Yes, thats what I meant but damn thats nicely phrased. So an object is infinitely grounded in itself. A set that describes a function such as a rational number sequence ids infinite in its potential reflection of itself on itself, where each reflection produces another integer, but there is not any infinitude of integers given unless that set is taken as the vessel. So the infinity opt the set is always infinity+1, the infinity of the number brings along the notion of the set. Which already shows its is not really infinite in capacity.
Damn, I dont now everyone can follow my thought here. Capacity as different from potential… well, like the capacity of a hose tied to an opened hydrant, and the potential of the closed hydrant and the rolled up hose.
Yes, a number only acquires a capacity to mean anything under certain circumstances, such as existence.
lol.
Pi is one of these numbers.
An irrational number. That speaks volumes. Its infinity is not a neat row or axial system, but more like snow on a tv. It is a better infinity if you want to come close to existence.
When I try to picture an infinite plane in my mind, it can only curve back on itself because I’m trying to grasp the full extents of it as one thing and when I do that, it turns concave until it eventually joins with where my mind is calling the center. An infinite plane that extends forever without end isn’t something I can imagine. I can fool myself into believing I can, but I’m lying if I claim such ability; the best I can do is make the edges fuzzy and call that infinite (that’s cheating). But if I REALLY make a plane that doesn’t end, then there is no other place to go than where it started. The only way to exist without also having beginning nor end is to be a loop (and why the wedding ring is a symbol of eternity and also a symbol of unity).
I think there is a way we can work with notions of infinity by working with the inevitable ramifications without actually conceptualizing infinity as a thing, but even that doesn’t pan-out in practice. For instance the Thompson Lamp where the switch is turned on after 1 min and off after 1/2 min and on after 1/4 min and so on. Eventually the speed of the switch will exceed the speed of light, so whatever state the lamp was in before crossing the velocity threshold (probably on) will be the final state of the lamp since the switch would be moving too fast for electrons to react. So we can say in our heads that the final state of the lamp should be half-on and half-off, but it can’t work in practice due to our finite universe. Even infinite velocity doesn’t make sense since speed can’t be faster than instant, which is c. Otherwise things could arrive before they left, and not only that, but arrive infinitely sooner than they left (whatever that means).
I think this is attained in the mirror loop metaphor for the set, where the set is a thing which is infinite inside but has no infinite capacity to change things, which would be infinite existence, which would mean infinite divisibility of meaning.
Conceptualizations of infinity are like that dream I had as a kid where a cat had its head in its own mouth (back in the days that I didn’t realize bicycle spokes held the bike up and trees didn’t make the wind blow); we probably can’t admit to ourselves infinity is absurd because at such an old age, we shouldn’t be that silly anymore, so it’s denial. Compounding that, people really want infinity to exist since it’s a good substitute for god and answers so many questions. The incentive to cheat (not be scientifically objective/unbiased) is high. And there is no proof or even good reason to believe an unbounded thing can be beheld by either our hands or our minds or even be said to exist, much like zero, which is also the bounded unbounded thing: limitless nothingness in a tidy package. Obviously we can think about “nothing” as the absence of something, but that’s not nothing. I don’t think anyone can truly think about nothing because there’s nothing there to focus on, conceptualize, and observe.
Im compelled by this image of the trees that cause the wind I must say. Thats pretty damn cool. Yes, as kids we clearly have a lot more touch with the contradictions that are thrown at us, the way things are set against each other.
Out of the blue, it reminds me of my first solar eclipse when I was just a 4 year old kid walking home with my friend from getting some candy, I don’t know why I was allowed, it was the 80s, and it suddenly got dark. It was a partial eclipse and no one was paying attention (it was the 80s) but for a moment I had the distinct sensation of “well that was it folks!”. Later if you know what an eclipse is, it loses most of its capacity. Unless you’re not in a horde of morons (humans) but in a field where suddenly every being is holding its breath, and you realize what you thought was silence was actually deafening noise.
wtf - I can now begin to undermine your claim that all infinity is just basically the same thing. All I need to do for this is follow the threads. A philosopher is a detective.
Let us start in the context of bijection on good ol wikipaedia…
“Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers.”
But I can add to this to make it stronger. Different infinities are also distinguished in terms of how they can be overlaid. If they can be overlaid, like the set of all even numbers with the set of all natural numbers, then it is the same type of infinity. The same goes for rational numbers, they too can be overlaid with the natural numbers. But irrational numbers can not. They form a different class in which even the distance between 1 and 0 contains more numbers than all of the natural or (thus) rational numbers.
This is orthodox math, so where do you want to go from here?