John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
Short video on using AI to estimate how to boost the Cracker Barrel restaurant and gift shop chain’s sales by improving advertising expenditures.
Short Article: http://wordpress.jmcgowan.com/wp/article-can-ai-boost-cracker-barrels-stagnant-sales/
Short Link: bit.ly/3ojdV9t
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John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
Cracker Barrel (NASDAQ: CBRL), the restaurant and gift shop chain, is one of many successful businesses whose sales in constant dollars have stagnated after a period of rapid, even exponential growth. Historically, Cracker Barrel relied almost exclusively on roadside billboards and word of mouth for its dramatic growth from a small business in Lebanon, TN in 1969 to sales of about $2.4 billion in 2004. Adjusted by the US Consumer Price Index (CPI), Cracker Barrel’s 2022 sales were only $2.1 billion in 2004 dollars.
This decline in real sales has occurred despite or even because of a sustained attempt to diversify away from the historically successful billboard advertising into other media.
Is it possible to use modern Artificial Intelligence (AI) technologies such as ChatGPT or other less well known methods to boost Cracker Barrel or other businesses now stagnant sales?
This article examines Cracker Barrel’s publicly reported expenditures on billboards and other media using Artificial Intelligence based Math Recognition to evaluate the effectiveness of Cracker Barrel’s strategies since 2004, generally supporting the company’s focus on other media, now about two thirds of ad expenditures, although also indicating the effectiveness of current advertising methods whether billboards or “other media” is small compared to the spectacular results in the 1980’s and 1990s.
Indeed the public financial data suggests Cracker Barrel may be fighting a negative effect from growing US Gross Domestic Product (GDP), needing to advertise more and more simply to sustain, never mind boost, company revenues.
Cracker Barrel’s publicly available information on the company’s marketing and advertising expenditures is very limited, falling into two aggregate categories: billboards and “other media” which includes radio, TV, Internet, and other non-billboard methods. The data is annual for the entire United States. There is no geographical breakdown, association with specific marketing or advertising campaigns in time, location, or other important factors.
It is almost certain our Math Recognition would construct more complex models from such details and likely make more reliable predictions from more detailed data which Cracker Barrel undoubtedly has in the internal accounting systems than the relatively simple model constructed from the public data.
What is Math Recognition?
Math recognition is a key part of scientific and engineering practice. It is identifying and recognizing the mathematical formulas and objects describing the data. The Bell Curve often encountered in grading in high school or college is a well known and relatively easy to identify mathematical formula. In addition to grades it describes the frequency of heights in adults of the same sex and many other common measured quantities.
However, scientists, engineers, and financial analysts often struggle to find a viable mathematical formula or formulas for real world data. Without such a formula it is impossible to make predictions or optimize the output of systems.
Our Math Recognizer has a large and growing database of known mathematics including obscure and difficult to identify mathematical objects: special functions, differential equations, etc.. The Math Recognizer uses AI methods to recognize these mathematical formulas in data.
What is the mathematical relationship if any between a company’s advertising expenditures on competing methods and actual sales?
Half the money I spend on advertising is wasted; the trouble is, I don’t know which half.
John Wanamaker (1838-1922)
This is an OLD problem in business.
The Math Recognizer is able to identify a relatively simple mathematical model for the Cracker Barrel data combined with the US Gross Domestic Product (GDP) from the St Louis Federal reserve. The GDP is used as a proxy for the overall state of the economy, something the company cannot control. For example, in the revenues reported by Cracker Barrel we can easily see a sharp drop attributable to the 2020 COVID pandemic lockdowns, something clearly beyond the control of the company.
The model roughly “explains” about 86 percent of the variation in the data. This is a roughly correct interpretation of the R**2 or coefficient of determination Goodness of Fit (GoF) metric used in the analysis.
Once we have identified a model with good agreement with the data, we can optimize the output, meaning maximize the sales in this case, given a projected budget. This is actually somewhat disappointing in that the program recommends to spend the entire budget on the “other media,” non-billboard, category with a slight dip in sales due to the negative effect of GDP according to the model.
Let’s consider a larger future budget of $150 million, an abrupt increase of about $60 million over 2022. In this case we see the expected sales in current dollars to jump from about $3.2 billion in 2022 to almost $4 billion, an increase of about $800 million per year.
For this increase to pay for itself, the additional $800 million in sales must cost no more than $740 million dollars — a profit margin of about 7.5% (seven point five percent). That is a good profit margin for a restaurant. Restaurants often average only 3-5 percent profit margins.
Conclusion
A simple model based on broad financial numbers like these should not be taken very seriously although it may give some insights into a company. Indeed this simple analysis appears to support Cracker Barrel’s existing policies of diversifying advertising out of billboards, despite the disappointing results with inflation adjusted sales stagnant.
An in depth analysis of finely grained internal accounting data may be able to yield more detailed, reliable, and actionable results including a predictive model.
(C) 2023 by John F. McGowan, Ph.D.
About Me
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
How to Boost Your Sales with AI short video using sales and advertising data from the annual reports of the McDonalds restaurant company as an example.
(C) 2023 by John F. McGowan, Ph.D.
About Me
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
Short video on how the Ukraine-Russia war could go nuclear and the urgent need to end the war to prevent global thermonuclear annihilation.
About Us:
Main Web Site: https://mathematical-software.com/ Censored Search: https://censored-search.com/ A search engine for censored Internet content. Find the answers to your problems censored by advertisers and other powerful interests!
Subscribe to our free Weekly Newsletter for articles and videos on practical mathematics, Internet Censorship, ways to fight back against censorship, and other topics by sending an email to: subscribe [at] mathematical-software.com
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John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
The first atomic bomb used in war — dropped on Hiroshima, Japan on August 6, 1945 killed about 140,000 people. The second atomic bomb used in war — dropped on Nagasaki on August 9, 1945 — killed a similar number. The bomb dropped on Hiroshima had an explosive yield equivalent to about 15-20,000 tons of TNT.
Castle Bravo, shown above, was the first test of a deliverable hydrogen or thermonuclear bomb — a bomb small enough to be launched on an intercontinental ballistic missile (ICBM) over the poles to strike Russia or any other target. The Castle Bravo bomb had an explosive yield about one-thousand times more powerful than the atomic bomb dropped on Hiroshima, with a yield of about 15 million tons of TNT (15 Megatons).
As this article is written, the United States and Russia, the two major nuclear powers in the world, are engaged in their most direct, extensive military confrontation in Ukraine ever. Tens of thousands — probably hundred of thousands — have already died. In the Cuban Missile Crisis in 1962, generally considered the closest approach to global thermonuclear war previously, only one person — U2 pilot Major Rudolph Anderson — died.
Cuba was about one thousand miles from Washington D.C. and separated from the mainland United States by an ocean. Ukraine is about five-hundred miles from Moscow and shares a harder to defend land border with Russia.
The United States and Russia are probably the closest to global thermonuclear war ever. The Bulletin of Atomic Scientists, founded by Albert Einstein and colleagues in the 1940’s agrees. They have placed their so-called Doomsday Clock at 90 seconds to midnight, where midnight represents global thermonuclear war, the closest ever — even closer than during the Cuban Missile Crisis of 1962.
The Soviet SS-18 ICBM that terrified people during the 1980’s at the peak of the Cold War could carry one giant 10-25 Megaton bomb, similar to the Castle Bravo weapon. Usually the SS-18 carried ten 550 Kiloton hydrogen bomb warheads.
A single 10 Megaton thermonuclear bomb detonated on Moffett Field in Northern California would completely destroy all building and kill everyone within a ten mile radius shown above. This would kill about 1.75 million immediately just in the zone of total destruction. Radiation and blast effects would cause injuries, deaths, and incomplete damage well beyond the red circle total destruction region shown above. Detonation of the bomb during the California dry season (late spring — early fall) would likely cause massive fires in the mountains circling the San Francisco Bay.
A global thermonuclear war between the United States and Russia would probably involve thousands of thermonuclear bombs on both sides. Hundreds of millions would probably die immediately. The war could exterminate the human race due to nuclear winter, large scale radioactive fallout, or unknown effects from detonating thousands of thermonuclear bombs nearly simultaneously — within hours or at most days.
Russia has been upgrading its nuclear force, both ICBM’s and probably warheads, over the last few decades. The modern force is almost certainly more powerful, faster, and more destructive than the SS-18 arsenal of the 1980’s. All or most of the post-Cold War nuclear disarmament agreements between the US and Russia have expired or been suspended.
What is the United States Doing in Ukraine?
What is the goal of confronting Russia in the Ukraine? What is the exit strategy? What is the benefit to the United States or the World of risking global thermonuclear war in a direct military confrontation half way around the world?
The strategy seems to be to bleed, weaken, Russia, perhaps in analogy to the Afghan war in the 1980’s, using the theory that the Soviet defeat in Afghanistan in the 1980’s caused the end of the Cold War.
The end of the Cold War was an exceptional event, unprecedented or almost unprecedented in world history. Everyone was caught off guard by the end. Almost no one anticipated the destruction of the Berlin Wall, the withdrawal of Soviet troops from Eastern Europe, let alone the dissolution of the Soviet Union, with many republics like Ukraine becoming separate nations.
It is probable that the Afghan war contributed to some degree, but it is quite unlikely it was the primary cause. The old Soviet Union was not defeated in battle. There was no hot war like Ukraine. Rather the Soviet Union was seemingly “defeated” in the realm of ideas. The Soviet Union decided to implement a range of reforms, with mixed results, and abandon hard core communist ideology.
Afghanistan is about 2,000 miles from Moscow, separated by mountain ranges and several non-Russian speaking regions. Ukraine is only 500 miles from Moscow.
Gambling with global nuclear war with a military confrontation in Ukraine based on a single flukish event, the end of the Cold War, is insane.
Time to Talk
We should talk now. Every day that the conflict in Ukraine continues, the United States, Russia and indeed the world are gambling with global thermonuclear war which would almost certainly kill hundreds of millions of people immediately and could cause the extinction of the human race.
Good fences make good neighbors. We’ve faced this before. In 1953, newly elected President Eisenhower went to Korea, talked with the Koreans, Chinese, and Russians and ended the disastrous Korean War which cost hundreds of thousands of lives, settling down into a bloody stalemate. The agreement established a wall, the Korean DMZ, between the North and South Korea. Certainly not an ideal solution, but it has kept the peace for seventy years.
If we can spend $100 billion on offensive weapons to kill Russians in Ukraine, we can spend $100 billion or more if needed to establish defensive fortifications and other methods to prevent either side, Russia or the Ukraine, NATO, and the United States from cheating on the peace agreement, as Hitler infamously did in Czeckoslovakia in March of 1939 after occupying the Sudetenland.
Most likely Russia will end up in control of the Crimea and other predominantly Russian speaking regions — a national divorce not unlike the breakup of Czeckoslovakia into the Czech Republic and Slovakia after the end of the Cold War.
We should talk now and eliminate the risk of global thermonuclear war as soon as possible. Such a war would likely destroy the United States and Russia — and possibly mankind.
Think about it. Contact your President, Senators, and Congress-persons: email, phone, in-person if possible.
(C) 2023 by John F. McGowan, Ph.D.
About Me
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
Sabine Hossenfelder, a disillusioned (former?) theoretical particle physicist and science popularizer, recently published a video “What’s going wrong in particle physics?” on her YouTube channel criticizing fifty years of common practice in particle physics. I’ve previously reviewed her book Lost in Math: How Beauty Leads Physics Astray published in 2018 and an editorial “The Uncertain Future of Particle Physics” in The New York Times (January 23, 2019) questioning the wisdom of funding CERN’s recent proposal to build a new particle accelerator, the Future Circular Collider (FCC), estimated to cost over $10 billion. See the links below for the Lost in Math book review and commentary on the editorial. Comments on the YouTube video follow these links.
Dr. Hossenfelder’s point in the video is fairly simple. She argues that since the formulation of the so-called “standard model” (formerly known as Glashow-Weinberg-Salam or Weinberg-Salam after theoretical physicists Sheldon Glashow, Stephen Weinberg, and Abdus Salam) in the 1960’s and 1970’s, particle physicists have confirmed the standard model, discovering the predicted W and Z bosons in the 1980s, the top quark at Fermilab, and finally the Higgs particle at CERN in 2012.
However, all attempts to find new physics and new particles beyond the standard model since the 1970’s have failed. Particle physicists continue to construct more complex theories that include the standard model such as the Grand Unified Theories (GUTs) of the 1970s that predicted the decay of the proton — never detected. These theories have predicted a long succession of hypothetical particles such as axions, supersymmetric partners, WIMPs (weakly interacting massive particles), other candidates for hypothetical dark matter in cosmology, and many, many more.
These complex beyond the standard model theories keep moving the energy level — usually expressed in billions or trillions of electron volts higher and higher, justifying the research, development, and construction of ever larger and more expensive particle accelerators such as the Tevatron at Fermilab in the United States, the Large Hadron Collider (LHC) at CERN in Switzerland, and the proposed Future Circular Collider (FCC) at CERN.
This lack of success was becoming apparent in the 1980’s when I was studying particle physics at Caltech — I worked briefly on the IMB proton decay experiment which surprise, surprise failed to find the proton decay predicted by the GUTs — and the University of Illinois at Urbana-Champaign on the Stanford Linear Accelerator Center (SLAC)’s disastrous Stanford Linear Collider (SLC) which ran many years over schedule, many millions of dollars over budget, and surprise, surprise discovered nothing beyond the standard model much as Dr. Hossenfelder complains in her recent YouTube video.
Cynical experimental particle physicists would make snide comments about how theory papers kept moving the energy scale for supersymmetry, technicolor, and other popular beyond the standard model theories just above the energy scale of the latest experiments.
Not surprisingly those who clearly perceived this pattern tended to leave the field, most often moving to some form of software development or occasionally other scientific fields. A few found jobs on Wall Street developing models and software for options and other derivative securities.
The second physics bubble burst in about 1993, following the end of the Cold War with huge numbers of freshly minted Ph.D.’s unable to find physics jobs and mostly turning into software developers. The first physics bubble expanded after the launch of Sputnik in 1957 and bust in about 1967. The Reagan administration’s military build-up in the 1980’s fueled another bubble — often unbeknownst to the physics graduate students of the 1980’s.
Dr. Hossenfelder’s recent video, like Lost in Math, focuses on scientific theory and rarely touches on the economic forces that complement and probably drive — consciously or not — both theory and practice independent of actual scientific results.
Scientific research has a high failure rate, sometimes claimed to be eighty to ninety percent when scientists are excusing obvious failures and/or huge cost and schedule overruns — which are common. Even the few successes are often theoretical — better understanding of some physical phenomenon that does not translate into practical results such as new power sources or nuclear weapons for example. But huge experimental mega-projects such as the Large Hadron Collider (LHC) or the Future Circular Collider (FCC), justified by the endless unsuccessful theorizing Dr. Hossenfelder criticizes, are money here and now, jobs for otherwise potentially unemployed physicists, huge construction projects, contracts for research and development of magnets for the accelerators etc.
Big Science creates huge interest groups that perpetuate themselves independent of actual public utility. President Eisenhower identified the problem in his famous Farewell Address in 1961 — best known for popularizing the phrase “military industrial complex.”
Akin to, and largely responsible for the sweeping changes in our industrial-military posture, has been the technological revolution during recent decades.
In this revolution, research has become central; it also becomes more formalized, complex, and costly. A steadily increasing share is conducted for, by, or at the direction of, the Federal government.
Today, the solitary inventor, tinkering in his shop, has been over shadowed by task forces of scientists in laboratories and testing fields. In the same fashion, the free university, historically the fountainhead of free ideas and scientific discovery, has experienced a revolution in the conduct of research. Partly because of the huge costs involved, a government contract becomes virtually a substitute for intellectual curiosity. For every old blackboard there are now hundreds of new electronic computers.
The prospect of domination of the nation’s scholars by Federal employment, project allocations, and the power of money is ever present and is gravely to be regarded.
Yet, in holding scientific research and discovery in respect, as we should, we must also be alert to the equal and opposite danger that public policy could itself become the captive of a scientific-technological elite.
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
This video discusses the dark legacy of World War II, how the persistent invocation of the trauma of World War II provides a powerful motivation and justification for wars, how this applies to Ukraine, and what the US, Russia, and Ukraine should do as quickly as possible to avert thermonuclear war.
Subscribe to our free Weekly Newsletter for articles and videos on practical mathematics, Internet Censorship, ways to fight back against censorship, and other topics by sending an email to: subscribe [at] mathematical-software.com
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
Twelve minute video on latest 2023 Microsoft layoffs, the long history of Microsoft layoffs while simultaneously claiminig a STEM worker shortage, and what it means for tech workers.
Subscribe to our free Weekly Newsletter for articles and videos on practical mathematics, Internet Censorship, ways to fight back against censorship, and other topics by sending an email to: subscribe [at] mathematical-software.com
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
Is the “conspiracy theory” label stopping you from reaching your desired audience?
Has the thought-stopping pejorative phrase “conspiracy theory” ever caused serious problems discussing certain ideas or even objective facts with your audience, friends, family, or colleagues? Today even the simple word “conspiracy” is increasingly used this way. How can you overcome the thought stopping effect of “conspiracy theory” and expand your audience?
“Conspiracy theory” labelers frequently use superficially plausible arguments backed up by no data or a single or few examples. For example: “conspiracies will always or almost always fail because someone would have talked,” citing for example the exposure of the Watergate burglary failure and the downfall of Richard Nixon. This would for example suggest unsolved murders by conspiracies, such as “gang,” “Mafia” or “organized crime” killings are exceptionally rare or nonexistent.
What does the data actually tell us about the frequency and success rate of conspiracies?
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).