Have a piece of Pi

[--Pete]

Hi,

(miles, yards, inches, psi, pounds, stones etc. remain bad choices, I wonder why after Independance day they didn't drop all these englisch units as well?.)
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First, I believe the USA was the second country to adopt the metric system. All the 'conventional' units are defined in terms of the SI.

Second, the metric system is severely flawed. It has one good point, that the multiples are all of ten. But the basic units were poorly chosen by a bunch of ivory tower types with no concern for practical utilization. Consider, there are two metric systems in use, the cgs and the mks, and neither uses base units, they need to go to multiples to get something useful. Because of the bad choices in base units, the Pascal (unit of pressure) is so small that an atmosphere is 10^5 Pa. The unit of force (the Newton) is so small that it is unusable, and metric torque wrenches are calibrated in kg-m or some other combination of mass times length, which isn't a torque in the first place. I can give you examples of this nature by the bushel, but these should suffice.

As a scientist, I am comfortable working in any system, or even mixed systems, and exponential notation does not put me off. But, for the average person, the base units of the old English system are much easier -- they reflect the size of things human. Had the academy picked the foot, pound, and second, and applied the powers of ten scaling to it, we would have a much better system than either in common use.

--Pete

[Doc]

If you want to know the metric system in and out, just start taking and or selling drugs.

See, drugs are good for something. Teaching the metric system.

[Griselda]

If you want to know the metric system in and out, just start taking and or selling drugs.

See, drugs are good for something. Teaching the metric system.
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Not if you buy in quantities larger than grams and smaller than kilograms.

[LemmingofGlory]

e? What the f?

From: Jack Wiedenman

(liberal snipping)

      Well, the fifth letter of the alphabet happens to be "e" and the
most famous mathematician whose name begins with e is of course,
Albert Einstein - well, guess what . . . Today (pi day) happens to be
Einstein's birthday!

      And, as an extra added attraction, the second most famous "e"
mathematician is Leonhard Euler from whom we get the irrational
number e = 2.718281828 . . Which is the basis of so many functions
from compound interest to radioactive decay to population growth.

With all due respect to Mr. Wiedenman, to call Euler the second most famous mathematician is a joke. Among mathematicians, it's difficult to say who is the most known, but there are certain names that appear in practically every mathematics book (Gauss and Euler are exceptionally ubiquitous). That said, I am not concerned with famousness because fame depends on who you ask. But I am shocked to see, in a list of mathematicians, Euler second to a physicist.

I would not call Einstein a mathematician. A physicist explains physical things using mathematics. A mathematician explains mathematics using mathematics. What did Einstein explain? Physics. If he was also a mathematician, I'd like to know where he made contributions, his field of study.

Two closing notes:

(1) The importance of e cannot be overstated. In mathematics, e is perhaps more ubiquitous than Euler, often appearing quite unexpectedly. If pi gets a day, e deserves a whole month.

(2) You can tell math majors who are not destined to become mathematicians by looking at those who, in their senior year of undergraduate studies, persist in pronouncing "Euler" so that it rhymes with "ruler."

-Lemmy

[LemmingofGlory]

Which (e) is the basis of so many functions from compound interest to radioactive decay to population growth.

Pardon me if I'm completely off the mark, but doesn't it not *really* matter what base logarithm you use when working with those problems? Just that e is often used, seeing as how it is the 'natural' logarithm's base.

The section you quoted refers to functions which are exponential (not logarithmic) in some base. (Because f(x) = e^x is injective) For any positive real number a there is a unique real number r such that e^r = a (r = ln(a)). This means that we can convert between an exponetial function in base a and an exponential function in base e thusly:

f(t) = (a)^t <=> f(t) = (e^r)^t = e^(rt)

So to answer your question: providing a > 0, it does not matter what base exponential we use, because it's equivalent to some exponential in base e. And e's prominence in growth modeling is not just because of some silly convention, but because functions that are exponential in e are amazingly easy to deal with when doing anything involving calculus.

Exponential functions with base e also come flying out of our asses when we do anything involving differential equations. In fact, the phrase "differential equations" comes to us (slightly bastardized) from the ancient Sumerian holy book e-cronomicon. The phrase means "a diarrhea of e".

-Lemmy

[Chaerophon]

(2) You can tell math majors who are not destined to become mathematicians by looking at those who, in their senior year of undergraduate studies, persist in pronouncing "Euler" so that it rhymes with "ruler."

-Lemmy
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Math majors become mathematicians? I thought they all went into economics!

[Doc]

Not if you buy in quantities larger than grams and smaller than kilograms.
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I am shocked, shocked I tell you!

I have always found it was easier to deal with lids. :whistling:

[LemmingofGlory]

Math majors become mathematicians?&nbsp; I thought they all went into economics!

They can become mathematicians, but they first must fail the prerequisite sanity examinations. From my own observations, the scruffier mathematicians tend to be pure mathematicians while the tidy ones are applied. YMMV.

-Lemmy