Warning: this is a long post dealing with an abstract concept, and will probably bore the pants off most anyone. You have been warned.
I have a question that’s been flying around in my head ever since I first thought of it about 8 years ago. It has to do with the concept of infinity. It just didn’t make any sense to me. Sure, it’s a useful mathematical concept for various reasons, but in the physical world, is there infinity or just indefinity? I thought about this for about a year until I came up with a very interesting thought experiment:
Think of a movie director’s clapper thing. I don’t know what it’s called, but you know what I’m talking about. It’s the thing that gets clapped shut to make that nifty noise when they call “action!” I’ve heard this was originally so that the sound track could be acurately aligned with the video track later. The point is that it makes that nifty sound because even though the bar on top of it is hinged to the bottom on one side (the fulcrum), when the two are brought together the entire contact surfaces of the top and bottom meet simultaneously.
Now apply this to an imaginary device that consists of two rays originating at the same point but pointing in different directions. Now imagine that this point is a hinge, so the angle between the two rays can be changed at will. Now imagine decreasing this angle to the point that the two rays physically meet. Now remember that all* points along both rays will contact the other ray simultaneously. The nature of a ray (mathematically speaking), is that it continues for infinity in one direction, making it infinitely long. Now, for the ends of these rays to meet, they have to travel an infinite distance, at an infinite speed, implying (at least to me), that they would never meet at the ends. An infinite distance can never be covered, and an infinite speed could never be attained. However, near the fulcrum, there would indeed be a measureable speed and distance. You could watch the two rays approach each other, and they would eventually hit and be in contact.
To me, this seems totally at odds with the entire idea of the rays being infinite in the first place. The idea that they are indefinitely long is more in line with the experiment, though I’m really not sure if there’s a distinction between the two.
Any thoughts on this one? Like I said, I’ve been thinking about it for a long time and am still no closer to deciding whether this thought experiment is at all relevant to the concept of infinity. Thanks in advance for any ideas.