494 Circles, Each, Adorning Two Great Rhombcuboctahedra, with Different (Apparent) Levels of Anxiety

 

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The design on each face of these great rhombcuboctahedra is made from 19 circles, and was created using both Geometer’s Sketchpad and MS-Paint. I then used a third program, Stella 4d (available here), to project this image on each of a great rhombcuboctahedron’s 26 faces, creating the image above.

If you watch carefully, you should notice an odd “jumping” effect on the red, octagonal faces in the polyhedron above, almost as if this polyhedron is suffering from an anxiety disorder, but trying to conceal it. Since I like that effect, I’m leaving it in the picture above, and then creating a new image, below, with no “jumpiness.” Bragging rights go to the first person who, in a comment to this post, figures out how I eliminated this anxiety-mimicking effect, and what caused it in the first place. 

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Your first hint is that no anti-anxiety medications were used. After all, these polyhedra do not have prescriptions for anything. How does one “calm down” an “anxious” great rhombcuboctahedron, then?

On a related note, it is amazing, to me, that simply writing about anxiety serves the purpose of reducing my own anxiety-levels. It is an effect I’ve noticed before, so I call it “therapeutic writing.” That helped me, as it has helped me before. (It is, of course, no substitute for getting therapy from a licensed therapist, and following that therapist.) However, therapeutic writing can’t explain how this “anxious polyhedron” was helped, for polyhedra can’t write.

For a second hint, see below.

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Second hint: the second image uses approximately twice as much memory-storage space as the first image used.

On Therapeutic Writing, and Putting Hexakaidekaphobia in Remission

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When my mother died, last November 16, I wrote an obituary for her, which I was then asked (unexpectedly) to read at her funeral, as one of two eulogies. This was one of the most difficult things I have ever done, but writing it did help me (somewhat) with the immediate problem I was having dealing with grief.

After the funeral, I felt numb much of the time, for months, until May 16 arrived — exactly six months after she died — at which point my tightly-controlled emotional state shattered, leaving me in worse shape (in some ways) than I was on, say, November 17 of last year. This was unexpected, and caused significant problems, including the development of monthly hexakaidekaphobia, a morbid dread and fear of the 16th day of every month. (The word is a modification of “triskaidekaphobia,” an irrational fear of the number thirteen).

June 16 was worse than May 16 — absolutely full of PTSD attacks. (I’ve had PTSD for most of my life; my mother’s death made it worse.) Fortunately, I don’t try to hide mental health problems, as I once did — I try to find the help I need, from physicians, to deal with such problems, and, when I find things that help me, I write about them. I also have long used recreational mathematics to help me feel better when depressed.

It was in this context that mid-July arrived. I went to sleep on July 15th with the knowledge that it was extremely important for me to find better coping mechanisms before the start of school in August. When I woke up on July 16, which could have been another horrific day of severe depression, anxiety, and other problems, I did not feel those negative emotions. This does not mean I had “gotten over” the facts that my mother did die, and that I miss her terribly. However, it did mean I was experiencing grief differently: I was feeling grief, rather than letting feelings of grief control me — and there is a huge difference between the two.

That morning, July 16, I knew what I needed to do as soon as I woke up: I needed to write. For me, that generally means blogging, and that’s what happened. This “therapeutic writing,” as I call it, was helpful enough on July 16 that I continued it the next day. When I next spoke to my doctors, I told them I was doing this, and why, and they agreed that such writing (like the “mathematical therapy” I have done for years) was an excellent, helpful activity. (This “check with professionals” step is essential, and I do not recommend attempting mental health therapy without the help of at least one licensed, qualified psychiatrist, and/or other type of therapist, such as a clinical psychologist.)

Of course, I could do this therapeutic writing in a spiral notebook, and keep it private; no writing has to go on the Internet. Why, then, do I choose to post such material where anyone can see it? I first explained why I blog about mental health issues in this post, but the short version is this: I hope that my openness on this subject can help reduce the social stigma which, unfortunately, still surrounds topics related mental health. This stigma is harmful because it keeps millions of people from seeking the professional help they need. I have also found it a personally liberating experience to come out of the “closet” on such issues, for, as with other metaphorical “closets,” it is the truth that closets are not good places for people to live their lives.

School starts on August 15 — only four days from now — and I’m going to do everything I can to make that day, the next day (the formerly-dreaded 16th of the month), and the rest of the days in the school year as good as they can possibly be for my students, as well as myself. I could tell I was on the right track when I decided to write about monthly hexakaidekaphobia early this morning, but in the past tense. Before I started writing, I “warmed up” by constructing the geometric art at the top of this post, which, if you examine carefully, you will see is based on — what else? — the number sixteen. In my case, at least, mathematical therapy and therapeutic writing go hand-in-hand, and this is what I am doing to try to leave my monthly hexakaidecaphobia in the past, where it belongs.

I still miss my mother. She was once, as I am, a science teacher, and was also involved in education in many other ways. She would want me to have good school days on August 16th, September 16th, and so on, as well as the days in-between — and, to properly honor her memory, and give my students the education they deserve, I am determined to do my best to do exactly that.

Why I Do Not Write Books

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It’s very simple: errors in writing, of any kind, horrify me. If I wrote a book, and it were published, some would likely slip through, such as the one in the image above. If a book with my name on the cover had been published, and I then discovered an error, I would end up trying to get corrected copies to every buyer of the first edition, eating all profits, and then some. I also just don’t need that type of stress.

Please do not misunderstand: I love books.

Therefore, I do two other things, in lieu of actually writing a book (which has been suggested, to me, more than once). First, I read other peoples’ books. I seek higher-quality books to avoid those irritating typos, for they actually cause me pain when I see them. Even so, some slip through — ouch! — but at least the mistakes aren’t mine. I am almost immune to conventional causes of embarrassment, but this isn’t a conventional cause, and I certainly have no immunity to it.

The other thing I do is to blog, which is, of course, another form of writing. It’s a perfect forum for someone with this writing-quirk — because, when I discover a mistake in my writing, even months or years later, I can edit it away in seconds. This is why, for me, blogging > writing books. However, I am grateful that there are good writers for whom the inequality symbol points in the other direction.

On Life, and Death, in the Marvel Comics Universe

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To write this, I did a lot of research, and had much help from friends. One of them, Craig Deaton, gave permission for his name to be used, but the others have not. I am grateful to them all.

This is a compilation of three lists, for purposes of comparison and analysis, and concerns life, death, being “unkilled,” then “re-killed” after being unkilled, and then, sometimes, being “re-unkilled,” and so on. In other words, the topic here is bad writing, and a terribly overused plot device. To (try to) keep this simple, I’m limiting this survey to the primary Marvel Comics universe, in which Earth is called, for reasons I do not understand, Earth-616. I started this yesterday, by simply posting some questions on Facebook, and watched, with growing amazement, as the information started pouring in.

The shortest of these lists includes only comic book characters who are currently dead, but whom I have high confidence Marvel will unkill, before too long.

  1. Wolverine, a/k/a James “Logan” Howlett
  2. Uatu, a/k/a The Watcher
  3. Charles Xavier, a/k/a Professor X

At least two of these characters (Wolverine and Professor X) have been killed, and then resurrrected, before, and I will be shocked if this process is not repeated, again (and again, and again, and again…).

The next list includes characters who have been killed, have actually remained dead, so far, and whose resurrections I do not (at least not fully) expect.

  1. The Abomination
  2. The Ancient One (associated with Dr. Strange)
  3. Hector Ayala, the Black, Hispanic, male version of the White Tiger, killed after Matt Murdock failed to secure his acquittal on a murder charge, of which Ayala was innocent
  4. Blink, of the X-Men
  5. Daken, son of Wolverine
  6. Jean DeWolf, a police detective who used to work with Spider-Man
  7. Dr. Doom’s mother
  8. Leland Drummond, a corrupt FBI man involved in “outing” Daredevil’s secret identity
  9. Richard Fisk, son of the Kingpin (Wilson Fisk)
  10. Flashback, a little-known mutant killed in a weird time-travel scenario created by his own superpowers
  11. Bill Foster, a/k/a Goliath, a/k/a Black Goliath
  12. Adolf Hitler, a/k/a Hate Monger (brought back from the dead, and then re-killed)
  13. Karen Page, the primary love interest of Matt Murdock’s (Daredevil’s) life
  14. Mar-Vell, a Kree warrior who went by the name “Captain Marvel”
  15. Microbe, of the New Warriors
  16. “Battlin’ Jack” Murdock, best-known as Daredevil’s father
  17. Namorita, of the New Warriors
  18. Night Thrasher, of the New Warriors
  19. Scott Perkins, a police officer whom Hector Ayala (see above) was falsely convicted of killing, despite Matt Murdock’s best efforts, as his lawyer, to secure Ayala’s acquittal
  20. Pyro, one of many foes of the X-Men, who was killed, brought back as a zombie, and then killed again
  21. Spider-Man’s father
  22. Spider-Man’s mother
  23. Spider-Man’s Uncle Ben
  24. Gwen Stacy, former girlfriend of Spider-Man
  25. Katherine Anne Summers, the mother of the mutants Cyclops, Havok, and Vulcan
  26. Turbo (the original one)
  27. The chain of unnamed criminals who first got Daredevil’s secret identity from Karen Page to Wilson Fisk, the Kingpin of crime, and were then ordered killed by Fisk
  28. Numerous unnamed people who lack superpowers, and also lack connections to superheroes who are neither Daredevil, nor Spider-Man
  29. The unnamed woman whom Daredevil’s wife Milla, under the influence of mind control, pushed in front of an oncoming subway train, leading to Milla’s institutionalization
  30. At least one person affected by the Wendigo curse (killed by the Red Hulk)

What can we learn from the list above? Well, for one thing, characters in the Marvel Universe who have no superpowers should stay far away from both Daredevil and Spider-Man.

The last list, and easily the longest, includes characters who have recovered from death at least once, and are currently alive in this fictional universe — one where death obviously “has a very loose grip,” as one of my friends on Facebook phrased it.

  1. Bucky Barnes / The Winter Soldier, and, briefly, Captain America
  2. Bullseye
  3. Cannonball
  4. Captain America / Steve Rogers
  5. Colossus, of the X-Men
  6. Cyclops / Scott Summers, of the X-Men
  7. Cypher / Doug Ramsey, of the New Mutants
  8. Daredevil / Matt Murdock
  9. Darwin, of the X-Men
  10. Dead Girl (except that she’s still sort of dead, being, after all, Dead Girl)
  11. Elektra
  12. Firebrand
  13. Vanessa Fisk, estranged wife of Wilson Fisk, the Kingpin
  14. Galactus
  15. Jean Grey (not exactly the same as Phoenix)
  16. The Grim Reaper (brother of Wonder Man)
  17. Havok / Alex Summers
  18. Hawkeye / Clint Barton / Ronin
  19. The Human Torch (original android version)
  20. Loki, Norse God of Mischief
  21. Longshot, of the X-Men
  22. Moira McTaggert, friend of the X-Men
  23. Mockingbird, ex-wife of Hawkeye
  24. Mysterio / Quintin Beck
  25. Nightcrawler, of the X-Men
  26. The Owl / Leland Owlsley
  27. Petra, of the X-Men
  28. Phoenix (not exactly the same as Jean Grey)
  29. Agent Preston
  30. Kathryn “Kitty” Pryde, of the X-Men
  31. Madelyne Pryor, estranged wife of Cyclops / Scott Summers
  32. Psylocke, of the X-Men
  33. The Punisher / Frank Castle
  34. The Red Skull
  35. Rogue, of the X-Men
  36. The Sentry
  37. Speed, of the Young Avengers
  38. Spider-Man / Peter Parker
  39. Spider-Man’s Aunt May
  40. Spider-Man’s clone
  41. Storm / Ororo Munroe, of the X-Men
  42. Hope Summers, of the X-Men
  43. Sway, of the X-Men
  44. Tarot
  45. The Thing / Benjamin Grimm
  46. Thunderbird, of the X-Men
  47. Toro, the original (android) version of the Human Torch
  48. Trickshot
  49. The Vision
  50. Vulcan, of the X-Men (brother of Cyclops and Havok)
  51. Wiccan, of the Young Avengers
  52. Wonder Man
  53. Wong, associated with Dr. Strange
  54. Zzzax

It is clear that the most effective way to cheat death, in the Marvel Universe, is simply to be one of the X-Men. Are there more characters who should be on this list? Yes, but we all got tired after several hours of this, and moved on to other things.

Seriously, though, Marvel needs to stop doing this.

However . . . they won’t.

At Least for Me, Blogging > Writing a Book

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I’ve been asked, more than once, if I’ve ever considered writing a book. The answer: writing a book, as compared to maintaining a blog, would drive me crazy. The reason is simple: every book I’ve every read has at least one typo in it — somewhere. If I wrote a book, got it published, and then found writing mistakes in it, I’d be mortified. With a blog, on the other hand, I can edit mistakes away, months, or even years, after making them.

There aren’t many things that embarrass me, but making errors in writing is definitely one of them. If others can see the errors, then having committed the “sin” of writing incorrectly feels like being caught naked in public — eeeeek!

The Evolution of Sam Harris’s Writing

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The Evolution of Sam Harris's Writing

Sam Harris is my favorite author of non-fiction, but this has not always been the case. He is usually classified as one of the “Four Horsemen” (along with Richard Dawkins, Daniel Dennett, and the late Christopher Hitchens), to the point where he has remarked that some treat them as “one creature with four heads.” I’ve read books by all four men, and they are very different. Harris started as my least favorite of the four, and has become my favorite. How did this happen? Well, it took some time.

Sam Harris began his career as a writer with a book called The End of Faith, written in the wake of, and largely in response to, the 9/11 attacks of 2001.

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Despite my atheism, I did not care for this book. It bashes Islam too much for my tastes, and Harris is still criticized for this fact, generally by people who have not read the rest of his work. Reactions like mine to this book are rare among atheists, for one simple reason: most atheists have a far less favorable view of Islam than I do. For more on that, please see my previous blog-post, and the earlier one it links to.

Islam is not the only religion criticized by Harris in his first book — not by any means. As someone who has never had a Muslim attempt to harm me, but who has suffered greatly at the hands of certain Christians, I was far more receptive to his arguments against the Christian religion. Many members of that religion noticed those arguments as well, and Harris was deluged with hate mail, much of it from enraged Christians in the USA. He wrote his second book as a response to this torrent of criticism.

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This second book paid much less attention to Islam, and far more, as the title implies, to Christianity. I enjoyed it more, but admit that this likely has as much to do with my personal history as anything else. Still, Letter to a Christian Nation remains the only book I have ever read in a single sitting; it was so compelling that I was unwilling to stop reading it until the last page.

Both of Harris’s first books may be described as “beating the drum of atheism,” an activity which is interesting and useful only up to a certain point. To his credit as an author, he realized that writing more books which repeat this process would be waste of time. He therefore decided to move on to other subjects — and, in my opinion, his books improved greatly as a result of that decision. Here’s his next one:

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The Moral Landscape is not a book about atheism, nor religion. Sam Harris is a neuroscientist, and this book considers human values from a scientific point of view:  questions of good and evil, and whether or not such questions can be addressed scientifically. Ethics and morality are things for which some people consider religion essential. Rather than belaboring the fact that he disagrees with this, Harris, in this book, simply makes a compelling case that such topics can indeed be addressed using the scientific method.

This was Harris’s first book after he made the excellent decision to move out, beyond his previous focus on atheism and religion. Were it not for this decision, I would not name Harris as my favorite non-fiction author. The arguments in this book are compelling, I learned much from reading it, and recommend it highly.

Harris’s fourth book tackles the topic of honesty, and its opposite:

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Is there ever a situation in which lying is justifiable? Most people would say “yes.” Harris disagrees, and, in this very short book, makes a compelling argument for honesty. His move away from the “drum of atheism” continues in this book, and the rule with Harris is simple:  the further away he goes from his original topic of choice, the better his writing becomes.

This brings me to his fifth book, the amazing Free Will.

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Do I have free will?  Do you?  Does Harris?  It certainly seems as if we do, but Harris takes the point of view that free will is an illusion, and supplies ample evidence to support this position. Denying free will is a dangerous game, of course, for, without free will, how can anyone be held responsible for their actions? Harris does not avoid this problem, but tackles it directly. Reading this book has had a powerful impact on how I view a great many things.

There is more of Harris to read, for those who are interested. I follow his blog regularly (http://www.samharris.org), and he has a new major book release coming soon, as well. Since he keeps getting better with each new book, I am looking forward to it with anticipation.