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Creation ex nihilo
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17 years 10 months ago #19348
by tvanflandern
Replied by tvanflandern on topic Reply from Tom Van Flandern
<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 />Do we have space in your model, or do we not have space? I know that space is not allowed in your model, and this is a reminder to you just in case you forgot.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If by "my model" you mean the Meta Model, which I wasn't specifically discussing, then the concepts of space, time, and scale play major roles. But of course there is no absolute space or time, meaning that those concepts are not physical entities and cannot act on or be acted on by physical entities.
In particular, because absolute (physical) space does not exist, the only value of the concept of "space" is for purposes of measuring distances between material bodies. In absolute space, one can tell which of two bodies in relative motion is doing the moving. In space as a concept, we not only can't tell which is moving, but the very idea has no defined meaning because there is no underlying "grid". We can just see one thing moving relative to another thing.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Apparent vacuums? Lets call a spade a spade here. There is no vacuum in your model, not even an apparent one.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Definitions, definitions, definitions. "Vacuum: a space from which all air or gas has been extracted". Physical vacuums are filled with many things such as photons, neutrinos, elysium, gravitons, and perhaps an infinity of other things. I use the word "void" for a volume containing absolutely nothing.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The space in your model is teaming with particles of every size imaginable. It is complete i.e. there is no space. It is such a composition, that if one particle moved, an infinity of particles would have to move with it in the direction of motion<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">For your objection to be valid, one of two things would have to be true:
(A) A continuum of the tiniest particles with the combined mass of a golf ball could stop a planet just because there was no space between the particles. Or
( Any space completely filled with particles has infinite mass.
I doubt you mean (A) because it is pretty absurd. So I'll address my answer to (. The <i>infinite</i> series 1 + 1/2 + 1/4 + 1/8 + ... has a finite sum of exactly 2. Proof: any proposed sum less than two can be shown to be exceeded. But no number of terms can ever exceed 2. Moreover, there is a one-to-one correspondence between this series and steps in crossing the street, where we first go half way, then half the remaining distance, and so on forever. No matter how many steps we take, there are always an infinite number of "half the remaining distance" steps left, although the other side is a finite distance away by construction.
Consider a particle occupying some volume of space. It is composed of ever smaller and smaller particles such that each particle has less than half the mass of the particle containing it, all the way to infinitesimal (infinitely small). So by another one-to-one correspondence with the series above, the total mass (the sum of masses on an infinity of smaller scales at a single point in space) is still finite, not infinite. -|Tom|-
<br />Do we have space in your model, or do we not have space? I know that space is not allowed in your model, and this is a reminder to you just in case you forgot.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If by "my model" you mean the Meta Model, which I wasn't specifically discussing, then the concepts of space, time, and scale play major roles. But of course there is no absolute space or time, meaning that those concepts are not physical entities and cannot act on or be acted on by physical entities.
In particular, because absolute (physical) space does not exist, the only value of the concept of "space" is for purposes of measuring distances between material bodies. In absolute space, one can tell which of two bodies in relative motion is doing the moving. In space as a concept, we not only can't tell which is moving, but the very idea has no defined meaning because there is no underlying "grid". We can just see one thing moving relative to another thing.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Apparent vacuums? Lets call a spade a spade here. There is no vacuum in your model, not even an apparent one.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Definitions, definitions, definitions. "Vacuum: a space from which all air or gas has been extracted". Physical vacuums are filled with many things such as photons, neutrinos, elysium, gravitons, and perhaps an infinity of other things. I use the word "void" for a volume containing absolutely nothing.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The space in your model is teaming with particles of every size imaginable. It is complete i.e. there is no space. It is such a composition, that if one particle moved, an infinity of particles would have to move with it in the direction of motion<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">For your objection to be valid, one of two things would have to be true:
(A) A continuum of the tiniest particles with the combined mass of a golf ball could stop a planet just because there was no space between the particles. Or
( Any space completely filled with particles has infinite mass.
I doubt you mean (A) because it is pretty absurd. So I'll address my answer to (. The <i>infinite</i> series 1 + 1/2 + 1/4 + 1/8 + ... has a finite sum of exactly 2. Proof: any proposed sum less than two can be shown to be exceeded. But no number of terms can ever exceed 2. Moreover, there is a one-to-one correspondence between this series and steps in crossing the street, where we first go half way, then half the remaining distance, and so on forever. No matter how many steps we take, there are always an infinite number of "half the remaining distance" steps left, although the other side is a finite distance away by construction.
Consider a particle occupying some volume of space. It is composed of ever smaller and smaller particles such that each particle has less than half the mass of the particle containing it, all the way to infinitesimal (infinitely small). So by another one-to-one correspondence with the series above, the total mass (the sum of masses on an infinity of smaller scales at a single point in space) is still finite, not infinite. -|Tom|-
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17 years 10 months ago #18707
by tvanflandern
Replied by tvanflandern on topic Reply from Tom Van Flandern
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Fopp</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[tvf]: 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!<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">You don't have to zigzag. You don't have to pass through all the cells.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If space is a chess board with horizontal squares lettered A through H, and vertical squares numbered 1 through 8, how do we get from A1 to C8 without passing inside supposedly indivisible cells and without zig-zagging?
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">There is no middle of a time unit. A time unit is basically a still picture. Many time units in succession gives the impression of movement. Think of the world as an animated cartoon.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Look closely at the animated cartoon. First one frame gradually appears as photons shine through that frame of film. That still picture exists for a finite but indefinite interval, then the photon source is shut off and that picture ceases to exist. Then, after another finite but indefinite interval, the projector advances to the next frame, and begins to shine light through it.
Your scenario likewise requires the entire universe to exist in a discrete state for an interval of undetermined length, then to cease to exist, then to be recreated from nothing in some new state without any intermediate states ever existing. It also requires an Intelligence to recreate the subsequent states in ways that resemble the previous state so as to maintain the illusion of motion, even though no possible connection exists between the conditions of similar particles in each of two states. There can’t be anything happening between the two states to account for the differences between them.
This scenario requires more miracles than I can count.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">it's not possible to complete an infinity of distances. An infinity of distances means that there is no end to them so you will never finish the race. Integers have nothing to do with it and you still haven't showed any such one-to-one correspondence. Please show it, don't just talk about it.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I’m crossing a street of width 2. I first cross half way, then half the remaining way, and so on forever. The corresponding series in a one-to-one correspondence with my steps is 1 + 1/2 + 1/4 + 1/8 + …, which sums to exactly 2, the width of the street. There are an infinite number of steps or intervals, yet a finite sum, and I can in fact cross the street.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">You keep saying something "from" nothing. But the first state didn't come "from" anything it all. It didn't "come". It was there, that's it. The problem is that you're unable to lose the concept of nothingness from your mind.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The problem is that you say “It didn’t come. It was there, that’s it.” And then you say that is not a miracle. A state without a cause is a miracle. Motion from non-motion is a miracle. You insist on both, and insist they are not miracles. That appears to be the end of the discussion.
To make any further progress, at a minimum, you would have to describe the origin of the "First State” and/or give a clear, concise definition of “miracle” that excludes a First State as something only God can bring about.
<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]: Despite a lot of word salad, you have still failed to communicate another possibility. So it remains a valid dichotomy in my mind.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I guess that's a failure for me as a communicator, but I don't think I can take the whole blame for that failure. I've tried my best.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Your “best” has left an infinite gulf between us. Try something simpler. Instead of a whole universe, let’s talk about a single tiny, indivisible particle. Did it always exist? Did it have an origin? What condition do you see that is neither of those two? Please avoid fuzziness. It’s a simple set of questions designed to cover all possibilities.
I do not doubt that you believe in magic. But to convince others that no magic is involved, you have to explain how the trick is done.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">There's nothing miraculous about the first state actually being the first state.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">An uncaused state is most definitely miraculous, meaning once again “an event that appears to be contrary to the laws of nature and is regarded as an act of God”. The laws of nature include cause and effect. The origin of beginning or First State is widely regarded as an act of God. On what basis do you deny any of this?
<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]: And “First Cause” is a synonym for God.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Then use the term "first state" instead.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Changing words does nothing to change the concepts being described.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">you keep mentioning intervals between states. There is no interval between states as I've already mentioned.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That means all the states are simultaneous. Or are you again using some other meaning for “interval” that you have not stated?
“Time is nature’s way of keeping everything from happening at once!” (Old physics joke) But time consists of intervals.
<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]: You didn’t grant me an eternity to complete the task, as you promised!<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">So you do admit that you didn't complete the one-to-one correspondence? If so, stop saying that you did.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Wrong. I did complete the one-to-one correspondence, But I just showed you a few examples, not the whole series, because you didn’t give me enough time. But a mind trained in logical thought can see that all the steps are present.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">To me, the only definition [of infinity] that makes sense is that of "unboundedness". In other words, only potential infinities make sense.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">What “bound” do you place on time that will prevent it being unbounded in the future? If none, then doesn’t that show that actual unbounded concepts do exist in reality? -|Tom|-
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">[tvf]: 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!<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">You don't have to zigzag. You don't have to pass through all the cells.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If space is a chess board with horizontal squares lettered A through H, and vertical squares numbered 1 through 8, how do we get from A1 to C8 without passing inside supposedly indivisible cells and without zig-zagging?
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">There is no middle of a time unit. A time unit is basically a still picture. Many time units in succession gives the impression of movement. Think of the world as an animated cartoon.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Look closely at the animated cartoon. First one frame gradually appears as photons shine through that frame of film. That still picture exists for a finite but indefinite interval, then the photon source is shut off and that picture ceases to exist. Then, after another finite but indefinite interval, the projector advances to the next frame, and begins to shine light through it.
Your scenario likewise requires the entire universe to exist in a discrete state for an interval of undetermined length, then to cease to exist, then to be recreated from nothing in some new state without any intermediate states ever existing. It also requires an Intelligence to recreate the subsequent states in ways that resemble the previous state so as to maintain the illusion of motion, even though no possible connection exists between the conditions of similar particles in each of two states. There can’t be anything happening between the two states to account for the differences between them.
This scenario requires more miracles than I can count.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">it's not possible to complete an infinity of distances. An infinity of distances means that there is no end to them so you will never finish the race. Integers have nothing to do with it and you still haven't showed any such one-to-one correspondence. Please show it, don't just talk about it.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I’m crossing a street of width 2. I first cross half way, then half the remaining way, and so on forever. The corresponding series in a one-to-one correspondence with my steps is 1 + 1/2 + 1/4 + 1/8 + …, which sums to exactly 2, the width of the street. There are an infinite number of steps or intervals, yet a finite sum, and I can in fact cross the street.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">You keep saying something "from" nothing. But the first state didn't come "from" anything it all. It didn't "come". It was there, that's it. The problem is that you're unable to lose the concept of nothingness from your mind.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The problem is that you say “It didn’t come. It was there, that’s it.” And then you say that is not a miracle. A state without a cause is a miracle. Motion from non-motion is a miracle. You insist on both, and insist they are not miracles. That appears to be the end of the discussion.
To make any further progress, at a minimum, you would have to describe the origin of the "First State” and/or give a clear, concise definition of “miracle” that excludes a First State as something only God can bring about.
<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]: Despite a lot of word salad, you have still failed to communicate another possibility. So it remains a valid dichotomy in my mind.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I guess that's a failure for me as a communicator, but I don't think I can take the whole blame for that failure. I've tried my best.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Your “best” has left an infinite gulf between us. Try something simpler. Instead of a whole universe, let’s talk about a single tiny, indivisible particle. Did it always exist? Did it have an origin? What condition do you see that is neither of those two? Please avoid fuzziness. It’s a simple set of questions designed to cover all possibilities.
I do not doubt that you believe in magic. But to convince others that no magic is involved, you have to explain how the trick is done.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">There's nothing miraculous about the first state actually being the first state.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">An uncaused state is most definitely miraculous, meaning once again “an event that appears to be contrary to the laws of nature and is regarded as an act of God”. The laws of nature include cause and effect. The origin of beginning or First State is widely regarded as an act of God. On what basis do you deny any of this?
<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]: And “First Cause” is a synonym for God.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Then use the term "first state" instead.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Changing words does nothing to change the concepts being described.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">you keep mentioning intervals between states. There is no interval between states as I've already mentioned.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That means all the states are simultaneous. Or are you again using some other meaning for “interval” that you have not stated?
“Time is nature’s way of keeping everything from happening at once!” (Old physics joke) But time consists of intervals.
<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]: You didn’t grant me an eternity to complete the task, as you promised!<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">So you do admit that you didn't complete the one-to-one correspondence? If so, stop saying that you did.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Wrong. I did complete the one-to-one correspondence, But I just showed you a few examples, not the whole series, because you didn’t give me enough time. But a mind trained in logical thought can see that all the steps are present.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">To me, the only definition [of infinity] that makes sense is that of "unboundedness". In other words, only potential infinities make sense.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">What “bound” do you place on time that will prevent it being unbounded in the future? If none, then doesn’t that show that actual unbounded concepts do exist in reality? -|Tom|-
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17 years 10 months ago #19244
by tvanflandern
Replied by tvanflandern on topic Reply from Tom Van Flandern
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by modu</i>
<br />TVF claims in one of his replies that the universe either existed for ever or else had to be created from nothingness.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Correct. There are no other possibilities when the universe is defined as “everything that exists”.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I think that what Fpop, Skarp and the rest saying is that the universe in its present form as its perceivable by us is finite, which doesn’t mean that it came from "nothing". All it mean is that at some point in the unknown universe (before people, opinion and theories existed) an event occur that led to the universe in its present form.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">We are not talking about any event that occurred along the way. We are talking about the ultimate origin of everything that exists. Can every state of the universe be traced back to a prior state, forever? Or was there a first state with nothing before it, which is a form of miracle by definition? -|Tom|-
<br />TVF claims in one of his replies that the universe either existed for ever or else had to be created from nothingness.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Correct. There are no other possibilities when the universe is defined as “everything that exists”.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I think that what Fpop, Skarp and the rest saying is that the universe in its present form as its perceivable by us is finite, which doesn’t mean that it came from "nothing". All it mean is that at some point in the unknown universe (before people, opinion and theories existed) an event occur that led to the universe in its present form.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">We are not talking about any event that occurred along the way. We are talking about the ultimate origin of everything that exists. Can every state of the universe be traced back to a prior state, forever? Or was there a first state with nothing before it, which is a form of miracle by definition? -|Tom|-
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17 years 10 months ago #18806
by modu
Replied by modu on topic Reply from
Hi TVF
I whould like clarification on two points please.
1. You say "a state without a cause is a miracle", (which I agree with) but isn't an "infinite universe" a state without a cause?
2. "1+1/2+1/4+1/8..... =2", but "1.999.....9+1.999.....8"=infinity
in other words the sum of an infinite series (providing we use all possible numbers) is infinite even if the series came origanely from a finite number (which seem somewhat paradoxial) and bring about the qustion - how a finite universe contain an infinite particles?
modu
I whould like clarification on two points please.
1. You say "a state without a cause is a miracle", (which I agree with) but isn't an "infinite universe" a state without a cause?
2. "1+1/2+1/4+1/8..... =2", but "1.999.....9+1.999.....8"=infinity
in other words the sum of an infinite series (providing we use all possible numbers) is infinite even if the series came origanely from a finite number (which seem somewhat paradoxial) and bring about the qustion - how a finite universe contain an infinite particles?
modu
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17 years 10 months ago #18709
by jrich
Replied by jrich on topic Reply from
Stoat, I explored the cardinality of the classical continuum and the MM continuum in the Hilbert Hotel topic a few years ago:<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">
The continuum is a geometric term. It is the set of all points having the same cardinality as the real numbers. A 1-dimensional line of any length is a continuum, as is a 2-dimensional plane and 3-dimensional space. I'm not positive (geometry's not my thing), but I think that the same is true for the dimensions in non-Euclidean geometry. In this way set theory is supposed to provide the axiomatic foundation for geometry. The problem is that set theory can show that the size of the continuum is greater than aleph-0, but it can't show that it is aleph-1, which is the next greater size, without adding another axiom. So right now the axiomatic foundation of geometry provided by set theory is incomplete. This means that when geometry is used to represent reality, we can't be logically certain that it is doing so correctly because the intuitively obvious axioms (that supposedly follow directly from nature) are insufficient.
Now my point is that in the MM with the addition of the scale dimension, the classical continuum is no longer needed for 3-dimensional space. The cardinality of the set of points in 3-dimensional Euclidean space becomes aleph-0 for any given scale. Furthermore, the number of points in a finite volume of space is finite at any given scale. The scale dimension essentially allows finite subsets of the continuum. Space becomes quantized at every scale and thus may be treated as finitely divisible at that scale.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
In MM <i>for every arbitrary scale</i> there exists a smallest distance. But there are infinitely many scales so there is no absolute smallest distance. This is how Zeno's paradox is resolved.
JR
The continuum is a geometric term. It is the set of all points having the same cardinality as the real numbers. A 1-dimensional line of any length is a continuum, as is a 2-dimensional plane and 3-dimensional space. I'm not positive (geometry's not my thing), but I think that the same is true for the dimensions in non-Euclidean geometry. In this way set theory is supposed to provide the axiomatic foundation for geometry. The problem is that set theory can show that the size of the continuum is greater than aleph-0, but it can't show that it is aleph-1, which is the next greater size, without adding another axiom. So right now the axiomatic foundation of geometry provided by set theory is incomplete. This means that when geometry is used to represent reality, we can't be logically certain that it is doing so correctly because the intuitively obvious axioms (that supposedly follow directly from nature) are insufficient.
Now my point is that in the MM with the addition of the scale dimension, the classical continuum is no longer needed for 3-dimensional space. The cardinality of the set of points in 3-dimensional Euclidean space becomes aleph-0 for any given scale. Furthermore, the number of points in a finite volume of space is finite at any given scale. The scale dimension essentially allows finite subsets of the continuum. Space becomes quantized at every scale and thus may be treated as finitely divisible at that scale.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
In MM <i>for every arbitrary scale</i> there exists a smallest distance. But there are infinitely many scales so there is no absolute smallest distance. This is how Zeno's paradox is resolved.
JR
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17 years 10 months ago #18711
by Fopp
Replied by Fopp on topic Reply from
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">If space is a chess board with horizontal squares lettered A through H, and vertical squares numbered 1 through 8, how do we get from A1 to C8 without passing inside supposedly indivisible cells and without zig-zagging?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
At state #1 you are at A1. At state #2 you are at C8.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Look closely at the animated cartoon. First one frame gradually appears as photons shine through that frame of film. That still picture exists for a finite but indefinite interval, then the photon source is shut off and that picture ceases to exist. Then, after another finite but indefinite interval, the projector advances to the next frame, and begins to shine light through it.
Your scenario likewise requires the entire universe to exist in a discrete state for an interval of undetermined length, then to cease to exist, then to be recreated from nothing in some new state without any intermediate states ever existing. It also requires an Intelligence to recreate the subsequent states in ways that resemble the previous state so as to maintain the illusion of motion, even though no possible connection exists between the conditions of similar particles in each of two states. There can’t be anything happening between the two states to account for the differences between them.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
I basically answered this in my last post. For some reason you decided not to respond to this part:
"<i>My description doesn't use the concept of nothingness. Since nothingness is non-existent it's totally irrelevant to use it in the description of events. It's nothing. Why even mention it at all? It adds nothing to my description because it is nothing. You're description is basically equivalent to mine, but the problems you're describing is not problems at all because they are related to something that doesn't exist. I use the exact same description as you do except that I remove all the parts that relate to something non-existent.
Think of it this way: You have two items and there is nothing in between them. That means they are right next to each other. If I say "the two items are right next to each other" and you say "the two items are right next to each other, and there is nothing in between them", the two statements are the same. Your extra statement doesn't actually add anything to the description. The same thing applies to the different states. Since nothingness doesn't exist, all the problems you mention in relation to it are also non-existent.</i>"
This is the best explanation of the concept of nothingness I've come up with so far so please read it carefully. To me, this is the root of our differing opinions regarding the first state.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I’m crossing a street of width 2. I first cross half way, then half the remaining way, and so on forever. The corresponding series in a one-to-one correspondence with my steps is 1 + 1/2 + 1/4 + 1/8 + …, which sums to exactly 2, the width of the street. There are an infinite number of steps or intervals, yet a finite sum, and I can in fact cross the street.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Once again, you're confusing mathematics and reality. In mathematics you can write "1 + 1/2 + 1/4 + 1/8" and then add "+..." and call it infinite. This doesn't work in real life. You can't just walk half the distance, stop, write three dots on the ground and claim that you've crossed the whole street.
It's nothing but a mathematical convention that the series you mentioned sums to 2. Logically it's not possible to sum an infinite amount of terms because infinity is not a set amount. You can't use a mathematical convention as a model for the universe. The universe doesn't care about your mathematical definitions.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The problem is that you say “It didn’t come. It was there, that’s it.” And then you say that is not a miracle. A state without a cause is a miracle. Motion from non-motion is a miracle. You insist on both, and insist they are not miracles. That appears to be the end of the discussion.
To make any further progress, at a minimum, you would have to describe the origin of the "First State” and/or give a clear, concise definition of “miracle” that excludes a First State as something only God can bring about.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Call it what you want. It doesn't change anything. It doesn't make your model any more likely. As I said earlier, there is no origin to describe. The first state wasn't brought about. We've been through this many times now. Remember that time is only a part of the universe. There is no before the first state. You seem to have a very hard time clearing your mind from the concepts of time and space, but this is what you have to do in order to understand what I'm saying.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Instead of a whole universe, let’s talk about a single tiny, indivisible particle. Did it always exist? Did it have an origin? What condition do you see that is neither of those two?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
It's the same as the universe. It didn't have an origin and it always existed.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">An uncaused state is most definitely miraculous, meaning once again “an event that appears to be contrary to the laws of nature and is regarded as an act of God”. The laws of nature include cause and effect. The origin of beginning or First State is widely regarded as an act of God. On what basis do you deny any of this?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Because my model includes cause and effect. State #1 causes state #2 which is therefore an effect of state #1. It only appears contrary to the laws of nature for you because you are unable to imagine the beginning of the universe as the beginning of time.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">That means all the states are simultaneous. Or are you again using some other meaning for “interval” that you have not stated?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
No, state #2 follows state #1. The change is what constitutes time. If nothing changed there wouldn't be time. Try not to view time as something independent of space. I admit that it's a difficult concept to imagine, but it's what makes the most sense.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">But time consists of intervals.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Time consists of change.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Wrong. I did complete the one-to-one correspondence, But I just showed you a few examples, not the whole series, because you didn’t give me enough time. But a mind trained in logical thought can see that all the steps are present.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
It's impossible to do the whole series and thats's exactly my point. Do you believe that if I gave you unlimited time, you would at some point reach a time when you had written down all the steps?
Maybe it's better not to be trained in logical thought. As you said in an earlier point, for some people it's impossible to unlearn something they were wrongly taught.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">What “bound” do you place on time that will prevent it being unbounded in the future? If none, then doesn’t that show that actual unbounded concepts do exist in reality?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Yes, it does. But I've never denied that unbounded concepts exist. Time is unbounded in the future, but this is only an example of a potential infinity. It's the actual infinities that I deny the existence of.
At state #1 you are at A1. At state #2 you are at C8.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Look closely at the animated cartoon. First one frame gradually appears as photons shine through that frame of film. That still picture exists for a finite but indefinite interval, then the photon source is shut off and that picture ceases to exist. Then, after another finite but indefinite interval, the projector advances to the next frame, and begins to shine light through it.
Your scenario likewise requires the entire universe to exist in a discrete state for an interval of undetermined length, then to cease to exist, then to be recreated from nothing in some new state without any intermediate states ever existing. It also requires an Intelligence to recreate the subsequent states in ways that resemble the previous state so as to maintain the illusion of motion, even though no possible connection exists between the conditions of similar particles in each of two states. There can’t be anything happening between the two states to account for the differences between them.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
I basically answered this in my last post. For some reason you decided not to respond to this part:
"<i>My description doesn't use the concept of nothingness. Since nothingness is non-existent it's totally irrelevant to use it in the description of events. It's nothing. Why even mention it at all? It adds nothing to my description because it is nothing. You're description is basically equivalent to mine, but the problems you're describing is not problems at all because they are related to something that doesn't exist. I use the exact same description as you do except that I remove all the parts that relate to something non-existent.
Think of it this way: You have two items and there is nothing in between them. That means they are right next to each other. If I say "the two items are right next to each other" and you say "the two items are right next to each other, and there is nothing in between them", the two statements are the same. Your extra statement doesn't actually add anything to the description. The same thing applies to the different states. Since nothingness doesn't exist, all the problems you mention in relation to it are also non-existent.</i>"
This is the best explanation of the concept of nothingness I've come up with so far so please read it carefully. To me, this is the root of our differing opinions regarding the first state.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">I’m crossing a street of width 2. I first cross half way, then half the remaining way, and so on forever. The corresponding series in a one-to-one correspondence with my steps is 1 + 1/2 + 1/4 + 1/8 + …, which sums to exactly 2, the width of the street. There are an infinite number of steps or intervals, yet a finite sum, and I can in fact cross the street.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Once again, you're confusing mathematics and reality. In mathematics you can write "1 + 1/2 + 1/4 + 1/8" and then add "+..." and call it infinite. This doesn't work in real life. You can't just walk half the distance, stop, write three dots on the ground and claim that you've crossed the whole street.
It's nothing but a mathematical convention that the series you mentioned sums to 2. Logically it's not possible to sum an infinite amount of terms because infinity is not a set amount. You can't use a mathematical convention as a model for the universe. The universe doesn't care about your mathematical definitions.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The problem is that you say “It didn’t come. It was there, that’s it.” And then you say that is not a miracle. A state without a cause is a miracle. Motion from non-motion is a miracle. You insist on both, and insist they are not miracles. That appears to be the end of the discussion.
To make any further progress, at a minimum, you would have to describe the origin of the "First State” and/or give a clear, concise definition of “miracle” that excludes a First State as something only God can bring about.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Call it what you want. It doesn't change anything. It doesn't make your model any more likely. As I said earlier, there is no origin to describe. The first state wasn't brought about. We've been through this many times now. Remember that time is only a part of the universe. There is no before the first state. You seem to have a very hard time clearing your mind from the concepts of time and space, but this is what you have to do in order to understand what I'm saying.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Instead of a whole universe, let’s talk about a single tiny, indivisible particle. Did it always exist? Did it have an origin? What condition do you see that is neither of those two?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
It's the same as the universe. It didn't have an origin and it always existed.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">An uncaused state is most definitely miraculous, meaning once again “an event that appears to be contrary to the laws of nature and is regarded as an act of God”. The laws of nature include cause and effect. The origin of beginning or First State is widely regarded as an act of God. On what basis do you deny any of this?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Because my model includes cause and effect. State #1 causes state #2 which is therefore an effect of state #1. It only appears contrary to the laws of nature for you because you are unable to imagine the beginning of the universe as the beginning of time.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">That means all the states are simultaneous. Or are you again using some other meaning for “interval” that you have not stated?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
No, state #2 follows state #1. The change is what constitutes time. If nothing changed there wouldn't be time. Try not to view time as something independent of space. I admit that it's a difficult concept to imagine, but it's what makes the most sense.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">But time consists of intervals.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Time consists of change.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Wrong. I did complete the one-to-one correspondence, But I just showed you a few examples, not the whole series, because you didn’t give me enough time. But a mind trained in logical thought can see that all the steps are present.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
It's impossible to do the whole series and thats's exactly my point. Do you believe that if I gave you unlimited time, you would at some point reach a time when you had written down all the steps?
Maybe it's better not to be trained in logical thought. As you said in an earlier point, for some people it's impossible to unlearn something they were wrongly taught.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">What “bound” do you place on time that will prevent it being unbounded in the future? If none, then doesn’t that show that actual unbounded concepts do exist in reality?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Yes, it does. But I've never denied that unbounded concepts exist. Time is unbounded in the future, but this is only an example of a potential infinity. It's the actual infinities that I deny the existence of.
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