«

ah - yes, of course

And parallel lines are merely those lines which meet at infinity

the Arty one

"David Littlewood" <> wrote in message
news:...
> In article <cfb0sl$ojs$>, Dave Martindale
> <> writes
> >"Arty Phacting" <> writes:
> >>ah - but are there infinitely many infinities?
> >
> >In what context? In optics, there is only one - it means the rays are
> >parallel.
> >
> >In mathematics, there are various things called infinity depending on
> >context.
> >
> >How many do you need?
> >
> > Dave
>
> There are, ahem, infinitely many in mathematics. The one usually
> referred to is aleph-null in Cantor's nomenclature: the countable
> numbers. Aleph-1, the real numbers, can be shown by a very elegant proof
> (by Cantor) to be such that it cannot be put into one-to-one
> correspondence with aleph-null. Higher orders similarly, though there is
> no easily understandable description as for the first two.
>
> Interestingly, not all mathematics proceeds on the basis that parallel
> lines continue forever at the same distance apart. This (Euclid's fifth?
> postulate) is no more than an assumption. In the geometry of Riemann,
> parallel lines will eventually meet, whereas in the geometry of
> Lobachevsky they will diverge. Some scientists have speculated that the
> universe may in fact follow Riemann geometry (but only over very great
> distances) and be finite without bounds.
>
> None of which is, of course, of any significance for photography.
> --
> David Littlewood

In message <>,
Ron Hunter <> wrote:

>For practical purposes, anything over 50 away from an ordinary sized
>lens will be 'infinite' focus.

That's a generalization that falls apart, however, with fast lenses or
telephoto lenses.
--

<>>< ><<> ><<> <>>< ><<> <>>< <>>< ><<>
John P Sheehy <>
><<> <>>< <>>< ><<> <>>< ><<> ><<> <>><

In message <RISRc.309$>,
"Arty Phacting" <> wrote:

>ah - but are there infinitely many infinities?

Sure -- if they are enumerated, and
there is no length limit to a number, then nothing can stop them from
being infinite in number, as long as their needs are meager enough for
them to exist only hypothetically (and not require any unique material
associations).

Hope this helps.
--

<>>< ><<> ><<> <>>< ><<> <>>< <>>< ><<>
John P Sheehy <>
><<> <>>< <>>< ><<> <>>< ><<> ><<> <>><

In message <g7wSc.1898$>,
"Arty Phacting" <> wrote:

>does hypothetical existence imply non-reality?

I'm sorry, but I'm not allowed to divulge that information.

><> wrote in message
>news:.. .
>> In message <RISRc.309$>,
>> "Arty Phacting" <> wrote:
>>
>> >ah - but are there infinitely many infinities?
>>
>> Sure -- if they are enumerated, and
>> there is no length limit to a number, then nothing can stop them from
>> being infinite in number, as long as their needs are meager enough for
>> them to exist only hypothetically (and not require any unique material
>> associations).
>>
>> Hope this helps.

--

<>>< ><<> ><<> <>>< ><<> <>>< <>>< ><<>
John P Sheehy <>
><<> <>>< <>>< ><<> <>>< ><<> ><<> <>><

does hypothetical existence imply non-reality?

Arts

<> wrote in message
news:...
> In message <RISRc.309$>,
> "Arty Phacting" <> wrote:
>
> >ah - but are there infinitely many infinities?
>
> Sure -- if they are enumerated, and
> there is no length limit to a number, then nothing can stop them from
> being infinite in number, as long as their needs are meager enough for
> them to exist only hypothetically (and not require any unique material
> associations).
>
> Hope this helps.
> --
>
> <>>< ><<> ><<> <>>< ><<> <>>< <>>< ><<>
> John P Sheehy <>
> ><<> <>>< <>>< ><<> <>>< ><<> ><<> <>><

David Littlewood <> wrote:
> In article <4118e022$0$524$>, Ian
> Stirling <> writes
>>Lazarus Long <> wrote:
>>> I'm a relative newbie to most of the features of a "modern" camera.
>>>
>>> My question is about focusing - how close, is infinite focus. My
>>> camera is a Coolpix 5400. 20 feet? 30 feet?
>>
>>Infinite focus means that the camera takes a parallel beam of light,
>>and focuses it onto one pixel.
>
> I think this loose thinking is likely to get you - or someone - into a
> mathematical mess. A lens would take parallel light from an
> infinitely-distant source and focus it onto a ^point^. That is a
<snip>

You are of course correct that it's not really a point, but a pixel.


>>Consider it in reverse as a projector, with the beams shining on a screen.
>>You can see that as you get closer, the beams start to overlap.
>>
>>As a ballpark, you can consider infinite focus to be where the pixel
>>pitch is equal to the lens diameter (more accurately it depends on what
>>the apature is, but lens diameter is easier, and can it can never be better
>>than this).
>>
>>Say the lens is 1cm across (to the beginning of the mounting).
>>
>>For a 5Mp camera, this is about 2000*2500Mp, so if the scene is more than
>>20m*25m, then it'll be in focus, if set to infinity.
>>
>>So, for pretty much most planes, if it's not filling the frame, you'r fine.
>>
>>
> This seems awfully optimistic to me, for a lens wide open. Of course, it
> depends how big and how sharp you want the final result to be, and how
> it's going to be viewed.

The above assumption is worst case.
In practice the size of the field at 'infinity' will be smaller than this,
due to the apature not being the same as the clear apature, and blurring
making it slightly less defined.

Or am I missing something.

"Ian Stirling" <> wrote in message
news:411a919c$0$513$...
> David Littlewood <> wrote:
> > In article <4118e022$0$524$>, Ian
> > Stirling <> writes
> >>Lazarus Long <> wrote:
> >>> I'm a relative newbie to most of the features of a "modern" camera.
> >>>
> >>> My question is about focusing - how close, is infinite focus. My
> >>> camera is a Coolpix 5400. 20 feet? 30 feet?
> >>
> >>Infinite focus means that the camera takes a parallel beam of light,
> >>and focuses it onto one pixel.
> >
> > I think this loose thinking is likely to get you - or someone - into a
> > mathematical mess. A lens would take parallel light from an
> > infinitely-distant source and focus it onto a ^point^. That is a
> <snip>
>
> You are of course correct that it's not really a point, but a pixel.
>
>
> >>Consider it in reverse as a projector, with the beams shining on a
screen.
> >>You can see that as you get closer, the beams start to overlap.
> >>
> >>As a ballpark, you can consider infinite focus to be where the pixel
> >>pitch is equal to the lens diameter (more accurately it depends on what
> >>the apature is, but lens diameter is easier, and can it can never be
better
> >>than this).
> >>
> >>Say the lens is 1cm across (to the beginning of the mounting).
> >>
> >>For a 5Mp camera, this is about 2000*2500Mp, so if the scene is more
than
> >>20m*25m, then it'll be in focus, if set to infinity.
> >>
> >>So, for pretty much most planes, if it's not filling the frame, you'r
fine.
> >>
> >>
> > This seems awfully optimistic to me, for a lens wide open. Of course, it
> > depends how big and how sharp you want the final result to be, and how
> > it's going to be viewed.
>
> The above assumption is worst case.
> In practice the size of the field at 'infinity' will be smaller than this,
> due to the apature not being the same as the clear apature, and blurring
> making it slightly less defined.
>
> Or am I missing something.

yes - his point really is a point and a pixel (altogether now) is a picture
element

you missed

Arts

David Littlewood <> writes:
> The bad news is that the limit (i.e. how close they get and still
> appear sharp) depends on the aperture of your camera lens, and its
> focal length; it also varies according to what you propose to do
> with the picture (small web picture to huge enlargement - they have
> different demands on sharpness). This zone for which objects appear
> sharp is known as depth of field (DoF).

> Unfortunately, because these numbers are different for every focal
> length of lens and every aperture, I can't tell you what they are. You
> will have to do some research yourself, either to work it out (the
> maths is not that difficult) or to find a suitable table.

This website has an "on-line DoF calculator" (click on the link in
the left margin) as well as a lot of other useful stuff about DoF -
including the formulas, if you want to do the math yourself:

http://dfleming.ameranet.com/

It will work out the DoF and hyperfocal distance for you. It has a
pull down menu that lists almost every popular digicam on the market.
--
- gisle hannemyr [ gisle{at}hannemyr.no - http://folk.uio.no/gisle/ ]
================================================== ======================
«To live outside the law, you must be honest.» (Bob Dylan)

Arty Phacting <> wrote:
>
> "Ian Stirling" <> wrote in message
> news:411a919c$0$513$...
>> David Littlewood <> wrote:
>> > In article <4118e022$0$524$>, Ian
>> > Stirling <> writes
>> >>Lazarus Long <> wrote:
>> >>> I'm a relative newbie to most of the features of a "modern" camera.
>> >>>
>> >>> My question is about focusing - how close, is infinite focus. My
>> >>> camera is a Coolpix 5400. 20 feet? 30 feet?
>> >>
>> >>Infinite focus means that the camera takes a parallel beam of light,
>> >>and focuses it onto one pixel.
>> >
>> > I think this loose thinking is likely to get you - or someone - into a
>> > mathematical mess. A lens would take parallel light from an
>> > infinitely-distant source and focus it onto a ^point^. That is a
>> <snip>
>>
>> You are of course correct that it's not really a point, but a pixel.
>>
>>
>> >>Consider it in reverse as a projector, with the beams shining on a
> screen.
>> >>You can see that as you get closer, the beams start to overlap.
>> >>
>> >>As a ballpark, you can consider infinite focus to be where the pixel
>> >>pitch is equal to the lens diameter (more accurately it depends on what
>> >>the apature is, but lens diameter is easier, and can it can never be
> better
>> >>than this).
>> >>
>> >>Say the lens is 1cm across (to the beginning of the mounting).
>> >>
>> >>For a 5Mp camera, this is about 2000*2500Mp, so if the scene is more
> than
>> >>20m*25m, then it'll be in focus, if set to infinity.
>> >>
>> >>So, for pretty much most planes, if it's not filling the frame, you'r
> fine.
>> >>
>> >>
>> > This seems awfully optimistic to me, for a lens wide open. Of course, it
>> > depends how big and how sharp you want the final result to be, and how
>> > it's going to be viewed.
>>
>> The above assumption is worst case.
>> In practice the size of the field at 'infinity' will be smaller than this,
>> due to the apature not being the same as the clear apature, and blurring
>> making it slightly less defined.
>>
>> Or am I missing something.
>
> yes - his point really is a point and a pixel (altogether now) is a picture
> element
>
> you missed

I know the difference between a point and a pixel.

Given that almost all digital cameras have antialiasing filters, so that
the angular response can't be much better than the pixel pitch, can there
really be much difference?

"Arty Phacting" <> writes:
>does hypothetical existence imply non-reality?

How would you determine whether a mathematical concept is "real" or "not
real"?

Dave