College was not, as it turned out, particularly useful for practical stuff. Although I learned a reasonable amount, it had a tendency to be the kind of thing that makes great conversation while playing Trivial Pursuit rather than  while trying to figure our your household budget for the month.

Consider the subject of infinite sets. I am not a mathematician. I’m okay with arithmetic and I can figure out a basic, algebraic equation if you give me enough time and scratch paper … but otherwise? Unless it’s part of a computer language, I’m at a loss.

Finite versus infinite sets. Equipotent sets. Countable sets. Example!

I remember infinite sets because it was similar to trying to understand time travel.

An infinite set is any combination of numbers that has not end. There are lots and lots of them. All positive numbers, like: 1,2,3,4,5,6,7 … and obviously, you can keep counting until the moon turns blue and the world is exhausted.

But what about an infinite set of all negative AND positive numbers, so that they go backward forever into the minuses as well and forward into the positives. Forever and a day. With no end. That would be twice as big as all positive number … but equally infinite.

There can be infinite sets of only numbers which divide by three or cardinal number and any bizarre combination of fractions. They are all infinite, but some are bigger than other.

Finite and infinite sets. Two sets have the same cardinality when there is bijective function associating them. Cardinality is is reflexive, symmetric and transitive. Countable sets: set of all integers, set of even numbers, positive rationals (Cantor diagonalization) Set of real numbers between 0 and 1 has same cardinality as set of all reals. Computability of functions.

How can one infinity be bigger than another infinity? Apparently universes are sort of like that and now, my brain is due for explosion because I can’t keep this kind of information in there.

Our personal numeric world consists of shockingly finite numbers. That’s one of the amazing parts of retirement. You have what you have and you will never have more, unless you hit the lottery or have an extremely rich relative planning to die and leave his fortune behind for you. Retirement income just “IS.” It won’t get bigger. Retirement income pretty much stays the same while the world trundles on. Life and the universe may be infinite, sort of, but retirement income is not.

It’s just a thought to ponder. If you feel like pondering.



It is time for another  PICK A WORD theme. Here are the words to choose from: vantage, bifurcated, intruding, jagged, quayside.

From this vantage point, you can see across to the other side where the factory stood in times past

Bifurcated – Two paths separate. One stays a dirt path while the other is smoothly paved

Photo: Garry Armstrong – Orange cones are an intruding eyesore on an idyllic spot along the river

The jagged Superstitions against the blue sky of the Arizona desert

The quayside path used to be the road on which the horses pulled the barges – Blackstone Canal

jupiter najnajnoviji


Not a beautiful day. It was so dark this morning, I had to keep looking at the clock to make sure it wasn’t night. A few minutes later, waves of thunder and heavy rain were passing over the house. The dogs got frantic. They don’t mind guns. They don’t care about fireworks. But rolling thunder and heavy rain?

A virtual painting …

Nothing I did would force them out that door. I had to hope they had been out earlier. Finally, in late afternoon, Garry physically forced them outside and locked the door so they would have to be out there long enough to take care of business. Now, back inside, they are chugging down dinner and avoiding any hint of going outside. Ever.

Earliest yellow leaves

An interesting story about this piece of construction (following) …

The previous picture shows a piece of old construction in the soil. This is usually invisible in the weeds and underbrush, but for some reason, my camera found it today. This old construction dates back to who knows when. Long before this house was built, for sure. It remained a secret until the second people who bought this property had it surveyed and they discovered this old piece of what was probably a foundation. A lot of legal work followed including a new deed and a new survey after much effort was made to find out who, if anyone, had a claim on this property.

This is the first time I’ve seen this famed piece of foundation. I had no idea it was so close to this house. I thought (from looking at the survey) that it was further back on the property. Unless this is yet another old foundation. For some other building.

Perish the thought! 

During a break in the rain, I went out back and took a few pictures. The first yellow is showing in the woods. The begonias are still blooming enthusiastically and I may bring them inside for the winter. Unlike Fuchsia which won’t grow inside, these are begonias and they might do alright. Worth a try.

Garry is shoving the dogs outside again. They are not happy campers.


This isn’t a friendly town. People fraternize with the people who attend their church and seem to regard anyone else as potentially hostile.

Of course we didn’t know that when we moved here. We knew that it was a very white town, that Garry was likely to be the first (only) person of color, and I might well be the first (only) Jew. In fact, apparently well-intentioned people said stuff like “Gee, I’ve never known a Jewish person before” and honestly didn’t see anything wrong with it.  Garry just got stares until they realized they’d seen him on TV. Celebrity beats skin color, at least here in the north.

Photo: Garry Armstrong

Our situation was made more complicated by our neighbor, Ned. Big guy. Rode a Harley. I love Harleys, but there are Harleys and then, there are Harleys. This one was chopped and loud. When Ned started his bike, the vibration alone could knock me out of bed.

Ned was massive. Tattooed. Hung with a bunch of skin-heads. They had raucous parties with lots of beer. We didn’t expect to be invited and we weren’t. Ned also flew a Confederate flag. Prominently. We learned he’d always done it. It was part of some family roots thing tying him to his original home state of Georgia. Me? I thought them — and still think — it’s time the south moved on. The war ended a long time ago. Get over it. But I’m from New York so I probably don’t get it. Apparently a lot of people don’t get it.

Our neighbor’s house was the only one in the Valley flying a confederate flag and we were the only mixed-race couple in town. Ironic, to say the least. And we were a poster couple for hate groups.

Garry is pragmatic and tough. His mild-mannered demeanor belies his Marine Corps interior. Semper fi. Moreover, he couldn’t have survived 40-years as a reporter without being tough. One fine summer’s day, music screaming from Ned’s boombox, Garry looked at me and murmured those fighting words: “This is ridiculous!”

Photo: Garry Armstrong

He marched down the driveway, through the woods that join our two houses, to Ned’s front door. Garry knocked. Loudly. When Ned finally answered, Garry said: “Hi. I’m your neighbor. Garry Armstrong. Do we have a problem?”

Shortly the flag disappeared along with a noxious black jockey statue. Turned out, Ned was a plumber. He fixed our bathroom pipes. The whole skinhead thing dissolved in the face of a brown-skinned guy who did news on Boston TV. Seemed it was less important who Ned was than who Ned, with a little encouragement, was willing to become.

Eventually Ned got into drugs. Or something. We were never sure what. His wife left. His life fell apart. One day, he vanished. Fortunately, he gave back our extension ladder before leaving.

Photo: Garry Armstrong

Other folks live there now. They are not actively hostile, which is about the best one could say of them. In the two and half years they have lived there, they’ve never said hello. I doubt they ever will. They object to our dogs barking. Hard to argue with that but they’ve got dogs who do their own share of barking. There are a lot of dogs around here. If you are outside in the evening, you can always hear a dog barking somewhere.

I miss Ned. No one fixed pipes like he did and gave us a huge discount. He turned out to be a funny guy and a good neighbor. Who’d have thunk it.