geoharvey

Chapter 5

Charlotte Norway

Charlotte Norway was born in Weymouth, Massachusetts, in 1860. Her parents had been hoping for a son.

Since she was not what they wanted, they never noticed anything extraordinary about the things she did. If she had been a son, they would have shown the pictures he drew to their friends, but because she was a girl, they did not share her work. That is a form of neglect, but it hurt them as much as it hurt her. People would have envied them if they had cared to take pride in her. But they didn’t.

Charlotte enjoyed drawing pictures of houses in perspective when she was not yet five years old. She was fond of drawing fairly accurate pictures of dogs and cats at the same age.

Her interests went beyond art, however. She was five when she found out about numbers, and they became a new source of interest. She was fascinated by what happened as she worked with them.

She first noticed patterns in multiples of nine. She wrote a table of integers from one to ten, along with the results when they were multiplied by nine. She quickly saw that from one to the next, the tens digits increased by one as the ones digits decreased by the same amount. She performed a few tests with larger numbers and realized that the digits in multiples of nine always added to multiples of nine. When she discovered that, she saw that magic was real.

She learned very quickly that other people could not really understand her. That did not bother her much for herself. But she felt sorry for them, because she knew they could not enjoy the magic.

In time, she found out about geometry, with its fascinating axioms and theorems. When she was twelve, she started borrowing books about geometry from the local high school. When she read that there were many ways to prove the Pythagorean theorem, she produced a proof of her own.

To check her work, she took it to a math teacher, Mr. Taft. He spent a bit longer studying it than it took her to create it. Then he said, “This is impressive. You did this?” She answered that she had. He tested her by asking for an explanation. When he was convinced that it was her work, he wrote a note to her parents to tell them what their daughter had done.

She took the note home and showed it to her father. He read it and told her in a stern voice, “Mr. Taft is a very busy man. Don’t bother him again.” Her mother just repeated her father’s admonition.

❦ ❦ ❦

Charlotte’s family moved to Boston when she was still twelve. The move gave her new things to study. She found libraries and museums full of interesting things to learn about. It seemed she spent years in them.

When she was fourteen, Charlotte started taking interest in the science courses at the high school she attended. In particular, she started borrowing slides of organisms from a biology teacher and looking at them under a microscope in the laboratory. She was not his student, but he was happy to help such a curious girl.

When she saw how beautiful the cells of some plants were, she started drawing pictures of them. She drew them as she saw them, but without understanding of what she was seeing.

The teacher saw that she was not getting everything quite right, so he explained some of what she was seeing, teaching her some biology as he did. With better understanding, she was able to make more accurate pictures. Whenever she finished a drawing, she showed it to him for his remarks.

Charlotte worked with pencil to do the drawings. When she had one that she was happy with, she would take it home and do an ink rendering. When that was done, she would bring it back to the laboratory, where she could color it with Conté crayons.

Coloring inked drawings was something she really enjoyed, and she started to use the technique for perspective drawings of the streets and buildings in Boston. She quickly could see that the pigments of the crayons were covering the inked lines, making them appear dull, so she devised a procedure of doing the coloring first and following that with drawing in ink.

To do this, she started with her original sketch, which was done using pencil. Then, she would duplicate it on fresh paper with very light pencil lines as an underdrawing. These lines provided guides for areas that were colored. Finally, she applied the ink to make the whole image sharp.

This process could be a challenge, because the wrong choice of crayon could make inking difficult or even impossible. The Conté crayons were made of clay and pigment with a binder. The trick for Charlotte was to experiment with brands of crayons to find one that would neither blot the ink nor block it from going down onto the paper.

❦ ❦ ❦

When Charlotte was eighteen, she went to a commercial art studio to see about getting a job. The studio did specialty work, producing perspective drawings of buildings from floor plans. The proprietor, Mr. John Dickson, looked at her portfolio and was impressed enough to hire her as an apprentice. Of course being an apprentice did not mean that she would make enough money to live on, but she was still able stay with her parents.

Mr. Dickson gave her some instruction on perspective theory. She saw that while the theory worked, after a fashion, it was derived purely empirically, without real mathematical basis. It consisted largely of rules of thumb, and from a mathematical point of view, it really was just an incomplete jumble of ideas.

She puzzled over this a while. And then she came to see that the problem had to do with perspective drawing being based on the wrong set of dimensions. When we construct things in the world, we do it in length, width, and height, but those are not the same dimensions we use to see the world. And when we draw things, we should use the same dimensions we use for observation.

Using her new insights, she worked out a theory of perspective drawing of her own. And as she did, she created a firm mathematical basis for perspective drawings.

❦ ❦ ❦

About four months after she started work at the studio, an architect came in for a set of drawings. Mr. John McKeever had the plans for three buildings along a single street, with small lawns between them. He asked if he could get them all in a single drawing to show how they would look from the sidewalk in front of the middle building.

Mr. Dickson told him he was sorry, but this was not possible. The rules of perspective limited the drawings in some ways. A rendering had to be less than ninety degrees wide to avoid obvious distortions, and sixty degrees was a better maximum width. What Mr. McKeever wanted would be almost a hundred and eighty degrees.

They discussed this only briefly before Charlotte broke in. She said, “Actually, there is a way to produce accurate perspective drawings of whatever width you want.”

Mr. Dickson was clearly annoyed by the fact that an apprentice would insert herself into a customer consultation, especially to make such an rude, untutored assertion. He told her, “Miss Norway, please stick to your work.”

“I’m sorry, Mr. Dickson. I was just trying to be helpful.”

“Well, you aren’t. The rules of perspective don’t allow that.”

Charlotte felt compelled to reply. “That’s because the rules are not based on real mathematics. In fact they’re not systematically derived at all. They’re just rules of thumb that work within rather narrow limitations. Sort of.”

“Miss Norway,” Mr. Dickson said rather emphatically, “Please stick to reality. We want things that work, not some sort of dream.”

“It’s not a dream. I have the mathematics all worked out.”

“Miss Norway!”

Surprised by what she was saying, Mr. McKeever intervened. “Please, Mr. Dickson, I might like to hear this. Do you mind?”

Mr. Dickson rolled his eyes, shook his head, waved his hands, and said, “No.” He sat on a stool at a drafting table and pretended to study a drawing that happened to be there.

“Please, Miss Norway, go ahead. You said you had this worked out. Please tell us what you have.”

“The problem is that we are working with the wrong set of dimensions.”

Mr. Dickson put his elbows on the table and covered his eyes with his hands. He moaned very softly.

Charlotte went on, “We think that we live in three dimensions, length, breadth, and height. Those are very useful dimensions if you want to build a building or design a machine. But they are not the dimensions we use to perceive things. And renderings should look like what we perceive.”

Mr. McKeever sounded puzzled as he said, “Okay.”

“Now, there are lots of dimensions. Longitude and latitude are dimensions. They are all you need to measure the surface of the Earth. If we know the longitude and latitude of Boston, then we can locate it on the globe. So globe’s surface is two-dimensional because we need only two dimensions to locate things on it.

“Let’s imagine we start by facing south. We can find the positions of everything we can see by measuring longitude – degrees right or left from due south – and latitude – degrees up or down from the horizon. Everything you can see can be referenced with just two dimensions: longitude and latitude.

“Of course, to measure something precisely in space, we need three dimensions. The third dimension is the distance to the object. But we can ignore perceptions of distance for renderings. We can’t measure them well at all by just looking, and they aren’t used for perspective drawings. A person with one eye doesn’t perceive them, but might draw just as well as anyone.”

Mr. Dickson was shaking his head slowly, with his hands still covering his eyes.

Charlotte went on. “Because we see in longitude and latitude, what we see can be mapped on a sphere. I call it the ‘Sphere of Perception.’ If we use that understanding and the dimensions it implies, we can do drawings that are of any width.

“We can formalize the mathematics of the perspective drawings we normally do as projections of the surface of the Sphere of Perception onto a plane tangent to it at a point. The direction lines – the lines that follow the train tracks to a point on the horizon – are straight. But if a view is too broad, it will have distortions.

“On the other hand, we can project the surface of the sphere onto a cylinder tangent to it along a great circle, such as the horizon. After we do that, we can cut the cylinder on a meridian and unroll it to create a plane surface. In this case, the problem with wide angle distortions disappears. The one thing that people might find unusual is that the direction lines are no longer straight. They follow curves.”

Losing patience, Mr. Dickson took his hands down from his eyes and said, “The direction lines are straight! We can prove it! Put a ruler on a direction line in a photograph! It’s straight!”

“Mr. Dickson, a camera projects the Sphere of Perception onto a plane at the camera back. It is the same projection we see in our perspective drawings. But you can see for yourself that the projection lines are curved just by looking at them.

“If you stand on a railroad track, facing a vanishing point, the tracks angle upward toward that point. But when you turn ninety degrees, you can see the same tracks look horizontal, down at your feet. Another ninety degree turn, and the tracks are angling up again, but in the opposite direction to what they had been. Over a hundred and eighty degrees, each track goes down, levels off, and then goes up again. They follow curves, and the curves happen to be sine waves.”

Mr. Dickson just shook his head and covered his eyes with his hands again.

Mr. McKeever glanced at Mr. Dickson and started to feel uneasy. He worried that Charlotte might have got into significant trouble by speaking up the way she did. He asked her rather slowly, “Have you actually done drawings like this?”

“A few. But they’re a lot of work.”

He thought about this for a few seconds. He was definitely feeling that he had pushed her into getting her employer angry with her. He wanted to stop the discussion. He said, “This is really interesting. In fact, it is fascinating and I want to hear more about it. But I am sorry to say that I don’t think I could use it just now.”

“Why not?”

“Well, I need a rendering that I can show to a group of investors. If I tried to use a drawing 30 degrees tall on the ‘Sphere of Perception,’ and 180 degrees across, it would be six times as long as it is tall. A drawing two feet tall would have to be twelve feet long. It would be hard to frame, hard to transport, and hard to hang, and hard to explain to the people I want to invest in the project. It’s really interesting concept, a beautiful concept, but I would not be able to justify buying one. At least not at the moment.”

He turned to her employer. “Mr. Dickson, your assistant may be brilliant, but she has convinced me that you are right. I need three separate drawings.”

The two men concluded a brief discussion of the order, and then Mr. McKeever left the studio.

About five minutes after that, Charlotte also left. She carried with her a portfolio full of the drawings she did on her lunch breaks and a box full of personal odds and ends. She was so upset and angry that she had tears running down her cheeks. She was quite surprised to find Mr. McKeever sitting on a bench in the hall. He had been waiting in case she came along.

“Are you all right, Miss Norway?”

“I just got fired.”

“I was afraid that might happen. And I blame myself in a way. That’s why I waited.” He paused, and then he continued. “There may be some good news for you out of this.”

“How could that be?”

“Well, your old employer might not have understood what you were saying, but that was because his mathematics are not all that well developed. He’s an artist, and a lot of artists are like that. I think I understood what you were saying – pretty much – well enough to see that it was real. I believe I honestly could recommend you for either of two openings I know of. Are you interested in looking into them?”

“Please!”

“Okay. I know an architect who is looking for an apprentice and a studio owner in search of a commercial wildlife artist. Of course, if I were you, I would choose a career in architecture. In fact, if you did, you could be the first woman to be an architect in this country. But you might prefer to be an artist. Would you like to know more about these? … Which would you like to look into first?”

“I think I might like to be a wildlife artist. Are these real offers?”

Mr. McKeever chuckled. “They are real. Miss Norway, I feel like I have contributed to your losing your job, and I would like to take you to the studio to introduce you. The owner is an old friend, and he has asked me to keep an eye out for talent.”

Charlotte and Mr. McKeever set out almost immediately, walking to a studio that turned out to be only four blocks away. Before she went in, she read the sign – just to know it was real.

Boston Nature Engravings specialized in sets of prints of flora and fauna. After a field artist did ink drawings and watercolors, another artist made a reversed engraving of the drawing. Images were then printed, which reversed them again to their original orientation, and watercolor artists hand-colored the prints, using the field artist’s watercolors as guides. The work was very popular, and the shop was always busy.

The studio was owned and operated by a Mr. Jonas Tenley. He was very interested when Mr. McKeever came in with a potential artist. Seeing that Charlotte was carrying a portfolio, he asked to see what she could show him.

“I’m sorry, Mr. Tenley,” Charlotte explained. “I didn’t put this together with the idea that I would be applying for a position. It is just personal drawings I do in my spare time.”

“Ah,” Mr. Tenley said with a smile. “But in a way, that is all the better. I would be ever so grateful if you show me. May I see?” He was so friendly that Charlotte felt quite comfortable letting him look at her work.

Leafing through the drawings, Mr. Tenley came to a one of a squirrel holding on to a small tree trunk in an unusual-looking pose. “Was the squirrel hiding from something?”

“Yes. A cat had just come into the yard.”

“Why wasn’t the squirrel hiding from you?”

“Squirrels seem to forget you are there, if you sit still for a while. When the cat came along, the squirrel might have been set to forget about me already. The cat took all its attention, and he moved to hide from it. So my model held still as I drew the picture.”

Looking further, Mr. Tenley came to a drawing of a fungus that had been partly eaten by some animal. He studied it, smiled, and went on.

He stopped to look at a drawing of a fox. He asked what it was that made it look unusual. It looked a bit odd.

“That’s a gray fox,” Charlotte said. “They have shorter snouts than red foxes. I saw it one evening over by the Fens. They climb trees really well, you know. They’re also very shy. People don’t usually see them.”

Mr. Tenley nodded and said, “Ah. Of course.” Then he found one of her wide-angle renderings.

Mr. McKeever spoke up. “I heard Miss Norway describe how renderings such as this are done. She developed the technique herself for wide angles. That was why I brought her to you.”

Mr. Tenley sounded very amused, as he said, “So she could use it to do wide-angle pictures of animals?”

“Well, …” Mr. McKeever started. But Mr. Tenley cut him off, chuckling as he did.

“Miss Norway, could you work on trial? When could you start?”

“Today, if you like.”

“Could you travel away from home for a week? Your expenses would all be paid, but you would have to travel alone. The trip would be to do flora and fauna of Cape Cod. If you do as well as these drawings suggest, I could give you assignments regularly.”

Charlotte was really surprised by the offer. It paid twice as much as the position she had just lost. She took it and spent the next week doing ink drawings and watercolor paintings on Cape Cod. After that, she was hired full-time. Her first assignment was to go back to the Cape to do more work there, and then to Martha’s Vineyard and Nantucket.

After that assignment, Mr. Tenley sent her to the Outer Banks of North Carolina. He nearly always sent artists to warmer climates during winter, unless the work involved winter scenes.

With spring, there came a another surprise. He asked Charlotte whether she might like to do studies of flora and fauna of the Great Plains. This was a special assignment, as it was funded by a benefactor who wanted an extensive set of engravings relating to the area. The problem was that Mr. Tenley wanted to have some assurance that the artist who took the assignment would be able to stay on the job for a long time, at least two years. He wanted the style of the art work to be consistent and did not want to have multiple artists.

He said the job would possibly expand to include more than just flora and fauna. At some point, it could have portraits of Plains Indians, men at work, railroad operations, riverboats, towns, cities, and a lot more. Her expenses would be paid, but if the job expanded as he hoped, it could last five years or even longer.

During the time she was to be on the plains, at sites between Canada and Mexico, between the mountains and the Mississippi River. She would send drawings and paintings to the studio in Boston at least every week or two, together with notes about each image. She would give details on where the images were done, as preciesely as possible. And she would need to give information on where she intended to go next, so they would know how to contact her. But for the most part, she would be able to go where she wished, when she wished to go there.

In later years, she sometimes thought about being fired. She often chuckled when she did. She was very glad that it had happened.

❦ ❦ ❦

© George Harvey 2023

If you like this chapter, you might want to take a look at my published work described at my blog page, “Fiction, &c, by George Harvey.” This chapter will be in the fourth book in the series starting with Where Heaven and Earth Meet. The books are self-published, and are available online at Barnes & Noble.