Friday, March 16, 2007

Making musical sense by email, part 2

As I promised, here's the first installment in a dialog between Greg Sandow and me on the future of classical music. You might want to start by reading Greg's essay "The short version"; then read my first email to Greg (below). Drew McManus was included in this dialog, although the emails you'll see all involve only Greg and me.


Greg,

I've been following your thoughts for a while, and I've been
discussing a few ideas they've provoked with Drew McManus,
now that he and I have collaborated on a column
(http://pegasuscom.com/aar/model7.html) and associated
computer model.

I'd like to share those ideas with you and see what you
think; perhaps they'll be of use, or perhaps you'll be able
to educate me and help me refine my thinking. I've copied
Drew on this, in case he has some comments he'd like to
make. As you'll note, this email is a bit lengthy; I hope
it's useful to you.

By the way, I'll be showing some text-mode graphics below in
an attempt to make this an easier email to read. Hopefully
you can view this email using a non-proportional font such
as Courier so that those graphs make sense. If that's a
problem, let me know, and I'll create this in another
format.

One thing that caught my attention was your claim of aging
audiences. In
http://www.artsjournal.com/sandow/2006/11/important_data.html,
you note that, among other facts, the average audience age
went from 45 in 1992 to 49 in 2002. You think about the
potential causes and implications of such a development.

One way to think of such a problem is to see if we can
"operationalize" it: can we generate an operational
description of the events that we conjecture are playing out
in the real world, is that operational description similar
structurally to the real problem, and is that operational
description capable of generating similar behavior? (See
the link near the end of
http://facilitatedsystems.com/weblog/2007/01/systems-language-for-business.html
for more on operational thinking.)

In simpler and more specific words, can I create a computer
model that captures your hypotheses, and does that model
behave as your data shows? Success doesn't mean I've proven
anything, but failure might indicate a need for modified
hypotheses. Enough success, combined with a bit of
triangulation, can strengthen our belief in those
hypotheses.

I like to start with really simple models, adding complexity
only when it becomes necessary. Often we can learn the most
from those simple models.

Here's a simple model of an "aging chain" that might
represent classical music audiences.

..+- . . .--...m.-
-+*.+.. +------------------+ ---% +-m++m-
.-.+m*++ | | . +###+#*#m.-.
-mm#*#%#. +--+ | Aging Chain of | +--+ --.#+mm%###++
+.#%#*+. =====>| A|====>+ +=====>| B|=====>.#*%-##+#m.-
.+%m*+++ . +--+ | Concert-Goers | +--+ ..m+%###m##..
..%-+% . | | . --++m+%+--.
..+. +--------+---------+ ..+-..%+ .
\ . +-.-
\
\
V

Average
Age

The "aging chain" in the middle is a series of "stocks," one
for each decade of age (arbitrarily twenties through
sixties; I don't think the dynamics change much if we add or
subtract a decade at one end or the other). People move
through those stocks, taking ten years to move from one to
the other. I've aggregated those stocks into one mega-stock
to simplify the graphics; if I had drawn the entire picture,
you'd have seen five rectangles, connected in a chain by
flows (pipes), instead of that one bigger rectangle.

The "clouds" at the left and right simply mean we don't care
where those people come from or where they go, at least for
the sake of understanding concert audiences; that's outside
the purview of this model. There are two flows, shown here
as valves called "A" and "B" on pipes that flow from one
stock (or cloud) to another. Flow A represents the number
of new concert-goers per year, and flow B represents the
number of people leaving the concert-going world each year.
In this simple model, 50-year-olds don't all of a sudden
decide to become concert-goers, and 30-year-olds don't all
of a sudden give up on classical music. Those are
constraints we can lift later, if we want to.

Now it's easy to talk about what changes the number of
concert-goers: if A is greater than B, you get more
concert-goers, while if B is greater than A, you get fewer.
If A = B, the aggregate audience size stays static.

I've shown "Average Age" as a statistic we can calculate to
describe concert-goers, the same as we can describe their
total number.

I created a computer simulation of that model. I set the
initial population of concert-goers to 1 million, spread
evenly in age across the five decades (stocks) I modeled.
If we have 20,000 new concert-goers each year, we'll exactly
replace the number of concert-goers who depart each year,
and the number of concert-goers will remain constant.

Because you hypothesized that young people had stopped
coming to concerts, I tested the model by running it over a
200-year period with 20,000 new concert-goers in the first
10 years and then half that thereafter. Would that
replicate the data you were quoting?

Here's the graph of the number of new concert-goers per
year:

20000 AAAA-------------+----------------+----------------+---------------++
+ + New Concert-Goers per year A +
| |
| |
| |
15000 ++ ++
| |
| |
| |
| |
10000 ++ AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
| |
| |
| |
| |
5000 ++ ++
| |
| |
| |
+ + + + +
0 ++---------------+----------------+----------------+---------------++
0 50 100 150 200

Year

It stays constant at 20,000 per year until year 10,
whereupon it drops to 10,000 per year throughout the rest of
the 200 year time horizon of this simulation.

Here's a graph of the total concert-going population from
that model:

1e+006 AAAAA------------+----------------+---------------+---------------++
+ AAA + + + Total A +
| AA |
| AA |
800000 ++ AAA ++
| AAA |
| AAA |
| AAA |
600000 ++ AAAA ++
| AAAAAAA |
| AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
| |
400000 ++ ++
| |
| |
| |
200000 ++ ++
| |
| |
+ + + + +
0 ++---------------+----------------+---------------+---------------++
0 50 100 150 200

As you can see, the number of concert-goers stays at 1
million for 10 years and then begins a steady decline,
stabilizing at 500,000 at about year 80.

Here's the average age:

48 ++---------------+----------------+-----------------+---------------++
+ AA + + Average Age A +
| AA AAA |
47.5 ++ A AA ++
| AA AA |
| A AA |
| A AA |
47 ++ A A ++
| A A |
| A A |
46.5 ++ A AA ++
| A AA |
| A AA |
46 ++ A AA ++
| A AA |
| A AA |
| A AA |
45.5 ++ A AAA ++
| AAAA |
+ A + + AAAAAA + +
45 AAAA-------------+----------------+------AAAAAAAAAAAAAAAAAAAAAAAAAAAAA
0 50 100 150 200

Note that the vertical axis starts at 45, not 0.

At first glance, this seems intriguing. Audience population
is declining and average age increases, at least for a bit.
Then, under these assumptions, average audience age drops
back to the same 45 years old. Could that be? Is it
possible that we're just on the front end of a declining
audience size, and audience age will correct itself
naturally?

There's something else a bit off here, though. In "Where we
stand (2)," you provide a graph that indicates the mode of
age has gone up about a decade from 1992 to 2002, consistent
with your cohort theory, and you note elsewhere that the
average age rose by about 4 years. This model only shows a
2.8 year increase in average age, and that's over about 30,
not 10, years.

What if the decline in the number of newcomers was a more
gradual and continuous decline? Here's an
exponentially-declining number of new concert-goers each
year, starting at 20,000 and declining to half that in 69
years:

20000 AA---------------+----------------+----------------+---------------++
+AA + New Concert-Goers per year A +
| AA |
| AA |
| AAA |
15000 ++ AAA ++
| AAA |
| AAA |
| AAAA |
| AAAA |
10000 ++ AAAA ++
| AAAA |
| AAAAA |
| AAAAA |
| AAAAAAA |
5000 ++ AAAAAAAA ++
| AAAAAAAAA |
| AAAAAAAAA
| |
+ + + + +
0 ++---------------+----------------+----------------+---------------++
0 50 100 150 200

Since the exponential doesn't drop as fast, you might expect
the number of total concert-goers to drop more slowly; since
the number of new concert-goers continues to drop forever,
you might expect the total concert-going population to
continue to decline. You'd be right:

1e+006 AAAAAA-----------+----------------+---------------+---------------++
+ AAAA + + + Total A +
| AAAA |
| AAA |
800000 ++ AAA ++
| AAAA |
| AAA |
| AAA |
600000 ++ AAAA ++
| AAAA |
| AAAAA |
| AAAAA |
400000 ++ AAAAA ++
| AAAAAA |
| AAAAAA |
| AAAAAAAA |
200000 ++ AAAAAAA
| |
| |
+ + + + +
0 ++---------------+----------------+---------------+---------------++
0 50 100 150 200

Remember that the drop-off starts in the first year in this
experiment, not the tenth year.

What about the average age of concert-goers? Since the
decline in new, young concert-goers continues forever, you
might expect the age boost to last forever. Since the
decline is less drastic, you might expect the age boost to
be less drastic. Let's see:

47.5 ++---------------+----------------+-----------------+---------------++
+ + + Average Age A +
| |
| AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
47 ++ AAAAAAAAAA ++
| AAAAA |
| AAA |
| AA |
46.5 ++ AA ++
| AAA |
| AA |
| AA |
46 ++ A ++
| A |
| A |
| A |
45.5 ++ AA ++
| AA |
| AA |
+ AA + + + +
45 AAA--------------+----------------+-----------------+---------------++
0 50 100 150 200

You'd be right in both cases, although the difference in the
peak average age is miniscule: 47.0971 vs. 47.7867 years.

So neither explanation seems to account for the drastic
aging of the concert-going audience as reported in the data.

What if we take a drastic approach and cut off new
concert-goers totally after 10 years? Under those
conditions, here is the total concert-going audience:

1e+006 *****------------+----------------+---------------+---------------++
+ * + + + Total ****** +
900000 ++ * ++
| * |
800000 ++ ** ++
| ** |
700000 ++ ** ++
| * |
600000 ++ * ++
| * |
500000 ++ * ++
| * |
400000 ++ * ++
| * |
300000 ++ ** ++
| ** |
200000 ++ *** ++
| *** |
100000 ++ **** ++
+ + ******* + + +
0 ++---------------+-------------*************************************
0 50 100 150 200

As you can see, the concert-going public drops to nothing
(technically, the model shows fewer than 10,000 people by
year 108); it is already down to 494,703 by year 36 (26
years after young people stopped becoming concert-goers).

What about the average age?

64 ++----------------+----------------+-----------------+----------------++
+ + + Average Age'*********
62 ++ ****************** ++
| ********** |
60 ++ ******* ++
| ***** |
58 ++ **** ++
| *** |
56 ++ ** ++
| ** |
54 ++ *** ++
| ** |
52 ++ ** ++
| ** |
50 ++ ** ++
| ** |
48 ++ ** ++
| ** |
46 ++ ** ++
***** + + + +
44 ++----------------+----------------+-----------------+----------------++
0 50 100 150 200

Finally, we're getting drastic changes in average ages.
According to
http://www.artsjournal.com/sandow/2006/11/important_data.html,
the age went from 45 in 1992 to 49 in 2002. In this model,
it went from 45 in year 10 to 48.75 in year 20. That's not
a bad match, and the model structure seems reasonable.

What's scary is that's a model of /no/ new concert-goers at
all! In other words, the data you're showing /could/ be
consistent with a sudden change to essentially no new
audience members forever. You came close to this same
conclusion in today's "The short version."

Now this model doesn't prove there are no new concert-goers.
There may be other ways to get similar results. For
example, perhaps it's not true that "once a concert-goer,
always a concert-goer." Perhaps younger people are starting
to attend concerts and then giving up in droves. Perhaps
orchestra marketing is drawing in baby boomers who have
never attended concerts. Perhaps multiple causes are at
work. Perhaps you have other conjectures. Any of these
hypotheses could be tested in such a model to see if they
are consistent with the reality you've been observing.

What I think is interesting is that a relatively simple
model can help shed light on the mental models we create to
explain the problems we face. In this case, the first,
simple approach suggests things may be as you suggest, with
the caution that they /may/ be even more serious than you
indicate. I'm curious in your thoughts on all this. I do
apologize for the length of this email; I don't yet know how
to walk someone through a model such as this without taking
a little bit of time.

Drew, did I miss anything fundamental?

I'll be expanding on related ideas using a different model
in a column I'm doing for Drew shortly. You can see some of
the blog postings I've made about music at
http://preview.tinyurl.com/2consf. In particular,
http://facilitatedsystems.com/weblog/2006/11/making-sense-with-numbers.html
was a very popular posting about the recent Knight report.
Drew and I have exchanged other thoughts sparked by your
columns, but this note is long enough as it is.

Thank you for your time,

Bill


Think about what your response would have been, had you received such a message. Then come back next week to see Greg's response.

Postscript: When I initially posted this, the fixed-width email section overlapped Blogger's sidebar material. I reformatted the width of the email but left the text-mode graphics in the original size.

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