### 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.

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.

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.

Labels: classical music business, making sense, simulation

## 1 Comments:

To make it easier for you to find the links in the original email, here they are again in clickable form:

* http://pegasuscom.com/aar/model7.html

* http://www.artsjournal.com/sandow/2006/11/important_data.html

* http://facilitatedsystems.com/weblog/2007/01/systems-language-for-business.html

* http://preview.tinyurl.com/2consf

* http://facilitatedsystems.com/weblog/2006/11/making-sense-with-numbers.html

Post a Comment

<< Home