Just like the question about the colored tool, many (most?) people react the same same way to the concept of infinity.
I really like thinking about infinity, I’ve been fascinated by it since I first learned of it.
Plenty of people deny the concept itself. When I mention that, many people often think I’m talking about uneducated types (Tell them it’s turtles all the way down!), but then other people come in and start talking about some hypothetical math and the surface of a sphere and how infinity is impossible.
People do not like infinity. This guy seems to think it’s not possible.
He has 3 questions.
1. Can a number that is finite but very large substitute for infinity?
Depends on who is doing the calculations. If you’re’s an engineer, you could use 10^100 and that would probably be good enough. If you’re a mathematician or a physicist, maybe but probably not.
He writes this
Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. Can it accommodate 1,000 new guests without increasing the number of guests in any of the occupied rooms?
What is “countably infinite”? I’m gonna assume it’s a term by someone who’s afraid of infinity. By definition, ‘infinity’ is not countable. No matter how high you count, you can always count higher. There just aren’t names for some numbers. I’ve named 10 to the 6 trillion (a one with 6 trillion zeroes), a veeshir so if you ever count that high, make sure you use the proper nomenclature.
But if you have an infinite number of rooms, you could add a veeshir more guests and you would have enough rooms for each one to have an infinite number of rooms. That’s how it works. If you have an infinite number of cars and every 10th car is red, you have the same number of cars as red cars, infinity.
2. What if there are physical limits to the smallest measurable amount of space?
Umm, what if this question made sense? He mentions the planck length (where quantum physics instead of newtonian physics works) but that’s not related. Now, if you’re going to say the smallest measurable length, you’re going to have to specify the technology. No matter how small a thing is, it can be smaller. If you make 10^-6 trillionth (veeshir^-1) of an inch a rihseevlength, what is 1/2 a rihseevlength? All you are doing is the same as infinity the other way. Now, you might not be able to measure it accurately until your technology is seriously advanced, but you can certainly write 10^-googol inches.
This one’s my favorite
3. How sharp is a geometric focus in the real world?
A more pertinent question: How tall is Bugs Bunny in the real world?
Both are equally valid.
A geometric focus is a mathematical concept, much like infinity and zero. It has no dimensions, by definition. Just as a point has no dimensions. Deal with it.
I say that if you fly at the speed of light (minus a smidgeon) that way (points up at an angle of 43.84 degrees from a tangent line on the Earth going exactly east from Niskayuna, NY) for veeshir to the veeshir years you would still have an infinite distance to travel ahead of you. If there’s something blocking you, what’s on the other side? Don’t talk about the surface of a sphere to me, I live in 3d land, not Flatland.
What I think bothers people the most is how insignificant we are if you think about infinity.
If the universe is 14 billions years old (or whatever they’re saying this year), what was going on 15 veeshir years ago? How about 15 veeshir years in the future?
Will anybody 75 trillion years from now even care that I lived? Well, you. I’m sure they’ll still remember me. I’m planning on being deified after my death.