Are Even Numbers Evil?

There’s a quite simple method for multiplying two numbers which just includes the mathematical operations of adding, dividing in half, and doubling. However, this method only works as long as we treat even numbers as “evil”.
Many ancient cultures made use of this technique and indeed some of them didn’t speak highly of even numbers.
So let’s do a sample calculation! Here’s how it works:

Take two arbitrary numbers (integers, preferably) and create a table as follows.

93  x  18
46 36
23 72
11 144
5 288
2 576
1 1152

What happens here is that the numbers of the left column are repeatedly divided in half while the decimal places are cut off. (That’s why 46.5 becomes just 46!) The numbers of the right column are systematically doubled.
Now, let’s assume that even numbers are bad for our calculation and discard all the rows which begin with an even/evil number:

93  x  18
46 36
23 72
11 144
5 288
2 576
1 1152

Finally, we have to add the remaining numbers of the right column together (and don’t forget to include the uppermost number 18!):
18+72++144+288+1152 = 1674.
Ta-dah! We obtained the product 93 x 18 = 1674.

The above-shown method requires us to ignore those rows which begin with even numbers. Since one gets the wrong answer if the particular rows are included in the final addition, the belief in the “evilness of the even numbers” wasn’t that unreasonable once. (Although this times were way back!)

Let me state another argument here: The sums of the first odd numbers all result in square numbers, which is very beautiful (because square numbers are especially noble, right?! 😉 ). Conversely, the sums of the first even numbers don’t produce nice square numbers.

By the way of illustration:

(square numbers, all of them) vs. (not square numbers)
1 = 1   2 = 2
1+3 = 3   2+4 = 6
1+3+5 = 9   2+4+6 = 12
1+3+5+7 = 16   2+4+6+8 = 20
1+3+5+7+9 = 25  

Is there really such a thing as “good” and “bad” numbers? If so, which numbers are the unlikeable ones – the odd or the even numbers?

Sadly, Pythagoras of Samos isn’t alive anymore! I’m sure he would have an opinion on this topic…

Bust of Pythagoras of Samos in the Capitoline Museums, Rome.
(Credit: Galilea, via Wikimedia Commons)

By the way, the multiplication method presented in this article can of course be explained mathematically and doesn’t have to use assumptions like “Even numbers are evil”. But you probably have already thought of that, right? 😉


About tempse

I think about physics, other stuff, and physics. Besides, I share some thoughts on the internet.

Posted on November 9, 2013, in Mathematics and tagged , , . Bookmark the permalink. Leave a comment.

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