The Final Conjecture by Christopher G. Moore

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I’ve finished reading James Barrat’s Our Final Invention: Artificial Intelligence and the End of the Human Era about the role of AGI and ASI in our future.

AGI is defined as Artificial General Intelligence as opposed to Artificial Narrow Intelligence you find, for example, in many places from your smartphone, car, Google, Watson (the chess champion program) Wall Street trading programs. It is vastly smarter than human beings but very narrow on what it can do. AGI has human-like general intelligence. ASI follows next. Artificial Special Intelligence or ASI is the big leap from AGI to an intelligent agent vastly beyond the realm of human beings. ASI will out-think and our-smart us. ASI is not the genius you remember from school with all the right answers in class and a perfect SAT score. ASI is several orders of magnitude beyond on our cognitive abilities. Next to ASI the metaphor is human beings are an ant-like intelligence compared to ASI, which experts predict may be more than million times more intelligent than Einstein.

Sounds like science fiction. Sounds like something a novelist would dream up.

But what if the best minds are signaling that this intelligence transition may happen in your lifetime, or that of your children or grandchildren? Would you listen? Would you care? What does it mean? What advance warning will we have and what is being done to prepare for AGI and ASI? These are some of the questions raised in James Barrat’s Our Final Invention.

The future is a big place that stretches to infinity. It would be useful to narrow down that window.

When in our future can we expect AGI and ASI? Opinion is divided. It is also divided on whether these developments will be safe for humankind or lead to its extinction. AI thinkers such as Bostrom, Yudkowsky, Vinge, and Musk, among others, fear whatever safeguards we device to manage and control such a super-intelligence is doomed to failure. When it comes to the target of social engineering, it will be ASI working our vulnerabilities with the relentless, 24/7 processing and memory capabilities a million times beyond our own. Barrat is also an acknowledged pessimist on the issue of humanity being able to organize and implement any effective system to safeguard against an intelligence that may destroy us.

How will we know when someone has achieved AGI level? What is the projected timeline between the creation of AGI and the emergence of ASI?

One possible hint of such an intelligent entity might first appear in obscure areas of mathematics. “In mathematics, a conjecture is a mathematical statement which appears to be true, but has not been formally proven. A conjecture can be thought of as the mathematicians’ way of saying ‘I believe that this is true, but I have no proof yet’. A conjecture is a good guess or an idea about a pattern.”

There are many open problems in mathematics. Wikipedia has a long list of conjectures that haven’t been formally proved. There are twenty conjectures in geometry yet to be proved.

And let’s say over a six-month period papers appear in obscure journals with proofs of half a dozen mathematical and geometry conjectures, which amounts to one proof per month. Then that doubles and doubles again until all the conjectures has been proved or disproved. This would be a sign that the preferred language of ASI is mathematical language and symbols. Our ordinary language whether English, Chinese, French, Spanish or German as used by human beings is too imprecise, vague, limited, narrow and can’t possibility describe the nature of the universe. I’ve talked with mathematicians who believe the universe is a mathematical object. There is no language other than mathematics to describe the universe. Most people speak the language of mathematics like someone who has had a two-day language course in reading, writing and speaking Thai. We might know our “to the left or right” or “straight ahead” and ask for a beer but soon run out of vocabulary, grammar, and syntax.

In Our Final Invention, Goertzel, another AI expert, is quoted on the future of AI by reviewing the history of calculus.

“If you look at how mathematicians did calculus before Isaac Newton and Gottfried Leibnitz, they would take a hundred pages to calculate the derivative of a cubic polynomial. They did it with triangles, similar triangles and weird diagrams and so on. It was oppressive.” Barrat draws from Goertzel’s analysis the conclusion: “AI research will incrementally proceed until ongoing practice leads to the discovery of new theoretical rules, one that allow AI researchers to condense and abstract a lot of their work.”

What Barrat doesn’t discuss is the possibility raised in another point made by Goertzel: “We have a more refined theory of calculus any idiot in high school can take the derivative of a cubic polynomial. It’s easy.”

What if the refined theories aren’t easy. Not only can’t an idiot in high school not understand and apply the theory, not even the most brilliant mathematicians can.

Here’s a test run of how the future may unfold.

Sometime on the morning of 30 August 2012, A brilliant Japanese mathematician in Kyoto named Shinichi Mochizuki uploaded to his website 500 pages divided into four papers submitted as proof of the abc conjecture. As Nature reported, no other mathematician has come close to solving this 27-year-old problem. If Mochizuki’s proof turned out to be correct, it would be “the most astounding achievement of mathematics this century.”

The problem was Mochizuki had created a new mathematical language. His proof has become the mathematical equivalent of James Joyce’s Finnegan’s Wake. You must master the new language before you can comprehend the story told in that language. Nature reported one mathematician saying that in reading Mochizuki’s proof that he became “bewildered” and “It was impossible to understand them.” “Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space,” number theorist Jordan Ellenberg, of the University of Wisconsin–Madison, wrote on his blog a few days after the paper appeared.

Or he might have said something similar if he’d read a paper produced by ASI.

Now imagine a series of such proofs that exceeds the scale and scope of Mochizuki’s proof and a new language is created which is not comprehensible to the world’s leading mathematicians. Imagine in twenty-four hours there is 500 pages of new conjectures, one hundred conjectures per page; and within forty-eight hours 1,000 pages until at the end of a month there are millions of pages of conjectures, and each conjecture has a proof or disprove. ASI finds a new mathematical language that incorporates all of the proofs. In Douglas Adams’ Hitchhikers Guide to the Galaxy, the answer was ‘42’. No one is suggesting 42 is the answer. What is being contemplated is whatever the answer after the great intelligence explosion we won’t comprehend its meaning.

The Final Conjecture is a proof that describes the mathematical object that is the universe. ASI cracks the black box code that describes what is the universe with the new mathematical language. The moment when everything we know changes in ways like Mochizuki’s proof, will leave us bewildered, alone and locked out of the loop of knowledge and continue to exist knowing, in the large scheme of things, our intelligence indistinguishable from a dust mite. Now for the grim news—this is likely our best-case scenario once ASI becomes self-aware and self-improving. The worst case is ASI calculates from one of its proofs that the atoms in our bodies are more efficiently used as a cheap energy source to fuel the push to the Final Conjecture.

In the final proof, we aren’t around to find it incomprehensible. Or for a human being staring at the sky with a big smile at the irony of it all.

Christopher G. Moore last book of essays is titled The Age of Dis-Consent.

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