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It IS kind of a strange concept, but no more so than that of an infinite variety of smaller infinities. They one springs from the other.

If we must accept that there are an endless slew of different sets that all contain infinity in them... it is not a conceptual leap to imagine that the sum total of all infinite sets is the grand ultimate infinity.

Even if we can not fully grasp all that that entails, we can hold a concept of it in our minds. As it is, we can not fully grasp any of the smaller infinities either. We develop a logical framework and demonstrate that it must point towards something that has the characteristic of infinity.

Of course, as you described infinity in your previous post... everything is infinite... every thing. If 0->1 is infinite, than every blade of grass, the distance between rings of electrons, and the interval between 2 adjacent nanoseconds is also infinite.

This doesn't bother me in the least, as I already saw plainly that all is infinite... on all levels... micro and macroscopically. And again... infinity = divinity

Thus, our somewhat feeble minds are (at the very least) an infinite collection of smaller infinites... a subset of the grand ultimate infinity. And, I don't discount the idea that my very own mind might, in fact, be the ultimate infinity. Solipsism is un-refutable logically or philosophically, after all.

Can a "smaller" infinity grasp or contain an infinitely larger infinity? Grasp... sure. Contain... who can say?

You used the phrase "fully understand." This is also a strange concept, no? To fully understand something, you would have to understand ALL of its connections and relations... which would bring you naturally to the grand ultimate infinite. In order to understand anything fully, you would have to understand everything (which is the ultimate infinity, no?).

So, then... does it make any sense to talk about fully understanding something?

I think it might, but even if it was impossible... it would be just as impossible to fully understand a butterfly as it was to understand the ultimate infinity.

Perhaps our minds understand other infinite things by recognizing our Self.

Perhaps we understand these things the way a mirror manages to contain images of things that are much larger than itself.

At any rate, I think a waterfall must understand something of the nature of the mountain lakes and glaciers that feed it. Maybe not in total... but certainly in essence. It understands the same water. It understands the cycles and relative flows... which would cause it to intuit or deduce the connection to rain... which could lead it to understand the complete cycle of water... IMHO.

Anyway, this is a fun little mind training any way you look at it. Thanks for bringing the varieties of infinity into this. Perhaps you could talk a little bit more about sempiternal for us? This is a term that I have almost no familiarity with.

<blockquote data-quote="Hyperspace Fool" data-source="post: 3575554" data-attributes="member: 10791">It IS kind of a strange concept, but no more so than that of an infinite variety of smaller infinities.&nbsp; They one springs from the other.&nbsp; If we must accept that there are an endless slew of different sets that all contain infinity in them... it is not a conceptual leap to imagine that the sum total of all infinite sets is the grand ultimate infinity.Even if we can not fully grasp all that that entails, we can hold a concept of it in our minds. As it is, we can not fully grasp any of the smaller infinities either.&nbsp; We develop a logical framework and demonstrate that it must point towards something that has the characteristic of infinity.&nbsp; Of course, as you described infinity in your previous post... everything is infinite... every thing.&nbsp; If 0-&gt;1 is infinite, than every blade of grass, the distance between rings of electrons, and the interval between 2 adjacent nanoseconds is also infinite. This doesn&#039;t bother me in the least, as I already saw plainly that all is infinite... on all levels... micro and macroscopically. And again... infinity = divinityThus, our somewhat feeble minds are (at the very least) an infinite collection of smaller infinites... a subset of the grand ultimate infinity.&nbsp; And, I don&#039;t discount the idea that my very own mind might, in fact, be the ultimate infinity.&nbsp; Solipsism is un-refutable logically or philosophically, after all.Can a &quot;smaller&quot; infinity grasp or contain an infinitely larger infinity? Grasp... sure.&nbsp; Contain... who can say?You used the phrase &quot;fully understand.&quot;&nbsp; This is also a strange concept, no?&nbsp; To fully understand something, you would have to understand ALL of its connections and relations... which would bring you naturally to the grand ultimate infinite.&nbsp; In order to understand anything fully, you would have to understand everything (which is the ultimate infinity, no?).So, then... does it make any sense to talk about fully understanding something?I think it might, but even if it was impossible... it would be just as impossible to fully understand a butterfly as it was to understand the ultimate infinity.&nbsp; Perhaps our minds understand other infinite things by recognizing our Self.Perhaps we understand these things the way a mirror manages to contain images of things that are much larger than itself.At any rate, I think a waterfall must understand something of the nature of the mountain lakes and glaciers that feed it.&nbsp; Maybe not in total... but certainly in essence.&nbsp; It understands the same water.&nbsp; It understands the cycles and relative flows... which would cause it to intuit or deduce the connection to rain... which could lead it to understand the complete cycle of water... IMHO.Anyway, this is a fun little mind training any way you look at it.&nbsp; Thanks for bringing the varieties of infinity into this.&nbsp; Perhaps you could talk a little bit more about sempiternal for us?&nbsp; This is a term that I have almost no familiarity with.</blockquote>

[QUOTE="Hyperspace Fool, post: 3575554, member: 10791"] It IS kind of a strange concept, but no more so than that of an infinite variety of smaller infinities. They one [i]springs[/i] from the other. If we must accept that there are an endless slew of different sets that all contain infinity in them... it is not a conceptual leap to imagine that the sum total of all infinite sets is the[b] grand ultimate infinity[/b]. Even if we can not fully grasp all that that entails, we can hold a concept of it in our minds. As it is, we can not fully grasp any of the smaller infinities either. We develop a logical framework and demonstrate that it must point towards something that has the characteristic of infinity. Of course, as you described infinity in your previous post... [i]everything[/i] is infinite... every [i]thing[/i]. If 0->1 is infinite, than every blade of grass, the distance between rings of electrons, and the interval between 2 adjacent nanoseconds is also infinite. This doesn't bother me in the least, as I already saw plainly that [b]all is infinite[/b]... on [i]all[/i] levels... micro [i]and[/i] macroscopically. And again... infinity = divinity Thus, our somewhat feeble minds [b]are[/b] (at the very least) an infinite collection of smaller infinites... a subset of the grand ultimate infinity. And, I[i] don't[/i] discount the idea that my very own mind might, in fact, [b]be[/b] the ultimate infinity. Solipsism is un-refutable logically or philosophically, after all. Can a "smaller" infinity grasp or contain an infinitely larger infinity? Grasp... sure. Contain... who can say? You used the phrase "fully understand." This is also a strange concept, no? To fully understand something, you would have to understand ALL of its connections and relations... which would bring you naturally to the grand ultimate infinite. In order to understand anything fully, you would have to understand everything (which is the ultimate infinity, no?). So, then... does it make any sense to talk about fully understanding something? I think it might, but even if it was impossible... it would be just as impossible to fully understand a butterfly as it was to understand the ultimate infinity. Perhaps our minds understand other infinite things by recognizing our Self. Perhaps we understand these things the way a mirror manages to contain images of things that are much larger than itself. At any rate, I think a waterfall must understand something of the nature of the mountain lakes and glaciers that feed it. Maybe not in total... but certainly in essence. It understands the same water. It understands the cycles and relative flows... which would cause it to intuit or deduce the connection to rain... which could lead it to understand the complete cycle of water... IMHO. Anyway, this is a fun little mind training any way you look at it. Thanks for bringing the varieties of infinity into this. Perhaps you could talk a little bit more about [b]sempiternal[/b] for us? This is a term that I have almost no familiarity with. [/QUOTE]