Mark Peaty wrote:
> Hello Moshen and welcome.
>
> I think it is a very good question, and succinctly put.
>
> I have been trying to ask the same question and get a plain-English
> answer, but without success. Of course, I could be missing 'the point'
> too, and it wouldn't be the first time by a long shot. :-)
>
> If there was simply nothing, utterly and absolutely nothing, well that
> would be the end of it: 'No problemas!' as the cool dudes say. But there
> seems to be something, because I seem to be here, at the moment anyway,
> and I have this distinct belief that I was here yesterday living in this
> same house with all these recalcitrantly individualistic people who all
> play along with a story about being my wife and children. Appeals to
> solipsism degenerate into incoherent babbling; I really am here, even
> though my grasp of the facts about my existence gets shaken loose every
> so often. And you are here too, except you are over there. In short
> there IS a universe and it seems to be remarkably self-consistent.
>
> I, like you, am confronted by the manifest existence of an objective
> reality. Being educated and impressed by the successes of the
> application of scientific method we are quite well equipped to accept
> certain problematic statements about the parts of the world we normally
> take for granted as 'real'. We have learned that the *appearances* of
> solidity, power, enduring nature, and so forth, which we experience as
> *qualities* of those things, are not the full story; that in fact the
> '*true* nature of things is that if you try and find absolute objective
> boundaries to things you can't and if you try to make any other kind of
> measurement, you have to make do with an approximation. Indeed, the more
> you wish to precisely specify anything about the location or motion of
> anything then the more you must accept a complex statistical description
> about the rest of its characteristics.
>
> Well and good; normally we don't have to worry about this too much. It
> is only when we start persistently asking *How does it all work?* that
> the seemingly intractable problems begin. And for each of us there is
> some kind of recursive process: we read and interact with others
> [indeed some lucky people can apparently just wander into the next room
> and straight away *talk* on the topic with someone who is interested!],
> and then we cogitate and imagine things and some of you scribble arcane
> arithmetic and run mathematical 'what-ifs' on computers; finally we
> reach some kind of internal stability of viewpoint that allows a
> reassessment of things previously held to be clear, or problematic
> perhaps. But after some time, doubt sets in, we think something far
> enough through and see a problem or, more likely, we read of some new
> viewpoint which challenges what we believe and we feel we must take it
> seriously because of its apparent validity, consistency, etc, or it is
> presented by someone we respect. Either way we have to work to either
> assimilate it or uncover valid reasons for rejecting it.
>
> The mathematicians who contribute here seemingly have no problems with a
> totally 'insubstantial' existence of numbers. Unlike me who has
> *ultimate* problems wrapping my head around the idea. I have not yet
> succeeded. You asked about 'assumptions' in you 'Joining' thread, but
> here by definition the only one is the existence of Many Worlds, which
> is hugely problematic because nobody really knows what it means. In my
> case it is obvious why, but in the case of those who *espouse* the
> Many-Worlds hypothesis, I have absolutely know idea how they can account
> for the purely logical - and therefore mathematically necessary, yes? -
> consequence of the problem you have so succinctly put. As I reason it,
> this 'continuous' aspect of location, even if it is only 'virtual'
> guarantees that the Many Worlds are always proliferating at a rate which
> must effectively be an infinity times an infinity of infinities. [I fear
> I might have underestimated the speed there, but as I say, my maths is
> not all that good!] In other words it seems to make no sense at all!
> Why? [Grin!] well because *my* world seems to be just one story. What
> keeps it together? It can't be any inherent smartness on my part! [Grin
> again; no false modesty there mate!] So *IT*, what I call 'The Great
> IT', is just doing IT'S thing.
>
> Nobody here has yet explained in plain-English why we have entropy.
I quite agree with you about Many Worlds - it's not even an hypothesis; it's a whole class of hypotheses. And I don't think numbers exist either in the way that I exist, though I'm open to defining different kinds of existence. But I think I can explain why we have entropy.
The short answer is that we have entropy for the same reason we have number and distance and duration and energy and temperature, etc. We invented them. They are variables in our model of the world. Usually in our model we, through ignorance or disinterest, only include a rough description of how things can be, the possible states we will consider significant. For example, we don't care where every molecule of air is in the room, just the density. So in such a model there are a lot of different possible states at the microscopic level that map into one state at the level of our model. If we assign a number to each macro state proportional to the logarithm of the number of micro states that map into it, then that number will be additive: if we put two different macro states together the number of micro states mapping into the sum state is the sum of those logs. Further, if we assume in our model that the system will occupy the microstates with equal probability of bei
ng in any one of them, this correctly predicts the equilibrium behavior of the system in terms of its macrostates. If we consider this logarithm, call it S, in the case of a system modeled in terms of it's internal energy, Q, and its temperature, T, we find that it satisfies an equation for small changes dS=dQ/T. This quantity, S, is called "the entropy". By extension the analogous quantity was called the entropy of a possible message by Shannon.
>Oh
> well, surely, in the Many Worlds, that's just one of the universes that
> can happen!
The problem is to get from "anything can happen" to "this is more probable than that".
>Except that, for plain-English reasons stated above, there
> are *and always have been* infinity x infinity x infinity of entropic
> universes.
"Entropic universes" doesn't convey anything to me. Our universe, because of its expansion, is very far from equilibrium: its entropy density is very small compared to its maximum possible value.
>
> It doesn't make sense. Call me a heretic if you like, but I will 'stick
> to my guns' here: If it can't be put into plain-English then it probably
> isn't true!
I commend to you the book "The Comprehensible Cosmos" by my friend Vic Stenger. It's pretty much in plain English, with equations confined to the appendices.
Brent Meeker
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Received on Mon Mar 05 2007 - 15:33:36 PST