Zooming In

Neil Gaiman tells the story of a Chinese emperor who became obsessed by his desire for the perfect map of the land that he ruled. He had all of China recreated on a little island, in miniature, every real mountain represented by a little molehill, every river represented by a miniature trickle of water.  The island world he created was enormously expensive and time-consuming to maintain, but with all the manpower and wealth of the realm at his disposal, he was somehow able to pull it off.  If the wind or birds damaged some part of the miniature island in the night, he’d have a team of men go out the next morning to repair it.  And if an earthquake or volcano in the real world changed the shape of a mountain or the course of a river, he’d have his repair crew go out the next day and make a corresponding change to his replica.

The emperor was so pleased with his miniature realm that he dreamed of having an even more detailed representation, one which included not only every mountain and river, but every house, every tree, every person, every bird, all in miniature, one one-hundredth of its actual size.

When told of the Emperor’s ambition, his advisor cautioned him about the expense of such a plan.  He even suggested it was impossible.  But not to be deterred, the emperor announced that this was only the beginning – that even as construction was underway on this newer, larger replica, he would be planning his real masterpiece – one in which every house would be represented by a full-sized house, ever tree by a full-sized tree, every man by an identical full-sized man.  There would be the real China, and there would be his perfect, full-sized replica.

All that would be left to do would be to figure out where to put it…

***

Imagine yourself standing in the middle of a railroad bed, looking down the tracks, seeing the two rails converge in the distance, becoming one.  You know the rails are parallel, you know they never meet, yet your eyes see them converge.  In other words, your eyes refuse to see what you know is real.

If you’re curious why it is that your mind refuses to see what’s real in this case, try to imagine what it would be like if this weren’t so.  Try to imagine having an improved set of eyes, so sharp they could see that the rails never converge.  In fact, imagine having eyes so sharp that just as you’re now able to see every piece of gravel in the five foot span between the rails at your feet, you could also see the individual pieces of gravel between the rails five hundred miles away, just as sharply as those beneath your feet.  In fact, imagine being able to see all the pieces of gravel, and all the ants crawling across them, in your entire field of vision, at a distance of five hundred miles away.  Or ten thousand miles away.  What would it be like to see such an image?

***

How good are you at estimating angles?  As I look down those railroad tracks, the two rails appear straight.  Seeing them converge, I sense that a very acute angle forms – in my brain, at least, if not in reality.  The angle I’m imagining isn’t 90 degrees, or 45 degrees; nor is it 30, or even 20.  I suppose that angle to be about a single degree. But is it really?  Why do I estimate that angle as a single degree?  Why not two degrees, or a half a degree?  Can I even tell the difference between a single degree, and a half of a degree, the way I can tell the difference between a 90 and a 45?  Remember, one angle is twice as large as the other.  I can easily see the difference between a man six feet tall and one who’s half his size, so why not the difference between a single degree and a half a degree?  What if our eyes – or perhaps I should be asking about our brains – were so sharp as to be able to see the difference between an angle of .59 degrees and one of .61 degrees with the same ease and confidence we can distinguish between two men standing next to each other, one who’s five foot nine and the other six foot one?

***

Yesterday, I was preparing digital scans of my grandfather’s Christmas cards for printing in the form of a book.  His Christmas cards are hand drawn cartoons, caricatures of famous personalities of his day.  Each is clearly recognizable, from Franklin Roosevelt and Adolf Hitler to Mae West and Mickey Mouse.  Some of the images were scanned at 300 pixels per inch, some at 600 etc.  Reflecting on pixel counts and resolutions so that my printed book would not appear blurry, I was testing the limits of my ability to distinguish different resolutions.   Of course, one neat thing about a computer is how it lets us zoom in.  As long as I zoomed in close enough, I could see huge differences between two versions of the same picture.  Every pixel was a distinct color, every image (of precisely the same part of the caricature) a very different pattern of colors  – indeed, a very different image.  Up close, the two scans of the cartoon of Mae West’s left eye looked nothing alike – but from that close up, I really had no idea what I was looking at – it could have been Mae West’s left eye, or Adolf Hitler’s rear end, for all I knew.  In any case, I knew, from my close-up examination, how very different the two scanned images of Mae West actually were.  Yet, only when I was far enough away was I able to identify either image as being a caricature of Mae West, rather than of Hitler, and at about that distance, the two images of Mae West looked (to my eye) exactly the same.

***

How long is the coastline of Ireland?

If I took a yardstick and walked the perimeter, I could lay my yardstick end to end the whole way around, count the number of lengths, and conclude that the coastline of Ireland was a certain number of feet long.  But if I used a twelve inch ruler instead, following the ins and outs of the jagged coast a little more precisely, the result would be a larger number of feet than if I had used the yardstick, because the yardstick was assuming straightness every time I laid it down, when it in fact the coastline is never perfectly straight.  My twelve inch ruler could more  closely follow the actual irregularity of the coastline, and the result I obtained would be a longer coastline.  Then, if I measured again, using a ruler that was only a centimeter long, I’d get a longer length still.  By the time my ruler was small enough to follow the curves within every molecule, or to measure the curvature around every nucleus of every atom, I’m pretty sure I’d have to conclude that the coastline of Ireland is infinitely long – putting it on a par, say, with the coastline of Asia.

***

How many rods and cones would my eyes have to contain, for me to be able to distinguish every ant and piece of gravel in every railroad bed, wheatfield and mountainside within my field of vision, at a distance of five hundred miles away?  How much larger would my brain have to be, to make sense of such a high-resolution image?  I suspect it wouldn’t fit inside my skull.

***

Why did we, so recently, believe that an atom was indivisible? Why did it take us so long to identify protons, neutrons, and electrons as the really smallest things?  What did it take us until 2012 to decide that that, too, was wrong, that not only were there quarks and leptons, that the smallest thing was the Higgs boson?  And not until 2014 that particles existed even smaller than that?

***

Given how long it took us to realize that our solar system was just one of billions in our galaxy, and how much longer to realize that our galaxy was just one of billions of galaxies, why are we now so confident of our scientists’ estimates of the size of the Universe – especially when told that the “dark matter” and “dark energy” they say accounts for most of it are just names given to variables necessary to make their equations come out right?  That, apart from their usefulness in making these equations come out right, the scientists have never seen this stuff and have no idea what it is?  Is it really so hard for us to say, “We simply have no idea”?

***

A human baby can distinguish between the faces of hundreds, even thousands, of human faces.  But to a human baby, all chimpanzees look alike. And to most of us Westerners, all Asians look alike.  Why do babies treat Asians and Chimpanzees like the rails of railroad tracks, converging them into “identical” images even when we know they are different?  Did our brains  evolve not to maximize perception and understanding, but to make them most efficient?  In other words, are we designed to have limited perception for good, sound reasons, reasons that are important to our very survival?

***

Why do we think, and talk, and act, as if our brains are capable of comprehending reality, in all its vast complexity?  Is it more efficient to feed and maintain fewer rods and cones, than it would take for us to feed and maintain enough of them to see the difference between quarks and Higgs bosons, or the individual pieces of gravel between the railroad tracks on all the planets of  Andromeda?

***

Mirror, mirror, on the wall: tell me, can I really achieve, within my brain, a true comprehension of the Universe? Or am I just like the Emperor of China?

– Joe

Please follow, share and like us:
Facebook
Follow by Email
Pinterest
Google+
https://wemaybewrong.org/wp/2018/04/24/zooming-in/
Twitter
RSS

One thought on “Zooming In”

  1. I believe the Higgs bozon is about 100 times the size of a proton. Discovering it came from one of those formulas based on theory. The Large Hedron Collider at CERN was an expensive way to follow a hunch based on a formula. But ra ra. Billions of dollars later it proved to be real, only it only exists for about 1/10 to the minus twenty of a second before it vanishes. The good news is maybe an entrepreneur somewhere will be able to make use of that information :p

Leave a Reply

Your email address will not be published. Required fields are marked *