Art – Auxiliary Memory

Studying Euclid’s Elements in Retirement

by James Wallace Harris, 8/2/26

Euclid is sometimes called the Father of Geometry because of his book The Elements. A literal translation of the word geometry could be “earth measurement.” Even Aristotle knew that the Egyptians and Babylonians used geometry to survey land and construct buildings. Euclid doesn’t use numbers or make measurements in The Elements, and his geometry does not match what is taught in Geometry classes today.

What Euclid teaches is an abstract construction, yet it drives a pylon into reality. What Euclid really teaches is how to think clearly and precisely, something humans seldom do. There is a story about Abraham Lincoln that claims he didn’t become a good lawyer until he mastered the first six books of The Elements. (If you understand the foundation of what Euclid teaches, you will follow that link. If you don’t follow the link, you will after you have studied Euclid.)

The reason I’m studying Euclid’s Elements in retirement is that it’s exercise for my aging brain. Crossword puzzles, Wordle, and Sudoku are decent stretching exercises for my flabby neurons, but The Elements is Nautilus machines. I’m only as far as Proposition 12 in Book 1, which has left my brain in a puddle on the floor.

It’s not that the problems in The Elements are hard; they mostly require persistence. Numbers and measurements aren’t involved. Just logic, reason, a straightedge, compass, and pencil. Even a tiny amount of exercise can make you feel weak and lightheaded if you’re out of shape.

At 74, the challenge is whether I can learn anything new at all. Especially since I can’t seem to retain new words and concepts. I can still recall old stuff, but keeping new stuff is difficult. Maybe studying Euclid will help with that.

Before I retired in 2013, I thought I’d work on a degree in computer science as a hobby once I retired. I’ve taken many computer courses at the undergraduate level while earning an English degree. Since I spent my working life with computers, I always wanted a computer degree to validate myself. However, when I investigated the requirements for a B.S. or M.S. in computer science, I learned that I needed 24 hours of math as a prerequisite.

I only had College Algebra, Calculus I, and Statistics from the 1970s. When I looked at textbooks in those courses, I realized I had forgotten everything. I’d need to start over from scratch. Not only that, but when I tried Khan Academy as a refresher, I learned I had forgotten the fundamentals of math from elementary school. I had to start over in the 2nd grade. I eventually worked my way up to 5th grade in Khan Academy, but my brain ran out of gas. I dropped the idea of going back to college as a retirement hobby.

Twelve years later, my mind is even more mushy. I do Wordle and the Mini Crossword at The New York Times every day. Even though I often have trouble remembering words, I’m pretty good at those puzzles. I gave up on learning math over a dozen years ago. I regret that. I should have stuck it out.

Recently, I read about the history of Euclid’s Elements. Supposedly, it’s only second to The Bible in the number of editions over the last two thousand years. Its main claim to fame is that it teaches more than basic geometry – it pushes its students to think logically.

The geometry in Elements is very basic, not like the geometry they teach in school today. All 13 books of the Elements use the same 5 Postulates and 5 Common Notions. From that foundation, 48 propositions (problems) are set up in Book 1. Each proposition is proved step by step with diagrams based on the 23 definitions. 131 total definitions cover 465 propositions in all 13 books. Most students only do the first 6 books.

For centuries, an educated person in the Western world would study Latin, Greek, and Euclid’s Elements. Before the scientific method, most knowledge was opinion. Euclid’s Elements set up the idea that knowledge should be built on a foundation. A foundation that is consistent across cultures. Every proposition has to be proved with definitions, postulates, and common notions. Look at this video; the visual demonstration will probably say more than I can in words.

The simplicity and limited domain of the Elements appealed to me. I may not be able to pass a university math course, but hopefully, I can work my way through the first book of the Elements.

I started with the free web version, and then bought a 99-cent Kindle edition of The Elements of Euclid for the Use of Schools and Colleges (Illustrated) so I could read on my phone. I also bought Delphi Collected Works of Euclid (Illustrated) because it had a long history of this famous book. It was only $2.99 for the Kindle edition, and I liked the scholarly history of how Euclid wrote the Elements and how people used it over the centuries.

I’ve been able to work through the early Propositions. I even bought a compass to draw them out myself. I’m not sure I’d even call this mathematics. It’s really just logic. The work is tedious, though. With each step, you’re supposed to cite the Definition, Postulate, or Common Notion you used to justify that step. You have to think hard as you follow along.

Here’s my work for Proposition 1. Most books describe the steps in words, and then show the final diagram. I find that confusing.

Proposition 1: To construct an equilateral triangle on a given finite straight line.

Look at how David E. Joyce works the problem at Clark University. It’s very wordy, but it also explains some of Euclid’s faults. But even Euclid’s description is very confusing, at least to me. It’s only clear when you follow the problem logically, step by step.

We start with a line segment with the endpoints being A and B. Ignore point C for now. Many teachers start by drawing line segment AB and immediately put a point C above it. I think that’s wrong.

Draw:

Then draw a circle with A at the center, with AB as the radius.

Then create a circle with B as the center, using AB as the radius.

Now, it’s time for point C. Where the circles intersect, designate points. Remember the definitions. They are abstractions, but we have to always build on them.

Definition 1: A point is that which has no part.

Definition 2: A line is a breadthless length.

Definition 3: The ends of a line are points.

Definition 15: A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure equal one another.

Definition 16: And the point is called the center of the circle.

Postulate 3: To describe a circle with any center and radius.

Euclid doesn’t state that when a line crosses another line, the intersection is a point, but we assume it. He should have included it as a definition.

Because the two circles intersect, we have defined two additional points, which we can label C and D; however, D is not needed for this proof.

Now we can draw lines AC and BC.

Definition 20: Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.

Postulate 1: To draw a straight line from any point to any point.

Common Notion 1: Things which equal the same thing also equal one another.

Common Notion 4: Things which coincide with one another equal one another.

Because AB is the radius of both circles, and AC and BC are also radii of those same circles, all sides of the triangle are equal.

Thus we have proved:

Proposition 1: To construct an equilateral triangle on a given finite straight line.

In modern geometry, we would have just drawn an equilateral triangle knowing that all three angles equal 60 degrees. And we could have measured the length of each side with a ruler. The point of Euclid is to create geometric objects with basic geometric building blocks. No numbers are involved.

The rest of The Elements involve creating ever-evolving complicated 2D and 3D geometric shapes. Some of which prove other mathematical problems, like Proposition 47. It’s an alternate method of proving the Pythagorean theorem.

But even after watching a video multiple times, it’s still hard to do it myself. Without practicing with drawing lines and circles, it’s hard to see how the proofs really work, even when they are shown to you.

JWH

The Things That We Love

by James Wallace Harris, 6/27/26

Susan and I just finished watching The Spoils of Poynton, a 1970 BBC production shown on Masterpiece Theater in 1971. It’s based on a 1897 novel by Henry James. Mrs. Adele Gereth has collected art objects, furniture, knick-knacks, lamps, glassware, and pottery for her entire life. Now that her son Owen is of age and will inherit the house and everything in it, she is distraught to learn that his fiancée, Mona Brigstock, lacks the taste and refinement to appreciate her treasure. So Adele connives to get Owen to marry someone else.

This is how things used to be. Families clung to generations of cherished things. Before my mother died, she wanted to know who wanted what of her things. She assumed that Becky, my sister, and I, as well as some of my cousins, would fight over her favorite things. After she died, I took the photo albums, my sister took some homemade quilts, and we gave away everything else.

I’m currently listening to Whistler, the new novel by Ann Patchett. At one point, Jonathan, the husband of the main character, Daphne Fuller, leaves her for several days to return home after his mother’s death to sort through her possessions with his siblings. Daphne begs Jonathan to hire an estate cleanout instead of putting himself through weeks of agony.

When Susan’s parents died, we bought their house because Susan and her brothers were too sentimental to let it go. So we lived with Robert and Mary’s stuff for a very long time. It was actually better than our stuff. And when my friend Janis moved to Mexico, we took in a bunch of her stuff. I think of these people by the things they owned.

All of this makes me think about the things I love to buy and own. Isn’t it weird how we love physical objects so intently? Susan and I are terrible at home decor. Our favorite kind of furniture is the La-Z-Boy. We have six single chairs and one double. We also love large screen TVs. My den has a 65″ TV, and her living room has a 75″ TV. We have hundreds of DVDs. And I have hundreds of CDs. I also have hundreds of books.

I don’t lust after cars, guns, or sports memorabilia like normal guys. I’m a bookworm, and books are what I get all sappy about. Susan says when I die, she’ll call Goodwill and Salvation Army and ask them to haul off everything I loved. Sometimes I think I should help her out by giving most of my books away before I die.

I especially love old science fiction magazines. I’d rather have them than diamonds. I would trade them for 19th-century artwork, but I’m realistic enough to know I’m no art collector. Besides, impressionist artworks really don’t go with La-Z-Boys.

The other day, I watched a YouTube video of the actor Paul Giamatti being interviewed about his book collecting. I felt a great affinity with these two guys. These are my people. I cherish crappy old paperbacks, too.

I always marvel when I visit friends and see how they’ve made their houses into museums of the things they admire. It makes me feel bad that I don’t love beautiful home furnishings. Our decor is functional for watching TV, listening to music, and reading.

After I’ve died, and someone is throwing out my science fiction magazine, I doubt they will see the beauty I saw. They won’t know that every issue of F&SF, Galaxy, or Astounding triggers memories. Most people remember the people they knew and the stories about them. I remember writers and the stories they wrote.

I wish I had a manor house and a lifetime of collected treasures like Adele Gereth, including my library of books and magazines. I love my house, even though it’s junky and cluttered. I do regret not having more refined tastes. But I never cared about dishes or doodads. My grandmother collected figurines of dogs. She had hundreds. That was cool. I wish I had gotten one to remember her by – a collie dog.

In Whistler, Jonathan’s first wife collected paintings of rabbits. I wish I had thought of something like that when I was young. Some kind of modest art that people throwing my stuff away could have identified me with. I’ve always admired 19th-century drawings by naturalists and scientists.

I visit the Friends of the Library bookstore once a week. People donate the kind of things I treasure. In fact, a lot of my treasure came from that bookstore. I think I’ll arrange to give my stuff to them when I die. I’ve already given them thousands of books, records, and CDs over the decades. It makes me sad when I see things I once loved left on the shelves for weeks. Hopefully, they will all find a new home with someone to love them. I guess I’m no different than Adele Gereth.

JWH

Why Do We Fall In Love With The Past?

By James Wallace Harris, Thursday, January 28, 2016

We explore the past through infinite paths. The past no longer exists, yet we recreate “what was” with artifacts that continue to exist in the now. We use our neurons as virtual reality machines to remember. Most of us have a rough map of our own life, and hazier maps of our own culture. Beyond those maps lie the unknown territory of the collective past, which we are all deeply rooted. We have all shook hands with someone who shook hands with a 19th century person, who had shaken hands with someone from the 18th century. I am old enough to have shaken hands with many people born in the 19th century. Every history book we read weaves thousands of threads that link us to a past.

Have you ever contemplated how we build the past in our minds? As individuals we use memories. We talk to other people and use their memories. Novels, movies, songs, television shows, paintings – are fundamental ways of recalling the past. Art is recorded memories. Think of cave paintings, probably among our oldest memories. Slowly, education and scholarship evolved to organize the details of the past. Whether you’re studying math or The New Testament, you’re recreating the past. The discipline of history isn’t that old in the big scheme of things. In recent times we have journalism and the internet to extend our sense of the past.

Whenever we play an old piece of music or see a work if art in a museum, it connects us to people, places and things who lived and died long ago. For example, I’m currently reading I Am Alive and You Are Dead by Emmanuel Carrère (1928–1982, San Francisco, Berkeley, Point Reyes, Santa Ana) a biography of Philip K. Dick. Or I recently saw The Revenant (1823, Montana, South Dakota) about Hugh Glass. I could link to dozen more movies and books I’ve recently seen that connect me to the past. Just follow those few links to understand how we network with the past, and how far and quickly that web of memory will carry you away. Trying to grasp the fullness of past is like falling into a black hole.

Here’s a photo of my father’s father, his brothers and their parents (my great grand parents). I know next to nothing about these people, and can only remember a couple of anecdotes. What would it take to learn about them?

The answer comes in a book I just finished, The Hare with the Amber Eyes by Edmund de Waal, who took a couple years out of his life to learn about his ancestors on his father’s side. This wondrous book will delight lovers of history, art and culture. There’s enough material here for six fascinating historical movies, and seeds for many more. The challenge here is for me to describe it in a way that will make you want to read it. It’s not a book for everyone, but it is a book for everyone that loves the past.

When I was young, I’d often hear or read that America had no old culture, not like the Europeans. It’s taken me a lifetime to understand what they meant. Except for a few mementos, like your granny’s quilt, or collecting antiques, we seldom dwell on our own heritage. We’re always thinking about the next new gadget to buy (as we throw away the old ones), or the next new show to binge-watch. Some Americans are into genealogy, but not that many. We generally embrace the pop culture of our teenage years, which we cherish our whole life, but few people branch from from there.

Edmund de Waal has written a book that succeeds in capturing a panoramic snapshot of his cultural heritage that spans three centuries. The Hare with the Amber Eyes starts off as a quiet unassuming memoir that slowly builds into an atomic explosion of multicultural history of art collecting. The story is anchored by a collection of 264 Japanese netsukes that came into his family in 19th century, and de Waal inherited in 21st. The book is set in Paris, Vienna, Odessa, Tokyo and London.

I have read this book for three book clubs now. It’s a challenge to explain its appeal. If you love art history, especially French Impressionism, or how Japanese art came to 19th century Europe and 20th century America, this book will appeal to you. If you like to read about Jewish history, especially about Jews living in Odessa, Vienna and Paris in the 19th and 20th century before WWII, this book will grab your attention. If you are fascinated by the American occupation of Japan after the war, the book has insights for you too. If you’re fascinated by Nazi art theft like The Monuments Men (the book, not the movie) and The Woman in Gold (the movie), then this book has stories for you. If you’ve ever tried to write your own families history and wondered what kind of effort it takes, then this book is for you. If you love the PBS shows Antiques Roadshow and Finding Your Roots, then this book is for you.

Most of all, if you’ve ever seen old photographs of your great grandparents and your great great grandparents and wonder what their daily lives were like, this book is for you.

I would be hard press to make a list of all the subjects de Waal touches upon in his small book. The frame of his story is to take his 21st readers back to the 19th century Paris to explain how his family first acquired the netsuke. His story begins in France as Impressionism is coming into vogue, which is concurrent with Europeans becoming obsessed with Japanese culture and art. The story then travels to turn of the century Vienna, past WWI, through the years between the wars, WWII in Europe, to the Japanese occupation by Americans, and then into the home stretch of this century. Along the way, The Hare With Amber Eyes encounters many famous people and events in 20th century history. If de Waal played six-degrees of separation, he’s only a few degrees from some very historical folk. Yet, de Waal current life is very unassuming. He’s an artist, a maker of porcelain. When heading into the past, you never know what you’ll find. Besides, we have four grandparents, eight great grandparents and sixteen great great grandparents. It gets pretty easy to make some marvelous connections.

My goal is to try and explain why I liked the particular details in The Hare With Amber Eyes, and that’s rather difficult. I’m not that into Japanese netsuke, although they are impressive little sculptures. There’s no reason for me to identify with de Waal’s genealogy, my family was nothing like his. What enchanted my reading is their love of art and culture. The book’s connections to 19th century Paris and early 20th century Vienna provides vivid details of what it’s like to be great patrons of art. The book gives me another side of the history of Impressionism – the buyers side. Charles Ephrussi, who originally bought the netsuke, was even painted into Renoir’s “Luncheon of the Boating Party.” Charles is the guy in the top hat. What a way to be remembered!

But why should I care about Charles? Reading The Hare with the Amber Eyes makes me wonder why I care about anyone in the past. But I do. We all do. Most of us are obsessed with the past. I keep looking at that painting above and wonder what it was like to have been at that party. In the book, the netsuke are touchstones to the past. De Waal owns them now, and the netsuke put him one degree from Charles and many of his relatives between the 1870s and now. They tie a family history together. De Waal focuses on three of his ancestors, and the cities that shaped their souls, Paris, Vienna and Tokyo.

I can’t think of anything I own that ties me to the past like that, other than photographs. I wonder how many hands have held that photograph of my great grand parents? My mother’s mother, Lou Dare Little, was born in 1881. She held my mother’s side of the family together for decades. She bore five daughters, which held the family together for several more decades. But now that only my Aunt Louise is still alive, the family seems to be coming undone. What de Waal shows with The Hare with Amber Eyes, is how history and art can sew a family back together. However, it took two years out of his regular life to accomplish that effort. My cousin Jane wrote a book many years ago that tied the descendants of Lou Dare Little together – at least for a while. How many of my cousins and their descendants will keep reading Jane’s book in the future? Will anyone from newer generations write another book? We don’t have anything like the netsuke to travel into the future, to get later generations to remember us. Or do we?

I’m not sure I’m accomplishing my goal here. All I can really say is read The Hare with the Amber Eyes, and let it convey what I want to say. It is a cornucopia of memory triggers. But also, every time you turn on your TV, or go to a movie, think about what you’re seeing is saying about the past. Whenever you read a book, have a family reunion, or go to an antiques dealer, think about how the past won’t let us go, or we won’t let it go.

JWH

Are Young Women More Artistically Beautiful Than Other People?

If we were robots, with video camera eyes, everything in our visual field would be of equal value. So, why do our brains light up when we see flowers, sunsets and young women? Will we ever be able to program a robot to have a sense of beauty?

Photograph Anna Bella by Sean Armenta on 500px

Anna Bella by Sean Armenta on 500px

And if biology is the basis of beauty, why isn’t food and potential mates the only things we see as beautiful? How did a sense of beauty evolve in our minds? Does it serve a purpose? Isn’t a sense of beauty one of our most motivating qualities?

I love looking at photographs. I have a dual monitor setup and use John’s Background Switcher to display 8 photos on my desktops every 10 seconds, chosen from sites like 500px, Flickr and others. This way I see scenes from all over the world, nature, animals, forests, oceans, lakes, mountains, stars, buildings, bridges, and sometimes people. What’s strange is for some sites, when they show people, 95% of the time it’s a young woman, probably age 18-25. Now these are supposed to be art photos, not sex photos. Why are young women more artistically appealing than other people? Is there a reason other than sex?

Photographers do like taking pictures of other kinds of people, but even then the range is limited. It’s cute kids, or very old people with tons of wrinkles. (I assume wrinkles are very artistically inspiring, especially in black and white.) But statistically, young women are the dominate subjects for photographs of humans. Why do young women trigger the neurons that define beauty in our brains – more than any other object in reality? I don’t know how woman and gay men rate the beauty of young women, but I often hear them talk about beautiful women, so it isn’t just us guys brainwashed into seeking sex objects.

It’s not news that young women appeal to photographers, but I’m wondering why. Is it just sex, or are young women more aesthetically pleasing than other types of people, or even natural objects? Can we ever see young women without our brain being distorted by sexual programming? Aren’t flowers, sunsets, old cars, dogs and cats just as beautiful? And if artistic photographs were mainly about sex, why aren’t women photographers uploading pictures of young men in equal numbers? And what explains heterosexual women preferring to look at young women? Why aren’t women’s magazines, and their ads, showing an equal distribution of women of all ages and sizes?

If you follow photography you eventually realize certain subjects are more popular than others. Today’s amateur photographers are just amazing, equal to the best professionals just decades ago. Just look at a site like 500px.com.

The annual Sports Illustrated swimsuit issue just came out, and it gets a lots of attention. Why does it only show young women in swimsuits? Why not older women, or men? Sure sex sells, but why don’t we have a wider range of sexual stimulation. It’s often said we are a youth oriented culture – is that because we define beauty by being young? Is it possible to culturally reprogram ourselves so old men and women in skimpy bathing suits would be beautiful?

I think the photo above of Anna Bella is beautiful because of the woman, and because of the photographic composition, but could not a sixty-something woman have posed for the picture and the photo been just as beautiful if the picture had been composed for artistic reasons? Or is lustrous hair and fair skill absolute aspects of beauty?

I think the picture of the pug dog below is beautiful. I have no sexual attraction for dogs, and think pug dogs are ugly, but I think this photo is artistically beautiful. However, most of the photos I think of as stunningly beautiful at 500px either have gorgeous nature scenes, or they are of young women. However, if I put the picture of the woman above on the wall, my wife will think I’m a dirty old man, but think nothing if I put up a picture of a pug.

Photograph Beautiful champ! Pug :) by Tijana Kacarevic on 500px

Beautiful champ! Pug 🙂 by Tijana Kacarevic on 500px

Even though I think pugs are butt-ugly, I think they are beautiful to look at. What explains that? Is cuteness an aspect of beauty? It would explain all the pictures of puppies, kittens and kids. How do we explain sunsets and flowers twisting our beauty sensors to 11? How much do bright colors figure in our sense of beauty. Think of fall trees.

Photography sites have billions of images of animals we find beautiful. What makes them beautiful? Not all animals are beautiful either. Puppies are cute, but a mangy dirty puppy isn’t. What makes one tiger stand out over another? Why are flowers so beautiful, or rolling hills? I’m sure there are thousands of books devoted to defining the philosophy of beauty, but shouldn’t it be obvious? Can beauty be scientifically determined? Or is it always something in the eye of the beholder? How many things do we find beautiful? Is it endless?

Photograph Stars by Besmir™ on 500px

Stars by Besmir™ on 500px

What moves us? That tree on the bare hill has impact, especially against the spectacular sky. What about the women below? The picture is beautiful, but there’s something beautiful about the woman too, as if her rich life experience shines out.

Photograph Wharf Lady by James Nielsen on 500px

Wharf Lady by James Nielsen on 500px

I’d like to know about the science of beauty. If we ever built robots with artificial intelligence that were self-aware, and conscious beings like ourselves, will they have a sense of beauty? And if they do, will what we think as beautiful overlap? Has there been any studies trying to find out if animals have a sense of beauty? Do dogs looking at people think some people are more beautiful than others? Are their favorites young women?

And is beauty just visual? Aren’t some smells wonderful, and others stinky? Are some sounds lovely and others ugly? Even textures and tastes have their aesthetics.

I keep an extra monitor going, not to have room for work windows, but to be constantly stimulated by beautiful scenes. Every ten second I see four more images on my left that inspire me about this world and reality. Lately, I’ve been most inspired by pug dogs. I’m not a dog person, I’m a cat person. But these weird little pugs have caught my attention. By the way, I like the gray woman below not because she’s beautiful, but because her grayness contrasts beautiful with the dirt and rocks. How can we possible explain why black and white is often more beautiful than color? Whatever beauty is I haven’t a clue to explain it.

JWH – 3/7/14

Visual Inspiration

Usually I am excited by words and concepts. I am a lifelong bookworm, so I’m obsessed with black marks on white backgrounds. Living in my head is my constant way of life, thinking wordy thoughts, even to the point of neglecting the colorful details of the external world around me. But during the day I’m often startled by something visual that inspires me. I love looking at the trees outside my window, which sets just above my computer monitor that I am typing at now. I have two windows, the one looking into the internet and the other out onto the world. The world is full of color, but because of my neglect of noticing it, I’m all the more moved by art. And maybe, I prefer seeing reality though art rather than viewing reality directly.

I love catching something visually fascinating as I drive to work each day – the structure of a church steeple, the outline of tree branches against the sky, the way shadows and glare affect my sight. I wish I could turn what I see into art. I wish I was the kind of guy that hiked in nature and captured it artistically. Because I spend so much time indoors, most of my visual stimulation comes from the computer screen or the television.

Every once in a while I see art that blows my mind, and generates a flood of thoughts. The other day I found this computer animation that set my neurons on fire.

Be sure and play this in full screen mode at the highest resolution your computer can handle. I’ve watched it many times now and it just gets better and better. This visuals makes me think of mathematics and musical harmony. This video is like seeing music. This video is like seeing mathematics as if math wasn’t an abstraction of nature. “Oscillate” was created by Daniel Sierra for his MFA Computer Art thesis, and you can see more about this work here.

What I find so inspiring about “Oscillate” is that it’s a visual abstraction that makes me see science. All paintings, no matter how realistic, are an abstraction, in the same way that words and concepts are an abstraction about reality. Art mimics the world. “Oscillate” mimics abstract thoughts. Daniel Sierra imagined seeing animated sine waves much like how classical Greeks imagined mathematics, but instead of putting his thoughts into words, he created a computer animation.

On one hand this video is like abstract art, it doesn’t look like the real world. But I see it as a realistic painting of an actual abstraction in the real world.

JWH – 6/26/13