The Melton Ring

Everyone is familiar with a Moebius Strip, a length of paper glued to its own end with a half-twist so that a line drawn down the middle of the paper goes twice around before meeting itself.

But a strip of paper is a real three-dimensional object. Imagine instead of being flat and thin that this paper has a thickness equal to its width. Now the Moebius strip has two edges, one with a line drawn down the middle and one without.

Now imagine that the cross-section of this object were five-sided instead of four-sided before the line was drawn down the middle. Now the line drawn down the middle goes five times around before meeting itself.

What if the object had seven sides? Nineteen? Six hundred and forty-one?

What if it had an infinite number of sides? In other words, a circular cross-section.
And you gave the ends a twist that was irrational to the circumference of the cross-section before gluing the ends together?

Now if you start anywhere on the surface of this object and draw a line perpendicular to the cross-section, that line will be a closed loop infinite in length before it comes back and meets itself. Furthermore, that line will touch every point on the surface.

Do you have a three-dimensional object with a one-dimensional surface? If not, why not?


For the last few months I’ve been working on some songs with my friend Bob Winter. He has three of the ones we’ve worked on together at his website:¬†Notes in a Bottle.

It’s quite a kick to hear someone singing something you’ve written. How this goes is that I write the words and sing (badly) a version of the tune for Bob to hear. Then he works on making it singable and providing chords and harmonies and doing the production. Since I’m a terrible singer, it’s amazing to me that he can come up with a tune that is so very like what I can hear in my head.

Also, my rhythms are often clumsy and Bob smoothes them out and we work on changing lyrics together to get the phrasing right. :) It’s a real collaboration and a heck of a lot of fun.

Real Estate

Another story based on a dream I had.

Real Estate

The old man eating lunch in the park didn’t seem to be interested in his sandwich. Sitting on the grass nearby, a taller, younger man in dirty clothes watched. The old man sighed for about the fortieth time then stood and carried his uneaten sandwich toward the trash can, frowning.

“If you’re not going to eat that, can I have it?” asked the young man.

The old man stopped and turned to look. “It’s salami and tomatoes on Italian,” he said.

The young man could not stop the visible rush of saliva to his mouth. “Sounds great.” He stood up, wiping one hand across his face.

The old man nodded and held out the meal, still mostly wrapped in the deli papers. “I’m Thomas, I’ve seen you here before.”

The younger man took the food from his hands, his face intent on the prize. “I’m Chris. And yeah, I uh, sort of live here.”

Thomas walked slowly back toward the bench. “Sit, eat,” he said nodding toward the other end as he sat down.

Chris sat, smiling briefly toward Thomas before he began eating. He treated the partially wrapped sandwich with care and almost reverence as he extracted a cut third of it from the papers.

Thomas watched him eat and his own face changed. By the time Chris had finished the first third with a bit of tomato dripping from his chin, Thomas smiled. “Glad to see you like that,” he said. “There’s a couple of napkins.”

Chris nodded, wiping away the ruby red remnants from his stubbly chin. “It’s good. And I’m not just saying that ’cause I hadn’t eaten since yesterday, the guys at Two Fat Italian Heroes know how to make a sandwich.”

Thomas smiled but it seemed to pain him. “They do,” he said. “I wish they were better at making the rent.”

“Huh,” said Chris. “How do you mean?”

“I’m the property manager for this block of shops.” He gestured toward one side of the park. “I collect the rents and turn them over to the owners. I take care of problems like roofs and sewers and dealing with police and building inspectors. But Leo and Gio are late with the rent, two months in a row. And short both times, besides. I have to tell the owner.”

Chris chewed his way through the second section of the sandwich and neither of them said anything for a while. Finally, Chris said, “You don’t want to do that.”

Thomas shook his head. “I don’t. But it’s my job. If they are short three times, they go on a list. From being on the list to getting evicted if you don’t make up everything you missed, takes about six months.”

Chris nodded. He looked at the last third of the sandwich, about four inches long and nearly as wide. Salami, provolone, tomatoes and onions with a light coating of olive oil and vinegar filled the bread to overflowing. “You want the last piece?” he asked Thomas.

Thomas looked at the remainder of the sandwich. He hadn’t wanted it at all but now that he had said something to someone, he felt a bit of hunger. It was his lunch after all and he had forced Leo and Gio to accept payment for it by leaving the money on the counter. “Maybe half?” he said, his mouth watering.

Chris carefully tore the sandwich in two and offered his choice of halves to Thomas and they both ate with obvious enjoyment.

“Good sandwich,” said Chris when they had finished and used the napkins to clean their hands and faces. “Thanks,” he added as he threw the trash into the can.

“They do make good sandwiches but hardly anyone is willing to pay eleven dollars for a foot-long hero anymore when there’s a chain sandwich shop on almost every block,” said Thomas.

“Yeah,” said Chris. “They have a nice corner location though, they ought to be able to grow a clientele if they can get through a year or so. You think?”

Thomas nodded. “Probably.”

“But if they go under in six months, the storefront is likely to be empty for a year or so?”

Thomas nodded again.

“That can’t be good for anybody on the block. Not good for the owners or you either.”

“No,” said Thomas. The small part of the sandwich he had eaten sat like a lump in his stomach.

Chris belched. “Pardon. So, what if you went to everyone on the block and asked them if they could help the sandwich guys out with rent for a while. And put it like a package deal to your bosses, reduced rent for a year while Leo and Gio get on their feet?”

Thomas gulped. “That just might work,” he said. “Why didn’t I think of that?”

“Too close to the problem, maybe?” suggested Chris. “It’s worth a try, anyway.”

Thomas started away, his face showing his optimism in the new solution.

“Hey,” said Chris. “You got any work for me? Run errands? Sweep up? Haul away the trash in the alley? Anything?”

Thomas blinked. “I’m not doing so good on the thinking things through bit today. Yeah, I probably do have some things for you to do.” He smiled at his new friend.

Chris smiled back. “I knew it couldn’t hurt to ask,” he said.


God, an IRS man, a priest, and a rabbi are playing mini-golf. After six holes, the IRS man is leading with 21, God at 24 and the two clergymen tied at 26. It’s a good tight game and everyone is playing well.

The priest has been trying to get up his nerve to talk privately to God and he finally manages to ask what’s been on his mind. “God, he says, I’ve been a good man, I’ve tried to help my flock and follow church teachings and abide by Your Holy Word. What I want, well, what I want to know, what I’d like is some assurance that I’m going to Heaven.”

God smiled on his priest. “Sure,” He said. “You’ve been a good man and a fine priest and if you continue as you’ve been doing, your place in Heaven is assured.” Much relieved to hear that, the priest thanked God, praised Him and moved away to smile happily as he prepared for the next hole.

Seeing the priest had spoken with God, the rabbi stepped up, too. “Sir,” he said. “We Jews don’t necessarily believe in Heaven but we are promised a reward if we keep Your Commandments. I think I have done so, I have certainly tried and I would like to receive the sort of assurance You gave the priest that my life has pleased You.”

God smiled down at him. “And aren’t you one of My Chosen People? You keep the Commandments, you have done mitzvahs as you should. And yes, you will be rewarded for being good and kind and faithful.” And the rabbi also moved away smiling.

Seeing the other two so happy to have received God’s blessing, the IRS man approached the Presence of the Deity. “I’m a humble man, God. I don’t have the knowledge the other two have of what I should do. I have a terrible job and I know that I have made other people unhappy. But wasn’t Matthew also a tax collector? I guess, what I’m asking is if there is going to be a place for me in Heaven, too.”

God frowned down at the tax man and the sky seemed to be a little less bright. “I hate to tell you this,” said God. “But if you keep hitting eagles like you did on the last two holes, you’re going to Hell.”


I dreamed about working on a comic strip again.

This one was called “Wisequackers” and was about a little boy and a little girl trying to run a farm by themselves with ‘help’ from the animals, all of whom could talk.

The particular sequence I was working on involved the little girl trying to get two enormous sheepdogs to round-up the sheep and keep them out of the corn. The dogs were watching Ren and Stimpy on TV and had no interest in this job.

“Besides,” said one of them, “we’re Great Pyrenees sheepdogs, not Border Collies. We protect sheep, not corn.”

So the little girl says, “It’s GMO corn and the sheep might eat it.”

The dogs look at each other horrified, jump up and charge out of the house to save the sheep.

The Inevitable Surprise

She fell.

Through the quiet darkness with the moon over her shoulder, she fell.

Toward the sea below, and the rocks, toward the foaming maelström between them, she fell.

She pulled her hands and arms into a point above her head, or rather below it, steering with her legs in the wind of her own passage.

Down and down and faster and faster, her breath tight and painful, not because she was holding it but because it came so fast that it could not be held.

She fell toward the water, silent except for the pounding of the wind and the roaring of her heart; she fell, not by accident but on purpose; she had jumped and she had not been pushed.

On the cliff above the men watched her fall, knowing that she had chosen escape into death rather than let them catch her, touch her, find out who she was, stop her from living to tell anyone what she had seen.

She struck the sea at the last, at the very end of her fall, the inevitable surprise at the bottom of every dive and she knifed cleanly through the water the way he had taught her and she knew that to the men above she had simply disappeared because she made no splash and hardly a sound at all, not one they could hear anyway though to her it sounded like the crash at the end of a world.

But, she lived.

Another Christmas

Another year ending,
Another Christmas come and gone.
We learned some sad songs,
And some glad ones, too.

And that’s why I’m sending,
To all my friends near and far,
Wishes for a joyful Christmas,
And love for the year that is new.

Another day dawning,
Another song we have learned,
A new world turning,
Its face to the sun.

And now night is yawning,
Its rhythm still young,
There’s joy even in sadness,
When we know our day is done.

Another year learning,
That Christmas always comes,
We can sing the glad songs,
And some sad ones, too.

And that’s why I’m yearning,
That all my friends near and far,
Enjoy a wishful Christmas,
And love in the year that is new.