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Re: value of pi and 22/7

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  Re: value of pi and 22/7 Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-17 16:12 -0700
    Re: value of pi and 22/7 Ian Kelly <ian.g.kelly@gmail.com> - 2016-06-17 17:49 -0600
      Re: value of pi and 22/7 Steven D'Aprano <steve@pearwood.info> - 2016-06-18 11:19 +1000
        Re: value of pi and 22/7 Ethan Furman <ethan@stoneleaf.us> - 2016-06-17 19:27 -0700
        Re: value of pi and 22/7 Tim Harig <timharig@eternal-september.org> - 2016-06-18 05:47 +0000
          Re: value of pi and 22/7 boB Stepp <robertvstepp@gmail.com> - 2016-06-18 10:22 -0500
        Re: value of pi and 22/7 Christian Gollwitzer <auriocus@gmx.de> - 2016-06-18 09:56 +0200
    Re: value of pi and 22/7 Random832 <random832@fastmail.com> - 2016-06-17 23:48 -0400
      Re: value of pi and 22/7 Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-17 21:30 -0700
        Re: value of pi and 22/7 Ian Kelly <ian.g.kelly@gmail.com> - 2016-06-17 23:18 -0600
          Re: value of pi and 22/7 Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-20 10:25 +1200
            Re: value of pi and 22/7 Steven D'Aprano <steve@pearwood.info> - 2016-06-20 12:07 +1000
              Re: value of pi and 22/7 Grant Edwards <grant.b.edwards@gmail.com> - 2016-06-20 18:06 +0000
            Re: value of pi and 22/7 Ian Kelly <ian.g.kelly@gmail.com> - 2016-06-19 23:19 -0600
              Re: value of pi and 22/7 Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-06-20 16:22 +1000
                Re: value of pi and 22/7 Ian Kelly <ian.g.kelly@gmail.com> - 2016-06-20 10:01 -0600
                  Re: value of pi and 22/7 Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-06-21 18:38 +1000
                Re: value of pi and 22/7 Ian Kelly <ian.g.kelly@gmail.com> - 2016-06-20 10:09 -0600
            Re: value of pi and 22/7 Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-19 22:51 -0700
              Re: value of pi and 22/7 Marko Rauhamaa <marko@pacujo.net> - 2016-06-20 10:32 +0300
                Re: value of pi and 22/7 Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-20 01:01 -0700
                  Re: value of pi and 22/7 Wildman <best_lay@yahoo.com> - 2016-06-20 17:24 -0500
                    Re: value of pi and 22/7 Marko Rauhamaa <marko@pacujo.net> - 2016-06-21 01:47 +0300
                    Re: value of pi and 22/7 Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-22 14:20 -0700
        Re: value of pi and 22/7 Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-20 10:14 +1200
          Re: value of pi and 22/7 Grant Edwards <grant.b.edwards@gmail.com> - 2016-06-20 17:53 +0000
          Re: value of pi and 22/7 Marko Rauhamaa <marko@pacujo.net> - 2016-06-20 21:52 +0300
            Re: value of pi and 22/7 Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-22 00:52 +1200
    Re: value of pi and 22/7 Pete Forman <petef4+usenet@gmail.com> - 2016-06-18 13:05 +0100
    Re: value of pi and 22/7 Johannes Bauer <dfnsonfsduifb@gmx.de> - 2016-06-18 18:09 +0200

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#110067 — Re: value of pi and 22/7

On Saturday, March 19, 2011 at 3:16:41 AM UTC+13, Grant Edwards wrote:
>
> On 2011-03-18, peter wrote:
> 
>> The Old Testament (1 Kings 7,23) says ... "And he made a molten sea,
>> ten cubits from the one brim to the other: it was round all about, and
>> his height was five cubits: and a line of thirty cubits did compass it
>> round about. ".  So pi=3.  End Of.
> 
> There's nothing wrong with that value.  The measurements were given
> with one significant digit, so the ratio of the two measurements
> should only have one significant digit.

I’m not sure how you can write “30” with one digit...

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#110068

On Jun 17, 2016 5:44 PM, "Lawrence D’Oliveiro" <lawrencedo99@gmail.com>
wrote:
>
> On Saturday, March 19, 2011 at 3:16:41 AM UTC+13, Grant Edwards wrote:
> >
> > On 2011-03-18, peter wrote:
> >
> >> The Old Testament (1 Kings 7,23) says ... "And he made a molten sea,
> >> ten cubits from the one brim to the other: it was round all about, and
> >> his height was five cubits: and a line of thirty cubits did compass it
> >> round about. ".  So pi=3.  End Of.
> >
> > There's nothing wrong with that value.  The measurements were given
> > with one significant digit, so the ratio of the two measurements
> > should only have one significant digit.
>
> I’m not sure how you can write “30” with one digit...

If I tell you that the speed of light is 300,000,000 m/s, do you think that
measurement has 9 significant digits? If you do, then you would be wrong.

By the way, you're also replying to posts that are more than 5 years old.

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#110075

On Sat, 18 Jun 2016 09:49 am, Ian Kelly wrote:

> If I tell you that the speed of light is 300,000,000 m/s, do you think
> that measurement has 9 significant digits? If you do, then you would be
> wrong.

Hmmm.

If I tell you that some physical phenomenon [let's call it the speed of
light] is 299,999,999 m/s, how many significant digits would I be using?

What if I tell you that it's 300,000,001 m/s?

What if the figure to nine significant digits *actually is* three followed
by eight zeroes?

For all that it is in widespread use, I think the concept of "significant
figures" is inherently ambiguous.



-- 
Steven

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#110080

On 06/17/2016 06:19 PM, Steven D'Aprano wrote:
> On Sat, 18 Jun 2016 09:49 am, Ian Kelly wrote:

>> If I tell you that the speed of light is 300,000,000 m/s, do you think
>> that measurement has 9 significant digits? If you do, then you would be
>> wrong.
>
> Hmmm.
>
> If I tell you that some physical phenomenon [let's call it the speed of
> light] is 299,999,999 m/s, how many significant digits would I be using?

I know!  I know!  9!

> What if I tell you that it's 300,000,001 m/s?

Oh!  9 again!

> What if the figure to nine significant digits *actually is* three followed
> by eight zeroes?

Hmmm... thinking.... thinking... oh yeah!  You put a bar over the last 
significant digit -- or you use scientific notation:

30e7 has two significant digits.

> For all that it is in widespread use, I think the concept of "significant
> figures" is inherently ambiguous.

Not at all -- just have to keep your notations correct*.

--
~Ethan~

* Mine might be 30 years out of date, but maybe not.

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#110086

On 2016-06-18, Steven D'Aprano <steve@pearwood.info> wrote:
> On Sat, 18 Jun 2016 09:49 am, Ian Kelly wrote:
>
>> If I tell you that the speed of light is 300,000,000 m/s, do you think
>> that measurement has 9 significant digits? If you do, then you would be
>> wrong.
> What if the figure to nine significant digits *actually is* three followed
> by eight zeroes?

The you can either write it as 300000000. (notice the trailing decimal
indicating that all of the zeros are indeed significant) or write it it
scientific notation.

> For all that it is in widespread use, I think the concept of "significant
> figures" is inherently ambiguous.

Only for those who do not understand it.

The main problem I have with significant figures is that measurement
accuracy is often not constrained to a decimal system.  A scale that can
measure in 1/5 units is more accurate than a scale that can measure only
in whole units but it is not as accurate as a scale that can measure
all 1/10 units.  Therefore it effectively has a fractional number of
significant figures.

I could just cut my loses and express the lower number of significant
figures but, I usually express the error explicitly instead:

<measurement> +- 0.2 units

where +- looks like the &plusmn; html entity.

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#110102

On Sat, Jun 18, 2016 at 12:47 AM, Tim Harig
<timharig@eternal-september.org> wrote:

>
> The main problem I have with significant figures is that measurement
> accuracy is often not constrained to a decimal system.  A scale that can
> measure in 1/5 units is more accurate than a scale that can measure only
> in whole units but it is not as accurate as a scale that can measure
> all 1/10 units.  Therefore it effectively has a fractional number of
> significant figures.

Probably in this type of discussion a more careful distinction between
"precision" and "accuracy" should be made.  A measuring instrument may
allow for many significant digits in its reported result, giving it a
high level of precision, but could, in fact, be giving an inaccurate
measurement (How close it is to the "true" value.), especially if it
is an instrument that has not been properly calibrated (Made to agree
as well as possible with known standards.).

boB

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#110090

Am 18.06.16 um 03:19 schrieb Steven D'Aprano:
> If I tell you that some physical phenomenon [let's call it the speed of
> light] is 299,999,999 m/s, how many significant digits would I be using?
>
> What if I tell you that it's 300,000,001 m/s?
>
> What if the figure to nine significant digits *actually is* three followed
> by eight zeroes?

You can't read off the number of significant figures from a value 
itself, it must be given as a side information. It is a common way to 
indicate uncertainty estimes, however, by giving a number to as many 
decimal places as there are significant digits, i.e. to indicate the 
uncertainty as a power of ten. You need to use exponential notation to 
express that clearly, in that case:

	3*10^8 -> (3 +/- 0.5) * 10^8
	3.0 *10^8 -> (3.0 +/- 0.05)*10^8

For more accurate error estimates, the second notation is used. Another 
common way to express this is something like

	3.42(3) which means 3.42 +/- 0.03

Note, however, that in current SI units the speed of light is known exactly:

	c = 299,792,458 m/s

There is no error! This is possible because the unit metre is defined by 
this value from the unit second.

	Christian

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#110081

On Fri, Jun 17, 2016, at 19:12, Lawrence D’Oliveiro wrote:
> I’m not sure how you can write “30” with one digit...

One *significant* digit. Though, as it happens, some ancient number
systems, including Hebrew and Greek, have one set of digits for 1-9, one
for 10-90, and one for 100-900.

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#110083

On Saturday, June 18, 2016 at 3:48:43 PM UTC+12, Random832 wrote:
>
> On Fri, Jun 17, 2016, at 19:12, Lawrence D’Oliveiro wrote:
>>
>> I’m not sure how you can write “30” with one digit...
> 
> One *significant* digit.

Like some credulous past-Bronze-age tribespeople understood the concept of “significant digits” ...

I wonder what the quality of their workmanship was like, if a measurement accurate to one significant digit was considered sufficient ...

I feel a new phrase coming on: “good enough for Bible work”!

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#110085

On Fri, Jun 17, 2016 at 10:30 PM, Lawrence D’Oliveiro
<lawrencedo99@gmail.com> wrote:
> On Saturday, June 18, 2016 at 3:48:43 PM UTC+12, Random832 wrote:
>>
>> On Fri, Jun 17, 2016, at 19:12, Lawrence D’Oliveiro wrote:
>>>
>>> I’m not sure how you can write “30” with one digit...
>>
>> One *significant* digit.
>
> Like some credulous past-Bronze-age tribespeople understood the concept of “significant digits” ...

I don't see why they should need to in order to measure one thing as
"thirty cubits" and another thing as "ten cubits" and write those
numbers down. Remember, the cubit was based on the length of the
forearm, so it's not like it was a terribly precise measurement to
begin with; they might not have understood significant figures, but
they probably wouldn't have been overly concerned about the difference
between thirty and thirty-one.

Check out the rest of the chapter. Every single measurement in it
above seven is a multiple of ten.

> I wonder what the quality of their workmanship was like, if a measurement accurate to one significant digit was considered sufficient ...

You realize there can be a difference between the quality to which
something is constructed and the precision of the measurements later
used to describe it? "Threescore cubits long"  is an impressive
figure. "61 and a half cubits" doesn't do the job of communicating the
scale any better, and ultimately amounts to wasted words in what was
originally an oral tradition.

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#110159

Ian Kelly wrote:
>  Remember, the cubit was based on the length of the
> forearm, so it's not like it was a terribly precise measurement to
> begin with;

Let's not sell them short. Just because it was based on a forearm
doesn't mean they didn't have a precise standard for it, any more
than people who measure things in "feet" do it by plonking down
their own foot.

No doubt it wasn't as precise as what we have nowadays, but
it was probably a lot better than human body part variations.

> they might not have understood significant figures, but
> they probably wouldn't have been overly concerned about the difference
> between thirty and thirty-one.

If you're building something the size of a pyramid, that could
add up to quite a lot of error.

-- 
Greg

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#110165

On Mon, 20 Jun 2016 08:25 am, Gregory Ewing wrote:

> Ian Kelly wrote:
>>  Remember, the cubit was based on the length of the
>> forearm, so it's not like it was a terribly precise measurement to
>> begin with;
> 
> Let's not sell them short. Just because it was based on a forearm
> doesn't mean they didn't have a precise standard for it, any more
> than people who measure things in "feet" do it by plonking down
> their own foot.
> 
> No doubt it wasn't as precise as what we have nowadays, but
> it was probably a lot better than human body part variations.

And let's not make the mistake of presentism, judging the past by the
standards of the present.

The biggest problem with the cubit is not that it is *inaccurate*, as that
different places had their own idea of what a cubit was. I dare say that on
any specific building site, the foreman would ensure that everyone was
working with more or less the same idea of what a cubit was. But once you
moved from one village or town to another, chances are that they were using
a different idea of a cubit that was not quite the same as yours.

To be honest, I don't actually know much about the situation in Ancient
Egypt. For all I know, every tradesman did measure his bit of the pyramid
by laying his forearm down on the rock and adjusting by eye. (But I doubt
it.) And they did have two distinct measures, what we today call the "Royal
cubit" and the "short cubit". So I expect that there actually was quite a
bit of day to day confusion and frustration due to the lack of accurate and
consistent measurements.

One of the most underrated yet critical functions of government is to
standardise weights and measures, and that function evolved very slowly
over time. I doubt that the Egyptian Pharoahs cared about it, although
their scribes probably did, a bit.

If you look at, say, Medieval and even Renaissance Europe, one of the
biggest problems people faced was the lack of standard definitions of
units. Every village and town had their own idea of what a hogshead was, to
say nothing of unscrupulous merchants who would deliberately underweigh or
undermeasure. It was a big enough problem that governments eventually
evolved entire bureaucracies to ensure that when you ordered 10000 yards of
cloth, you got 10000 yards of cloth, and not an argument about what a yard
actually is.

But even today, we still have lack of agreement at the national level:
1,000,000 US gallons are about 832,674 UK gallons. Similarly for miles: US
statute miles are ever-so-slightly less than UK miles.

But at least the metric system is the same everywhere.


>> they might not have understood significant figures, but
>> they probably wouldn't have been overly concerned about the difference
>> between thirty and thirty-one.
> 
> If you're building something the size of a pyramid, that could
> add up to quite a lot of error.

Indeed.


-- 
Steven

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#110210

On 2016-06-20, Steven D'Aprano <steve@pearwood.info> wrote:

> One of the most underrated yet critical functions of government is
> to standardise weights and measures, and that function evolved very
> slowly over time. I doubt that the Egyptian Pharoahs cared about it,

Oh, I bet they did.  How you measure things affects how much tax you
collect -- and the people at the top of every government pay a lot of
attention to that.  The state doesn't check all those gas pumps
against a volumetric flask every year to protect Joe Carowner.  I've
designed various sorts of measurement and instrumentation, and when a
device is used for doing a measurement that affects how much tax gets
paid, things get deadly serious.

> although their scribes probably did, a bit.

-- 
Grant Edwards               grant.b.edwards        Yow! Vote for ME -- I'm
                                  at               well-tapered, half-cocked,
                              gmail.com            ill-conceived and
                                                   TAX-DEFERRED!

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#110174

On Sun, Jun 19, 2016 at 4:25 PM, Gregory Ewing
<greg.ewing@canterbury.ac.nz> wrote:
> Ian Kelly wrote:
>>
>>  Remember, the cubit was based on the length of the
>> forearm, so it's not like it was a terribly precise measurement to
>> begin with;
>
>
> Let's not sell them short. Just because it was based on a forearm
> doesn't mean they didn't have a precise standard for it, any more
> than people who measure things in "feet" do it by plonking down
> their own foot.
>
> No doubt it wasn't as precise as what we have nowadays, but
> it was probably a lot better than human body part variations.

Sure, but I think you've missed my central point, which is not that
they wouldn't have made reasonably precise measurements in
construction, but only that the storytellers would have rounded things
off for their audience.

We still do the same thing today. A house appraisal will report its
footprint to the nearest square foot, but most people when talking
about it casually aren't going to say "my house is 1936 square feet".
More likely they'll just say "about 1900 square feet", since past the
first couple of digits nobody really cares.

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#110179

On Monday 20 June 2016 15:19, Ian Kelly wrote:

> Sure, but I think you've missed my central point, which is not that
> they wouldn't have made reasonably precise measurements in
> construction, but only that the storytellers would have rounded things
> off for their audience.
> 
> We still do the same thing today. A house appraisal will report its
> footprint to the nearest square foot, but most people when talking
> about it casually aren't going to say "my house is 1936 square feet".
> More likely they'll just say "about 1900 square feet", since past the
> first couple of digits nobody really cares.

There's a difference though. Nobody has tried to legislate the value of pi to 
match your casual reference to "about 1900 square feet", but there's been at 
least one serious attempt to legislate the value of pi to match the implied 
value given by the Bible.

And some very large percentage of people in the world, especially in but not 
limited to the USA, will dispute your suggestion that "storytellers would have 
rounded things off for their audience" on the basis that every single word in 
the Bible is the inerrant, literal word of the god known as God. If the Bible 
implies that pi is 3, then by gum, that means it is 3.

Or at least, that's what they *say* they believe. In practice, the literalists 
accept that the Bible contains metaphors, stories, and other non-literal text 
the same as everyone else does, they just pick and choose[1] which bits they 
choose to accept as literal in ways that strike others as naive, stupid, out-
dated or outright wicked.




[1] To be fair, as we all do, as the ancient Hebrews unaccountably failed to 
mark up their texts using <metaphor> <sarcasm> <just kidding> <we really mean 
this one> tags.

-- 
Steve

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#110206

On Mon, Jun 20, 2016 at 12:22 AM, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> There's a difference though. Nobody has tried to legislate the value of pi to
> match your casual reference to "about 1900 square feet", but there's been at
> least one serious attempt to legislate the value of pi to match the implied
> value given by the Bible.

If you're referring the Indiana Pi Bill of 1897, it was actually a
poorly conceived attempt to publish an amateur mathematician's claim
of a way to square the circle. It had nothing to do with biblical
interpretation and would have implied a value for pi of 3.2, not 3.

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

I'm not aware of any other such legislative attempts. Snopes records
one that allegedly occurred in Indiana but dismisses the claim as
false.

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#110223

On Tuesday 21 June 2016 02:01, Ian Kelly wrote:

> On Mon, Jun 20, 2016 at 12:22 AM, Steven D'Aprano
> <steve+comp.lang.python@pearwood.info> wrote:
>> There's a difference though. Nobody has tried to legislate the value of pi
>> to match your casual reference to "about 1900 square feet", but there's been
>> at least one serious attempt to legislate the value of pi to match the
>> implied value given by the Bible.
> 
> If you're referring the Indiana Pi Bill of 1897, it was actually a
> poorly conceived attempt to publish an amateur mathematician's claim
> of a way to square the circle. It had nothing to do with biblical
> interpretation and would have implied a value for pi of 3.2, not 3.
> 
> https://en.wikipedia.org/wiki/Indiana_Pi_Bill

Thanks for the link, that's interesting.




-- 
Steve

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#110207

On Mon, Jun 20, 2016 at 10:01 AM, Ian Kelly <ian.g.kelly@gmail.com> wrote:
> I'm not aware of any other such legislative attempts. Snopes records
> one that allegedly occurred in Indiana but dismisses the claim as
> false.

s/Indiana/Alabama

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#110176

On Monday, June 20, 2016 at 10:26:03 AM UTC+12, Gregory Ewing wrote:

> If you're building something the size of a pyramid, that could
> add up to quite a lot of error.

Particularly since so many of their neighbours had worked out how to do much better than that, thousands of years earlier...

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#110181

Lawrence D’Oliveiro <lawrencedo99@gmail.com>:

> On Monday, June 20, 2016 at 10:26:03 AM UTC+12, Gregory Ewing wrote:
>
>> If you're building something the size of a pyramid, that could
>> add up to quite a lot of error.
>
> Particularly since so many of their neighbours had worked out how to
> do much better than that, thousands of years earlier...

Width/height ratio of the pyramid of Cheops was so close to π/2 that UFO
enthusiasts were convinced alien technology was used in the construction
of the pyramids.

The whole story involving cubits, drums and fingers is here: <URL:
http://doernenburg.alien.de/alternativ/pyramide/pyr12_e.php>.

   This is the definite proof, that no god, astronaut or Atlantean
   wizard had any intention of coding Pi into one of the many pyramids
   erected in Egypt. Pi is simply a result of the measurement methods
   used in old Egypt!


Marko

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