Provincial Letters

Far from the mad crowds of the city, Blaise Pascal passed comment on the strange behaviour of this urban contemporaries in his Provincial Letters. The connection between them and this blog is somewhat tenuous.

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Location: Grimsby, N E Lincolnshire, United Kingdom

My star sign in Superstition. And I didn't believe in reincarnation last time, either. The only thing I can't tolerate is intolerance. I am a fanatical ant-fanaticist. I am bigotted only where bigots are concerned. I am a fundamentalist atheist. I'm proud to be a product of evolution; I know it in my genes.

Sunday, January 21, 2007

Posted @ 18:46Lies, Damned Lies & Advertising

There's currently an advertisement on British TV for some optician service or other — I can't be bothered to remember which — which claims our eyes process "more than 24 million images in our lifetimes" (or words to that effect). This afternoon, for some reason or other, I wondered what that meant. So I did a little calculation.

Let's assume that the average human life is 70 years and that a year is exactly 365 days long. This equates (do the arithmetic!) to 36,792,000 minutes of life. Therefore, the advertisement claims our eyes only process one image approximately every 1½ minutes. This seems a little slow and implies we must have our eyes shut most of the time.

The advertisement doesn't say that we remember more that 24 million images, just that our eyes process them. It appears that the advertisement says our eyes are limited to processing one image every 90 seconds. Now, think, most films display images at the rate of 24 frames per second, which — taken together with the advertiser's claim — implies that our eyes only process one in 2,160 frames whilst watching a film. Is this credible?

Consequently, it seems obvious that the advertiser's claim is strictly correct: our eyes do process more than 24 million images in our lifetime. But how many more? Ten more? A hundred more? A thousand more? A million more?

Firstly, we need to know how fast the human eye works, how many images per second it can process. The answer to this question is not simple and a full discussion can be found at (which is very worthwhile reading). As this excellent article points out, it's not simply a case of asking how fast the individual receptor cells (rods and cones) of the eye work, since the eye is a complex of these cells and they work together to process the image.

Tests with Air Force pilots have shown that for very bright images — images flashed onto a black background in a dark room — the human eye (together with the human brain) can recognise images of less than 0.005 seconds duration. That's a frame rate of 200 per second. Other considerations show that our perception of some sort of flashing only goes away when the frame rate exceeds 500 per second. That would equate to one image every 0.002 seconds. But that's the extreme.

Let's be very conservative about this and only assume that our eyes can achieve a resolution of one image every 0.01 seconds (a frame rate of 100 per second). This would mean our eyes would process 220,752,000,000 images in a 70 year lifetime. That's over 220 billion images. Yes, it's "more than 24 million". By a factor of approximately 10,000. And, consider, if we were to take the extreme value of 500 frames per second, the total would be five times larger — over a trillion images (and, it's worth remembering, this is the cognitive processing of the eye plus brain system, not that of the — mechanical — eye alone, which is likely to be larger).

Now let's complete the sums. The claim was "more than 24 million images in a lifetime". How many more? Conservatively, 220,728,000,000 more. One feels that the advertiser should really claim "more than 200 billion images in a lifetime" — that would be just a little more realistic and truthful, wouldn't it?

Imagine you and I are looking at a field of cows and you ask me how many there are. Let's say there's 50 cows in the field. What would be your reaction if I said there were "more than 5" cows in the field? You might well consider me a little strange or deranged. And that answer's only a factor of 10 less than the real number, only 10% of the true value. The advertiser's claim is 0.01% of the true value. Yes, I admit, their claim is not false, but it's certainly misleading; and, in the circumstances — considering it took me a little over an hour to research and write this post, considerably less than the production time for a TV advertisement — a damned lie.

Correction Note: Forgot Something

As, Seany has so excellently pointed out, the above calculations assumed we are awake all the time. Assuming we sleep for one-third of our lives, the total images now becomes only 165,564,000,000 which is only 6,898.5 times the quoted figure. And, to recalculate the remaining figures: the actual number is only 165,540,000,000 more than 24,000,000; 24,000,000 is still about 0.01% of 165,564,000,000. Oh, and the quoted 24,000,000 equates to, approximately, 1 image per minute (which would mean we only see one frame of a film in every 1,440 frames). Hope that clears it up.

And, to clear up the "blink" factor that Seany mentions in his comment, we would have to blink at an astonishing rate to bring down these figures in any significant quantity.


Blogger Seany said...

But of each of those days, we are asleep for an average of a third of the time and we should also take the blink factor into account.

Perhaps if I had spent my weekend more responsibly by being in the pub, my brain would have been to numb to give it a second thought!

Sun Jan 21, 10:39:00 pm GMT 
Blogger woja said...

OK, good pint... ...err, point... Seany. So, we'll reduce that number by a third, making it only about 15 billion. The "blink" factor is there in the stuff about the way the eye works. I'll add a note about the sleep factor, though (and recalculate the numbers).

Sun Jan 21, 10:44:00 pm GMT 
Blogger woja said...

That should be 150 billion, of course.

Sun Jan 21, 10:49:00 pm GMT 
Anonymous Anonymous said...

You also have to factor in the amount of time spent with double-vision, due to, ahem, a "relaxed" control of the optical focussing muscles. As I have only ever spoken to Seany when in the pub,and on all those occasions he has been in such a Zen-like state, therefore one can only assume that by statistical extrapolation ALL SEANY'S WAKING MOMENTS ARE LIKE THAT-therefore the figure has to be doubled for every instance of "n", where n=i2 ("i" being Seany's perceived optical sensory input after "y" pints of Hobgoblin.)"y" is any integer greater than, say, 5. Q.E.D-Ian O

Mon Jan 22, 11:12:00 pm GMT 
Blogger woja said...

Ah, a sensible comment.

I think we shall call this the Sean-Hobgoblin Factor and introduce it into science as a fundamental constant up there with the Speed Of Light In A Vacuum, the Gravitational Constant and the Curvature Of The Universe.

Well done, Ian, gold star for you (and a pint of cider).

Mon Jan 22, 11:22:00 pm GMT 
Blogger Seany said...

Its a fair cop guv...

Sat Jan 27, 09:51:00 am GMT 

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