Math, Boxes, Knots, and True Love

By Bobby Neal Winters

When we are teaching a complicated subject, we break the subject down into bite-sized pieces so that the student can digest it.  This is especially true in mathematics.  The whole is incredibly complicated, so we find a piece--one simple piece--and start there.  We then continue adding small bits to the student’s knowledge.  

We hope that the student will master these little bits.  Good teachers will provide opportunities to review the previous little bits along the way.  But at the end, there comes an opportunity to bring it all together into a coherent whole.  We call this integration.

Here let me step out and remind the math teachers that are reading this that I am using “integration” in its educational sense rather than its mathematical sense.

When we teach the calculus sequence in mathematics--and this sequence begins in college algebra--we teach numerous techniques, and I do mean a lot of them.  But unless the student is an engineering major or a physics major they never know why.

That is unless they take a course called differential equations.  Differential equations is a course that stands out vividly in my mind. On one hand, I don’t believe I learned a single new mathematical concept in the course; on the other hand, I used every single mathematical technique I’d ever learned going all the way back to kindergarten.

Everything I knew was brought together in one place.  My mathematical knowledge was integrated.

Deeper in mathematics, the subject of knot theory is similar.  This is an area that not even many mathematicians know well. I became familiar with it while I was working on my PhD. It is an area that brings together many tools from higher mathematics: Algebra, topology, analysis, geometry.

The subject of knot theory is right there in the name: knots.  It is the study of knots in the mathematical sense.  Believe me when I tell you I am capable of taking you down the rabbit hole with this, but I will keep it simple. 

We represent knots with diagrams.  That is, we pretend that we’ve tied a knot in a piece of string that we’ve laid neatly down on the table, and we draw it.  Most mathematicians aren’t artists so we keep it simple.  The main points of interest are the crossings, that is when one piece of the knot goes over the top of another piece.  We draw our diagrams so that you can tell which piece is on top.

It is a fact that mathematicians don’t like reasoning with diagrams, and that is one of the reasons so many sophisticated mathematical tools are used: We use them to cover our butts, as it were.

Knot theory is a part of me, but it is a part of me I put aside years ago.  Books about it have been on my bookshelf occupying space. Memories of it have been in my brain doing the same.  It is now coming back to me in a surprising way. It is coming back through my woodworking.

I’ve been making boxes for a while, but they’ve been plain, unadorned boxes.  At one point, I made boxes for my grandsons and put their initials on the lids so they would know which boxes to fight over.  Then I made a Harry Potter magic wand box with the Deathly Hallows on the lid. Then I made a couple of Bible boxes, one with the Borromean rings and another with a trefoil.

At that point, a thought came to me. I make these boxes to give away because otherwise I will be buried under them. I need to craft my designs to be something to give away. This is an issue because there usually has to be an occasion for a gift such as the birth of a baby or a wedding. You need to give them away in such a way that they can’t give them back.  

I decided to craft my carvings with that thought in mind.

I carved a “Hopf Link” on the top of a box.  Those of you who are not burdened with my level of knowledge about knots might easily mistake this for linked wedding rings.

Having succeeded at this, I decided I would like to try something more challenging and nerdier.  I remembered having read about something called a “True Lover’s Knot.” 

I had to dig into my library, find a book I’ve had for 40 years, and look it up.  After I looked it up, I had to learn to draw it. This was a challenge because it’s an 8-crossing knot.  Every place where the knot crosses itself makes the diagram that much more complicated.

My first attempt at carving it into wood was a failure for a number of reasons. The knot was so complicated that it made carving difficult and in going too quickly I damaged it.

I glued up some new boards and started over. I sketch the knot on the wood in a way that was more spread out.  Then I began to carve in a deliberately slow, organized way. In doing something this complicated, I had to be much more intentional. I had to use a lot of techniques that I had learned about using chisels, gouges, and knives.

I had to integrate my learning.

I’ve been taking a lot of pictures of it. This is because I will be gluing it into a box--integrating it, as it were--and there are all sorts of disasters that can happen along the way.

But it’s wonderful when it all comes together.

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.