Limits 2/24/19

By Richard E. Bleil, Ph.D.

The interesting thing about science is the half-baked theories you get to hear in seminars. It seems like old ideas return periodically. For example, if you keep an eye out, you’ll see another report of the benefits of alcohol every few years. Another study by another (probably alcoholic) scientist will help support drinking habits, and a few months will pass before a follow up study from another group that will say “Well, yes, but only within limits!” I can’t help but wonder how long this pattern will continue.

For some reason, the one I am thinking about to day was a hypothesis by a couple of (if I recall correctly) physicists who were trying to sell the idea (and it seemed to be gathering traction) that every object possible must exist somewhere in space. Their argument is that, space is vast and reaches infinity, and therefore must contain every possible shape, large or small, imaginable. Their “proof” was a so-called “Klein Bottle”, a geometric shape that looks vaguely like a pitcher but is twisted on itself that it has no inside or outside. They had used a 3-D printer to create such a construct, and carried it with them. “See?” they would say, triumphantly holding their Klein bottle up, “this geometric construct has been proposed, and here it exists! In OUR universe!!!”

Gee whiz, thank you, Mr. Science.

The problem is that this argument has been around since the ancient Greek civilization, whose philosophers posed a logic question. Of course, they formulated the argument to include one of their heroic figures, so they might have said something like “Achilles cannot even cross the road!” The argument goes as halves; to cross the road, Achilles must cross the halfway point. Before crossing that halfway point, he must first cross that halfway point. And before that another, and so on. There are an infinite number of halfway points, and therefore, if you add up all of the distances of all of the halfway points, since there are an infinite number of distances the distance is infinite.

Is your mind swirling yet?

The upshot of the argument is that, since an infinite distance between all objects is (clearly) infinite, all motion is impossible, and therefore motion is an illusion.

If any of my mathematician friends are reading this, they’re pulling their hair out by now. “But what about limits?” they’re shouting at the top of their lungs at their inanimate computer screens, thereby irritating their spouses who are wondering what the issue is THIS time?!?

See, it is true that there are an infinite number of halfway points from any two objects. That much the pre-calculus philosophers got right, but what they forgot to take into account is that these distances are approaching zero as quickly as halfway points are added. They’ll never quite get to zero. The term is “asymptotic”; the distances will get closer and closer to zero without ever actually touching it, much like my so-called love life. You can add up these infinite distances as they become infinitesimally small. It’s called “integration”. You’ll discover that the distance between any two objects is actually equal to (are you sitting down?) the distance between the two objects.

So, yes space is infinitely large, but there are also an infinite number of possible shapes. So, if you integrate, you’ll discover that the number of shapes in the universe is actually equal to the number of shapes in the universe. You would think a scientist would know this much about calculus.

In economics, this is called the “Law of Diminishing Returns.” It’s funny how well people get concepts when there is money involved. See, in this economics law, they point out that if you own a factory and increase one component while holding everything else constant, your profit increase will become smaller and smaller. In other words, if you add more workers, but no more machinery, eventually you will be paying more for no significant increase in profit.

It’s funny some of the crackpot theories you hear from respectable scientists in these seminars. I heard one well-respected scientist working in medicine claiming that he discovered a compound that cured all forms of cancer. The only unfortunate side effect is that it also killed the host. Every time.

Well, yeah, kill the host, and the cancer stops. Kinda funny how that works out.

In another seminar, a physicist claimed he discovered that classical Newtonian laws can, in fact, replace quantum theory. All you have to do is add enough additional unjustified “fudge factor” constants and terms to the already existing laws. Well, yeah, you can make anything fit if you just add terms willy-nilly.

In fact, the earth IS, in fact, the center of the universe. It’s all a matter of definition, in fact. See, if you assume the center of the universe is, well, the center of the universe, then the equations of motion work out simply. But, the center of any axis is (mathematically) arbitrary, so if you really want to work out the complexities of the mathematical formulae involved with re-defining the center of the universe such that it is, in fact, earth, you can do that. Good luck ever passing an astrophysics exam again, though.

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