Creation ex nihilo

Two infinite sets can be put into one to one correspondence. By definition it's pointless to try and count an infinity. An infinity is "complete," you seem to want to make it complete by making it finite, in which case it's not complete. We can't have a situation in which an infinity is only a "potential" infinity untill we have have counted its last number, for then all we could say was that it was just a very large number and not after all an infinity.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Two infinite sets can be put into one to one correspondence.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Yes, but only a finite part of the set.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">By definition it's pointless to try and count an infinity.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Yes, so I think it's a bit strange to differentiate between countable and uncountable infinite sets. They're all uncountable.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">An infinity is "complete," you seem to want to make it complete by making it finite, in which case it's not complete.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
No, my whole point is that it can only ever be finite and therefore it's not complete. An infinity is not a number, it's a description of properties.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">We can't have a situation in which an infinity is only a "potential" infinity untill we have have counted its last number, for then all we could say was that it was just a very large number and not after all an infinity.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
By potential infinity I simply mean that there is no upper bound to the amount of possible members of the set. In the case of integers there is no upper bound to the size of integers you can create, but you can never exhaust them. The set can never be complete.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Stoat</i>
<br />most people believe they have an intuitive understanding of infinity.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">My experience is opposite to that. Most people I know have a hard time with infinities, and do not even know the basic math relations about infinities and indeterminates such as:
1/0 = inf (= infinity = aleph null); 0/0 = indeterminate; inf+1 = inf; inf+inf = inf; inf-inf = indeterminate; inf*inf = inf; inf/inf = indeterminate; inf^inf = aleph 1; etc.

BTW, thanks for the useful link. It does explain the basics of one-to-one correspondences, although not as easily as Gamow’s book does. I read the latter in early high school, well before I was ready for set theory.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Perhaps all science students should be given a primer course in logic.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I’d generalize that to “all students”. Most people don’t have a clue how syllogisms work. They get taken in by easy logic violations such as in the following example quoted from chapter 20 of my book:

Suppose we are given this statement as a fact: "96% of heroin users previously smoked marijuana." Can we conclude that it is likely that smoking marijuana leads to heroin use? Can we conclude there is the slightest tendency in that direction on the basis of the given hypothetical fact? By the rules of logic, we cannot. The conclusion is entirely an association in our minds and cannot be derived to the slightest degree from the given fact. To see this, consider a second hypothetical fact: "99% of heroin users previously drank milk." ... -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Skarp</i>
<br />Zeno argued that if there were an infinity of points to cross in any length of distance, that we could never reach any distance.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">It sounds to me as if you read a source pushing the “time can be quantized” school of thought. Zeno had eight paradoxes, and they ruled out motion either way. Here are just some of the paradoxes in chapter one of my book that occur when space or time or matter is quantized:

SPACE
[If] there is a smallest possible increment of distance, this leads to all sorts of conceptual problems. Consider points X and Y, separated by the smallest possible increment of distance. Now consider another point Z, also separated from X by the minimum possible distance, but in a slightly different direction. Then the distance between points Y and Z is less than the minimum possible distance, contradicting the starting assumption. But if space were "grid-like," so that adjacent cells had no overlap, then motion in any desired direction would not be possible, unless one took a zigzag path from grid-point to grid-point! Clearly, the postulate of a "minimum possible distance" is problematical.

TIME
If time is treated like just another dimension (a "fourth dimension" of space), the same remarks might be extended to include the concept of a "minimum possible time unit." Or we may make a separate argument about time. If there were a minimum possible time unit, then all existing substance would have one condition at one time moment, and some slightly different condition at the next time moment. By hypothesis, there is no possible interval in time, nor any moment in between when anything could have happened to provide a transition from the first condition to the second. It is therefore just exactly as if everything existing at the first time moment ceased to exist, and then was created from nothingness in its new condition at the next time instant. Even imagining a smooth transition from one place to another during a minimum possible time unit does not rescue one from a logical paradox. What if a collision occurs through the intervention of other matter in the middle of the minimum possible time unit? How can the new condition of matter at the end of such a time unit be dependent upon conditions which occur during an unresolvably small time unit? There is no logical way for the condition of existing substance to change, let alone change in an orderly way, from one time instant to the next.

MATTER
[If] there is a smallest possible unit of matter or substance, ... it must be utterly uncomposed. It therefore cannot be broken or divided, nor even deformed by spin or collision -- since these are properties of bodies composed of yet smaller particles. What then are we to assume will happen when two such unit particles collide? What density will the unit particle have? Indeed, will there be anything inside it at all? (It would seem that the substance in its interior could never contribute in any way to anything in the universe outside the particle, since it can never interact with it.) What would the unit particle's "surface" be like? Could it be hollow inside? With what thickness of shell? Would two colliding unit particles have to stick, since they can't rebound elastically? If they rebounded, with what resultant velocity? What about the slightest of grazing collisions? Would the unit particles be spherical in shape? Why would they have finite space dimensions, yet infinite dimension in time? Or do they come into and go out of existence constantly? Where and when would they appear and disappear?

These Zeno paradoxes are unresolvable. The infinitely divisible paradox is easily resolvable by one-to-one correspondences, the standard way of dealing with infinities.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[tvf]: The math of infinities finally allows us to understand a way out of those paradoxes, but only if everything is infinitely divisible and infinitely constructible.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">No, it doesn't. The math you're talking about only shows how you can deal with it mathematically by creating certain rules that don't apply in real life.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The whole point of the exercise is that these things do apply to reality through one-to-one correspondences. So there is no problem at all with sets being infinite or eternal in reality even though all forms have finite extend and duration. You are confusing the two. All integers are finite, yet the set of all integers is infinite. The same is true of ticks on a conceptual clock.

The logical fact that substance can never be created or destroyed guarantees its eternity in both directions in time.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Something from nothing is the classic example of a logical impossibility requiring a miracle.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Yes, but I've never claimed that something came from nothing so that's a moot point.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">But you have claimed that you can have a first step with nothing before that, which is what most of us consider “something from nothing”. You just choose to say it’s not a miracle; yet it fulfills the standard definition of miracle for me and most folks.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Substance either came from nothing, or it always existed.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">This is a false dichotomy. I've already challenged this statement of yours. Repeating something several times doesn't make it true.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Despite a lot of word salad, you have still failed to communicate another possibility. So it remains a valid dichotomy in my mind.

To fix that, you need to address the origin of your first state. You can’t say that “it just is” and “that’s not a miracle” because those two premises are mutually contradictory. Your first state came from nothing (non-existence), even if you insist on denying that for no logical reason I can fathom.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">You arbitrarily chose to label your “first state” as State #1.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Arbitrarily? There was nothing arbitrary about that choice. I chose to label it state #1 because it is state #1. The first state.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">And “First Cause” is a synonym for God. An uncaused state is either a convoluted way of describing a miracle, or is a contradiction of logic.

I agree we are going in circles. There is no point in being repetitious. Beliefs are hard to shake, especially after one has invested heavily in one. Some people even lack the ability to unlearn something learned wrongly. Apparently, we will have to agree to disagree about who has the belief and who has the valid counterargument.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The next state replaces the last, but everything in the universe is the same, it only changes location. The change in location of the particles in the universe constitutes the transition from one state to the next.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">But this is change of location without motion because there are no transition states. So it is just as if everything in one state ceased to exist, then everything was recreated from nothing in a new state after an arbitrarily long interval. What relevant difference is there between my description of two consecutive states and yours?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Are State #1 and State #2 simultaneous, or separated in time? If the former, then they co-exist. If the latter, then there is an interval, the length of a time unit, which is apparently arbitrary and could be anything.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Neither. They are separated in order. It wouldn't make sense to talk about time intervals between the different states since it's the transitions between states that constitute time.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The problem again is word salad. You have “transitions” (undefined), where everything hinges on what that means. You prefer not to open Pandora’s box and examine the essential nature of a transition. My point is only that it is impossible to define “transition" in your scenario without a miracle.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">It's impossible for an infinity to be complete.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The set of all integers is a complete infinity. Anything we can put in a one-to-one correspondence with the set of all integers is also a complete infinity. These are concepts, not material things; so they are not subject to the limitation that all forms must be finite.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">All integers are finite, yet the set of all integers is infinite. All time intervals are finite, yet the set of all time intervals is infinite. All forms are finite, yet the set of all forms is infinite. Note the one-to-one correspondences with the integers.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
As I said before, integers are only an abstract mathematical concept and they do not actually exist. The fact that you can come up with the concept of infinity doesn't mean that it is applicable to the real world. You can't actually even imagine the complete set of integers. You can only imagine that it has certain (made up) characteristics.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">My imagination is not feeling any limitation in that way, and both integers and the set of all integers exist in my world. I am very comfortable with imagining infinities. If your read Gamow’s book, you could be too.

Other than for that, you are simply ignoring me. I agree that ALL forms (material, tangible entities) are finite. Yet the set of all forms does not have any need to be finite. That is a false generalization on your part, and is disproved by consideration of integers. But now you deny that integers exist. The next natural step to maintain your comfort level is to deny that I exist. Well, you remain welcome in my world even if I am not welcome in yours. []

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">But I just did. Show me where the one-to-one correspondence is incomplete.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">No you didn't! Please show me where you did. You said that you could do it but you didn't actually do it. The one-to-one correspondence is incomplete because you didn't even start, although I can imagine that if you tried, the correspondence would be incomplete where you stopped writing integers and replaced them with dots and an infinity symbol.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">You didn’t grant me an eternity to complete the task, as you promised! [}]

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I could even argue that the set of integers is not infinite at all. The fact that you call it infinite only means that there is no upper (or lower) bound to the size of integers you can create.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">”Unbounded” is part of the definition of infinite. We would have made more progress if you used standard definitions for your words, or stated the definitions you intended to use. -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">It sounds to me as if you read a source pushing the “time can be quantized” school of thought.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">What I would mean by quantized is that space (nothing) is parceled out into discrete entities, by which all entities can vary in size. There is no smallest size nor largest. Space or anything else for that matter need not be a one size fits all scenerio. Space (nothing) is still infinitely divisible, yet it is not divied up that way. It is quantized with no upper or lower limit to size of any single parcel. In this scenerio no real problems arise.

As to the problems one might have with a minimum time unit, I would have to agree under your scenerio, but there are no problems if time is the nothing that all entities are composed of. Hence time is infinitely divisible as it should be.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">MATTER
[If] there is a smallest possible unit of matter or substance, ... it must be utterly uncomposed. It therefore cannot be broken or divided, nor even deformed by spin or collision -- since these are properties of bodies composed of yet smaller particles. What then are we to assume will happen when two such unit particles collide? What density will the unit particle have? Indeed, will there be anything inside it at all? (It would seem that the substance in its interior could never contribute in any way to anything in the universe outside the particle, since it can never interact with it.) What would the unit particle's "surface" be like? Could it be hollow inside? With what thickness of shell? Would two colliding unit particles have to stick, since they can't rebound elastically? If they rebounded, with what resultant velocity? What about the slightest of grazing collisions? Would the unit particles be spherical in shape? Why would they have finite space dimensions, yet infinite dimension in time? Or do they come into and go out of existence constantly? Where and when would they appear and disappear?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
This is where the waters get muddied up, for what is matter really? Many will use the marble analogy. This is so wrong in every which way but loose. The only thing right about a marble is that it has form. That form part however is important, because it's the most significant aspect of reality. The absense of form would put the universe back to square one. My contention is that there are no marbles, so a discussion about the smallest unit of marble (matter) is pointless, however your summations in the paragraph under the heading (matter) can be addressed.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[If] there is a smallest possible unit of matter or substance, ... it must be utterly uncomposed.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"> This would be a correct statement if you are playing with marbles, and somewhat true if a fundamental unit were composed of nothing. A fundy unit composed of nothing could be construed as uncomposed and I wouldn't split hairs with you. what is important here is the form of the unit.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">It therefore cannot be broken or divided, nor even deformed by spin or collision -- since these are properties of bodies composed of yet smaller particles.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Still playing with marbles. A unit (form) composed of nothing can and will perform this trick.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">What then are we to assume will happen when two such unit particles collide?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">No units (forms) composed of nothing will ever collide .... they interact.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">What density will the unit particle have? <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">No density in a fundy, lest there be other fundies around for a party called density.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Indeed, will there be anything inside it at all? (It would seem that the substance in its interior could never contribute in any way to anything in the universe outside the particle, since it can never interact with it.)<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Nothing inside a fundy, but the contribution to the universe is {time} within it's form. The form stands as a marker/markers for the time within it's boundries. Nothing within the boundries of a fundamental form interacts, thats what makes it possible to sense, because it is up against that which does interact (it's form). In this sense (nothing) becomes real. The non-event is real because we sense it through the interactions of it's form!
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">What would the unit particle's "surface" be like? Could it be hollow inside? With what thickness of shell?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"> A fundy units analogy would go like this - A hollow shell, wherein the shell has no thickness. This is a conceptual undertaking, as I've said in the past, the universe is the conceptual definition of nothing. Nothing is a conceptual beast. it must be slain by conceptual means. A fundamental form of nothing is no more than a thought. It can move around just like your marbles, and interact with other forms of nothing.

One point I'm trying to make here is that we could use the word matter, but the marble needs to be stricken as an associate. Matter could be considered as a localization of energy, and energy is the fundamental unit, which is composed of nothing, so you can see why a marble doesn't fit into any discription of matter.

There is also the subject of mass. This is no more than a resistance to being moved. It constitutes a self interaction. Imagine a bird flying in a circle representing a fundamental unit, in a clockwise direction. Now imagine a spiral pattern emanating from the left wing of the bird, and this pattern propogates away at C, and this spiral continues as long as the bird continues to circle. This spiral pattern is the gravitational field. The entire field is connected to the bird flying in a circle. The field is every bit as much the fundamental unit as the body of the bird. Now if you were to in some way push that bird in a direction while it was flying in a circle, there would be a self interaction with that birds extended spiraled wing. The harder you push it the more it resist the motion. We can see here why it would be more and more difficult to accelerate the bird as it got closer to the speed of C, because of this self interaction.

I realize this isn't the normal way of looking at things, so comprehension may not set in all that quickly.

Zeno got most of his schtick right, but he didn't know NOTHING like I know NOTHING. Don't know why I like using a line like that, I just do.

from tvf<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"> inf/inf = indeterminate<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote"> For the people who want to get to grips with the idea of infinity. A countable infinity, divided by a countable infinity is a constant. An uncountable infinnity divided by an uncountable infinity gives an ambiguous solution, maths speak for, we don't know if in fact it's indeterminate. Tidying up another point, dividing by zero is indeterminate but we can say, as x approaches the limit of 0 superscript +, or superscript -, we get either plus or minus infinity.

Now, some people want to quantize time, so that they can duck the issue of the ambiguous result of dividing uncountable infinities. That has to be a dubious procedure [] I think it's going to be tried but I'm putting money on it being a poison chalice.

The last post points. If I abstract from something the Kantian categories, I'm left with Being, and this being is a logical null, or nothing. However, existence is a higher category of logic than being, it cannot simply be negated. A logical nothing is real but doesn't exist. We simply cannot give existence to nothing, then construct a geometry from it. Though I suspect that that is exactly what Einstein did. [8D][]