Here are more comments on Jotting #72.
Joe
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Subject: re: Joe's Jottings #72 - No Napping [00003-37808]
Author: RICK TINKER at HP-USA,om1
Date: 5/12/97 5:48 AM
Joe,
A very timely jotting (#72) - I read it between sessions at a week long
conference in Orlando - I can confirm for you, that there were speakers
that were driving me to Mickey (i.e. wanted to leave and go to the Magic
Kingdom as a better use of my time) and then there were those that made me
think that HP got it's money's worth out of the conference fee.
Despite my choosing a couple of sessions that were perhaps not right for
me, I learning something in one of them because the speaker used all of
the right tricks to keep me interested and alert. In another session, I
wanted to get a lot out of it, and the information being presented was all
good -- new information for me, but the speaker was so dry that I fought
sleep most of the session and thus learned very little (need to go read
the presentation handouts several times to get the information now...)
One tidbit I recommend adding to the use of humor is, if you can't control
WHEN your presentation time is, and you end up presenting just before
lunch, or as the last speaker of the day, or in opposition to a more
popular presentation that you can hear through the conference hall walls,
etc., then use that to your advantage: generate some jokes ABOUT your
presentation timeslot and show your appreciation for the audiences'
attention when it may be at a hard time for them to give it. I had one
presenter a year or so ago that mentioned food items at random times
during his presentation because he was the last presenter before a large
dinner and thought it would be fun to see who salivated and who didn't!
("So when we enumerate the registry, we get Apple Pie... oh, I mean we get
a list of...")
Regards,
Rick Tinker
AGO Technology Solutions Lab
========================================================
(The following is a conversation between Alan Falk and James
Carrington. I distributed Alan's original comment before, but I've
included a small part of it again so that the full discussion is all
in one place.)
-----------------------------------------------------------
...
Last:
while everyone seems to love the concave-upward swoopy-line curves
that show growth, there's just one thing wrong with them: you can't
compare two curved lines very well in your head, no matter how much
you think you can, and one way or the other, YOU CAN'T EXTRAPOLATE A
CURVED LINE. Growth should ONLY be plotted on semi-log scales:
ratios up the side and years, weeks, or whatever, across the bottom
(ordinate and abscissa to those of you who took your lessons in the
60s).... When you do that, three things happen: 1) You can
extrapolate the lines, because constant growth rate shows up as a
STRAIGHT LINE, 2) slopes of straight lines can be compared more
easily, and 3) you get to wean yourself off the swoopy-curved lines.
Thanks for listening!
Alan Falk
HP ESY Business Development, Cupertino
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(James' reply:)
Subject: reply to jotting #27
Author: JAMES H. CARRINGTON at HP-Chelmsford,om1 Date: 5/12/97
9:14 AM
While I read all of Joe's jottings and replies with great interest, I
was taken quite aback by the assertion laid out in your (Alan's) reply
regarding the comparison of linear and nonlinear data.
First, I was wondering where you came up with the notion that you
cannot extrapolate a curved line (more properly, a curve). Since the
very idea of plotting nonlinear functions on a linear Cartesian
quadrant involves extrapolation (projecting) and interpolation of
non-empiracle data points, it would seem that the human mind can in
fact comprehend the concept of nonlinear functions being presented in
a linear format. Imagine, for example, an engineer attempting to
determine the period of a sinusoidal waveform if the y-axis were
presented on a logarithmic scale. Given two waveforms of identical
amplitude but different periods, how would one ever compare the
nonlinear aspect of the two functions if they were presented in a
nonlinear format resulting in two straight lines? (Try,for example,
presenting a bell curve as a straight line and see how long you can
hold on to your audience) In this case, presentation of the data on a
linear plot is necessary in order to accuratly compare the two
functions. Therefore, it would seem to follow that mentally comparing
nonlinear functions on a linear plot would make a lot more sense
(especially to those not well versed in the calculus) in certain
applications.
Second, the reason for a logarithmic scale is not to turn
"concave-upward swoopy-line curves" into straight lines. It is to
present and compare an extremely wide range of values that are the
result of nonlinear, non-trigonometric functions. The fact that
logarithmic functions appear as straight lines on a logarithmic scales
is more of a byproduct than by design. Granted, presenting a
asymptotic function on a logarithmic scale may be easier to comprehend
as an extrapolated datum gets further from the origin. But since when
is growth representative of a regular (linear or nonlinear) function?
If you really need to present growth as more of a linear function, try
showing it as percent growth. Five percent growth across five years
will show up as a straight line on a linear scale without confusing a
business client with no trigonometry background.
James Carrington
HP- CERJAC Telecom Operation
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(Alan's response:)
Guilty, as charged, in some ways, and not-guilty in others. Again,
some of this usually turns into a religious argument, which I'll try
to avoid.
When I was a product marketing engineer at a now-non-existent division
of HP, I was faced with several problems [understatement, eh?], one of
which was to price products across a wide range of potential order
volumes. At the same time, I needed to keep the products profitable.
I discovered that if you plotted price on a vertical log scale and
quantity on a horizontal log scale, a funny thing happened: No matter
what I plotted, from jelly beans to automobiles, it started to appear
that the slope was negative, but all the slopes were about the same.
That was about 17-17 years ago, so most of the details escape me, now,
but the gist of it was that, it seemed that no matter what you put a
price on, if you bought enough of them, the hundredth one cost about
the same percentage less than the first one. Houses, automobiles,
jellybeans, light-emitting-diodes.
Nobody cared, and my work was tossed out the door when I left the
division.
Similarly, a friend of mine at RCA's Solid State Division in
Somerville, NJ, was a kind of radical guy. As a result, while his
product lines did well, he didn't have a lot of friends in management.
To "reward him" for his outlandish views, he was given responsibility
for one of the least profitable product lines. It had a negative
variance to standard cost of about $20-30K/month (pretty big for us,
back in the early 70s, and there was essentially zero yield to the
premium product selections. The month-to-month variance in yield made
it impossible for marketing to sell any premium product on a regular
basis.
After about a year or two, he turned the line around. Yield was so
high in the premium product category, that all of the current customer
commitments had to be downgrades of the premium product, which really
annoyed marketing. Variance to standard was about $25-40K/month, in
the positive direction.
What had he done differently? He'd graphed things on paper that made
them straight lines. It turned out that many semiconductor
characteristics can get a linear plot on "extreme-value" paper. Beta,
or gain of a distribution of transistors, is extreme-value
distributed. [actually 1/IB, the reciprocal of base current at a
given collector current. Beta has no linear plot of distribution I
could ever find, but I'm an engineer by training, not a
mathematician!]
Whenever the marketing or manufacturing folks graphed things, they
ended up with curved lines, and tried to extrapolate them. Yes, you
CAN extrapolate a curved line, but only if you know the function that
drives it. If you know the function that drives it, I'd [religious
issue!] really like to know what the value is of graphing it on
anything other than the paper that transforms the function into a line
that can be extrapolated with a straightedge.
You see, [dangerous way to put it, eh?] your mention of "(Try,for
example, presenting a bell curve as a straight line and see how long
you can hold on to your audience)" is exactly the point! If you
transform the "bell curve" onto the right kind of paper, it CAN BE
[sorry for shouting] a straight line. My friend's graphs related to
extreme-value curves which, at first glance, look like leptokurtic
bell-curves (or whatever the kind is that leans the other way,
too...).
The real issue is that people, on average, have been trained [taught]
to look at things in simple, comfortable ways, and even if a new tool
is fundamentally simpler, the human will take the approach of fitting
the new tool into their consciousness as a "variation of the old
tool", and steadfastly refuse to use the new tool.
To wit: yes, log scales DO compress a wide range of data into the
space of one sheet of paper. What a nice benefit.
But that's not the reason for using 'em!!!! If I have a product line
growing at 15% per year on a base of $1Billion a year, comparing it to
a competitor growing at 25% per year on a $300Million per year base
may or may not be easy to do on standard [linear-linear] paper. But
it's one SNAP to figure out EXACTLY when the competitor will overtake
you [assuming both growth rates stay the same] when it's done on the
OTHER kind of paper (semilog).
One of my favorite quotes of a manager back there was, "Well, sure,
that extreme-value probability stuff is fine, but the regular graphs
are ok: Half a loaf is better than none." His point: if you have a
"fairly workable tool", you don't have a big reason to replace it.
It took me a few years to come up with the appropriate retort:
"Half a loaf may be better than none, but half a BRIDGE is nothing."
i.e., if the right tool can give you more exact answers or easier to
predict events, etc., and you choose to not use the new tool, you are
a victim of the process called "Believing is seeing." No, I didn't
say it wrong: "Seeing is believing" almost never happens. People
never see things until they believe 'em. If you didn't believe that
regraphing that "swoopy curve" is better than using those tools you're
so comfortable with (and afraid of losing your audience, rather than
having to get THEM to believe along with you...), you'll never use the
new tools, or believe in them.
The part that bugs me, is that I BELIEVE that if more people at HP saw
the same facts in a [oh-oh, bad terminology....] more nonlinear way
[ironic, since the lines would be straighter], we'd do better as a
company.
But, as I said before, and will say again, it's my soapbox topic and
my windmill to tilt at. I appreciate your reply, and thanks for the
conversation.
+af
ps.
What if that engineer were troubled by the fact that the "sinusoidal"
curves didn't QUITE look sinusoidal, but had some strange-looking
peaks near the tops and bottoms. Would they say "well, it's close to
a sinusoidal waveform" and let it go at that? Perhaps if they plotted
the data on some nonlinear paper, they'd discover that y=log(sin x)
produced an exactly sinusoidal waveform, and some new discovery would
come out of it? Nah, never happen.
pps.
Volumetric flow of water through river channels is extreme-value
distributed. With the right kind of paper, you can easily see if your
house is above the 20-year, 50-year, 100-year or 500-year flood level.
Nothing else is as accurate.
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(And James' reply to that:)
It seems somehow that we have shifted gears. You did bring up many
valid points that I agree with and it seems that your reply was in
complete concurrence with the allusion of my reply which was 'the
right tool for the job'.
As I said, there are certain instances where presentation of nonlinear
data in nonlinear formats are appropriate and solid state electronics
is a wonderful example! Indeed, I can think of many examples that are
even more convoluted. For instance, the human average hearing response
Decibels Sound Pressure Level (dBspl) reference level is referred to
as 0 dBhl (0 decibel hearing level) and on an +x Cartesian plot (dBhl
on the y axis and frequency on the x axis) statistically perfect
hearing is presented as a straight line along the x axis. In
actuality, there is approximately 7 dBspl difference between 0 dBhl at
250Hz and 0 dBhl at 1KHz. So they are using a linear plot to display a
frequency dependent power function. This presentation, which gives a
straight line reference, is an example of the right tool for the job.
Would an engineer comparing two sinusoidal wave forms be interested in
plotting out the one with the spurious emissions on a nonlinear graph?
Probably not. A more likely case would be to perform a spectral
analysis, typically a linear representation of power versus frequency,
but many times (as in solid state electronics) a linear representation
of a logarithmic function (power) versus a logarithmic representation
of a linear function (frequency)! The right tool for the job.
A bell curve can be shown as a straight line, but isn't kind of hard
to demonstrate irregular distribution using a straight line? The right
tool for the job.
My initial reply had nothing whatsoever to do with whether or not a
logarithmic plot of growth versus time is the right tool for the job,
but rather the implication that the human mind was incapable of
comparing and extrapolating data in a linear representation of a
logarithmic function, to which you seem to have conceded to the
affirmative.
Straight lines never exist in this world however, except in
theoretical models. A torque and horsepower curve, whether presented
in a logarithmic or a linear plot, will still not be a straight line.
Which brings me, in closing, to one of my favorite sayings
"forever forward, never straight"
JHC
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