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

 

Trunc Cubocta

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. 

Trunc Cubocta

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

hexadeka

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.

The Inverted Popularity of This Aspie’s Phobias and Philias, Part I: An Explanation

phobias and philias

The image above contains three colors: white, black, and red. The words appear in red because I see it as a color denoting positive or negative intensity, and phobias and philias are both certainly intense. To “see red,” I have learned, does not usually mean what it would mean if I said it myself. Consistent with Asperger’s Syndrome, which I have, I tend to be almost completely literal in the words I use, while the non-Aspie majority often uses words in confusing (to me) non-literal ways. Over the years, I have figured out that this phrase means, when non-Aspies say it,  that they are extremely angry. (I, however, would only say “I see red” if I was actually seeing light with the wavelength-range, ~620 to ~740 nm, which our species has labeled, in English, as “red.”) On the other hand, red roses and Valentine’s Day hearts are popularly used to symbolize romantic love, which is an intensely positive emotion, while extreme anger is extremely negative. White and black, the other colors above, in much of the world, are commonly associated with, respectively, positive and negative things. I, on the other hand, view these colors the opposite way: I have avoided sunlight for much of my life, and continue to do so (to the point where I need to take supplements of vitamin D), while also reveling in darkness, in much the same way that I revel in my “Aspieness.” Right now, it is daytime here, and I am writing this inside, in a dark room, with the only artificial light reaching me coming from computer screens.

It is a common misconception that Aspies (an informal term many people with Asperger’s use for ourselves) are non-emotional. After all, two well-known fictional characters from different incarnations of Star Trek, Spock and Data, are based, in my opinion, on Aspie stereotypes. Stereotypes, I have observed, are usually based on some real phenomenon, and in this case, that phenomenon is that many Aspies experience emotions in radically different ways from the non-Aspie majority — so differently that we are sometimes perceived by non-Aspies to be emotionless, although that is not the case. This causes a considerable amount of tension, and no small amount of outright hostility, between the community of Aspies and the non-Aspie majority. When I write on the subject of Asperger’s Syndrome, I try to do so with the goal of explaining and understanding our differences, in order to reduce Aspie/non-Aspie misunderstanding, which is both common and unhelpful — in both directions. This is the reason I use the factual, non-hostile term “non-Aspie,” in place of the unhelpful and perjorative term “neurotypical” (a word in common use within the Aspie community), one of three unfortunate words discussed in this post.

Explaining my choices of colors in the image above was a prelude to a personal, mathematical analysis of the inverted popularity of my own phobias and philias. I have long observed that I have an intense, inexplicable affinity (in many cases, reaching the level of a “philia,” an often-misunderstood word and suffix, for reasons I will discuss below) for things which the majority, in my part of the world (the American South) hates and/or fears. Examples include spiders, cats, the number thirteen (and all other prime numbers), mathematics in general, geometry in particular (strangely, even many people who like mathematics still dislike the subfield of geometry), being different from those around me, darkness, the color black, night, the physical sciences, evolution (which happens, like it or not), enclosed spaces, heights, flying on airplanes, women, and Muslims. I have also struggled with phobias, working (with professional help) on eliminating them, one by one, but they tend to be less common. Examples of targets for my current and past phobias include light, especially sunlight, to the point where I actually have to take vitamin D supplements; as well as voice calls on cell phones (human voices coming out of small boxes freak me out); death; the life sciences; insurance; sports (and related events, such as pep rallies); loud noises; efforts to control me; and, since my mother died, last November 16, the 16th day of any month, especially at, and after, six months after her death.

I’m a teacher, and it’s the 16th of July, and I simply do not have the option of falling apart on the 16th of every month when school starts again next month, at a new school, with new students, for, as the saying goes, the students will arrive — whether I’m ready or not. That’s no way to start a school year.

I have much to be optimistic about, for I will be teaching in a different building, but on a much-improved schedule, with far fewer different subjects to prepare for each day than I had last year. When I fell asleep last night, after completing four full days of training to teach Pre-AP Physical Science for the first time, starting next month, some part of me knew that mental health improvement — before the 16th hit again, today — was essential. Was that something about which I was consciously thinking? No. I apparently rewrote my mental software (again) last night, an ability I have worked on developing for over thirty-five years. When this brain-software-debugging process first became evident, a few years back, it was happening in my sleep, just as happened again last night, and it took some time for me to figure out exactly what was going on, and how my ability to rapidly adapt to change had improved. 

In Part II of this post, I will analyze, mathematically, the inverted popularity of my phobias, compared to the most common phobias, ranked by incidence among the population. First, however, it is necessary for me to explain what I mean — and do not mean — by the word “philia.” There is a serious problem with this word, in English, when it appears as a suffix, and that is due to an unfortunate linguistic error: the incorrect application of a Greek idea, and word, to the horrific, disgusting, and criminal behavior of child molesters, as well as those who have sex with corpses. The ancient Greeks, as is well-known, used four different words for different kinds of love, and “philia” (φιλία) referred specifically to fraternal, or “brotherly,” love. This was not a word the ancient Greeks used for any type of sexual act. The words “pedophilia” and “necrophilia” are, for this reason, historical anomalies. Both terms are misnomers, meaning, simply, that they are messed-up words, and their existence creates the potential for misunderstanding. A philia, properly understood, is simply the opposite of a phobia. Phobias are better-understood, of course, and require no detailed explanation. 

One example of what I mean by my own philias should suffice. I have, for many years, had an abnormally strong fascination with spiders. I like them — a lot — so much so, in fact, that I actually have a tattoo of a spider, and often wear a spider necklace, to express how much I like this one biological order, the largest within the class of arachnids. Despite my strong affinity for spiders, however, I have zero sexual interest in them. It is accurate to call me an arachnophiliac, which is the opposite of an arachnophobe.

It is now near 9 pm on Saturday, November 16, and Friday night’s sleep therapy gave me the energy to work on the needed improvements to my mental health during the day today, by using reflective writing as a therapeutic technique. I also have a new appreciation for sleep, which will come soon. Part II will be posted soon, but it will not be written until after I have enjoyed a full night of sleep — starting, hopefully, in a few minutes. Goodnight, and thank you for reading Part I.

[Update, July 17: Part II is now posted here.]

Mathematical Therapy

When I need to, I make mathematical images to improve my mood. For me, it works. These are three I created yesterday, using MS-Paint and Geometer’s Sketchpad.

I have a hunch this sort of thing would only work for a very few people, and we’re probably all Aspies, whether diagnosed or not.

I also call this sort of thing “recreational mathematics.” It’s better than Prozac, at least for me.

I’ve been doing this sort of thing for far longer than I’ve been on WordPress. These are just the latest such images.