# UNLESS YOU’RE A SERIAL NUMBER, CORRUPTION MATTERS – Marilyn Armstrong

The entire quote is from Paul Krugman of The New York Times:

### Why corruption matters. Hint: It’s not the money, it’s the incentives.

When money corrupts the decision-makers, the decisions they make may ultimately have nothing to do with right or wrong, the public interest or private needs — or anything but how the decision affects a business interest or pay-day.

If everything is about money, the moral and ethical elements that should be part of the decision-making process vanish. When the bottom line is the only line, decisions can be made by computers. And probably will be it they aren’t already.

# HOW MUCH IS THREE-QUARTERS? – Marilyn Armstrong

I was out of lunch meat, so Garry went to the deli. It was Monday and they were out of everything except (sigh) turkey breast. Not my favorite, but I’m betting today is a delivery day.

Like a deer caught in headlights, she was lost. She could probably “do” a pound — or half a pound. But what was 3/4? She obviously didn’t recognize it as 75% of a pound, or even that it’s likely the line between the half pound and full pound markers.

Schools don’t teach math in any way that might be useful to those they have taught. They have gotten into systems so complicated that no one under 40 can do any math in their head. They need a calculator. Even to subtract one number from another. Oh, and they can’t count on their fingers.

Eventually, the boss stopped what he was doing and came over to rescue her.

Garry came home. He commented that there’s a scale and surely the young women (in her 20s) could tell that there was a line between half a pound and one pound and that would be the three-quarter, right?

Wrong. She doesn’t know that 3/4 (of one) = 75% (of one). Have you ever tried to explain to a clerk how to turn 99-cents into a dollar?

“Look, I’ll give you a penny and you can give me a dollar.”

“It says 99-cents.”

“So that means that if I give you a penny, you can give me a dollar.”

“It says 99-cents.”

This is because she doesn’t understand that 100 cents (pennies) equal one dollar. We are worried that our “below age 40” youngsters aren’t going to vote. I’m beginning to worry that they can’t think. Apparently, thinking is no longer taught in any school. So if you don’t get a head start at home with the whole “thinking” thing? You’re doomed.

Vote? If they don’t know that 99-cents plus a penny equal a dollar, how can we expect them to vote? Or have a grip on the issues? Or even know what kind of government we have or want?

# WHEN ONE INFINITY IS BIGGER THAN THE OTHER – Marilyn Armstrong

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 out 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 no 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 they go back forever into the minuses as well and forward into the positives. Forever and a day. Without 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 others.

Finite and infinite sets. Two sets have the same cardinality when there is bijective function associating them. Cardinality is reflexive, symmetric and transitive. Countable sets: a set of all integers, set of even numbers, positive rationals (Cantor diagonalization) Set of real numbers between 0 and 1 has the same cardinality as a 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 an explosion because I can’t keep this kind of information 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, but retirement is not.

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

# THIS INFINITY IS TOO SMALL – Marilyn Armstrong

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 out 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 back forever into the minuses as well and infinitely 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 others.

Finite and infinite sets. Two sets have the same cardinality when there is bijective function associating them. Cardinality it is reflexive, symmetric and transitive. Countable sets: the set of all integers, set of even numbers, positive rationals (Cantor diagonalization). Set of real numbers between 0 and 1 has same cardinality asset 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 to explode 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 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, but retirement income is not.

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

# MY STUPID DAY – Marilyn Armstrong

### FOWC with Fandango — My Stupid Day

Some days, I’m smart. I can feel the smarts buzzing around my head, but this is not one of those days.

Let me start with my first stupidity of the day. I needed a refill on a medication. It said that I’d had 120 of them in the bottle a little more than a month ago and I have 15 now because I don’t always take the full amount I’m allowed. It’s for pain so I can do that.

I called the doctor’s office hoping for something with a refill on it but was told they’ve changed the law, so I can’t get refills anymore. I pointed out it isn’t an opioid. She pointed out “It’s amazing what things people will misuse.”

We both agreed that 120 pill was good for two months, even though I’m supposed to take four of them and it’s only 120 pills — but should be good for two months.

I called the pharmacy and complained I hadn’t gotten enough pills, except when I hung up, I multiplied 4 times 3o and came up with 120 — for ONE month. I should mention the pharmacist didn’t notice the problem either.

Apparently, no one can multiply 4 times 30 and come up with a one month supply of 4 pills a day.

Damn.

I called back the office and said: “Hey, how much are 4 times 30?”

She sighed. “120. After you hung up, I realized we weren’t quite getting the multiplying thing right.”

I explained that I felt like a moron having just argued this point with the pharmacy. She said that math was never her good subject either. Neither one of us could multiply 4 times 30 and get 120. How depressing is that?

Then I spent a fair amount of time calculating which of two barn jackets — the classic LL Bean or the very not classic Land’s End lined version. I was going to buy it until I realized the LL Bean jacket is much nicer looking coat, but the Land’s End would be more user-friendly given our weather. At which point I also realized — I don’t need a coat. What’s more, I can’t afford one. And also — I have that same LL Bean jacket in my coat closet. Same size, color, style. Just from last year.

Not even at 50% off.

And my hand is killing me because I took my brace off (because I can’t type with it on) and now, I’m back where I was yesterday.

So much for today’s smarts.

# THREE-QUARTERS OF A POUND – Marilyn Armstrong

I was out of lunch meat, so Garry went to the deli. It was Monday and they were out of everything except (sigh) turkey breast. Not my favorite, but I’m betting today is a delivery day.

Like a deer caught in headlights, she was lost. She could probably “do” a pound — or half a pound. But what was 3/4? She obviously didn’t recognize it as 75% of a pound, or even that it’s likely the line between the half pound and full pound markers.

Schools don’t teach math in any way that might be useful to those they have taught. They have gotten into systems so complicated that no one under 40 can do any math in their head. They need a calculator. Even to subtract one number from another. Oh, and they can’t count on their fingers.

Eventually, the boss stopped what he was doing and came over to rescue her.

Garry came home. He commented that there’s a scale and surely the young women (in her 20s) could tell that there was a line between half a pound and one pound and that would be the three-quarter, right?

Wrong. She doesn’t know that 3/4 (of one) = 75% (of one). Have you ever tried to explain to a clerk how to turn 99-cents into a dollar?

“Look, I’ll give you a penny and you can give me a dollar.”

“It says 99-cents.”

“So that means that if I give you a penny, you can give me a dollar.”

“It says 99-cents.”

This is because she doesn’t understand that 100 cents (pennies) equal one dollar. We are worried that our “below age 40” youngsters aren’t going to vote. I’m beginning to worry that they can’t think. Apparently, thinking is no longer taught in any school. So if you don’t get a head start at home with the whole “thinking” thing? You’re doomed.

Vote? If they don’t know that 99-cents plus a penny equal a dollar, how can we expect them to vote? Or have a grip on the issues? Or even know what kind of government we have or want?

# THE TRUTH OF SCHOOL

I always find myself defending school to kids. They complain it’s dull. That there’s nothing in it that “grabs” or fascinates them — and nothing they will find useful in life.

I find myself trying to explain that school wasn’t fascinating, but that many of the boring stuff you learn in it is indeed going to be useful. Like arithmetic, the ability to add and subtract mentally without a calculator or even a piece of paper and a pencil. The point of school wasn’t only to intrigue or titillate us but to make us ready to face the real world in which we all must live.

High School, really

Some studies were dull, but you needed to know it because while there’s creativity, there is day-to-day life too and unless you are one of the entitled few, you will have to do your share of it.

I was the kid who had a book in my lap so when no one was looking, I would read. Although I love science today, in school, it wasn’t interesting. Maybe it was the teachers who were dull. In high school I had a double period of botany beginning at eight in the morning when I was already half asleep. The class went on for two hours. We had a teacher who knew her stuff, but talked in a monotone. She’d start to talk — and I’d black out. Gone.

I did not do well in that class. A pity because I was interested, but she was better than a sleeping pill. Twice as good, really. Nothing I ever took knocked me out as well as she did.

Social studies which would today be … what? Social science? History? Some weird version of both? It consisted of everything that wasn’t English, math, or science. What we called “the rest of the stuff.” I was a passionate, ardent, enthusiastic reader.  I loved history and the world. But social studies? With those stupid work books where you would answer a question and then you had to color the pictures. Seriously? Color the pictures?

I flunked coloring.

English was dull, too. We had to read books that were of no interest to anyone. I suspected the teachers found them dull too, but it was in the curriculum and that’s what they were supposed to teach. They did. We yawned. I drew pictures of horses in my notebooks. Sometimes, when I got tired of horses — I never got the feet right — I moved into castles. I was better at castles.

If they let us write, I was good at that. But being good at it didn’t make it interesting. My summer vacation wasn’t the stuff to brighten my week.

The teachers droned on and on. Those of us who intended to go to college hung in there. It never — not once, not for a split second — crossed my mind that I should drop out and work at an entry-level jobs for the rest of my life because I was bored at school.

1893 Thayer Library Photo: Garry Armstrong

For me, going to college was exactly the same as going to heaven. I would go to college because I knew I could learn. I never doubted my ability to think. I was sure if I made it to college, the rest would follow. And so it did.

I learned a lot of things in college. Ultimately, the really interesting parts of my education were learned at work, when math, science, and statistics were relevant and meaningful.

When you are working, the things you learn are in a context. You discover science has a purpose. Numbers are not random shapes which you jiggle around until you get the answer or sit with empty eyes wondering what this is supposed to mean. I did stuff at work I had found impossible in a classroom.

It wasn’t my fault. It was their fault. They taught the material so poorly no one who didn’t have a special fervor for it figured it out. What a pity for everyone. Worst of all, they meant well. They genuinely did the best they knew how.

College had its share of drones and bores … but there were enough wonderful teachers — maybe a dozen — who were inspirational.
They were was enough.  For each year of school, there was at least one or two teachers who made a difference in my life. Plus, I was in an environment where everyone wanted to learn. We needed to learn.

We chose it.

I have never properly explained the whole school thing to my kid or granddaughter. I told them “Oh, it’s not that bad.”

PS 35, Queens

Except, it really can be that bad. Sometimes, it’s even worse and comes with boring teachers and brutal classmates. That is very bad. Whether they are teasing you because of your color or because you are smart and they aren’t … cruelty is cruelty and kids can be cruel.

The thing is, you don’t stay in school because it’s fun. Or because the quality of education is uplifting. You are there because you know that this is what you must do if you want to have a real life.

If you also get wonderful, inspiring, enlightening teachers, that’s better. But even if they are dull, you still need to be there.

School is the work of childhood. It’s the “why of the how” of growing up.

# How Big Is Infinity?

I’ve always loved this concept. May the bigger infinity win!

Infinity is a concept that refers to something that grows without bound. But, is there any definitive explanation of how big can it grow? In this TED-Ed video, Dennis Wildfogel explores the mind-bending concept of the “infinity of infinities” and explains how it led mathematicians to conclude that math itself contains unanswerable questions.

### THIS IS COOL. I WANT TO LEARN SOMETHING ELSE, TOO!

Video via – TED-Ed
Further Readings and References @ Infinity (Wikipedia), Skulls in the Stars, Stack Exchange

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# WHEN THIS INFINITY IS BIGGER THAN THAT ONE

###### FINITE RESOURCES IN AN INFINITY OF UNIVERSES

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.