Jump to content

Thinking about aspect ratio


Frank Barrera

Recommended Posts

So we might represent (say) a pendulum in terms of the arc it traces out in space. One dimension of our representation identifies the position of the pendulum at any given moment, and the other dimension composes a representation of changes in that position, ie. changes in space.

 

In this we obtain a spatial representation of movement.

Not quite right. You can't represent a pendulum's motion by drawing the arc. You have both dimensions representing space, none representing time. You've made a time-lapse photo instead of a movie. Spatial representation of the pendulum's motion requires three dimensions.

 

Then your film strip which recorded the pendulum's motion is a puzzle. For the film strip is just two dimensional, but we just decided that a spatial representation of the pendulum requires three dimensions. The solution: film cheats the time dimension. A sequence of images, even made at 24 per second, is not an honest representation of time. We can cut the film strip into its frames and then stack them up like a deck of cards. This stack is the three dimensional spatial representation of the pendulum's motion required. But on close inspection there are spaces between frames in the stack. The stack isn't really a three-dimensional thing. For of course from a two-dimensional thing you can't make a three dimensional thing. But the stack looks three-dimensional, and that might do.

 

The crux of the invention of cinema was the replacement of time with a discrete approximation to time. So please let's count our dimensions correctly. Four-dimensional world, 3 spatial + 1 temporal, is represented in a movie. The three spatial dimensions are compressed to two in the movie, by geometric perspective, and the time dimension is sampled in the film strip or other media, to be displayed in continuous time.

 

The strip of movie film is not the movie. In fact the strip isn't quite the complete encoding of the movie. There's also the fps instruction in its metadata as it were. There's also the presumed 2-blade or 3-blade shutter that will determine how the movie looks -- how flickery the movie is. Not just how flickery it looks, but how flickery it is. There's also the spectral power distibution of the intended illuminant for projection. This is not the same illuminant as we use when we examine the film in our hands, so the colors we eyeball are not quite the colors of the movie. The movie is the display on the screen. It doesn't make a bit of difference whether the frames encode time in a strip or pop separately out of a corn popper. They're a discrete sampling of the time either way. It also doesn't make a bit of difference whether the frames are little rectangles of transparent film, or rectangles of gold, or lists of 0s and 1s in a digital file, so long as the display on the screen is correct.

 

A movie-maker might pick up a camera and shoot some action and then instruct an editor how to cut it and finally show it without ever knowing whether the camera shot wide gauge or narrow, reversal or negative, or shot film at all -- it might have been video. Which "medium" did this movie-maker work in? The movie medium.

 

So the movie is simpler than the recording. It's a 2+1 dimensional thing, 2 space and 1 time, wherein points have colors which keep changing, and when examined closer the changes are discontinuous according the the fps. These ideas rest on a Newtonian separation of space from time. Do not race ahead to Einstein-Minkowski space-time. Actually no aesthetic thought since 1905 has ever made a correct use of space-time. (It is an important question why.)

Link to comment
Share on other sites

Hi Dennis,

 

re-reading your proposal the difference between temporal art and durational art is becoming clearer.

 

"A temporal art involves changes of form/color/sound/pressure/etc. in time. Durational art concerns the observer and the work."

 

By this definition, and to this all I can say (and have said) is that all art would be "temporal art". All art involves changes, in time.

 

For zero change is still change.

 

For Zero is a number (an actual value). Zero is not the same as null. Null refers to a number that is not yet defined. Null is a space reserved for a value (be it zero or any other number).

 

But null is also a fiction of sorts, for the space reserved will have a number, but we treat the number there as one to be erased and replaced with another which we have yet to define. In the interim we treat the number there as null instead.

 

C

Edited by Carl Looper
Link to comment
Share on other sites

Not quite right. You can't represent a pendulum's motion by drawing the arc. You have both dimensions representing space, none representing time. You've made a time-lapse photo instead of a movie. Spatial representation of the pendulum's motion requires three dimensions.

 

Then your film strip which recorded the pendulum's motion is a puzzle. For the film strip is just two dimensional, but we just decided that a spatial representation of the pendulum requires three dimensions. The solution: film cheats the time dimension. A sequence of images, even made at 24 per second, is not an honest representation of time. We can cut the film strip into its frames and then stack them up like a deck of cards. This stack is the three dimensional spatial representation of the pendulum's motion required. But on close inspection there are spaces between frames in the stack. The stack isn't really a three-dimensional thing. For of course from a two-dimensional thing you can't make a three dimensional thing. But the stack looks three-dimensional, and that might do.

 

The crux of the invention of cinema was the replacement of time with a discrete approximation to time. So please let's count our dimensions correctly. Four-dimensional world, 3 spatial + 1 temporal, is represented in a movie. The three spatial dimensions are compressed to two in the movie, by geometric perspective, and the time dimension is sampled in the film strip or other media, to be displayed in continuous time.

 

The strip of movie film is not the movie. In fact the strip isn't quite the complete encoding of the movie. There's also the fps instruction in its metadata as it were. There's also the presumed 2-blade or 3-blade shutter that will determine how the movie looks -- how flickery the movie is. Not just how flickery it looks, but how flickery it is. There's also the spectral power distibution of the intended illuminant for projection. This is not the same illuminant as we use when we examine the film in our hands, so the colors we eyeball are not quite the colors of the movie. The movie is the display on the screen. It doesn't make a bit of difference whether the frames encode time in a strip or pop separately out of a corn popper. They're a discrete sampling of the time either way. It also doesn't make a bit of difference whether the frames are little rectangles of transparent film, or rectangles of gold, or lists of 0s and 1s in a digital file, so long as the display on the screen is correct.

 

A movie-maker might pick up a camera and shoot some action and then instruct an editor how to cut it and finally show it without ever knowing whether the camera shot wide gauge or narrow, reversal or negative, or shot film at all -- it might have been video. Which "medium" did this movie-maker work in? The movie medium.

 

So the movie is simpler than the recording. It's a 2+1 dimensional thing, 2 space and 1 time, wherein points have colors which keep changing, and when examined closer the changes are discontinuous according the the fps. These ideas rest on a Newtonian separation of space from time. Do not race ahead to Einstein-Minkowski space-time. Actually no aesthetic thought since 1905 has ever made a correct use of space-time. (It is an important question why.)

 

Hi Dennis,

 

I'm not in disagreement with you, and on many points.

 

"You can't represent a pendulum's motion by drawing the arc. You have both dimensions representing space, none representing time. You've made a time-lapse photo instead of a movie. Spatial representation of the pendulum's motion requires three dimensions."

 

Yes, that's true. But the point I was making is not that the representation is two dimensional (over three) although I did make the mistake of citing two dimensions. But that the representation is in terms of space in the first place. That the representation is in terms of dimensions.

 

And of course one can represent it in terms of even more dimensions, as you elaborate.

 

The point I'm making is that such a representation is spatial, encoded within an n-dimensional space. A hyper-space.

 

In hyper-space there is no movement. No change. Everything co-exists at the same time, in a kind of eternal stasis. In suspended animation.

 

Entombed.

 

Against this I'm working to elaborate an alternative sense of time, which the cinema gives us, where everything is not co-existant, and equally accessible, at all times. Where it's not understood in terms of random-access-memory. Where it's not Manovich's hyper-spatial dream of an infinite database.

 

C

Link to comment
Share on other sites

Also, I should just add I'm not racing ahead to Einstein and Minkowski. I'm returning there - revisiting it. I understand Einstein. And I understand Neils Bohr, and Werner Hesienberg, etc.

 

But I challenge such work, not in terms of science - for the science is excellent. Indeed brilliant. Rather I challenge it in terms of what it can say in terms of art.

 

From the point of view of science, images are treated as "representations" of otherwise more fundamental concepts best expressed mathematically. However I take the view that mathematics (with which I work every day) represents, but can not fully represent, what is otherwise observable in art (or the universe).

 

Furthermore I treat an image, not as a representation of anything, but as a thing in itself. A reality in itself. It is a reality which can otherwise be represented mathematically, or algorithmically. Such as in a computer animation.

 

But the photographic image comes from the other side. Empericism. The sensual. The experienced as distinct from that which is so by definition.

 

It is an affinity for, and an elaboration of this side, where art leads, and science follows.

 

But that said, I often reverse this logic in order to resolve a particular technical challenge. To work both sides of this divide, trying not to compromise either. Not always that successfully.

 

C

Link to comment
Share on other sites

So this is an interesting question.

 

"The interesting question is whether durational art is a subset of temporal art. I don't think so."

 

On face value I don't see how it could be otherwise. If all art is temporal art (as it seems from a definition of such) then durational art (being art) must also be temporal art (since all art is temporal art).

 

In order for it to be otherwise we'd have to suggest that all art wasn't temporal art.

 

One way might be to redefine temporal art as that which involves change, but excludes zero change.

 

So, for example, a painting or a pot, which doesn't involve change, might be excluded from a definition of temporal art.

 

But to do that requires bringing the observer back into play, for it's a frame of reference that will determine whether something can be said to be static, or otherwise.

 

But if we stick to the definitions previously posed (that durational art involves an observer) we are back to talking about durational art, ie. in order to make a distinction between stasis and movement.

 

Which actually suits me just fine. I'd just end up saying all art is durational art, but not all art (of the visual variety) explores or exploits duration in any great depth.

 

And I'd suggest the reason for this has been an ancient preoccupation with space.

 

C

Link to comment
Share on other sites

I mean, we should be able to survive for a long time with 1.85 and 2.35, and maybe 2:1. I mean, with digital cinema you can accomplish almost any aspect ratio...but I like having limitations.

Edited by Leon Liang
Link to comment
Share on other sites

Einstein-Minkowski space-time is a framework for the representation of space and time in terms of space (in terms of dimensions).

You seem to be confusing Minkowski diagrams, which as diagrams are of course spatial, with Einstein-Minkowski space-time. Minkowski famously said in 1908:

 

Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

Einstein-Minkowski space-time is not space. Space-time intervals are not distances. (How could distances take imaginary values?)

You gained nothing at all by going ahead (from Newton) to Einstein, since you only find spatiality in every representation of time that falls short of your requirement of expressiveness. You also confuse abstract mathematical spaces with terrestrial space -- same word "space" but two different meanings. You seem to imagine a ruler when you write "dimension".

 

From the point of view of science, images are treated as "representations" of otherwise more fundamental concepts best expressed mathematically.

 

What do you mean? In optics, images aren't that. In the mathematics I know, images aren't that.

Link to comment
Share on other sites

So this is an interesting question.

 

"The interesting question is whether durational art is a subset of temporal art. I don't think so."

 

On face value I don't see how it could be otherwise. If all art is temporal art (as it seems from a definition of such) then durational art (being art) must also be temporal art (since all art is temporal art).

 

In order for it to be otherwise we'd have to suggest that all art wasn't temporal art.

 

One way might be to redefine temporal art as that which involves change, but excludes zero change.

 

So, for example, a painting or a pot, which doesn't involve change, might be excluded from a definition of temporal art.

 

But to do that requires bringing the observer back into play, for it's a frame of reference that will determine whether something can be said to be static, or otherwise.

 

But if we stick to the definitions previously posed (that durational art involves an observer) we are back to talking about durational art, ie. in order to make a distinction between stasis and movement.

 

Which actually suits me just fine. I'd just end up saying all art is durational art, but not all art (of the visual variety) explores or exploits duration in any great depth.

 

And I'd suggest the reason for this has been an ancient preoccupation with space.

 

C

 

I tried to make a distinction between durational art and temporal art, which you're partly accepting. Temporal art involves change, motion being a popular kind of change, but change in color works too, change in pitch, etc. Paintings are certainly excluded from the temporal arts. They might fade or crumple over years but it's not observable as change, nor is it intended change.

 

Observability is required in any aesthetic feature of anything. Yes, what's observable by one person with normal senses might not be observable by another person with normal senses. In those rare cases we're unsure whether we have a temporal art work.

 

But the role of the observer is quite different for durational artwork. Durational artwork is designed so its continuity through time, and the durations of its parts are aesthetically relevant. The observer must observe the work from beginning to end without pause to grasp its "temporal shape".

 

The human mechanisms for change perception and duration perception are very different. There are surprisingly few psychologists who work on any kind of time perception. I luckily attended talks on aspects of this in Berlin last year: http://www.statefestival.org/program#statetalks-section Not all art is durational art. Movies, plays, dances, music, can be. Static arts like painting and written literature can't be, but also mobiles, video installations, etc.

 

Neither temporal art nor durational art needs to be about time, or revelatory or expressive about time. They just use time in one or both of its modalities. I've enjoyed many more films than have taught me about time.

 

One reason for making the distinction now is because durational art films might be disappearing, as, as Carl put it, film reverts to an orgy of movement. But even the exploration of cinematic time-flow, which does not require that it be durational art, is now endangered by developments in the medium, such as elimination of constant frame rate.

 

Spatiality hasn't dominated over temporality in the arts. Music, drama and dance are ancient arts, and they will survive.

Cinema has been especially non-revelatory or inexpressive about space. The major spatial discoveries were made in paintings, sculpture, architecture, dance. Hard-up 2.40:1 cinema is a case in point.

Edited by Dennis Couzin
Link to comment
Share on other sites

If one cares to read my words more carefully, one will see I see I mention quite happily, theatre and music, amongst others, as that which constitutes examples of art with which the cinema shares an affinity.

 

It is in relation to visual art, which I also specifically mention, as that which entertains an ancient pre-occupation with space, for obvious reasons. What is not so obvious is why the cinema, or the visual component of such, should remain pre-occupied with space. And in fact it doesn't.

 

Now all of this is framed in terms of a discussion regarding the art gallery, (vs the cinema/theatre/auditorium), as an appropriate venue for works of cinema.

 

The argument is that the art gallery is not as effective since is designed (or perhaps even defined) for expressions of space more than time.

 

The fourth axis of Einstein-Minkowsi's space time framework is spatial. The term "hyper-space" employs the term "space", and it is not an abuse of terms that it does so. Hyperspace is an extension of Descartes three dimensional space. The fourth axis of this hyper-space is used to represent time. Time itself is not spatial. But we can represent time in terms of space, ie. as a fourth axis in hyperspace. But as a result we can also start confusing time with space. As if time were the same thing as space.

 

The language of space is geometry. The language of geometry is mathematics. At least once one dispenses with rulers and drawings on paper. But we should not readily dispense with rulers, or drawings on paper, or images on film, or paint on canvas. They provide a way back to the world of experience.

 

To experience time, is something different from an experience of space. We should not confuse time with space.

 

C

Link to comment
Share on other sites

Hi Dennis,

 

re-reading your post I realise you are not overlooking what I said about an affinity between cinema and theatre/music, but rather confirming agreement with such, so my apologies for becoming defensive in my opening remarks.

 

The section on hyperspace remains a challenge.

 

C

Link to comment
Share on other sites

"Neither temporal art nor durational art needs to be about time, or revelatory or expressive about time. They just use time in one or both of its modalities. I've enjoyed many more films than have taught me about time."

 

Yes, I agree.

 

Time is used. But in any use of time will be the particular conception of time used. Ancient or modern, Newtonian, Kantian, Einsteinian, Bergsonian, and so on. A work will express whatever concept of time it uses, ie. in addition to whatever else the work is expressing.

 

It is of interest.

 

C

Link to comment
Share on other sites

I mean, we should be able to survive for a long time with 1.85 and 2.35, and maybe 2:1. I mean, with digital cinema you can accomplish almost any aspect ratio...but I like having limitations.

 

Given the rise of 16:9, probably 1.77 should be in the options list...

 

I personally liked the 1.5, 35mm still ratio, and 1.66, some artsyfartsy euro ratio... but for most of my short films I ever envision making, 1.77 or 1.85 are fine. I've also contemplated using 1.33 as well...

 

I have never really liked the 2+ ratios for my stuff, and while I like the various Hollywood films in that ratio that come out, when I view 'youtube' clips I find most of them totally 'wrong'... sort of like the excessive use of shallow DoF...

Link to comment
Share on other sites

 

The language of space is geometry. The language of geometry is mathematics. At least once one dispenses with rulers and drawings on paper. But we should not readily dispense with rulers, or drawings on paper, or images on film, or paint on canvas. They provide a way back to the world of experience.

 

To experience time, is something different from an experience of space. We should not confuse time with space.

 

C

 

Have an apple...

 

81aEUlUkh2L.jpg

Link to comment
Share on other sites

 

I'm wondering a few things about this set.

Has Mr Kubrick put a mirror at the far end of the lounge.

It looks like he might not have but my experience is that Stanley is often one step ahead of you so maybe he did and disguised it well.

Also I'm wondering if the room really curves or if the lines on the floor have been painted to give that illusion.

 

Does anyone know?

 

Freya

Link to comment
Share on other sites

The fourth axis of Einstein-Minkowsi's space time framework is spatial. The term "hyper-space" employs the term "space", and it is not an abuse of terms that it does so. Hyperspace is an extension of Descartes three dimensional space. The fourth axis of this hyper-space is used to represent time. Time itself is not spatial. But we can represent time in terms of space, ie. as a fourth axis in hyperspace. But as a result we can also start confusing time with space. As if time were the same thing as space.

 

The fourth axis of Einstein-Minkowski's space-time is not spatial. In that space-time the four axes have the same units which can be indifferently length units or time units. You miss the main accomplishment of Einstein-Minkowski by denying this. As of 1905 (or 1908) we lived in space-time and there were no longer strictly lengths and times but space-time intervals. Feynmann put it:

Thus we shall try to think of objects in a new kind of world, of space and time mixed together, in the same sense that the objects in our ordinary space-world are real, and can be looked at from different directions. We shall then consider that objects occupying space and lasting for a certain length of time occupy a kind of "blob" in a new kind of world, and that we look at this "blob" from different points of view when we are moving at different velocities. This new world, this geometrical entity in which the "blobs" exist by occupying position and taking up a certain amount of time, is called space-time.

 

Yes, he uses the expression "geometrical entity", for there is some analogy with the geometry of the space-world, but the time axis isn't spatial. Space-time is 4-dimensional but it's not a hyperspace that extends an underlying 3-space, the way Euclidean 4-space does. Space-time is actually a mathematical oddity. Beyond being non-Euclidean it doesn't have a real-valued metric as required for topological metric spaces. It's a physicist's space for the physical world. And "space" assuredly does not imply spatial here. Physicists have phase spaces. Mathematicians have spaces for which there is no dimension. Etc.

 

I'm surprised that Einstein-Minkowski space-time is being discussed in a cinematography forum without the usual yearning: Can't the admixing of space and time in cinema be elucidated through some analogy with space-time? I've never seen it pulled-off. Then better stick with Newtonian space&time and not bother with space-time.

 

And I suggest not to so much rely on "represent" which implies second-take. We're dealing with conceptual models which underly.

Edited by Dennis Couzin
Link to comment
Share on other sites

I have never really liked the 2+ ratios for my stuff, and while I like the various Hollywood films in that ratio that come out, when I view 'youtube' clips I find most of them totally 'wrong'... sort of like the excessive use of shallow DoF...

 

When you view the wide format clips on YouTube you are probably too far from the screen for them to subtend the expected visual angle. And if you try viewing from closer you have the problem of binocularity. Perhaps monocular viewing from appropriate distance will work for you. (And make the surround dark, and the whole room.)

Link to comment
Share on other sites

  • Premium Member

 

I'm wondering a few things about this set.

Has Mr Kubrick put a mirror at the far end of the lounge.

It looks like he might not have but my experience is that Stanley is often one step ahead of you so maybe he did and disguised it well.

Also I'm wondering if the room really curves or if the lines on the floor have been painted to give that illusion.

 

Does anyone know?

 

Freya

 

Normally, I would say that it's quite possible, but doesn't Heywood Floyd come walking down from the far end a few moments later?...

Link to comment
Share on other sites

 

Normally, I would say that it's quite possible, but doesn't Heywood Floyd come walking down from the far end a few moments later?...

 

You could be right!

The production design is always so amazing in so many of Stanleys movies tho and it always makes me wonder about how it all works!

 

Freya

Link to comment
Share on other sites

"Neither temporal art nor durational art needs to be about time, or revelatory or expressive about time. They just use time in one or both of its modalities. I've enjoyed many more films than have taught me about time."

 

Yes, I agree.

 

Time is used. But in any use of time will be the particular conception of time used. Ancient or modern, Newtonian, Kantian, Einsteinian, Bergsonian, and so on. A work will express whatever concept of time it uses, ie. in addition to whatever else the work is expressing.

 

That probably best summarizes our disagreement. When I say time is used by some artwork I do not mean that some "conception of time" is used. Time, whatever it is, is used in one of two basic ways: either for the changes (e.g. motions) observable in the work or the durations observable in the work. I mean unembellished time derivatives or time spans, by the clock.

 

Movies don't in general express any conception of time. When they do, it not any of the physicists' or philosophers', but one that is usually quaint and incomplete, but original: a conception of time that requires cinema for its expression.

Link to comment
Share on other sites

 

That probably best summarizes our disagreement. When I say time is used by some artwork I do not mean that some "conception of time" is used. Time, whatever it is, is used in one of two basic ways: either for the changes (e.g. motions) observable in the work or the durations observable in the work. I mean unembellished time derivatives or time spans, by the clock.

 

Movies don't in general express any conception of time. When they do, it not any of the physicists' or philosophers', but one that is usually quaint and incomplete, but original: a conception of time that requires cinema for its expression.

 

Well, yes, one could also say an apple falling out of a tree isn't, in general, meant to be an expression of gravity.

 

Conceptions of time make their way into a work. Intentionally or otherwise. They become part of a work. A conception of time in a painting differs from a conception of time in cinema. A conception of time in a long exposure photograph differs from a conception of time in a snapshot.

 

But what do we mean by concept?

 

In the history of art we can see conceptions of time that parallel, to some extent, conceptions of time in traditional physics and philosophy. But a concept in art is also very different from a concept in physics/philosophy. One is not fundamentally an expression of the other (although they can express each other). By this is meant that art is not an illustration of physics/philosophy. It is not about physics/philosophy. It does not represent physics/philosophy. Although it can (eg. in science fiction). Rather one might say it is in itself a physics/philosophy. Or it becomes a physics/philosophy. In itself. A particular kind of physics/philosophy. Or it becomes an alternative to physics/philosophy, if one would prefer to keep a lid on what the terms " physics/philosophy" mean.

 

The concepts of art can be said to be expressed in the language of experience - of the senses - the sensual. The visual. The aural. This is the raw conceptual material with which art works.

 

Re. space-time. This is not a "sort-of-geometry". It is geometry, but one extended to include how one might measure/represent/define time. The same concepts used in Ancient Greece to measure/represent/define space are extended to include a representation of time. And without in any way compromising the mathematical logic of geometry so extended.

 

Of course, what inspires this act of homogenisation is the speed of light. That the speed of light is a constant. It inspires unification.

 

And space is the great unifier.

 

Against this we can introduce a concept of time that is not represented in terms of space. Or rather, re-introduce it, for it is not a new idea. Rather it is a suppressed idea.

 

In the same way that an apple falling out of a tree, without any intention of doing so, can nevertheless expresses gravity, the cinema (or any art) can expresses a concept of time.

 

C

Link to comment
Share on other sites

The cinema introduces a new idea in terms of how time might be conceived.

 

Instead of representing time (duration) in terms of space (a screen, a canvas, a diagram, a mathematical expression) time (duration) will be directly used and find expression through such use. The short interval between the display of one frame, and the next, is time in the raw. Real time. Time is added to the film strip - inserted between the frames. Time itself. Not space. Not a representation of time.

 

If we call this a "conception" of time it is keep in mind that we could be wrong about this. In other words we want to maintain that this concept of time as still a theory. But it's a theory written in terms other than space. This doesn't stop us from representing this particular "concept" of time (that I otherwise call "real time") in terms of space. We might resort to speaking of some sort of 3D volume, in which 2D cross sections would stand in for frames of the film, between which is the "distance" of each interval. And we might store the interval as a number in computer memory, or it's reciprical: the frame rate. In the case of the mechanical projector, this interval, or it's reciprical (frame rate) is encoded in the mechanics of the projector.

 

But the cinema is not to be found in how it's encoded, but in how it's decoded, to use a digital age metaphor. When decoded we find that the result is no longer a concept of time in the language of space, but in the language of experience, whether from the point of view of an audience, or those creating the experience. Music had already explored this of course. Music paves the way for cinema.

 

In the cinema is discovered (or re-discovered) real time - well, once the cinema had got over obsessions with space and movement within space.

 

In the cinema, as much as in painting, or any other art, the image (or sound, or experience) is not to be confused with what it might represent, or what might represent it. It is to be treated as a "reality" in it's own right. The world of the senses. This world is just as capable of elaborating complex ideas as any other domain, but it does so in it's own way, and in ways that may not be translatable in any other way. One must experience the work itself, or at least not treat any commentary, as an equal substitute.

 

 

C

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...