Do You Have The Wisdom To See What’s Not There and To Not See What Is There?

I woke up one morning to find this in my text messages: “Hi, Mr. Math Award. I need your opinion on this.”

Not “good morning” but “hi.” It was from my west coast daughter. It was a group text for some reason, so, although the question was directed at me, the whole family was involved.

About the “Mr. Math Award” thing. It’s an inside joke about a speech I once gave to a class of graduating seniors of my old high school. It told the story of my greatest high school disappointment – winning the math award instead of the science award. But, as they say, that is another story.

This story is about one of those rare occasions when my kids actually thought I was funny. And it’s about math.

A little about math. More about philosophy.

And by philosophy, I mean wisdom.

And by wisdom, I mean common sense.

Yes, it will require a bit of intellectual spelunking, which no doubt will meet with some disapproval from my sister-in-law, but, I promise, the payoff at the end makes it all worthwhile.

I’m sure she’s not alone in wondering why I often wander down these rabbit holes of deep thought. Ha! I call it deep thought, but others might think of it as “arcane trivia.”

We all have our own points of view, I guess.

Actually, I don’t guess. I’m counting on it. And what may be perceived as “arcane trivia” to one represents “deep thought” to another.

And so down the rabbit holes we go.

But not too far. Far enough, though, to extract the maximum amount of intellectual entertainment with the least amount of digging. And then its back to the surface to find another rabbit hole.

Over and under and over and under we go again and again. Until we’ve collected enough pieces of the mosaic to see the picture before us. It was always there. Sometimes it’s just a little harder to see.

Before we venture into the underground homes of our cotton-tail friends, you must know of what I was asked to opine upon.

[Spoiler Alert: It involves math.]

[Reassurance Alert: You like classic movies, don’t you?]

Daughter text: “Hi, Mr. Math Award. I need your opinion on this.”

What followed was a link to a Tik Tok video featuring a young woman. Some might call her a “girl” because she comes across as an overly enthusiastic high schooler. Of course, the gratuitous nose piercing helps, too. Personally, I think she’s a woman who wants people to believe she’s still in high school.

Using graphs to illustrate her point, she showed the function x=y and explained the line goes on forever – infinitely in both directions. Then she showed the line that begin at 1 and ended at 2. She asked, “There’s an infinite number of fractions (because decimal places go on forever) between one and two, how does it get from 1 to 2? How does it hit all the decimals in between?”

Great question. But only because it’s not a math question, as you’ll see in a moment. For those curious, however, I’ve included my response to the math part of this riddle:

Daddy text (1): This is an analog vs. digital question. The line between 1 and 2 captures all fractions between those numbers in an analog way. It does not attempt to plot each fractional point. Doing that would be like looking at it in a digital way. Think of digital as a collection of individual dots (or points). When you have enough, they look like one continuous line.

OK, so the better answer would have been explaining the difference between “unbounded” infinity (i.e., infinite additions like we see in x=y) and “bounded” infinity (i.e., infinite divisions, like the number of decimals between 1 and 2). But I doubt my kids would have continued reading the text beyond the first “i.e.” For that matter, did you?

Anyway, I went on:

Daddy text (2): Also, this is a play on words. What is a “number”? There are an infinite amount of whole numbers. There are also an infinite amount of decimal places. However, when the decimal places go out far enough, the mind cannot distinguish the difference and, in effect, rounds up (because we think in analog fashion). A computer, however, does recognize each decimal point (because it thinks in a digital way). Come to think of it, this might make a great sci-fi premise. Wait. It already has. This is how Captain Kirk tricks computers into self-destructing. Kirk: “[insert rogue computer name], tell me the last digit of pi.” Computer: “Working… working… 3.1415926535897 KABOOM!” End of computer. Kirk saves the universe (again).

Now things really start to get interesting. And not just in math. This idea could have implications for major Hollywood franchises. Here’s what I mean:

Imagine if Captain Kirk had appeared in Terminator. We would never have had to suffer through that di-trilogy of movies (i.e., six movies/sequels as opposed to the tri-trilogy – nine movies/sequels – we had to suffer through – and that was really suffering! – of the original Star Wars saga – after all, we are talking math, aren’t we?). No, with Captain Kirk at the helm, Terminator would have lasted as long (and been just as satisfying) as that classic animated short Bambi vs. Godzilla. (Although, while it’s easy to see Kirk as Godzilla, it does stretch the imagination a bit to picture Arnold Schwarzenegger’s T-800 as Bambi. Oh, well, it is what it is.)

Which ultimately returns us to our original idea.

Tik Tok girl’s question lacks common sense. [Classic high schooler.]

We can see why x=y goes on to infinity. Unbounded infinity makes sense to us because we can see it. It therefore matters to us. We readily recognize it and can easily discuss it.

On the other hand, we cannot see the infinitesimal number of decimal points between 1 and 2. We can’t see bounded infinity, so, unless you’re having lunch with a group of socially awkward mathematicians, why bother talking about it?

In other words, do you have the wisdom to see what’s not there and the wisdom to not see what is there?

Common sense tells us short cuts make life a lot easier to live. Maybe that’s what makes us human.

Which leads us to this last text:

Daddy’s final text: The lesson: Tik Tok girl should watch more Star Trek (The Original Series)…

…or she’s a robot.