The Derivative in the Real World

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Alex leus
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Joined: Fri Mar 29, 2002 3:39 am

The Derivative in the Real World

Post by Alex leus »

About 1 year ago, I think we had a detailed discussion on, if the derivative exists in the real world. The conconculsion was NO, everything is described as an accumulation. Would someone refer me to where I can find this dialog. I have a new computer and I lost my references.

[ Host's Note: As always the list is archived with a search feature at

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Thank you in advance,
Alex
leusa@tds.net
Marc Abrams
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The Derivative in the Real World

Post by Marc Abrams »

Alex,

Check out Dr. Jay W. Forrester's argument in _Principles of Systems_ if you
can gat your hands on a copy, it's in there.

[ Host's Note this is still available from Pegasus
http://www.pegasuscom.com/ ]

Marc
From: ""Marc Abrams"" <mabrams@nvbb.net>
Tom Fiddaman
Senior Member
Posts: 55
Joined: Fri Mar 29, 2002 3:39 am

The Derivative in the Real World

Post by Tom Fiddaman »

>I still say that mountain sides (i.e. slopes) are examples of derivatives
>with respect to distance in the real world.

I think this suffers from the same problem as the idea of time derivatives
in Forester's argument: how would you measure the slope of a mountainside,
except by integrating (i.e. measuring the rise and run over some finite
interval)? The problem is not that a mountain doesn't have a slope, but
that perception of slope is not independent of scale, and becomes uselessly
noisy on fine scales.

Because we can see in all directions (barring heavy fog) it's generally
easy to estimate the slope of one's locale. Not so with temporal slopes,
where we can only see backwards and must trade responsiveness to
short-duration changes in trend against volatility of the measurement.

Tom


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Tom Fiddaman
Ventana Systems, Inc. http://www.vensim.com
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Jim Thompson
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The Derivative in the Real World

Post by Jim Thompson »

I take Weaver to be saying that a derivative is part of a mental model and that a mountain slope is an observable manifestation of a meaning-making concept called derivative. I take Fiddaman to be saying that the usefulness of that mental construction is limited until we make some other observations and have a way to make sense of them.

We might start with the position that we can only access the real world through our senses or instrumental extensions of our senses. In other words, we can take the question of whether there is an absolute or real world off the table.

Next, I think we have to decide on just what a derivative is. To my way of thinking, a derivative is a construction of our thoughts that is used to make meaning of our experiences. That construct 'derivative' has proved so useful as a way of making sense of experience that one person passes it along to another, such as math teachers do with students.

Fiddaman observes that our ""perception of slope is not independent of scale and becomes uselessly noisy on fine scales."" I take that to mean that our mental model or computer model or physical model does not produce useful understanding of our experiences when the scale is wrong for the problem at hand. That is, I understand Fiddaman to be saying that there are practical limits on the use of derivatives as part of one's mental model and the limitation on the usefulness of derivatives can be estimated by comparing the granularity produced by the derivative to the maximum value of another construct of thought, the integral.

Fiddaman implies that we cannot experience the future now and that we can accurately recall our past experiences. As Yogi Berra said about past experience, ""You can look it up."" Or was it Casey Stengel who said that? In any case, if you have had some experience with mountains and see one some distance away from you, your organised experience can give you a sense of what that pile of earth might mean to your travels. But that mountain can only be in your future. If your mental model includes constructs -- knowledge -- of integrals and derivatives, you might make some observations and useful predictions about any mountain in your future.
Jim
From: ""Jim Thompson"" <
james.thompson@strath.ac.uk>
Ray Joseph
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The Derivative in the Real World

Post by Ray Joseph »

OK, let's see how much fun we can have:

The world has no real derivatives? The world only integrates? Derivatives
are not real because they are hard/difficult to measure. Derivatives are
not real because we always perceive the solution as an integral.
Derivatives are useless because they are a mathematical construct.

The world only integrates. Integrals are easy to use because we can all add
things up. Integrals are better tools because the integration process
smoothes out local irregularities.

Both derivatives and integrals rely on past and present values. Both are
mathematical constructs. Both are defined through a limiting process. Both
can be transformed into a different mathematical space so both transformed
operations are only algebraic.

Integration was chosen as the guiding operation of SD because it is simple.
It is by no means the only method or the only tool. The SD method of
analysis was designed to allow non-math majors to describe the dynamics of a
system without the need for fundamental mathematical concepts. This brings
a giant set of solution to the world that would otherwise have taken decades
if not centuries. We now have a tools set that can be applied by domain
experts rather than limited modeling experts. We can always make things
look more complicated and state that a tools expert is needed, but that is
not why SD was developed. SD was built for the people, keep it simple,
everything is allowed as long as the user can understand it.

The Wizard of OZ made this look terrible and showed that he was the only one
with a solution.

Ray
From: ""Ray Joseph"" <rtjoseph@ev1.net>
Bruce Skarin
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The Derivative in the Real World

Post by Bruce Skarin »

I recall this discussion from before, but Ray's 'fun' has prompted another
thought. I agree now that the statement ""the world has no real derivative""
is technically incorrect.

The last time we discussed this. I noted that the best reason to choose a
state/integral to represent action of interest is because without potential
(or space) for action there is no derivative.

A review of entropy and the second law of thermodynamics
http://www.2ndlaw.com/ is a great example of this point (Frank Lambert
provides an entertaining and simply stated explanation of the 2nd law as a
'tendency' and makes the interesting observation that life exists only as a
result of the obstruction of the 2nd law).

There is a dependency on one another, and yet it of course does work both
ways. Without the derivative there is no explanation for how the state came
into being. Of the two however, the integral does appear far easier to
grasp, measure, and represent.

The angle that Ray brings in is: ""derivatives are useless because they are a
mathematical construct."" Yet this statement is only fair if integrals are
also useless because they are a mathematical construct! ;-)

Neither seems technically correct again however because they do at lease
describe the 'perfect' world of traditional/algebraic math (there is of
course math helpful in describing the imperfect world, but that is another
discussion).

I think Ray points out a worthy reminder to us all that the 'real' world is
forever more complex than what can truly be represented mathematically or
logically. This issue becomes quite evident as we attempt to link our
macro-world models with the quantum-world.

For example, if we take the simple model of water flow from a higher tank to
a lower tank. In SD we would define the states and resulting rate of flow.
And this would be accurate enough for many applications. Yet if we wanted to
know very precisely, say the number of hydrogen atoms in the lower tank at
time 1.10x10^-1,000,000 seconds.

To model this level of detail 'accurately' we would have to move towards the
quantum-world and know every detail about 'real' system we were modeling. At
first it only seems complex, we do know do know a lot about the atomic
world. Yet, ultimately you reach a quantum-world that is more than complex,
it is downright illogical!

The conclusion perhaps is that mathematical models, as it stands today and
perhaps forever, are all fundamentally flawed, no mater how 'perfect' we
think they might be. They will never be 'real' as long as they are
incomplete in the representation of the quantum world.

This of course has nothing really to do with SD, but as enthusiasts of
understanding complexity, it is still an interesting and humbling discussion
to have. Thanks Ray!

-Bruce
From: ""Bruce Skarin"" <bruceskarin@hotmail.com>
Tom Fiddaman
Senior Member
Posts: 55
Joined: Fri Mar 29, 2002 3:39 am

The Derivative in the Real World

Post by Tom Fiddaman »

In the interest of stirring the pot, I'll make a few bold (but not really
original) assertions about derivatives:

Generally I find it pointless (though admittedly fun) to debate whether
differential or integral equations are a better mental model or description
of reality given that the models we're talking about can be described
either way. The practical point boils down to just two things: don't
confuse levels and rates, and don't connect rates to other rates. It is the
second of these principles that's really at stake here.

Forrester asserted long ago that all measurement devices available to us
report averaged rates (which are levels), not instantaneous rates. I have
yet to see a counter-example that proves him wrong. Admittedly, sometimes
our measurement devices have short time constants, so that it is useful to
treat them as if they were instantaneous. And sometimes (as with coflows)
it is convenient to connect flows to flows rather than to their common
determining levels, but I think this does not undermine the argument.

As to the more general assertion that ""nature never takes a derivative"" I
also have yet to hear a convincing counter-example, though I believe that
Ray and Bruce may be correct to suggest that one could exist, e.g. at the
quantum level (if that's what they meant). Since this theoretical problem
is remote from the practical problem of policy makers presuming that the
earth will cool off the moment energy efficiency technology improves, I'm
content to wallow in my ignorance and bumble along with my rates neatly
segregated.

>From: ""Weaver, Elise A"" <eweaver@WPI.EDU>
>That was a good answer. But then, integrals don't exist in nature either,
>because they also depend on our choice of scale.

Are you suggesting that the volume of water in a bathtub or some other
quantity we would normally think of as a stock/level/state in SD is
indeterminate at a given point in time (neglecting Heisenberg)? Or merely
that the process of integration becomes as elusive as the derivative when
you start to look at it at finer and finer scales? Or ... ?

>From: ""Jim Thompson"" <james.thompson@strath.ac.uk>
>We might start with the position that we can only access the real world
>through our senses or instrumental extensions of our senses. In other
>words, we can take the question of whether there is an absolute or real
>world off the table.

Great idea ... then we can skip the discrete/continuous debate as well.

>Fiddaman observes that our ""perception of slope is not independent of
>scale and becomes uselessly noisy on fine scales."" I take that to mean
>that our mental model or computer model or physical model does not produce
>useful understanding of our experiences when the scale is wrong for the
>problem at hand. That is, I understand Fiddaman to be saying that there
>are practical limits on the use of derivatives as part of one's mental
>model and the limitation on the usefulness of derivatives can be estimated
>by comparing the granularity produced by the derivative to the maximum
>value of another construct of thought, the integral.

Again, since SD models written as integral equations can easily be
rewritten as differential equations I'd hesitate to say that derivatives
are less useful than integrals as a mental model, though integrals work for
me personally. I'd simply suggest that, whether or not derivatives (slopes
in time) exist, we (or, more to the point, the decision makers we model)
have little if any practical ability to make direct use of them.

>Fiddaman implies that we cannot experience the future now and that we can
>accurately recall our past experiences. As Yogi Berra said about past
>experience, ""You can look it up."" Or was it Casey Stengel who said
>that? In any case, if you have had some experience with mountains and see
>one some distance away from you, your organised experience can give you a
>sense of what that pile of earth might mean to your travels. But that
>mountain can only be in your future. If your mental model includes
>constructs -- knowledge -- of integrals and derivatives, you might make
>some observations and useful predictions about any mountain in your future.

In the spirit of Forrester's caution against rate-to-rate connections, I
would merely suggest that slope, as perceived by a mountaineer wearing a
large sombrero and neck brace (""You can't look up"" in this case), is likely
to be biased towards the downhill terrain. In heavy fog, it is likely only
the recent downhill terrain that will be salient.

Tom



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Tom Fiddaman
Ventana Systems, Inc. http://www.vensim.com
PO Box 153 Tel (406) 578 2168
Wilsall MT 59086 Fax (406) 578 2254
Tom@Vensim.com http://www.sd3.info
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Weaver, Elise A
Junior Member
Posts: 5
Joined: Fri Mar 29, 2002 3:39 am

The Derivative in the Real World

Post by Weaver, Elise A »

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