The Works of Our Hands

 The Works of Our Hands

By Bobby Neal Winters

Math teachers are strange.

I wrote that because every once in a while I like to write something that no one will argue with.  Because it’s true.

We are so very strange and we will not argue with that because math teachers, above all, value the truth.

We like blackboards.  There are multiple reasons for that. One of them is that we don’t like change. We absolutely don’t. 

To quote Richard Neuhaus: “Change is bad.”

But there is a more important reason.

The teaching and learning of mathematics is a work of the hands.  It is a physical thing. 

I think I’ve “known” this for years. In grad school, some of the lecturers would talk about the “need to get your hands dirty” in doing the calculation. 

It has been something my colleagues and I have discussed among ourselves, but with my journey into woodworking it has really gelled with me: Our hands know how to do things our conscious mind does not.  The author of Psalm 137 knew this: “If I forget thee, O Jerusalem,let my right hand forget her cunning.”

Users of hand tools call it “muscle memory.”  I would say it’s the unconscious mind.

But I’ve seen it in other places.

When I do my Duolingo Spanish in the morning, I find my hand typing certain words before I get a chance to myself.  My left hand seems quite fond of typing aqui.

This realization is disturbing to be because of the changes technology has wrought in the way I teach.

When I started teaching, I would go into a classroom and fill up the blackboards with writing. (And I do mean blackboards. Whiteboards with markers are not the same. I’ve never picked up a piece of chalk and discovered it was empty!!)  The classroom was best when there were chalkboards on all four walls.  Sometimes the kids sprained their necks, but we all have to suffer for our art, eh?

Then came the introduction of technology into the classroom and there was encouragement--not to say pressure--to switch to something that would project onto the screen. There is a place for this, but it is a matter of finding the correct proportion.

You could make out slides.   Give your students copies of the slides.  Then as you showed the slides, they could make notes on their copies of the slides, while paying better attention to you.  

All very efficient, but not a good learning experience for the students.  Oh, they will learn very well how to just sit there and watch someone show them a presentation involving mathematics or statistics, but they will not become practitioners of the Art itself.

To learn how to do it themselves, they need to see someone performing the calculations.  They need to see the calculations being done in real time, and they need to replicate the calculations themselves.

Not only do they need to copy what the teacher is physically putting on the board, but it wouldn’t hurt them to wait a space and then recopy their notes, while trying to understand the process at their own pace.

I will say there is a place for technology in learning.  I’ve learned woodworking from watching videos, but the folks in the videos don’t just show slides stating what they are doing.  They don’t just talk about it.

They do it.

And those of us who want to learn, see it and try to replicate it as soon after watching the video as we can.  After we goof up, we can then rewatch and see what we missed.

The motto of Pittsburg State, where I teach, is “By Doing, Learn.”  

It’s a good motto.  We do give lip service to it now and then. But a lot of us take it seriously, and we ought to.

It’s a good way to learn, and we needn’t be ashamed of getting our hands dirty.  We should be proud, and we need to learn that.

Bobby Winters, a native of Harden City, Oklahoma, blogs at redneckmath.blogspot.com and okieinexile.blogspot.com. He invites you to “like” the National Association of Lawn Mowers on Facebook. Search for him by name on YouTube.

Living in a New World with an Old Soul

 Living in a New World with an Old Soul

By Bobby Neal Winters

The Biblical prophets were poets.  They expressed many of their prophecies in verse. Today, we consume the overwhelming bulk of our poetry in the form of songs.  It is for this reason and others that I refer to some singers--Bob Dylan for instance--as prophets.  I am not joking when I do this.

There are some who believe that the only function of a prophet is to foretell the future.  I am not going to argue with that, but I will share my opinion.  True prophets speak for God.  They will share God’s message.  Sometimes that message is foretelling the future.  Sometimes that message is the creation of a vision upon which a future can be built.  Sometimes, it is like when the prophet Nathan confronts King David: Speaking the Truth to Power.

Here’s the kicker though. How do you know who’s a prophet and who is not?  Jesus said that you just have to wait and see whose prophecies come true.

I’ve recently heard the voice of someone who sounds like a prophet.  His name is Oliver Anthony. His putative prophecy is entitled “Rich Men North of Richmond.”

I used a $20-dollar word up there: putative.  Is it a prophecy or not? Don’t know.  But when I listen to it I find myself listening for the truth with it.

I’ve read a column about this song by an economist named Tyler Cowen writing for Bloomberg.  As learned as Professor Cowen is, he might be missing the point.  Though he does acknowledge the emotional impact of the song, he looks at it in a very left-brained way.  One needs to view the song through the words of Napoleon: “"A man does not have himself killed for a half pence a day or for a petty distinction. You must speak to the soul in order to electrify him."

In “Rich Men North of Richmond,” Oliver Anthony is speaking to the soul.

In listening to the song, I hear the pain and frustration of the working people.  Out of habit, I almost wrote “working man” instead of “working people,” but these emotions are not confined to that sex. Neither are they confined to whites.  

Working people of every color, ethnicity, and religion (or irreligion) are frustrated. I’ve listened to a few of them. The frustration is real.

In this age of identity politics, they are an identity that has been left out because “working people” are just not sexy enough and they don’t have enough money to fund political campaigns.

In the days of the New Deal, the working people belonged to the democrats to a large degree, but currently they feel spurned. The republicans--through Donald Trump--have made passes at them with the same nuance Trump uses in all the passes he makes. They’ve been playing along so far, but they are smart enough to know that the republicans are just after one thing: their votes to get into office.

These people--the working people--are the people who get things done in this country.  They know how to do things. They are effective.  And this song--”Rich Men North of Richmond”--is coming out of the tradition of country music that birthed such songs as “A Country Boy Can Survive,” “Long-haired Country Boy,” “Copperhead Road,” and “Wait in the Truck.”  These are all songs coming from the rural, anti-city slicker tradition that lives somewhere in the continuum between libertarianism and lawlessness.

We are all shocked by the events of January 6th, but one might wonder what would’ve happened if the people involved had been set up for success as opposed to being set up to be patsies.  Working people don’t dress like buffalos and take selfies.  They know how to get things done, and when they believe they’ve been pushed too far, they do them.

If you listen to ”Rich Men North of Richmond,” you are listening to a warning.  It is like the prophecy Jonah delivered to Nineveh.   Repent or you will be destroyed.

Is Oliver Anthony a prophet?  Only time will tell.  It is my hope that the “rich men north of Richmond” will heed his prophecy and repent.  It is my hope that they will turn from indulging themselves and trying to appease the people, to governing the country and nurturing its people.

In the book of Jonah, Nineveh did repent.  Will it do so again?  We will just have to pray and wait.

Bobby Winters, a native of Harden City, Oklahoma, blogs at redneckmath.blogspot.com and okieinexile.blogspot.com. He invites you to “like” the National Association of Lawn Mowers on Facebook. Search for him by name on YouTube.

 The Journey through Terra Incognita

By Bobby Neal Winters

The subject of mathematics offers us a wonderful mixture.  It teaches us down to earth useful skills, but it also teaches us the disciplined use of imagination.

I love trigonometry. I took a class in it in high school back in 1978.  That would be 45 years ago.  I have good friends who are adults of some level of achievement that have not been alive as long.

Trigonometry has two parts to it.  One part is its use for measuring physical objects.  If you know how far you are from a tower, you can measure the angle from the ground to the top and use trigonometry to tell you how tall the tower is.

That’s just cool.  Students of a practical mind can get their teeth into that and chew even if they don’t think it’s cool.

The other part consists of functional identities.  Let me explain what I mean by that. You see, you’ve got these trigonometric functions sine, cosine, tangent, secant, and cosecant, and there are all sorts of formulas about how they relate to each other.  A large part of a well-taught course consists of proving those formulas are true.  

You can go on for hours and hours filling page after page with formulas that would make a hawk dizzy.

While I think the first part is cool, I think the second part is really cool.  But that sets me apart as a person with a peculiar turn of mind.

The thing is: When you learn the first part in your initial course, that is just about all there is to it.  What you see is what you get. You’ve got something that is quite useful in the practical world, but you are done. It’s over. Fini!

The functional identities are a doorway to a whole new world. (Key music from Aladdin: “A whole new world...’)  The functional identities are used in integral calculus, Fourier series, vector analysis, complex analysis, differential equations, quantum mechanics, et cetera, et cetera, et cetera.

A freshman in trigonometry will look at these functional identities and say that they are useless. They will cling to the measurement formulas as being the only part that should be taught. But the stone that was rejected by the builders has become the chief of the corner.  Where did I hear that?  I think another teacher said it.

Mathematics puts things in order.  It finds patterns.  While this statement will put quite a few chins on the floor, I will say it anyway: It seeks to make things easy.

Every once in a while we find a pattern we can extend and extend and extend.  It will go on like Michael Pena’s stories in the first Ant Man movie.  It goes all over town, all around the world, but then it comes back to the here and now and points out a truth.

In mathematics, we create a language in which we talk about things that we can’t see, things that no one can see.  But we are careful.  We mark our paths with every step that we take.  We map out territory through terra incognita indeed through terra incomprehensibilis.  However wild our maps might be, we are vindicated because when we come back to good ol’ terra firma we are right.

We are living in an odd age.  I wrote that and immediately thought maybe not. Maybe it’s always been this way.  What I mean is that we don’t trust experts, but we don’t have patience. 

On one hand, we praise--and perhaps rightly so--those who won’t just take someone’s word that something is true.  Trust has been lost.  On the other hand,  these same people don’t have the skills to ferret out the truth themselves.  Not only do they lack the skills, but they won’t take the time.

Mathematics, by its nature, teaches skills that allow us to ferret out certain kinds of truth.  But this takes patience. Patience is one of those gifts of the Holy Spirit that is mentioned in the Bible.  I’ve been accused of having too much of it, and I listened to that accusation...patiently.  It might be true; I will figure that out eventually.

Bobby Winters, a native of Harden City, Oklahoma, blogs at redneckmath.blogspot.com and okieinexile.blogspot.com. He invites you to “like” the National Association of Lawn Mowers on Facebook. Search for him by name on YouTube.

 Civilization is Coming to Pieces

By Bobby Neal Winters

Civilization is coming to pieces.

There is a group of you who read that last sentence and said, “Yeah, so what else is new?”

And I get it, people say this all the time.  They’ve been saying it for years. For centuries. For millennia.

They’ve been saying it because it is always true.  Civilization is always coming to pieces because civilization has to be actively held together.

Civilization is a human creation. It requires active attention. It must be taught and carried from one generation to the other.  Humans, while on one hand create civilization, on the other hand are constantly playing a game: What can we get away with?

The economists will tell you it is natural for the consumer to want to get a product for the lowest price possible.  That is just common sense.  Trouble is that in the case of civilization we might not know just what that lowest price is.

There are those among us who study such things professionally, so in what I say next I will certainly welcome correction from those people.

Civilization is knowledge.  It is group knowledge.  Knowledge has some nice qualities.  No one can take it from you.  If you give it away, you keep it as well. Those are kind of magical, really.

In the particulars of human life, however, there are ways knowledge can be lost.  There is a phenomenon among the elderly.  I’ve seen it in my own family.  

Jean’s mom went into the hospital with something that had nothing to do with her mental health but within a short time was loopy as all get-out. She came home, recovered, and had to go in again a year or two later and the same thing happened. 

This is a real thing.  I’ve read about it since her passing.  There is a name for it, but I forget.

My explanation for this--and again I welcome correction from those who actually know something--is that our intelligence extends beyond our bodies into our environment.  We set up things so as to help us remember.  An example to make what I am saying plain.  

I have a table saw in my workshop.  Those who use such things know that when you use a table saw you use either the fence or the miter gauge, and only rarely both at the same time.  I use the fence much more frequently than the miter gauge.  Because of this, I am always losing the miter gauge.  What I have done, therefore, is to create a special spot where I keep my miter gauge.  Actually, miter gauges, plural, because I also have a miter gauge for my router table.

To summarize, I have modified my environment to help my memory.

By the time you reach my age, you’ve done that thousands of times and have created a memory environment for ourselves.  It helps us old farts to sort through the thousands of things that we’ve learned over the course of our lives.  If you pull us out of that, then we have to flounder a bit for our minds to find purchase on something.

That is why so many of us are set in our ways. 

Civilization is like this. It is a structure that reinforces the collective knowledge of the human race. (Yes, it is more complicated than that, but I’ve got a column, not a textbook.)

Civilization consists of many interconnected structures: Art, Religion, Science, Education, Great Books, and on and on.  There are things in each of these we need and we might not know that we need it.

For example, let us consider religion, and in particular the Roman Catholic Mass.  The few times I’ve attended mass, I’ve been fascinated by the care taken in its performance by the priest. At the end, the chalice that held the hosts is filled with wine and the priest swirls it around to get all of the tiny pieces that are left.  Seeing such care taken week-after-week must have an effect.  To me, at least, it seems that it will offer a model of taking care that would percolate through the community at large whether they had ever been to mass or not.

This is just a small thing, perhaps, with a small effect. But it is one that would stop if religion were no longer a thing. (I hear John Lennon singing “Imagine” in my head right now; and I have followed his instructions.)

Among the structures that the human race has created that is becoming part of Civilization that I left out earlier is the Internet.

This has been done very recently and it has all come on so very quickly, and as a function of this it is very scary.

Very scary.

Our young people, while they can come up with answers very quickly, often don’t remember them. They don’t keep anything in their heads.  They aren’t learning the internal structures to remember.  They are missing the organic patterns that exist within knowledge.

This also happened when the printing press became a thing, and when writing became a thing.  They dealt with it then, and we will deal with it now.

And we’d better, because Civilization is coming to pieces.

Bobby Winters, a native of Harden City, Oklahoma, blogs at redneckmath.blogspot.com and okieinexile.blogspot.com. He invites you to “like” the National Association of Lawn Mowers on Facebook. Search for him by name on YouTube.

  

The Saga of Cowboy and Percy

 The Saga of Cowboy and Percy

By Bobby Neal Winters

With the death of Obidiah, Jean and I have been between dogs.  

We’ve never been intentional about dogs. We’ve always gone emotionally.  We’ve not planned; we’ve been in the moment.

Obidiah’s death was a release to him.  He’d been slowly going blind, but that didn’t cause him to slack in his duties: He would bark at danger whether it was there or not.

He’d been preceded in death by his partner in mischief Charlie, who was the more easy-going of the two.  Obidiah was a schnauzer, dutiful and regimented like the German he was.  Charlie was a spaniel.  His personality was that of a Celt: He was calm, placid, and good company until something triggered him.

We’d chosen not to replace Charlie when he’d passed as we’d done before.  Previously, we had tried to have dogs in pairs so they would keep each other entertained.  But Obie’s blindness--and perhaps dementia--was keeping him entertained enough.

So we allowed Obie to live out his remaining time alone.  It turned out to be a year.

Since that time, I was allowed to have a simple pleasure.  I could mow the backyard without fear of stepping in anything...nasty.

That was glorious.  And it happened exactly once.

This is because my youngest got a dog.  She lives part time in town and part time away.  For reasons known only to her and God, she got a dog of her own.  Spent money on it.  Yep.  A non-trivial amount of money.  This goes against years of tradition in the Winters Family.

When I was growing up, we didn’t buy dogs.  We lived in the country and they just turned up.  There was never a time we didn’t have dogs.  We fed our dogs table scraps.  If a new dog turned up, and could find a place among the rest, we had a new dog.  

When I got all educated and civilized and married someone who wasn’t a hick, we got rescue dogs for free, never paying more than the price of neutering them.

My daughter, however, ignored years of tradition and paid money for a dog.  His name is Cowboy and he is an Aussidoodle.  For those of you who don’t know, that’s a mixture of Australian Shepherd and poodle.

Cowboy is a smart dog.  He’s smarter than at least one of my grandsons.  

I won’t say which one.

Cowboy is a frequent guest at our house.  He’s a house dog.  This is something else that is new in my family. 

This is where I will tread some hazardous ground.  I ask you to read my full explanation before you get mad at me. If you are mad at me after that, I am okay with it, but at least you will be fully informed on why you are mad at me.

We never had a dog in the house when I was a boy because we knew we were not good enough people to handle it.  To understand that, let me tell you a story.  I once went to pay a workman who’d done some work for me.  He was “the business,” so I went to his house to pay.  I was invited in and greeted by his dogs and the intense smell of partially digested protein.

This was an incredibly vivid experience.

Two things have to happen to have an inside dog without the above consequence: You have to train them; and you have to allow them to train you.

I am learning this now not only because of Cowboy, my frequent house guest, but because this same daughter badgered my wife into paying money for a dog herself.

There was five minutes between the period in the previous sentence while I sat at the keyboard, shaking my head, not believing what I’d just written. 

We now have an inside dog--a cocker spaniel--named Percy.

While I thought of Obie and Charlie as being a German and an Irishman, I have to think of Cowboy and Percy as being an Aussie and a posh Englishman. Cowboy is gregarious.  Cowboy will get in your face. Cowboy loves the out-of-doors.

By way of contrast, Percy is more reserved in his behavior. He is calm.  He’s not sure he even likes the out-of-doors as an abstract concept.  We took him out to do his business when there was a heavy dew on the ground and he was horrified. 

So we are training Percy, and Percy is training us.  I just spent an hour improving an egress to the backyard for the dogs to use.  

Yes, dogs. Plural.

We are keeping Cowboy for our youngest daughter as she’s had to move to a new place that doesn’t allow dogs. (Hallmark: You should develop a new line of cards for this; it happens a lot.)

Bobby Winters, a native of Harden City, Oklahoma, blogs at redneckmath.blogspot.com and okieinexile.blogspot.com. He invites you to “like” the National Association of Lawn Mowers on Facebook. Search for him by name on YouTube.