Here are my answers to the puzzle about what happens when we point a camera at its monitor. The problem has a flavour of infinite regress about it, and sounds a little like a Buddhist koan – a question designed to make us realise (amongst other things) the limitations of logic. But whereas a ‘correct’ answer to a koan is usually something bizarre like barking like a dog, or hitting the questioner with a stick, the four questions I posed do actually have perfectly logical answers. And I find them quite interesting.
Let’s kick things off by showing a picture of what one might see when one looks into the webcam that is perched on top of the monitor, looking outwards. This is a screenshot of what my monitor showed when I did that (Figure 1).
The image is framed within the window labelled ‘Cheese’ – which is the name of the webcam program I was using. That’s me wearing the red cravat.
When we turn the camera around and point it at the monitor, we will see an infinite regress of windows within windows, as the whole picture will be reduced and fitted into the image area where I am above. Then that reduce-and-insert step will be repeated as many times as it takes until the reduced image gets down to a single pixel and can contain no more strip-images. Here’s an image I made of what it should look like (Figure 2):
In every window, the green desktop background, the desktop icons and the file explorer window to the left are reproduced, and the series shrinks off into the distance. I can tell you it was pretty fiddly putting the tiniest innermost parts into that picture. Infinitely small objects are notoriously difficult to manipulate.
The picture looks a little like a classical picture that uses perspective to show a long, straight road disappearing into the distance, with the point of disappearance at which all the lines converge being in the top-right quadrant of the screen.
But there’s an important and fascinating difference: the dimension along which the images disappear here is of time, not distance. That’s because each nested window is an image captured by the camera’s sensor a short interval earlier than the window that contains it. That interval will vary slightly as we move through the nested sequence, based on the relationship between the rate at which the monitor screen is redrawn (the ‘refresh rate’) and the number of snapshot images captured per second by the camera sensor (the ‘frame rate’). But it will always be more than some minimum value that depends on how long the information takes to travel along the wire from the sensor, through any processor chips in the camera, along another wire to the computer, through any processing algorithms in the computer, and then through the video cable to the monitor. Even without knowing anything about the computer, we know that that time – called the ‘lag’ – will be greater than the lengths of the wires involved, divided by the speed of light (because electrical signals cannot travel faster than light).
So each nested window is earlier than the one outside it, and as we look through the sequence of windows towards the point of convergence at infinity, we are looking back through time!
Now we maximise the Cheese window. First let’s see what it looks like with the camera the correct way around, pointing at me (Figure 3):
You can tell from my expression that I’m quite enjoying this little exercise, can’t you?
Here there is nothing outside the Cheese frame, but the Cheese frame still has a broad, non-image bar at the bottom, a narrower bar at the top, and black vertical bars at either side, which are needed to preserve the image’s ‘aspect ratio’ – the ratio of its width to its height.
With that setting, we turn the camera on the monitor, and this is what we would see (Figure 4):
The lower, upper, left and right bars are reproduced as a series of receding frames, and there is nothing in view other than the receding frames. There is no room left for an actual image of anything other than frames.
Figure 4 gives an even better sense of the ‘time tunnel’ that we mentioned in the previous section. Those white borders really do regress away in a spooky way. It looks like something out of Doctor Who.
The ratio of the height of one window to the height of the window immediately inside it is 1/(1-p) where p is the sum of the heights of the upper and lower margins of the outermost window divided by the total height of the outermost window. The ratios of the widths is the same. In this case it looks like p is around 1/5, so each window will be about 4/5 of the height of the window that contains it.
I used my webcam and shaky hands to try an empirical verification of this. I maximised the Cheese window and, pointed the hand-held webcam at the monitor, centering it as closely as I could. Then I asked my partner to press the Screenshot button on the keyboard to record what the monitor was showing. Below is what we got (Figure 5).
It’s a bit rough, but you can see it does the same sort of thing as Figure 4.
When one is holding the camera like this, the little involuntary movements one makes cause the trail of receding frames to wobble left and right in waves, that remind me of the effects used in 1970s television to produce a psychedelic impression – particularly prevalent in rock music film clips.
Here’s a link to a video I captured of this effect.
Question 3 asks what we will see on the monitor after we click the full-screen icon.
When we click the full-screen icon, we have no borders, so there can be no infinite, reducing regress of nested borders. How can we work out what is shown, assuming that we started in non-full-screen mode with a maximised window, so that the monitor was showing Figure 4?
The answer turns out to be remarkably simple. We just note that, when the full-screen icon is clicked, the computer will do some computing and then redraw the screen using the whole monitor area for the image from the camera. When it has finished the computing it will draw the screen using the image received most recently from the sensor and, since that image was captured before the screen redraw, it will be the same as whatever the screen was showing previously. This assumes that the previous image is left in place on the monitor until the computer is ready to draw the new one. We consider later on what happens if that is not the case.
That re-drawn screen will then be captured again by the camera sensor, sent to the computer and then drawn again on the monitor, and so on. So the image will remain exactly as it was before the full-screen icon was clicked! In this case, since the Cheese window was previously maximised, it will continue to show something like Figure 4.
The image remains static until either the camera is pointed away or the computer is switched out of full-screen mode, using the keyboard or mouse. Barring earthquakes, electricity blackouts and such-like, we would expect the monitor to still be displaying Figure 4 if we locked the room it was in, went away and returned to inspect it ten years later.
We can understand this a different way by considering the time tunnel we talked about in the responses to questions 2 and 3. In those cases, as we travel inwards through the tunnel to successively smaller windows, each window’s image was captured a short while earlier than the image of the window around it. The interval between the capture time of those windows will be much less than a second, typically 1/24 seconds. In Figure 4 each window’s height is about 4/5 of the height of the window that contains it. So to see what the monitor was showing t seconds ago we have to go to the nth window in the sequence, counting from the outside, where n=24t. The height of that window, assuming the height of the monitor’s display area is 300mm, is 300 x 0.8-24t mm. The window size reduces rapidly as we go back through time. A little calculation shows that the 26th window in the sequence is the first to have height less than 1mm, and that window shows what the monitor was showing just over one second earlier.
Without constraint, that time tunnel would continue to go back, getting smaller at an increasing rate, window by nested window (like Russian dolls, or the cats in the Cat in the Hat’s hat), until we got to the time before the camera program window was opened on the computer, and that image would show whatever was on the monitor before the window was opened. But it would be indescribably tiny. If we opened the window – in maximised form – five minutes ago, the height of the window that now showed that image from back then would be 300mm x 0.8–7200, which is approximately 10-688 mm. This is indescribably smaller than the smallest atom (Hydrogen, with diameter 10-7 mm) or even just a proton (diameter 10-11 mm).
I expect our eyes probably could discern no more than the first twenty windows in the sequence. Further, since my screen has about three pixels per mm, the windows would reach the size of a single pixel by the 31st window in the sequence, and the regress would stop there. Hence the sequence would look back in time no more than 1.3 seconds.
When we move to full screen mode, we still have a time tunnel of nested windows, but each one is exactly the same size as the one before it – the height ratio is 1, rather than 0.8. That means that how far we look back in time is no longer limited by shrinking to the size of a pixel, and the sequence will go all the way back to the last image the monitor showed before drawing its first screen in full-screen mode – which will be Figure 4.
In practice, as my friend Moonbi points out, the slight distortions in the image arising from imperfections in the camera lenses, although they may be imperceptible at first, will compound on each other with each layer of nesting so that what is actually shown will be a distorted mess. Like a secret whispered from one person to another around a large circle, or a notice copied from copies of itself dozens of times recursively, the distortions – however tiny they may be at first – will grow exponentially to eventually dominate and destroy the image. One minute after full-screen mode has been commenced, the monitor will be showing a 600 times recopied image of Figure 4, which will be more than enough to obliterate the image.
But this is a thought experiment, so we allow ourselves the luxury of assuming that are lenses are somehow perfect, that there is zero distortion, and each copy is indistinguishable from the original.
What if the screen blacks out?
Above we assumed that the display does not change until the computer is ready to redraw the full-screen image. If you go to YouTube, start playing a video and then click the full-screen icon (at bottom right of the image area) you will see that is not what it does. It actually makes the whole screen go black for a considerable portion of a second, and only then redraws the screen. If the camera program we are using does that then the screen will go black and remain black indefinitely.
If the black-out is shorter than YouTube’s, different behaviour may arise. It depends on four things:
- the time from image capture to display, which we call the lag and denote by L,
- the interval between image captures, which we call the frame period and denote by T, and
- the time the blackout period commences and the time it ends, both measured in milliseconds from the last image capture before the blackout. We’ll denote these by t1 and t2.
If no image capture occurs during the blackout, which will happen if t2<T, the blackout will have no effect on the final image and we can ignore it. The eventual image will still be Figure 4.
If images are captured during the blackout, and the first image shown on the monitor after the blackout was captured during the blackout, the screen will thereafter remain black indefinitely. This will be the case if both L and T are less than t2.
The other possibility is that T<t2 and L>t2. In this case the first image shown after the blackout will be a picture of the pre-blackout monitor, ie Figure 4, but it will be followed sooner or later by one or more black images captured during the blackout. What will follow then will be an alternation between images showing Figure 4 and black images. It will look like a stroboscopic Figure 4. The strobe cycle will have period approximately equal to L, and the dark period will have approximately the same length as the blackout, ie t2–t1. In essence, the monitor will indefinitely replay what it showed in the period of length L ending at the end of the blackout.
This black-screen issue will also arise if the monitor is an old-style, boxy, CRT (Cathode Ray Tube) rather than a LCD, Plasma or LED device. CRT screens typically draw around 75 images per second, made up of bright dots on a photo-sensitive screen, by shooting electrons at it. In between those drawings, the screen is black. That’s why those screens sometimes appear to flicker, especially viewed through a video camera.
For a CRT screen, the image captured immediately before the redraw may be Figure 4 or black, or something in-between – a partial Figure 4, with a complex dependency based on four parameters: the length of exposure used by the sensor (shutter speed), the length of time taken for a single redraw of the CRT screen and the refresh rate and frame rate. Unless there were a particularly unusual and fortuitous relationship between those four numbers, the image on the monitor would not be Figure 4. I think instead it would either be just black or an unpredictable mess. But one would need more knowledge of CRT technology than I have, to predict that.
Anyway, we don’t want to get bogged down in practical technology. This is principally a thought experiment. And for that ideal situation, we assume an LCD monitor with a computer that, upon receiving a full-screen-mode command, leaves the prior image in place until it is ready to redraw the image on the full screen. And the answer in that situation is Figure 4.
Doing a careful experimental verification of this is beyond me because, amongst other things, I don’t have a camera program that has a full-screen mode. But just for fun, I made a video like the one above under Question 4, where I focused the camera on the area of the monitor that displayed the image, trying to exclude the borders. It wobbles about, partly because of my shaky hands. It is mostly black, but there’s a blue smudge that appears in the lower half and wobbles around. I think that is a degraded version of the regressing images of the lower border. But under such uncontrolled conditions, who knows?
We are now in a position to work out the answer to question 4, which is ‘what will we see after we point the camera to the right of the monitor and then pan left until it exactly points at the monitor, and stop there?‘
To start with, we know that, once the camera has panned to the final position of exactly capturing the image of the entire monitor, it will hold that image indefinitely, and that image will be whatever the monitor was showing immediately before the camera finished panning.
We’ll be a little more precise. A video camera captures a number f of images (‘frames’) per second, typically 24. The final image shown by the camera will be whatever the camera captured in the last frame it shot before completing the pan. The nature of that image depends on relationships between the pan speed, the frame rate and the width of the monitor screen, which we will explore shortly. But, to avoid suspense, let’s assume a frame rate of 24, that 32 frames are shot while performing the pan, and that the view to the right of the monitor display area, including the black right-hand frame of the monitor itself, being this (Figure 6):
Then, on completion of the pan, the camera will show, and continue to show indefinitely thereafter, the following image (Figure 7 – note that the image was made by editing, not shot through a camera. My equipment is nowhere near precise enough to do this accurately):
C’est bizarre, non?
Those of you that enjoy exploring intricate patterns may wish to read on, to see the explanation of this phenomenon. I will not be offended if most don’t.
The answer depends on the ratio of the speed at which the camera pans left, to the width of the screen. If we want to be precise, these speeds and widths must be measured in degrees (angles) rather than millimetres. But millimetres are easier to understand so we’ll use them and ignore the slight inaccuracy it introduces (otherwise I’d need to start using words like ‘subtend’, and we wouldn’t want that would we?).
Say the camera rotates at a speed of s mm per second, and that it shoots f frames per second. Hence it shifts view leftwards by s/f mm per frame. So, if the width of the monitor’s display area is w mm, it shoots N=wf/s frames between when the camera first captures part of the monitor’s display area (on the monitor’s right side) and when the camera is in the final position where it exactly captures the view of the whole monitor display area, not counting the last frame. We label the positions of the camera at each of those frames as 1 to N, going from earliest to latest. We omit the last frame because we know that, once the camera is pointing exactly at the monitor, the image will remain fixed on whatever the monitor is showing at that time, which will be what the camera saw in position N.
By the way, we assume that N is an integer even though in practice it won’t be, because it will have a fractional part. It doesn’t make the calculation significantly more difficult if it’s a non-integer, but it is messier, longer, and the differences are not terribly interesting, so we’ll assume it’s an integer.
Divide the view to the right of the monitor’s display area, as shown in Figure 6 above, into N vertical strips of equal width. Number those strips 1 to N from left to right. We will call these ‘strip-images‘, as each is a tall, thin picture. Next, number the positions the camera has when each frame is shot as follows:
- Frame 0 is when the left-hand edge of the image captured by the camera coincides with the right-hand edge of the monitor display area, so that the camera captures exactly the image of Figure 6, ie strip-images 1 to N. At that time the monitor will be showing what the camera captured one frame earlier, which will be an image made up of strip-images 2 to N+1 (strip-image N+1 is what we can see in an area the same size as the opther strip-images, immediately to the right of Figure 6)
- The frames shot after that are labelled 1, 2, etc.
Label the times when the camera is in position 0, 1, 2 etc as ‘time 0’, ‘time 1’, ‘time 2’ etc.
With this scheme, Frame N will be the one that is shot when the camera is in the final position, when it exactly captures what is on the monitor, so that that image remains on the monitor indefinitely thereafter.
The following table depicts what is shown by the monitor and what is captured by the camera at each position, in the situation we used to produce Figure 7, which has N=32.
The rows are labelled by the camera positions/times. The first 32 columns (the ‘left panel’) correspond to the 32 vertical, rectangular strips of the monitor display area, numbered from left to right. The next 32 columns (the ‘right panel’) correspond to the strips of what can be seen to the right of the monitor. The number in each cell shows which strip-image can be seen by looking in that direction. The yellow shading in each row shows what images are captured by the camera at that time, to be shown on the monitor in the next row. (Figure 8):
A few key points of interest are:
- The numbers in the right panel do not change from one row to the next, because rotating the camera does not change what can be seen to the right of the monitor.
- The numbers in the left panel change with each row, to reflect that what was captured by the camera at the previous camera position was different from what was captured at the one before that, because of the camera’s movement.
- The yellow area denoting what the camera captures moves to the left as we go down the table, reflecting the camera’s panning to the left.
There are lots of lovely number patterns in the left panel, which I will leave the reader to explore.
Here is a zoomed-in image of just the left panel for those whose eyes, like mine, have trouble making out small numbers (Figure 9):
Referring back to Figure 7 we see that, as we move from the right to the left side, it has a series of eight vertical images of increasing width. The first one is just the monitor’s right-hand frame – a black plastic strip. The next is twice as wide and has the monitor frame plus the strip-image to its right. The one after than is three times the width and so on. This corresponds to the last row of Figure 9:
5 6 7 8, 1 2 3 4 5 6 7, 1 2 3 4 5 6, 1 2 3 4 5, 1 2 3 4, 1 2 3, 1 2, 1
I have put commas between each contiguous set of strip-images. I call each such contiguous set a ‘sub-image‘. The first sub-image is incomplete – being 5 6 7 8 instead of 1 2 3 4 5 6 7 8 – because N is not a triangular number.
The time tunnel applies here, with a slightly different flavour. The newest sub-image is the one on the far right, composed solely of strip-image 1. This was captured from the world outside the monitor one frame period ago. The next, the ‘1 2’, was shot from the monitor last time, and came from the real world outsider the monitor two frame periods ago. The oldest sub-image is the one on the left, which has been through the camera-monitor loop seven times, having first been captured from the real world eight frame periods ago.
It’s quite fun to trace the path of these images as they repeatedly traverse the camera-monitor loop, by the numbers in the above table. Here’s the lower part of the table showing how the first, third and sixth sub-images from the left (using blue, grey and pink shading respectively), make their way from the real world (to the right of the vertical dividing line), into the camera-monitor loop (to the left of that line), around that loop as many times as needed, and finally to the ultimate static image (Figure 10):
My example with N=32 involves a high panning speed. Shooting 24 frames per second, the pan would need to to completed in 32/24 = 1.33 seconds. One would need extremely good equipment to accomplish that without getting a bounce or wobble when the camera stops at the end of the pan – and avoiding wobble is critical to getting the indefinite static picture we have discussed.
It may be that in order to avoid camera bounce one would need a slower pan, giving us a (perhaps much) higher N. What would be the outcome of that? Well, the right-most sub-image contains only one strip-image and, as we move left, each image contains one more strip-image than the one to its right. So, if the number of sub-images is r, then N will be greater than the sum of the numbers from 1 to r-1 (the (r-1)th triangular number) and not exceeding the sum from 1 to r (the rth triangular number). A little maths tells us that this is from (r-1)r/2 to r(r+1)/2. For large N this means that there will be approximately √(2N) sub-images and the largest will be comprised of about √(2N) strip-images. Since for a display width of w the width of a strip-image is w/N, that means the widest sub-image will have width about w√(2N)/N=w√(2/N), which will get smaller as N increases. If N=2048, corresponding to a very slow pan time of about 85 seconds, the widest sub-image would be narrower than the frame of my monitor, so all we would see in the final static image would be black plastic monitor frame, something like this (Figure 11):
The bars of light are from the screen reflecting on the shiny monitor frame. Because I couldn’t hold the camera straight, they are bigger at the bottom than at the top.
I will leave you with my synthesis of the sequence of 32 images that would be seen, given near-perfect equipment, in the 32-step pan that ends with Figure 7 above. They are simply a realisation in pictures of the patterns shown in figure 9, when applied to the image Figure 6. The sequence is in a pdf at this address. If you go to page 1 and then repeatedly hit Page Down rapidly, you will see a slow-motion video representation of what it would look like as the camera panned. You may need to download it first in order to be able to view it in single-page view, which is necessary in order to achieve a video-like effect. Alternatively, it is represented below, albeit somewhat more crudely, as a pretend film strip.
Bondi Junction, February 2017
I was listening to a talk by Alan Watts about some aspect of Eastern mysticism. I can’t remember the exact context. I think he was describing the impossibility of truly understanding the nature of one’s own mind. He said that trying to use one’s mind to understand one’s own mind was ‘like pointing the camera at the monitor’.
I was immediately struck by this. Partly I was surprised at his using such a simile, which involves common enough concepts in 2017, in a talk that he gave in the sixties, when computers only existed in large research establishments and occupied enormous rooms. There was certainly no such thing as a webcam back then. I realised later that he probably had in mind a closed-circuit television arrangement, which they did have in the sixties.
But beyond that, I was struck by the fact that it’s actually a very interesting question – what does happen when one points the camera at the monitor? It’s a classically self-referential problem. But unlike some self-referential problems, like the question of the truth of the statement ‘This sentence is false’, it must have a precise answer, because we can point a camera at a monitor, and when we do that the monitor must show something. But what will it show?
There are a number of practical considerations that can lead us towards different types of answers. While each of those considerations leads to an interesting problem in its own right, I tried to remove as many of them as possible to make the problem as close to ‘ideal’ as I could. So here it is.
Imagine we have a computer connected to a monitor and a digital video camera. A webcam is a digital video camera but, since the camera we are imagining here needs to be extremely accurate, a high-quality professional video camera would be more suitable. The monitor uses a rectangular array of display pixels to display an image and the camera uses a sensor that is a rectangular array of light-sensitive pixels, and the dimensions of the display and the sensor, in pixels (not in millimetres) are identical.i
On the computer we run a program that shows the image recorded by the camera. The telecommunication program Skype is a well-known such program that can do that, amongst other things. There are also dedicated camera-only programs, which webcam manufacturers typically include on a CD bundled with the webcams they sell. Let’s call our program CamView (not a real program name). We start up CamView on the computer in a non-maximised window, which we’ll call the ‘CamView window’. Then we turn the camera on and point it at the monitor. We aim and focus the camera so precisely that an image of the display area of the monitor fills the image-display area of the CamView window. Ideally this would mean that each pixel on the camera’s sensor is recording an image of the corresponding pixel on the monitor screen. In practice there will be some distortion, but we’ll ignore that for now.
Question 1: what does the monitor show?
Question 2: Next we maximise the CamView window. What does the monitor show now?
Those questions are easy enough to answer, when we remember that the window for any computer program, in default mode, typically has an upper border with tool icons on it, a lower border with status info on it, and sometimes left or right borders as well.
These questions are fairly similar to the question of what one sees when one stands between two parallel, opposing mirrors, as is the case in some lifts (elevators).
Now comes the hard one. In most video-viewing computer programs there is an icon that, upon clicking, maximises the window and removes all borders so that the image-display area occupies the entire display area of the monitor. Call it the ‘full screen icon’ and say that we are in ‘full screen mode’ after it is clicked – until a command is given that terminates that mode and returns to the default mode – ie restores the borders etc. In full screen mode the display area of the monitor corresponds exactly to the images recorded by the camera’s sensor.
Question 3: We now click the full screen icon. Describe what appears on the monitor, and how it changes, from the instant before the icon is clicked, until ten minutes after clicking it – assuming the program remains in full screen mode for that entire time.
That is the difficult one. It took me a while to figure it out, and I was surprised by the answer. It is possible that what I worked out was wrong. If so, I hope that someone will point that out to me.
I have one more question, and it has an even more peculiar answer – one that I found quite charming.
Question 4: Assume the camera is mounted on a very stable tripod. Still in full-screen mode, we pan the camera to the right until it no longer shows any of the monitor. Then we pan the camera back at a constant speed until it again sees only the display area of the monitor, and we stop the panning at that point. What is visible on the monitor after the camera has panned back to the original position? Does that change subsequently? What does it look like ten minutes later? Does the monitor image depend on the panning speed, or on the number of frames per second the camera shoots? If so, how?
In order to avoid spoiling anybody’s fun in trying to work out the answers to these puzzles for themself, I will not post answers now. I will post them a little later on. It will also take me a little while to make some nice pictures to help explain what I am talking about.
Bondi Junction, February 2017
i Although most camera sensors have a 3:2 aspect ratio, which is different from the 16:9 aspect ratio of most modern computer monitors, it is possible on a sophisticated camera to alter the aspect ratio to 16:9, which is achieved by deactivating the sensor pixels in an upper and lower band of the sensor, so that the area used to record an image has the required aspect ratio. We’ll assume that is done and that the number of pixels in the active sensor area equals that on the monitor.
‘Partial differentiation’ is an important mathematical technique which, although I have used it for decades, always confused me until a few years ago. When I finally had the blinding insight that de-confused me, I vowed to share that insight so that others could be spared the same trouble (or was it just me that was confused?). It took a while to get around to it, but here it is:
My daughter Eleanor make a drawing for it, of a maths monster (or partial differentiation monster, to be specific) terrorising a hapless student. The picture only displays in a small frame at the linked site, so I’m reproducing it in all its glory here.
Bondi Junction, October 2016
Books are too long. People talk for too long. Academic papers are too long. Almost everything is too long.
Why? Partly, because to be concise is very difficult. Urban legend has it that Blaise Pascal once wrote at the end of a letter to a friend: ‘I’m sorry this letter is so long. I didn’t have time to write a short one’.
I struggle with conciseness. Part of the problem is that, when I am trying to explain something, I worry about whether what I have said is clear enough, so I keep on saying it over, in a slightly different way each time, in the vague hope that one of the attempts will make the connection.
I think a better strategy might be to make one brief attempt at an explanation and then wait for a response. If more is needed, I imagine my interlocutor will tell me. If they do, the particular nature of their response will better enable me to tailor my next statement to fill in the information that was missing in my first.
But that requires discipline, and nerves of steel. It is like being silent in an interview after giving a short reply to a question – forcing the interviewer (or interrogator) to make the next move. Few people can carry that off, and I suspect I am not one of them.
Academic papers can be particularly irritating, droning on about all the references and who has written what, so that by the time one gets to the bit about what the authors have done that’s actually new, one is exhausted and wants to retire for a tea break. It’s not clear to me whether this is a stylistic practice, imposed by the producers and reviewers of journals, or whether it reflects insecurity on the part of the authors, who may feel that they need to mention some minimum number of other papers in order to be taken seriously.
Arthur Schopenhauer railed against this sort of writing in a series of essays collected under the title ‘The Art of Literature’. He opens with an unrestrained broadside ‘There are, first of all, two kinds of authors: those who write for the subject’s sake, and those who write for writing’s sake.‘ Schopenhauer loved the first (and of course considered himself to be one of them) and loathed the second.
If someone really has something important to say, it usually doesn’t take very long. When Neville Chamberlain announced the grim news to the British people in 1939 that Britain had declared war on Germany, the message had been delivered by the end of the 67th word. I did a test reading just now and it took about 26 seconds, including pauses for effect.
Einstein’s legendary 1905 paper that presented his special theory of relativity to the world, ending decades of confusion amongst physicists, is only 24 pages, and the key part that resolves the paradoxes by which physics was previously beset is complete by the end of page 12! John Bell’s paper that turned the world of Quantum Mechanics upside down in 1964 is only six pages. Bell cited only five references. Einstein cited none.
In general communication, most people use too many words. I do too, but I am trying to correct that. I feel that, where possible, I would like to conduct a post-mortem on every sentence I utter and work out whether that sentence has added any new information. If it hasn’t, then it was probably a waste of everybody’s time.
Politicians exploit this deliberately. They are trained to, when asked a difficult question by a journalist, give a long-winded, emphatic speech about something only tangentially related, thereby avoiding the issue and (they hope) making the journalist despair of persisting with the question because of the pressure of time. Even better, if the politician sounds confident in their ‘answer’, the less analytic watchers will form the impression that the politician is competent and frank. The more analytic types just shrug their shoulders in disgust and turn the telly off.
A sentence can be very long and yet not reveal what information it contains until late in the sentence. Sometimes there is a key word that makes it all fall into place, The words before that one stack up like the numbers in a long calculation on a Reverse Polish calculator, impotent while they wait for release. Then the key word comes and it all falls into place. It attains a meaning. The wait for that word can sometimes be prolonged, like in this:
Though they all came from different social strata, sub-cultures and occupations, crammed together against their will in the prison cell from which they wondered if there would ever be any release, though none of them had known each other – or even known of each other – in their previous lives, though they squabbled and quarrelled over the tiniest of things, the one thing that bound them together despite the rivalries and petty jealousies, the perceived slights and reconciliations, the development, disintegration and reformation of cliques, was a single shared emotion, an emotion so powerful that they could feel it oozing out of one anothers’ pores, smell it on their breath and discern it in the tones of voice – the emotion of fear.
In some cases, the key word never comes. Perhaps the writer or speaker confuses themselves by their excessive verbiage and ends the sentence with an admission of defeat.
Books are too long as well! Novels are generally OK, as it takes time to get to know and care about the characters. But I have a strong sense that non-fiction books are often padded to reach whatever is considered a minimum page count for a book – usually at least 200. There isn’t really a strong market for writings that are halfway between essay and book length. In many cases a book really only has one idea, which could make a decent essay, but doesn’t justify a book. But essays don’t get to be put on a prominent shelf that catches your eye as you enter the bookshop, nor do they get listed on the New York Times best sellers’ list.
Nassim Taleb’s famous book ‘The Black Swan’ is like that. It really only contains one idea, which is that investors, bankers and other financiers have for decades been making crucial financial decisions based on theories in which they assume that the future will be like the past, and that all occurrences of randomness must follow the Normal Distribution (the nice friendly old ‘Bell Curve’). Decisions based on that erroneous, oversimplified assumption have repeatedly led to disasters, because events tend to be more extreme than is predicted by the Bell Curve. Taleb’s is a good insight, and definitely worth saying, but probably not worth stringing out to book length.
And then, if the book sells well, they write it again, ever so slightly differently, and pretend it’s a new book, with new ideas. Taleb did that. Self-help authors do it all the time – which raises the question ‘If your first book about how to live a better life was so incomplete that it needs to be supplemented by a second, why did I waste my time reading it?‘ I suspect Richard Dawkins may do it too. As far as I can tell he has written at least four popular explanations of evolution. I read The Blind Watchmaker and thought it was great (but too long, of course!). But I didn’t read The Selfish Gene, The Ancestors’ Tale or The Greatest Show on Earth because I couldn’t see any indicators that they would contain much substance that hadn’t already been covered in the one I had read. I imagine there is some new material in each of them, but I would guess it’s more likely to be a dozen pages’ worth rather than 200+.
Fiction authors and other creative artists do this too. Stravinsky acidly observed that Vivaldi wrote the same marvellous concerto five hundred times. Bach shamelessly reused his work (goodness knows he was paid little enough for it!) and Enid Blyton invented maybe a dozen adventure and fantasy stories, which she recycled into what seems like hundreds of similar tales (surely I’m not the only one that’s noticed the remarkable similarity between Dame Slap’s School for Bad Pixies and Mr Grim’s School for Mischievous Brownies?). And let’s not even mention Mills and Boon. But somehow I don’t mind that so much. We humans are story-telling animals, and telling the same story repeatedly, changing it just a little every time, is what we have always done. I find myself able to smile indulgently on the prolixity of Enid and Antonio and Mills (?), but alas not on that of Nassim or Richard, or Deepak Chopra.
I think I’ve ranted for long enough now about how We All (including me) need to work on being more concise with our communication. It’s time to relent a little.
Not all language is just about conveying information, so the efficiency with which the information is conveyed is not always the best test. In comforting a frightened child, information communication is not the purpose of our speech. I will restrain myself from objecting that the second half of the soothing phrase ‘There, there‘ is informationally redundant. In fact, I think I could even stretch to approving of its repetition, if its first invocation was insufficient to assuage the poor mite’s distress.
Declarations of love, expressions of support, telling jokes, goodbyes, hellos and well-wishes are all ‘speech acts’ that have important non-informational components. It seems appropriate to apply different expectations to those speech acts from those we apply to informational speech. Even there, there are limits though. Many’s the operatic love aria I’ve sat through where after a while I just feel like screaming ‘OK, you love him, we get it, can we move on with the plot now please?’ And waiting for Mimi to die in La Boheme (of consumption, what else?) in between faint protestations of her love for Rodolfo, can become a little trying on one’s patience after the first ten minutes of the death scene.
But communication of information is the purpose of much of the language we use, especially in our work lives. It is a pity that so much of it is ill-considered.
Hmmm. 1,742 words. I wonder if I could turn this into a book.
Bondi Junction, November 2015
I like helping people with their homework on the internet. I do this when I can on physicsforums.com, which is a forum for discussing physics, and philosophyforums.com, which is for discussing philosophy. Both have sections where people can ask questions about problems they are having trouble understanding – usually for homework in a degree course. The physics forum has Help sections covering physics, mathematics and chemistry. The philosophy forum’s Help section is focused on symbolic logic, which is a branch of maths closely related to set theory.
There’s an art to both asking and answering questions on such forums. It is not acceptable to just post a question straight out of an assignment and hope somebody solves it for you. That would be lazy, and possibly also cheating. Equally, it is not the done thing to just post a solution to somebody’s problem, even though that would often be the easiest thing to do. The paradigm of quality advice on the internet seems to be to give carefully chosen hints that will lead the student towards being able to solve the problem by themself. It is quite challenging to choose one’s hints to be not so obvious that they give the game away, and not so obscure that the student remains helplessly lost.
Now you might expect there to be an imbalance between people needing advice and people offering it, so that many people remain unhelped. Well there is an imbalance, but it’s the other way around. There are far more willing advisers than there are people wanting to be advised! How does such an odd situation arise? I can only guess at it based on my own attitude to internet advice – which is that I love giving it. I think there is a deep-seated need in most humans to feel useful. In some it is stronger than others, and in me it is quite strong. In some professions, like being a doctor, one has frequent opportunities to provide advice to one’s acquaintances. People seem to have an inexhaustible appetite for free medical advice. But the knowledge of art critics, journalists, electricians and accountants is drawn upon far less frequently in private life. Of course people would be very happy to draw upon the skills of an electrician without cost, for instance to get them to fix some circuits in one’s house. But that is very different from asking for advice. Spending an hour alone in a dusty roof cavity fiddling with dangerous wires is far less fun than dispensing advice to an agog and appreciative audience. A notable example of this difference is the poor old professional photographer. Goodness knows how many times they get asked by friends, relatives and acquaintances to come to a wedding and take some photos – for no fee, of course. And like the electrician in the attic, it is solitary work, with little appreciation except at the time when one actually delivers the photos.
The few professional photographers I have known have had policies of not doing photography for anybody’s wedding except as a fully professional, paid gig. I thought that policy a bit harsh when I first came across it. But after reflection I realised it was the only way to end up avoiding spending countless hours doing work for free, as well as missing out on being able to enjoy one’s friends’ weddings. Life is hard enough for photographers these days, with news organisations slashing their headcounts of journalists and photographers – preferring to just get stock clips from Getty images. It adds to the woe to be be constantly asked to work for nothing.
On the other hand, if people were to gather around them in adoring circles at parties, asking their advice on shutter speeds, apertures, lenses and filters, that would be a different thing altogether. So far as I can tell, that doesn’t happen very often.
My areas of expertise are not under such hard times as photographers, but neither are they as socially sought-after as those of doctors. They include finance, music, bicycles and fitness, philosophy, physics and mathematics. Once or twice a year I get asked for advice on bicycles, fitness or investment. I don’t think I’ve ever been asked about physics, philosophy, music or maths, unless we count my children asking for homework help when they were little.
So, to fulfil my need to feel useful, I go to the internet to see who needs help integrating x sin x, working out whether a pendulum has enough energy to swing right over the top of its arc, working out whether ‘Dark Energy’ would break a wire stretched between two galaxies, or understanding the significance of the Bell Inequality or Godel’s First Incompleteness Theorem.
And what do I find when I go there? Any question that is expressed even moderately clearly has received three or more responses within half an hour of being posted. It’s almost as though people are falling over one another to be the first to respond. You might think that one response is all that’s needed. But it’s not. There is often room to contribute even when there have already been two or three responses to the request. Remember that answers are supposed to be hints, not answers to the homework problem. The best answers are often in the form of questions to the original poster, like ‘what is the component of the gravitational force that points diagonally down the banked track?‘ They serve just to get the student thinking in the right direction, or even in just a more productive manner. Often responders need to ask questions to clarify the problem because the student has not explained it well enough. In logic, the standard question is ‘what tools are you allowed to use?‘ because the typical problem is to prove a statement, given a number of premises and a set of deduction rules, and there are many different logical systems, with different ‘toolboxes’ of deduction rules. Most students just post ‘how do I prove such-and-such, given the following premises’, without specifying what tools are available to them.
So I still sometimes find questions to which I can helpfully respond. Some questions are expressed so unclearly that nobody wants to touch them. I quite enjoy the forensic work of trying to work out what the communicationally-challenged student was trying to say. In other cases, the question may be clear enough but the responders may have gone off on a false trail, or been insufficiently clear, leaving room for me to contribute. But it’s only the occasional question that I find has received little enough helpful attention for me to respond without giving too much of the answer away.
I have said that I get enjoyment from answering questions. And maybe I am a little more than averagely susceptible to enjoying the fulfilment that comes from that. But there are many people that seem to have a much stronger desire for that fulfilment than I. Many of the responders have made tens of thousands of posts to the forums, and their presence can be seen in most of the questions ever asked. Those that have responded to very large numbers of questions have little electronic trophy icons below their on-line avatar, saying things like ‘Homework Helper’. It reminds me of the Fat Controller, who would occasionally, when Thomas or one of his friends had done especially well, reward them by proclaiming that they were a Really Useful Engine – the ultimate accolade!
Why do people like helping so much on the internet? This wish to be useful is so widespread, and so strong. And it isn’t mirrored in off-line life – or is it? Perhaps it is. Most doctors appear to enjoy being consulted by family and friends on the selection of a surgeon for Tristram’s grommets, and I’m sure the electrician would revel in the opportunity to dispense wisdom on the difference between the connections of a Neutral and an Earth wire, as long as they weren’t then dispatched to the attic to do some free clipping and splicing. I once consulted an electrician on just this topic and, as far as I could tell, they enjoyed providing the information.
Is it possible to harness this human tendency? There are so many people in the world that need help and don’t get it. Maybe it is. But on the other hand maybe the seeming disconnect between the large number of willing advisers on the internet and the large number of people in real life desperately needing help can be explained by the above-mentioned difference between advice and work. Giving advice is often easy, takes little time, costs nothing and is a social activity, as one does it in conversation with the advisee. Work, on the other hand, whether it be fixing wires, taking photos, preparing a pathology slide, or constructing a Monte Carlo model to measure financial risk is time-consuming, usually solitary and often frustrating.
There are exceptions. I’ve always liked the idea of raising a barn, like the Amish do in Pennsylvania, because it seems such an enjoyable, social, neighbourly form of work. Sadly, not many barn raisings happen in my neighbourhood.
Bondi Junction, August 2015