Page 1 of 19

The Olympic Long Jump Records And a little known Mathematical Property of

a Straight Line: Yes, there is one!

http://www.dailymail.co.uk/news/article-2183904/Breathtaking-photo-shows-

moon-forming-sixth-ring-Olympic-display-Londons-Tower-Bridge.html

Summary:

In his recent Slate magazine article, Daniel Lametti discusses the theory that

Olympic long jumpers are not training (i.e., working hard) to beat earlier long

jump records, since this sporting event, unfortunately, does not seem to offer any

post-Olympic financial rewards. Interestingly, “working hard” to beat the Olympic

record can be shown to be related to the idea of a “work function” introduced into

physics by Einstein, in 1905.

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

Page 2 of 19

The 2012 London Olympics, with its dramatic picture of the full moon providing a

sixth Olympic ring, see below, also provided us with memorable history: Michael

Phelps’ 22 gold medals, Gabby Douglas, the gymnast, with her enchanting smile

(never mind the hair, ☺), and Usain Bolt! It also provided this sorry tale of

Olympic long jumpers who are NOT jumping long anymore.

Olympians seem to be running and swimming faster, throwing further than their

predecessors, but when it comes to jumping (both the men and the women) they

seem to be regressing. Great Britain’s Greg Rutherford won the gold with the

shortest jump (8.31 m) in 40 years, lamented Daniel Lametti in the Slate

magazine, see link below, citing the stats from 1968, 1988, 2008. After the

Olympic record set by Bob Beamon in1968 (at 8.90 meters), only once has this

been exceeded (by Mike Powell, at Tokyo in 1991, with 8.95 meters). If we

extrapolate forward using the negative trend, the Olympic long jump gold may

soon be for the taking at 8 meters or less, by 2028 or 2032, see Figure 1.

Courtesy : data:image/jpeg;base64,/……… ridiculously long URL follows here

http://www.slate.com/blogs/five_ring_circus/2012/08/03/long_jump_olympics_wh

y_do_the_best_long_jumpers_in_the_world_seem_to_be_jumping_shorter_distanc

es_.html

http://en.wikipedia.org/wiki/Athletics_at_the_2004_Summer_Olympics_%E2%80

%93_Men%27s_long_jump

Page 3 of 19

Figure 1: A small selection of the Olympic long jump records since Bob Beamon’s

record jump in 1968. A linear equation D = ht + c with a slope h and intercept c

can be fitted to the data. Virtually identical slopes h = - 0.01425 and h = -0.01429

are obtained if we consider the 1968 (Bob Beamon) and 2008 (Irving Saladino)

jumps and the 1968 and 1996 (Carl Lewis) jumps, see Table 1. The 1988 data falls

above this Type III line (see text for the explanation for the Type III designation).

Rutherford’s golden jump of 8.31 m was slightly longer (see Figure 2) than the

predicted 8.27m using the equation D = -0.01428t + 37.01 where t is in calendar

years. The slope h = (8.90 – 8.33)/(1968 – 2008) and intercept c =( y – hx) follows.

Table 1: Small selection of Olympic gold medal winning jumps since 1968

Year, t Jump, D

(meters)

Change ∆D

(meters)

Change ∆t

years

Slope

h = ∆D/∆t (m/yr)

1968 8.90

1988 8.72

1996 8.50 -0.40 28 -0.01429

2008 8.33 -0.57 40 -0.01425

7.80

8.00

8.20

8.40

8.60

8.80

9.00

9.20

1948 1956 1964 1972 1980 1988 1996 2004 2012 2020 2028 2036

Time, t [Calendar Year]

Oly

mp

ic g

old

win

nin

g lo

ng

ju

mp

[m

]

Page 4 of 19

The Olympic long jump records are being discussed here for two reasons.

1. First, it can be shown that the negative trend (Type III) is not a sustainable

one and must necessarily be preceded by a positive trend (Type I or Type II),

as confirmed by the historical data for earlier years (Figure 2).

2. Second, the meaning of “working hard” to beat Olympic records can be

related to the idea of a work function introduced into physics, in 1905, by

Einstein. This, as we will see now, can be extended beyond physics.

Figure 2: The gold medal winning Long Jump distance D versus time t in years

going back to 1956 when Gregory Bell won the gold with a jump of 7.83 meters.

With a little research, the long jump records for other intervening years, not found

in the Slate article, can be shown to confirm the negative trend, see Figure 2. The

American athletic hero, Carl Lewis, who won this event 1984, 1988, 1992, and

1996, won the gold in 1996 with a 8.50 meter jump, 22 cm less than his own gold

winning jump of 8.72 m in 1988. The gold mark has thus clearly been lowered in

7.60

7.80

8.00

8.20

8.40

8.60

8.80

9.00

9.20

1952 1960 1968 1976 1984 1992 2000 2008 2016 2024 2032

Time, t [Calendar Year]

Beamon, 1968 8.90 m

Powell, 1991 8.95 m

Type III D = -0.0143t + 37.01

Oly

mp

ic g

old

win

nin

g lo

ng

ju

mp

[m

]

2012

Page 5 of 19

this event in recent years. The data for all the Olympic gold winning jumps, going

back to 1896, may be found in the Wikipedia article. Only the recent trend, going

back 1956, preceding and following the record jumps by Bob Beamon (1968) and

Mike Powell (1991), is considered in Figure 2.

However, as discussed in detail in another recent article on an interesting

mathematical property of a straight line (see box), the appearance of a such a

negative trend in the data (called a Type III trend) usually signifies the existence of

an earlier Type I or Type II trend with a positive slope.

Why?

The Little Known Mathematical Property of a Straight Line

The general equation of a straight line is y = hx + c. The nonzero intercept c means

that the ratio y/x = m = h + (c/x) is NOT a constant and can either increase or

decrease as x increases, even if all of the (x, y) points (which describe the data

compiled for a problem of interest to us) lie on a PERFECT straight line. The ratio

y/x = m = h if and only if the straight line passes through the origin and c= 0.

The implications of this important property of a straight line do NOT seem to have

widely appreciated. Specifically, the “ratio” y/x is not the same as the “rate” h at

which y increases or decreases as x increases or decreases.

The implications of the widespread use of y/x “ratios” as “rates”, as in the

unemployment rate, the teen pregnancy rate, etc. and in financial performance

measures such as profit margin and earnings per share, should thus be carefully re-

examined.

http://www.scribd.com/doc/102000311/A-Little-Known-Mathematical-Property-of-a-

Straight-Line-Strange-but-true-there-is-one

Page 6 of 19

Very briefly, the general equation of a straight line is y = hx + c where x and y are

the variables of interest to us (for the long jump problem, x is time t in calendar

years and y is the winning long jump distance D), h is the slope of the line and c is

the intercept made on the y-axis. When x goes to zero, y = c. Hence, this general

straight line does NOT pass through the origin (0, 0). Depending on the numerical

values of h and c, we have at least three types of straight lines.

The Type I line has a positive slope and negative intercept (h > 0, c < 0).

The Type II line has a positive slope and positive intercept (h > 0, c > 0) and

The Type III line has a negative slope with a positive intercept (h < 0, c > 0).

However, a Type III trend, as we see here with the Olympic long jump records, is

unsustainable and usually implies the existence of a prior Type I or Type II trend.

The reason is very simple. We cannot extrapolate the negative (Type III) trend

backwards, indefinitely, or forwards, indefinitely.

The Type III equation, D = -0.014t + 37 (deduced from the data 1968 and 2008)

implies that if we extrapolate to earlier years, at time t = 0, the gold medal winning

jump distance D would be a ridiculously high 37 m. Or, in 2592, anyone can show

up to claim the gold since the winning jump distance D = 0 in that landmark year!

Although a Type III trend has been established in recent years, since the first

observance of a peak in 1968, the data for the earlier years reveals a Type I

equation, D = 0.089t – 166.6. Gregory Bell won the gold in 1956 with a 7.83 m

jump, well under the 8 m mark. This Type I equation was deduced using the 1956

and record 1968 data. A smaller Type I slope can be deduced using the 1956 and

1991 data. The negative intercept with the Type I trend means that the ratio D/t =

0.089 – (166.6/t) was increasing with each succeeding year. This increasing ratio

is the mathematical manifestation of the effort made by Olympians to beat the

records held by their predecessors.

Why then the recent Type III trend?

Page 7 of 19

This brings us to the second reason why the Olympic long jump data is being

highlighted here.

As hypothesized by Lametti (he refers to discussions he had with sports coaches)

in the Slate magazine article, the reason Olympians are NOT jumping as long may

just be the lack of lucrative post-Olympic monetary rewards. The long jump is not

in the same league as other athletic events. The key to being a successful long

jumper (running long jump as opposed to standing) is to have world class speed (to

gain the momentum before jumping). Such an athlete can make more money being

a world class 100-meter runner than training for the long jump.

Usain Bolt, who has made history by winning both the 100-meter and 200-meter

sprints in successive Olympics (as of this writing on August 10, 2012), is said to

have signed a lucrative three year contract with Puma, rumored at about $32

million. (Mike Powell believes Bolt should start training for the long jump after

2012 and beat his 1991 long jump record of 8.95 m and Bolt himself has now

hinted that he would try for it at Rio 2016. So, don’t bet anymore on that Type III

prediction for 2028 or 2032.)

Being the world’s fastest man apparently seems to have greater commercial value

than being the world’s longest jumper! And so, it is argued that Olympians are just

NOT making the effort, in other words working hard, to improve the record held

by their predecessors!

Work done, effort made, this is exactly what we mean by the work function W, or

the nonzero intercept c in the law y = hx + c. The transition from Type I to Type III

behavior that we see in the Olympic Long Jump records (the three types of

straight lines are “local” segments of a smooth curve with a maximum point)

is a manifestation of the nonzero intercept c, or the generalization of Einstein’s

idea of a work function W, well beyond physics.

This has already been discussed in detail in other articles by the author and will not

be repeated here (see bibliography provided at the end of this article). Only some

brief comments are included in Appendix 1 to highlight the important of the

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nonzero intercept c, recognized by both Planck and Einstein, when they developed

quantum physics in 1900 and 1905, respectively.

In what follows here we will see how this idea of a work function W also seems to

extend to the Olympic long jump records. Let’s discuss Einstein’s law briefly.

Einstein’s photoelectric law K = E – W = hf – W is a simple linear law relating K

and f, which can be understood as follows. E = hf is the elementary quantum of

energy, introduced by Planck into physics, in 1900, with h being the Planck

constant and f the frequency. Then, in 1905, building on Planck’s ideas (especially

the idea of entropy of radiation, see Appendix I), Einstein showed that light can be

thought of as being made up of a stream of particles (now called photons) with

each particle having the elementary energy quantum E = hf.

When the photons strike the surface of a metal, an electron, with the maximum

(kinetic) energy K is ejected (and produce a current in an external electrical circuit,

if they are properly collected, modern photocells, used in many applications, work

on this principle). The maximum K < E since some work W must be done to

overcome the forces binding the electron to the metal. Einstein called this the work

function of the metal and is to be determined experimentally for each metal from

the K-f graph. The slope of the graph is the fundamental constant, called the

Planck constant h. The intercept c = - W, the work function.

Einstein’s law also implies that the K-f graph is a series of parallels, if we perform

experiments with different metals, each having its own work function W.

Examples of such movement along (nearly PERFECT) parallels can be found

when we analyze the profits (variable y) and revenues (variable x) data for various

companies, e.g., article on Microsoft, Refs. [18,19] and Kia [16].

We see a similar movement along essentially parallel lines when we consider all of

the earlier Olympic Long Jump records, going back to 1896. This is illustrated in

Figure 3. The historical data seems to segregate along three parallel Type I lines.

Page 9 of 19

Figure 3: Historical Olympic Long Jump Records 1896-2012, with a few Word

Records like Mike Powell’s 1991 Tokyo World Record of 8.95 m. The Type III

trend established since 1968 was preceded by a Type I trend over many years.

Line A, joining 1900 to 1912, D = 0.035t – 58.5. Line B, joining 1923 to 1935,

D = 0.037t -62.82. Line C, joining 1896 to 1968, D = 0.035t – 60.8.

Notice that the Type I Lines A and C have EXACTLY the same slope. The slope

for Line B differs very slightly.

The transitions from lines A to B to C were not always chronological with a jump

from C to A between 1896 to 1900 and then a movement along A, then a jump

back to C and then to B. Nonetheless, the existence of such jumps is significant

since this implies something like a “work function”.

A fourth Type I line can be added (1956 and 1991, with slope h = 0.032) but has

not been done here.

6.00

6.50

7.00

7.50

8.00

8.50

9.00

9.50

1860 1880 1900 1920 1940 1960 1980 2000 2020 2040 2060

Time, t [Calendar years]

Oly

mp

ic w

inn

ing

ju

mp

, D

[m

ete

rs]

Type III, D = -0.014t +37

Type I, D = 0.035t – 60.8 Line C: 1896 and 1968

B

A

C

Page 10 of 19

Appendix I The nonzero intercept c in many problems

Einstein uses a simplified version of Max Planck’s radiation law, which can be

written in its most generalized form as (see also the discussion in Refs. [6, 9] cited

in the bibliography):

y = [ mxne

-ax/(1 + be

-ax) ] + c …………(1)

This is a power-exponential law with the power law term xn multiplying the

exponential term e-ax

. Hence, the x-y graph reveals a maximum point. In Planck’s

law b = - 1and c = 0, i.e., the intercept is taken to be zero. Einstein uses the

simplified version of this law, y = mxne

-ax (with b = 0, c = 0), which also reveals a

maximum point. It can be shown the derivative dy/dx = (n – ax)(y/x) for this

simplified function and so the maximum point occurs when n = ax, or x = a/n.

As discussed very nicely by Neuenschwander, Einstein uses this simplified

expression to derive certain expressions for the entropy of light which then lead

him to the conclusion that light can be viewed as a stream of particles (photons)

each having the elementary energy quantum hf.

In other words, Einstein did not just propose the idea of light being made up of

“particles”, an idea that had long been discredited in the physics community

(originally due to Newton, who viewed the different colors of light as being due to

the different momentum, rather than different energy, of the particles). He draws

upon the analogy between how the entropy of a volume of light will change

according to the simplified Planck law and how the entropy of a gas (with N

particles) changes as it is allowed to expand or contract.

Indeed, the concept of entropy is also the starting point of Planck’s discussion in

developing quantum physics. The reader is referred to the references cited. Of

interest to us here is the following expression for entropy S, which is the very first

Page 11 of 19

step taken by Planck, in his history making December 1900 paper. Planck writes

(following Boltzmann’s statistical arguments about entropy of a system of N

particles)

S = k ln Ω + unknown constant …………(2)

Planck was interested in the problem of how a fixed total energy UN = NU can be

distributed among N particles (which he envisioned as being oscillators, charged

particles, which vibrate about a fixed position, radiating electromagnetic energy in

the process). The expression for the average energy U derived by Planck marks the

beginning of quantum physics.

There are many different ways in which a fixed total energy can be distributed

between N particles. This gives rise to the entropy S, which is a measure of extent

of disorder, or chaos in the system. The parameter Ω in equation 2 above is the

number of ways and can be determined using the laws of permutations and

combinations. This involves factorials of large numbers. Hence, instead of a linear

law, we now have a logarithmic relation between S and Ω.

The proportionality constant in this relation is k, which Planck refers to as the

Boltzmann constant in honor of Ludwig Boltzmann who spent all of his

professional life developing the field that we now call statistical mechanics. In fact,

we find the above entropy equation carved on Boltzmann’s tombstone. (Sadly,

Boltzmann’s ideas were not widely appreciated by his peers. He suffered from

bouts of severe depression and ultimately committed suicide, just before he was

about to be vindicated, such as by Planck’s use of the above entropy equation to

develop quantum physics).

Notice how Planck is careful to introduce an unknown constant into equation 2.

This is the nonzero intercept made by the S-Ω graph. We can rewrite this as

S = k ln Ω + S0 . When Ω = 1, i.e., when there is only one way to distribute the

energy (as when there is only one particle, or when only one particle has all the

energy) the natural logarithm ln Ω = 0 and the entropy S = S0.

What is S0?

Page 12 of 19

This is a question that was later settled by physicists by actually formulating a new

law of thermodynamics, called the Zeroth law, which states that the entropy of a

PERFECT crystal, at the Absolute Zero temperature, will be exactly equal to

ZERO. This is NOT a proof. It is more like a postulate.

Planck recognizes the importance of the nonzero intercept S0 when he takes the

first steps to develop quantum physics. Likewise, Einstein recognizes the

importance of the nonzero intercept in the photoelectric law K = E – W = hf – W =

h(f – f0). The cut-off frequency f0 = W/h observed by experimental researchers

before Einstein cannot be explained if the work function W is zero. The cut-off

frequency is actually a manifestation of the nonzero intercept, or the work function

W. In Einstein’s law, W represents the work that must be done to overcome the

forces that bind the electron within the metal. This work, or energy used up to

produce the electron, cannot be calculated a priori and will depend on the metal.

Einstein calls it W and must be deduced for each metal experimentally.

The purpose of the discussion here is to highlight the importance of the nonzero

intercept in the real world using the Type III behavior observed in the Olympic

long jump record as an interesting example. There is a maximum point on this

graph. It is the “effort” or the work that must be done by the Olympian that is

subtly manifested in the nonzero intercept and hence also the maximum point since

Type III must give way to Type I at earlier times.

Like Planck and Einstein, we must recognize the importance of this nonzero

intercept whenever we analyze (x, y) data, as discussed here. We make

observations and use numbers to quantify these observations. One of the variables

x is usually taken as the independent variable, or the stimulus function. This gives

rise to the second observation, the dependent variable y, or the response function.

The most general relationship between x and y is y = hx + c, not y = mx.

For example, this nonzero intercept also affects the unemployment problem (one

that engages our attention because of the severe jobs crisis now faced in the USA)

and in the contentious discussions on labor productivity.

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Labor productivity = y/x = Number of units produced /Number of labor hours

Is there a nonzero intercept c that affects labor productivity? The potential

existence a nonzero intercept c means we must be careful when we use the ratio

y/x = m to draw conclusions and formulate policies (as is done routinely by

management using labor productivity data for various manufacturing plants, or to

decide which retail stores to close, etc. in the retail industry, using per store

statistics). The ratio y/x does not tell us anything about the “rate” of change y as x

increases or decreases. y/x = m = h + (c/x). The slope h is the “rate” of change and

h = m, if and only if the intercept c = 0. If not, we must be careful to consider what

may be called the size effect, the dependence of the ratio y/x on the value of x.

The implications of the nonzero c have been discussed for the unemployment

problem, for the profits-revenues problem, for the traffic-fatality problem, and for

the teenage pregnancy problem, see Refs. [29,30]. The nonzero c is Einstein’s

work function outside physics. Planck’s idea about entropy and the radiation law,

generalized as equation 1, can also be applied well beyond physics.

We have just found a maximum point in the most unlikely of places, in the

Olympic long jump record this morning, August 5, 2012!

Quantum physics was conceived to explain the appearance of such a maximum

point on the radiation curve for a heated body. Einstein’s law and the expression

relating the average entropy S and the average energy U, derived by Planck, can be

generalized and applied beyond physics.

Page 14 of 19

Appendix II: Bibliography

Related Internet articles posted at this website

Since the Facebook IPO on May 18, 2012

The first article listed below discusses a little known mathematical property of a

straight line. Figures 1 to 3 in this article provide the philosophical basis for

considering the significance of the significance of a nonzero intercept c as it

applies to many problems in the real world. We make observations (x and y values

of interest to us) to deduce y/x, usually called “rates”, “ratios”, or percentages.

1. http://www.scribd.com/doc/102000311/A-Little-Known-Mathematical-

Property-of-a-Straight-Line-Strange-but-true-there-is-one Published August 4,

2012.

Financial data (Profits-Revenues) analysis and Generalization of Planck’s law

beyond physics.

2. http://www.scribd.com/doc/95906902/Simple-Mathematical-Laws-Govern-

Corporate-Financial-Behavior-A-Brief-Compilation-of-Profits-Revenues-

Data Current article with all others above cited for completeness, Published

June 4, 2012 with several revisions incorporating more examples.

3. http://www.scribd.com/doc/94647467/Three-Types-of-Companies-From-

Quantum-Physics-to-Economics Basic discussion of three types of

companies, Published May 24, 2012. Examples of Google, Facebook,

ExxonMobil, Best Buy, Ford, Universal Insurance Holdings

4. http://www.scribd.com/doc/96228131/The-Perfect-Apple-How-it-can-be-

destroyed Detailed discussion of Apple Inc. data. Published June 7, 2012.

5. http://www.scribd.com/doc/95140101/Ford-Motor-Company-Data-Reveals-

Mount-Profit Ford Motor Company graph illustrating pronounced maximum

point, Published May 29, 2012.

Page 15 of 19

6. http://www.scribd.com/doc/95329905/Planck-s-Blackbody-Radiation-Law-

Rederived-for-more-General-Case Generalization of Planck’s law,

Published May 30, 2012.

7. http://www.scribd.com/doc/94325593/The-Future-of-Facebook-I Facebook

and Google data are compared here. Published May 21, 2012.

8. http://www.scribd.com/doc/94103265/The-FaceBook-Future Published May

19, 2012 (the day after IPO launch on Friday May 18, 2012).

9. http://www.scribd.com/doc/95728457/What-is-Entropy Discussion of the

meaning of entropy (using example given by Boltzmann in 1877, later also

used by Planck to develop quantum physics in 1900). The example here shows

the concepts of entropy S and energy U (and the derivative T = dU/dS) can be

extended beyond physics with energy = money, or any property of interest.

Published June 3, 2012.

10. The Future of Southwest Airlines, Completed June 14, 2012 (to be

published).

11. The Air Tran Story: An Important Link to the Future of Southwest Airlines,

Completed June 27, 2012 (to be published).

12. Annie’s Inc. A Single-Product Company Analyzed using a New

Methodology, http://www.scribd.com/doc/98652561/Annie-s-Inc-A-Single-

Product-Company-Analyzed-Using-a-New-Methodology Published June 29,

2012

13. Google Inc. A Lovable One-Trick Pony Another Single-product Company

Analyzed using the New Methodology.

http://www.scribd.com/doc/98825141/Google-A-Lovable-One-Trick-Pony-

Another-Single-Product-Company-Analyzed-Using-the-New-Methodology,

Published July 1, 2012.

14. GT Advanced Technologies, Inc. Analysis of Recent Financial Data,

Completed on July 4, 2012. (To be published).

15. Disappearing Brands: Research in Motion Limited. An Interesting type of

Maximum Point on the Profits-Revenues Graph

http://www.scribd.com/doc/99181402/Research-in-Motion-RIM-Limited-Will-

Disappear-in-2013 Published July 5, 2012.

Page 16 of 19

16. Kia Motor Company: A Disappearing Brand

http://www.scribd.com/doc/99333764/Kia-Motor-Company-A-Disppearing-

Brand, Published July 6, 2012.

17. The Perfect Apple-II: Taking A Second Bite: A Simple Methodology for

Revenues Predictions (Completed July 8, 2012, To be Published)

http://www.scribd.com/doc/101503988/The-Perfect-Apple-II, Published

July 30, 2012.

18. http://www.scribd.com/doc/101062823/A-Fresh-Look-at-Microsoft-After-its-

Historic-Quarterly-Loss Microsoft after the quarterly loss, Published July 25,

2012.

19. http://www.scribd.com/doc/101518117/A-Second-Look-at-Microsoft-After-the-

Historic-Quarterly-Loss , Published July 30, 2012.

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

The Unemployment Problem: Evidence for a Universal value of h in the

unemployment law.

20. http://www.scribd.com/doc/100984613/Further-Empirical-Evidence-for-the-

Universal-Constant-h-and-the-Economic-Work-Function-Analysis-of-

Historical-Unemployment-data-for-Japan-1953-2011 Single universal value of

h for US, Canada and Japan in the unemployment law y = hx + c, Published

July 24, 2012.

21. http://www.scribd.com/doc/100939758/An-Economy-Under-Stress-

Preliminary-Analysis-of-Historical-Unemployment-Data-for-Japan, Published

July 24, 2012.

22. http://www.scribd.com/doc/100910302/Further-Evidence-for-a-Universal-

Constant-h-and-the-Economic-Work-Function-Analysis-of-US-1941-2011-and-

Canadian-1976-2011-Unemployment-Data Published July 24, 2012.

23. http://www.scribd.com/doc/100720086/A-Second-Look-at-Australian-2012-

Unemployment-Data, Published July 22, 2012.

24. http://www.scribd.com/doc/100500017/A-First-Look-at-Australian-

Unemployment-Statistics-A-New-Methodology-for-Analyzing-Unemployment-

Data , Published July 19, 2012.

25. http://www.scribd.com/doc/99857981/The-Highest-US-Unemployment-Rates-

Obama-years-compared-with-historic-highs-in-Unemployment-levels ,

Published July 12, 2012.

Page 17 of 19

26. http://www.scribd.com/doc/99647215/The-US-Unemployment-Rate-What-

happened-in-the-Obama-years , Published July 10, 2012.

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

Traffic-fatality and Teen pregnancy problem

27. http://www.scribd.com/doc/101982715/Does-Speed-Kill-Forgotten-US-

Highway-Deaths-in-1950s-and-1960s Published August 4, 2012.

28. http://www.scribd.com/doc/101983375/Effect-of-Speed-Limits-on-Fatalities-

Texas-Proofing-of-Vehciles Published August 4, 2012.

29. http://www.scribd.com/doc/101828233/The-US-Teenage-Pregnancy-Rates-1

Published August 2, 2012.

30. http://www.scribd.com/doc/102384514/A-Second-Look-at-the-US-Teenage-

Pregnancy-Rates-Evidence-for-a-Predominant-Natural-Law Published August

8, 2012.

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

Page 18 of 19

About the author

V. Laxmanan, Sc. D.

The author obtained his Bachelor’s degree (B. E.) in Mechanical Engineering from

the University of Poona and his Master’s degree (M. E.), also in Mechanical

Engineering, from the Indian Institute of Science, Bangalore, followed by a

Master’s (S. M.) and Doctoral (Sc. D.) degrees in Materials Engineering from the

Massachusetts Institute of Technology, Cambridge, MA, USA. He then spent his

entire professional career at leading US research institutions (MIT, Allied

Chemical Corporate R & D, now part of Honeywell, NASA, Case Western Reserve

University (CWRU), and General Motors Research and Development Center in

Warren, MI). He holds four patents in materials processing, has co-authored two

books and published several scientific papers in leading peer-reviewed

international journals. His expertise includes developing simple mathematical

models to explain the behavior of complex systems.

While at NASA and CWRU, he was responsible for developing material processing

experiments to be performed aboard the space shuttle and developed a simple

mathematical model to explain the growth Christmas-tree, or snowflake, like

structures (called dendrites) widely observed in many types of liquid-to-solid phase

transformations (e.g., freezing of all commercial metals and alloys, freezing of

water, and, yes, production of snowflakes!). This led to a simple model to explain

the growth of dendritic structures in both the ground-based experiments and in the

space shuttle experiments.

More recently, he has been interested in the analysis of the large volumes of data

from financial and economic systems and has developed what may be called the

Quantum Business Model (QBM). This extends (to financial and economic

systems) the mathematical arguments used by Max Planck to develop quantum

physics using the analogy Energy = Money, i.e., energy in physics is like money in

economics. Einstein applied Planck’s ideas to describe the photoelectric effect (by

treating light as being composed of particles called photons, each with the fixed

quantum of energy conceived by Planck). The mathematical law deduced by

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Planck, referred to here as the generalized power-exponential law, might actually

have many applications far beyond blackbody radiation studies where it was first

conceived.

Einstein’s photoelectric law is a simple linear law, as we see here, and was

deduced from Planck’s non-linear law for describing blackbody radiation. It

appears that financial and economic systems can be modeled using a similar

approach. Finance, business, economics and management sciences now essentially

seem to operate like astronomy and physics before the advent of Kepler and

Newton.

Cover page of AirTran 2000 Annual Report