My Klein bottle

(Klein bottles only exist in four-dimensional space, but a self-intersecting model of a Klein bottle can be made in 3D.)

Sometime in my teen years, I read the Time-Life book Mathematics. One photo caught my eye: Princeton math professor Albert W. Tucker's Klein bottle: 

I wrote to him asking where he had got it.  He wrote back and said the University glassblower had made it for him, but had found it very difficult, and wasn't going to do it again! 

But in 1999, a story in the San Jose Mercury News said someone in Berkeley was selling these. I bought the small one pictured at the top of this piece. I exchanged a few emails with the seller, Cliff Stoll, and realized I had read his book The Cuckoo's Egg. Click here for his Klein bottle store.

Scammers

 

Although I've used craigslist before with no problems, I've now had two bad experiences, one as a buyer and one as a seller.

I previously wrote about the seller who was a fraud and cost me a large amount of money in 2024.

Now, a buyer has tried to cheat me. It was close, but I avoided this one:

Someone replied to a craigslist ad I posted, sent a large check so I could pay $2190 to the person who was going to pick up my item and transport it to another state. 

The buyer kept pushing to speed this all up, but fortunately, I waited long enough to see my bank reporting that the check was bad!

Poetry Analysis

Early in my freshman English class at Rice, we were asked to write a brief analysis of a specific poem. Mine received a mediocre grade, and the grad student Teaching Assistant explained that I had completely ignored the obvious Christian religious symbolism.

Well, duh. Not being a Christian, it wasn't obvious to me. 

But that convinced me: for the rest of the semester, I adapted Cliffs Notes analyses and got better grades. 

And I took no further English courses.

Jack Kirby exhibit

 

Link to more photos.

As I've written before, I loved reading comic books when I was younger. My two favorite comic book artists were Steve Ditko for his occasional surreal psychedelic vistas, and Jack Kirby for both his muscular super-heroes and his action scenes. When I read that the Skirball Cultural Center was going to have a major Jack Kirby exhibit, I had to go.

I did not know that Kirby was Jewish, but I'm glad that that led the Skirball to hold this exhibit. I had not been there before.

It was fun seeing all the Kirby artwork. I never knew he worked for DC for a time, but that was in 1970, when I was no longer buying comic books.

2024 was a somewhat difficult year

It started with a bang... literally: A car hit me as I was walking across the street in January 2024. This, along with arthritis, has left me with long-term pain in my lower back and in my right hip, and has forced me to cut back on walking, my only exercise. I also struggle to find comfortable sleeping positions. I decided I should try a hip replacement, but Physical Medicine doctors tell me not in my case. Many different meds and a bit of acupuncture have made no difference. Some stretching exercises sometimes help a bit. This is seriously hurting my well-being.

After years of fighting leaks, I asked for a quote about roof repair. But they insisted city inspectors would also want the big roof beams repaired, and I wasn't interested in that.

Upon turning 60 in December 2023, Victor learned that he has over $10,000 in retirement funds! After much paperwork over many trips throughout 2024, and with help from some of his family, he has yet to see a cent. We're still working on it. (If this ever concludes, I'll write it up here.(P.S. Now (2025) he's getting monthly payments. Click here for the full story.))

In September, I bought an almost new car. But it turned out to be stolen, and I lost both the car and the $19,000 I paid for it! All I'm left with is a police report stating that I am the victim of "theft by trickery" (a crime I never before heard of). It's not even tax deductible, because it's not related a federal disaster declaration.

And, to top off the year, there was the dismal Presidential election, which left me depressed.

My sad car story

Last month, I found a super deal on craigslist on an almost-new 2024 Honda Accord. The seller said he was going through a divorce. After a test drive, I bought it. I went to AAA the next day to do owner transfer. They said the title I had was not legit and they suggested that the car might be stolen, and I should talk to the police!

I used an online site that checks to see if a VIN is reported stolen; it said this VIN was clean. Because of that and because we were leaving for 8 days early the next day, I decided to wait.

When we returned from travel, the online VIN check still said clean. I found a DMV form which I could print, mail with $10, and find the car's "Current Record" and "Ownership History". On Sept. 23, I did that, and I didn't drive the car, waiting to hear back from DMV.

As of this Tuesday, DMV still had not cashed my check. Late yesterday afternoon, the putative owner showed up at my house! He says he has a tracker on the car. He has a key that makes the car (in my garage) beep. He has the permanent plates for the car. (He opened the plate package as I watched.) VIN on the paperwork matches.

We agreed to call the police. After about an hour, they showed up. After another hour of talking to us and checking with DMV and LAPD, they agreed that this guy was the true owner, and they had me turn the car over to him. When examining my driver's license, they noted that it was my birthday. At the end, they apologized for this happening on my birthday.

They will report all this, listing me as the victim of "theft by trickery". They think they might have enough information to track down the thief, but I'm doubtful.

I'm back to my old car, and out all the money I paid for the newer one.

Thoughts I dare not ponder

 

As I've always said, I decided in high school that my goal in life was to retire. And in retirement I wanted to read, write, and travel. After I retired, that shifted to read, travel, and exercise.

But lately, I've begun to think that the "why" is no longer self-evident. 

To what end? To what purpose? What's the point?

Yes, of course, increasing thoughts of mortality are part of this. So I quickly labeled these "thoughts I dare not ponder".

About those retirement activities:

 - Reading 

I have always been a print media junkie (including online print). 

I love news, information, learning. I'm even rather competive about it. (See here.) 

There are still tons of books on my reading list, and I still add more, but now I sometimes wonder why.

It's no longer self-evident. 

Similarly, I check the news repeatedly. But what if I stopped?

 - Travel

There are tons of places I've never been, but I've hit the top places on my list. (See here.)

TSA, airlines, and my aging body make the journeys (not the destinations) increasingly unpleasant.

And to what end?

 - Exercise

In my first year of retirement, I lost more than 50 pounds, and I kept it off for years, but lately, I've began to put some back on. 

Arthritis slows me down and makes hills and long walks ever more difficult. 

Diabetes is ever-present. 

Dietary self-restraint in the face of mortality: Why?

A Father's Day Memory

My father built this vacuum tube radio when he was a young man. It's one foot wide. Later, he incorporated it into the upper left corner of a large wooden bookcase he built, about four feet by four feet. By the time I remember it, the radio was empty and no longer worked. 

When I first moved to an unfurnished apartment in 1985, the bookcase was one piece I brought from San Antonio to Los Angeles, and I still have it, including the empty shell of the old radio.

Loosely related: When I was a boy, my father came home one day and asked, "Where is that music coming from?" I pointed to his shirt pocket, and he pulled out a transistor radio. I could tell he was disappointed that I wasn't more surprised, but how was I to know that a pocket-sized radio was something brand new?

Maps

(See five photo links below.)

I'm another map freak. I have hundreds of maps. Printed maps. Even in this digital age when all maps are available online, I still like printed maps. 

Many are from AAA and National Geographic. But some are from more obscure map-makers. And, from my father, some are older than I am. And, from my father's workplace as they were being discarded, a handful pre-date him!

The photo albums linked below show just a few of my maps. Each album begins with a description of the maps shown. Click on any image to see it larger.

1918 map (date circled in red)

Map Album 1: Some of my oldest maps (1900-1921)

Map Album 2: Topographic maps

Map Album 3: Thematic maps

Map Album 4: Trend maps

Map Album 5: Miscellaneous maps

Rubik's Cube

Link to more photos. 

I have a collection of Rubik's Cubes and similar objects, about 20 of them (See the photo album.)

When I first read about it, in a fourth-generation copy of an article in a German magazine, I couldn't see how it was possible —  how a cube of smaller cubes could possibly rotate slices in all three dimensions. 

At the time, they were only available in Europe, not in the U.S. My Occidental math faculty colleague Don Goldberg managed to get one from abroad, and I borrowed it for a day. In that time, I did learn how to fix one side, but that's all I could reliably do.

Sometime later, the May Co. department store was the first place in town to have Rubik's Cube to sell. As a promotion, they advertised that, for one day, they would be giving $50 gift certificates to anyone who could solve one side in three minutes.

I went there on that day as soon as they opened, and I was one of the first set of three people who were given a chance. Of course, I won a $50 gift certificate. As the day went on, more and more Oxy students were showing up and winning. They quickly cut back to one group of three contestants every hour instead of every thirty minutes, and long before the day was done, they stopped the promotion altogether. Oxy students who never got a chance protested, and there was even some TV coverage of it all.

In his 1981 book, Notes on Rubik's Magic Cube, David Singmaster writes, "A Los Angeles department store offered $50 to anyone who could put one face right in three minutes.  They lost $600 to a group of Don Goldberg's students at Occidental College."

For years afterwards, I bought and received as gifts many variations of the cube. I also participated in the Cube-Lovers email group (now long gone).

Aging

Another sign of aging. 

Today's LATimes has a feature story on Luis Zapata. In the opening, it mentions that he died earlier this month. 

As I see that, it just adds to the losses evoked by the story. As I've written previously, Kieran knew Zapata and, at my request, got him to autograph a book for Victor, who loaned the book and it never came back. Any mention of Zapata brings Kieran to mind. He died many years ago. 

So, even before getting very far into the story, I'm feeling the loss of Kieran, of Zapata, and of the autographed book. 

And I realize that this is just another sign of aging. More and more things will inevitably remind me of people and things now gone.

Or, as Julia Wick writes in the LATimes about a supercentenarian, "To defy death is to endure a long onslaught of loss."

Or, as Lawrence Wright writes in The New Yorker about Austin, "If you live long enough in a place, it becomes haunted by ghosts: memories of events and friends long gone still inhabit spaces that have been levelled and covered over by the unstoppable newness. It’s a form of double vision: you see things that are no longer there."

Medical problems

After the virus-related problems previously mentioned, our next biggest problem has been getting medical appointments. I'm paying a lot to add Victor to my insurance as of January. We made an appointment for a physical on Friday, March 20^th. On Monday, March 16^th, they began changing all optional appointments to a telephone call because of the virus. I also wanted an optometry appointment for Victor, but now the earliest would be July.

In June, we re-scheduled his physical for July. That actually happened, finally. But then the latest closures took away the optometry appointment. GRRR. I'll try again later.

Separately, a new medical problem for me. I had a red bump on my groin that wasn't a pimple. Days later, I had a larger red patch on my thigh. A couple of more days and another one. This past Tuesday night, a third, and I decided I needed to see a doctor. Overnight, it occurred to me that it might be shingles. As soon as I googled some images, that seemed certain. Yesterday afternoon, an Urgent Care doctor confirmed it (and prescribed a week of three-times-a-day generic Valtrex). Fortunately, my shingles are only slightly painful. 

Aging

Aging has never much concerned me. Until now.

I turn 70 in October. That frightens me. It's the first time any specific age has bothered me. It sounds old. It feels like death is right around the corner.

Because Dad died too young and because I have no older brother, I have had no men in their seventies to watch closely.

It doesn't help that I'm also slowing down. I still walk a lot, but I'm slower now.

Virus woes

Virus woes? Ours are minor. The biggest is canceled travel. So far, we've lost one planned trip in March, two in May, and one in July. (And the one in July was already a second attempt, after we couldn't grab seats in 2019. Now, it's out until 2021.) 

We still have bookings for travel in August and in October, but who knows if they will stand.

After travel, I miss libraries!

Stonewall 1969

Today, June 28, 2019, is the 50^th anniversary of the Stonewall Riots. In San Antonio in 1969, I certainly heard nothing about this as it happened. It was the summer after my first year at Rice.

But in those years, I did make an effort to follow counterculture news. In particular, I occasionally visited one small bookstore / head shop (I can't remember the name, but according to notes by others, it might have been "Joint Effort") and browse and buy alternative newspapers. Sometime that summer, I bought an issue of the Los Angeles Free Press, and it had a small note about Stonewall.

I was not even fully out to myself yet, wondering whether I might be bisexual, but I definitely paid attention to this news.

After Stonewall

In my first summer in Los Angeles, in 1973, I made a point of going to Hollywood to watch the Christopher Street West parade.

It would still be years before I started coming out.

Years later, during a visit to New York, I attended a special gay pride program where several of the Stonewall Riot participants spoke. I don't remember their names. Based on this button I still have, this may have been in 1985:

In 2016, President Obama designated the area as the Stonewall National Monument.

Sweepstakes and a minor rarity

I enter sweepstakes all the time. I win small prizes now and then. In recent years, I've won a digital camera and a couple of $100 gift cards. My largest wins, years ago, have been travel: my Katmai and Puerto Vallarta trips. I also won $10,000 cash in an LATimes sweepstakes. That was in 2010, and helped me decide to retire in 2011.

In the current Albertsons Monopoly sweepstakes, I won $5 cash in the first weeks and again last week. I've also won a free bagel twice. The other day, I got this game ticket:

It's good for a $5 gift card, and it's highly unusual. It's uncommon for one game ticket to have even two pieces for the same prize. This one has four! Since this prize requires exactly those four pieces, this is a winner all by itself! Unheard of!

When I turned it in, the clerk agreed she had never seen this before.

Dick and Jane recursion

I remember reading Dick and Jane books as a child. In particular, I have long remembered one red Dick and Jane book with a recursive cover illustration: Dick and Jane reading the very same Dick and Jane book whose cover shows Dick and Jane reading the same Dick and Jane book, and so on. 

But I can find no such Dick and Jane book cover. Did I imagine it? Did I dream it? If it doesn't exist, how in the world did I come up with that at such a young age? Maybe I really was born to be a math and computer software guy.

Update (9 March). Found it! Thanks to Richard Tamez. The cover is even red, as I remembered. OK, so it's not quite Dick and Jane. Published in 1948:

And, having found that, I now find this one, too:

And, probably finally, this:

That last was from a seller on eBay. I made an offer and bought the set of three books.

Getting legally stoned

Now that pot is state-legal, I've been experimenting for the first time in decades. Here's what I've done this year:

In February, I bought THC tincture. One dropper sublingually (Feb) did nothing. Two droppers (June) did nothing. Three droppers (July) got me very slightly "fuzzy".

In August, I bought a vaping pen and one cartridge. But in October, before I had a chance to try them, I was given a tin of THC-and-chocolate-coated blueberries. On Oct 18, I tried two berries got a very slight, short-lived buzz.

On Oct. 26, I had four berries and finally got high! After 2 hours, I felt unstable mentally and physically and had time dilation. I was also quite happy. All of this lasted for more than two more hours.

The other day, I noticed the tin has a Best By Date of 11/17/18, and they are berries, after all; they might indeed go bad. So I decided to use some more yesterday. I tried five this time, hoping for one more thing I remember from decades ago and still hadn't experienced since: the urge to speak or write some discoveries. It worked! I think 5 berries (25 mg THC) is the perfect ingested dose for what I was after.

Details (from notes written while high!) : 

• 10:50 am - early lunch
• 1 pm - five berries
• 1:10 to 2:10 - walk to Nina, walk with Nina, walk to park bench
• 2 - slightly woozy ... medium-term memory effects
• 2:15 - time dilation; easily distractable; thoughts jumpy; easy to "follow" a flock of circling crows ― pick out the leader(s), see the flight pattern
• 2:20 - colder wind, less sun on the bench; start to move indoors. Time dilation: walking home seemed to take a long time, but it didn't, according to my watch
• 2:30 - more loquacious [than last time]; unsteady; happy; mental maps falter
• 2:40 - further time dilation. This is probably the perfect dose for what I was seeking!
• 2:45 - The physical unsteadiness may just be a side-effect of time dilation: I seem to feel the various tiny movements of my body that I feel (!) must be always there, and it registers as unsteadiness.
• 3 - Might the same be true of thoughts?!
• 3:15 -  More of the same; nothing new. I think it's mostly time dilation that causes the rest.
• 3:40 - Can still play FreeCell (but probably not sudoku)
• 4 - continuing; intermittently, just a smidge euphoric; now I want to close my eyes, maybe sleep
• 5 - continuing
• 5:30 - continuing
• 6:30 - almost all gone
• 7:30 - slight residual wooziness. Also, I wasn't especially hungry during most of this time, but once I started eating dinner (around 6), I've been noshing since!

Reflecting the next day, I still think my stoned revelation was correct: I think most of my "unsteadiness" when stoned, both physical and mental, is a side-effect of the time dilation.

Addendum

I did it once more on 14 January. I decided ahead of time to find out what the effect of time dilation would be on listening to music, reading, doodling, and sex. I wrote these down so I wouldn't forget. I ate five berries.

From notes written while high, here are the results:

Music — At first, just background. Hard to focus on. Somewhat difficult to physically "keep time" (hand or finger or foot tapping) Music is too darn fast! But an hour later, it sometimes seemed too slow; different, in part, depending on whether I'm trying to physically keep time or not.

Reading — I can't read even a single sentence if it's a bit long; by the time I get to the end, I don't remember the beginning.

Doodling — At first, hesitation / indecision / reluctance (or is it only time delay?) No inspiration. But soon, the hesitation was mostly gone or, at least, different: No longer a reluctance to draw, just "Where now?". I'm seeing shapes / directions (more than usual) in the doodles that make me want to either change (if I don't like what I see) or reinforce (if I do) the design. Examples: Oh, that is beginning to look like part of an alligator / a dog / a person... but I don't want that here, so stop that line and go somewhere else. As time went on, my doodling simplified and worsened.

Sex (masturbation) — It seemed difficult to get a full erection, but maybe that was just time dilation. I did eventually come, in a usual amount. No heightened sensations.

One other thing: Quantitative adjectives and adverbs (very much, somewhat, more, etc.) are difficult while stoned: If I start one, I immediately interrupt myself: "Are you sure or just stoned?"

That's it for the berries. 

My math publication

My only mathematics "publication"

In 1984, The Mathematical Intelligencer magazine asked for pithy definitions of applied and pure mathematicians. A definition just came to me, I got an honorable mention for it, and it was printed in the magazine, as you can see in the lower right above:

   An applied mathematician loves the theorem.
   A pure mathematician loves the proof.

I still like this a lot.

An apparently religious boy

Chip Levine Memorial Award (CLMA) 

Rodney Hoffman

for Devotion to Jewish Studies, 1964

To all appearances, I was quite a religious boy. I'll say why, and then talk about what happened.

We didn't go to services every week, but we did go on major holidays and some other occasions. 

I started kindergarten at the synagogue, learning to read before I entered first grade. 

I went to Sunday School through confirmation at age 16. I won the Jewish Community Center's Bible Bowl (named and modeled after TV's College Bowl). 

I went to Hebrew School twice a week. Almost everyone stopped going to Hebrew School after Bar Mitzvah, but because my Bar Mitzvah was in October, and I had already begun the new academic year, I finished out that year, almost a full extra year of Hebrew School. Because of that, in May, I won the gold watch pictured above. 

I was in SAFTY, the San Antonio chapter of the the North American Federation of Temple Youth, and went to SAFTY and TOFTY (Texas) events. I won one of the Temple's four camperships to NFTY's Hagigah, a two-week arts camp in Warwick, NY. 

In college, I went to quite a few Hillel events. In grad school, I still went to a few.

But starting years earlier, I found the number of religions, each claiming The Revealed Truth, baffling and impossible and the very idea of God dubious. Conflicts between religion and science, historical and current, pushed me away from religion. Coming to terms with being gay was the final breaking point.

I have now been an atheist for decades. My hatred of religion has only grown over the years. I think raising children to be religious is child abuse. (See all my blog posts tagged 'religion.')

I reluctantly attend religious weddings and funerals, but otherwise I don't even step into churches, temples, or cathedrals. I respond negatively to anyone pushing their religion in my face, including fish on cars and crosses on homes, saying, if only silently, "Keep it to yourself!"