Axioms and Postulates

Mr. Parker

I was a horrible tenth grade geometry student.  The subject combined two of my least favorite subjects:  art (shapes and drawings) and math (numbers, numbers, numbers, or worse, letters, letters, letters).   And then there was Mr. Parker, Wyoming High School boys basketball coach and my geometry teacher.  I was a new student at Wyoming that year, trying to find my way “in” the school society.  And I was a wrestler and a track guy, not a basketball player.  When I got cut from the fifth grade team, the coaches were right!!  

So it was math, with drawings, taught by a basketball coach.  And, truth be known, he was a basketball coach with an addiction to chalk.  It wasn’t that he used it too much; he ate it. He would lick his fingers, then run them through the dusty chalk tray, then lick the chalk off (really!!).  So there was that distraction.   (Now a retired teacher and coach, I recognize that there are all sorts of things kids pick up that we don’t notice!!) 

I think I got Wyoming’s version of the “gentlemen’s ‘C’”.  I did enough work to pass the course, but really didn’t get it.  As my college Spanish professor would later say, “I will give you a ‘B’ if you promise to never take Spanish again”.  I raised my hand in a sacred oath. But in Geometry I did learn a couple of things, including about axioms and postulates. 

The Rules

Axioms are self-evident truths (I remember that because of the Declaration of Independence, my specialty).

  • Things which are equal to the same thing are also equal to one another
  • If equals be added to equals, the wholes are equal.
  • If equals be subtracted from equals, the remainders are equal.
  • Things which coincide with one another are equal to one another.
  • The whole is greater than the part.

Postulates could be “derived” from the axioms.  Here are some examples:

  • To draw a straight line from any point to any point.
  • To produce a finite straight line continuously in a straight line.
  • To describe a circle with any center and distance.
  • That all right angles are equal to one another.
  • That if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which the angles are less than two right angles. (SFU).

Axiomatic

OK, now that I’ve given all the “math-block kids” among us renewed nightmares, let me get to the point.  I recently heard a debate about the future of Artificial Intelligence.  One of the debaters took an “axiomatic” view of AI.  To paraphrase:  we will see in five years that AI is “good” for society, but we will need to live through the turmoil, wide-spread unemployment for example, that will occur in the meantime.  To him, AI was a done deal, beyond control, and humanity needs to “ride-out” the storm to reach the benefits on the other side.  

Several other participants in the conversation agreed, seeing AI’s expansion as an “axiom”.  AI is happening, it’s too late to stop it, and no one can control it, perhaps, including the billionaires who are building AI in the first place.  In Islam, there is a term, Inshallah:  only Allah controls the future.  In this case it’s Insh-AI, an AI inevitability that cannot be controlled.

Derivative

But another commentator took exception to this axiomatic approach.  He argued that there is no guarantee of five years to “AI Paradise”. And while he didn’t suggest an “AI Armageddon” either, what he did say is that the economic dislocation, unemployment, and upheaval of an “AI Revolution” has no guarantee of good outcomes for humanity.  He spoke up for rigorous regulation by government, in spite of the supposed “good faith” promises of the billionaires who will grow even richer from an AI boom whatever else happens to the nation and world. 

This commentator also asserted a controversial “fact”.  He said that the younger generation, particularly adolescents, don’t like AI.  Perhaps they realize that the entry level of many of the professions they aspire to, could soon be filled by Claude, or Gemini, or Chat GPT.  Regardless of the veracity of that “fact”, the reality is this.  If AI fills the lowest level positions, how will future employees get the experience to become the “middle managers” and more in the future?

I take a similar view.  None of us can really foresee the future.  But we can reasonably expect that there will be economic dislocations (real life unemployment) due to Artificial Intelligence.  It’s already occurring.  And the idea that the “founders” of Artificial Intelligence, the ones who have the most vested financial interest in these programs, should be put “in charge” makes no sense.  Self-regulation by those who have the most to lose by restriction makes the control “equation” completely unbalanced, regardless of what Mark Zuckerberg says. He is the best example: how well did self-control work with social media?

Fly the Plane

The United States Government regulates air travel.  That seems logical:  air travel is inherently dangerous.  It’s not like pulling the car over with a flat tire; if a plane fails, it falls from the sky.  It’s reasonable that the government should take control of both quality and traffic control.  

And the obvious example is Boeing, one of the largest manufacturers in the world.  Like Meta, Anthropic and Open AI, Boeing had the most to lose by an “out of control” product.  Boeing makes billions of dollars in profit, all predicated on their airplanes being safe.  And they marketed the Boeing 737 Max 8 as the newest, “best-est”, safest, passenger aircraft.  

Except for one “little” glitch.  Somewhere buried in the computer program that balanced the aircraft in flight was a flaw.  It was designed to keep the plane from stalling and falling from the sky.  If a sensor detected a possible stall, the program forced the nose of the plane down to increase speed and keep it flying.  But, the sensor failed.  And the computer did exactly what it was supposed to do:  it pushed the plane into a dive, one that pilots were unable to correct manually. 

Three hundred and forty six people were killed in two different crashes.  Boeing ultimately found the sensor issue, and adjusted the computer program.  But they didn’t do it “on the fly”. In fact, the 737 Max 8 fleet was grounded for over a year and a half, by the government.

The Public Interest

Today, we hear folks say that Congress can’t regulate Artificial Intelligence.  It’s noted that many Congressmen don’t even know how to operate  simple computer functions, like checking Google or using email.  So how could they regulate Artificial Intelligence, especially as the field is advancing so quickly? 

The vast majority of Congress (Senator Mark Kelly excluded) can’t fly complicated aircraft.  But they still manage to regulate air travel.  In the same sense, Congress doesn’t have to be able to program Artificial Intelligence.  It doesn’t stop them from getting experts, not tainted by the future profitability of the field, and empowering them to write regulations. 

We can’t just hope that AI will be “good”.  The first axiom should be:  protect ourselves. 

Author: Marty Dahlman

I'm Marty Dahlman. After forty years of teaching and coaching track and cross country, I've finally retired!!! I've also spent a lot of time in politics, working campaigns from local school elections to Presidential campaigns.

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