minor math fact OTD

[quietann]

A difference between two logged quantities, when unlogged, gives one a RATIO between the quantities, not a difference.

E.g. if log10(A) - log10(B) = X, then 10^X = A/B, *not* A - B.

Good thing I caught this. Most of the mistakes I make in my work are due to simple mathematical issues like this.

gah!

Comments

[feste-sylvain.livejournal.com]

Yes. That's how slide rules work.

[quietann.livejournal.com]

I should practice using the slide rule in our living room. It's about 9 feet long and mounted on the wall.

[whitebird.livejournal.com]

I almost bought one of those once! (A nine foot long slide rule, not just any one.)

[halleyscomet.livejournal.com]

I don't know. I would think a slide rule tie clip or cuff links would be more practical and portable.

The slide rule lighters on the other hand, are just plain silly.

[halleyscomet.livejournal.com]

Simple?????

Well for extremely large definitions of "simple" I suppose so.

[quietann.livejournal.com]

Biostatisticians work with log-scaled variables a lot, for various reasons. So the rules of logging and anti-logging *should* be burnt into our brains.

(reason #1 -- a lot of techniques require that a variable be "normally distributed" -- that is, have a histogram that looks like a bell curve. If a variable is highly skewed, taking its natural or base 10 log often changes the distribution to normal, or closer to it, anyway.)

(reason #2 -- more complicated, but basically taking the natural log of a ratio puts it onto a negative infinity to positive infinity scale instead of a zero to positive infinity one. This change allows one to use some very traditional and useful techniques for analyzing proportions and/or ratios. But I'd have to show you with pen and paper to really make sense of it.)

[halleyscomet.livejournal.com]

After the land dried and Noah let the animals out of the Ark, he set about making sure the animals were comfortable and had the opportunity to raise their young. To this end, he found himself wandering the surrounding area, making sure all the animals were having young.

The elephants were of course taking their time about it, but most of the other animals were getting by just fine, except for two snakes.

Noah questioned them, and the snakes asked him to cut down a couple of nearby trees for them. He did so and left.

A few months later he came by the snakes again, and found a massive number of baby snakes swarming over the ground, and the two proud parents glowing with pride.

"That's good to see," Noah said, "But why did you need me to cut down those trees?"

One of the snakes replied, "We're adders, we need logs to multiply."