On 19/09/2022 23.11, The Horny Goat wrote:

> It has been mathematically proven that pi (and e) are irrational
> numbers - which means in decimal terms an endless fraction never
> repeating. (A 'rational number' aka what most of us call a fraction
> DOES repeat even though it goes on endlessly and can always be defined
> as x/y where x is the numerator y the denominator)

Specifically, with x and y being integers (and y non-zero)

> That particular one >IS< proven. Plenty more in mathematics are not -
> doesn't mean the correct answer isn't A or B that just means we
> haven't figured out how to prove it yet.

And there are plenty more that can neither be proved nor disproved,
at least within standard mathematics. (Obviously, if you add an
axiom, what can be proven changes.)

--
Michael F. Stemper
Economists have correctly predicted seven of the last three recessions.

On Tue, 20 Sep 2022 08:14:38 -0500, "Michael F. Stemper"
<michael.stemper@gmail.com> wrote:

>On 19/09/2022 23.11, The Horny Goat wrote:
>
>> It has been mathematically proven that pi (and e) are irrational
>> numbers - which means in decimal terms an endless fraction never
>> repeating. (A 'rational number' aka what most of us call a fraction
>> DOES repeat even though it goes on endlessly and can always be defined
>> as x/y where x is the numerator y the denominator)
>
>Specifically, with x and y being integers (and y non-zero)
>
>> That particular one >IS< proven. Plenty more in mathematics are not -
>> doesn't mean the correct answer isn't A or B that just means we
>> haven't figured out how to prove it yet.
>
>And there are plenty more that can neither be proved nor disproved,
>at least within standard mathematics. (Obviously, if you add an
>axiom, what can be proven changes.)

Did not Goedel prove that there will /always/ be statements (in any
logic system able to support mathematics) that are clearly true but
not provable -- ie, new axioms?
--
"In this connexion, unquestionably the most significant
development was the disintegration, under Christian
influence, of classical conceptions of the family and
of family right."

On 20/09/2022 11.04, Paul S Person wrote:
> On Tue, 20 Sep 2022 08:14:38 -0500, "Michael F. Stemper"
> <michael.stemper@gmail.com> wrote:
>> On 19/09/2022 23.11, The Horny Goat wrote:

>>> That particular one >IS< proven. Plenty more in mathematics are not -
>>> doesn't mean the correct answer isn't A or B that just means we
>>> haven't figured out how to prove it yet.
>>
>> And there are plenty more that can neither be proved nor disproved,
>> at least within standard mathematics. (Obviously, if you add an
>> axiom, what can be proven changes.)
>
> Did not Goedel prove that there will /always/ be statements (in any
> logic system able to support mathematics) that are clearly true but
> not provable -- ie, new axioms?

You got it in one! Right down to the qualifier about "able to support..."

--
Michael F. Stemper
Outside of a dog, a book is man's best friend.
Inside of a dog, it's too dark to read.

On Tue, 13 Sep 2022 09:14:50 -0700, Paul S Person
<psperson@old.netcom.invalid> wrote:

>And on how large a "cubit" was.
>
>Which probably varied over time.

Of course it did - the 'cubit' was a much older unit of measurement
than the 'foot' and THAT was 14-15 inches in early medieval times
based on the actual length of the foot of which king? Edward I I think
it was?

It certainly wasn't based on the length of a platinum bar (accurate to
7 decimal places) kept under strict atmospheric conditions in a
basement vault in Paris or whatever the meter is currently based on.

On 20/09/2022 12.44, The Horny Goat wrote:
> On Tue, 13 Sep 2022 09:14:50 -0700, Paul S Person
> <psperson@old.netcom.invalid> wrote:
>
>> And on how large a "cubit" was.
>>
>> Which probably varied over time.
>
> Of course it did - the 'cubit' was a much older unit of measurement
> than the 'foot' and THAT was 14-15 inches in early medieval times
> based on the actual length of the foot of which king? Edward I I think
> it was?
>
> It certainly wasn't based on the length of a platinum bar (accurate to
> 7 decimal places) kept under strict atmospheric conditions in a
> basement vault in Paris or whatever the meter is currently based on.

Interestingly, according to NIST[1], it was standardized:

Because of its great importance, the royal cubit was standardized using
rods made from granite. These granite cubits were further subdivided
into shorter lengths reminiscent of centimeters and millimeters.

We no longer use artifacts to define the meter. Since 1983, it has been
defined in terms of a physical constant, the speed of light:

Building upon these and other advances, the meter was redefined by
international agreement in 1983 as the length of the path traveled
by light in a vacuum in 1/299,792,458 of a second.

[1] <https://www.nist.gov/si-redefinition/meter>

--
Michael F. Stemper
Outside of a dog, a book is man's best friend.
Inside of a dog, it's too dark to read.

In article <nqujih17qkvjquu6g1r7l506nfjvle9a2g@4ax.com>,
The Horny Goat <lcraver@home.ca> wrote:
>On Tue, 13 Sep 2022 09:14:50 -0700, Paul S Person
><psperson@old.netcom.invalid> wrote:
>
>>And on how large a "cubit" was.
>>
>>Which probably varied over time.
>
>Of course it did - the 'cubit' was a much older unit of measurement
>than the 'foot' and THAT was 14-15 inches in early medieval times
>based on the actual length of the foot of which king? Edward I I think
>it was?
>
>It certainly wasn't based on the length of a platinum bar (accurate to
>7 decimal places) kept under strict atmospheric conditions in a
>basement vault in Paris or whatever the meter is currently based on.

(Hal Heydt)
I beleive the meter is currently based on a specific wavelength
of light. It used to be a particular (Cesium?) hyperfine
transition, but I think that choice has been changed relatively
recently.

On 2022-09-20 11:51, Dorothy J Heydt wrote:
> In article <nqujih17qkvjquu6g1r7l506nfjvle9a2g@4ax.com>,
> The Horny Goat <lcraver@home.ca> wrote:
>> On Tue, 13 Sep 2022 09:14:50 -0700, Paul S Person
>> <psperson@old.netcom.invalid> wrote:
>>
>>> And on how large a "cubit" was.
>>>
>>> Which probably varied over time.
>>
>> Of course it did - the 'cubit' was a much older unit of measurement
>> than the 'foot' and THAT was 14-15 inches in early medieval times
>> based on the actual length of the foot of which king? Edward I I think
>> it was?
>>
>> It certainly wasn't based on the length of a platinum bar (accurate to
>> 7 decimal places) kept under strict atmospheric conditions in a
>> basement vault in Paris or whatever the meter is currently based on.
>
> (Hal Heydt)
> I beleive the meter is currently based on a specific wavelength
> of light. It used to be a particular (Cesium?) hyperfine
> transition, but I think that choice has been changed relatively
> recently.

I believe the official definition is the distance light travels in a
vacuum in 1/299,792,458 of a second, and has been since 1983.

Prior to that, in 1960, the metre was defined in terms of the the wave
length of light emitted by the krypton-86 atom; 1,650,763.73 wavelengths
to be precise.

The Horny Goat <lcraver@home.ca> wrote in
news:v2eiih53do78hvmeavf6l1lb3e87ir1fhq@4ax.com:

> On Sat, 10 Sep 2022 04:05:38 GMT, Ninapenda Jibini
> <taustinca@gmail.com> wrote:
>
>>> Don't tell me I don't know what I'm talking about because
>>> these are close family to me and clearly the message is that
>>> if you are a Catholic (however nominal) it is better to marry
>>> an atheist than a Protestant since the former MIGHT convert
>>> while the latter is far less likely to.
>>>
>>Or perhaps attitudes changed in . . . 15 years.
>>
>>But don't let that get in the way of your hate-on.
>
> Fact is I DON'T have a Catholic hate on. There are lots of
> historical reasons I could never be one but I do have family
> members who are and we get along fine.
>
> But no question I was surprised when they married my sister in
> law at the high altar given her husband's beliefs vs mine.
> Surprised - not enraged.

Then perhaps it's just too complicated for you to consider that
things might have changed in . . . 15 years.

--
Terry Austin

"Terry Austin: like the polio vaccine, only with more asshole."
-- David Bilek

Jesus forgives sinners, not criminals.

Paul S Person <psperson@old.netcom.invalid> wrote in
news:62pjihlsg6g6qkr3iak52nlnfr5ldkmdkn@4ax.com:

> On Tue, 20 Sep 2022 08:14:38 -0500, "Michael F. Stemper"
> <michael.stemper@gmail.com> wrote:
>
>>On 19/09/2022 23.11, The Horny Goat wrote:
>>
>>> It has been mathematically proven that pi (and e) are
>>> irrational numbers - which means in decimal terms an endless
>>> fraction never repeating. (A 'rational number' aka what most
>>> of us call a fraction DOES repeat even though it goes on
>>> endlessly and can always be defined as x/y where x is the
>>> numerator y the denominator)
>>
>>Specifically, with x and y being integers (and y non-zero)
>>
>>> That particular one >IS< proven. Plenty more in mathematics
>>> are not - doesn't mean the correct answer isn't A or B that
>>> just means we haven't figured out how to prove it yet.
>>
>>And there are plenty more that can neither be proved nor
>>disproved, at least within standard mathematics. (Obviously, if
>>you add an axiom, what can be proven changes.)
>
> Did not Goedel prove that there will /always/ be statements (in
> any logic system able to support mathematics) that are clearly
> true but not provable -- ie, new axioms?

I recall reading somewhere that there is a class of mathematical
hypotheses that can be proven to be true by proving (in the
mathematical sense) that they can't be proven to be false. (Or maybe
it was the other way around.)

--
Terry Austin

"Terry Austin: like the polio vaccine, only with more asshole."
-- David Bilek

Jesus forgives sinners, not criminals.

On 9/20/2022 12:20 PM, Alan wrote:
> On 2022-09-20 11:51, Dorothy J Heydt wrote:
>> In article <nqujih17qkvjquu6g1r7l506nfjvle9a2g@4ax.com>,
>> The Horny Goat  <lcraver@home.ca> wrote:
>>> On Tue, 13 Sep 2022 09:14:50 -0700, Paul S Person
>>> <psperson@old.netcom.invalid> wrote:
>>>
>>>> And on how large a "cubit" was.
>>>>
>>>> Which probably varied over time.
>>>
>>> Of course it did - the 'cubit' was a much older unit of measurement
>>> than the 'foot' and THAT was 14-15 inches in early medieval times
>>> based on the actual length of the foot of which king? Edward I I think
>>> it was?
>>>
>>> It certainly wasn't based on the length of a platinum bar (accurate to
>>> 7 decimal places) kept under strict atmospheric conditions in a
>>> basement vault in Paris or whatever the meter is currently based on.
>>
>> (Hal Heydt)
>> I beleive the meter is currently based on a specific wavelength
>> of light.  It used to be a particular (Cesium?) hyperfine
>> transition, but I think that choice has been changed relatively
>> recently.
>
> I believe the official definition is the distance light travels in a
> vacuum in 1/299,792,458 of a second, and has been since 1983.
>
> Prior to that, in 1960, the metre was defined in terms of the the wave
> length of light emitted by the krypton-86 atom; 1,650,763.73 wavelengths
> to be precise.
>
There's a Superman joke in there, I'm sure of it.

--
I've done good in this world. Now I'm tired and just want to be a cranky
dirty old man.

On Tuesday, 20 September 2022 at 18:37:52 UTC+1, Michael F. Stemper wrote:
> On 20/09/2022 11.04, Paul S Person wrote:
> > On Tue, 20 Sep 2022 08:14:38 -0500, "Michael F. Stemper"
> > <michael...@gmail.com> wrote:
> >> On 19/09/2022 23.11, The Horny Goat wrote:
>
> >>> That particular one >IS< proven. Plenty more in mathematics are not -
> >>> doesn't mean the correct answer isn't A or B that just means we
> >>> haven't figured out how to prove it yet.
> >>
> >> And there are plenty more that can neither be proved nor disproved,
> >> at least within standard mathematics. (Obviously, if you add an
> >> axiom, what can be proven changes.)
> >
> > Did not Goedel prove that there will /always/ be statements (in any
> > logic system able to support mathematics) that are clearly true but
> > not provable -- ie, new axioms?
> You got it in one! Right down to the qualifier about "able to support..."

I don't remember "clearly true", just "true". And meaning,
true in every "real" system to which the axioms apply
(for instance: axioms address how integers work,
but not what colors they are) - but not provable.
Or is it - not decidable?

I think that "Goldbach's Conjecture" could be one such
truth that can't be proved, as it hasn't: that every even
number is the sum of two prime numbers. (You need
1 as a prime number to make 2, but never mind that.)

If it isn't true, then it's "easy" to show that some number
isn't the sum of two prime numbers, although numbers
up to 4 squillion have been checked (Wikipedia) and
aren't that number. If it is true - there may be no proof
that it's true.

And despite someone checking up to 4 squillion,
I wouldn't call it "clearly true".

And if someone does prove it - then I will need another
example for this situation.

On Tuesday, September 20, 2022 at 1:20:31 PM UTC-6, Alan wrote:
> On 2022-09-20 11:51, Hal Heydt wrote:

> > I beleive the meter is currently based on a specific wavelength
> > of light. It used to be a particular (Cesium?) hyperfine
> > transition, but I think that choice has been changed relatively
> > recently.

> I believe the official definition is the distance light travels in a
> vacuum in 1/299,792,458 of a second, and has been since 1983.

> Prior to that, in 1960, the metre was defined in terms of the the wave
> length of light emitted by the krypton-86 atom; 1,650,763.73 wavelengths
> to be precise.

Of course, though, that doesn't really make him _wrong_. Because, after
all, you still have to define the *second*.

That is defined as 9,192,631,770 oscillations of Cesium-133. So the metre
is 30.66331698849836976219... wavelengths of that particular frequency of
microwaves. But since that's a complicated fraction, of course, it's not really
much of a definition...

30 and 198,858,030/299,792,458 of those Cesium wavelengths.

John Savard

On 20/09/2022 15.19, Jibini Kula Tumbili Kujisalimisha wrote:
> Paul S Person <psperson@old.netcom.invalid> wrote in
> news:62pjihlsg6g6qkr3iak52nlnfr5ldkmdkn@4ax.com:

>> On Tue, 20 Sep 2022 08:14:38 -0500, "Michael F. Stemper"
>> <michael.stemper@gmail.com> wrote:
>>
>>> On 19/09/2022 23.11, The Horny Goat wrote:

>>>> That particular one >IS< proven. Plenty more in mathematics
>>>> are not - doesn't mean the correct answer isn't A or B that
>>>> just means we haven't figured out how to prove it yet.
>>>
>>> And there are plenty more that can neither be proved nor
>>> disproved, at least within standard mathematics. (Obviously, if
>>> you add an axiom, what can be proven changes.)
>>
>> Did not Goedel prove that there will /always/ be statements (in
>> any logic system able to support mathematics) that are clearly
>> true but not provable -- ie, new axioms?
>
> I recall reading somewhere that there is a class of mathematical
> hypotheses that can be proven to be true by proving (in the
> mathematical sense) that they can't be proven to be false. (Or maybe
> it was the other way around.)

I'm doubtful. For instance, Goedel proved that the Continuum Hypothesis
cannot be proven false (under the ZFC axioms). Much later, Cohen proved
that it cannot be proven true (again, under ZFC).

So the idea that some conjecture could be proven true by proving that
it cannot be proven false seems unlikely, to say the least. This leaves
out existence conjectures, since actually coming up with a whatever the
conjecture says exists would simultaneously prove that the conjecture
could not be disproved and prove that the conjecture was true.

But, I am not a mathematician. If only there was a mathematician who
regularly posted to this group.

--
Michael F. Stemper
Psalm 82:3-4

"Michael F. Stemper" <michael.stemper@gmail.com> wrote in
news:tgda5n$1jloa$1@dont-email.me:

> On 20/09/2022 15.19, Jibini Kula Tumbili Kujisalimisha wrote:
>> Paul S Person <psperson@old.netcom.invalid> wrote in
>> news:62pjihlsg6g6qkr3iak52nlnfr5ldkmdkn@4ax.com:
>
>>> On Tue, 20 Sep 2022 08:14:38 -0500, "Michael F. Stemper"
>>> <michael.stemper@gmail.com> wrote:
>>>
>>>> On 19/09/2022 23.11, The Horny Goat wrote:
>
>>>>> That particular one >IS< proven. Plenty more in mathematics
>>>>> are not - doesn't mean the correct answer isn't A or B that
>>>>> just means we haven't figured out how to prove it yet.
>>>>
>>>> And there are plenty more that can neither be proved nor
>>>> disproved, at least within standard mathematics. (Obviously,
>>>> if you add an axiom, what can be proven changes.)
>>>
>>> Did not Goedel prove that there will /always/ be statements
>>> (in any logic system able to support mathematics) that are
>>> clearly true but not provable -- ie, new axioms?
>>
>> I recall reading somewhere that there is a class of
>> mathematical hypotheses that can be proven to be true by
>> proving (in the mathematical sense) that they can't be proven
>> to be false. (Or maybe it was the other way around.)
>
> I'm doubtful. For instance, Goedel proved that the Continuum
> Hypothesis cannot be proven false (under the ZFC axioms). Much
> later, Cohen proved that it cannot be proven true (again, under
> ZFC).

There is another category that specifically can't be proven that
way.
>
> So the idea that some conjecture could be proven true by proving
> that it cannot be proven false seems unlikely, to say the least.
> This leaves out existence conjectures, since actually coming up
> with a whatever the conjecture says exists would simultaneously
> prove that the conjecture could not be disproved and prove that
> the conjecture was true.
>
> But, I am not a mathematician. If only there was a mathematician
> who regularly posted to this group.
>
If there were, he (or she) would be incomoprehensible to everybody
else. And, possibly, themselves.

--
Terry Austin

"Terry Austin: like the polio vaccine, only with more asshole."
-- David Bilek

Jesus forgives sinners, not criminals.

Quadibloc wrote:
> On Tuesday, September 20, 2022 at 1:20:31 PM UTC-6, Alan wrote:
> > On 2022-09-20 11:51, Hal Heydt wrote:
>
> > > I beleive the meter is currently based on a specific wavelength
> > > of light. It used to be a particular (Cesium?) hyperfine
> > > transition, but I think that choice has been changed relatively
> > > recently.
>
> > I believe the official definition is the distance light travels in a
> > vacuum in 1/299,792,458 of a second, and has been since 1983.
>
> > Prior to that, in 1960, the metre was defined in terms of the the wave
> > length of light emitted by the krypton-86 atom; 1,650,763.73 wavelengths
> > to be precise.
> Of course, though, that doesn't really make him _wrong_. Because, after
> all, you still have to define the *second*.
>
> That is defined as 9,192,631,770 oscillations of Cesium-133. So the metre
> is 30.66331698849836976219... wavelengths of that particular frequency of
> microwaves. But since that's a complicated fraction, of course, it's not really
> much of a definition...

If they'da had the guts, they'd've used a transcendental number of oscillations!
The number of digits given puts us about in the range of practically no difference for more digits, (I'm picturing scientists throwing krypton wavelengths on one of those official engraved bars: "1,650,764... but it's overhanging the last atom before the mark, a bit more than a quarter wavelength over.") calculating 25 digits after the decimal would put us in the land of philosophically no difference with more digits.

--
-Jack

On 2022-09-20, Robert Carnegie <rja.carnegie@excite.com> wrote:
> On Tuesday, 20 September 2022 at 18:37:52 UTC+1, Michael F. Stemper wrote:
>> On 20/09/2022 11.04, Paul S Person wrote:
>> > On Tue, 20 Sep 2022 08:14:38 -0500, "Michael F. Stemper"
>> > <michael...@gmail.com> wrote:
>> >> On 19/09/2022 23.11, The Horny Goat wrote:
>>
>> >>> That particular one >IS< proven. Plenty more in mathematics are not -
>> >>> doesn't mean the correct answer isn't A or B that just means we
>> >>> haven't figured out how to prove it yet.
>> >>
>> >> And there are plenty more that can neither be proved nor disproved,
>> >> at least within standard mathematics. (Obviously, if you add an
>> >> axiom, what can be proven changes.)
>> >
>> > Did not Goedel prove that there will /always/ be statements (in any
>> > logic system able to support mathematics) that are clearly true but
>> > not provable -- ie, new axioms?
>> You got it in one! Right down to the qualifier about "able to support..."
>
> I don't remember "clearly true", just "true". And meaning,
> true in every "real" system to which the axioms apply
> (for instance: axioms address how integers work,
> but not what colors they are) - but not provable.
> Or is it - not decidable?
>
> I think that "Goldbach's Conjecture" could be one such
> truth that can't be proved, as it hasn't: that every even
> number is the sum of two prime numbers. (You need
> 1 as a prime number to make 2, but never mind that.)
>
> If it isn't true, then it's "easy" to show that some number
> isn't the sum of two prime numbers, although numbers
> up to 4 squillion have been checked (Wikipedia) and
> aren't that number. If it is true - there may be no proof
> that it's true.
>
> And despite someone checking up to 4 squillion,
> I wouldn't call it "clearly true".
>
> And if someone does prove it - then I will need another
> example for this situation.

No, Goldbach's Conjecture is not a good example of such a "true"
unprovable formula. There is no proof (or even inkling of a proof)
that Goldbach's Conjecture cannot be proved in Peano Arithmetic (PA).

Godel came up with such a formula. What he proved (all using PA) was
1. That all formulas and proofs of PA could be effectively encoded as
numbers.
2. That he could then effectively list all proofs of PA. Ie, the proofs (and
provable theorems) of PA were recursivly enumerable or countable or could be
put into a one to one correspondence with the integers.
3. That using this list and the rules of PA he could then come up with a
formula P that he could prove (using the rules of PA) that
3a. No proof of P existed (P was constructed so that any valid attempt
at a proof for it differed from each member on the list of all proofs.)
3b. No proof of NOT (P) existed (he showed if a proof for NOT (P) existed,
then P could be proved thus a contradiction.)

In the standard model of arithmetic, P would be considered "true" (it
is basically stating that any proof for it differs from each proof in
the list of valid proofs. Ie, that it is unprovable). In somewhat sloppy
terminology, what Godel eventually proved was that while the set of
provable theorems in PA is countable, the set of true theorems in PA
is uncountable (much bigger - basically the difference between the
number of integers and the number of real numbers). There are lots
of true formulas in PA that can't be proved!

Chris

On Tue, 20 Sep 2022 10:44:00 -0700, The Horny Goat <lcraver@home.ca>
wrote:

>On Tue, 13 Sep 2022 09:14:50 -0700, Paul S Person
><psperson@old.netcom.invalid> wrote:
>
>>And on how large a "cubit" was.
>>
>>Which probably varied over time.
>
>Of course it did - the 'cubit' was a much older unit of measurement
>than the 'foot' and THAT was 14-15 inches in early medieval times
>based on the actual length of the foot of which king? Edward I I think
>it was?
>
>It certainly wasn't based on the length of a platinum bar (accurate to
>7 decimal places) kept under strict atmospheric conditions in a
>basement vault in Paris or whatever the meter is currently based on.

I suspect you are thinking of the metre ... well, before they decided
to use light wavelengths and similar items to define it. Talk about
(hand)wavium!

The foot would then have been defined in terms of the metre.

For real fun, see how many values of "inch" there are. [1]

Each one, of course, implying a different value of "foot".

Each of them a different fraction of the metre.

[1] When I helped work on a conversion function for a project to
reproduce the behavior of a program to which the source code was
unavailable, I made two discoveries:
1. The conversion factors were very nasty; I stopped in each case when
values up to 1000 units worked properly, on the theory that paper
sizes above 1000mm were ... unlikely.
2. The space measures Pica and Cicero define "point" and "Didot point"
(respectively) as 1/72nd inch, but they turned out to be using
different inch values.
If they still do, and they very well may as they are part of the
traditional printing process, that means that at least three inch
values exist, as neither matched the value used for "inch" as a
measure of space.
--
"In this connexion, unquestionably the most significant
development was the disintegration, under Christian
influence, of classical conceptions of the family and
of family right."

On Wednesday, 21 September 2022 at 17:18:36 UTC+1, Paul S Person wrote:
> On Tue, 20 Sep 2022 10:44:00 -0700, The Horny Goat <lcr...@home.ca>
> wrote:
> >On Tue, 13 Sep 2022 09:14:50 -0700, Paul S Person
> ><pspe...@old.netcom.invalid> wrote:
> >
> >>And on how large a "cubit" was.
> >>
> >>Which probably varied over time.
> >
> >Of course it did - the 'cubit' was a much older unit of measurement
> >than the 'foot' and THAT was 14-15 inches in early medieval times
> >based on the actual length of the foot of which king? Edward I I think
> >it was?
> >
> >It certainly wasn't based on the length of a platinum bar (accurate to
> >7 decimal places) kept under strict atmospheric conditions in a
> >basement vault in Paris or whatever the meter is currently based on.
> I suspect you are thinking of the metre ... well, before they decided
> to use light wavelengths and similar items to define it. Talk about
> (hand)wavium!
>
> The foot would then have been defined in terms of the metre.
>
> For real fun, see how many values of "inch" there are. [1]
>
> Each one, of course, implying a different value of "foot".
>
> Each of them a different fraction of the metre.
>
> [1] When I helped work on a conversion function for a project to
> reproduce the behavior of a program to which the source code was
> unavailable, I made two discoveries:
> 1. The conversion factors were very nasty; I stopped in each case when
> values up to 1000 units worked properly, on the theory that paper
> sizes above 1000mm were ... unlikely.
> 2. The space measures Pica and Cicero define "point" and "Didot point"
> (respectively) as 1/72nd inch, but they turned out to be using
> different inch values.
> If they still do, and they very well may as they are part of the
> traditional printing process, that means that at least three inch
> values exist, as neither matched the value used for "inch" as a
> measure of space.

Indeed <https://en.wikipedia.org/wiki/International_yard_and_pound>
is a long story. Specifically, 0.9144 meters long (the yard),
making an inch defined, in fact, as 25.4 millimeters.

That this was being called "the industrial inch" for a while,
apparently, confirms that confusion was not quickly banished.

On Wednesday, 21 September 2022 at 16:19:11 UTC+1, Chris Buckley wrote:
> On 2022-09-20, Robert Carnegie <rja.ca...@excite.com> wrote:
> > On Tuesday, 20 September 2022 at 18:37:52 UTC+1, Michael F. Stemper wrote:
> >> On 20/09/2022 11.04, Paul S Person wrote:
> >> > On Tue, 20 Sep 2022 08:14:38 -0500, "Michael F. Stemper"
> >> > <michael...@gmail.com> wrote:
> >> >> On 19/09/2022 23.11, The Horny Goat wrote:
> >>
> >> >>> That particular one >IS< proven. Plenty more in mathematics are not -
> >> >>> doesn't mean the correct answer isn't A or B that just means we
> >> >>> haven't figured out how to prove it yet.
> >> >>
> >> >> And there are plenty more that can neither be proved nor disproved,
> >> >> at least within standard mathematics. (Obviously, if you add an
> >> >> axiom, what can be proven changes.)
> >> >
> >> > Did not Goedel prove that there will /always/ be statements (in any
> >> > logic system able to support mathematics) that are clearly true but
> >> > not provable -- ie, new axioms?
> >> You got it in one! Right down to the qualifier about "able to support..."
> >
> > I don't remember "clearly true", just "true". And meaning,
> > true in every "real" system to which the axioms apply
> > (for instance: axioms address how integers work,
> > but not what colors they are) - but not provable.
> > Or is it - not decidable?
> >
> > I think that "Goldbach's Conjecture" could be one such
> > truth that can't be proved, as it hasn't: that every even
> > number is the sum of two prime numbers. (You need
> > 1 as a prime number to make 2, but never mind that.)
> >
> > If it isn't true, then it's "easy" to show that some number
> > isn't the sum of two prime numbers, although numbers
> > up to 4 squillion have been checked (Wikipedia) and
> > aren't that number. If it is true - there may be no proof
> > that it's true.
> >
> > And despite someone checking up to 4 squillion,
> > I wouldn't call it "clearly true".
> >
> > And if someone does prove it - then I will need another
> > example for this situation.
> No, Goldbach's Conjecture is not a good example of such a "true"
> unprovable formula. There is no proof (or even inkling of a proof)
> that Goldbach's Conjecture cannot be proved in Peano Arithmetic (PA).
>
> Godel came up with such a formula. What he proved (all using PA) was
> 1. That all formulas and proofs of PA could be effectively encoded as
> numbers.
> 2. That he could then effectively list all proofs of PA. Ie, the proofs (and
> provable theorems) of PA were recursivly enumerable or countable or could be
> put into a one to one correspondence with the integers.
> 3. That using this list and the rules of PA he could then come up with a
> formula P that he could prove (using the rules of PA) that
> 3a. No proof of P existed (P was constructed so that any valid attempt
> at a proof for it differed from each member on the list of all proofs.)
> 3b. No proof of NOT (P) existed (he showed if a proof for NOT (P) existed,
> then P could be proved thus a contradiction.)
>
> In the standard model of arithmetic, P would be considered "true" (it
> is basically stating that any proof for it differs from each proof in
> the list of valid proofs. Ie, that it is unprovable). In somewhat sloppy
> terminology, what Godel eventually proved was that while the set of
> provable theorems in PA is countable, the set of true theorems in PA
> is uncountable (much bigger - basically the difference between the
> number of integers and the number of real numbers). There are lots
> of true formulas in PA that can't be proved!

Of course, Godel did it properly. But the point of doing
it, I supposed, was to establish that statements that a
mathematician might call "interesting", statements about
something other than the statement itself, might be true
as a consequence of the axioms, but not provable.
It's an answer to David Hilbert's call for the axioms of
mathematics to be refined so that those interesting
questions can all be proved or disproved (as well as the
less interesting ones), with that answer being that it
can't be done, not if the result is to be mathematics
"as we know it".

Now of course, Godel did not have a formula to decide
whether a mathematical statement is interesting.
Goldbach's conjecture surely is at least slightly interesting,
although I don't know if anything, ciphering is the main
example, could really turn on whether "the prime numbers
A and B that add up to a given even number C" exist for
every C. And it should interest most people that a
mathematical question which is reasonably easy to
understand, as a question, is either very very difficult
or actually impossible to answer. I think it shows that
there's something to this stuff.

On Wed, 21 Sep 2022 14:18:09 -0700 (PDT), Robert Carnegie
<rja.carnegie@excite.com> wrote:

>On Wednesday, 21 September 2022 at 17:18:36 UTC+1, Paul S Person wrote:
>> On Tue, 20 Sep 2022 10:44:00 -0700, The Horny Goat <lcr...@home.ca>
>> wrote:
>> >On Tue, 13 Sep 2022 09:14:50 -0700, Paul S Person
>> ><pspe...@old.netcom.invalid> wrote:
>> >
>> >>And on how large a "cubit" was.
>> >>
>> >>Which probably varied over time.
>> >
>> >Of course it did - the 'cubit' was a much older unit of measurement
>> >than the 'foot' and THAT was 14-15 inches in early medieval times
>> >based on the actual length of the foot of which king? Edward I I think
>> >it was?
>> >
>> >It certainly wasn't based on the length of a platinum bar (accurate to
>> >7 decimal places) kept under strict atmospheric conditions in a
>> >basement vault in Paris or whatever the meter is currently based on.
>> I suspect you are thinking of the metre ... well, before they decided
>> to use light wavelengths and similar items to define it. Talk about
>> (hand)wavium!
>>
>> The foot would then have been defined in terms of the metre.
>>
>> For real fun, see how many values of "inch" there are. [1]
>>
>> Each one, of course, implying a different value of "foot".
>>
>> Each of them a different fraction of the metre.
>>
>> [1] When I helped work on a conversion function for a project to
>> reproduce the behavior of a program to which the source code was
>> unavailable, I made two discoveries:
>> 1. The conversion factors were very nasty; I stopped in each case when
>> values up to 1000 units worked properly, on the theory that paper
>> sizes above 1000mm were ... unlikely.
>> 2. The space measures Pica and Cicero define "point" and "Didot point"
>> (respectively) as 1/72nd inch, but they turned out to be using
>> different inch values.
>> If they still do, and they very well may as they are part of the
>> traditional printing process, that means that at least three inch
>> values exist, as neither matched the value used for "inch" as a
>> measure of space.
>
>Indeed <https://en.wikipedia.org/wiki/International_yard_and_pound>
>is a long story. Specifically, 0.9144 meters long (the yard),
>making an inch defined, in fact, as 25.4 millimeters.
>
>That this was being called "the industrial inch" for a while,
>apparently, confirms that confusion was not quickly banished.

Did it say anything about Pica and/or Cicero converting to the
industrial inch? Or have they just dropped out of use entirely?
--
"In this connexion, unquestionably the most significant
development was the disintegration, under Christian
influence, of classical conceptions of the family and
of family right."

On Thursday, September 22, 2022 at 9:47:57 AM UTC-6, Paul S Person wrote:

> Did it say anything about Pica and/or Cicero converting to the
> industrial inch? Or have they just dropped out of use entirely?

Oh, my dear, no. It is still the case, at least in English-speaking countries,
that a point is 0.013837 inches rather than 1/72 of an inch. However, it
very likely _is_ true that the point is now 0.013837 of an inch of 2.54
centimeters (the "industrial inch" that was an unofficial standard before it
became the official standard) rather than 0.013837 of what is still the
inch of U.S. survey measure... 39.37 inches to the metre. That would simply
be due to the fact that people making printing equipment would use whatever
precise measuring tools they had available.

As for the Didot point, however, twelve of which make a Cicero rather than a
Pica, the Europeans have been more ready to somehow convert it to metric.
However, there is no one single standard for the new metric Didot point.

In 1879, Berthold revised the Didot point by decoupling it from the old _pied du
Roi_ by making it 1/2660th of a metre. Later on, the most common European
Didot point was 0.376065 mm; Berthold rounded it to 0.376; 0.375 has been proposed,
and 0.4 was actually used by the French Imprimerie Nationale. So the situation
is quite chaotic with multiple standards as far as I know. But my information may
be out of date. Perhaps the situation is already resolved, or everybody is just
using Japanese-made laser printers and a point of exactly 1/72 of a U.S. inch.

John Savard

On Friday, September 23, 2022 at 9:18:47 AM UTC-6, Quadibloc wrote:
> On Thursday, September 22, 2022 at 9:47:57 AM UTC-6, Paul S Person wrote:

> > Did it say anything about Pica and/or Cicero converting to the
> > industrial inch? Or have they just dropped out of use entirely?

> That would simply
> be due to the fact that people making printing equipment would use whatever
> precise measuring tools they had available.

I've checked up on this a bit more. The American Typefounders Association adopted
the point of 0.013837 inches in 1886; while it wasn't until 1959 that the U.S. adopted
the inch of 2.54 centimeters officially (the United Kingdom in 1964, Canada in 1951)
machinists had started using that inch ever since 1912, thanks to the calibration blocks
made by Carl Edvard Johansson.

Since 1886 predates 1912, it actually _is_ meaningful to speak of converting the
Anglo-American printer's point to the "industrial inch", even if I suspect this was just
done automatically and unconsciously.

John Savard

On Tuesday, September 20, 2022 at 4:20:19 PM UTC-4, Dimensional Traveler wrote:
> On 9/20/2022 12:20 PM, Alan wrote:
> > On 2022-09-20 11:51, Dorothy J Heydt wrote:
> >> In article <nqujih17qkvjquu6g...@4ax.com>,
> >> The Horny Goat <lcr...@home.ca> wrote:
> >>> On Tue, 13 Sep 2022 09:14:50 -0700, Paul S Person
> >>> <pspe...@old.netcom.invalid> wrote:
> >>>
> >>>> And on how large a "cubit" was.
> >>>>
> >>>> Which probably varied over time.
> >>>
> >>> Of course it did - the 'cubit' was a much older unit of measurement
> >>> than the 'foot' and THAT was 14-15 inches in early medieval times
> >>> based on the actual length of the foot of which king? Edward I I think
> >>> it was?
> >>>
> >>> It certainly wasn't based on the length of a platinum bar (accurate to
> >>> 7 decimal places) kept under strict atmospheric conditions in a
> >>> basement vault in Paris or whatever the meter is currently based on.
> >>
> >> (Hal Heydt)
> >> I beleive the meter is currently based on a specific wavelength
> >> of light. It used to be a particular (Cesium?) hyperfine
> >> transition, but I think that choice has been changed relatively
> >> recently.
> >
> > I believe the official definition is the distance light travels in a
> > vacuum in 1/299,792,458 of a second, and has been since 1983.
> >
> > Prior to that, in 1960, the metre was defined in terms of the the wave
> > length of light emitted by the krypton-86 atom; 1,650,763.73 wavelengths
> > to be precise.
> >
> There's a Superman joke in there, I'm sure of it.
>

"Faster than a speeding photon...."

Photons don't go "ka-pweeng"* though, AFAIK.

* https://kittysneezes.com/mad-4/

--
Kevin R

On Friday, September 23, 2022 at 12:12:14 PM UTC-4, Quadibloc wrote:
> On Friday, September 23, 2022 at 9:18:47 AM UTC-6, Quadibloc wrote:
> > On Thursday, September 22, 2022 at 9:47:57 AM UTC-6, Paul S Person wrote:
>
> > > Did it say anything about Pica and/or Cicero converting to the
> > > industrial inch? Or have they just dropped out of use entirely?
> > That would simply
> > be due to the fact that people making printing equipment would use whatever
> > precise measuring tools they had available.
> I've checked up on this a bit more. The American Typefounders Association adopted
> the point of 0.013837 inches in 1886; while it wasn't until 1959 that the U.S. adopted
> the inch of 2.54 centimeters officially (the United Kingdom in 1964, Canada in 1951)
> machinists had started using that inch ever since 1912, thanks to the calibration blocks
> made by Carl Edvard Johansson.
>
> Since 1886 predates 1912, it actually _is_ meaningful to speak of converting the
> Anglo-American printer's point to the "industrial inch", even if I suspect this was just
> done automatically and unconsciously.

There was something called a "Disney inch" mentioned in an animation book I read once. Back when they were inventing the tools of animation, the Disney company -I forget if by accident or on purpose- built one piece of a different size than the rest of the industry. Animators moving back and forth complained. I've tried researching it online, but I don't know what words to look for. "Disney inch" does find a study on the shrinking of the plastic used for the animation drawings, and a site with the sentence, "Contrary to popular belief, the Weber designed animation furniture for Disney was not built on the Studio lot." which makes me feel really uninformed.

--
-Jack

On Fri, 23 Sep 2022 08:18:45 -0700 (PDT), Quadibloc
<jsavard@ecn.ab.ca> wrote:

>On Thursday, September 22, 2022 at 9:47:57 AM UTC-6, Paul S Person wrote:
>
>> Did it say anything about Pica and/or Cicero converting to the
>> industrial inch? Or have they just dropped out of use entirely?
>
>Oh, my dear, no. It is still the case, at least in English-speaking countries,
>that a point is 0.013837 inches rather than 1/72 of an inch. However, it
>very likely _is_ true that the point is now 0.013837 of an inch of 2.54
>centimeters (the "industrial inch" that was an unofficial standard before it
>became the official standard) rather than 0.013837 of what is still the
>inch of U.S. survey measure... 39.37 inches to the metre. That would simply
>be due to the fact that people making printing equipment would use whatever
>precise measuring tools they had available.
>
>As for the Didot point, however, twelve of which make a Cicero rather than a
>Pica, the Europeans have been more ready to somehow convert it to metric.
>However, there is no one single standard for the new metric Didot point.
>
>In 1879, Berthold revised the Didot point by decoupling it from the old _pied du
>Roi_ by making it 1/2660th of a metre. Later on, the most common European
>Didot point was 0.376065 mm; Berthold rounded it to 0.376; 0.375 has been proposed,
>and 0.4 was actually used by the French Imprimerie Nationale. So the situation
>is quite chaotic with multiple standards as far as I know. But my information may
>be out of date. Perhaps the situation is already resolved, or everybody is just
>using Japanese-made laser printers and a point of exactly 1/72 of a U.S. inch.

Thankfully, all /I/ had to do was match the original. Whatever
conversion factor was needed.

This is like a math class where the instructor stated that base-10
logs were obsolete and never to be used, only to be reminded that
decibals, earthquakes and (IIRC) hurricanes are /all/ measured on
base-10 scales.

And they appear to be measured that way yet today.

The French may have succeeded with the meter and related physical
units, but their attempt to do the same with time (calendar, week (?),
hours (?)) failed miserably.
--
"In this connexion, unquestionably the most significant
development was the disintegration, under Christian
influence, of classical conceptions of the family and
of family right."