On 3/18/2007 9:59:03 PM, Tom_Gutman wrote:
>>"While they have the same dimensions (none)" is not true; they havedimension 1.<<
== Dimension one means no dimensions. The dimensions of a quantity are the various base dimensions raised to appropriate powers. Zero powers are elided. When all basic dimensions cancel out (all the exponents work out to
zero) the quantity is dimensionless, it has no dimensions. In contexts where this is unacceptable (say a table where there is a column for dimensions that is not allowed to be blank) the numer one is used, presumably on the basis that anything, even if not a number, raised to the zeroth power is one. Factors of one can be added or deleted from any product and are completely irrelevant. The concept of "dimension one" is meaningless -- it means something is dimensionless, just a pure number.
I disagree. Having a dimension is the thing that distinguishes a quantity from a pure number and makes sense of giving it a unit.
>>Based on this, it's not too unreasonable to suggest that Mathcad should provide an automated facility for tracking, and displaying, quantities.<<
== Without some specification of what that means, and how (logically) this is to be done, it is meaningless.
Correct; without some specification it is meaningless. And this is relevant how?
What's meaningless about "Mathcad should provide an automated facility for tracking, and displaying, quantities.", given that I'd provided in-context reference to the SI Brochure? Taking the thread as a whole, I have referenced the VIM, the ISO-31 and the SI Brochure to provide definitions of the various terms (ie, quantity, dimension), which any reasonably competent requirements engineer should be able to convert from a high-level user need to a system requirement specification.
I have no intention of telling any product engineer how they should logically do anything. Why impose the limits of my imagination on them? If they say it can't
be done, *then* I might tell them how, but not before.
== Just a general pious hope.
You mean like your general pious hope that I'll know what you mean by 'metaphorical' angle without a specification 🙂
== I know what needs to be done for angles, and have worked out how it works.
Uh huh. If you manage to properly define an angle, I might have a degree more confidence in that statement.
== I have no idea what it would mean for moles,
That's OK, we'll ask a domain expert.
== where three moles of oxygen might, under various physical conditions, turn into two moles of ozone or six moles of atomic oxygen.
One possible solution is to create a quantity 'number of oxygen atoms' and declare it to be a base quantity. Now define a molecule (I presume that's what you meant) of oxygen as having an oxygen count of 2. A quantity equation will determine the actual transformation , and balance the number of oxygen atoms.
That's one of the underlying reasons why I've asked for a general user capability to add base quantities.
>>++ the relationship "one hertz is equal to two � radians per second" is well defined and is either true or not.
++ True meaning for all values, not just coincidentally for particular isolated values.
++ So, is it true or is it not true?
-- It is false.<<
== So all these EEs who take a 10hz signal and make it 20πradians per second are wrong, at least if SI is accepted as correct.
== That may well be true. They are not wrong in making the conversion, they just know that SI is really wrong and ignore it, doing what they know is right, regardless of what SI says.
I have my doubts that most of 'all these EEs' have ever considered the rights and wrongs of the SI. I'll bet they've been told something amounting to '1 hertz = 1 cycle per second' and 'a cycle is a unit of angle such that 1 cycle == 2 π radian', and never put a moments thought into what the SI and ISO actually say.
As, most of the time, they manually carry out unit manipulation, they keep mental track of the quantities involved and write down the correct units for angles. However, because they are unaware of the actual definitions and do not understand the limitations of dimensional analysis[*], they have problems when SI-compliant dimensional
analysis tools don't give the answer they are expecting.
[*] or haven't stepped back far enough from the problem to think about it.
>>Replace 'should' with 'could'. (+2)�=4 and (-2)�=4, why 'should' the square root of 4 map to -2?<<
== What does that have to do with the price of tea in China? The term "square root" is not well defined, and it is well known that it is not well defined. At various times various authors have used the expressions ?x and x� as expressly different.
The term "square root" seems to be sufficiently well defined that many mathematicians, physicists, and engineers (including the EE subtype) are happy to use it and know that 4 has two "square roots". They also can (and do) make use of any problem-related constraints to identify which "square root" is applicable to their problem. http://mathworld.wolfram.com/SquareRoot.html
So if it's good enough for general usage, then it's good enough for me to use it as an analogy to point out that merely saying that "angle is defined by length/length" does not imply that all ratios of length/length are angles. You can add contextual material to identify them as such, but without this information, there is no immediate justification for making that identity.
>>A 'metaphoric' angle?
== I've been using this term for years now. You just noticed?
How unobservant of me.
But I'm a little puzzled. If you've been using it for years, then I would expect that you have come up with a formal definition of a metaphoric angle by now.
>> ... Can I use a protractor to measure them?<<
== No, you cannot use a protractor to measure them (at least, not a real protractor, possibly a metaphoric protractor).
A 'metaphorical protractor'. Is that a complex device or purely imaginary (given that it's not real)?
== But never fear. Just go find the nearest EE -- he will have no trouble measuring those angles.
Not until you can provide a formal definition that allows him (or her) to be sure they're measuring the thing you mean.