View Full Version : Stupid Math Question! Hooray!

Spiny Norman

06-21-2007, 08:56 PM

I have a part in my book where the MC is watching snow fall and he wonders out loud if it's possible to mathematically "map" snow - that is, if there's a way to mathematically express the amount, placement, and regularity of snow falling within a square inch of space in the air. The thing is that he's a burned out mathematical and scientific prodigy. It's been almost a decade since he did anything with thought, but I assume he still know a few things.

I guess it goes without saying that I am not a mathematical prodigy.

So... is this feasible? If so, how would one go about doing it? Are there wicked-cool terms like "algorithm" and such involved? Or is there just any way to go about making this sound legit?

Sophia

06-21-2007, 09:09 PM

Possibly - I'd think about the humidity that day, which (I'm assuming) is a measure of the number of water molecules per cubic metre of air. Then consider the temperature of the air. If it is at freezing point, then the statistical likelihood of one water molecule solidifying would be described by a probability curve. He'd need to take into consideration things like polluting factors in the air that might contaminate the water molecules, changing the freezing point of the resulting compound.

ETA: This is off the top of my head. You might like to look at descriptions of atmospheric modelling to see what the typical initial assumptions are for the models.

Spiny Norman

06-21-2007, 09:33 PM

Well, what I was really thinking about was, like... God, this is hard to explain as I don't know much about this... Not the science of the amount of snow falling, but just the idea that, at that very moment, if he took a square inch of space (or smaller), would there be a mathematical expression to record snow fall for five seconds of time through that square inch and then extrapolate and use that data to predict how snow would fall though that same square inch in the next five seconds, or minutes, or ten minutes, and so on?

I think Feynman did something with this on sand sitting on top of a drum, and trying to map and predict how it would jump each time it was struck. I don't need you guys to figure out how to go about doing it - you can't just grab a Richard Feynman off the street and ask him - I just need ways to make it sound legitimate. Like he had a vague idea and was just considering it. Or am I just nuts?

TheIT

06-21-2007, 09:43 PM

Sounds like something a math person would idly speculate about. You might want to look into chaos theory, too. Is your character going to actually come up with the formula?

benbradley

06-21-2007, 09:44 PM

Yes, I'd say this is possible. Maybe if you can find a friendly meteorologist who would like to talk about it...

Possibly - I'd think about the humidity that day, which (I'm assuming) is a measure of the number of water molecules per cubic metre of air. Then consider the temperature of the air. If it is at freezing point, then the statistical likelihood of one water molecule solidifying

ARGH... whether something is a solid, liquid or gas is determined by SEVERAL molecules in relation to one another...

would be described by a probability curve. He'd need to take into consideration things like polluting factors in the air that might contaminate the water molecules, changing the freezing point of the resulting compound.

ETA: This is off the top of my head. You might like to look at descriptions of atmospheric modelling to see what the typical initial assumptions are for the models.

dobiwon

06-21-2007, 09:44 PM

Hmmm, reminds me of a problem a PChem prof gave us in grad school.

What he could do:

Get a spotlight and shine it toward himself

Calculate the area of the spotlight lens

Stand a fixed distance from the spotlight looking into the light

Measure the distance he is from the spotlight

Calculate the volume of the cylinder defined by the distance from him to the spotlight and the area of the spotlight lens

Estimate the intensity of the light given off without any snow falling

Move the spotlight into the falling snow and stand the same distance away as before

Estimate the reduction in intensity of the light

Estimate the reflectivity of a single "average" snowflake

Estimate the size of a single "average" snowflake

Estimate the weight of a single "average" snowflake

Use all this to calculate the number of snowflakes per unit area and the amount (weight) of snowflakes per unit volume

Repeat the observations by moving the spotlight to different spots and varying the distance he is from it

Use these data to estimate the "regularity" or homogeneity of the snowfall

He would have to make the assumption that the "placement", or distribution of the snowflakes in three dimensional space, is uniform.

The results he gets would be considered empirical. That is, they would be based on assumptions, estimations, and physical data rather than on proven facts.

Have fun with it.

(BTW, in case you're curious, the problem the PChem prof gave us was to estimate the number of leaves on a tree by estimating the reduction of sunlight when viewed from under the tree compared to out in the open.)

alleycat

06-21-2007, 09:44 PM

If you just want something for a story, use chaos theory. Then you can throw out terms and theorems like crazy.

benbradley

06-21-2007, 09:56 PM

If you just want something for a story, use chaos theory. Then you can throw out terms and theorems like crazy.

Jurrasic Park!

Spiny Norman

06-21-2007, 09:58 PM

Sounds like something a math person would idly speculate about. You might want to look into chaos theory, too. Is your character going to actually come up with the formula?

Nope. I just want to know what word terms to use, really. Like, he would say, "I wonder if I could map this, and make a _____ that would express the regularity of snowfall through a square inch of space." Like, algorithm or parabola or equation or something

If you just want something for a story, use chaos theory. Then you can throw out terms and theorems like crazy.

...you didn't get your avatar from Something Awful, did you?

Higgins

06-21-2007, 10:21 PM

Nope. I just want to know what word terms to use, really. Like, he would say, "I wonder if I could map this, and make a _____ that would express the regularity of snowfall through a square inch of space." Like, algorithm or parabola or equation or something

...you didn't get your avatar from Something Awful, did you?

He would think of Stokes Theorem (which is about volumes with amounts crossing their boundaries over time) and a "surface integral" of "flux".

see: http://www.mth.uct.ac.za/omei/a-calculus/chap4/node5.html

Possibly you could also use a "tensor" or a "fiber bundle" formulation.

alleycat

06-21-2007, 10:34 PM

...you didn't get your avatar from Something Awful, did you?

I've got so many cat avatars that I don't remember where most of them came from.

Spiny Norman

06-21-2007, 10:56 PM

I've got so many cat avatars that I don't remember where most of them came from.

I just remembered that there was a massive thread on that forum with the title CAT IS DRIVING, leading to an inundation of photoshops and image macros of varying hilarity. Of course, it was that very image. Maybe about a year old.

The internet is sort like a plague carrier for silliness.

Oh, and thanks for the Stokes Theorem!

electric.avenue

06-28-2007, 10:54 PM

It sounds to me like a basic fluid mechanics problem - and not to do with chaos theory.

So taking that square inch of space, the MC wants to know how much snow is flowing through that space per second. Yeah, sounds like some sort of flux problem. You could do it with number of snow crystals passing through per second, mass of ice per second, number of water molecules per second.

threedogpeople

06-29-2007, 07:24 AM

My resident genius (hubby) says that it would be multi-variate regression analysis. Which he defined as using past experiences and measurements to predict or describe present or future outcomes. The hard part would be to minimize the variance, the standard deviation and/or the level of sampling error.

Spiny Norman

07-03-2007, 05:41 PM

My resident genius (hubby) says that it would be multi-variate regression analysis. Which he defined as using past experiences and measurements to predict or describe present or future outcomes. The hard part would be to minimize the variance, the standard deviation and/or the level of sampling error.

That actually sounds like it's more in line with what I'm trying to do. "Variance" is a word I wouldn't have come up with. Thanks a bunch! And thank your resident genius, too!

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