Musings on Photography

Transfinite Mathematics, Hamlet, and Landscape Photography.

Posted in ethics, landscape by Paul Butzi on January 27, 2007

A little lesson in mathematics history.  Even if you’re not mathematically inclined, soldier on.  I promise that by the end, we’ll have come around to the problem of the photographer, the fence, and the fact that the grass is always greener on the other side of the fence.

Long ago (in 1874-84) and far away (in Halle, Germany) a mathematician named Georg Cantor published his seminal work establishing the field of set theory.  In this work, Cantor established that (surprisingly) there is more than one size of ‘infinity’ – that is, not all infinities are equal; some are larger than others.  This caused quite a stir, and Cantor’s work was roundly rejected by many. 

Anyway, it turns out that there are infinities, and there are infinities, and some are larger than others and they’re not all the same.  This brings us to the fence – the one we are tempted to jump so that we might partake of the photographs on the other side.

Part of the reason we’re tempted is that we know that there are infinitely many photographs to be taken on the other side of the fence.  Assign any nonzero value to each of those photographs, and the value of the set of photos we can take only if we jump the fence is infinite, and thus we’re strongly tempted to become a Bad Person, jump the fence, and start filling up those really large CF cards we just bought.  Who can resist a treasure trove of infinite value?  It’s right there, taunting us from the other side of the fence!

But there are infinitely many potential photos on BOTH sides of the fence, and it turns out the two infinities are the same.  Humans being what they are, we sense that if we add the photos on the other side of the fence to the photos on this side of the fence, we’ll end up with access to more photos.  Cantor, having drawn distinctions amongst the possible sizes of infinite sets, however, would tell us that we haven’t actually increased the size of the set of potential photos- we have an infinity of potential photos on one side of the fence, an equal infinity on the other side, and strangely enough, the sum of the two is an infinity the same as the two sides independently.

So the perception that we’ll have access to more photos if we jump the fence is a failing of human intuition, not an actual fact.  Jumping the fence doesn’t get us access to more photos, it gets us access to different photos.  Somehow, the fact that we can’t have those potential photos on the other side makes them more valuable to us than the potential photos we can walk right up to.  We think of the photos on this side of the fence as ‘bad’, and of the photos on the other side of the fence as ‘good’.

But, as a famous Dane once observed, “there is nothing either good or bad, but thinking makes it so.”  We view the accessible side of the fence as a prison, and the inaccessible side as a land of unparalleled freedom of expression.  But, if you see the accessible side as a prison, it’s because “your ambition makes it one, ’tis too narrow for your mind.”  It’s our attitudes that say the photos on the road side of the fence are undesirable, and the ones on the field side are desirable.

Photographers aren’t frustrated because they want to take photographs of the real world and think it exists solely on the other side of the fence; that’s just silly.  They’re frustrated because they want to make photographs of a fictional world, a world that exists only in their mind.  They know that world isn’t on this side of the fence, and they conclude (quite wrongly) that it must be on the other side.  And it’s not.  It’s just more real world on the other side of the fence.

This fictional mental world that landscape photographers covet is just that – a invented fiction.  In that fictional world, there are no telephone poles or wires.  There are no road signs, no roads, no cars, no drainage ditches and no fences.  There are no houses, no farm equipment, no signs of human interaction with the environment at all.  It’s Yosemite without the parking lots and visitors and trails and footprints.  It’s nature, pure and pristine but without any reality.  It’s the lovely world of Bambi without that nasty hunter – a world where idyllic deer amble peacefully through a strangely unrealistic wood and stop to drink daintily from a surreal but beautiful tranquil pool without any fear.  The real world isn’t like that.

Somewhere along the way, landscape photography has lost its way, and it stopped being about the landscape as it actually exists and became entirely about attempting to exclude reality.  It’s become the photography of whatever is left after you crop out the ‘real world’.

And the reason all those photographers are so frustrated is that when you’re done cropping out the ‘real world’, there’s almost nothing left to photograph.

4 Responses

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  1. Oren Grad said, on January 27, 2007 at 12:09 pm

    Your insight re Cantor and photographic opportunity applies to time as well as space: I no longer worry about “missing a great shot”. There will be something else tomorrow. I don’t know what it will be, but there will be something; if not tomorrow, then the next day, or the day after that.

  2. JohnL said, on January 28, 2007 at 1:35 am

    Interesting comments Paul but I must say there is just nothing of interest to photograph on my side of the fence today but by just taking a sneaky peak I can see so much potential over there! lol

  3. Nicolai said, on January 28, 2007 at 5:21 pm

    A few thoughts:

    First, great observation in general.

    Second, we’re always missing great shots. I’m missing a potentially infinite number of them as I write this, just as you are as you read it. Even if you average 100 exposures a day at an average shutter speed of 1/125, you’re only capturing photons for 0.8 seconds. What about the other 86399.2 seconds of the day? Missing shots is a fact of life.

    Third, re: “when you’re done cropping out the ‘real world’, there’s almost nothing left to photograph”, I disagree. It’s true if you don’t want to go more than 100 feet from a car that stays on paved roads, but there are plenty of places without telephone wires, vast parking lots, and a McDonald’s. It just requires a little more effort than in the past, or that you find new places and listen to them.

  4. Gordon said, on January 31, 2007 at 8:36 am

    I think a lot of photographers suffer from this, particularly early on. They go looking for the right subject to photograph. The pictures would be good, if only; they were somewhere photogenic, had a better looking model, had a better camera, could get over the fence and so on. It isn’t a peculiarity of landscape photographers – every photographer seems to think they have to ‘go’ somewhere else to shoot a good photograph.

    It is always a search for the right ‘thing’ to photograph because for a long time we think of photographs being about things, rather than being an expression of what we already see. Rather than stopping, looking, thinking and making a photograph where you are, it becomes something of a treasure hunt, but usually a frustrating one. Because when you find the ‘thing’ the photograph isn’t as good as if it were a better subject or more attractive model or better place to stand.

    At some point you have to try to internalise the search for good compositions. They don’t just fall in front of the lenses of good photographers. They didn’t happen to stumble across the right place and right composition by accident. It isn’t where you are that makes your pictures not as good as you want them, it is who you currently are.

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