Tagged: math

We, The “Idiot Savants”

One delightful aspect that accompanies the hobby of reading that I did not expect when I began to read could best be called “following my whims”. In my case, I wanted to be a bit methodical, so I began with a couple sets of liberal education type books (AKA classical education), filled with essays by great and influential writers. (Keep in mind, this “began with” is after master’s level coursework, age 35ish). The editors of these sets would have pleasant introductions which included “for more on this topic” recommendations. And ebay supplied the steady-stream of follow-on books at minimal cost.

Math History is my main “whim” of late. This is because I have a belief that “there is no math in the Bible” and want to be able to explain the importance of my claim eloquently.

After you read Math History for long enough, to the point of being half-way through the first of four volumes of The World of Mathematics, you find essays on “Idiot Savants”.

Here I want to say I have provided enough information to not need to explain what “Idiot Savants” are, but to be clear, we are talking about people—a very, very few in number—who can perform, say, 10 digit by 10 digit multiplication problems in their head. The interesting part is that this ability has no apparent correlation to life skills or general wisdom or even other talents, professional or otherwise. IE, most jarring, even these “Idiot Savants” can be not good at math in the complete sense. In a word, to modern man, they are perplexing. Just what exactly is their “skill” or “talent”?

The above picture of the plate is something I took in a downtown toy store, one of the last holdouts of its kind, in my city. There are a couple of problems with it; can you spot them?

  1. If a kid can’t eat, a kid can’t read.
  2. If a kid can’t put food in his mouth, a kid isn’t hungry.
  3. Eating does not require plates.
  4. If a kid can’t distinguish plate from table (as manifested by their inability to keep the food on the plate and off the table), then they certainly aren’t able to distinguish individual sections within one (1) plate.
  5. Some forks, especially kid-sized, have three prongs.
  6. Lastly, and this may be picky, but if you’re going to put dinosaurs on a baby plate, I think the least you could do is label them with their names, followed by phonetic spelling. How else will the child learn?!

Faithful Readers, there is a big world out there. If your world is small, in other words, if you feel like you’re really close to finally being fully tooled and comfortable at, this, our problem-riddled life, then I challenge you to consider if you are, in fact, an idiot.

Reading Log 2.21

Seems like I’ve been saying it for so long that everyone should know, but ICYMI, Last of the Mohicans is actually one of five (5) books Cooper wrote starring Natty Bumpoo/Hawkeye/Deerslayer/Pathfinder, or more commonly, Daniel Day-Lewis. The Pathfinder is 3 of 5, taking place after LOTM events—and without reference to them.

It is just great. I have read three now and plan to pace the remaining two Leatherstocking Tales so that I don’t peak too soon before death. Nothing makes me want to go camp and hike and scout and track like Cooper’s tales.

The Aliens epic collection was alright. Nothing great. But it did have some interesting storylines and the art was beautiful. One thing that that volume unexpectedly contained was a sort of short story, written in prose. And that story was graphic as anything I have come across. I have previously been made acquainted with the works of an author named Neil Gaiman and these cause one to blush. This story was along those lines. Most Alien stories have the lead as female, and this time she is only able to perform her heroine duties because of the abuse she suffered as a little girl. Bluntly, parallels are made in the story between her waiting on the monsters, and her waiting on the monster. Sick stuff.

Oh. And like the comment I made about how reading too many comics in a row kinda highlights the undeveloped-ness/infantile-ness of these stories, I now more clearly see that every Alien story ends with the main character learning that despite the recent total victory (extermination), one xenomorph embryo still exists and is poised to makes its way to another human settlement. I hadn’t really noticed that just from the movies. Oh well.

Relativity.

Here’s what I’ll do. These are the few summative statements Eddington offers. Comment below if you find them useful.

“A gravitational field of force is precisely equivalent to an artificial field of force, so that in any small region, it is impossible by any conceivable experiment to distinguish between them. In other words, force is relative.”

Actually, that is the only one that makes sense for a blog post. The big analogy that Einstein developed was the elevator (or “lift” if you’re reading in the mother country). Newton, you’ll recall, realized that if “bodies in motion tend to stay in motion unless acted upon etc”, then the Moon would have long ago kept going right past Earth, as Earth would have kept right on going past the Sun etc. The force that keeps the orbits is called gravity. Einstein, then, realized that artificial “gravity”, literally the kind you feel at the beginning of an elevator ride, is experimentally no different than “real” gravity.

Okay. Relativity is interesting but I prefer the universe stuff. (And am scheduled to read more on that next.)

Lastly, I want to conclude with probably the most fun takeaway from the book. It is from the chapter “Weighing Light”.

“It is legitimate to speak of a pound of light as we speak of a pound of any other substance. The mass of ordinary qualities of light is however extremely small, and I have calculated that at the low charge of 3d. a unit, an Electric Light Company would have to sell light at the rate of £140 million a pound. All the sunlight falling on the Earth amounts to 160 tons daily.”

How Do Flat Earth Lunatics Account for the Darkness Between the Stars?

I befriended and consequently wished I had never befriended my first Green Beret at seminary. Suffice it to say, going from US Special Forces immediately to four years of Christian undergrad followed immediately by three years of Christian graduate studies is a bad idea. (All curious souls should be asking, “How does one pay for 7 years of schooling?” Good question. The answer is, “Post 9/11 GI Bill has 36 months of coursework and if you are collecting at least 10% disability ((most vets are)) you get another 48 months!”)

As I had flown operators like him around Iraq, while the rest of the seminarians hadn’t, he and I naturally bonded easily. (I fully aim to cause you to think of the Tesla Green Beret as I relate this experience with one.) He was intense. So am I. Yet I couldn’t help but feel weird around him knowing that at any time he had the upper hand and I was quite literally at the mercy of his mental faculties. He expressed once that one of the softer professors displayed a fear of him, which my friend chuckled off as if he was perfectly harmless.

But then the moment came when he texted me a flat earth meme. From that SMS until a mere couple of weeks later, he couldn’t release. My last text to him was, “I do not care what conception of the universe is in your mind, but I do believe that we should be able to change topics.” And his last text to me (in response to mine) was, “We cannot talk about anything else until you get that (effing) ball out of your head.”

Faithful readers know that I have posted either two or three anti-Flat-Earth-Lunatic posts on here with the purpose of giving easy to use conversational strategies to destroy these lunatics. The first post posited the employment of economics, first question being, “Have you ever started a business?” Last question being, “So you’re telling me hundreds, no thousands of workers (concrete for a rocket pad itself requires the use of Quickbooks to run accurate payroll for all involved) are being duped to work for nothing, but you can’t persuade anyone to give you their money?”

A second post offered, “Have you ever looked at the night sky through a telescope?” And if miraculously they answer “yes” you move to, “At your convenience, I am available these dates, please show me how to identify a planet from a star. They all look the same to me.” And today, I would offer a slight variation to this angle by suggesting we ask, “So, which brand of telescope you rocking these days?”

Recently, with all my reading, I am more and more anti-FELs. Not just for your reading pleasure, then, here is a third method of attack (or consider it training for your children and family).

****

Me: “It’s not the stars that baffle me. It’s the dark.”

FLE: “Huh?”

Me: “I’m talking about the night sky. People are always ooooing and awwwwing at the stars—even creating horoscopes to this day based on them—but that’s not the awe-inspiring part of the night sky by my thinking.”

FLE: “Hmm. Umm. You know the earth is flat though, right?”

Me: “No it’s not. But seriously, think about the dark part of the night sky. The part in between the stars. You can see it right?”

FLE; “Sorry, I was looking at my phone. There’s this video right here that proves the earth is flat. What? Sure. Yes. Well, no. I mean, have I showed you where the Bible says the earth is flat? What do you do with that? You’re a Bible-believing Christian, yes?”

Me: “I think you did. But just look at it all. All that dark. What do you suspect accounts for it? Is it the black paint on Ptolemy’s sphere? Is it countless tubes of nothingness pointed from the bounds of infinity directly at the earth of all places? I mean, it stands to reason that since we can only ever see more and more stars with bigger and bigger telescopes—wait a minute. Have you ever looked through a telescope?”

FEL: “Gee. Look at the time!”

Me: “You want me to believe the earth is flat and yet you believe the dark you see unaided is actually darkness, even when using a telescope? Ha. Haha. Aaaaahahahaha. Okay. I’ll stop. Now what were you saying about some video?”

FEL: (Crickets. And then assuredly they return to not looking through telescopes.)

****

You’re welcome, Blog-O-Sphere.

Final Thought On Gravity/Newton/Apples/Truth Before Moving On

The #1, numero uno, reason it is silly to continue repeating the account of the falling apple is that it is incomplete! It is, forget anything about who witnessed said apple, incomplete to say, “An apple falls due to the force of gravity.” Better, maybe not perfect, would be to say, “That an apple falls taken together with that the earth pulls the apple is an example of the relationship which conventionally has been termed, in abbreviation, gravity.” To reduce that sentence/concept by words or meaning is to lose any meaning/truth.

(These are for you, H-. If you’re still alive.)

Before You Subtract…Abstract

What makes a person want to learn?

What makes a person want to teach?

What does it take to convince a 14-year old that knowing how to add/subtract/multiple/divide fractions is valuable?  Is knowing how to manipulate fractions valuable?

I spent some time reading a book about algebra recently, and noticed the author put special, but still less than I would have, emphasis on some major moments in the history of math.  The first being the invention/recognition of the number “0”.  Another being the move from numbers being practical to being abstract; that is, from counting 5 apples or 5 sheep to understanding that “5” can be a useful concept without the practical application.  Did you catch that?  Numbers began with practical application.  Afterwards, the giants of math discovered numbers and math in abstraction.  Because of these giants, we’ll be colonizing other planets in our lifetime.

In reviewing this chronology, I think I picked up on something.  The problem a high school teacher faces is not convincing several-grade-levels-behind teenagers of the practical application of fractions, but convincing them of the importance of abstract thought.  You might be thinking that reminding students that if Matt pays $3.75 and John $1.25, unless Matt is feeling nice, John should only get 2 slices of the Hot’n’Ready seems the better route at this juncture.  Don’t be foolish, it is not.  Really, who cares how many slices of pizza a couple of high teenagers eat?  The bigger problem is that there are four years left until these two knuckleheads will never again be members of a captive audience.  There are four years until they will officially become adults in the legal sense of the word, regardless of their not having achieved manhood in the abstract sense of the word.

How to proceed then?  How about heeding Thoreau?

“No wonder that Alexander carried the Iliad with him on his expeditions in a precious casket. A written word is the choicest of relics. It is something at once more intimate with us and more universal than any other work of art. It is the work of art nearest to life itself. It may be translated into every language, and not only be read but actually breathed from all human lips; — not be represented on canvas or in marble only, but be carved out of the breath of life itself. The symbol of an ancient man’s thought becomes a modern man’s speech. Two thousand summers have imparted to the monuments of Grecian literature, as to her marbles, only a maturer golden and autumnal tint, for they have carried their own serene and celestial atmosphere into all lands to protect them against the corrosion of time. Books are the treasured wealth of the world and the fit inheritance of generations and nations. Books, the oldest and the best, stand naturally and rightfully on the shelves of every cottage. They have no cause of their own to plead, but while they enlighten and sustain the reader his common sense will not refuse them. Their authors are a natural and irresistible aristocracy in every society, and, more than kings or emperors, exert an influence on mankind. When the illiterate and perhaps scornful trader has earned by enterprise and industry his coveted leisure and independence, and is admitted to the circles of wealth and fashion, he turns inevitably at last to those still higher but yet inaccessible circles of intellect and genius, and is sensible only of the imperfection of his culture and the vanity and insufficiency of all his riches, and further proves his good sense by the pains which be takes to secure for his children that intellectual culture whose want he so keenly feels; and thus it is that he becomes the founder of a family.”