How would you pronounce an infinite sentence?

Well, it’s Saturday, April 1st, 2023, AD or CE, and I am writing a blog post today because I am working today.  You can’t say I didn’t warn you.

Well, you can say it, but it wouldn’t be true.  You can say almost anything, really.  There is a functionally limitless number of sentences that you can utter, and not all of them will be true.  It’s a vaguely interesting question whether the number of truthful sentences that can be uttered is as limitless as the number of sentences one can utter.  At first glance, it seems, one being a subset of the other, that it should not be the case, but when dealing with infinities, one has to be cautious—initial intuitions can be misleading.

If one restricts oneself to existing words or compound words, and one restricts oneself to sentences that follow standard grammatical rules, one can build a functionally limitless number of sentences simply by including compound sentences or nested phrases, like, “He knew that she knew that he knew that she knew that he was a pedantic idiot.”  That feels a bit like a cheat to me, but logically speaking, it can be done.

Of course, even if, in principle, the number of such possible sentences is infinite, there is a practical limit to the number of them one could possibly construct before the heat death of the universe—or, if the universe “ends” in some other way, before that happens.  This is part of why I wonder whether the number of truthful statements potentially constructible is actually as large—in practice, even if not in principle—as the total number of possible statements.

One could, in principle, construct sentences describing, to the degree possible, the quantum state of every describable aspect of all of accessible reality.  Of course, one could also just make up descriptions of quantum states that have nothing to do with our reality, but if Everett was right, or if the String landscape is right, or what have you, they might all be true somewhere, depending on how you define “some” and “where”.

But, of course, it’s trivially easier to describe quantum states in ways that are physically nonsensical, e.g. “The quantum state of that electron is blue with purple polka dots and smells like ripe bleu cheese”.  Or one can make impossible statements using more formal terminology, such as, “The precise location and momentum of this particular ‘particle’ are, at this precise moment: x and y, with no rounding of digits anywhere.”  As far as we know, that’s physically impossible.

It’s not as exciting as the physically impossible tale, “Bob accelerated his ordinary human body instantly from a standstill to the speed of light, at which speed he stayed long enough to go to the sun and back.  It was an incredible sixteen minutes, and everyone who watched him do it was amazed and thrilled.”

We know that can’t be true because, for one thing, nothing with “rest mass” can reach the speed of light at all—that would require an infinite amount of energy.  Also, if you’re going the speed of light, you can’t experience it, because for you, time ceases to pass.  Also, it’s questionable whether anyone could “see” you moving at that speed, and not just because you would become a black hole before you could ever achieve light speed.

Or would you?  I’ve tried to ask people who should know what would happen if a spaceship (for instance) was accelerated to close enough to the speed of light that, given length contraction and “relativistic mass” it compressed to a front-back length that was shorter than its Schwarzschild radius*, but I haven’t seen or received a reply about it.

This is one of the reasons I bought no fewer than two big textbooks on General Relativity; if I couldn’t get someone to give me the answer, I wanted to try to work it out.  I suspect that the fact that the length contraction is along one axis might make it a complicated situation for any large-scale object; maybe no one has done the mathematics on such questions, but that feels unlikely.

It also feels unlikely that I’ll find the time and discipline to work my way through the appropriate textbooks before I die.  There is background mathematics involved that I would need to master if I were to be able to apply the theory properly.

I don’t doubt that I’m capable of it; it’s not like playing professional basketball, where there are fundamental, physical limits to what someone my height (and age and athletic ability) could accomplish.  But there are so many things that interfere, and my time (and my will) is burned up daily upon matters of even more trivial character than all the pointless things I’ve already done in my life.

At least I’m gaining back some time thanks to my new bicycle.  I am now troubled, though (as I always am when I have some structure outside of myself upon which I have chosen to rely) with worries about maintenance, such as:  What will happen if the tires go flat while I’m en route to the train station?  It’s not that such a thing would be an unsolvable problem; I’ve dealt with such occurrences before.  But I don’t want to deal with them.  Even having to think about them constitutes one more straw piled on the camel’s back, and I’ve been carrying too much straw for too long.  I’m tired.  I want to lie down and just stay that way.

At least I’m getting good exercise.  And now that the seat is fixed, the bicycle seems to be operating well.  I may need to edit (slightly) my scathing review of it on Amazon.  We’ll see.  I’m going to watch and wait a bit longer for any other problems that may arise before I do that.

In closing, I’ll grudgingly acknowledge the fact that it’s “April Fool’s Day” just to remind you that you are all fools…but that I am a fool as well.  So were Einstein and Newton and Socrates and Marcus Aurelius and the Buddha and Lao Tzu and Confucius and, well, everybody else.  As Einstein is credited with saying**, “There are two things that are infinite:  the universe and human stupidity.  And I’m not sure about the universe.”

Depending on what you mean by stupidity, that can be trivially true in the mathematical sense, i.e., the number of unknown things in the universe is infinite.  There are other uses of the word stupidity about which the statement might not be true.  For instance, there are those who define stupidity as doing something in ways that are less efficient than randomness, such as trying to get to the airport by repeatedly driving around the block from your house until your car wears out.  Moving randomly could at least eventually get you to the airport, whereas going in “circles” will never get you there, even with a car that lasts forever.

Enough!  I wrote “in closing” and I haven’t closed yet, so I’ll do that now.  Have a nice remainder of your weekend***.  I’ll be back writing on Monday, barring the unexpected.


*According to outside observers, that is.  For those on the spaceship, it would be the outside world that would constrict into an ever-narrower “tunnel” in the direction of travel.

**I think this attribution is a correct one, which is not reliably so with many quotes attributed to Einstein online.

***What’s the modulus of a weekend?

One thought on “How would you pronounce an infinite sentence?

  1. That was a fun to read blog. Herd your Mom in there made me think of some fun times. Thank You for that. I will try to enjoy my weekend and you should too. Love and miss so much of our family Lance

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