Recovery Board
: RfM

Recovery from Mormonism (RfM) discussion forum.

There was recently an article in the NYTimes by a man who decided to restudy math after he retired. His change in perspective 45 years after the first crack at math is interesting. I'll put that in this post, and then do two other posts on some of the things mathematicians do.

This is for Nightingale, because she seems to enjoy my little math excursions here in spite of her math phobia, though I have discovered there are more math nerds here that I would have guessed. Feel free to chime in, y'all.

------------------

https://www.nytimes.com/2022/09/18/opinion/math-adolescence-mystery.html

Mr. Alec Wilkinson is the author of “A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age.”

As a boy in the first weeks of algebra class, I felt confused and then I went sort of numb. Adolescents order the world from fragments of information. In its way, adolescence is a kind of algebra. The unknowns can be determined but doing so requires a special aptitude, not to mention a comfort with having things withheld. Straightforward, logical thinking is required, and a willingness to follow rules, which aren’t evenly distributed adolescent capabilities.

When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life. Balancing a checkbook or drawing up a budget was the answer we were given for how math would prove necessary later, but you don’t need algebra or geometry or calculus to do either of those things.

But if I had understood how deeply mathematics is embedded in the world, how it figures in every gesture we make, whether crossing a crowded street or catching a ball, how it figures in painting and perspective and in architecture and in the natural world and so on, then perhaps I might have seen it the way the ancients had seen it, as a fundamental part of the world’s design, perhaps even the design itself. If I had felt that the world was connected in its parts, I might have been provoked to a kind of wonder and enthusiasm. I might have wanted to learn.

Five years ago, when I was 65, I decided to see if I could learn adolescent mathematics — algebra, geometry and calculus — because I had done poorly at algebra and geometry and I hadn’t taken calculus at all. I didn’t do well at it the second time, either, but I have become a kind of math evangelist.

Mathematics, I now see, is important because it expands the world. It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention. To be made to consider a problem carefully discourages scattershot and slovenly thinking and encourages systematic thought, an advantage, so far as I can tell, in all endeavors. Abraham Lincoln said he spent a year reading Euclid in order to learn to think logically.

... As a boy, trying to follow a path in a failing light, I never saw the mysteries I was moving among, but on my second pass I began to. Nothing had changed about math, but I had changed. The person I had become was someone whom I couldn’t have imagined as an adolescent. Math was different, because I was different.

---------------------

Even people who claim to not understand or appreciate math are awe-struck by giant sweeping curves - catenaries like the Golden Gate Bridge, arguably the most photographed bridge in America, or the St Louis Arch, also a catenary. We are fascinated by the sweeping undulations of the Northern Lights, looking like a screen saver on a cosmic scale. String art, making complex curves using straight lines of thread - that had a moment back 40 years ago, and Etsy still offers kits and finished string art for sale.

We watch airshows for the giant sweeping curves.

We love symmetry - the Palace of Versailles is perhaps the most monumental example of Symmetry Gone Wild. We love practiced asymmetry as a change-of-pace - a lot of the fancier dress necklines right now are deliberately asymmetric.

Machines were built in the 1600s that could carve what are basically giant stone pillars that looked like rounded spirally screws. By the 1800s, there were machines to automatically carve oval picture frames. You've all seen those on photographs or paintings from the late 1800s. That was very high-tech at the time. I actually saw one of those machines in action. They are amazing to watch.

Math is everywhere.

Next post, a little math music, with apologies to Mozart

This is for Nightingale, because she seems to enjoy my little math excursions here in spite of her math phobia, though I have discovered there are more math nerds here that I would have guessed. Feel free to chime in, y'all.

------------------

https://www.nytimes.com/2022/09/18/opinion/math-adolescence-mystery.html

Mr. Alec Wilkinson is the author of “A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age.”

As a boy in the first weeks of algebra class, I felt confused and then I went sort of numb. Adolescents order the world from fragments of information. In its way, adolescence is a kind of algebra. The unknowns can be determined but doing so requires a special aptitude, not to mention a comfort with having things withheld. Straightforward, logical thinking is required, and a willingness to follow rules, which aren’t evenly distributed adolescent capabilities.

When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life. Balancing a checkbook or drawing up a budget was the answer we were given for how math would prove necessary later, but you don’t need algebra or geometry or calculus to do either of those things.

But if I had understood how deeply mathematics is embedded in the world, how it figures in every gesture we make, whether crossing a crowded street or catching a ball, how it figures in painting and perspective and in architecture and in the natural world and so on, then perhaps I might have seen it the way the ancients had seen it, as a fundamental part of the world’s design, perhaps even the design itself. If I had felt that the world was connected in its parts, I might have been provoked to a kind of wonder and enthusiasm. I might have wanted to learn.

Five years ago, when I was 65, I decided to see if I could learn adolescent mathematics — algebra, geometry and calculus — because I had done poorly at algebra and geometry and I hadn’t taken calculus at all. I didn’t do well at it the second time, either, but I have become a kind of math evangelist.

Mathematics, I now see, is important because it expands the world. It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention. To be made to consider a problem carefully discourages scattershot and slovenly thinking and encourages systematic thought, an advantage, so far as I can tell, in all endeavors. Abraham Lincoln said he spent a year reading Euclid in order to learn to think logically.

... As a boy, trying to follow a path in a failing light, I never saw the mysteries I was moving among, but on my second pass I began to. Nothing had changed about math, but I had changed. The person I had become was someone whom I couldn’t have imagined as an adolescent. Math was different, because I was different.

---------------------

Even people who claim to not understand or appreciate math are awe-struck by giant sweeping curves - catenaries like the Golden Gate Bridge, arguably the most photographed bridge in America, or the St Louis Arch, also a catenary. We are fascinated by the sweeping undulations of the Northern Lights, looking like a screen saver on a cosmic scale. String art, making complex curves using straight lines of thread - that had a moment back 40 years ago, and Etsy still offers kits and finished string art for sale.

We watch airshows for the giant sweeping curves.

We love symmetry - the Palace of Versailles is perhaps the most monumental example of Symmetry Gone Wild. We love practiced asymmetry as a change-of-pace - a lot of the fancier dress necklines right now are deliberately asymmetric.

Machines were built in the 1600s that could carve what are basically giant stone pillars that looked like rounded spirally screws. By the 1800s, there were machines to automatically carve oval picture frames. You've all seen those on photographs or paintings from the late 1800s. That was very high-tech at the time. I actually saw one of those machines in action. They are amazing to watch.

Math is everywhere.

Next post, a little math music, with apologies to Mozart

OK, mathematics is basically pattern recognition, and solving puzzles. It's much like Wordle, Sudoku, crosswords, jigsaw puzzles, recognizing faces, and on and on. We are pattern matching creatures.

Some of what mathematicians do is look for patterns in the normal systems we are all familiar with, and then try to prove that their observed pattern is always true. Usually the pattern does prove to be true, though every once in a while something may be true for a lot of consecutive examples, and the next case fails, so the pattern does not hold for all integers. A proof proves that there will be no failures, or if there are, exactly when that will occur.

So what do I mean by a "pattern". Every other integer is an even number. That's a pattern, and yes, it applies to all integers.

Every third number is a multiple of 3. That's a slightly more complicated pattern, but it shouldn't take long to convince yourself it is true.

A Russian mathematician named Christian Goldbach (at this point, all the math nerds know precisely where I am going with this) proposed to Leonhard Euler, arguably the best mathematician who ever lived, a simple observation. In its modern form, it boils down to this: every even number greater than 2 can be written as the sum of two primes.

All you need to understand the problem is to know what a prime number is. I think the average sixth grader can grasp that. Back in Euler's day, 1 was considered a prime. We don't do that anymore, but it doesn't matter. The conjecture still works, except for 2, which could be 1+1 if 1 were allowed as a prime.

Try it for small even numbers. Not only is it possible, but as the numbers get larger, there are more and more ways to do it. 14 = 3+11 = 7+7. 24 = 19+5 = 17+5 = 13+11.

The fly in the ointment is that as you go farther out in the integers, primes become scarcer and scarcer. Declaring 2 a prime eliminates half of all integers right there, because half of them are even, and divisible by 2. Declaring 3 a prime eliminates one third of all the remaining integers. (You may need to think about that for a minute to convince yourself it is true - feel free to scribble on an envelope. Mathematicians do that all the time).

Maybe somewhere way the hell out there where most numbers are composite (i.e. can be factored into smaller primes), there may be an even number that can't be represented as the sum of two primes.

Writing a computer program to test that conjecture is a freshman programming assignment. Easy. The conjecture has been tested out to a million trillion and is true for all even integers to that point.

But that is not a proof that it is alway true.

There you have it. Simple problem, middle school student should be able to grasp it. It was proposed in 1742 and the best mathematicians in the world for the last nearly 300 years have not been able to prove the conjecture true, though everybody believes it to be true,

You crack that problem and your name will go down in mathematical history for as long as human culture exists. It is one of the two great unsolved problems in mathematics IMHO, the other being the Riemann Conjecture, which is NOT a simple problem.

Next example, mathematicians change the rules, to see what happens.

Edited 1 time(s). Last edit at 09/22/2022 11:40PM by Brother Of Jerry.

Some of what mathematicians do is look for patterns in the normal systems we are all familiar with, and then try to prove that their observed pattern is always true. Usually the pattern does prove to be true, though every once in a while something may be true for a lot of consecutive examples, and the next case fails, so the pattern does not hold for all integers. A proof proves that there will be no failures, or if there are, exactly when that will occur.

So what do I mean by a "pattern". Every other integer is an even number. That's a pattern, and yes, it applies to all integers.

Every third number is a multiple of 3. That's a slightly more complicated pattern, but it shouldn't take long to convince yourself it is true.

A Russian mathematician named Christian Goldbach (at this point, all the math nerds know precisely where I am going with this) proposed to Leonhard Euler, arguably the best mathematician who ever lived, a simple observation. In its modern form, it boils down to this: every even number greater than 2 can be written as the sum of two primes.

All you need to understand the problem is to know what a prime number is. I think the average sixth grader can grasp that. Back in Euler's day, 1 was considered a prime. We don't do that anymore, but it doesn't matter. The conjecture still works, except for 2, which could be 1+1 if 1 were allowed as a prime.

Try it for small even numbers. Not only is it possible, but as the numbers get larger, there are more and more ways to do it. 14 = 3+11 = 7+7. 24 = 19+5 = 17+5 = 13+11.

The fly in the ointment is that as you go farther out in the integers, primes become scarcer and scarcer. Declaring 2 a prime eliminates half of all integers right there, because half of them are even, and divisible by 2. Declaring 3 a prime eliminates one third of all the remaining integers. (You may need to think about that for a minute to convince yourself it is true - feel free to scribble on an envelope. Mathematicians do that all the time).

Maybe somewhere way the hell out there where most numbers are composite (i.e. can be factored into smaller primes), there may be an even number that can't be represented as the sum of two primes.

Writing a computer program to test that conjecture is a freshman programming assignment. Easy. The conjecture has been tested out to a million trillion and is true for all even integers to that point.

But that is not a proof that it is alway true.

There you have it. Simple problem, middle school student should be able to grasp it. It was proposed in 1742 and the best mathematicians in the world for the last nearly 300 years have not been able to prove the conjecture true, though everybody believes it to be true,

You crack that problem and your name will go down in mathematical history for as long as human culture exists. It is one of the two great unsolved problems in mathematics IMHO, the other being the Riemann Conjecture, which is NOT a simple problem.

Next example, mathematicians change the rules, to see what happens.

Edited 1 time(s). Last edit at 09/22/2022 11:40PM by Brother Of Jerry.

I'm still awaiting your discussion of numbers without unique factorizations.

In the meantime, I take issue (in a juvenile way) with this assertion:

> Every other integer is an even number. That's a pattern, and

> yes, it applies to all integers.

Surely that's only true if you start with an even number. If you start with an odd, then every other integer is an odd number.

I will now go and sit in my corner.

In the meantime, I take issue (in a juvenile way) with this assertion:

> Every other integer is an even number. That's a pattern, and

> yes, it applies to all integers.

Surely that's only true if you start with an even number. If you start with an odd, then every other integer is an odd number.

I will now go and sit in my corner.

If I recall correctly, BOJ stated that those factorizations involved square roots.

If you allow the use of square roots in factors (and particularly if you allow complex factors), then every real number has an infinite number of factorizations of the form

n=(a+√(a^2-n))*(a-√(a^2-n)) where n and a are any real numbers.

The proof is easy

n=(a+√(a^2-n))*(a-√(a^2-n))=a^2 -(√a^2-n)^2= a^2-a^2 -(-n)=n

Since a can be any real number, an there are an infinite number of real numbers, the number n can be factored in an infinite number of ways.

If n>a^2, then you need to have complex factors i.e. the square root of a negative number.

If you allow the use of square roots in factors (and particularly if you allow complex factors), then every real number has an infinite number of factorizations of the form

n=(a+√(a^2-n))*(a-√(a^2-n)) where n and a are any real numbers.

The proof is easy

n=(a+√(a^2-n))*(a-√(a^2-n))=a^2 -(√a^2-n)^2= a^2-a^2 -(-n)=n

Since a can be any real number, an there are an infinite number of real numbers, the number n can be factored in an infinite number of ways.

If n>a^2, then you need to have complex factors i.e. the square root of a negative number.

See below, and yours is exactly the type of example that made my head hurt. Your explanation doesn't make my head hurt too much now. Either the explanation or my head has improved with time. Or both. :)

Edited 1 time(s). Last edit at 09/23/2022 01:35AM by Brother Of Jerry.

Edited 1 time(s). Last edit at 09/23/2022 01:35AM by Brother Of Jerry.

That makes sense. If you expand the number of possible factors infinitely, you get infinite equally valid factorizations.

Thank you.

Thank you.

Sometimes mathematicians change the rules of a mathematical system to solve a problem they can't solve otherwise. A guy named Kronecker famously said "God created the integers, all the rest is the work of man."

A case can be made for that. We still don't much like negative numbers, and even the name has a, um, negative connotation. Integers, the stuff God created, have integrity. they are solid, one thing. Rational numbers we pretty much like. Calculators always give you rational number results. Irrational numbers make us very nervous. Imaginary numbers are even worse, and by the time we get to complex numbers, we run screaming from the room.

We are still uncomfortable with negative numbers. Corporate reports and tax forms tend to either put them in parentheses, or in red ink. The idea of just slapping a minus sign in front of the number didn't really catch on until the 1750s, and by then corporate reports were already a thing, and they still put negatives in parens.

One of the wonders that Alec Wilkinson discovered in his late life study of math is the question "why are there prime numbers". Nobody designed prime numbers. They just wanted to count stuff. If a Nephite brought in 5 senum of wheat, he wanted a receipt that indicated he had paid his wheat tax. Nobody asked for prime numbers.

So why did primes happen? They are just there, and it is a pattern we spotted.

Sometimes mathematicians change a rule to solve a problem, like "what happens if we have a number less than zero? Wait, have we invented zero yet?"

And sometimes they are just curious, or bored, or whatever.

I did an experiment that probably falls into the bored/curious category. I decided to see what would happen if you tried to restrict the 4 math operations strictly to even integers. Pretend that for math operation purposes, odd numbers do not exist. What will happen?

Let's give the system a name. Since we are dealing with Even Integers, let's call it EvInt Arithmetic.

In EvInt arithmetic, addition and subtraction work exactly as they do in regular arithmetic. Add or subtract two even numbers, you always get an even number as a result. There is even an additive identity (math-babble for a number you can add that changes nothing - add 0)

That was easy.

Multiply. If you multiply two even numbers, you always get an even result. In fact, since both numbers you multiply have at least one 2 as a factor, the product will have 4 as a factor. In the EvInt world, all composite numbers will be multiples of 4.

That may not be obvious to you, but try to verify to your own satisfaction that if you multiply two even numbers, the result is ALWAYS divisible by 4.

OK, if we are living in a world of nothing but even numbers, multiply seems to work too. There is one small catch: we do not have a multiplicative identity, a number that we can multiply by that changes nothing. One (1) is the multiplicative identity in integer arithmetic, and 1 doesn't exist in our EvInt system.

OK, no multiplicative identity. Who cares. We can live without that. Moving on....

Divison. In regular division, if you divide one number by another, there is a quotient, and a remainder, that is less than the divisor. For example, if you divide a number by 3, you get a quotient of whatever, and 3 either divides evenly, with a remainder of 0, or there is a remainder of 1, or a remainder of 2. That's how you learned it in grade 4, or wherever that gets taught.

Let's try division in our system.

2/2. Uh Oh. big problem. 1 does not exist in our system, so, can't divide a number by itself. Damn. And add, sub and multiply operations went so smoothly. :(

4/2 = 2. OK, that worked.

6/2 = 3. No no no. There are no odd numbers. 6/2 = quotient 2 with remainder of 2. reverse engineering the division, 2*2 + 2 =6

Note that the remainder was not less than the divisor. it was equal to the divisor. Can we do that with the earlier examples?

2/2 = quotient 0, remainder 2. Um, a little weird, but OK.

4/2 = quotient 2, remainder 0

6/2 = quotient 2, remainder 2

8/2 = quotient 4, remainder 0

10/2= quotient 4, remainder 2

4/4 = quotient 0, remainder 4

6/4 = quotient 0, remainder 6

8/4 = quotient 2, remainder 0

10/4= quotient 2, remainder 2

12/4= quotient 2, remainder 4 (remember, the quotient can't be 3 in EvInt)

14/4= quotient 2, remainder 6

16/4= quotient 4, remainder 0

It looks pretty weird, but it is all even numbers, and seems to work OK. We just have to allow the remainder to be less than twice the divisor, rather than just less than the divisor.

And, take my word for it, with those alterations to the rule about the remainder, and remembering not to use odd numbers anywhere, yeah, however weird, this division algorithm works.

So there you have it. I had to cut a few boards a bit, but we can get a pretty functional system of arithmetic using only even integers.

Why would anyone want to do that? Hell if I know. You'd be surprised how much math (binary, for example) had no practical application when it was developed.

Then I had one more thought about my little experiment, which had gone so nicely.

What is a prime number in this system?

2 is prime. So far, so good.

3 doesn't exist here, so not my problem.

4 is 2*2, so not prime.

6. Hmmm. Not evenly divisible by 2. See table above. There is a remainder. 3 doesn't exist for our purposes.

6 must be an EvInt prime.

Uh oh. this could be bad.

8 = 2*4 = 2*2*2. Not prime, composite.

10 not evenly divisible by 2 or 6, our only primes so far, so 10 must be prime.

12 = 2*6, so not prime

14 is not evenly divisible by 2 (no 7), 6, or 10, so 14 must be prime.

16 = 2*8 = 4*4 = 2*2*2*2

OK, let's see if there is a pattern here.

It looks like every other EvInt is prime (the ones that are multiples of 2 but not multiples of 4) 2, 6, 10, 14, 18

The alternating numbers that are multiples of 4, which is every other EvInt (4, 8, 12, 16, ...) are composite, and not prime.

That's really weird, but it looks like it works. Two is prime, and every alternate EvInt number after 2 is prime. The numbers in between are all composite.

Fully factoring a number into primes still works just fine as long as you use our definition for prime (any number divisible by 2 but not divisible by 4 is prime) - see example for 16, above, factored into four 2s.

Let's go on identifying primes and factoring numbers and see what happens.

18 not evenly divisible by 2, 6, 10, 14, so prime

20 = 2*10 = um, only 1 way to factor 20

22 prime (every other number is going to be prime. I'm willing to just accept that at this point.)

24 = 2*12 = 4*6 = 2*2*6

26 prime

28 = 2*14 (we're done. 2 and 14 are both prime EvInts)

30 prime

32 = 2*16=4*8=2*2*2*2*2. Just like regular integers.

34 prime

36 = 2*18 = 6*6

HOUSTON, WE HAVE A PROBLEM!!!!

2 is a prime in EvInts, as is 18, as is 6. That means 36 can be factored into unique primes two different ways.

EvInts breaks unique factorization which we all take totally for granted in our normal balance-the-checkbook math lives. Any integer can be factored into primes in only one way, except for the order of the primes, which doesn't matter.

UFD is kind of obscure, and because of that, a number of pretty famous mathematicians created systems and did not realize they had by accident created a system where factoring was not unique, and incorrectly proved theorems based on assuming that factorization was still unique in their new system.

I have seen other examples of non-UFDs, but they were all pretty complicated. I though this was simple, and I stumbled on it myself. I did see it some years later in a book by one of my fave math authors, Paul Nahin, so that made my day.

I just changed the rules to see what would happen. It very nearly worked except I broke UFD. Unless breaking UFD was what I was going for, but it was not. I was very very surprised and tickled.

Edited 1 time(s). Last edit at 09/23/2022 01:30AM by Brother Of Jerry.

A case can be made for that. We still don't much like negative numbers, and even the name has a, um, negative connotation. Integers, the stuff God created, have integrity. they are solid, one thing. Rational numbers we pretty much like. Calculators always give you rational number results. Irrational numbers make us very nervous. Imaginary numbers are even worse, and by the time we get to complex numbers, we run screaming from the room.

We are still uncomfortable with negative numbers. Corporate reports and tax forms tend to either put them in parentheses, or in red ink. The idea of just slapping a minus sign in front of the number didn't really catch on until the 1750s, and by then corporate reports were already a thing, and they still put negatives in parens.

One of the wonders that Alec Wilkinson discovered in his late life study of math is the question "why are there prime numbers". Nobody designed prime numbers. They just wanted to count stuff. If a Nephite brought in 5 senum of wheat, he wanted a receipt that indicated he had paid his wheat tax. Nobody asked for prime numbers.

So why did primes happen? They are just there, and it is a pattern we spotted.

Sometimes mathematicians change a rule to solve a problem, like "what happens if we have a number less than zero? Wait, have we invented zero yet?"

And sometimes they are just curious, or bored, or whatever.

I did an experiment that probably falls into the bored/curious category. I decided to see what would happen if you tried to restrict the 4 math operations strictly to even integers. Pretend that for math operation purposes, odd numbers do not exist. What will happen?

Let's give the system a name. Since we are dealing with Even Integers, let's call it EvInt Arithmetic.

In EvInt arithmetic, addition and subtraction work exactly as they do in regular arithmetic. Add or subtract two even numbers, you always get an even number as a result. There is even an additive identity (math-babble for a number you can add that changes nothing - add 0)

That was easy.

Multiply. If you multiply two even numbers, you always get an even result. In fact, since both numbers you multiply have at least one 2 as a factor, the product will have 4 as a factor. In the EvInt world, all composite numbers will be multiples of 4.

That may not be obvious to you, but try to verify to your own satisfaction that if you multiply two even numbers, the result is ALWAYS divisible by 4.

OK, if we are living in a world of nothing but even numbers, multiply seems to work too. There is one small catch: we do not have a multiplicative identity, a number that we can multiply by that changes nothing. One (1) is the multiplicative identity in integer arithmetic, and 1 doesn't exist in our EvInt system.

OK, no multiplicative identity. Who cares. We can live without that. Moving on....

Divison. In regular division, if you divide one number by another, there is a quotient, and a remainder, that is less than the divisor. For example, if you divide a number by 3, you get a quotient of whatever, and 3 either divides evenly, with a remainder of 0, or there is a remainder of 1, or a remainder of 2. That's how you learned it in grade 4, or wherever that gets taught.

Let's try division in our system.

2/2. Uh Oh. big problem. 1 does not exist in our system, so, can't divide a number by itself. Damn. And add, sub and multiply operations went so smoothly. :(

4/2 = 2. OK, that worked.

6/2 = 3. No no no. There are no odd numbers. 6/2 = quotient 2 with remainder of 2. reverse engineering the division, 2*2 + 2 =6

Note that the remainder was not less than the divisor. it was equal to the divisor. Can we do that with the earlier examples?

2/2 = quotient 0, remainder 2. Um, a little weird, but OK.

4/2 = quotient 2, remainder 0

6/2 = quotient 2, remainder 2

8/2 = quotient 4, remainder 0

10/2= quotient 4, remainder 2

4/4 = quotient 0, remainder 4

6/4 = quotient 0, remainder 6

8/4 = quotient 2, remainder 0

10/4= quotient 2, remainder 2

12/4= quotient 2, remainder 4 (remember, the quotient can't be 3 in EvInt)

14/4= quotient 2, remainder 6

16/4= quotient 4, remainder 0

It looks pretty weird, but it is all even numbers, and seems to work OK. We just have to allow the remainder to be less than twice the divisor, rather than just less than the divisor.

And, take my word for it, with those alterations to the rule about the remainder, and remembering not to use odd numbers anywhere, yeah, however weird, this division algorithm works.

So there you have it. I had to cut a few boards a bit, but we can get a pretty functional system of arithmetic using only even integers.

Why would anyone want to do that? Hell if I know. You'd be surprised how much math (binary, for example) had no practical application when it was developed.

Then I had one more thought about my little experiment, which had gone so nicely.

What is a prime number in this system?

2 is prime. So far, so good.

3 doesn't exist here, so not my problem.

4 is 2*2, so not prime.

6. Hmmm. Not evenly divisible by 2. See table above. There is a remainder. 3 doesn't exist for our purposes.

6 must be an EvInt prime.

Uh oh. this could be bad.

8 = 2*4 = 2*2*2. Not prime, composite.

10 not evenly divisible by 2 or 6, our only primes so far, so 10 must be prime.

12 = 2*6, so not prime

14 is not evenly divisible by 2 (no 7), 6, or 10, so 14 must be prime.

16 = 2*8 = 4*4 = 2*2*2*2

OK, let's see if there is a pattern here.

It looks like every other EvInt is prime (the ones that are multiples of 2 but not multiples of 4) 2, 6, 10, 14, 18

The alternating numbers that are multiples of 4, which is every other EvInt (4, 8, 12, 16, ...) are composite, and not prime.

That's really weird, but it looks like it works. Two is prime, and every alternate EvInt number after 2 is prime. The numbers in between are all composite.

Fully factoring a number into primes still works just fine as long as you use our definition for prime (any number divisible by 2 but not divisible by 4 is prime) - see example for 16, above, factored into four 2s.

Let's go on identifying primes and factoring numbers and see what happens.

18 not evenly divisible by 2, 6, 10, 14, so prime

20 = 2*10 = um, only 1 way to factor 20

22 prime (every other number is going to be prime. I'm willing to just accept that at this point.)

24 = 2*12 = 4*6 = 2*2*6

26 prime

28 = 2*14 (we're done. 2 and 14 are both prime EvInts)

30 prime

32 = 2*16=4*8=2*2*2*2*2. Just like regular integers.

34 prime

36 = 2*18 = 6*6

HOUSTON, WE HAVE A PROBLEM!!!!

2 is a prime in EvInts, as is 18, as is 6. That means 36 can be factored into unique primes two different ways.

EvInts breaks unique factorization which we all take totally for granted in our normal balance-the-checkbook math lives. Any integer can be factored into primes in only one way, except for the order of the primes, which doesn't matter.

UFD is kind of obscure, and because of that, a number of pretty famous mathematicians created systems and did not realize they had by accident created a system where factoring was not unique, and incorrectly proved theorems based on assuming that factorization was still unique in their new system.

I have seen other examples of non-UFDs, but they were all pretty complicated. I though this was simple, and I stumbled on it myself. I did see it some years later in a book by one of my fave math authors, Paul Nahin, so that made my day.

I just changed the rules to see what would happen. It very nearly worked except I broke UFD. Unless breaking UFD was what I was going for, but it was not. I was very very surprised and tickled.

Edited 1 time(s). Last edit at 09/23/2022 01:30AM by Brother Of Jerry.

The step from addition to multiplication is obvious because multiplication is a form of addition.

I'm often struck by the very high probability that most math arises from daydreaming, if I can use that term, that ends up working in the real world. Imaginary and complex numbers are a great example.

A mundane illustration from my own life arose when long ago I was in a class doing a finance chapter in a statistics book. The CAPM line (wowbagger, take pity) is a linear pricing relationship that is graphed from X=0 and moves upward as you move to the right. The Y-intercept is whatever the risk free rate is in a particular market.

So one day I'm sitting there looking at the one-quadrant graph and thought, "hmm, Gladys, what would happen if you extended that line into the second or even the third quadrant?" The answer in the second quadrant, is that you get increasingly less than the risk free rate of return in exchange for increasing increments of negative risk. What is negative risk? It's insurance or, in the argot, hedging. So far, so good..

But what happens when the line crosses the X-axis and you end up in the third quadrant? There your risk continues to decrease but you are earning a negative return on your money. In effect, you are paying someone else to use your cash. That seemed nonsensical, but it's where my daydreaming took me and I was pretty confident that it had to be possible in the real world.

Then many years later the subprime crisis pushed everyone into a deflationary world and central banks were so frightened of precautionary saving that they started "paying" negative rates of interest--meaning you had to pay for the right to park money in the bank. What we were seeing was a market-driven attempt by the monetary authorities to encourage spending by penalizing saving. And in many countries that third-quadrant situation persisted until this very year.

So stepping back from these examples of imagination leading to insights that don't initially make sense in the real world but later do, it seems to me that there is more at work here than just daydreaming and imagination. The fact is that our environment--scientific, technological, engineering, financial--drives us to a point where certain questions arise logically. We then discover things that at first make no sense but are soon vindicated, at which point we congratulate ourselves for our astounding creativity, discounting the likelihood that other people are making the same connections at more or less the same time. We are not, in fact, working independently.

Stated differently, there is always a Leibniz out there to put us in our place.

Edited 1 time(s). Last edit at 09/23/2022 02:29AM by Lot's Wife.

I'm often struck by the very high probability that most math arises from daydreaming, if I can use that term, that ends up working in the real world. Imaginary and complex numbers are a great example.

A mundane illustration from my own life arose when long ago I was in a class doing a finance chapter in a statistics book. The CAPM line (wowbagger, take pity) is a linear pricing relationship that is graphed from X=0 and moves upward as you move to the right. The Y-intercept is whatever the risk free rate is in a particular market.

So one day I'm sitting there looking at the one-quadrant graph and thought, "hmm, Gladys, what would happen if you extended that line into the second or even the third quadrant?" The answer in the second quadrant, is that you get increasingly less than the risk free rate of return in exchange for increasing increments of negative risk. What is negative risk? It's insurance or, in the argot, hedging. So far, so good..

But what happens when the line crosses the X-axis and you end up in the third quadrant? There your risk continues to decrease but you are earning a negative return on your money. In effect, you are paying someone else to use your cash. That seemed nonsensical, but it's where my daydreaming took me and I was pretty confident that it had to be possible in the real world.

Then many years later the subprime crisis pushed everyone into a deflationary world and central banks were so frightened of precautionary saving that they started "paying" negative rates of interest--meaning you had to pay for the right to park money in the bank. What we were seeing was a market-driven attempt by the monetary authorities to encourage spending by penalizing saving. And in many countries that third-quadrant situation persisted until this very year.

So stepping back from these examples of imagination leading to insights that don't initially make sense in the real world but later do, it seems to me that there is more at work here than just daydreaming and imagination. The fact is that our environment--scientific, technological, engineering, financial--drives us to a point where certain questions arise logically. We then discover things that at first make no sense but are soon vindicated, at which point we congratulate ourselves for our astounding creativity, discounting the likelihood that other people are making the same connections at more or less the same time. We are not, in fact, working independently.

Stated differently, there is always a Leibniz out there to put us in our place.

Edited 1 time(s). Last edit at 09/23/2022 02:29AM by Lot's Wife.

Appreciate the shout-out Gladys and love the thought experiment

I was told as an undergraduate that mathematics was bifurcated into pure and corrupt

I was told as an undergraduate that mathematics was bifurcated into pure and corrupt

We are all corrupt. ;-)

"We have to accept, I think, mathematics either in the new definition, or the old one. In the Renaissance cosmology of John Dee, mathematics is seen as the joint therapist of Father Sky and Mother Earth, or a kind of an intellectual, spiritual, elastic medium connecting up the heavenly realms and Gaia herself. That puts mathematics on the same level as the logos, or the holy spirit."

- Ralph Abraham

- Ralph Abraham

Leibniz, BTW, as far as I know, was the first person to write about binary number system, in the 1600s. He seemed to think it was proof that God (1) created the universe out of nothing (0), and everything can be represented by 1s and 0s.

G H Hardy, Ramanujan's mentor/host in England, took great pride in being in a field (number theory) that was completely unsullied by practical usage. Goldbach's Conjecture is a number theory problem. If somebody proves that it is true, what great problem will it solve in the real world. Nothing that I can think of.

Joke was on Hardy. All that "https" stuff you see about publicly encrypted web sites so you can securely send your credit card info over the internet - there is some very spiffy number theory behind that, so Hardy's field is no longer unsullied by practicality.

G H Hardy, Ramanujan's mentor/host in England, took great pride in being in a field (number theory) that was completely unsullied by practical usage. Goldbach's Conjecture is a number theory problem. If somebody proves that it is true, what great problem will it solve in the real world. Nothing that I can think of.

Joke was on Hardy. All that "https" stuff you see about publicly encrypted web sites so you can securely send your credit card info over the internet - there is some very spiffy number theory behind that, so Hardy's field is no longer unsullied by practicality.

I seriously wonder if any mathematics is sterile. Math is logic, and logic often outpaces our understanding of reality but not reality itself.

The question came up here a while ago about whether math is discovered or created. I believe most replies fell into the "discovered" camp. I am mostly in that camp myself, but uncomfortably so.

One of Wilkinson's questions as a retired adult math student was if math is discovered, where exactly does it exist before it is discovered?

I know. "It is woven into the fabric of the universe." I suppose, but I don't find that terribly satisfying.

One of Wilkinson's questions as a retired adult math student was if math is discovered, where exactly does it exist before it is discovered?

I know. "It is woven into the fabric of the universe." I suppose, but I don't find that terribly satisfying.

Can you conceive of a universe devoid of logic?

Put differently, doesn't the anthropic principle apply here?

Edited 1 time(s). Last edit at 09/23/2022 03:34AM by Lot's Wife.

Put differently, doesn't the anthropic principle apply here?

Edited 1 time(s). Last edit at 09/23/2022 03:34AM by Lot's Wife.

The universe I'm told existed before the modern human brain. Existence appears to me to be based upon spacial causation. Apart from my brain's linear perceptions I can't speak. But I don't give logos apriori status. I think therefore there is something logical for me to think about. Other times and other hominids thought differently. Their view isn't less valid than my thinking's Greek genealogy in my opinion.

"Can you conceive of a universe devoid of logic?"

COMMENT: Yes. It is a universe that is entirely random, with no order, no laws to create such order.

______________________________________

"Put differently, doesn't the anthropic principle apply here?"

COMMENT: The anthropic principle has to do with the existence of natural laws and constants that are 'fine-tuned' for intelligent life. It is not generally related to logic or the existence of laws per se.

However, there is, I think, a point here. Why does the universe have any order -life or no life? Why are there any laws at all? Notice also that at the big bang the entropy of the universe was supposedly extremely low; that is, highly ordered. This order is presumably related to the existent natural laws of the universe that underlie such order. That strikes me as a lot of heavy lifting for a multiverse theory.

COMMENT: Yes. It is a universe that is entirely random, with no order, no laws to create such order.

______________________________________

"Put differently, doesn't the anthropic principle apply here?"

COMMENT: The anthropic principle has to do with the existence of natural laws and constants that are 'fine-tuned' for intelligent life. It is not generally related to logic or the existence of laws per se.

However, there is, I think, a point here. Why does the universe have any order -life or no life? Why are there any laws at all? Notice also that at the big bang the entropy of the universe was supposedly extremely low; that is, highly ordered. This order is presumably related to the existent natural laws of the universe that underlie such order. That strikes me as a lot of heavy lifting for a multiverse theory.

"The question came up here a while ago about whether math is discovered or created. I believe most replies fell into the "discovered" camp. I am mostly in that camp myself, but uncomfortably so."

COMMENT: Finally, you come clean. You are an uncomfortable Platonist, as are, I believe, most mathematicians. In other words, mathematics represents a separate ontological reality that must be discovered by mathematicians, and not invented.

Do you feel the same way about consciousness and mind? After all, there could be no 'discovery' of mathematics without a mind to discover it, and there is no 'mind-stuff' in either the theories of mathematics or physics.

_______________________________________

One of Wilkinson's questions as a retired adult math student was if math is discovered, where exactly does it exist before it is discovered?

I know. "It is woven into the fabric of the universe." I suppose, but I don't find that terribly satisfying.

COMMENT: Me either. What then is the 'fabric of the universe?' Presumably, from modern field theory, it represents a host of interacting quantum fields. So, I guess we need a 'mathematics field' and a 'mind field' to interact with the standard 'physical' fields of the Standard Model. I assume the mathematics field is swarming with numbers and equations of all sorts. What, then, is the mind field swarming with? Thoughts? Ideas? Whose?

COMMENT: Finally, you come clean. You are an uncomfortable Platonist, as are, I believe, most mathematicians. In other words, mathematics represents a separate ontological reality that must be discovered by mathematicians, and not invented.

Do you feel the same way about consciousness and mind? After all, there could be no 'discovery' of mathematics without a mind to discover it, and there is no 'mind-stuff' in either the theories of mathematics or physics.

_______________________________________

One of Wilkinson's questions as a retired adult math student was if math is discovered, where exactly does it exist before it is discovered?

I know. "It is woven into the fabric of the universe." I suppose, but I don't find that terribly satisfying.

COMMENT: Me either. What then is the 'fabric of the universe?' Presumably, from modern field theory, it represents a host of interacting quantum fields. So, I guess we need a 'mathematics field' and a 'mind field' to interact with the standard 'physical' fields of the Standard Model. I assume the mathematics field is swarming with numbers and equations of all sorts. What, then, is the mind field swarming with? Thoughts? Ideas? Whose?

**shriek**

LOL

Breath into a paper bag for a minute. You’ll be ok.

Unique factorization is on the esoteric side. I threw that in because Lot’s Wife asked for it.

Goldbach is basically grade school math. See if you can write down all the even numbers from 6 to 30 as the sum of two odd primes. Four is the oddball because it is the only one that uses the even prime, 2+2.

Doing it for a dozen or so even numbers should be enough to give you a feeling that yes, that appears to be possible. You *can* write even numbers as the sum of two primes.

Questions you’re not going to get answers to:

Why does that work? We don’t know.

Does it always work for all even integers? We don’t know.

Questions we can sort of answer

So what good is it? It is a simple mathematical pattern that pretty much anybody can verify in a few minutes. It is famous for one reason and one reason only. Despite its simplicity and obvious truth (you should be able to do this for any even number), nobody has been able to prove that it is always possible.

Nobody asks what good is Beethoven’s Fifth. People listen to it for personal enjoyment. They learn to perform it for the sense of accomplishment, and for personal enjoyment, and if they are good enough, they do it to get paid.

Don’t ask why. Just treat it for what it is. A simple little puzzle.

Ok, you can put the paper bag down now. ;)

Unique factorization is on the esoteric side. I threw that in because Lot’s Wife asked for it.

Goldbach is basically grade school math. See if you can write down all the even numbers from 6 to 30 as the sum of two odd primes. Four is the oddball because it is the only one that uses the even prime, 2+2.

Doing it for a dozen or so even numbers should be enough to give you a feeling that yes, that appears to be possible. You *can* write even numbers as the sum of two primes.

Questions you’re not going to get answers to:

Why does that work? We don’t know.

Does it always work for all even integers? We don’t know.

Questions we can sort of answer

So what good is it? It is a simple mathematical pattern that pretty much anybody can verify in a few minutes. It is famous for one reason and one reason only. Despite its simplicity and obvious truth (you should be able to do this for any even number), nobody has been able to prove that it is always possible.

Nobody asks what good is Beethoven’s Fifth. People listen to it for personal enjoyment. They learn to perform it for the sense of accomplishment, and for personal enjoyment, and if they are good enough, they do it to get paid.

Don’t ask why. Just treat it for what it is. A simple little puzzle.

Ok, you can put the paper bag down now. ;)

Yes, but - What's it all about, BoJ?

https://www.youtube.com/watch?v=YL06i9aiM4o

Edited 2 time(s). Last edit at 09/23/2022 01:00PM by Nightingale.

https://www.youtube.com/watch?v=YL06i9aiM4o

Edited 2 time(s). Last edit at 09/23/2022 01:00PM by Nightingale.

I also need to re-study math.

I've forgotten most of it because I rarely use it.

I remember Pythagorean theorem because I use it extensively in carpentry when building roofs.

I've forgotten most of it because I rarely use it.

I remember Pythagorean theorem because I use it extensively in carpentry when building roofs.

Being able to build roof trusses was an important and valuable skill.

Thanks to computers, higher end home have much more complicated roof profiles that would cost a fortune now if they had to find enough carpenters who could do that work. Now the trusses are built in a factory and shipped to the site on a truck.

Another disappearing skill.

Thanks to computers, higher end home have much more complicated roof profiles that would cost a fortune now if they had to find enough carpenters who could do that work. Now the trusses are built in a factory and shipped to the site on a truck.

Another disappearing skill.

> Another disappearing skill.

Like your slide rule!

Like your slide rule!

+1

Re slide rules: sadly also disappearing. They were a visual lesson in logarithmic and exponential spacing. Their sole reason for existence now is nostalgia. Same for trig tables and logarithm tables.

I of course still have a slide rule, and an Original Odhner mechanical calculator, “Original” to differentiate the Swedish version from a Russian knock-off, or something like that. It is mostly useful for learning how Swedes spell Sweden.

I of course still have a slide rule, and an Original Odhner mechanical calculator, “Original” to differentiate the Swedish version from a Russian knock-off, or something like that. It is mostly useful for learning how Swedes spell Sweden.

When I built the Stein Erickson lodge in Park City Utah the roof was built out of truss joists which was very strong to support the snow loading. That took some calculations for the custom joist cutting.

Mathematics is plural. Why is the abbreviation math and not maths? Asking for a friend as I know how I say it lol.

Kentish Wrote:

-------------------------------------------------------

> Mathematics is plural. Why is the abbreviation

> math and not maths? Asking for a friend as I know

> how I say it lol.

Only Mad Dogs and Englishmen

Edited 1 time(s). Last edit at 09/23/2022 11:28PM by Nightingale.

-------------------------------------------------------

> Mathematics is plural. Why is the abbreviation

> math and not maths? Asking for a friend as I know

> how I say it lol.

Only Mad Dogs and Englishmen

Edited 1 time(s). Last edit at 09/23/2022 11:28PM by Nightingale.

And why didn’t you write “mathematics are plural”?

Same reason that it’s zee, not zed. Because we’re America and we said so. ;)

Besides, I think mathemata is also plural. That would abbreviate to math.

Same reason that it’s zee, not zed. Because we’re America and we said so. ;)

Besides, I think mathemata is also plural. That would abbreviate to math.

I say "zed" just because I used to work for a Canadian company.

Kentish Wrote:

-------------------------------------------------------

> Mathematics is plural. Why is the abbreviation

> math and not maths?

I hate to do this to you with the OED, which will smart, but "mathematics, n.pl 1 (also treated as sing.). . ."

Thus God's own dictionary says it can go either way.

-------------------------------------------------------

> Mathematics is plural. Why is the abbreviation

> math and not maths?

I hate to do this to you with the OED, which will smart, but "mathematics, n.pl 1 (also treated as sing.). . ."

Thus God's own dictionary says it can go either way.

Bowing to the modernists. Dr. Murray would turn in his grave. No wonder my kids got their sums wrong.

I think you would agree, based on the full OED, that the vast majority of words in the English language have undergone shifts in meaning and usage over the decades and centuries.

I'm a conservative when it comes to English. I recall once sitting at baggage claim in JFK when the lights went out and the conveyor belts seized. An announcer said over the communication system that the airport had suffered a "power outage" and I heard a burst of laughter from several people. I looked over at them and saw that they were a BA flight crew, laughing at the neologism "outage."

But given the "five reported usages and a word is in" standard employed by Dr. Murray's successors, I'll bet the singular/plural usage has been acceptable for a very long time.

PS. Fowler's recognizes both usages as well.

I'm a conservative when it comes to English. I recall once sitting at baggage claim in JFK when the lights went out and the conveyor belts seized. An announcer said over the communication system that the airport had suffered a "power outage" and I heard a burst of laughter from several people. I looked over at them and saw that they were a BA flight crew, laughing at the neologism "outage."

But given the "five reported usages and a word is in" standard employed by Dr. Murray's successors, I'll bet the singular/plural usage has been acceptable for a very long time.

PS. Fowler's recognizes both usages as well.

One of my favorite phrases from the Economist Magazine--I must have been doing some research because he was before my time--was a description of Alexander Haig as "that infamous verber of nouns."

I'm confident that usage has not been attested the requisite five times.

I'm confident that usage has not been attested the requisite five times.

Some turns of phrase are unforgettable.

Lot's Wife Wrote:

-------------------------------------------------------

> I think you would agree, based on the full OED,

> that the vast majority of words in the English

> language have undergone shifts in meaning and

> usage over the decades and centuries.

I find myself more often looking words up to ensure the meaning/connotation is what I intend. It's interesting to note the seemingly increasingly rapid changes. I often check now to ensure I'm not using hopelessly dated expressions (although sometimes I do it on purpose). I didn't know in younger years that such evolution occurred within one's own living memory.

One example is that yesterday I found myself looking up the expression "nowt so queer as folk". (I can't now recall the reason for my query - I mean - it was yesterday - sheesh). As an aside, it was interesting to me that it's listed as "colloquial, Yorkshire" as that's where my dad's father was from. I was wondering how it came to its current meaning and especially how it transformed from an intended deadly insult to a term now accepted and used by those it was previously meant to disparage.

My sweet little English mum, without a mean sinew in her body, often used that word, such as saying "I feel queer" to mean not well, or something is "queer", meaning a mystery. I had to finally tell her at some point that the connotation wasn't positive. She bit her tongue for a while but eventually caught up. It can be challenging to continually update one's vocabulary as times change. Who ever thought that once you'd learned words you'd one day have to revisit your vocab choices.

This site is interesting:

https://www.cjr.org/language_corner/queer.php

Excerpts:

"Originally a derogatory name for a homosexual, “queer” has been embraced by some in the nonheterosexual community. In response, some activists in the gay community (to use a broad term) started calling themselves “queer” in a prideful way.

"Since it first showed up in English about 1513, “queer” has always meant something not normal, something peculiar, something odd. Counterfeit money was “queer”; someone who is sick might say they “feel queer”; playground bullies would call someone “queer” without knowing or intending any sexual connotations."

"The Dictionary of American Slang says “in the early 1990s queer was adopted as a non-pejorative designation by some homosexuals, in the spirit of ‘gay pride.’"

"Some sources trace the first adoption of “queer” as a positive self-label to the group Queer Nation, founded in the early 1990s as a radical organization to combat violence against homosexuals. “By co-opting the word ‘queer,’ QN claims, they have disarmed homophobes,” Newsweek wrote in 1991."

"Since then, “queer” has expanded beyond meaning only “homosexual.” In fact, “queer” does not have a single meaning, except perhaps “not heterosexual.” Some people who identify as neither male nor female call themselves “genderqueer,” while others who identify that same way might call themselves “gender-fluid” or “nonbinary.” Even the “Q” in LGBTQ could stand for either “queer” or “questioning.”

“Queer” is a label, one adopted by some people, rejected by others. So it can’t be used to describe individuals, a group of specific individuals, or their gender orientations, unless their preference is known. And it can still sting. As the AP Stylebook says: “Queer is acceptable for people and organizations that use the term to identify themselves. Do not use it when intended as a slur.”

That should be obvious and not too much to ask: Don't use a word when intended as a slur.

Mum was a librarian and was Chief Book Lady to us, bringing home armfuls of good and great books every weekend for us all to enjoy. It felt like big love that she knew what each one of us would enjoy reading. My father used to sit and read the dictionary (Oxford English, of course). As a kid I thought that was ever so slightly strange (as in, not very interesting). But Dad used big words and encouraged us to check out their definitions. My parents' influence rubbed off on all of us kids as the 5 of us are all voracious readers, not always of erudite texts but still, even a "dime store" novel is reading. In our teen years my older sister and I were thrilled to go into a grotty used book store every Saturday to pick up a few well-thumbed novels to get us through the week. I've graduated now to a cute little shop with brand new books where the staff knows my favourite authors and also my name. They love books and so do I.

I look on it as a fine inheritance that all my parents' children haunt bookstores and libraries, finding treasures and sharing them out amongst ourselves. Thanks, folks. You did OK by us on this score.

Edited 2 time(s). Last edit at 09/24/2022 03:11PM by Nightingale.

-------------------------------------------------------

> I think you would agree, based on the full OED,

> that the vast majority of words in the English

> language have undergone shifts in meaning and

> usage over the decades and centuries.

I find myself more often looking words up to ensure the meaning/connotation is what I intend. It's interesting to note the seemingly increasingly rapid changes. I often check now to ensure I'm not using hopelessly dated expressions (although sometimes I do it on purpose). I didn't know in younger years that such evolution occurred within one's own living memory.

One example is that yesterday I found myself looking up the expression "nowt so queer as folk". (I can't now recall the reason for my query - I mean - it was yesterday - sheesh). As an aside, it was interesting to me that it's listed as "colloquial, Yorkshire" as that's where my dad's father was from. I was wondering how it came to its current meaning and especially how it transformed from an intended deadly insult to a term now accepted and used by those it was previously meant to disparage.

My sweet little English mum, without a mean sinew in her body, often used that word, such as saying "I feel queer" to mean not well, or something is "queer", meaning a mystery. I had to finally tell her at some point that the connotation wasn't positive. She bit her tongue for a while but eventually caught up. It can be challenging to continually update one's vocabulary as times change. Who ever thought that once you'd learned words you'd one day have to revisit your vocab choices.

This site is interesting:

https://www.cjr.org/language_corner/queer.php

Excerpts:

"Originally a derogatory name for a homosexual, “queer” has been embraced by some in the nonheterosexual community. In response, some activists in the gay community (to use a broad term) started calling themselves “queer” in a prideful way.

"Since it first showed up in English about 1513, “queer” has always meant something not normal, something peculiar, something odd. Counterfeit money was “queer”; someone who is sick might say they “feel queer”; playground bullies would call someone “queer” without knowing or intending any sexual connotations."

"The Dictionary of American Slang says “in the early 1990s queer was adopted as a non-pejorative designation by some homosexuals, in the spirit of ‘gay pride.’"

"Some sources trace the first adoption of “queer” as a positive self-label to the group Queer Nation, founded in the early 1990s as a radical organization to combat violence against homosexuals. “By co-opting the word ‘queer,’ QN claims, they have disarmed homophobes,” Newsweek wrote in 1991."

"Since then, “queer” has expanded beyond meaning only “homosexual.” In fact, “queer” does not have a single meaning, except perhaps “not heterosexual.” Some people who identify as neither male nor female call themselves “genderqueer,” while others who identify that same way might call themselves “gender-fluid” or “nonbinary.” Even the “Q” in LGBTQ could stand for either “queer” or “questioning.”

“Queer” is a label, one adopted by some people, rejected by others. So it can’t be used to describe individuals, a group of specific individuals, or their gender orientations, unless their preference is known. And it can still sting. As the AP Stylebook says: “Queer is acceptable for people and organizations that use the term to identify themselves. Do not use it when intended as a slur.”

That should be obvious and not too much to ask: Don't use a word when intended as a slur.

Mum was a librarian and was Chief Book Lady to us, bringing home armfuls of good and great books every weekend for us all to enjoy. It felt like big love that she knew what each one of us would enjoy reading. My father used to sit and read the dictionary (Oxford English, of course). As a kid I thought that was ever so slightly strange (as in, not very interesting). But Dad used big words and encouraged us to check out their definitions. My parents' influence rubbed off on all of us kids as the 5 of us are all voracious readers, not always of erudite texts but still, even a "dime store" novel is reading. In our teen years my older sister and I were thrilled to go into a grotty used book store every Saturday to pick up a few well-thumbed novels to get us through the week. I've graduated now to a cute little shop with brand new books where the staff knows my favourite authors and also my name. They love books and so do I.

I look on it as a fine inheritance that all my parents' children haunt bookstores and libraries, finding treasures and sharing them out amongst ourselves. Thanks, folks. You did OK by us on this score.

Edited 2 time(s). Last edit at 09/24/2022 03:11PM by Nightingale.

That's the wonderful thing about the unabridged OED: it traces, with examples, the evolution of words over the centuries and hence comprises, in Foucault's phrase, an archaeology of knowledge.

Ever encounter a word in Shakespeare that makes no sense to the modern reader? The OED explains what it meant in his day. 'Tis a joy to read.

As for the word "queer," I share your mixed feelings. Its traditional definition was richly variable and and then evolved into a narrower meaning that has recently begun to expand again in new ways. If I recall correctly, some months ago our beloved D&D described himself as queer in that latest sense, thereby rendering it in my mind as legitimate as anything in the recondite dictionary.

Ever encounter a word in Shakespeare that makes no sense to the modern reader? The OED explains what it meant in his day. 'Tis a joy to read.

As for the word "queer," I share your mixed feelings. Its traditional definition was richly variable and and then evolved into a narrower meaning that has recently begun to expand again in new ways. If I recall correctly, some months ago our beloved D&D described himself as queer in that latest sense, thereby rendering it in my mind as legitimate as anything in the recondite dictionary.

Of course, and now they are undergoing major changes with the increasing use of American English. Just today I saw a headline in a British newspaper that indicated someone was going to "raise" their children in certain way. Never would have seen that once since we would say you raise corn but rear children.

My Concise OED offers Maths as the British term and Math as the north American term. Two nations separated by a common language and all that.

My Concise OED offers Maths as the British term and Math as the north American term. Two nations separated by a common language and all that.

Horse of a different colour is still a horse. That applies to assess as well.

The edition I have with me now--I have the full set in storage (alas) and a couple of other versions, including a two-volume one that may be the Concise--is the Oxford Encyclopedic English Dictionary. It does treat math as American and maths as British, but the "mathematics" entry simply says the word is both singular and plural.

More generally, I think the standards for publication are dropping like a stone. I see news headlines, including from reputable sources, that are incomprehensible and articles that contain all sorts of lexicographical and grammatical errors. It's tragic, disrespectful to language and hence to thought.

More generally, I think the standards for publication are dropping like a stone. I see news headlines, including from reputable sources, that are incomprehensible and articles that contain all sorts of lexicographical and grammatical errors. It's tragic, disrespectful to language and hence to thought.