fox | my turn to ask math questions.

I'm turning myself around a bit with a thing I'm trying to set up that has to do with squares.

Suppose for every x minutes you spend doing activity A, you have to spend x² minutes doing activity B. No problem, right? If you do A for two minutes, you do B for four. If you do A for three minutes, you do B for nine. If you do A for fifteen minutes, you do B for three hours and 45 minutes. That's where I'm running into trouble, is switching between orders of magnitude. If you do A for an hour, that's 60 minutes, so you do B for 60*60 = 3600 minutes, or 60 hours, or two and a half days. So far so good, right?

If you do A for a solid week, that's 168 hours, by my calculations. So now you do B for 168*168 = 28,224 hours, or (divided by 24 hours per day) 1176 days, or (divided by 365 days per year) three years and almost a quarter.

If you do A for a solid month, that's 30 days, so you do B for 30*30 = 900 days ...

... but how can a square month be shorter than a square week? Even if I make the month 31 days, I only get 961.

The obvious answer is that I've skipped some necessary step somewhere, but for the life of me, I can't work out what I'm doing wrong. Someone who didn't need special tutoring in geometry and trig, help me out, wouldya?

I may have worked it out myself: is the answer that if I want to talk about how many minutes I have to do B, I have to work out how many minutes I've done A, and shortcutting to days and weeks and months and so on isn't going to work until I've got a total? Because (7*24)²/24 is just not the same thing as 7²? Because if I do the month example with hours, I get 720*720 = 518,400 hours, or (divided etc.) 21,600 days, which is rather more than three years, I admit.

Flat | Top-Level Comments Only

What you said. Squaring minutes gives you different results from squaring hours or days or weeks.

ETA, because I can't help it: Thinking of minutes in terms of fractions of hours might help you make sense of it. 15 minutes is 1/4 of an hour, right? But if you spend a quarter of an hour doing A, it doesn't mean you spend 1/16 of an hour doing B.

I could go on if you need me to, but I'll just stop before this gets insane.

I was actually trying to think about fractions in the first place, but I had to split and I could see that that way lay madness. And that was the end of my intention of making the hour the base unit of this problem. (Because if I do set it up where for x hours doing A you do x^2 hours of B, and you do 15 minutes of A, how the hell long do you spend on B? Not three minutes and three quarters, as you say -- but not three hours and three quarters, either, because I'm trying to square the hours, not the minutes. ARGH.)

(See, it's better that I left math when I did. Minutes is fine. I'd much rather multiply everything in my life by 60 for the next day and a half than try to work out how to square fractions of hours without squaring fractions. For the degree to which this is all going to matter, I've already spent too long worrying about it. [g])

I'm mostly dying to know why you're thinking about this in the first place.

And remember, with positive fractions less than one, when you square them they get smaller. Freaks my GMAT students out every time. So, yeah, in the case here you would do 3.75 minutes of B.

I do remember that; but that works mathematically, not practically. Which is why the unit of analysis is now the minute. :-) Works out fine. I have done my calculations and worked out that if you do A for a solid day, you'll be doing B for close to four years; if you do A for five days, you'll be doing B for almost 99 years, which is great.

:-D

Yeah, you got it.

To compare the two, you need to use the *same* unit. In the week, you used hours but in the month you used days. If you convert the week to 7 days, then you can compare 7 days to 30 days.

And to compare across the board, you have to do the same thing. Convert all the time units to the lowest common unit (i.e. a minute).

Just not fair. :-)

Because (7*24)²/24 is just not the same thing as 72?

Exactly... (7*24)²/24 = (7²*24²)/24 = 7² * 24

God, it's all coming back to me now. [runs away]

Hi, I drifted here from the math thread in

ellen_fredemon a couple of days ago. I hope you don't mind comments from a total stranger.

What people said above; your units matter. Technically, if you square the number, and you want units to still work, you've got to square the units also. Think about doing something similar with lengths, instead of time. If you have a length that's 24 inches (or 2 feet), and you square it without keeping track of units, you'd get a 576 inch length -- that's 24 feet. But 24 inches is 2 foot, and 2 squared is 4 feet -- it's just like your days vs. minutes problem.

But if you square your units also, you don't get a 576 inch length, you get a square that's 24 inches on a side, for an area of 576 square inches -- and that same square is 2 feet on a side, or 4 square feet. (576 square inches is equal to 4 square feet.) So if you square your units as well as your numbers, then you get the same answer no matter what units you use -- inches, feet, cms, whatever.

Unfortunately, your answer is in square inches, or square feet -- it's different units. And square minutes really don't mean anything. (Well, there are situation in physics where you work with squared time -- acceleration due to gravity is 32 feet per second squared -- but that's way tangential.) If you're not going to treat the units nicely, then you've got to pick one units -- minutes, or hours, or days -- and always use that.

(Just as one square foot is 144 square inches, which you can see by drawing a square and dividing it into a 12x12 grid, one square week is equal to 49 square days; one square (30-day) month is equal to 900 square days.)

... actually, the grid thing does make complete sense. I can't use it for these purposes, but it does help a person to visualize it.

I am going to work hard to make this not mean there is a lot of multiplying by 60 in my future. :-D

I have absolutely no clue about math problems. I'm here to wish you a happy birthday!

Thank you! (ooh, that icon has cake!)

my turn to ask math questions.

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