Okay, but my definition of "Rideout-Sorkin causet" was based on this line (top of p.3) of this R&S paper:Originally Posted bySquatch347

Acausal set(or “causet”) is a locally ﬁnite, partially ordered set (or “poset”).

Given this definition by Rideout-Sorkin, I thought it was reasonable to call a locally finite (here meaning "interval finite") partially ordered set a "Rideout-Sorkin causet".

"Initial conditions" don't necessarily happen at the "beginning" of the process. You might start at some arbitrary point in a doubly-infinite sequence {xLet's assume for a second that this is true. What is the initial condition for this process? It would seem to me that in an infinitely old universe there is no initial condition and therefore this process becomes problematic._{z}} (where z is an integer), and with the transition rule xz = 2x_{z-1}+ 1 you could reconstruct all "future" (x_{k}, k > z) and "past" (x_{j}, j < z) points.

Right, what matters are theI mean it in the same sense we used when initially discussing the difference between a causet labeled by a natural number set and a causet labelled by integers or letters or shapes. The form of the label cannot have an effect on the physical interpretation of the causet. Any order inherent or used in the labeling system must be consistent with the order inherent in the causet. This is the same argument we made back when we were discussing the original "Labeled Causets in Discrete Quantum Gravity" paper.

Link again for easy reference: http://www.du.edu/nsm/departments/ma...ints/m1410.pdf

Just as covariance dictates that the laws of physics are independent of the coordinate system employed, in the discrete theory, covariance implies that

order isomorphic causets should be identified. That is, a causet should be independent of labeling.orderproperties of the labeling set, not whether it's, say, English letters or Roman numerals.

I think my point still stands, though; there are Rideout-Sorkin causets (i.e., locally finite posets) that do not admit a Rideout-Sorkin labeling (a map L from the causet C to the natural numbers N that satisfies c_{1}< c_{2}implies f(c_{1}) < f(c_{2})).

I assume that Prof. Gudder knows the mathematical meaning of his statements about "growing" causets. I do not make the same assumption for you, Squatch.You are appealing to a different meaning that simply doesn't exist. Your argument has been essentially that I was implying something different by misusing the term, but you can't point out how I implied something incorrect. Nor do your peers seem to have such compunctions:In the causal set approach to discrete quantum gravity, a causal set (causet) represents a possible universe at a certain time instant and a possible completed" universe is represented by a path of growing causets [2, 5, 6, 8, 9].ibid.

Is Prof. Gudder misusing terminology when he speaks of growing causets here?

If you're going to claim that your definition is commonly used in pure mathematics, it is incumbent on you to support your claim. I know at least that the definitions of recursive functions, primitive recursive functions, what is sometimes calledIt would perhaps be true if there were a different definition for iterative used by mathematicians, but there isn't. It is a word that means the same thing in project management, computer science and pure mathematics. That is why you find the same definition of the word on Wolfram Mathematics, or in peer reviewed papers. Do you really have no idea what these authors mean when they invoke the term iterative? If no, is that idea substantively different from the one I offered as the definition?countableinduction, andtransfiniteinduction use much more precise language even at the undergraduate level. I doubt that the definitions get any easier in graduate and postgraduate literature, but perhaps I'm wrong.

It's fine to claim that the examples I gave fail to be iterative; what matters is that you show it.Because you are using the term in a different manner than is generally accepted. If you wish to communicate effectively, it is a better policy to use terms in a manner that your readers will understand. Crack pot has a specific meaning and it differs from the meaning you meant to imply. However, even the definition you offered does little to alter the objection. No support was offered to indicate that they were doing science in a non-standard or sub-standard way, the term was simply lobbed out as a dismissal.

I have done years and years of my own research in mathematics, Squatch. How much have you done?Why not do your own research? Why must I be the one to justify myself to you? That is the merit of my objection. Both you and GP have shown that you seem to view yourselves as the academic panel to which I must defend myself and which has the final say on a source's "worthiness." That is not the case here. I made a claim which I defended, if either of you wished to make an objection to that claim then make an argument countering the claim or showing how the source is incorrect.

For the gregarious child, the empty partial stem is chosen for the maximal element (see e.g. the diagram on page 6).You are correct, I misspoke. Gregarious children are notcasuallyrelated across space, they are simply related across space. As I understand it, as you pick a maximal element to be a child you also pick a partial stem to describe its relation to. In this case the child is not causally related the the particular partial stem in question, it exists in spacial relationship to the elements of its parent. This selection also involves (by default) the selection of an anti-chain that contains the causally related elements to the new element (para 3, page 5).

No, this has been the definition of "spacelike" relation among causet elements that I have been expounding. You have insisted to the contrary that there is a "spacelike" relation aside from the (I assume "temporal") partial order defined on the causet.I think that this is essentially correct. c_{1}does not come before or after c_{2}in a temporal sense. If I were to describe c_{1}in relation to c_{2}I would use only changes to physical coordinates rather than any temporal coordinates. Do you think that R/S mean something different when they say "spacelike?"

Assuming that "different ways" refer to the different possible posets that can be formed where the "additional" element is maximal, yes.You didn't quote the additional sentence, I just wanted to be clear. Do you also agree with me when I said: "Each of the different ways of adjoining e are children, taken together they are siblings."

It depends on what you're calling the "age". You proposed that the "age" of the universe is the length of the longest (temporal, if you're insisting that there are different partial orders) chain of elements from the causet representing the universe. For the universe represented by the causet I gave above, there is no longest chain; therefore, the universe has no age.Fair enough. But the age of the universe in your example would still be finite right?

You could take a slightly different approach, and say that if there is a chain of length k in C, then C's age is "at least" k. If there is some k such that for all N > k, C's age isnot"at least" N, then C has a finite age. If C doesn't have a finite age, then C has an infinite age.

Under that definition, the universe represented by the causet I gave would have an infinite age.

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