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by vanderZwan 456 days ago
Related: in a reaction to a comment I wrote about logarithms about a month ago[0], saulpw recently linked his own idea of making logarithms more "accessible" to the masses by introducing magnitude-based notation:

https://saul.pw/mag/

I think it is a really nice idea that should be spread more widely. It might be Pi day, and while I traditionally complain that Tau is better for contrarian reasons (hey at least I'm honest), we might as well co-opt the extra attention maths gets for other mathematical causes.

[0] https://news.ycombinator.com/item?id=43036094
1 comments
Enginerrrd 456 days ago
For what it's worth, I'm really not a fan.

There's a reason we use scientific notation, and it's actually partly because in the era of slide-rules, it was INCREDIBLY helpful notation that makes it trivial to estimate things like order of magnitude. People performed all manner of operations and kept the magnitude part in their head. It MADE people more magnitude aware.

This magnitude-only based notation is the one that's actually more needlessly complex and error prone. There's no sensible way to manage significant figures or rounding error in simple operations like addition and subtraction. And simple operations, like adding/subtracting two numbers are really non-trivial. If you have to start each operation by converting to a useful format and then converting back, what have you gained exactly by using the notation?

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anjakefala 456 days ago
I think the argument is that for non-scientific usecases, folks don't really need to think about error or significant digits. By focusing on the significand too much laypeople aren't grasping how large and small these numbers are relative to each other.

It's not being put forward as a recommended tool for scientists when reasoning about precise values. It's put forward for laypeople when trying to understand the vastness of the universe.

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vanderZwan 456 days ago
Yes, that was my take-away too. I suspect it's a wonderful way of teaching intuition for differences in scale, which is something that's a lot more important to us today than it was a few centuries ago. Easy mental guesstimates should not be underestimated as a valuable tool
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