C

#### Charmed

Dear Covers:

The following was posted by Mike S in another related thread. What I have outlined here is at least in part inspired by what I see being discussed in that thread.

*****************

To quote Mike,

I read an interesting article recently in Inc. Magazine about the "open book management" philosophy -- basically letting the employees see all of the business' financials and educating them on how to understand and positively influence them.

I was wondering how fellow Covers felt about this type of policy, and if you've ever done it or been in a company where it was done, etc.

**********************

Let's say you work for XYZ Inc. which had sold 100,00 units of a widget last year. To be specific, let's take Toyota. It plans to sell 300,000 Toyota Prius, gasoline electric hybrids in 2005. Let's imagine this "division" as a separate stand alone company. Or, Ford has a new hybrid the Focus Escape on the market. Let's say 100,000 hybrids will be offered for sale, next year and the following year Ford expects to sell 150,000 units.

We can think of any company, even very large companies, in this fashion and subdivide them into the smallest unit imaginable that provides a very specific "product" or "service". This new unit must be self supporting and must be profitable. GM tried this experiment with Saturn. Saturn employees even had a modified UAW contract. Needless to say, and sadly so, Saturn was unable to show a profit, even after many years. It is now absorbed into Ma GM, for financial purposes. Let's be idealistic now.

Can a division of a company that plans to sell 100,000 units, or more generally N units, be profitable? Why not?

Let us assume that each unit sells for $ y. The total revenues generated by the sale of N units will be NY. Even if the product is "differentiated" (for example different options are offered, although all units are hybrids), we can take Y as the "average" price per unit sold with N being the total number of units. With product differentiation, we have

NY = N1Y1 + N2Y2 + N3Y3 + ....... (1)

N = N1 + N2 + N3 + ...... (2)

Now, N1 units are sold at the unit price of Y1 and N2 units are sold at the unit price of Y2 and N3 units are sold at the unit price of Y3, and so on. The summations given as equations 1 and 2 can continue ad infinitum, and include all the products/services offered by any large corporation (like a GE, Ford, Walmart, HPQ, IBM, ExxonMobil, etc.)

Where do we go from here? As the mix of products changes something is obviously changing. With modern computerization, a OEM automotive company will produce a car only after the customer has "speced" the car out with a dealer. Theoretically specifically, the dealer need not carry any inventory. After some "lead time" has elapsed, the dealer is only delivering vehicle, on any given day, for which orders were received say 2 to 4 weeks ago. The manufacturer knows exactly the type of car that has been ordered including all the minutes details. I don't see why the car could not be delivered with the name of customer actually plastered on it! (Sounds a bit too far, doesn't it. I have some customers actually flash their names on their license plates!)

Anyway, where do we go from here? As demand changes and the mix of cars (or computers, or refrigerators, or printers,...) to be made at the factory changes something is changing. This something is called "chaos" or "disorder" or "entropy". The recognition of this "chaos", or "disorder", in the system is the beginning of modern quantum physics, as conceived by Max Planck, and described in his December 1900 paper. An English translation of Planck's paper is readily available in the book

Let me quote the introductory paragraph from Planck's paper (pages 301 to 314). Shamos includes a nice biographical note that provides the context and some explanatory notes as well. The following is the first paragraph on page 307.

Let me stop here. We have reached the key word, the idea of "work". We have also met the idea of "energy". Now, let's simplify this and understand what Planck is talking about in more general terms, which has wider applications, including the problem of interest to us here. We can generalize Planck's theory and arrive a very general expression for the "average" value of Y in equation 1.

Planck talks about resonators and amplitude and phase and time and vibrational energy. There are N resonators in a heated body. This is what Planck was studying back in 1900. There are N divisions in a company. This is what I want to study now in 2004. There are N products or services that are offered by each division. This is what we are interested in here. The "vibration" that Planck talks about is like the "vibrations" sensed between customer and the company. In some abstract sense there are "vibrations", amplitudes, phases, and time-averaged effects, in every problem that is governed by equations 1 and 2. This is the broad generalization of Planck's idea. Let's see what Planck offers as an explanation for what he is trying to do. He gives the following list of "numbers" associated with ten resonators. In other words, he considers the simple case when N = 10. Each N is associated with a "number". Planck calls it energy. We could call it revenues, profits, costs, or more generally "money". Just like there are different kinds of "energy" there are different kinds of "money". Here's Planck's example from page 308.

N (resonator, particles, entities): 1 2 3 4 5 6 7 8 9 10

Energy, money, profits, revenues: 7 38 11 0 9 2 20 4 4 5

Planck says that we can think of the total energy (or money) in two different ways. The total energy is NU where U is the average energy. For, us the total money is NY where Y is the average sales revenues, or average cost, or average profit, per unit. Planck says, let NU = Pe where "e" represents some, yet to be fixed elementary unit of energy (Greek symbol epsilon is used by Planck). In this example, N = 10 and P = 100. Imagine dividing $100 between 10 people. Person number 1 gets $7, person 2 gets $38 and so on. Planck is thinking about energy. We can think about money instead.

Or even "quality", such as number of "defects" in each car being surveyed, or the "opportunities" for defects in each product, and so on. Quantum theory can be extended readily, if we use our imagination.

Planck tells us that many different arrangements of the ten numbers in the second row (many different energy configurations, or money configurations) can be conceived, for the same total energy of 100e units (or same total revenues, or profits, the goal set by a company). And, he says, even if the same numbers appear in the second row, but in a different order, something has changed. This something is what Planck says must be called entropy.

So, there is another property entropy. Let the average entropy be S and the total entropy is then equal to NS. Now, Planck defines a new quantity called temperature T. What is temperature? Very simple. T = NU/NS = U/S.

Is it too much of a stretch now to say that we have the same entropy lurking in our problem and that our company also exhibits something called temperature? After we use such terms figuratively when we talk about a hot player, a hot movie, a hot stock, and so on. May be we can quantify this concept with some "numbers" now if we learn to quantify the idea of entropy. Let's see what Planck does next with entropy, or chaos, or disorder in his system of N resonators, particles (or for us N units sold, or N products and services offered).

Planck invokes the following equation for entropy S. This, amazingly, has to do with statistics and elementary combinatorial analysis that everyone interested in "quality" and SPC/SQC/TQM/Six Sigma, etc. is interested in.

S = k ln (Omega) ........(3)

where Omega = (N + P - 1)! / P! (N - 1)! ........(4)

here k is a proportionality constant. When Omega = 1, S = 0 since the natural logarithm of unity is zero. To understand the meaning of Omega think of the simpler combinatorial formula,

Omega = N! / r! (N - r)! .........(5)

This is the number of combinations of N objects of which r are identical. Further explanations for equation 4 may be found in Longair's book

In Planck's problem, N and P are very large

The average Y = e / [exp(e/kT) - 1] ........(6)

Here "exp" means the exponential function. The average value of any property (or entity) of interest, or the average revenue, cost, profits etc. depend on three quantities. The elementary unit called "e", the constant k and what is called the temperature T.

What is "e" that has not yet been clarified? In Planck's theory, he sets e = hf where h is another constant (we now call it Planck's constant) and f is the frequency of vibration of the resonator. Now, we can do the same thing with our elementary "e" which is an elementary "quantum of money" instead of an elementary "quantum of energy".

So, I say, let e = hx where h is a new constant and x is some unknown property, or variable that we can observe, measure, and quantify using numbers, that affects profits, revenues, costs, defects, etc.

Hence, the general law is Y = hx /[exp(hx/kT) - 1] ........(7)

Next, we come to Einstein's extension of Planck's theory and his idea of a work function. This takes us to the simpler equation y = hx + c = hx - W where W is the work function. The idea of the work function has been discussed in my post on Law relating Views and Replies.

So, here we have a generalization of Planck's law. This, I believe, can be used to "design" corporations to deliver a rated amount of profits, just like we design heat engines to deliver a certain rated horsepower. From the heat engine, we thus go to what I call a Profits Engine.

Now, enough theoretical nonsense. Prove it, you say. I hear you. We are now ready to discuss how companies like Google, Microsoft and Toyota behave. I have picked these companies since these are examples of companies that are obviously "excellent" in some sense. Google has become a houshold word since its founding in 1998, as are Microsoft and Toyota, soon to become, they say, the largest automotive company in the world, surpassing GM.

We can learn how quantum physics of Planck can be applied, even in the business world, by studying the profits-revenues data for these companies. Cheers! It is reeaaalllly very very

Charmed

P. S. For completeness, let me add that Entropy is also defined as the negative of information. According to Brillouin, "Entropy measures the lack of information about the exact state of a system." (Quote from page 270 in the text Heat and Thermodynamics, by Zemansky.) Hence, as entropy S increases, information I decreases. The equation relation entropy and information is a simple one and is written as S = S0 - I. When I = 0, the entropy S = S0 has its maximum value. This is the "reference value", just like we must use some kind of a reference level for measuring heights, energies, temperature, etc. As information I increases, S decreases.

The following was posted by Mike S in another related thread. What I have outlined here is at least in part inspired by what I see being discussed in that thread.

*****************

To quote Mike,

I read an interesting article recently in Inc. Magazine about the "open book management" philosophy -- basically letting the employees see all of the business' financials and educating them on how to understand and positively influence them.

I was wondering how fellow Covers felt about this type of policy, and if you've ever done it or been in a company where it was done, etc.

**********************

Let's say you work for XYZ Inc. which had sold 100,00 units of a widget last year. To be specific, let's take Toyota. It plans to sell 300,000 Toyota Prius, gasoline electric hybrids in 2005. Let's imagine this "division" as a separate stand alone company. Or, Ford has a new hybrid the Focus Escape on the market. Let's say 100,000 hybrids will be offered for sale, next year and the following year Ford expects to sell 150,000 units.

We can think of any company, even very large companies, in this fashion and subdivide them into the smallest unit imaginable that provides a very specific "product" or "service". This new unit must be self supporting and must be profitable. GM tried this experiment with Saturn. Saturn employees even had a modified UAW contract. Needless to say, and sadly so, Saturn was unable to show a profit, even after many years. It is now absorbed into Ma GM, for financial purposes. Let's be idealistic now.

Can a division of a company that plans to sell 100,000 units, or more generally N units, be profitable? Why not?

Let us assume that each unit sells for $ y. The total revenues generated by the sale of N units will be NY. Even if the product is "differentiated" (for example different options are offered, although all units are hybrids), we can take Y as the "average" price per unit sold with N being the total number of units. With product differentiation, we have

NY = N1Y1 + N2Y2 + N3Y3 + ....... (1)

N = N1 + N2 + N3 + ...... (2)

Now, N1 units are sold at the unit price of Y1 and N2 units are sold at the unit price of Y2 and N3 units are sold at the unit price of Y3, and so on. The summations given as equations 1 and 2 can continue ad infinitum, and include all the products/services offered by any large corporation (like a GE, Ford, Walmart, HPQ, IBM, ExxonMobil, etc.)

Where do we go from here? As the mix of products changes something is obviously changing. With modern computerization, a OEM automotive company will produce a car only after the customer has "speced" the car out with a dealer. Theoretically specifically, the dealer need not carry any inventory. After some "lead time" has elapsed, the dealer is only delivering vehicle, on any given day, for which orders were received say 2 to 4 weeks ago. The manufacturer knows exactly the type of car that has been ordered including all the minutes details. I don't see why the car could not be delivered with the name of customer actually plastered on it! (Sounds a bit too far, doesn't it. I have some customers actually flash their names on their license plates!)

Anyway, where do we go from here? As demand changes and the mix of cars (or computers, or refrigerators, or printers,...) to be made at the factory changes something is changing. This something is called "chaos" or "disorder" or "entropy". The recognition of this "chaos", or "disorder", in the system is the beginning of modern quantum physics, as conceived by Max Planck, and described in his December 1900 paper. An English translation of Planck's paper is readily available in the book

**Great Experiments in Physics**(Edited by Morris Shamos, Dover Publications, $12.95, available at most bookstores).Let me quote the introductory paragraph from Planck's paper (pages 301 to 314). Shamos includes a nice biographical note that provides the context and some explanatory notes as well. The following is the first paragraph on page 307.

*Entropy depends on disorder and this disorder (according to the electromagnetic theory of radiation for the monochromatic vibrations of a resonator when situated in a permanent stationary radiation field) depends on the irregularity with which it (the resonator) changes its amplitude and phase, provided one consider time intervals large compared to the time of one vibration but small compared to the duration of a measurement. If amplitude and phase are absolutely constant, which means completely homogenous vibrations, no entropy could exist and the vibrational energy would have to be completely free to be converted to work.*Let me stop here. We have reached the key word, the idea of "work". We have also met the idea of "energy". Now, let's simplify this and understand what Planck is talking about in more general terms, which has wider applications, including the problem of interest to us here. We can generalize Planck's theory and arrive a very general expression for the "average" value of Y in equation 1.

Planck talks about resonators and amplitude and phase and time and vibrational energy. There are N resonators in a heated body. This is what Planck was studying back in 1900. There are N divisions in a company. This is what I want to study now in 2004. There are N products or services that are offered by each division. This is what we are interested in here. The "vibration" that Planck talks about is like the "vibrations" sensed between customer and the company. In some abstract sense there are "vibrations", amplitudes, phases, and time-averaged effects, in every problem that is governed by equations 1 and 2. This is the broad generalization of Planck's idea. Let's see what Planck offers as an explanation for what he is trying to do. He gives the following list of "numbers" associated with ten resonators. In other words, he considers the simple case when N = 10. Each N is associated with a "number". Planck calls it energy. We could call it revenues, profits, costs, or more generally "money". Just like there are different kinds of "energy" there are different kinds of "money". Here's Planck's example from page 308.

N (resonator, particles, entities): 1 2 3 4 5 6 7 8 9 10

Energy, money, profits, revenues: 7 38 11 0 9 2 20 4 4 5

Planck says that we can think of the total energy (or money) in two different ways. The total energy is NU where U is the average energy. For, us the total money is NY where Y is the average sales revenues, or average cost, or average profit, per unit. Planck says, let NU = Pe where "e" represents some, yet to be fixed elementary unit of energy (Greek symbol epsilon is used by Planck). In this example, N = 10 and P = 100. Imagine dividing $100 between 10 people. Person number 1 gets $7, person 2 gets $38 and so on. Planck is thinking about energy. We can think about money instead.

Or even "quality", such as number of "defects" in each car being surveyed, or the "opportunities" for defects in each product, and so on. Quantum theory can be extended readily, if we use our imagination.

Planck tells us that many different arrangements of the ten numbers in the second row (many different energy configurations, or money configurations) can be conceived, for the same total energy of 100e units (or same total revenues, or profits, the goal set by a company). And, he says, even if the same numbers appear in the second row, but in a different order, something has changed. This something is what Planck says must be called entropy.

So, there is another property entropy. Let the average entropy be S and the total entropy is then equal to NS. Now, Planck defines a new quantity called temperature T. What is temperature? Very simple. T = NU/NS = U/S.

Is it too much of a stretch now to say that we have the same entropy lurking in our problem and that our company also exhibits something called temperature? After we use such terms figuratively when we talk about a hot player, a hot movie, a hot stock, and so on. May be we can quantify this concept with some "numbers" now if we learn to quantify the idea of entropy. Let's see what Planck does next with entropy, or chaos, or disorder in his system of N resonators, particles (or for us N units sold, or N products and services offered).

Planck invokes the following equation for entropy S. This, amazingly, has to do with statistics and elementary combinatorial analysis that everyone interested in "quality" and SPC/SQC/TQM/Six Sigma, etc. is interested in.

S = k ln (Omega) ........(3)

where Omega = (N + P - 1)! / P! (N - 1)! ........(4)

here k is a proportionality constant. When Omega = 1, S = 0 since the natural logarithm of unity is zero. To understand the meaning of Omega think of the simpler combinatorial formula,

Omega = N! / r! (N - r)! .........(5)

This is the number of combinations of N objects of which r are identical. Further explanations for equation 4 may be found in Longair's book

**Theoretical concepts in physics**(page 218, Figure 10.1, Cambridge Univ. Press, 1994) , and in the college textbook by Halliday, Resnick and Walker (**Fundamentals of Physics**, 1997, pages 521 to 525).In Planck's problem, N and P are very large

**whole numbers.**After a few simple and straghtforward steps, Planck approximates the factorials uses exponents (N- 1)! + N^N, P! = P^P and (N + P - 1)! = (N + P)^ (N + P). He is thus able to arrive at the formula relating entropy S and the average U, or in our case the average Y. This is given below. Interested Covers can have some fun and derive this result. It is actually quite simple to do.The average Y = e / [exp(e/kT) - 1] ........(6)

Here "exp" means the exponential function. The average value of any property (or entity) of interest, or the average revenue, cost, profits etc. depend on three quantities. The elementary unit called "e", the constant k and what is called the temperature T.

What is "e" that has not yet been clarified? In Planck's theory, he sets e = hf where h is another constant (we now call it Planck's constant) and f is the frequency of vibration of the resonator. Now, we can do the same thing with our elementary "e" which is an elementary "quantum of money" instead of an elementary "quantum of energy".

So, I say, let e = hx where h is a new constant and x is some unknown property, or variable that we can observe, measure, and quantify using numbers, that affects profits, revenues, costs, defects, etc.

Hence, the general law is Y = hx /[exp(hx/kT) - 1] ........(7)

Next, we come to Einstein's extension of Planck's theory and his idea of a work function. This takes us to the simpler equation y = hx + c = hx - W where W is the work function. The idea of the work function has been discussed in my post on Law relating Views and Replies.

So, here we have a generalization of Planck's law. This, I believe, can be used to "design" corporations to deliver a rated amount of profits, just like we design heat engines to deliver a certain rated horsepower. From the heat engine, we thus go to what I call a Profits Engine.

Now, enough theoretical nonsense. Prove it, you say. I hear you. We are now ready to discuss how companies like Google, Microsoft and Toyota behave. I have picked these companies since these are examples of companies that are obviously "excellent" in some sense. Google has become a houshold word since its founding in 1998, as are Microsoft and Toyota, soon to become, they say, the largest automotive company in the world, surpassing GM.

We can learn how quantum physics of Planck can be applied, even in the business world, by studying the profits-revenues data for these companies. Cheers! It is reeaaalllly very very

Charmed

P. S. For completeness, let me add that Entropy is also defined as the negative of information. According to Brillouin, "Entropy measures the lack of information about the exact state of a system." (Quote from page 270 in the text Heat and Thermodynamics, by Zemansky.) Hence, as entropy S increases, information I decreases. The equation relation entropy and information is a simple one and is written as S = S0 - I. When I = 0, the entropy S = S0 has its maximum value. This is the "reference value", just like we must use some kind of a reference level for measuring heights, energies, temperature, etc. As information I increases, S decreases.

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