mmar@sphinx.UChicago.UUCP (Mitchell Marks) (12/25/85)
Subject: multiplier legend on dials & meters
Newsgroups: misc
Distribution: net
[Naw, I don't really believe there's a line-eater.] really believe there's a line-eater.
Can anyone explain the rationale for the explanatory legend that goes on a
dial or meter when the actual numbers shown represent some fixed multiple
of a standard unit? It seems to me that they often have it exactly
backwards.
I'll use a tachometer in a car as the example, though you can see this
lots of places. The numbers printed on the dial are just 1, 2, 3, 4, etc,,
to indicate 1000 RPM, 2000 RPM, 3000 RPM, etc. (Some of them may show the
number in full, but no matter: we're considering the case where they
abbreviate.) Then somewhere on or near the dial you'll find a notation
like this:
RPM X 1000
But that's not right! Suppose the dial says 3. Then
RPM X 1000 = 3
RPM = 3/1000 = .003
In other words, your engine is turning over at .003 RPM. Well, that's
obviously too low (by a factor of a million). Let's work it the other way.
Your engine is turning over at 3000 RPM, what should the dial show?
RPM = 3000
RPM = 3 X 1000
RPM/1000 = 3
That is, when the dial shows 3 to mean 3000 RPM, the 3 indicates the actual
rotational frequency of your engine (in RPM) *divided* by 1000, not *times*
1000. (I should have said earlier that I've been writing RPM not for the
unit, but as a variable meaning "rotational speed of the engine measured in
RPM", which seems the sense involved in the notation RPM X 1000.)
The alternative I seem to be supporting above is that the notation should
be instead
RPM / 1000
but there would also be nothing wrong with
1000 RPM(s)
which works quite differently from RPM X 1000. The legend 1000 RPM would
mean "this dial shows the rotational speed of the engine, measured in units
of 1000 RPM".
Okay, okay, so everybody does it that way. But will you explain clearly
where I've gone wrong, if they're right?
--
-- Mitch Marks @ UChicago
...ihnp4!gargoyle!sphinx!mmardarrell@sdcsvax.UUCP (Darrell Long) (12/28/85)
In article <1471@sphinx.UChicago.UUCP> mmar@sphinx.UChicago.UUCP (Mitchell Marks) writes: > > >Can anyone explain the rationale for the explanatory legend that goes on a >dial or meter when the actual numbers shown represent some fixed multiple >of a standard unit? It seems to me that they often have it exactly >The alternative I seem to be supporting above is that the notation should >be instead > > RPM / 1000 > > >which works quite differently from RPM X 1000. The legend 1000 RPM would >mean "this dial shows the rotational speed of the engine, measured in units >of 1000 RPM". > >Okay, okay, so everybody does it that way. But will you explain clearly >where I've gone wrong, if they're right? > >-- > > -- Mitch Marks @ UChicago > ...ihnp4!gargoyle!sphinx!mmar Most people aren't clever enough to divide, or alternatively they do not think like mathematicians. I have asked a few people, and the notation that you suggest confuses them. -- Darrell Long Department of Electrical Engineering and Computer Science University of California, San Diego UUCP: sdcsvax!darrell ARPA: darrell@sdcsvax
mauney@ncsu.UUCP (Jon Mauney) (12/30/85)
> Can anyone explain the rationale for the explanatory legend that goes on a > dial or meter when the actual numbers shown represent some fixed multiple > of a standard unit? It seems to me that they often have it exactly > backwards. > ... > Suppose the dial says 3. Then > > RPM X 1000 = 3 > RPM = 3/1000 = .003 You are putting the dial reading in the wrong place. It should read 3 RPM X 1000 or 3000 rpm. Or to put it another way, the units are (RPM X 1000) which is the same as (1000 RPM) {because multiplication is commutative, hooray for new math}. Your big mistake, however, is that you actually tried to think about something that appears on a mass-market product. That is not how it was intended to be used. -- Jon Mauney, mcnc!ncsu!mauney North Carolina State University "It's so simple, so very simple, that only a child can do it."
throopw@dg_rtp.UUCP (Wayne Throop) (12/30/85)
[ The discussion so far: Mitch Marks (sphinx!mmar) wonders why
legends on meters are, for example "RPM X 1000" rather than "RPM /
1000", since to get to a meter reading from RPM, you divide, not
multiply. Darrell Long (darrell@sdcsvax) conjectures that most
folks don't think like mathematicians, and so the proposed that an
"RPM / 1000" legend would confuse them. ]
Use of "/" is indeed confusing, but not entirely because people don't
think like mathematicians.
The legend is giving the units in which the dial is marked, *not* a
procedure for getting from RPM to meter reading. Since it is marked in
thousands of RPM, it seems quite straightforward to have the legend be
"RPM X 1000". So "X" is formally correct.
Division is indeed how to get from RPM to a meter reading, but most
folks want to go from a meter reading to RPM. Thus, most folks feel
confusion when division is used... *multiplication* is how you get from
where you are (meter reading in "hand") to where you want to be (current
RPM in "hand"). So "X" is procedurally correct (even if notationally
perverse when used procedurally).
To get a procedural legend, the notation might be changed to "X 1000 ->
RPM", or some such, but I repeat that the legend is *not* *procedural*,
and I suspect that taking it to be procedural is the source of the
original question.
Note also that Mark's suggestion of "1000 RPM" as the legend is
*identical* in meaning to the current "RPM X 1000". A breifer (and thus
maybe better) legend might be "KRPM" (or "K RPM"), but I suppose all the
overly-compuliterate would then think the dial was marked in units of
1024 RPM...
--
Wayne Throop at Data General, RTP, NC
<the-known-world>!mcnc!rti-sel!dg_rtp!throopw