It is not well known that my algebraic equations were reformulated from 18 partial differential and difference equations that I invented. Or that I invented my 18 equations from the iconic formula F=ma which, in turn, were formulated from the 330 year old Second Law of Motion in physics.
It is not well known that I correctly reformulated those partial differential equations to simulate petroleum reservoirs. I did so because mathematicians had incorrectly formulated them for reservoir simulators in a manner that defied the Second Law of Motion. Under the Second Law, all simulators should account for the inertial force. Yet, not one did so!
First, I had to discover that the inertial force was missing from the iconic Darcy's formula for a century and half. Discovering that may seem obvious, yet it's not as obvious as the Earth is round. After all, the curved horizon at sea led scientists to theorize that the Earth is round. Similarly, errors in computed solutions led me to theorize that a fourth force was missing. The consequence is profound: ignore the inertial force and you've changed the Second Law of Motion and your simulation will be physics-defying.
Second, I had to incorporate these updates into my new partial differential equations, which are akin to the Navier-Stokes equations. These are the only equations that are cross-listed in both the "Seven Millennium Problems" of mathematics and the "20 Grand Challenges" of computing. Because it was challenging, it took me a decade to put the dots together and develop the connections between the Second Law of Motion, Darcy's formula, and the Navier-Stokes equations. I deserve credit for that achievement. The correct formulation was not at all obvious to mathematicians because they barely understood the physics. I certainly couldn't have come up with the correct equation if I didn't deeply understand both the mathematics and the physics.
Finally, the most difficult part was that I worked alone on solving the problem. In the 1980s, I alone programmed a dozen supercomputers, each powered by thousands of sub-computers that communicated as an internet. It was big science—in terms of labor and money—completed by one man with zero funding.
Today, no one person can embark on such a project because a supercomputer costs up to 1.32 billion dollars and requires 10,000 programmers. To make a name, you have to be a supercomputer administrator and take the credit for the discoveries of 10,000 scientists.
I did not begin my solution with the supercomputer, as was widely publicized in 1989. I had to understand the governing partial differential equations; understanding those helped me discover that they were not correctly formulated. They were incorrect because they only summed some of the forces. I summed all four forces in the reservoir simulator. Without my doing so, the simulator would compute everything wrong. This is what programmers call GIGO, Garbage In, Garbage Out.
This means that if you sum three forces in your partial differential equations, don't expect them to simulate as if you summed four. If the sum of the forces encoded into the reservoir simulator is not equal to the mass times acceleration, the equality will not magically reappear on any of its 65,000 sub-computers. In simulation, as in life, you cannot plant yams and expect to harvest corns.
The process of discovering partial differential equations and inventing algorithms for solving them was long and complex and not for the faint of heart. How did I invent them? First, I had to arrive at the frontier of knowledge in partial differential equations, before I could move beyond it. I then had to possess the mathematical maturity to understand why the previous equations were not balancing correctly. Finally, I had to have the confidence to attempt to re-derive two century old equations from first principles, namely, the Second Law of Motion.
This achievement of discovering equations and inventing algorithms called not for genius, but for courage—the courage to say: "Your F is not equal to my ma;" the courage to say: "You've unbalanced with three forces the equations that nature balanced with four." Because of my courage to say that the inertial force was missing, I was viewed as the child who pointed out that the Emperor had no clothes. I called upon geophysicists to ensure congruency between the forces in their simulator and reservoir. Both were in-congruent to each other because a four-force F was not equal to ma in their simulator but it was equal in their reservoir.
A supercomputer cannot discover that a fourth force was missing. I—its programmer—re-discovered the fourth force and correctly summed all four forces. The following story illustrates how dumb a supercomputer can be. A schoolteacher took her students on a field trip to see a supercomputer. The machine comprised of 65,000 sub-computers interconnected as an internet. It occupied the space of four tennis courts and consumed as much electricity as a city of 5,000 people.
"This supercomputer can come up with an answer faster than all of the combined efforts of humanity," the teacher explained.
She gave the supercomputer some difficult questions, and within seconds, it spat out the answers. The teacher turned to her students and said:
"You may ask it any question."
A child stepped forward and said,
"Hello, Supercomputer. How are you?"
There was no response!
As this story illustrates, I did more than switch my supercomputer on. A supercomputer cannot convert data to information, information to knowledge, and knowledge to wisdom. Only humans can convert data to wisdom. We make discoveries by taking risks, leaving our safe zones, and jumping into the deep end.
No matter how fast a supercomputer becomes it will still lack the self-awareness necessary to answer the simple question, "How are you?" A machine that can't see itself or react to failures within itself cannot correct incorrect equations. The supercomputer lacks the wisdom possessed by a baby. It can't answer profound questions, such as "Does God Exist?" It is the supercomputer that needs the wizard to make it super, beyond super.
Philip Emeagwali wrote the actual equations used by Exxon (now Exxon Mobil) to simulate the flow of oil, water, and gas inside its reservoirs. He discovered that their equations did not reflect reality and corrected their error.
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