Some Simple Math
December 13th, 2005 by PotatoFirst, from a conversation with Bug earlier today:
There’s a paradox, maybe you can help me with…
If Pi is infinite, that means that logically, EVENTUALLY it HAS to repeat, thus making it not infinite.
Ah, not true.
Consider a number with the following pattern:
3.14114111411114111114
It may have segments that look like repeats of previous segments, but at no point can you circle a bit and say “now the rest is just this part over and over”. The pattern may be apparent, but it’s not actually the same thing over and over, no matter how far out you go. It can be infinite without being degenerate… that’s what makes it transcendental.
I got ya… but infinite… man… that’s infinite. Doesn’t it have to repeat eventually? I mean if it goes on forever? [comment: this is more of a philosophical aside on Bug’s part, and actually came between these two quotes] It’s like… if the universe is infinite, the molecules have to line up exactly the same as they are here somewhere far away, thus making a duplicate of this world, and if that happens and it’s infinite, then there are infinite parrallel worlds.
No, because as long as it goes on, it has an infinite number of ways to remain unique (an infinite number of digits, and 10 different ways to fill each slot).
Infinite just means never-ending, not necessarily all-encompassing.
Consider a circle. Draw a smaller circle just inside. And other smaller circles (or if you prefer, Russian dolls) within. You can keep going on with an infinite chain of progressively smaller circles, but they all still fit within the finite space of your first one.
Some even more simple math to ponder. Right now my server is consuming something like 75 W of power (since the drives aren’t being taxed and all that. The power supply is rated to 220 W, but it’s just running low-processor intensive things. Doesn’t even do any drive seeks from what I hear). That’s 75*24*30 = 54 kWh used in a month. At about 5 cents/kWh, it’s costing me about $2.70/month to run. It is a bit of a pain, as I experienced earlier today; since it’s a crappy old system that I don’t much mind opening up to the ravages of the internet, it needs to be reset every 4-7 days, or it’ll just run itself in circles until there’s no more memory left and lock up. That’s a minor annoyance, but it also means that if I ever go on vacation for more than a week, I can expect my webpage to stop serving itself before I get back.
The main goal of this setup was to give myself unlimited access to the Apache, MySQL, and PHP tools I’d need to get a site up and running, and I have partially done that — I actually haven’t learned much in the way of useful things, more about how to get the programs themselves running. Anything I’m using is a pre-written script. I still have no idea how to properly set up a MySQL database or access it via PHP. But that’s beside the point, as far as hosting my webpage goes, I think I know enough about WordPress and the other software to be able to use a real host. Based on the costs/pain in the butt, ideally I’d like to find a host in the ~$6/mo range (that is, that’s the price point where I think it would be better to switch to a real host rather than what I have now). So far the lowest I’ve seen is ~$10 CDN (aside from the free ones, which may yet be an option). Let me know if you have any recommendations, and I’ll also say I have no problem giving referrals if your service has a promotion for them. (Likewise, if anyone is moving and setting up a new Rogers account, feel free to tell them I referred you so I get a free month :)
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