Comment by mewse | Hacker News Reader

Comment by mewse | Hacker News Reader

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> But 0.9 bar isn't equal to 1. Oh! I see what you did there!

This is a foundational problem in our anthropogenic decimal system of math (which we only use because of the evolutionary accident of a modal (n.b.: not average) human happening to have ten fingers); the whole issue doesn't even exist in the only correct representation of numbers, ternary (base-3).

For example, let's multiply 1 / 3 * 3:

In decimal `1.0 / 3.0 == 0.3 bar * 3 == 0.9 bar` and we've proven that 1 equals 0.9 bar, which is clearly nonsense and falsifies the whole concept of decimal representation of numbers.

In ternary, though, `1.0 / 10.0 == 0.1 * 10 == 1.0` -- see? no contradiction. Maths just work properly if you use the true numeric base.

Thank you for coming to my TED talk. I will not be taking any blasphemous questions from unbelievers about dividing and multiplying by two.

In a ternary system, wouldn't 1.222... equal 2?

Yes; the joke I was going for was that decimal one half would be written as 0.1 bar when converted to ternary. And then multiplying that value by 2 gives you 0.2 bar. Which is equal to ternary 1, in the same way that decimal 0.9 bar equals 1.

I find it really fascinating that different numeric bases all suffer from this same issue, but for different values. That the division by three which breaks decimal representation survives in ternary, but the division by two which is fine in decimal breaks ternary.

Of course, it seems to me that the real underlying problem is that we insist on writing these values out as an infinite series of fractional digits in the first place, instead of keeping the values in a precise fraction form. One third times three equals one; there’s no controversy there even in decimal. It’s only when someone insists on actually performing the division and representing that initial “one third” value as being a zero followed by an infinite number of fractional threes that the whole “omg 0.9 bar equals one??” paradox appears.

The last paragraph indicates the whole comment is in jest.

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