Yeah, I’m positive that my example for my class involved money as well.
Some of my classmates had pretty creative examples not related to money / debt, and a few had idiotic ones IMO. I wish I could recall some of the better examples.
too complicated, dude
But debt is not a real thing. It is a promise. It is sometimes a promise of a real thing, although as often is a promise of money, which is also just a promise, at best.
Generally, I would say a negative number inside of an equation is a promise too. It is the promise that you will do some subtraction.
I’m not sure if the stickman’s deviation is quite “real” either? Maybe?
You could similarly say your distance South it the negative amount that you’ve traveled North. Sort of… But it’s definitely a bit nonsensical. You are assigning North and South as opposite that you know cancel each other out. But it’s only knowledge of the fact they subtract makes it “work”. It doesn’t mean that south IS negative north or that you did negative walking?
Time works that way too. If we’ve been eating for 10 minutes, that means that dinner will be ready in -10 minutes. If dinner will be ready in 10 minutes, that means you’ve been eating for -10 minutes?
Anyway, negatives are great inside of an equation. For sure. But if you get a negative as an answer, it can be weird. Which is how imaginary numbers work too.
It would be if you’re isolating “equations” from “interpretation of what the numbers mean” when applied ot a “real-world setting.”
A $10 loss is the same as a $-10 profit. Defining “profit” as strictly “Revenue less Expenditures” will result in . . . a value that isn’t going to “mean” much w/o some way to indicate an answer when expenditures are larger than revenues (as they occasionally do).
“Old School” accounting was to take the larger of Expenses and Revenues and subtract off the smaller. If the process was “Rev - Exp”, then the answer is labeled “Profit!”. If it was “Exp - Rev”, then the answer was labeled “Loss”.
“Negative numbers” allow for a more simplified presentation of this calculation and interpretation of the answer.
But perhaps the best place to consider the value of “negative numbers” is with temperature. Celsius has the advantage that “zero” indicates the freezing point of water as the “benchmark”.
Fahrenheit’s “benchmark” is where a winter coat is needed for being outside for more than 15 minutes.
Not if you work it in incremental steps to understand what’s going on.
And it’ll reinforce “why” subtracting a negative is the same as “adding the positive” w/o it being just “some rule to mindlessly apply”.
I recall being assigned to come up with a word problem that actually made sense and involved multiplying two negative numbers as an assignment in my “Theory of Teaching Mathematics” class.
Using the latest mind-reading technology our future-police killed 10 people who were each going to kill 10 people-- therefore we saved 90 lives.
But perhaps the best place to consider the value of “negative numbers” is with temperature. Celsius has the advantage that “zero” indicates the freezing point of water as the “benchmark”.
Fahrenheit’s “benchmark” is where a winter coat is needed for being outside for more than 15 minutes.
Temperature is not great either, since of course there’s a third option (Kelvin) that describes the objective fact of temperature, which is an average amount of kinetic energy (or something like that?), and is always positive.
When we talk about “negative degrees Celsius” we are secretly implying a math equation rather than describing a “real thing”.
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You know that 0 Fahrenheit is not random, right? It’s the freezing point of saltwater.
I would argue that 0 Fahrenheit is perhaps an even more practical benchmark than 0 Celsius in that it represents the point at which salt cannot melt ice/snow. That’s very useful if you’re trying to decide if you should salt your driveway & sidewalk or not.
I guess 0 Celsius is useful for setting your refrigerator and freezer temperatures, but that’s kind of a one and done kind of thing, and mine have the recommended settings listed right on them so there’s no need to remember anything.
And yeah, there’s nothing magical about negative temperatures… that’s pretty arbitrary. I can’t think of a scenario where multiplying a negative temperature would be useful.
If you’re looking for something “real” in regards to “Negative One”:
But in the broader context, negatives were always used in the context of some baseline/bench-mark and not in isolation.
That is, you need a “starting point” (call it zero), and a definitive (one-dimensional) “direction.”
I know . . . but when you’re not around “salt water”, it’s not all that meaningful.
But where I grew up, “needing a winter coat” was far more meaningful.
See the rest of my post. If you live where there’s a real chance of the temperature dropping below 0 F then it’s useful in determining whether you should use salt as a de-icer.
Where I live sub-zero is rare, but it has happened and I’ve reminded my husband to not salt the driveway because it might get below zero and salt will just make it worse.
Started googling this, and it is interesting… only have to put my DUMB KID TO BED. Uhg. Mathematical secrets of the universe will have to wait!
Where I lived, the temp was regularly below 0F . . . and we never used salt for de-icing. It was shovel the snow off before it “iced” or use sand.
FWIW, understanding the history of math (and the use of different “types” of numbers) often help to illustrate why the “new” types of numbers were introduced.
Yeah if you get used to not using it when it’s below 0 then you might not feel like you need it when it’s above 0 but below freezing.
Hubby feels like he is not finished clearing the driveway and walk if he has not salted it. And as long as it’s above 0, which it usually is, the salt melts the little bits of snow he didn’t get up.
I just have to remind him to not use it when it gets below 0 or close enough to 0 that I don’t want him to risk it.
If you put down salt when it’s 2 above and then it goes to 2 below then all that snow you melted refreezes as black ice and is WAY worse than just having 1/4 of an inch of snow on the ground that you couldn’t get with the snow-blower.
I am personally pretty ambivalent on salt usage when it’s above 0. If hubby is gone and I have to clear the driveway myself I don’t bother. But he is meticulous about the driveway when he’s home. And as long as it’s above 0 I don’t mind the salt, so if he’s doing it the driveway gets salted.
What’s this “snow blower” you talk about? 
Our streets never got treated with salt. Dealing with snow from late Oct through mid-March and temps being below freezing for 18 hours per day from early Dec to late Feb (with sub-zero F for much of the night) . . . salt wasn’t viewed as a good option given its property to accelerate rusting of vehicles.
Plus, in my hometown, the storm drains went straight to the nearest creek; so salting was further discouraged. (Might’ve also been against local ordinances.)
Heh, best purchase we ever made. We don’t need it for every snow: less than 3 inches of dry snow is easily pushed off the driveway with a shovel.
But for lots of snow or wet / heavy snow it’s a back-saver.
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IFYP