Mr. Trump, Please Get Some Sleep

sleep

Sleep is essential for good mental and physical health. It helps us heal when we need healing. I went to bed very early last night, and got all the sleep I need to do well at work today. I wish to suggest to our president that he do the same.

At least eight hours of sleep a night is healthy and helpful. Also, especially for a man in his seventies who is under a great deal of stress, long naps during the day can be a literal life-saver. In Mr. Trump’s case, the number of lives saved can be very large indeed.

To free up time for sleep, I have one more piece of advice for the president: limit yourself to one tweet per day.

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The T-Shirt from the Future: A Short Short Story

Time travel cube

Someone nudged my shoulder, stirring me from deep sleep. “Wake up, grandpa,” said an unfamiliar voice. Grandpa? Who’s that? I opened my eyes to see a young woman, dressed in black, looking back at me. Her face was brown, and her eyes looked like deep pools of water.

She smiled. Nothing in twenty-plus years of teaching could have prepared me for this, I thought. I looked around, trying to find my cell phone, without success. Nothing here was like anything I’d seen before. Small lights, like fireflies, circled us in the darkness.

“I know it’s confusing to be called ‘grandpa,'” she said, answering a question I had not yet had the chance to ask. “This is, well, complicated.” Her voice sounded excited, even though she was speaking softly. She reminded me of teachers new to the profession, positively bursting with new ideas, and looking forward, enthusiastically, to the new school year ahead. 

“It would have to be complicated,” I mumbled. Sleep was fading as I rubbed my eyes, trying to see where I was. A light came on, but it was unclear where the lightbulbs were. We were alone, inside a blue and white cube. The cube slowly moved, but its direction kept changing. “What am I doing here? Where’s my wife? Where am I, and who are you?”

“So many questions! I expected that, though. I will explain what I can.”

“That’s good, because . . . .”

“Please don’t interrupt,” she said. I stopped talking, but did not stop thinking. It appeared to be time to listen, not talk. “Thank you,” my alleged granddaughter continued. “In order, here are the answers to your questions. First, you are here for an important conversation. Second, your wife is peacefully sleeping. Third and fourth, you’re in my time-travel cube, and my name is Xiahong Al-Nasr. Technically, you’re my great-great-great-great-great-grandfather, but . . . .” I raised my hand to ask a question, as if I were in class myself. She shook her head, and continued, “. . . I’ve always thought of you as, simply, ‘grandpa.’ It’s a time-saver. May I continue explaining why we are here, or can your question wait?”

I thought fast. What should I say next? There was only one logical response. “I’ll listen,” I replied, and put my hand back down.

“You’re about to go back to school,” she said, “and you’re the teacher. It’s important that you understand why you are doing what you do, this year, above all others.” This reminded me of advice I’d heard before, but this time I was listening as if I were hearing for the first time.

This woman’s name, Xiaohong Al-Nasr, combined a Chinese given name with an Arabic surname. I hoped she would explain how that had happened.

“You’re wondering about my name,” she said. I swallowed, and nodded. My mouth was too dry to speak. “I’m from the 23rd Century,” she continued. “Nearly everyone where I work and learn, including me, has DNA from every continent on Earth. I’ve also got a little from off-world colonies, but I’m 100% human, just as you are. I was given my name by all of my parents.” She paused. Her gaze was locked to my own. “I’ve been authorized to tell you that much, but I have to be careful about revealing more, to prevent altering the timestream. Do you believe me?”

“If you know anything about me, you know that I teach science, as well as other subjects.” It was a relief to finally have my turn to speak. My alleged descendant, Xiaohong, was listening to me now. Finally! “You’ve either studied me, somehow, or you’re reading my mind, or it’s something else even more complicated, but you seem to know what I know. You must know, then, that scientists are trained to be skeptical. Everything has to have evidence to support it. In science, there is no higher authority than experiment.”

“I understand that, grandpa. We knew you would need evidence, so I do have a gift for you. It’s a t-shirt. You like t-shirts, after all.” Xiaohong smiled, and removed a small capsule from her pocket, no larger than a quarter. She opened it, and — somehow — pulled a full-size t-shirt from that impossibly small place.

t-shirt

I took the t-shirt from my descendant. Touching it was, well, real! I turned it over. It said “Go Bears!” on the back. Even if I believed her, though, I knew I would need more than just a t-shirt to convince anyone else. After all, time travel to the past was considered impossible by every scientist I had studied. Quickly, I did the arithmetic, using the year on the shirt. “That’s the year I would turn 300 years old, if I could live that long!” I was now catching Xiaohong’s excitement. “Clearly, Arthur C. Clarke’s Three Laws apply here, as does the Sagan Standard, Feynman’s First Principle, the grandfather paradox, and — and — and — the entire scientific method!”

“You’re absolutely correct, and it will be important for your students to understand all those things as well.” She was right; these are all things I talked about in science class, every year. This year, though, I can try to explain them differently, or perhaps have my students research them, and then have the students explain them to my class. Correction: my classes. My students. All of them.

Something fell into place in my mind at that moment, and I finally understood what was going on. It wasn’t my own accomplishments that had brought my descendant back in time to visit me, but the unknown creations of a student of mine — from the school year about to begin. Xiaohong smiled.

“You’ve figured it out, haven’t you?” She was asking a question, and, this time, I had the answer.

“Yes. You came back through time to refocus my attention to my own true purpose in the classroom. My job is to help my students learn to do great things. It’s not about me. It’s about them!” Xiaohong’s smile grew larger. I continued. “This school year is critical. This is true of all school years, in fact. Each year is both important, and urgent. In every school, and for every student, we must always do our best to learn — together.”

Xiaohong extended her hand, and received a firm handshake from me. “Now that you know the truth, grandpa, our work here is finished. You’ll wake up in the morning, in bed with your sleeping wife, and after that, you’ll find your t-shirt, in the dryer, at home. I have to go, though; I’m needed back in the 23rd Century. After all, I have my own classes to teach, quite soon, at our Time Travel Academy, where I got your t-shirt. Goodbye, and have a great school year! I know I will, as I continue my training to become a teacher myself.”

“I will do that,” I replied. “Thank you so much! As for this evidence you’ve given me, I know how I’ll handle that. I will let the students evaluate it, with help from me, on an ‘as needed’ basis.”

“Exactly,” Xiaohong said, and then she spoke to the ceiling of her time travel cube. “Send us both back to where we were — now.” A humming sound started, then became louder. The lights began to dim. After a few minutes, everything faded to darkness, and silence, once more.

When I awoke, home again, I checked the dryer, and found it — my t-shirt from the future — waiting for me. This school year will be amazing!

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The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part Two

Just like I did in the first part of this two-part post, I’m starting with the snub dodecahedron’s 43rd stellation.

43rd stellation Snub Dodeca

This time, though, this polyhedral exploration is going in another direction. In the image below, the yellow kites seen above are shown augmented with prisms. The height of the prisms is equal to the average edge length of those kites.

Augmented Stellated Snub Dodeca

Creating the convex hull of this augmented polyhedron is the next step.

Cool polyhedron before TTMFR

The program I’m using to make these changes to polyhedra is called Stella 4d (it’s available here). The next step is using a function of Stella called “try to make faces regular.” The result is shown below.

242 faces 20 hex and 12 penta and 2x60 quads of two types and 30 quads of a third type and 60 triangles

Finally, I’m adjusting the coloring scheme so hexagons, pentagon, and triangles each get their own color, with a fourth color used for all three types of quadrilateral.

cool polyhedron colored by number of sides per face

Because I like this result, I’m stopping here.

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The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part One

If you stellate the snub dodecahedron 43 times, this is the result. The yellow faces are kites, not rhombi.

Stellated Snub Dodeca refl

Like the snub dodecahedron itself, this polyhedron is chiral. Here is the mirror-image of the polyhedron shown above.

Stellated Snub Dodeca 43rd mirror image

Any chiral polyhedron may be combined with its own mirror-image to create a compound.

Compound of enantiomorphic pair x

This is the dual of the snub dodecahedron’s 43rd stellation.

Stellated Snub Dodeca refl chiral dual

This dual is also chiral. Here is its reflection.

43rd stellation snub dodeca dual reflection

Finally, here is the compound of both duals.

Compound of enantiomorphic pair duals

I used Stella 4d: Polyhedron Navigator to create these images. You may try this program for yourself at http://www.software3d.com/Stella.php.

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A Black-on-Black Polyhedron: The Final Stellation of the Icosahedron

Icosa

I made this using Stella 4d: Polyhedron Navigator, which you may try for free right here.

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Selected Stellations of the Truncated Dodecahedron

This is the truncated dodecahedron. It is one of the Archimedean solids.

Trunc Dodeca

This polyhedron has a long stellation-series, from which I selected several on aesthetic grounds. The figure immediately below is the truncated dodecahedron’s 16th stellation.

16th stellation of Trunc Dodeca

Here is the 21st stellation.

21st stellation of Trunc Dodeca

It’s easy to stellate polyhedra rapidly, and make many other changes to them, with Stella 4d: Polyhedron Navigator. You can try it for free at http://www.software3d.com/Stella.php.

25th stellation of Trunc Dodeca.gif

The stellation shown immediately above is the 25th, and the one shown immediately below is the 27th.

27th stellation of Trunc Dodeca

Here is the next stellation: the 28th. Unlike the ones shown above, it is chiral.

28th stellation of Trunc Dodeca.gif

This is the truncated dodecahedron’s 31st stellation.

31st stellation of Trunc Dodeca.gif

This one is the 38th stellation.

38th stellation of Trunc Dodeca.gif

This one is the 44th.

44th stellation of Trunc Dodeca.gif

The last one shown here is called the truncated dodecahedron’s final stellation because, if it is stellated once more, it returns to the original truncated dodecahedron.

Final stellation of Trunc Dodeca

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We should not have to be ashamed of our president.

shame

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