Post on 29-Jul-2015
description
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
Page 8 of 19
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.
Page 13 of 19
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
Page 19 of 19
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