kid ichorous does, I first write out the powers of 2 (performing simple multiplications in my head), then start doing basic algebra (365 is greater than 256, so 256 gets a 1. Now I subtract 256 from 365, take the remainder, and go on to the next digit, etc...). All that work adds up to be more complex than the initial base 10 calculations.

What I like is simple math formulas that allow you to "cheat". Here's two good examples of what I'm talking about:

Any number ending in 5 squared can be abbreviated to x * x+1, append 25. So 35 squared is 3*4 = 12, append 25 = 1225. 55 squared is 5*6, append 25 = 3025, etc...

Another example: 9 multiplication. 9*x = x-1, append 9-(x-1). Examples:
9 * 8 = (8-1) append (9-7) = 72
( * 3 = (3 - 1) append (9 - 2) = 27

These are pretty easy to remember, and easy to prove if you want to verify they always work. Anyone have more?
posted by Crash at 10:01 AM on December 9, 2010 [1 favorite]


For 5s, [x]5 * [(x+1)]5 = [x(x+2)]75. i.e. 35*45 = 1575, 55*65 = 3575, etc.

9 is a useful crude checksum for addition and multiplication. First, realize that the remainder of a number when divided by 9 (modulo 9, in other words) is the same as the remainder of the sum of the digits of the number when divided by 9. In other words, 3751 mod 9 is the same as (3+7+5+1) mod 9 = 16 mod 9 = 7 mod 9. As a checksum, that operation (adding up the digits mod 9, let's call it α) is preserved by addition and multiplication. In other words, for any two intergers a and b

α(a+b) = α(a) + α(b) (mod 9)
and
α(a*b) = α(a) * α(b) (mod 9)

So, let's say you need to add 572+723. You come up with 1295. Are you correct? A basic checksum here would be that α(572) = (5+7+2) mod 9 = 5 mod 9 and α(723) = (7+2+3) mod 9 = 3 mod 9, so we hope that &alpha(1295) is 3+5 mod 9 = 8 mod 9. And in fact (1+2+9+5) mod 9 is equal to 8. Similary, for multiplication, we would know that the product's α value would have to be 5*3 mod 9 = 6 mod 9. And in fact α(413556) = (4+1+3+5+5+6) mod 9 = 24 mod 9 = 6 mod 9.

Now, obviously this is a very crude checksum. If your calculations were off by some multiple of 9, it wouldn't catch it. But it should help eliminate a good chunk of off-by-one carrying errors and the like.
posted by kmz at 10:59 AM on December 9, 2010


You math nerds are blowing my mind.
posted by msali at 8:24 PM on December 9, 2010


For 5s, [x]5 * [(x+1)]5 = [x(x+2)]75. i.e. 35*45 = 1575, 55*65 = 3575, etc.

I'm confused. Isn't 35*45 [x]5 * [(x+2)]5 where x=7?

And I honestly don't see how this could possibly be true.

[x]5 * [(x+1)]5 = 75*x(x+2)
25*(x)(x+1) = 75*x(x+2)
25(x^2+x)=75(x^2+2x)
x^2+x=3x^2+2x
For x = 7
49+7 = 3*49 + 14

Surely I'm missing something?

Using Crash's tip for squares of 5s, you can come up with formulas for numbers ending in other digits as well.

For example, for two digit numbers ending in 1, the square is 100x*x + 20x + 1, so for example:
31^2
900
 60
  1
---
961

71 ^ 2
4900
 140
   1
----
5041
Not nearly as elegant as the squares for 5.
posted by Deathalicious at 7:09 AM on December 10, 2010


Ohhhhhhh never mind. x is a digit, not a variable being multiplied by 5.

D'oh.
posted by Deathalicious at 7:11 AM on December 10, 2010


Relatedly
posted by The 10th Regiment of Foot at 9:54 AM on December 10, 2010


Why the hell is this a related video?
posted by azarbayejani at 9:00 AM on December 12, 2010


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