Dangerous Arithmetic: A Trillion Greenback Downside

“Our recommendation: Watch out for geeks bearing formulation.”
— Warren Buffett, Letter to Shareholders of Berkshire Hathaway, Reporting Large Losses

Within the basic 1961 Disney science fiction comedy film The Absent Minded Professor, Professor Ned Brainard of Medfield School of Know-how has been struggling for 3 months to make a breakthrough in his storage, dwelling to a low funds chemistry lab and his vintage Mannequin “T” automobile. A blackboard reveals a set of cryptic formulation together with:

[tex] H = E $-$ PV [/tex]

Professor Brainard has a sudden realization that the system is in error and modifications it to:

[tex] H = E + PV [/tex]

The Professor proceeds to make a collection of frantic modifications to his effervescent chemistry experiment, forgetting about his wedding ceremony, and there may be an explosion. When he wakes up (after lacking his wedding ceremony and dropping his fiance), he has found “flying rubber” or “flubber,” a miraculous materials that appears to violate each legislation of physics and offers the driving force for the remainder of the comedy. The film ends with the Professor (and his fiance in a real Disney pleased ending) flying his flubber-powered Mannequin “T” to the US capital the place he outflies jet fighters despatched to intercept him. By the way, the corrected system is definitely the system for the enthalpy, a typical thermodynamic idea.

This portrayal of the close to magical energy of arithmetic is frequent in science fiction, particularly standard films and video, critical in addition to comedic. The basic science fiction film The Day The Earth Stood Nonetheless (1951) includes a well-known scene during which the alien customer Klaatu solves an issue in celestial mechanics on the blackboard of Professor Jacob Barnhardt, supposedly revealing the key of interplanetary (maybe interstellar) journey, a considerably curious act for the consultant of an interplanetary civilization supposedly fearing atomic assault from the barbaric Earth males. The unique Star Trek tv collection featured a number of episodes during which both the science officer Mr. Spock or the ship’s super-intelligent pc solved some new, by no means earlier than encountered downside by performing some mysterious calculations, all by the tip of every lower than one hour episode. The 2003 catastrophe film The Core, which has the doubtful distinction of a few of the worst and most inaccurate physics in any main film, options a number of scenes the place the scientists carry out some complicated calculation, generally of their heads in seconds, and clear up an in any other case deadly downside (e.g. the tip of the world). The tv collection Numb3rs options mathematicians who assist the FBI clear up in any other case unsolvable prison circumstances by the magic energy of arithmetic.

Generally, it’s common to come across a scene in science fiction films and video with a scientist, engineer, or mathematician at a blackboard lined with cryptic symbols. The blackboard often faces the digicam and infrequently dominates the scene. Typically a contemporary whiteboard or a pocket book web page could also be used, however the blackboard continues to be the most typical icon. Incessantly, these scenes depict the scientist performing some kind of mysterious symbolic manipulation, resembling a substitution of 1 expression for one more or the signal change in The Absent Minded Professor. This symbolic manipulation is usually adopted explicitly or implicitly by miraculous outcomes. There are some apparent causes for these scenes in films and video. A blackboard lined with cryptic symbols is a extremely visible picture; it tells the story in a short time and clearly. The usage of cryptic symbols and mysterious symbolic manipulations saves the script author from explaining the invention or discovery: how would an actual flubber work? Lastly, these scenes are similar to conventional portrayals of ceremonial magic the place the magician performs marvels by mysterious symbols, hand gestures, and incantations.

How lifelike are these portrayals? Based mostly on the historical past of arithmetic, they’re removed from lifelike. For instance, in The Absent Minded Professor, Professor Brainard is stumped for 3 months — solely three months — earlier than making his breakthrough. Most main breakthroughs just like the fictional flubber have taken years, often not less than 5 years. Fairly often, the inventor or discoverer was stumped, on the fallacious observe, for many of that interval; on this respect, the portrayal in The Absent Minded Professor is considerably correct.

How necessary have mathematical calculations been in breakthroughs in energy and propulsion applied sciences, such because the fictional flubber? Not as a lot as one would suppose. Main breakthroughs in energy and propulsion applied sciences often contain a conceptual leap during which the structure of the system is modified. This often means both the introduction of a brand new element or a radical redesign of the system. It has typically been tough or unimaginable to calculate what would occur with the brand new design. Even fashionable pc simulations are sometimes calibrated on present designs, elements, and so forth. A brand new element or, even worse, a radical new structure typically falls exterior the realm of validation of present simulation fashions. Think about attempting to design an anti-gravity drive utilizing the simulation software program for the House Shuttle. In quite a few engineering fields resembling aviation the Navier-Stokes equation is assumed to explain fluid dynamics, air and water for instance. The Navier-Stokes equation has confirmed unimaginable to precisely simulate numerically on a pc in lots of circumstances for deep mathematical causes that stay unresolved. This is likely one of the causes that the Navier-Stokes equation is likely one of the Millennium Issues for which the Clay Institute has supplied a a million greenback prize. Consequently, engineers and designers should nonetheless depend on empirical strategies in lots of circumstances: wind tunnels, flight checks, and so forth.

Professor Brainard bears a suspicious resemblance to the rocket pioneer Robert Goddard (1882-1945), who was very a lot within the information and public consciousness in 1961, the peak of the post-Sputnik area race (Hubert Alyea (1903-1996), a Professor of Chemistry at Princeton who gave entertaining chemistry demonstrations considerably just like Brainard’s antics within the film typically claimed to be the mannequin for the character). Goddard was a professor at a small technical college, Clark College. He even married the secretary of the College President, as Professor Brainard does within the film. Goddard was a physicist who definitely used mathematical calculations in his work. But, remarkably, a lot of the rocket elements had been developed empirically by impressed trial and error. The arithmetic of Goddard’s time was just too primitive to simulate the operation of complicated shapes like rocket motors, turbo-pumps and so forth. Goddard made all the identical key advances in rocketry additionally made by the German rocketeers together with switching from unreliable powder explosives to liquid propellants, the torpedo formed design with the payload on prime, the tank within the center, and the rocket engine trailing behind (sure, early liquid propellant rockets had the engine in entrance), and the usage of the extraordinarily complicated turbo-pump to realize the excessive thrust wanted for lengthy vary and ultimately orbit. These had been all conceptual leaps that might not be discovered by symbolic manipulation of mathematical formulation. Notice that it took Goddard over 5 years simply to comprehend to discard unreliable powdered explosives and change to liquid propellant rockets. Every main conceptual leap in his rocket design took years!

Goddard’s arch-nemesis, Professor Theodor von Karman (1881-1963) of Caltech, grew to become a key adviser to the Air Power and United States Federal Authorities within the years after World Battle II. A graduate of the extremely mathematical College of Gottingen in Germany, Von Karman closely promoted the idea of utilizing detailed theoretical calculations to carry out aviation and rocketry analysis and improvement in a extremely “scientific” approach, contrasted to the instinct and trial and error of conventional “inventors.” The irony of that is that the event of the Jet Assisted Take Off (JATO) rockets throughout World Battle II that made Von Karman’s fame is about as removed from the best of mathematically pushed analysis and improvement as one may think about. The precise inventor “Jack” Parsons (1914-1952) was a really weird character with negligible mathematical abilities. He did have nonetheless a few years of hands-on expertise in constructing rockets, which largely blew up unsuccessfully, and explosives. Someday in 1942, he by some means realized that one may make steady, dependable strong gasoline rockets by changing the unreliable explosive powders of the day with a mix of asphalt and potassium perchlorate (a extensively used oxidizer in explosives). By some accounts, he was impressed by his studying concerning the mysterious Greek Hearth weapon of the medieval Byzantine Empire which can have been a mix of oil and a strong oxidizing agent. Once more, this was a conceptual leap with negligible math. With the correct idea, it took just a few weeks in 1942 for Parsons and his associates, often known as the “Suicide Squad,” to construct some working prototypes, largely by trial and error. Notice, nonetheless, that Parsons had been engaged on rockets, largely failing, for nearly ten years earlier than his breakthrough.

In fact, as an utilized mathematician, the creator doesn’t wish to give the impression that arithmetic and calculations are ineffective or unimportant. That is definitely not the case. There are circumstances the place machines had been constructed in accordance with theoretical calculations and labored (largely) proper the primary time. The primary atomic bomb, constructed based mostly partially on theoretical calculations, labored the primary time. Nevertheless, even with the atomic bomb, there was an infinite quantity of instinct and trial and error on the element stage. The House Shuttle was designed based mostly on wind tunnel knowledge, experimental flight knowledge from the X-15, some flight checks of partial mockups, and theoretical calculations. Nonetheless, the primary flight of the House Shuttle was a hit, though the mission got here near catastrophic failure throughout reentry when the management system started to oscillate unexpectedly; the theoretical calculations weren’t fairly proper. Machines that work proper the primary time based mostly on theoretical calculations seem like uncommon, even with fashionable pc simulations. In a current instance, the extremely pc oriented area startup SpaceX needed to strive 4 instances earlier than efficiently launching a satellite tv for pc into orbit. Three pc designed rockets in a row blew up or crashed throughout launch.

The magical arithmetic of science fiction has appreciable affect. That is how many individuals, together with many scientists and engineers who ought to most likely know higher, view arithmetic. Theodor von Karman and others like him promoted a really related image of the facility of arithmetic in public coverage circles after World Battle II and to at the present time. Fashionable science, which presumably isn’t fiction, such because the PBS Nova specials, Scientific American articles, and different sources typically portrays basically the identical image of arithmetic. Coverage makers, enterprise leaders, and most of the people typically have an image of arithmetic and mathematicians, particularly the facility of symbolic manipulation of mathematical formulation, that borders on magic. Many individuals are blissfully unaware of the massive quantity of trial and error and calendar time often concerned in creating utilized mathematical formulation (or pc packages based mostly on them) that clear up actual issues. The position of conceptual leaps in invention and discovery has been deprecated in favor of the facility of symbolic manipulations like Professor Brainard’s change from [tex]$-$[/tex] to [tex]$+$[/tex] in his magic system. The overused cliche “considering out of the field” is usually a synonym for attempting a barely totally different time period in a mathematical system moderately than, for instance, realizing that combining asphalt and potassium perchlorate avoids the issues of explosive powders in rocketry. The creator has truly heard somebody use “out of the field” to seek advice from utilizing a unique compiler flag on the GNU C Compiler to compile a mathematical program carried out within the C programming language.

There are a number of the reason why sci-fi math appears plausible even to scientists, engineers, and mathematicians who ought to presumably know higher. First, some individuals are capable of obtain phenomenal efficiency on standardized math checks (e.g. the SAT, GRE), educational exams, qualifying exams in graduate college, formal contests such because the Worldwide Math Olympiad and the Putnam Examination, and so forth. Some folks can reply these checks very precisely, even completely, in a short while interval. This appears to match the efficiency of mathematicians in science fiction. It’s seemingly it’s because most checks and exams take a look at the data of identified info, calculations, and strategies. The very prime graduate faculties are populated virtually solely by folks of this kind. When prodigies of this kind encounter new, unknown issues their error fee typically rises dramatically. Additional, the tutorial checks hardly ever measure the conceptual reasoning abilities typically utilized in breakthroughs; we don’t even know precisely what these abilities are.

It isn’t clear why some folks can carry out so effectively on varied checks, exams, competitions, educational homework, and so forth. This excessive efficiency is usually attributed to extraordinarily excessive innate intelligence. The psychologist Ok. Anders Ericsson has argued that knowledgeable efficiency is because of what he calls “deliberate observe.” These concepts have been popularized by Malcolm Gladwell in his current ebook Outliers. Ericsson argues that extraordinarily excessive performers in video games resembling chess, sports activities, performing arts, and arithmetic interact in “deliberate observe” the place they spend many, many hours training comparatively uncommon issues, strategies, and strategies. This differs from unusual expertise or observe. The instance that Ericsson typically makes use of is the backhand in tennis. The backhand is comparatively uncommon in tennis. Normally a tennis participant doesn’t have to carry out the backhand tennis swing. Consequently, even extremely skilled informal tennis gamers could also be weak on the backhand. In distinction, champion tennis gamers observe the backhand closely. Thus, once they encounter the backhand, they will simply defeat gamers who haven’t practiced this uncommon transfer. Though Ericsson typically makes use of the tennis analogy, he began from research of champion chess gamers resembling Bobby Fischer and generalized the outcomes to most fields of experience, arguing related patterns happen in most fields of experience.

It’s seemingly that somebody who engaged in giant quantities of deliberate observe in arithmetic may carry out extraordinarily effectively on mathematical checks, exams, and different aggressive measures as long as these checks concerned calculations or derivations that had been practiced. The issue is that by their nature innovations and discoveries contain issues which have by no means been solved by anybody. There is no such thing as a approach to observe on this approach. Deliberate observe could be very time consuming. Ericsson argues that almost all consultants interact in 10,000 hours of deliberate observe, sometimes over ten years. Partially that is derived from unique research of chess the place champion chess gamers have virtually all the time spent not less than ten years of intensive research and observe earlier than reaching the Worldwide Grand Grasp stage. Ericsson has discovered related patterns in lots of different fields. It’s fairly potential that deliberate observe at this stage can considerably scale back the time accessible to check fundamental ideas and to develop the conceptual reasoning abilities often utilized in invention and discovery.

Each Ericsson and Malcolm Gladwell have a powerful environmental bias, that’s attributing experience and excessive ranges of success to exterior environmental elements moderately than innate, presumably genetic, traits of the person. In his analysis papers, Ericsson assumes that knowledgeable efficiency interprets into invention and discovery, creating a brand new methodology or approach in a single’s subject of experience. One will get higher and higher by years of deliberate observe and at last reaches the rareified stage the place one begins to make unique contributions to at least one’s subject, innovations and discoveries. One downside with Ericsson’s principle is that some inventors and discoverers (just like the physicist Albert Einstein) truly will not be that technically proficient (knowledgeable) as conventionally outlined of their subject. In excessive circumstances, they’ve needed to hunt down technical consultants to implement their concepts and ideas. Nonetheless, there may be most likely some fact in Ericsson’s principle of “deliberate observe.”

Second, standard science accounts, textbooks, and even many scholarly research of scientific and technological breakthroughs often downplay or omit the lengthy interval of calendar time and enormous quantities of trial and error typically concerned. Many accounts deal with the “flash of perception”, the “Eureka second” which may occur very quickly in accordance with many accounts, however virtually all the time after a protracted interval of research, preparation, and infrequently failure. Much more outstanding, the “flash of perception” typically happens when the inventor or discoverer is taking a break — not considering consciously about the issue. There are numerous accounts of breakthroughs throughout leisure walks, holidays, and different leisure actions. In his research of mathematical invention, the nice mathematician Jacques Hadamard concluded this was typical of mathematical innovations. Taken out of context, these dramatic leaps ahead sound like situations of maximum intelligence, extraordinarily speedy options of issues by distinctive folks, identical to the superhuman feats in science fiction. Trial and error, particularly the numerous failures, is extraordinarily boring and tedious to explain; it is usually not the best way to encourage college students to pursue scientific, engineering, or mathematical careers.

Third, many working scientists, engineers, and mathematicians are unaware of the particular historical past of the innovations or discoveries of their subject. To the extent that they’ve studied this, they’re often relying consciously or not on tales in textbooks or standard science accounts and even phrase of mouth which might be typically fairly inaccurate on shut examination. Working scientists, engineers, and mathematicians are busy with their work and don’t have time to check the previous. A variety of accounts of main innovations in US historical past textbooks (such because the Wright brothers and the airplane) are extremely deceptive. They’re most likely supposed to encourage college students and promote patriotism.

A Comparability of Sci-Fi Math and Actual Math
Sci-Fi Math Actual Math
Quick. Tough calculations in seconds. Even breakthroughs in moments, hours, a number of months. Slower. Breakthroughs often take a number of years, typically 5 or extra.
Little or no trial and error. Few or no errors. Normally greater error charges. Breakthroughs often contain giant quantities of trial and error: typically tons of to tens of hundreds of trials.
Symbolic manipulation typically ends in solutions or breakthroughs. Conceptual evaluation and conceptual leaps. Exact math is usually used to confirm {that a} new idea will work or is prone to work.

Astonishingly, the prices of the widespread perception in science fiction arithmetic could run into the trillions of {dollars}. Questionable mathematical fashions for the valuation of mortgage-backed securities performed a central position within the monetary disaster of 2008 and the on-going financial and monetary issues. Economist Dean Baker estimates that the housing bubble in the US amounted to $8 trillion in extra valuation, a lot of this within the type of loans bundled into mortgage-backed securities, most of which stay to be written off. Related mathematical fashions had been implicated within the failure of the Lengthy Time period Capital Administration (LTCM) hedge fund, a number of spinoff securities failures in 1994, and the inventory market crash of 1987.

One can discover quite a few examples of start-up firms resembling Lernout and Hauspie and Kurzweill Utilized Intelligence whose exaggerated inventory valuations trusted unrealistic concepts concerning the prospects for shortly fixing synthetic intelligence issues resembling speech recognition, handwriting recognition (the pen computing fad of the early Nineties), and even reproducing human thought solely. Stagnant analysis packages like tokamaks for nuclear fusion and superstrings in theoretical physics typically appear based mostly on exaggerated concepts concerning the energy of arithmetic, particularly symbolic manipulation, and pc simulations to take the place of the conceptual considering and conceptual leaps often concerned in main breakthroughs.

Arithmetic, particularly cryptic symbolic formulation, is usually each intimidating and awe-inspiring, particularly since arithmetic has generally resulted in or contributed to astonishing accomplishments such because the atomic bomb, the manned touchdown on the Moon, GPS navigation, DVD video, and lots of different marvels of the fashionable world. Mastering fashionable arithmetic is a significant endeavor. Even prime mathematicians like Andrew Wiles are sometimes specialists in a single space of arithmetic. How are non-mathematicians to navigate the rising hazards of our more and more mathematical world? Coverage makers, enterprise leaders, and most of the people can confirm the lengthy calendar time and enormous quantities of trial and error often reported in mathematical in addition to different innovations and discoveries with cautious analysis. The large largely failed efforts by extremely certified scientists and engineers in quite a few areas resembling synthetic intelligence may be verified from publicly accessible federal budgets. In lots of circumstances, the efficiency of the arithmetic may be independently evaluated (the accuracy of speech recognition, energy output of tokamaks, and many others.) with none understanding of the abstruse arithmetic.

Enterprise leaders and coverage makers grew to become enamored, sincerely or not, with complicated monetary engineering within the housing market that appeared to supply a fast repair to the recession that adopted the collapse of the Web Bubble and the September 11 terrorist assaults, all on the time scale of the subsequent election and even the subsequent quarterly earnings report. Within the current extreme financial downturn, the enchantment of one other seeming scientific-technical fast repair — whether or not within the type of exaggerated expectations for machine studying algorithms, miraculous inexperienced power applied sciences, or different purported “breakthroughs” — is straightforward to anticipate. Within the present monetary and power crises, everybody ought to turn into conversant in the historic document of mathematical analysis and improvement: counting on major historic sources the place potential and never on science fiction portrayals or standard science that’s actually science fiction. In any other case trillions extra — private financial savings, pension funds, public funds — could also be squandered on ineffective high-tech panaceas supplied, sincerely or not, as fast fixes to present financial issues and rising power costs.

Appendix: Some Mathematically Oriented Innovations and Discoveries
Invention or Discovery Inventor/Discoverer (s) Length Heureka Second
Kepler’s First Two Legal guidelines of Planetary Movement Johannes Kepler 1600-1605 (5 years) Sudden realization of reply over Easter Season 1605; most likely on trip.
Kepler’s Third Legislation of Planetary Movement Johannes Kepler 1600-1619 (19 years) Sudden realization of reply in a number of weeks in 1619.
Separate Condenser Steam Engine James Watt (some help from John Robison and Joseph Black) 1759-1765 (5 years) Sudden realization throughout a stroll within the park on the College of Glasgow in April 1765
Excessive Strain Steam Engine/Steam Boat John Fitch, Henry Voigt c. 1782-1787 (about 5 years) None identified.
Precision Nautical Chronometer for Measuring Longitude John Harrison c. 1730-1761 (31 years) None identified.
Maxwell’s Equations (Mathematical Principle of Electromagnetism) James Clerk Maxwell, Michael Faraday c. 1860-1865 (about 5 years) None identified.
Powered Plane Wilbur Wright, Orville Wright, Octave Chanute c. 1897-1906 (9 years) Sudden realization of wing warping steering mechanism whereas working at bike retailer.
Particular Principle of Relativity Albert Einstein c. 1898 – 1905 (7 years) Sudden leap ahead in 1905: “a storm in my thoughts”
Principle of Photoelectric Impact Albert Einstein c. 1898 – 1905 (7 years) Sudden leap ahead in 1905: “a storm in my thoughts”
Principle of Brownian Movement (“proof” of atoms) Albert Einstein c. 1898 – 1905 (7 years) Sudden leap ahead in 1905: “a storm in my thoughts”
Normal Principle of Relativity Albert Einstein c. 1908 – 1915 (7 years) None identified. Publishes a number of failed makes an attempt earlier than 1915.
Schrodinger’s Equation Erwin Schrodinger c. 1921 – 1926 (about 5 years) Sudden realization throughout ski trip within the alps with girlfriend.
EPR (Non-Native Nature of Quantum Mechanics) Albert Einstein, Boris Podolsky, Nathan Rosen c. 1927 – 1935 (7 years) None identified.
Atomic Bomb Manhattan Challenge (enormous group) 1939-1945 (6 years) None identified.
Sounding Rocket (USA) Robert Goddard (group of about six technicians, engineers, physicists) 1914-1941 (27 years) ( A number of leaps ahead — see textual content above.
Jet Assisted Take Off (JATO) strong gasoline rocket Marvel Whiteside “Jack” Parsons c. 1932 – 1942 (about 10 years) Sudden realization in early 1942.
Orbital Rocket (USA) Werner Von Braun and “Rocket Crew” (about 200 folks) 1927-1958 (31 years) A number of leaps ahead; parallels Goddard.
Manned Touchdown on Moon (USA) Apollo Challenge 1962-1969 (7 years) None identified. Largely scaling up confirmed orbital rocket design.
Proof of Fermat’s Final Theorem Andrew Wiles, Richard Taylor 1986-1995 (9 years) Not identified. Incorrect proof revealed in 1993.
Proof of Poincare Conjecture Grigoriy Perelman 1995-2002 (7 years) None identified.


It’s tough to outline precisely when an inventor or discoverer started engaged on an invention or discovery in addition to once they succeeded. For instance, the well-known 1903 Kitty Hawk flight of the supposed first airplane happened in an especially excessive wind; for this reason the experiments had been accomplished at Kitty Hawk which had the best winds in the US in accordance with US Climate Service knowledge. The Wright Flyer of 1903 virtually definitely couldn’t have flown in nonetheless air. It was not till years later that the Wright Brothers (and Octave Chanute) achieved a flyer that might take off and land in nonetheless air.

The position of arithmetic in mechanical innovations is usually onerous to find out. Through the nineteenth century, an elaborate mathematical principle of thermodynamics often attributed to Sadi Carnot was developed to clarify the operation of steam engines. On shut examination, early steam pioneers like John Fitch and Henry Voigt, Oliver Evans, and others developed excessive efficiency steam engines effectively earlier than this principle, largely by instinct and trial and error. James Watt, with help from John Robison and Joseph Black, clearly used arithmetic to grasp the effectivity of the steam engine, however he exaggerated the significance of the arithmetic later in life, partially to put declare to being a real “scientist” moderately than a mere “tinkerer.” Equally, extra not too long ago, Theodor Von Karman made an enormous deal out of arithmetic and theoretical calculations by his graduate pupil Frank Malina within the improvement of the JATO rockets, however on shut examination this invention was largely “instinct” and empirical trial and error, particularly by Jack Parsons.

Innovations and discoveries range quite a bit. Whereas many contain the “flash of perception” or “Heureka second,” there are additionally many the place there isn’t any clearly identifiable single leap ahead of this kind. The “flash of perception” is a really dramatic story, superb for standard science articles or a film.

Accounts of innovations and inventors on Wikipedia are likely to considerably understate the quantity of trial and error concerned in many innovations and discoveries. It is a frequent characteristic of standard and even scholarly accounts. It’s typically vital to trace down unique notebooks, first hand accounts and so forth to totally understand the quantity of trial and error often concerned in breakthrough innovations and discoveries.

Recommended Studying/References

The Papers of Robert H. Goddard: Volumes I-III
Esther C. Goddard (Editor) et al.
McGraw Hill E-book Firm
New York, 1970

Unusual Angel: The Otherwordly Lifetime of Rocket Scientist John Whiteside Parsons
George Pendle
Harcourt Inc.
Oakland, 2005

Intercourse and Rockets: The Occult World of Jack Parsons
John Carter, Robert Anton Wilson (Introduction)
Feral Home
Los Angeles, 2004

The Wind and Past
Theodor Von Karman
Little and Brown Firm
Boston, 1967

The Rocket Crew
Frederick C. Ordway III, Mitchell R. Sharpe
Foreward by Werner Von Braun
Apogee Books, 2003 (unique copyright 1979)

From Runway to Orbit: Reflections of a NASA Engineer
Kenneth W. Iliff and Curtis L. Peebles
Nationwide Aeronautics and House Administration
NASA Historical past Workplace
Washington, D.C.

The Making of the Atomic Bomb
Richard Rhodes
Simon and Schuster, New York, 1986

The Mathematician’s Thoughts: The Psychology of Invention within the Mathematical Subject
Jacques Hadamard
One in every of Princeton College Press’s Notable Centenary Titles.
With a brand new preface by P. N. Johnson-Laird

Outliers: The Story of Success
Malcolm Gladwell
Little, Brown and Firm

False Earnings: Recovering from the Bubble Economic system
Dean Baker
Polipoint Press

When Genius Failed: The Rise and Fall of Lengthy Time period Capital Markets
Roger Lowenstein
Random Home
New York, 2000

Startup: A Silicon Valley Journey
Jerry Kaplan
Houghton Mifflin Co, Boston, 1995

“How Excessive-Tech Dream Shattered in Scandal at Lernout & Hauspie”, by Mark Maremont, Jesse Eisinger, and John Carreyrou, Wall Road Journal, December 7, 2000

How Kurzweil’s straight-arrow CEO went awry”
By Mark Maremont in Waltham, Mass.
Enterprise Week,
September 16, 1996

Copyright © 2010 John F. McGowan, Ph.D.

In regards to the Creator

John F. McGowan, Ph.D. is a software program developer, analysis scientist, and advisor. He works primarily within the space of complicated algorithms that embody superior mathematical and logical ideas, together with speech recognition and video compression applied sciences. He has intensive expertise creating software program in C, C++, Visible Fundamental, Mathematica, MATLAB, and lots of different programming languages. He’s most likely finest identified for his AVI Overview, an Web FAQ (Incessantly Requested Questions) on the Microsoft AVI (Audio Video Interleave) file format. He has labored as a contractor at NASA Ames Analysis Middle concerned within the analysis and improvement of picture and video processing algorithms and know-how. He has revealed articles on the origin and evolution of life, the exploration of Mars (anticipating the invention of methane on Mars), and low-cost entry to area. He has a Ph.D. in physics from the College of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Know-how (Caltech). He may be reached at [email protected].

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