Mathematics

Trachtenberg Speed Mathematics

If it’s only arithmetic then why is it called mathematics?

Image attribution: https://www.youtube.com/attribution_link?a=sGDzwVyfBL4&u=/watch?v=2zRrkQAOSAU&feature=share

Why is it called mathematics when it’s only arithmetic?

That’s an easy one. It’s mathematics because it involves number theory, albeit on a fairly basic level.

Jakow (later Professor) Trachtenberg was incarcerated in a Nazi concentration camp during World War II and kept himself sane by thinking about numbers and structure, until he and his wife escaped to Switzerland.

He built his system of speed math on the basis of the principle that any number can be represented as a sum of powers of two, with each power being multiplied by a different prime number. For example, the number 12 can be represented as 2 + 2 + 3 = 5 × 3 = 15.

The Trachtenberg system uses this idea to represent numbers in an efficient way in the brain but it requires good mental visualization by the user.

I read most of the book when I was about 13 years old and although I’m a lifelong lover of textbooks that one turned me off. I would probably have gained by being taught the system in a classroom and tested on it, just as I learned about the Fourier transform before passing the exam and forgetting about it. And then Schrödinger came along…

If you’re interested, here’s a sequence as demonstrated in Wikipedia:

Multiplying by 7

Rule:

1. Double each digit.
2. Add half of its neighbor (dropping decimals, if any).
3. If the base-digit is odd, add 5.

Example: 523 × 7 = 3,661

Working from right to left:

3×2 + 0 + 5 = 11, 1.

2×2 + 1 + 1 = 6.

5×2 + 1 + 5 = 16, 6.

0×2 + 2 + 1 = 3.

That’s a simple one (scratches head), but with practice it is possible to very quickly multiply two 4 digit numbers together almost instantly. I’d have to use paper to do that. Or a calculator on my phone.

Is mental arithmetic a thing of the past? Nowadays students can use calculators in exams. In my day it was log tables and slide rules — remember those?

Now there’s a thought! Log tables where every number is represented as a power of 10 (or Euler’s number, e, for natural logs). Wasn’t Trachtenberg just using log base 2 plus a bit on the end? Maybe. My brain is hurting.

I still have the book somewhere in a box on the other side of the world.

[embed]The Trachtenberg System of Speed Mathematics Was I too lazy to learn it?medium.com

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