Ok, so by now you should know I'm a math major. I usually like science, the precision and the ability to predict from a model (usually built on a mathematical footing) future behavior, etc., etc..
BUT, at the beginning of every science class they give a lecture on a mathematicians nightmare... Significant Figures...
Why do I hate sig. figs.? Because they compromise PRECISION. Why would you round? Why are there some really weird messed up rules that allow you to round a calculation from 3.275 or something to 3?
I understand why they are there, the rules I mean, but come on there's got to be another way to do this.
So yeah, I hate significant figures. Does that make me weird?
7 comments:
I'm not sure if there's another way to do it or not, but you don't compromise precision when you account for significant figures. Pure mathematics is inherently perfect. Experimental observations aren't. If the extra "precision" you desire is better than the equipment can give, it doesn't add any new information. Including the extra figures would be akin to removing the essential information about how precise your measurement is.
By the way, if you want to put it on a real mathematical footing, look at error propagation in statistics.
at the same time though, because of the addition/subtraction rules for significant figures, you can end up with odd answers in the end.
In lab today, we measured a whole bunch of things with some clamp thing, I'd have to look up the name, and the measurements looked something like .9 cm or something.
When it goes through all the calculations, you end up with something like the density of an object is 165.78 g/cm3 or something like that.
In effect, because of the .9 cm object measurement somewhere down the road, that 165 something density turns into 200g/cm3.
200g/cm3 I tell you.
That's a bit of a stretch to keep significant figures, I think.
I'd rather write 165.785 or something to show the calculations instead of feeling like everything is rounded in an awful manner down the way.
That's why I don't like stats either.
I use them, sometimes, but really don't like them. They seem to algorithmic to me.
I use them, sometimes, but really don't like them. They seem to algorithmic to me.
Statistics can be algorithmic, but, that doesn't lead to a deep understanding. Actually, many published papers run through the statistical algorithms and state conclusions without bothering to verify that they're using the right statistical algorithms! The thought is involved in (1) developing new techniques that enlighten us on uncertainties, and (2) determining which statistics are appropriate under which circumstances. Most real-world phenomena are based on some uncertainties.
And, your answer still can't be any more precise than your original measurement. Instead of reading 0.9 cm, you should be thinking of it as: (0.9+/-0.1) cm, or the like. That's a somewhat more mathematically sound way of keeping track of sig-figs.
I'd have to say that I understand statistics well enough for the purposes that I need it for.
I do not know how to prove theorems in statistics, rather I understand what the equations, variables and output means well enough to interpret data and know what's wrong with an experiment.
I'm not fond of statistics because, like accounting (not to knock on accounting or statistics people), the formulas you use, you use them over and over again. It's the same relative process that you use to find a particular answer.
Yes, there are differing cases that you have to account for, but once you've done a T or Z test, you've done it a million times.
I think I have a clear understanding, before my post, why one would use significant figures to show how accurate thier instrumentation is, but I still don't like it and consider rounding inaccurate. I'd rather write sqrt of 2 than 1.4 whatever, I'm just that kind of a math person.
I really don't think it says anything about my stats skills, as I can do statistics and explain it to others very well. I just don't particularly like stats. There are people who are good at things and don't necessarily like them.
vito, you are right about the micrometer, that's what one of them was. The other had a name that started with a "v" or something (again, will get book sometime today I think).
But yeah, I've figured out that Pure Math is definately for me. Algebra and Topology all the way!
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