Hi everyone! I’ve got another guest post for you, from one of my readers, Craig, over at [Insert Witty Title]. (We’re actually doing a post trade, so I submitted to him an edit of a post I did over here about women in math and science careers (that was an interesting process, editing a post I had already written, and incorporating some stuff from the comments to make it even more clear. If you want in on that discussion, go visit Craig’s blog!) He’s a science guy, and likes explaining science-y stuff to people who don’t have a background in science. Perfect! I thought, I sure could use some of that, since science totally overwhelms me. Maybe if I’d had a science teacher like Craig, I wouldn’t have dropped science classes in grade 10!
Enjoy!
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Infinity is Quite Big
Infinity is one of those concepts that everybody gets in theory but nobody really thinks about too hard. Personally I find infinity very hard to visualise, but that desn’t stop me from trying. Almost without fail I struggle for ages and then just for one horrible second almost manage to grasp how big everything is; for one moment everything else in life feels painfully insignificant and comically small. The feeling always slips away again quickly.
I’m going to try and make everybody feel like that today, using this:
http://www.zeiros.net/infinity/cat.jpg
No, not just a cat: A picture. In fact this picture is 50 by 50 pixels in size, greyscale, and (believe it or not) will make for a really good demonstration of how big numbers can actually go.
When you display a greyscale image on your computer it actually shows only
256 shades of grey. Bearing that in mind lets ask an interesting question: How many different 50 by 50 pixel greyscale images can my computer possibly show?
Not that many, right? It’s such a small picture, there can’t be that many different combinations, right? Wrong!
The answer is actually approximately 10 followed by 6020 zeroes, or more precisely, this (click for big number). This is an absolutely overwhelming, mindblowing number. Looking at a page of digits doesn’t even begin to get over how stupendously large it is, it’s nearly impossible to visualise.
To give us some sort of perspective, imagine if each of our tiny greyscale photographs were printed out and piled on top of each other. The resulting stack would not fit on the Earth, or in our solar system, or our galaxy, it wouldn’t even fit inside the entire Universe, not by a long shot! It would, in fact, need this many (click again for another big number). Universes to contain the stack of images. Quadrillions and quadrillions of Universes needed to hold just that one patch of light.
To ground us a little bit, lets do exactly the same thing again with this picture:
http://www.zeiros.net/infinity/tiny.png
Yes, there is a picture there, it is 5 by 4 pixels in size and has only two colours, black and white. How many of these could there possibly be? Following the same method as before we can calculate that there are 1048576, or just over a million.
I have far too much spare time and went out and made every single one of these million pictures, then mirror imaged them so they look like space invaders. Here are one million space invaders (beware, web browser destroying 6.8Mb png lies beyond that link), here is a tiny fraction of that image:
http://www.zeiros.net/infinity/invaderfragment.png
No repeats, nothing missing, this is every image that could possibly be taken from our hypothetical 5 by 4 pixel black and white camera. Even this little patch of 20 pixels is pretty much mindblowing.
One final thought to leave you with — If you multiply these results up to everything else in life: Every pixel on your monitor and television, every photograph in your house and every image you’ve ever drawn then suddenly reality feels (at least to me) terrifyingly large and at least a little bit more incomprehensible.
So next time you’re bored and feeling like you’ve seen it all before, just remember our quadrillions of Universes and millions of space invaders, and remember exactly how much you haven’t seen.
Oh my! That HTML doesn’t look healthy.
shouldn’t be too hard to fix
remove all the tags, make the text between and italic, swap out the
that’s weird, the markup just worked in the comments, but didn’t work in the original post.
I hate computers. The last comment should have read:
remove all the [p] tags, make the text between [i] and [/i] italic and swap each of the [a href=”….] tag for a link to a text file, and each of the [img src=”…] tags for the corresponding image.
Sorry for the inconvenience, I was hoping this would just work 🙂
there, that should be better!
This reminds me of a exercice a friend of mine had me try:
imagine a point in an empty space
add another point
add a third one at the same distance from each (they will form a triangle)
then add a forth one, equal distance from these three (we have to add a third dimension here and make a three-sided pyramid).
So far so good. Now comes the tricky part: add a fifth point, at equal distance from the four others…
I know what Craig means here when he describes those moments when you can almost grasp how big infinity is. I’ve had those moments as well, and they are so fleeting.
When I was younger, I had super-long hair. I was slightly obsessed with the way it looked in the back, because of course I couldn’t see it so well. In my bathroom, we had this medicine cabinet with three compartments, the doors swung open, and they were mirrored on the outside. I would set them up so that I could see myself from the back in the large mirror on the sliding shower door, perpendicular and about 5 feet away. I remember being somewhat mesmerized by looking into that mirrored set-up, because it seemed like I could see so many facets of myself and it went on forever and ever. Those moments were the ones for me when I could almost feel like time was something I was outside of, and I could see it from a distance. It was really weird, and then I would snap out of it and go back to arranging the curls in the back of my head.
anyway.
Also, deja vu – that really weirds me out, in the same kind of way. I get deja vu all the time, and I can almost always trace it back to a dream I’ve had. Does time wind back on itself at some point? Is it always linear?
Ah, time. I can remember listening to a radio talk program about astrophysics, and they were talking about string theory, multiple dimensions beyond the four we experience, etc., and the guest mentioned that scientists were looking at the possibility there was more than one dimension of time.
The host asked, “What does it mean to say there’s a second dimension of time?”
And the astrophysicist replied, “Well, it’s kind of hard to answer that because we really don’t know what it means to say there’s a first dimension of time!”
I heard an hypothesis somewhere that time was like a river and not a line. Like a river, it goes one way, but parts of it goes faster than others (which is consistent with relativity). Events are like pebbles thrown in this river: the ripples goes both ways. Déjà-vu (and precognition) would be when we pick up these ripples.
[…] Same faulty logic: why should there be a before and an after?We are, in this culture, so caught up in the idea of causality that it is nigh impossible to question it. That wouldn’t fit with our idea of reason. For example, I recently made the following comment, over at Thinking Girl’s, about déjà-vu: I heard an hypothesis somewhere that time was like a river and not a line. Like a river, it goes one way, but parts of it goes faster than others (which is consistent with relativity). Events are like pebbles thrown in this river: the ripples goes both ways. Déjà-vu (and precognition) would be when we pick up these ripples. Causality is still there, only the flow of time changes. […]
[…] Thinking Girl: Infinity Is Quite Big (guest post by Craig) […]
You do realise that all these numbers are finite. They’re not even particularly large compared with the monsters mathematicians are able to come up with when they try hard. Here’s a good essay on the subject.
It is one thing to be able to write down a number and another entirely to be able to visualise what it means. The point of this post was to try and get people thinking about what a mind boggling number of possibilities there are in something so simple as a tiny image, and to try and relate these utterly insane numbers to something that is graspable by the human mind.
Unfortunately I think I failed at this one because who can imagine a stack of photographs tall enough to fill this many universes?
Unfortunately the html got a bit messed up somewhere along the line and it is a bit tricky to get to a couple of the links and images that should be there, which somewhat diminishes the point I was trying to make.
Besides, as an astrophysicist I also tend to cut off worrying about numbers around 10^78 to 10^81, since there are ‘only’ that many atoms in the universe 🙂