On 3/14/2023 4:01 PM, Steven Schweda wrote:
>> If you stop 100 random people on the street and ask about integers, then
>> 99 won't have a clue what you are talking about.
>
> 99 might be high, but I'd guess at least 90. Unless you choose the
> street _very_ carefully.
>
>
>> Those that remember their math should think of Z.
>
> You can't remember what you never learned. I live in a country where
> store clerks can't make change for a dollar in their heads. Back when I
> commonly used cash, and wasn't feeling depressed enough, I could buy
> something, hand over some bills, wait for the register to calculate the
> change, and then hand over some coins to reduce the number of coins
> returned. And watch the puny-brain at the register suffer a complete
> intellectual collapse.
>
> So, no, I wouldn't expect 99% of "random people on the street" to
> have any idea what an integer is.
>
>> The rest should vaguely remember that "numbers without decimals" are
>> called integers.
>
> "should" and "would" are spelled differently for a reason.
>
> Thirty-odd years ago, on a business trip to California, I had
> breakfast a few times at a Burger King in Fremont which was convenient
> to the motel. I was late enough to miss the morning rush, so I dealt
> with the manager, who rang up the sale, entering the purchase total as
> the amount tendered. He then made change, correctly, using his head
> rather than the register. I was so thrilled by this performance that I
> almost wrote a commendation letter to the company. But I realized that
> he was violating company policy, and decided not to risk getting him
> reprimanded (or worse).
>
> But he was an immigrant, not educated here.

I would expect those that went through high school to
know that:

N = natural
Z = integer
Q = rational
R = real

and those that went through college in something STEM related
to have heard of algebraic numbers, transcendental numbers and
complex numbers.

But maybe I have too high expectations.

Arne

> I would expect those that went through high school to
> know that:
> [...]

I know nothing about the high schools in your neighborhood, but
around here there's no way to complete that expectation (with any
significant content) with any confidence close to even 50%.

> and those that went through college in something STEM related
> to have heard of algebraic numbers, transcendental numbers and
> complex numbers.

Why would a pre-med biology major care about transcendental numbers?
(Have a happy Pi Day?)

> But maybe I have too high expectations.

I'd say so. Perhaps you don't get out much. Or the schools in your
neighborhood differ greatly from those around here.

Steven Schweda <sms.antinode@gmail.com> wrote:
> Why would a pre-med biology major care about transcendental numbers?
>(Have a happy Pi Day?)

They'll care when they get to Organic Chem and have to deal with lots of
sqrt(2) and sqrt(3) stuff.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

On 3/14/2023 6:41 PM, Arne Vajhøj wrote:
> On 3/14/2023 4:01 PM, Steven Schweda wrote:
>>> If you stop 100 random people on the street and ask about integers, then
>>> 99 won't have a clue what you are talking about.
>>
>> 99 might be high, but I'd guess at least 90. Unless you choose the
>> street _very_ carefully.
>>
>>
>>> Those that remember their math should think of Z.
>>
>> You can't remember what you never learned. I live in a country where
>> store clerks can't make change for a dollar in their heads. Back when I
>> commonly used cash, and wasn't feeling depressed enough, I could buy
>> something, hand over some bills, wait for the register to calculate the
>> change, and then hand over some coins to reduce the number of coins
>> returned. And watch the puny-brain at the register suffer a complete
>> intellectual collapse.
>>
>> So, no, I wouldn't expect 99% of "random people on the street" to
>> have any idea what an integer is.
>>
>>> The rest should vaguely remember that "numbers without decimals" are
>>> called integers.
>>
>> "should" and "would" are spelled differently for a reason.
>>
>> Thirty-odd years ago, on a business trip to California, I had
>> breakfast a few times at a Burger King in Fremont which was convenient
>> to the motel. I was late enough to miss the morning rush, so I dealt
>> with the manager, who rang up the sale, entering the purchase total as
>> the amount tendered. He then made change, correctly, using his head
>> rather than the register. I was so thrilled by this performance that I
>> almost wrote a commendation letter to the company. But I realized that
>> he was violating company policy, and decided not to risk getting him
>> reprimanded (or worse).
>>
>> But he was an immigrant, not educated here.
>
> I would expect those that went through high school to
> know that:
>
> N = natural
> Z = integer
> Q = rational
> R = real
>
> and those that went through college in something STEM related
> to have heard of algebraic numbers, transcendental numbers and
> complex numbers.
>
> But maybe I have too high expectations.
>
> Arne
>

Perhaps. What is a transcendental number?

And, I do have a BS in Math from the University of Pittsburgh.

--
David Froble Tel: 724-529-0450
Dave Froble Enterprises, Inc. E-Mail: davef@tsoft-inc.com
DFE Ultralights, Inc.
170 Grimplin Road
Vanderbilt, PA 15486

> > Why would a pre-med biology major care about transcendental numbers?

> They'll care when they get to Organic Chem and have to deal with lots of
> sqrt(2) and sqrt(3) stuff.

I never took organic or physical chemistry, so I don't know why/where
such square roots might appear (especially in organic chem), but...

A calculator can do square roots whether or not the operator knows
whether the result is transcendental. As illustrated by the fact that
those particular square roots are irrational, but algebraic, not
transcendental.

I rest my case.

> [...] What is a transcendental number?

According to this new Inter-Web thing:

https://en.wikipedia.org/wiki/Transcendental_number

> And, I do have a BS in Math from the University of Pittsburgh.

And with all that education, still can't do a basic Web search?

On the bright side, there are more transcendental numbers than there
are algebraic numbers (which don't outnumber the integers). And, as I
suggested, you don't need to be able to classify them in order to use
them.

On 3/14/2023 9:11 PM, Steven Schweda wrote:
>> and those that went through college in something STEM related
>> to have heard of algebraic numbers, transcendental numbers and
>> complex numbers.
>
> Why would a pre-med biology major care about transcendental numbers?
> (Have a happy Pi Day?)

I believe biology requires math skills.

And this is pretty basic math stuff. Whether it is direct
applicable or just context I don't know enough about biology to say.

Arne

On 3/14/2023 9:55 PM, Scott Dorsey wrote:
> Steven Schweda <sms.antinode@gmail.com> wrote:
>> Why would a pre-med biology major care about transcendental numbers?
>> (Have a happy Pi Day?)
>
> They'll care when they get to Organic Chem and have to deal with lots of
> sqrt(2) and sqrt(3) stuff.

Those are not transcendental numbers.

But there are probably other numbers that are. I don't know
much about biology but I suspect logarithms are used.

Arne

On 3/14/2023 10:24 PM, Steven Schweda wrote:
>>> Why would a pre-med biology major care about transcendental numbers?
>
>> They'll care when they get to Organic Chem and have to deal with lots of
>> sqrt(2) and sqrt(3) stuff.
>
> I never took organic or physical chemistry, so I don't know why/where
> such square roots might appear (especially in organic chem), but...
>
> A calculator can do square roots whether or not the operator knows
> whether the result is transcendental.

As I said then I have some expectations to the educational system.

That includes having expectations that someone with a STEM degree
can more than just use a calculator - that the person actually
understand the background for the math.

Calculus, linear algebra, number theory, probability theory etc..

Arne

On 3/14/2023 10:20 PM, Dave Froble wrote:
> On 3/14/2023 6:41 PM, Arne Vajhøj wrote:
>> and those that went through college in something STEM related
>> to have heard of algebraic numbers, transcendental numbers and
>> complex numbers.
>>
>> But maybe I have too high expectations.
>
> Perhaps.  What is a transcendental number?
>
> And, I do have a BS in Math from the University of Pittsburgh.

You may have known back then. I believe it has been a few
years since you graduated.

:-)

Algebraic numbers are formally those that are roots
to polynomials with integer/rational coefficients.
More informal anything from integers, basic operators
and nth-root.

Transcendental numbers are the real numbers that are
not algebraic. All the "weird" numbers like e, pi,
results from logarithmic or trigonometric functions (except
for a a few selected inputs).

Arne

On 3/15/2023 4:58 PM, Arne Vajhøj wrote:
> On 3/14/2023 10:20 PM, Dave Froble wrote:
>> On 3/14/2023 6:41 PM, Arne Vajhøj wrote:
>>> and those that went through college in something STEM related
>>> to have heard of algebraic numbers, transcendental numbers and
>>> complex numbers.
>>>
>>> But maybe I have too high expectations.
>>
>> Perhaps. What is a transcendental number?
>>
>> And, I do have a BS in Math from the University of Pittsburgh.
>
> You may have known back then. I believe it has been a few
> years since you graduated.

Yeah, like over 50 ...

> :-)
>
> Algebraic numbers are formally those that are roots
> to polynomials with integer/rational coefficients.
> More informal anything from integers, basic operators
> and nth-root.
>
> Transcendental numbers are the real numbers that are
> not algebraic. All the "weird" numbers like e, pi,
> results from logarithmic or trigonometric functions (except
> for a a few selected inputs).

I think I still remember all that, but, I don't recall ever hearing them
referred to by that name. But, over 50 years ...

--
David Froble Tel: 724-529-0450
Dave Froble Enterprises, Inc. E-Mail: davef@tsoft-inc.com
DFE Ultralights, Inc.
170 Grimplin Road
Vanderbilt, PA 15486

Although I doubt the relevance to VMS of any of this digression, ...

> [...] I don't know much about biology but I suspect logarithms are
> used.

Even if some knowledge of logarithms were required to get a biology
degree, which I doubt, someone can know plenty about logarithms without
knowing what a transcendental number might be.

And you're getting the lyrics mixed up. It's:

Don't know much about history
Don't know much biology
[...]

When it comes to formal education, I don't remember ever taking a
course in number theory, either, so I suspect that I first learned about
transcendental numbers (while in high school?) from a book by Martin
Gardner, obtained from the local public library, rather than from any
formal school work. Which is one more reason I wouldn't expect a
typical high-school grad to have encountered the concept.

> [...] roots to polynomials with integer/rational coefficients. [...]

Is that different from roots of polynomials with integer
coefficients? (Hint: No. And I can prove it.)

On 3/15/2023 6:12 PM, Steven Schweda wrote:
>> [...] roots to polynomials with integer/rational coefficients. [...]
>
> Is that different from roots of polynomials with integer
> coefficients?

The definition is the same whether one say integer coefficient
or rational coefficients.

But they are both sometimes used so that is why I mentioned both.

> (Hint: No. And I can prove it.)

That is very easy to do.

Arne

On 3/10/2023 4:01 PM, Arne Vajhøj wrote:
> Pre-release for comments:
>
> https://www.vajhoej.dk/arne/articles/vms64.html

Updated to version 1.0 based on comments.

Arne

Arne Vajhøj schrieb am Donnerstag, 16. März 2023 um 01:47:31 UTC+1:
> On 3/10/2023 4:01 PM, Arne Vajhøj wrote:
> > Pre-release for comments:
> >
> > https://www.vajhoej.dk/arne/articles/vms64.html
>
> Updated to version 1.0 based on comments.
>
> Arne
Small correction: PASCAL/USAGE=64BIT_TO_DESCR does NOT change the compiler's treatment of pointers. Interpreting pointers as unsigned values has to be provided by the programmer. The qualifier only allows for P2 structures to be used as actual routine parameters via descriptor, which otherwise would be flagged as a compile time error.

On 2023-03-15 21:58, Arne Vajhøj wrote:
> Transcendental numbers are the real numbers that are
> not algebraic. All the "weird" numbers like e, pi,
> results from logarithmic or trigonometric functions (except
> for a a few selected inputs).

Am I confused? I was under the impression that pi comes from the
division of the diameter with the circumference of a circle.
No logarithmic or trigonometric anywhere near that...

Johnny

> Am I confused? [...]

Perhaps.

> [...] I was under the impression that pi comes from the
> division of the diameter with the circumference of a circle.
> No logarithmic or trigonometric anywhere near that...

arccos( -1) = ?

Trying to disconnect trig functions from circles and pi seems (to me)
perverse and unproductive. Or does your Web search for:
trigonometry "unit circle"
find nothing?

In article <tv1ver$9ls$1@news.misty.com>,
Johnny Billquist <bqt@softjar.se> wrote:
>On 2023-03-15 21:58, Arne Vajhøj wrote:
>> Transcendental numbers are the real numbers that are
>> not algebraic. All the "weird" numbers like e, pi,
>> results from logarithmic or trigonometric functions (except
>> for a a few selected inputs).
>
>Am I confused? I was under the impression that pi comes from the
>division of the diameter with the circumference of a circle.

It does but it ALSO is the sum of 4 - 4/3 + 4/5 - 4/7 + 4/9 - ....

Or it's tan-1 of 0.

It's everywhere you look. It's pretty creepy.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

> Or it's tan-1 of 0.

As arctan is usually defined, arctan( 0) = 0. I chose arccos for a
reason. Inverse functions of periodic functions generally achieve
unique results by careful limits on their domains. tan( n* pi) = 0, but
arctan( 0) != n* pi.

Advice on math and science found on comp.os.vms is generally
unreliable, I claim.

On 3/17/2023 11:02 AM, Johnny Billquist wrote:
> On 2023-03-15 21:58, Arne Vajhøj wrote:
>> Transcendental numbers are the real numbers that are
>> not algebraic. All the "weird" numbers like e, pi,
>> results from logarithmic or trigonometric functions (except
>> for a a few selected inputs).
>
> Am I confused? I was under the impression that pi comes from the
> division of the diameter with the circumference of a circle.
> No logarithmic or trigonometric anywhere near that...

The above was really just a list of 4 examples. I did
not intend to imply any overlap of the list.

But there is an overlap. Pi can be calculated by both
a trigonometric and a logarithmic function.

$ type pi.for
program pi
implicit none
write(*,*) dacos(-1.0d0)
write(*,*) cdlog((-1.0d0,0.0d0))/cdsqrt((-1.0d0,0.0d0))
end
$ link pi
$ run pi
3.14159265358979
(3.14159265358979,0.000000000000000E+000)

Arne

On 3/16/2023 5:05 AM, Andreas Gruhl wrote:
> Arne Vajhøj schrieb am Donnerstag, 16. März 2023 um 01:47:31 UTC+1:
>> On 3/10/2023 4:01 PM, Arne Vajhøj wrote:
>>> Pre-release for comments:
>>>
>>> https://www.vajhoej.dk/arne/articles/vms64.html
>>
>> Updated to version 1.0 based on comments.

> Small correction: PASCAL/USAGE=64BIT_TO_DESCR does NOT change the
> compiler's treatment of pointers. Interpreting pointers as unsigned
> values has to be provided by the programmer. The qualifier only
> allows for P2 structures to be used as actual routine parameters via
> descriptor, which otherwise would be flagged as a compile time
> error.
So it does not change the treatment of pointers.

It disables a compiler check.

Like allowing this to compile:

procedure whatever(...; %STDESCR somearg; ...); external;
....
(* z is in lower 2 GB of P2 space *)
....
whatever(..., z, ...);

?

Arne

On Fri, 2023-03-17 at 16:06 -0400, Arne Vajhøj wrote:
>    3.14159265358979

Looks correct but NASA doesn't use more than 15 digits for calculations
within the solar system, the biggest error at that distance is the
width of one's little finger.

They do say that we only need 37 decimal places to encompass the entire
universe (estimated to be 46 billion light years) to slice an hydrogen
atom into two at that distance.
--
Tactical Nuclear Kittens

On 3/18/2023 9:23 AM, Single Stage to Orbit wrote:
> On Fri, 2023-03-17 at 16:06 -0400, Arne Vajhøj wrote:
>>    3.14159265358979
>
> Looks correct but NASA doesn't use more than 15 digits for calculations
> within the solar system, the biggest error at that distance is the
> width of one's little finger.
>
> They do say that we only need 37 decimal places to encompass the entire
> universe (estimated to be 46 billion light years) to slice an hydrogen
> atom into two at that distance.

The test was done on VMS Alpha so with no
/FLOAT qualifier the first result was a G-float
and the second result a pair of G-float.

Arne

On Sat, 2023-03-18 at 10:51 -0400, Arne Vajhøj wrote:
> > Looks correct but NASA doesn't use more than 15 digits for
> > calculations within the solar system, the biggest error at that
> > distance is the width of one's little finger.
> >
> > They do say that we only need 37 decimal places to encompass the
> > entire universe (estimated to be 46 billion light years) to slice
> > an hydrogen atom into two at that distance.
>
> The test was done on VMS Alpha so with no
> /FLOAT qualifier the first result was a G-float
> and the second result a pair of G-float.

My point was that nobody needs to calculate billions of decimal places
for Pi. 15 places is more than though. And if we ever make it outside
the Solar system, 37 places is more than enough.

I tire of hearing about people calculating Pi to billions of digits.
What good does that do?
--
Tactical Nuclear Kittens

On 18/03/2023 19:41, Single Stage to Orbit wrote:
> On Sat, 2023-03-18 at 10:51 -0400, Arne Vajhøj wrote:
>>> Looks correct but NASA doesn't use more than 15 digits for
>>> calculations within the solar system, the biggest error at that
>>> distance is the width of one's little finger.
>>>
>>> They do say that we only need 37 decimal places to encompass the
>>> entire universe (estimated to be 46 billion light years) to slice
>>> an hydrogen atom into two at that distance.
>>
>> The test was done on VMS Alpha so with no
>> /FLOAT qualifier the first result was a G-float
>> and the second result a pair of G-float.
>
> My point was that nobody needs to calculate billions of decimal places
> for Pi. 15 places is more than though. And if we ever make it outside
> the Solar system, 37 places is more than enough.
>
> I tire of hearing about people calculating Pi to billions of digits.
> What good does that do?

Some people just like to break records!

--
Chris