I wanted to name this post as Infinity in a Jar, but then i thought, why jar, why not a cup? Or a saucer, maybe? That wouldnt end anywhere, so i just reached a point where the point was where the infinity could be. And this is why the title of this post is about a point, and not a jar.
These guys were talking about how strange infinity can be. On an empty stomach, mind you … The essence of what Hardy was going on about was the fact that every single interval of numbers on the number line can be broken down into an infinity. No matter how big, no matter how small. Take 1 to 10. You can break it into a number of parts, with one of the parts being lets say 1 to 2. Now, this part can further be broken into a part which includes 1.5 to 2, and this can further be broken down into smaller, and yet smaller parts. Whats interesting here is that in this way, there is an infinity hiding in a length of a line measuring 0.5 centimetres.
Another aspect which is fascinating is that there are some things which we just cant exactly, and the key word here is exactly, define. Lets take a circle, and try to find out what is the circumference of this circle. While one could take a thread and measure this, in theory, this measurement will be never correct. This is because the value of pi is irrational, and the decimal values never come to an end, or at least, over more than 2 millenia no one has seen an end to the decimal values. So while you may be able to see it all, you can never measure, or get to know it all. Put another way, what you see doesnt necessarily describe reality.
Or, for that matter, try to find the fraction 1/3 on the number line. While you may be able to see it (you can, after all, see the entire number line, and the point 1/3 is on the number line, you can definitely see it), but theres no way you can pinpoint it, because there is an infinite series of numbers which make up that particular point (in this case 0.333333333 …). And this is the idea, according to Hardy, of finding infinity at a point.
When talking about the question of infinity, there is of course the question of whether there is only one infinity, or whether there is indeed an infinity of infinities?
So what do you think?