About
Content
Store
Forum

Rebirth of Reason
War
People
Archives
Objectivism

Post to this threadMark all messages in this thread as readMark all messages in this thread as unreadPage 0Page 1Forward one pageLast Page


Sanction: 5, No Sanction: 0
Sanction: 5, No Sanction: 0
Post 0

Saturday, October 19 - 4:54pmSanction this postReply
Bookmark
Link
Edit
A true idea is a collection of parts of reality who's relative relation to each other can be decoded, who's decoder output is consistent with observation (sensor output).

To verify an idea is true, you need one part of reality to store the idea, another part for the decoder (if the idea was encoded), another for the sensor, and another part for a comparitor (compares the decoder output to the sensor output), and another part to store the result of the comparitor (a part of reality that can be changed into at least two different symbols, where one of the symbols is used to indicate equality and the other symbols mean different).

Knowledge is a collection of stored ideas. Omnipotence is said to be knowledge of the entirety of reality. Such cannot be possible, because for an idea to exist, a part of reality must be used to store an idea about another part of reality -- and to store all of the relations between parts of reality one would need at least a duplicate of reality somewhere else... but if reality already is all that exists, then such a duplicate cannot exist. Hence there cannot be an entity within reality that is omnipotent.

Yet... potentially what we know of our reality is something like a computer simulation that is only a small subset of an encompassing reality. In this case what we currently call and think of as the universe is actually only a subset of the universe. In such a case, there could be a God who runs and knows all of the part of the universe known to us.



Post 1

Saturday, October 19 - 8:37pmSanction this postReply
Bookmark
Link
Edit
In this case what we currently call and think of as the universe is actually only a subset of the universe.
If the definition of the universe is all that exist, as Manfred stated, then it include everything that we don't yet know of. Nothing unusual in that. Here is what Manfred said, "By definition, the universe is the totality of ALL that exists. It doesn’t define 'part of what exists,' for this would be a contradiction against itself and require a new word to define ALL that exists, a useless undertaking, since there is already a word to define ALL that exists, namely 'Universe'."

I don't know about every mouse in the state of Arizona, but that does not invalidate the fact that they exist and by definition, known or not, they are every mouse in the state of Arizona.
--------

Dean, you said:
In such a case, there could be a God who runs and knows all of the part of the universe known to us.
To believe is something in the absence of any evidence is faith, and in this case, mysticism.



Post 2

Sunday, October 20 - 4:51amSanction this postReply
Bookmark
Link
Edit
Steve (Reply to Post 1): You understood perfectly well every word I said. Your reply to Dean is exact, for my statement that the uníverse is ALL that exists (whether already known or not) INCLUDES what is up to now not yet known (I used the definition given by the encyclopedia). Further on, it surprises me greatly that someone as Dean, who should , at least, know that Objectivists are atheists, come up now with religious trash.



Post 3

Sunday, October 20 - 6:12amSanction this postReply
Bookmark
Link
Edit
"Religious trash?" I did not make a contradiction. I didn't say "all we know to be the universe is all the universe". I just implied that in a religious person's head, all they have to do to make themselves consistent is to expand it to include God, (but then also adjust God's omnipotence to not include all that is God). And I do agree with Steve's statement that accepting that such a God exists would be by faith, not by using evidence nor reason... its unverifiable. We here all agree that unverifiable information is frequently either worthless or harmful, particularly if coming from an untrustworthy source.

I had a major headache last night so I felt like going to bed rather than expanding my post to include the above info. I've been reading, thinking, and writing too much this last week, not getting enough sleep.

====
I just had the inspiration to define what a true idea is down to its real substance in reality as a physical object. AFAIK no one has ever done that before. That was not religious trash. That was a positive revolution in mankind's knowledge.
(Edited by Dean Michael Gores on 10/20, 6:54am)




Post 4

Sunday, October 20 - 8:24amSanction this postReply
Bookmark
Link
Edit
To Dean: "expand it to include god". As Ayn Rand would have said: Think twice, for you're involved in a contradiction of terms. Even a religious person would have pointed this out to you immediately. The uníverse "includes" "god"? My oh my! :-)



Post 5

Sunday, October 20 - 9:55amSanction this postReply
Bookmark
Link
Edit
Given what I defined God is, there was no contradiction.

Cheers,
Dean



Post 6

Sunday, October 20 - 10:24amSanction this postReply
Bookmark
Link
Edit
As physics evolves, we need new words.

The concept Universe gets applied in two contexts; the common sense one here, but also, the only region of physics we are permitted-- by physics -- to experience as reality, to touch, to acknowledge as 'real' as opposed to purely hypothetical. There is a philisophical argument to be made that those are for all practical purposes one in the same; of what significance is a hypothetical region of physics that by definition is unavailable to realize? Might as well not be 'real' because it can't be real.

However, restricting ourselves to that Universe of physical permitted access results in a singularity that can't be dismissed, awaiting a physical explanation. Many of those -- must be hypothetical by definition-- physical explanations divide 'the Universe' into bits that we can experience, and bits that, by definition, we cannot experience within our local physical constraints.

An example: M/brane theory. Nothing to do with magic. But this purely hypothetical posits ours as one of many possible physical universes, a transient thing. Might as well be magic. So if M/brane theory were ever someday proven, we'd just redefine what is meant by 'Universe' to include that new understanding of physics. Semantics...

Same thing with the following theory:


0=0 :Nothing

A + -A = 0 :postive A plus negative A = nothing

A=A :A is not nothing, but now, two A's for the price of none.

Matter, anti-matter. A local, rare, yet statistically permitted fluctuation in the net local 'production' -- appearance -- of net matter or anti-matter happens constantly in some 'universe' of cosmic grey 'foam' -- a region of sameness. A bubbling local imbalance of low-level balance. But matter is annilated by anti-matter and vice versa, so the foam 'sparks' occasionally and keeps itself in balance at net zero. But statistically, every so many billions of years, the roulette wheel of randomness creates two statistically out of balance regions to appear close enough to each other to drive each other apart from each other -- a region of net matter flying away from a region of net anti-matter, both of which can now persist over much longer periods of time, because in each, either matter or anti-matter dominates. What drives them apart? The violence of the initial close proximity annilation of enough of each other to propel them apart...at the speed of light, no longer able to communicate with each other in order to restore balance to 'zero' in the bubbling foam...

The physics that dominates in each of these 'half universese' results in the unwinding we see. But each half universe can only experience itself-- not only because it is separating from the other at the speed of light, but because to communicate would be annilation. So not in the sense of an obeyed law, but of a consequence that would mean end of both universes. It just hasn't happened.

Pure fantasy, agreed. And yet, in our present universe, still no explanation for the following:

Consider either total energy or total mass, or use Einstein to consider them interchangeably, but

State 1: 0

State 2: A

Based on our present knowledge of and definition of 'the Universe' how did it get from State 1 to State 2?

The fantast above says that we are only seeing half the ledger.

0=0
A + -A = 0
A=A

In each half universe:

State 1: 0
State 2: A

But the are matter/anti-matter universes. Two for the price of none.

We can choose our paradoxes, but we can't escape them. In our universe we have the paradox:

State 1: 0
State 2: A

In the hypothetical two half universe, we have the paradox that we can never prove it, and likely same for other theories, like M/brane theory...

So pick your paradox/singularity.

regards,
Fred

PS: Apparently, the 'new' word Multiverse was coined by physics in the late 1800s...

As in, we live inside our Universe, one of many possible in the Multiverse...



(Edited by Fred Bartlett on 10/20, 10:51am)




Post 7

Sunday, October 20 - 11:06amSanction this postReply
Bookmark
Link
Edit
Matter, anti-matter universes.

Via Einstein, then energy, anti-energy.

The basis:

Imagine a level field; that is 'the cosmic foam.'

It is jiggly and randomly, fluctuations appear locally in the cosmic foam. Why? Why not? Who or what is going to stop it; it's 'cosmic foam.'

Now, imagine creating a pile of matter, by imagining a fluctuation creating a 'pile' of matter in the field. It does so by creating a local 'hole' in the field. Hey, look, a pile of something. That is A.

The hole is the -A.

If that is all that happens -- a little pile next to a litle hole, then they annihilate each other. 'spark'

Now, every so many billion years, two such fluctuations appear at the same time, in close proximity. There is a violent annilation as always, but now, a pile of matter and a hole of anti-matter is flung away from each other by the violence of the anniliation...

Now, not just a level field.

There is a net pile, called A.

There is a net anti-pile-- the hole left by creating the pile A in the level field. That is anti-A.

They are hurtling away from each other. They now persist over long periods of time. THey both still wind down, but now, over a much longer period of time, via alternative physcial processing; long term entropic processes, not short term violent matter/anti-matter annilation. Each half universe kicked into a new phsical realm, because matter dominates in one and anti-matter in the other...

As far as the foam is concerned, no paradox... a pile balanced by a hole.

Want to imagine the flat gray field of cosmic foam as God, saying "Have fun, kids!" Feel free...

Two A's for the price of none, with conservative signs attached to them.

regards,
Fred





Post 8

Sunday, October 20 - 11:15amSanction this postReply
Bookmark
Link
Edit
From wikipedia:

There is considerable speculation as to why the observable universe is apparently composed almost entirely of ordinary matter, as opposed to a more symmetric combination of matter and antimatter. This asymmetry of matter and antimatter in the visible universe is one of the greatest unsolved problems in physics.[2] The process by which this asymmetry between particles and antiparticles developed is called baryogenesis.

..unless there is a second anti-universe, hurtling away from our universe, in which anti-matter dominates.

If that were true, then no paradox in either.

The cunundrum is, neither universe can know about the other.

Not only because they are hurtling away from each other at the speed of light, but because if they did communicate, they would annilate each other.

That is some catch, that catch-22...

So pick your paradox...

regards,
Fred

PS. Relative to where the pile/hole was created, the pile is moving away at some speed greater than 1/2 the speed of light, and the hole is moving in the opposite direction at some speed greater than 1/2 the speed of light, and so only relative to each other are they moving away at the speed of light or greater...


(Edited by Fred Bartlett on 10/20, 11:16am)




Post 9

Sunday, October 20 - 12:48pmSanction this postReply
Bookmark
Link
Edit
Fred,

That does an excellent job of explaining why what we observe is mostly matter (instead of half antimatter). But then say, if reality is determinitic, what might cause this initial split in the first place?

My best explanation is that for every possible self consistent (truth system) set of physical laws and energy/matter states, there is a reality. We exist in one of such, and there is no way for us to "travel" from one reality (truth system) to another, such would be a contradiction.

It doesn't really matter to us that other truth systems are true... because we can't interact with them. This is just satisfying to me because it answers the questions: "Where did the universe come from? Why is there energy/matter in the first place?" The answer is: because we are in a truth system, our truth system is as it is, and there are others for the infinite possible truth systems possible.

I hope that makes sense to you. For example, there would then exist a truth system that is just a single hydrogen atom. And also there exists truth systems of simple mathematical logic like 1 + 1 = 2. Mathematical truth systems are subsets of ours. There is a book by Neil Stephenson that plays around this idea.

Cheers,
Dean



Post 10

Sunday, October 20 - 7:09pmSanction this postReply
Bookmark
Link
Edit
Dean:

One of us could ask "what would cause it?" The other could ask "What could stop it?"


what is statistically infrequent or rare is not impossible- just rare. Wait long enough and it happens.

but it just kicks the can down the road in a way.

Or does it , anymore than the oscillating universe theory?

The flat foam always was...is no different than the universe always was. But a balance of negative positive mass and energy. A flat uninteresting field of jittery nothing. What is rare, because it is statistically not prohibited is the odd pairs of universes, the result of the alignment of two rare events. Statistically rare but with finite probability. Someone wins the lottery. Some permitted because they are not prohibited(by who or what?) Universes erupt out of the flat field.

the alternative is a conservation singularity...something from nothing.

which is more bizarre? A multiverse that always was that rarely emits interesting universes or something from nothing?

Regards,
Fred



Post 11

Sunday, October 20 - 7:21pmSanction this postReply
Bookmark
Link
Edit
Dean:

I agree ... my example is one of many hypotheticals. It is certainly one with a built in gatekeeper in that communication with the complementary balancing universe would in this example destroy each of them, truth and all. And yet without knowledge of each other a conservation paradox would exist in both. They each have certain knowledge of only one side of a two sided ledger.

an interesting hypothetical would be an alternate explanation that explains the conservation paradox.
What would be interesting is would it also result in a similar gatekeeper preventing confirmation...

regards,
Fred



Post 12

Monday, October 21 - 7:53amSanction this postReply
Bookmark
Link
Edit
To Dean (Post 3):
"I just implied that in a religious person's head, all they have to do to make themselves consistent is to expand it to include God."
With this statement you commit the mistake of including "god" into the universe, which is NOT what neither the "Bible" nor religion holds (that's why I pointed out the contradiction in terms), for the way in which the "creation" of the universe is mentioned indicates that "god" (one entity) created the "universe" (another entity) out of Nothingness. Hence, while you state that all that "they" (the religious people) have to do, is to INCLUDE "god" into the universe, this contradicts both what the "Bible" and religion state, since, for both of them, both entities ("god" and the "universe") are SEPARATE entities, not one and the same. Therefore, the contradiction. Besides, if you ADD "god" to the universe you're starting to be involved with pantheism, which is a religious anathema and, far worse, also a logical incongruity.

You'll find my whole analysis at an early version of my book "Ayn Rand, I and the Universe," (the book is copyrighted at the Library of Congress/Washington D.C. starting at "Ayn Rand and Rational Egoism: The dynamo of human Progress," though please look at post 5 of the "Discuss this Article" section, since I changed chapter 1 (The post also lists the chapters sequence published at "Rebirth of Reason"). Further on, in relation with the chapter "The Structure of the Universe" there's a typographical error which could lead the reader to a wrong calculation. I corrected this on Post 9 of the "Discuss this Article" part corresponding to mentioned chapter.

May I add a bit more?: Given that "god" "made" the world (the universe) out of a void (emptiness in the sense of nothingness) "god" must have also been a void in him/her/itself, which brings up the question of how can a "void" (an entity, impossible as it is) create something out of another void (another "entity" and more impossibles here). So, by "adding" "god" in any way you intend to do, you get more and more involved in one contradiction on top of another on top of of another one and on top of a further one and so forth.

The other Quote IS a Quote (and my portal at Facebook, should you want to take a look at it, though it's not necessary) and, further on, a MOST serious recommendation, in view of how mankind has behaved through history (and nowadays as well) against our fellow beings. Hence, it should be taken seriously and I don't think that any humorous or sarcastic comment is proper.



Post 13

Monday, October 21 - 2:13pmSanction this postReply
Bookmark
Link
Edit
The quotes on this website are meant to be like one liners. Like ya know, vertical space on a website's home page is valuable, so you don't go into all your details of your article or your thoughts there. You just put the one liner. The focus grabbing title. Get what I mean? So even if your quote quotes some article which makes it validly following the definition of what a quote is... your quote does not follow the quick one liner pattern as intended for vertical space usage on the home page.

I'm snappy/sarcastic with you because you said that I "come up now with religious trash". FYI I take that as a major insult, of which you have yet to apologize for.
May I add a bit more?: Given that "god" "made" the world (the universe) out of a void (emptiness in the sense of nothingness) "god" must have also been a void in him/her/itself, which brings up the question of how can a "void" (an entity, impossible as it is) create something out of another void (another "entity" and more impossibles here).
You are putting words into the religious person's mouth. The religious people don't say that God was in the void, or void himself. They say that first there was God.

Let me put these words into the religious person's mouth:
First there was God and a bunch of practically random stuff other than God, that was just kind of a mess that you couldn't see because it didn't emit electromagnetic waves, so if you were to look at the other stuff you'd just call it a "void" as a layman. Then God formed out of that other stuff (the "void"): the Sun, the Earth, and everything we can sense with our electromagnetic sensors.
So you see, there is no contradiction here, just a little play of words adjustment. Religious people are good at falling back on their positions like this. Its still the case that we could ask "but where did God come from?" like they ask "but where did the universe come from?" and we look at each other with angry eyes. Of course we have the better position because we don't believe in things unless we have observation and reason as Steve pointed out.

But then above I answered the question of where did our universe come from without using God and while still maintaining the laws of conservation of mass/energy. I said our reality is a truth system... that there are an infinite number of self-consistent yet fully independent truth systems, and all truth systems are true. We just happen to be in this truth system.

Cheers,
Dean



Post 14

Monday, October 21 - 5:19pmSanction this postReply
Bookmark
Link
Edit


Not exactly what I mean, but physics keeps showing up with odd symmetries...



(Edited by Fred Bartlett on 10/21, 5:24pm)




Post 15

Monday, October 21 - 6:30pmSanction this postReply
Bookmark
Link
Edit
Fred,

The "oscillating universe theory", as in like history eventually repeats itself? I'd agree that such could be a truth system, and furthermore that our reality could be such a system. Although I don't think its possible to determine or collect evidence on whether we are in such a system.

"What could cause it, what could stop it, statistically infrequent things eventually happen..."

Statistically infrequent things that are possible (and hence at least somewhat frequent no matter how infrequent). But things that completely contradict a truth system's nature, such as the appearance of some energy/matter (an increase in energy) in a reality where conservation of energy is part of its definition... is not possible.

Currently I think along the lines of that all truth systems are fully deterministic. This is because its just inconceivable to me to think of how a truth system can maintain self consistency if it has chaos... its just a contradiction. Conservation of energy/matter. Conservation of extants unless modified/changed via the exact laws (reason) of how that truth system changes. I'm getting into this detail because...

You say some blob may be stable goo and then like explode in opposite directions, one side with matter, other side anti-matter. But then where did the goo come from? Or if there wasn't goo, why would there be the case where matter and anti-matter split? If they split, then there must have been something before they split right? But I am denying to you the possibility that there was goo. You only have the option to say... that right before the split anti-matter was on the left side and matter was on the right, but now after the split, the sides reversed. Or maybe before the split but before they came together they span around each other for a while (goo?). But with this, we still come to the same conclusion: the energy/matter in our reality has always existed.



Post 16

Tuesday, October 22 - 11:15amSanction this postReply
Bookmark
Link
Edit
Dean:

Not what I meant. By oscillating universe theory, I meant that the current universe eventually slows down its expansion, then reverses back to a singularity, and then 'rebounds' and starts another expansion cycle. So, all the 'stuff' in the universe always was and always is, just, it goes through cycles of expansion and contraction. No conservation singularity -- something from nothing. Just...always something, in a process either of expansion or contraction.

Each cycle might, for all anyone knows, have unique histories or even, universal 'constants' and be unique.

Moot; the only indirect evidence we'd have that this is happening is, to be able to detect a slowdown in the rate of expansion of the universe(like it was eventually going to stop expanding and reverse iself.)

I think the latest observational assertion on this is, if anything, the rate of expansion of the universe is accelerating, not slowing down-- as if there were 'dark matter' that was pulling this universe apart and speeding its expansion.

There are three possibilities; 1] it is decelerating, and will reverse 2] it is expanding just fast enough that it will never reverse and 3] it is accelerating and might never reverse.

I think the observational assertion used to be 2]...but has been changed to 3]

There is another set of possibilities, that nobody can yet explain; not only varying rates of expansion over time, but varying regimes of acceleration/deceleration in those rates over time(such that, if we were to observe a period of either accleration or deceleration in the rate of expansion, we could not be sure that if we waited long enough, we we would detect the opposite...

But as far as I can tell, that makes no claims about history itself repeating.

regards,
Fred




Post 17

Tuesday, October 22 - 11:44amSanction this postReply
Bookmark
Link
Edit
Dean:

That's right -- the 'goo' theory says that the 'goo' always existed.

But the 'goo' has the following characteristics: it is flat, and uninteresting. It is a balance of matter and anti-matter, of energy and anti-energy. It is 'flat' without significant gradient(unlike our current universe, which is jam packed with all kinds of gradient.)

The cosmic 'goo' theory, in that sense, is similar to the oscilating single universe theory, in that all that is always was, just in a different form-- no built in conservsational singularity, something from nothing. Just, since it is, that means, it always was, else a singularity is required. A paradox. A conundrum. An inconsistency.

What the cosmic goo theory posits is how to get an interesting universe full of dynamicism and gradients, apparently on its way from an intensely dense state to a dim 3 deg K cloud of sameness without resulting in a conservational paradox: by emitting two of them of opposite sense, one dominated by matter, the other by anti-matter.

Anti-matter isn't a theory. It is observed in our universe, just, rarely. As well, what can be constructed with matter can be constructed from anti-matter(like hydrogen atoms, etc.) But matter and anti-matter annihilate each other.

What 'causes' the dim, vibrating, goo to emit regions of statistically dominant matter or anti-matter?

What is to stop them? Remember, what is statistically rare is not the same thing as impossible. People win the lottery. The cosmos has all the time in the Universe to erupt. It may be an exceptionally rare event. (I am of course speaking totally hypothetically, and yet as we speak, NASA is looking for evidence of far off galaxies composed of anti-matter. They would be hard to detect directly. They could only be readily detected by boundary interactions with matter galaxies, and the immense energy released.)

Consder the following. In the rooms you and I are in, there is a random distribution of O2 molecules. We claim to know the % as somewhere around 20%, on average. But these are all just random O2 molecules jiggling about. There is nothing preventing them, say, from randomly arranging themselves in regions of net O2 dominance or deficit, randomly. It might be a statistical rarity. It might take billions of years for the dice to roll. But at some point, a significant maldistrubuted arrangment of O2 molecules in these rooms is not prohibied by the dice.

Someone wins the lottery.

Now, back to the goo/foam. For a universe to erupt, not just one rare event, but two rare events must align. An even bigger longshot.

Gazzillions of years go by, and nothing of interest erupts from the goo...so wait another gazzillion years. If not long enough, then wait another...and another...until finally, the battling infinities result in a finite result: two "interesting' universes for the price of none.

Soon enough, back to the dim 3 deg K goo...in the meantime, we all enjoy this rare ride.

Take a look sometime at the real phenemona of 'oscillons' in vibrating media (sand, brass beads--even colloidal suspensions). From bits of seemingly random vibrating bits of sand or beads will erupt, spontaneously(well, shake the box with a shaker at the right frequencies and amplitude) larger structures that exhibit the characteristics of particles; some repel, some attract, some combine to form larger structures. The identity of these larger structures -- 'oscillons' is not uniquely associated with individual bits of sand or brass beads-- the y 'move through' individual regions of vibrating sand/beads, and maintain their own identity and rules of interaction.

'Oscillons' are not a theory, they are an observation of what is possible.



Notice...there are piles...and there are holes...in an otherwise flat field...

Also notice, in the sample above(a timelapse)...all three are 'in phase'. (They are all either 'piles' or 'holes' at the same time.) That isn't a requirement, is just a characteristic of the three examples above. There can be 'oscillons' that are out of phase, that have different 'rules' of interaction than oscillons that are in phase...

Also notice, in the three 'hole' example... what is erupting in the middle, between the three 'holes'? Is that thegenesis of a new 'pile' out of phase with the other piles?

regards,
Fred


(Edited by Fred Bartlett on 10/22, 11:54am)




Post 18

Wednesday, October 23 - 5:39amSanction this postReply
Bookmark
Link
Edit
Dean:

At approximately 13.8 billion years from the time of the eruption, parts of that which erupted from the uninteresting goo became self-aware.

What 'caused' that?

Or...what was there to prevent it? Life is a rare thing in this bit of the goo that tore off from the goo. Self-aware, intelligent life an even rarer thing.

What % of this universe's mass is self-aware? An exceedingly smalle, infinitesimal amount.

What % of the goo is self-aware? Infinitesimal squared? Qubed?

But 'rare' is not prohibited by the dice; it is just rare. Nearly infinitesimal is tamed by throwing nearly infinite time at it. In calculus, we learn that infinities do battle all the time, the result of which is something finite. There are infinities, and there are infinities. Not all infinities are equal. When you divide two 'infinite' series, the results can be finite.

Said another way: folks actually win the lottery. So...what was going to prevent rare from happening? We've had all the time in the cosmos to roll the dice, and then some.

regards,
Fred
(Edited by Fred Bartlett on 10/23, 5:46am)




Post 19

Wednesday, October 23 - 5:56amSanction this postReply
Bookmark
Link
Edit
Dean:

"But things that completely contradict a truth system's nature, such as the appearance of some energy/matter (an increase in energy) in a reality where conservation of energy is part of its definition... is not possible."

Exactly. That is exactly the conservational contradiction -in what we call our universe- without a balancing universe or explanation.

In the 'multiverse' -- in the goo, in my hypothetical -- the mass and energy were always there, in balance...and are still in balance, precisely because there are emitted two universes -- one in which there is an apparent imbalance of matter, and one in which there is an apparent imbalance of anti-matter.

Locally...in each emitted universe--imbalance.

Globally...in balance.

I am not saying this is 'the' explanation. I am hypothesizing this could be one explanation.

A consequence of the hypothesis is, such events are rare. Is that inconsistent with observation? We're aware of 'once.'

regards,
Fred



Post to this threadPage 0Page 1Forward one pageLast Page
User ID Password reminder or create a free account.