Thought Association

I was jogging on the beach, trying to think of something else because the last couple of days had been rather upsetting. I settled on thinking about an essay I am trying to write about The End of The World. Very soon I found that I had the REM song It’s the end of the world as we know it running through my head on repeat.

After a while I noticed somebody running along next to the concrete promenade, where the sand is softest because it is furthest from the water and almost never gets wet from the sea. The sand was pretty soft where I was, about halfway between the promenade and the water. But maybe it was softer over near that other guy. In any case, we’d had heaps of rain recently, so if water makes sand pack together harder, presumably where I was would be just as water-hardened as next to the promenade.

But then maybe seawater has a different effect. Perhaps it makes the sand stick together better than rainwater does. If so then the sand next to the promenade really would be softer, unless the sea ever gets up to there.

That led to me wondering about whether, in the wildest sorts of weather, the sea ever came all the way up to the concrete wall below the promenade (about fifty metres from the high tide mark).

Thinking of stormy weather made me think of the scene in the movie The French Lieutenant’s Woman where the female lead stands at the end of a long jetty in a storm, only a metre or two above the rough sea – a precarious position, deeply evocative.

That led me to wonder whether it is sexist to refer to the character as somebody’s ‘woman’, thereby seeming to suggest ownership. That led to my thinking about the reverse phrase ‘somebody’s man’, which led me to think of the Tammy Wynette song Stand by your man.

And without any conscious decision to do so, there I was, jogging along the beach, mentally humming Stand by your man instead of It’s the End of the World as we know it.

Thought association.

Andrew Kirk

Bondi Junction, April 2017

Featured Image is from the 1981 movie The French Lieutenant’s Woman, showing the jetty called ‘The Cobb’ at Lyme Regis UK.


The End of the World

One day the sun will grow so large that it will first dessicate, then bake, then engulf and vaporise, the Earth and everything on it. No life will survive that. Perhaps some people will have escaped to habitable places in other solar systems, but it’s hard to imagine it would be many, given the enormous energy that is likely to be involved in any interstellar travel. I expect ordinary people will be unable to escape.

Even escapees will be wiped out eventually, as the universe, many billions of years from now, slides inexorably into heat death. No life will survive that.

So there it is: the end of the world is a matter of when, not if. We are powerless to prevent it.

That background makes it a bit confusing to work out what moral obligation we have to take actions that prevent a near-term end of the world, and to avoid actions that would hasten it.

If we are talking about preventing the end of the world in our lifetime, it can be easier to resolve, because that would affect people that are alive now, and most people recognise that they have at least some obligation of care to other people that cohabit the world with them.

But that obligation is less widely accepted when it comes to future generations, and the farther away those generations are, the fewer people tend to feel an obligation towards them. Politicians sometimes talk about intergenerational equity and caring for the future of our children, maybe even our grandchildren. But it’s a rare politician that argues for a policy on the basis of its effect on our great-great-great-great-great-great-great-great-children.

At some stage, life on Earth will come to an end, and it seems likely that that end, unless it occurs in the blink of an eye – which it is hard to imagine happening – will be accompanied by tremendous suffering. If that is inevitable then how can we work out whether it matters whether it occurs sooner or later?

We cannot solve this by reason alone. As David Hume so acutely observed “Tis not contrary to reason to prefer the destruction of the whole world to the scratching of my finger.” Of course he wasn’t saying he did prefer the destruction of the world. He was saying that one must look to one’s emotions to find an answer.

Looking to my own emotions, I confess that I am more alarmed at the prospect of the world ending in a catastrophe in 100 years than in 100 million years, despite the fact that I will not be here to see either..

I use the word ‘catastrophe’ rather than ‘cataclysm’ because I think the end would be lingering and painful. We should be so lucky as to be extinguished in the blink of an eye. Philosophers who have nothing better to do with their time make up thought experiments involving a button you could press to instantaneously end the world, and ask under what circumstances you would press it. But there are no such buttons, nor ever likely to be, so we need to contend with the end being a drawn-out, painful process. I suspect widespread famine would be a major part of it. That would lead to outbreaks of uncontrolled violence as people compete for the dwindling resources of food and water. Disease would spread to accompany the famine – perhaps providing a more merciful end for some. We see this sort of catastrophe already in some parts of the Earth, and we will see them more often as climate change becomes more severe.

Is a ‘soft landing’ possible? What if, realising that the world will become uninhabitable within 200 years, we were to decide that we were morally obliged to not have children, in order not to inflict on those new people the pain of experiencing the world’s slow death? What would a world with no new children be like? Most of us, including me, feel that it would be very sad. I know of two novels that explore this: ‘The Children of Men‘ by PD James, and ‘I who have not known men‘ by Jacqueline Harpmann. In the first, for some unknown reason, humans cease to be able to conceive. The novel is set about twenty-six years after the last baby was born. In the second novel, a group of female prisoners escape from their underground dungeon to find the Earth deserted. They wander for many years in vain search of other survivors and after a while start to die of old age, with no replacement.

Both novels are confronting, bleak and sad. The James also has a thriller element to it (which I won’t spoil for you), but the basic premise is still bleak.

It would be very hard for us now to decide ‘No more babies’. Imagine us all gradually dying one by one, deprived of that feeling of continuity – the circle of life – that one gets from seeing younger generations. But what if society had the time to work up to that over several generations? What if, realising that all life would cease within ten generations, society worked to change its culture in order to equip people to feel more positive about non-procreation and less reliant on younger generations. It would be a very difficult psychological shift to accomplish. It would have to counteract the powerful impulse embedded in our psyche by evolution – to perpetuate the species. But who knows what techniques of psychological manipulation humans may have managed to invent in a thousand or more years’ time? Maybe they could condition future humans to find fulfilment in bringing their species in for a soft landing – for instance in working as a childless carer for old people until one becomes too old to work. Things could be set up so that the last remaining people have all the food, water, clothes, medicine, shelter, power and entertainment they need to survive solo (we would also need to train people to be comfortable with isolation, which we current humans are definitely not). They might also be provided with pills to provide a painless end to life once they near the point where they will no longer be able to feed themselves. That is not how it happens in ‘The Children of Men‘. But that book is set in 2021, not 3021, and with no notice for society to prepare for the landing (for some reason fertility just suddenly ceases in 1994).

If a soft landing were possible then, while an end of the world may be inevitable, its accompaniment by great suffering would not be. It would then become easy to argue for doing what we can to delay the end of the world. It is simply to prevent a great suffering.

What if it’s not possible, so that the great suffering is simply a matter of ‘when’ rather than ‘if’? What if the amount of suffering accompanying the end of the world will be roughly the same regardless of whether it occurs in 200 years or 200 million years? Are we morally obliged to do what we can to defer it beyond 200 years? I pick 200 years by the way because that should be long enough to be fairly certain that nobody currently alive will be around to experience a world’s end in 200 years.

It seems to me that the main difference between the two end dates is all the currently-unconceived humans that would experience life in the intervening 199,999,800 years. Is it a good thing or a bad thing that such lives should come to pass? There is very little moral guidance on this. Even religions have little to say about this, with only a very few religions (albeit big powerful ones) forbidding contraception.

A group that has a decisive opinion that is the direct opposite of the anti-contraceptionists is the anti-natalists, led by the prominent South African philosopher David Benatar. Benatar argues that, since all life contains some suffering, it is immoral to create any new life. He does not accept that suffering may be offset by pleasure at other times in a life. Even a few moments of mild pain in an otherwise long, happy life makes the creation of that life a moral mistake, in Benatar’s book. Less extreme anti-natalists argue that procreating is OK if we think the new life will have more pleasure than suffering but that, since we can’t be sure, we are obliged to not procreate. A more folksy version of this is the comment uttered at many a late-night D&M discussion, that ‘this is no world to bring an innocent child into‘.

Not many people are anti-natalists. Most people, despite the exaggerated doom and gloom on the news – terrorist this and serial-killer that – (of course no mention of the real dangers like climate change, malaria, poverty, road carnage and plutocratic hijack of our democracies) see life as a generally pleasant experience and look positively on conferring it on new humans. But that tends to be a very personal feeling, in which the moral dimension cannot be disentangled from the powerful personal urge to procreate.

For those of us who are neither anti-natalists nor anti-contraceptionists, the question of those lives in the intervening 199,000,800 years remains a mystery to be explored. Is it important that they come to pass? Is it good that they do so?

Lest you decide I sound like a homicidal maniac and ring Homeland Security to have me ‘dealt with’, let me state here that I feel that it is better to do what we can to delay the end of the world. That’s a major factor in why I think action on climate change is the most important issue facing humanity today. But I won’t go into the reasons why in this essay, because this topic will be discussed at my upcoming philosophy club meeting and I want to avoid spoilers. In any case, I’m more interested in what other people think about this.

The dilemma posed by this essay was first raised by Oliver Kirk.

Andrew Kirk

Bondi Junction, April 2017

Questions

  1. What, if any, obligations do we have to unborn generations? Do they include an obligation to ensure their existence?
  2. Does the nature or strength of the obligation change with the remoteness of the future generation?
  3. If we accept that the end of humanity will occur, and will be accompanied by great suffering, are we obliged to do what we can to delay it for as many centuries or millennia as possible (taking as agreed that we are obliged to delay it beyond the lifespan of anybody currently alive)?
  4. If we do feel obliged to delay, does that imply an obligation to maximise the population of the Earth, subject to being able to maintain adequate living standards?
  5. How do I feel about the fact that a time will come when there is no more life? Does it strip life of meaning? Or does it enhance meaning? Or neither?
  6. How would I feel about a world in which human reproduction became impossible?
  7. Do I feel differently about the world ending in 200 years from how I feel about it ending in 200 million years?
  8. What implications do our opinions on the above have on our feelings of what stance we should take on current future-oriented issues like climate change, balancing government budgets, infrastructure building, asteroid mapping, solar flare prediction?

References

PD James: ‘The Children of Men’

Jacqueline Harpmann: ‘I Who Have Never Known Men’ (‘Moi qui n’ai pas connu les hommes’)

Peter Singer: “Practical Ethics’. Discussion of obligations to future generations on p108-118 of Third Edition (2011, Cambridge University Press).


Pointing the Camera at the Monitor – An Answer

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).

figure-01-q0a-screenshot-cheese-bear-non-max

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.

Question 1

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):

figure-02-q1_image

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!

Question 2

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):

figure-03-q0b-screenshot-bear-maximised

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):

figure-04-q2_image

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).

figure-05-q2-empirical-non-full-screen

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

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  t2t1. 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?

Here’s the video.

Question 4

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):

pan_image_1

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):

pan_image_32

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):

figure-08-pan-table-fullA 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):

figure-09-pan-table-left-panel

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):

figure-10-pan-table-with-locii

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):

figure-11-final2048_smaller

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.

Andrew Kirk

Bondi Junction, February 2017

strip01-08strip09-16strip17-24strip25-32


Pointing the Camera at the Monitor – A Puzzle

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.

Andrew Kirk

Bondi Junction, February 2017

Footnotes

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.


Hypotheticals, counterfactuals and probability

This essay considers the notion of events occurring that we do not know to either have occurred, or to be almost certain to occur in the future. Imagination of such events is everywhere in everyday speech, but we rarely stop to consider what we mean by it, or what effect imagining such things has on us.

It is dotted with numbered questions, so it can be used as a basis for a discussion.

Counterfactuals

A counterfactual is where we imagine something happening that we know did not happen.

This is fertile ground for fiction. Philip K Dick’s acclaimed novel ‘The Man in the High Castle’, written in 1962, depicts events in a world in which the Axis powers won World War II, and the USA has been divided into parts occupied by Japan and Germany. The movie ‘Sliding Doors’ is another well-known example, that imagines what ‘might have happened’ if Gwyneth Paltrow’s hadn’t missed a train by a second as the sliding doors closed in front of her..

When something terrible happens, many people torment themselves by considering what would have happened if they, or somebody else, had done something differently:

  • What if I had been breathing out rather than in when the airborne polio germ floated by? (from Alan Marshall’s ‘I can jump puddles’)
  • If she hadn’t missed her flight and had to catch the next one (doomed to crash), she’d still be alive now.
  • What would life have been like if I hadn’t broken up with Sylvie / Serge?

We can also consider counterfactuals where the outcome would have been worse than what really happened, such as ‘What would my life have been like if I hadn’t met that inspirational person that helped me kick my heroin habit‘. But for some reason – so it appears to me – most counterfactuals that we entertain are where the real events are worse than the imagined ones. We could call these ‘regretful counterfactuals‘ and the other ones ‘thankful counterfactuals‘.

Then there are the really illogical-seeming ones, like the not-uncommon musing: ‘Who would I be [or what would I be like] if my parents were somebody else?‘ which makes about as much sense as ‘what would black look like if it were a lightish colour?

Here are some questions:

  1. why do we entertain counterfactuals? What, if any, benefits are there from considering regretful counterfactuals? What about thankful ones?
  2. given that for many counterfactuals, consideration of them just makes us feel bad, could we avoid entertaining them, or is it too instinctive an urge to be avoidable?
  3. Do counterfactuals have any meaning? Given that Alan Marshall did breathe in, and did contract polio, what does it mean to ask ‘If he had been breathing out instead, would he have become a top-level athlete rather than an author?‘ Are we in that case talking about a person – real or imaginary – other than Alan Marshall, since part of what made him who he is, was his polio?

That last question can lead in some very odd directions. My pragmatic approach is that counterfactuals are made-up stories about an imaginary universe that is very similar to this one, but in which slightly different things happen. Just as we make up stories about non-existent lands, princesses and far away galaxies, we can make up stories about imaginary worlds that are very similar to this one except in a handful of crucial respects.

Some philosophers insist that counterfactuals are not about imaginary people and worlds but about the real people we know. My objection to that is that, for example, the Marshall counterfactual cannot be about the Alan Marshall, because he had polio. It can only be about an imaginary boy whose life was almost identical to Marshall’s up the point when the real one contracted polio. My opponents (who would include Saul Kripke, that we mention later) would counter that polio is not what defines Alan Marshall, that it is an ‘inessential’ aka ‘accidental’ property of that person, and changing it would not change his being that person. Which begs the question of what, if any, properties are essential, such that changing them would make the subject a different person. Old Aristotle believed that objects, including people, have essential and inessential properties, and wrote reams about that. In the Middle Ages Thomas Aquinas picked up on that and wrote many more reams about it. The ‘essential properties’ of an object are called its ‘essence’, and believing in such things is called ‘Essentialism’. That is how certain RC theologians are able to claim that an object that looks, feels, smells, sounds, tastes and behaves like a small, round, white wafer is actually the body of Jesus of Nazareth – apparently because, although every property we can discern is that of a wafer, the ‘essential’ properties (which we cannot perceive) are those of Jesus, thus its essence is that of Jesus. I tried for years to make sense of that and believe it, but all it succeeded in doing was giving me a headache and making me sad. For me, essentialism is bunk.

  1. Can you make any sense of Essentialism? If so can you help those of us who can’t, to understand it?

I can’t help but muse that maybe thankful counterfactuals have some practical value, as they can enable us to put our current sorrows into perspective. They are a very real way of Operationalizing (I know, right?) what Garrison Keillor suggests is the Minnesotan state motto – ‘It could be worse‘.

Maybe regretful counterfactuals sometimes have a role too, when they encourage us to learn from our mistakes and be more careful in the future. But they are of no use in the three examples given above. What are we going to learn from them: Never breathe in? Never fly on an aeroplane? Never break up with a romantic partner (no matter how unsuitable the match turns out to be)?

If we do something that leads to somebody else suffering harm, considering the regretful counterfactual can be useful. If I hadn’t done that, they wouldn’t be so sad. How can I make it up to them? I know, I’ll do such-and-such. That won’t fix it completely, but it’s all I can think of and at least it’ll make them feel somewhat better.

But once we’ve done all we can along those lines, the counterfactual has outlived its usefulness and is best dismissed. Otherwise we end up punishing ourselves with pointless guilt, which benefits nobody. Yet we so often do this anyway, perhaps because we can’t help it, as speculated in question 2.

I am completely useless at banishing guilt. But the techniques I have, feeble as they are, revolve around reminding myself that the universe is as it is, and cannot be otherwise. The past cannot be changed. If I had not done that hurtful thing I would not have been who I am, and the universe would be a different one, not this one. I am sorry I did it, and will do my best to make restitution, and to avoid causing harm in that way again. But the counterfactual of my not doing it is just an imaginary story about a different universe, that is (once I’ve covered the restitution and self-improvement aspects) of no use to anybody, and not even a good story. Better to read about Harry Potter’s imaginary universe instead.

This universe-could-not-have-been-otherwise approach is currently working moderately well in helping me cope with the recent Fascist ascendancy in the US. There are so many ‘if only…’ situations we could torture ourselves with: ‘If only the Democrats had picked Bernie Sanders’, ‘If only Ms Clinton hadn’t made the offhand comment about the basket of deplorables’, ‘If only the Republicans had picked John Kasich’. Those ‘If only’s are about a different universe, not this one. They could not happen in this universe, because in this universe they didn’t happen.

Counterfactuals also come into Quantum Mechanics. Arguably the most profound and shocking finding of quantum mechanics is Bell’s Theorem which, together with the results of a series of experiments that physicists did after the theorem was published, implies that either influences can travel faster than light – which appears to destroy the theory of relativity that is the basis of much modern physics – or Counterfactual Definiteness is not true. Counterfactual Definiteness states that we can validly and meaningfully reason about what would have been the result if, in a given experiment, a scientist had made a different type of measurement from the one she actually made – eg if she had pointed a particular measuring device in a different direction. Many find it ridiculous that we cannot validly consider what would have happened in such an alternative experiment, but that (or the seemingly equally ridiculous alternative of faster-than-light influences) is what Bell’s Theorem tells us, and the maths has been checked exhaustively.

Hypotheticals

A counterfactual deals with the case where something happens that we know did not happen. What about when we don’t know? I use the word hypothetical or possibility to refer to where we consider events which we do not know whether or not they occur in the history of the universe. These events may be past or future:

  • a past hypothetical is that Lee Harvey Oswald shot JFK from the book depository window. Some people believe he did. Others think the shot came from the ‘grassy knoll’.
  • a future hypothetical is that the USA will have a trade war against China

What do we mean when we say those events are ‘possible’ or, putting it differently, that they ‘could have happened‘ (for past hypotheticals) or that they ‘could happen‘ (for future hypotheticals)? I suggest that we are simply indicating our lack of knowledge. That is, we are saying that we cannot be certain whether, in a theoretical Complete History of the Earth, written by omniscient aliens after the Earth has been engulfed by the Sun and vaporised, those events would be included.

Some people would insist that the future type is different from the past type – that while a past hypothetical is indeed just about a lack of knowledge about what actually happened, a future hypothetical is about something more fundamental and concrete than just knowledge. This leads me to ask:

  1. Does saying that a certain event is ‘possible’ in the future indicate anything more than a lack of certainty on the part of the speaker as to whether it will occur? If so, what?

I incline to the view that it indicates nothing other than the speaker’s current the state of knowledge. What some people find uncomfortable about that is that it makes the notion of possibility depend on who is speaking. For a medieval peasant it is impossible that an enormous metal device could fly. For a 21st century person it is not only possible but commonplace. As Arthur C Clarke said ‘Any sufficiently advanced technology is indistinguishable from magic.’ To us, mind-reading is impossible, but maybe in five hundred years we will be able to buy a device at the chemist for five dollars that reads people’s minds by measuring the electrical fields emitted by their brain.

Under this view, the notion of possibility is mind-dependent. What would a mind-independent notion of possibility be?

There is a whole branch of philosophy called ‘Modal Logic’, and an associated theory of language – from the brilliant logician Saul Kripke – that is based on the notion that possibility means something deep and fundamental that is not just about knowledge, or minds. To me the whole thing seems as meaningful as debates over how many angels can dance on the head of a pin, but maybe one day I will meet somebody that can demonstrate a meaning to such word games.

Sometimes counterfactuals sound like past possibilities. That happens when we say that something which didn’t happen, could have happened. Marlon Brando’s character Terry in ‘On the Waterfront‘ complains ‘I coulda been a contender … instead of a bum, which is what I am‘. As I said above, I don’t think it makes literal sense to say it could have happened, since it didn’t. But if we didn’t know whether it had happened or not, we wouldn’t have been surprised to find out that it did happen. So in a sense we are saying that a person in the past, prior to when the event did or didn’t occur, evaluating it from that perspective, would regard it as possible. Brando’s Terry was saying that, back in the early days of his boxing career, he would not have been at all surprised if he had become a star. But he didn’t, and now it was too late.

What would happen / have happened next?

With both counterfactuals and hypotheticals, we often ask whether some other thing would have happened if the first thing had happened differently from how it did. For instance:

  • [counterfactual] If the FBI director had not announced an inquiry into Hilary Clinton’s emails days before the 2016 US presidential election, would she have won?
  • [past hypothetical] If Henry V really did give a stirring speech like the ‘band of brothers’ one in Shakespeare’s play, exhorting his men to fight just for the glory of having represented England, God and Henry, were any of the men cynical about his asking them to risk death just in order to increase Henry’s personal power?
  • [future hypothetical] If Australia’s Turnbull government continues with its current anti-environment policies, will it be trounced at the next election?

Which leads to another question:

  1. What exactly do these questions mean?

The first relates to something that we know did not happen and the other two relate to what is currently unknowable.

My opinion is that, like with counterfactuals, they are about making up stories. In the US election case we are imagining a story in which certain events in the election were different, and we are free, within the bounds of the constraints imposed by what we know of the laws of nature, to imagine what happened next. Perhaps in the story Ms Clinton wins. Perhaps she then goes on to become the most beloved and successful president the country has ever had, overseeing a resurgence of employment, creativity, and brotherly and sisterly love never before encountered. Or perhaps she declares martial law, suspends the constitution and becomes dictator for life, building coliseums around the country where Christians and men are regularly fed to lions. Within the bounds of the laws of nature we are free to make up whatever story we like.

The same goes for the past hypothetical of Henry’s speech. We can imagine the men swooning in awe and devotion, murmuring Amen after every sentence, or we can imagine them rolling their eyes and making bawdy, cynical quips to one another – but nevertheless eventually going in to battle because otherwise they won’t be paid and their families will starve.

However, the future hypothetical seems to be about more than a made-up story. If the first thing happens – continued anti-environmentalism – then we will definitely know after the next election whether the second thing has also happened. At that point it becomes a matter of fact rather than imagination.

To which I say, so what? Until it happens, or else it becomes clear that it will not happen, it is a matter of future possibilities and can be covered by any of the scientifically-valid imaginative scenarios we can dream up. It is only if the scientific constraint massively narrows down those scenarios that it has significance. If, for instance, we could be sure that any government that fails to make a credible attempt to protect the environment will be booted out office, our future possibility would become a certainty: If the government doesn’t change its track then it will be ejected. But in politics nothing is ever that certain. Other issues come up and change the agenda, scandals happen, natural and man-made disasters, personal retirements and deaths of key politicians. At best we can talk about whether maintaining the anti-environment stance makes it more probable that the government will lose office. Which leads on to the next thorny issue.

Probability

Probability, aka chance, aka risk, aka likelihood and many other synonyms and partial synonyms, is a word that most people feel they know what it means, but nobody can explain what that is.

What do we mean when we say that the probability of a tossed coin giving heads is 0.5? Introductory probability courses often explain this by saying that if we did a very large number of tosses we would expect about half of them to be heads. But if we ask what ‘expect’ means we find ourselves stuck in a circular definition. Why? Because what we ‘expect’ is what we consider most ‘likely’, which is the outcome that has the highest ‘probability’. We cannot define ‘probability’ without first defining ‘expect’, and we cannot define ‘expect’ without first defining ‘probability’ or one of its synonyms.

We could try to escape by saying that what we ‘expect’ is what we think will happen, only that would be wrong. The word ‘will’ is too definite here, implying certainty. When we say we expect a die will roll a number less than five, we are not saying that we are certain that will be the case. If it were, and we rolled the die one hundred times in succession, we would have that expectation before each roll, so we would be certain that no fives or sixes occurred in the hundred rolls. Yet the probability of getting no fives or sixes in a hundred rolls is about two in a billion billion, which is not very likely at all. We could dispense with the ‘certainty’ and instead say that we think a one, two, three or four is the ‘most probable’ outcome for the next roll. But then we’re back in the vicious circle, as we need to know what ‘probable’ means.

  1. What does ‘expected’ mean?

There is a formal mathematical definition of probability, that removes all vagueness from a mathematical point of view, and enables us to get on with any calculation, however complex. Essentially it says that ‘probability’ is any scheme for assigning a number between 0 and 1 to every imaginable outcome (note how I carefully avoid using the word ‘possible’ here), in such a way that the sum of the numbers for all the different imaginable outcomes is 1.

But that definition tells us nothing about how we assign numbers to outcomes. It would be just as valid to assign 0.9 to heads and 0.1 to tails as it would to assign 0.5 to both of them. Indeed, advanced probability of the kind used in pricing financial instruments involves using more than one different scheme at the same time, which assign different numbers (probabilities) to the same outcome.

This brings us no closer to understanding why we assign 0.5 to heads.

Another approach is to say that we divide up the set of all potential outcomes as finely as we can, so that every outcome is equally likely. Then if the number of ‘equally likely’ outcomes is N, we assign the probability 1/N to each one.

That seems great until we ask what ‘equally likely’ means, and then realise (with a sickening thud) that ‘equally likely’ means ‘has the same probability as’, which means we’re stuck in a circular definition again.

  1. What does ‘equally likely’ mean?

After much running around in metaphorical circles, I have come to the tentative conclusion that ‘likely’ is a concept that is fundamental to how we interpret the world, so fundamental that it transcends language. It cannot be defined. There are other words like this, but not many. Most words are defined in terms of other words, but in order to avoid the whole system becoming circular, there must be some words that are taken as understood without definition – language has to start somewhere. Other examples might be ‘feel’, ‘think’ and ‘happy’. We assume that others know what is meant by each of these words, or a synonym thereof, and if they don’t then communication is simply impossible on any subject that touches on the concept.

Or perhaps ‘likely’ and ‘expect’ may be best related to a (perhaps) more fundamental concept, which is that of ‘confidence’, and its almost-antonym ‘surprise’. Something is ‘likely’ if we are confident – but not necessarily certain – that it will happen, which is that we would be somewhat surprised – but not necessarily dumbfounded – if it did not happen. I think the twin notions of confidence and surprise may be fundamental because even weeks-old babies seem to understand surprise. The game of peek-a-boo relies on it entirely.

Once we have these concepts, I think we may be able to bootstrap the entire probability project. The six imaginable dice roll numbers will be equally likely if we would be very surprised if out of six million rolls, any of the numbers occurred more than two million times, or not at all.

There are various frameworks for assigning probabilities to events that are discussed by philosophers thinking about probability. The most popular are

  • the Frequentist framework, which bases the probability of an event on the number of times it has been observed to occur in the past;
  • the Bayesian approach, which starts with an intuitively sensed prior probability, and then adjusts to take account of subsequent observations that using Bayes’ Law; and
  • the Symmetry approach, which argues that events that are similar to one another via some symmetry should have the same probability.

It would make this essay much too long to go into any of these in greater detail. But none of them lay out a complete method. I suspect they all have a role to play in how we intuitively sense probabilities of certain simple events. But I feel that there is still some fundamental, unanalysable concept of confidence vs surprise that is needed to cover the gaps left by the large vague areas in each framework.

Here is one last question to consider:

  1. A surgeon tells a parent that their three-year old daughter, who is in a coma with internal abdominal bleeding following a car accident, has a 98% chance of a successful outcome of the operation, with complete recovery of health. In the light of the above discussion, it seems that nobody can explain what that 98% means. Yet despite the lack of any explicable meaning, the parent is so relieved that they dissolve in tears. Why?

Andrew Kirk

Bondi Junction, January 2017


Surprising oneself

I like to surprise myself. Sometimes life is a mystery novel, in which we wait with bated breath to see what it is that we will do. This only seems to apply in certain particular situations – mostly where the decision really doesn’t matter.

I live near the top of a hill and, approaching my house from the West or the South one has to climb that hill. There are several ways of doing that, but two main ones. As I climb the road next to the park on my bicycle I have the option of continuing up that road until I come to my street, and turning up that. Or I can turn earlier and climb up a side street instead. The climb along the side street is shorter but steeper. So when I’m coming home I have the choice of the shorter, steeper hill, or the longer, shallower – but also more dull – route.

As I climb towards the turn I wonder – which one shall I take? I could try to reason my way about it, making up lists of pros and cons in my head and weighing them up. But I don’t. Instead I wait to find out which I will do. The secret answer to the question is already there – perhaps buried deep inside my nervous system, or perhaps still awaiting some final external stimulus to tip the decision one way or the other – a breath of wind, a car passing by, a creak of the cranks. Who knows what it is that determines the final choice?

All I know is that, as I approach within about ten metres of the possible turn, I will start to know what has been decided. Sometimes I will know straightaway, and be able to revel in, or marvel at, the certainty of the decision for a second or so before the actual turn. Sometimes I trick myself though – I find myself thinking it has been decided that there will be no turn today, when all of a sudden, at the very last second, there I am turning the corner.

One might say that I like to keep myself guessing.

There is a strange feeling of irresponsibility about it, as if the decision were nothing to do with me. It happens sometimes too with little quips that I think of possibly contributing to a conversation. I see the sentence fully-formed in my mind, but do not know whether I will say it, because I do not know whether it will amuse my interlocutors. So I wait and see whether it gets said, by me. Sometimes it does, and sometimes it doesn’t. I never know which until I’ve already started talking, or the opportunity has passed. Why the difference? Nobody knows.

This may be all very interesting, but it would be less fun if it applied to decisions of significant moral importance. Fortunately, for me and, apparently, for most other people, it doesn’t. I think of Camus’ outsider, Meursault, looking at the man before him on the beach, at whom he is pointing a loaded, cocked pistol (for no good reason), and wondering whether he, Meursault, will pull the trigger. I have never been in a similar situation – one of the many advantages of not owning a gun – but I would hate to think that I could look on the question of which way I would decide on an issue of such significance, as something amusing, diverting, outside my control.

While one can make theoretical arguments that whether or not I will choose to do X is purely determined by pre-existing circumstances, there is nevertheless a powerful, nay dominant, feeling of being involved in the decision, of being in control of one’s actions, when the stakes are high. So it is for me at least. Perhaps that’s what was so disconcerting about Meursault – that he had no greater feeling of involvement in, or responsibility for, the decision to shoot the man than he would for a decision to take the shorter, steeper path up the hill, or to risk telling a lame joke.

I cannot like Meursault, but I do feel sorry for him. There but for the grace of God and all that. Perhaps that’s part of what Camus was trying to do. He dissolved the black and white certainties of good and evil that plagued the world at the time of his writing.

Andrew Kirk

 

Bondi Junction, December 2016


Voldemort Dreams

Last night I dreamed of Voldemort.

There’s nothing so strange about that – he’s a memorable character. What makes this worthy of comment is that I realised this morning, for the first time, that I regularly have dreams about Voldemort. But until recently, I have always forgotten them. This is the first time I realised that they are a recurring phenomenon.

They are fairly dramatic dreams. It’s a classic tale of the good (presumably that’s me, and my companions if I have any) trying to find the courage to face up to evil, to confront it, struggle against it – and the fear it evokes – and, one hopes, to vanquish it. Or at least to banish it until the next time it shows up.

Details are sketchy, and would be boring to relate. But the recurring scenario seems to be that, like Harry Potter, I need to venture into Voldemort’s lair (like Frodo going into Mordor) in order to try to bring his plans undone.

There is no absolute need for me to fight Voldemort – no duel with wands at twelve paces or anything like that. But I need to sneak into his headquarters like a secret agent, perhaps to steal some plans or sabotage some special evil-doing equipment he has constructed. I can’t remember the reasons why I need to go into his headquarters, but I do remember that the mission is essential if evil is not to triumph, and that I am very afraid that he will detect my presence and leap out of a wardrobe or somesuch and fling the full weight of his malevolent powers at me. And he does – every time. No matter how quietly I creep about, Voldemort always detects my presence and suddenly leaps out of a wardrobe to attack me with a splendid and terrifying roar.

What happens next I cannot remember. But something extended happens, because he doesn’t win instantly, killing me stone dead on the spot. Maybe some sort of supernatural scuffle and or flight/pursuit ensues and sooner or later I wake up out of that on account of all the excitement.

I don’t want to get too Freudian, but I can’t help feeling that these dreams tell me something. The idea of confronting one’s fears and deliberately going into danger, because it is the right thing to do, may have a strong emotional pull on me. I am, at heart, a romantic, notwithstanding my obsession with mathematics and the correct use of grammar.

A rather more surprising aspect is that the dream involves imagining a character that is supposed to be pure evil. It surprised me because I believe the idea of ‘pure evil’ is dangerous, hyperbolic nonsense. I don’t believe anybody is purely evili. We all do some good things and some bad things. Some people – serial killers, dictators, rednecked talkback radio hosts – do lots of extremely bad things, but I expect even they are not purely evil. I expect they are sometimes kind – to family, to friends, even to strangers that manage to excite their interest or compassion – in those occasional lulls of peace between slaughtering hitchhikers, invading neutral countries and stoking up hatred in resentful white heterosexuals for Muslims, gays or environmental activists.

I don’t believe that evil can be personified – that people like Sauron, Satan, Voldemort or The Penguin are possible. Although I then ask myself ‘Are we really supposed to see the mythological figure of Satan as pure evil?‘. Satan is actually a very interesting fictional character. Some of his complexity may stem from the delightfully baroque Roman Catholic teaching on evil – first cooked up by St Augustine in the fourth century. It says that evil is not a ‘thing’, ie it is not a substance or spirit or anything like that. It is just an absence of another thing that is a thing, which is the ‘good‘. It’s an interesting position, and quite appeals to me, up until the bit where it suggests that the ‘good‘ is a thing. That’s a bit too ectoplasmic for me – the idea that there’s some sort of invisible, nonphysical substance called ‘good’ that floats about and goes here but not there (one wonders, can it be hoovered up by those ectoplasm suction guns that the Ghostbusters use?). It’s needlessly multiplying entities, I reckon. Much easier to just say that people sometimes do kind things and sometimes do mean things, and some people do more of one than the other. William of Ockham would not approve of ‘goodness as a thing‘ (although, being RC, maybe he pretended to, in order to avoid being burnt).

Back to Satan, then: the interesting thing about him is that he isn’t portrayed even in orthodox Christian texts as being pure evil. His story is just that of an angel that didn’t want to serve as an angel any more and so – in what appears to me to be an admirable display of honesty and integrity – resigned. Some bits of the Bible such as the book of Job portray Satan as pretty nasty (but then Yahweh doesn’t come out of Job looking very nice either) but there seems room to view him as a complex, conflicted, multi-faceted figure. Certainly not the sort of person you’d want your daughter to marry, or that you’d trust to do your tax accounts, but not bad enough to deserve exile to an eternity of torment either. I haven’t read Paradise Lost but, by eavesdropping on more literate people that have, I have gained the impression that maybe what Milton was trying to do there was investigate that complexity: Satan as exile, as rebel, as lonely iconoclast.

I digress. Sorry about that. Yes, well I don’t believe in evil as freestanding substance, and I certainly don’t believe in entities that personify evil. So it’s interesting that I dream regularly about battling a character who was created to represent pure evil. Does it mean that my disbelief in evil is purely intellectual, and that deep down I am as credulous and fearful of evil spirits as a Neolithic cave-dweller? Perhaps. Who knows?

Or perhaps even Voldemort is not pure evil. After all, JK Rowling does give him an unhappy childhood, to hint at the idea that maybe he was not always that way – that he was as much a product of his environment as anybody else.

But then I can’t be 100% sure that the terrifying Dark Lord in my dream is always Voldemort. All I know for sure is that in the most recent dream it was Voldemort, and that the dream series in general is about a stupendously powerful being (much more powerful than me) that wishes harm to all sentient beings in the universe. Perhaps other dreams are about Sauron, the Wicked Witch of the West, Darth Vader, or John Le Carré’s Soviet spymaster Karlaii.

Thank goodness my dream self has enough courage to go through with the daring mission each time. It would be mortifying if the last scene of the dream, instead of a big fight-or-flight with a terrifying Dark Lord, saw me skulking about at home in shame and humiliation, having realised that I was too scared to go on the mission that was the free world’s last chance.

I think I can say, without fear of contradiction, that I have one of the bravest dream selves in the observable universe. Now there’s a boast to conjure with! Who else can claim as much?

Andrew Kirk

Bondi Junction, March 2016

 

And No, Tim Minchin, – much as I love most of your work and, like you, detest the power structures and many of the teachings of the RC church – not even George Pell.

ii  Or perhaps the Daleks of course. We mustn’t forget about them!