View source for Talk:Mathematical universe hypothesis

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==Theory?==

While I find Tegmark's proposals intriguing, I dispute calling this one a "theory".  It's more of a provacative proposal that future theories adopt a particular and controversial feature[[User:Hillman|CH ]] [[User_talk:Hillman|(talk)]] 21:44, 21 August 2005 (UTC)

Isn't this just one of those ideas that occurs to pretty much everyone independently at some time or another? At least to philosophy students or distracted physics undergrads.
:I'm not sure what "feature" you are referring to. Tegmark's "everything" or UE is frequently discussed as a potential TOE (for example in "New Scientist" magazine http://space.mit.edu/home/tegmark/toe_frames.html   or...  http://scienceweek.com/2003/sc031031-1.htm). It appears to be a theory rather than a tautology (which it is sometimes derided as). Please elaborate on what you mean by "feature" and why it should not be referred to as a TOE. In the meantime I'm going to remove the "feature of" insertion.[[User:Joncolvin|Joncolvin]] 07:24, 9 December 2006 (UTC)

::Being non-falsifiable, this proposal would not even qualify as science, let alone as a theory of everything. It is perhaps a "theory of everything" in a philosophical sense, but not in a scientific sense. Intriguing and attractive as it is, there is no way that experiment could possibly shed any light on the matter and therefore it lies outside the realms of science. [[User:Robin S|Robin S]] 01:06, 27 January 2007 (UTC)

:::An extremely positivist viewpoint, Robin. This theory does in fact make predictions: one such prediction is that physics will become more "mathematical" as it progresses deeper towards the ultimate TOE. To date this prediction has been successful. Tegmark does not pretend that his theory is science; it is metaphysics, but metaphysics of a predictive nature. It bridges science and philosophy in a similar manner to the anthropic principle. [[User:Joncolvin|Joncolvin]] 05:44, 18 April 2007 (UTC)

The last point of criticism "is self-contradictory because one cannot subsume all possible (partly contradictory) mathematical structures into one structure" is the result of a misunderstanding and has no bearing. The Ultimate Ensemble is not "one structure" ... the parts have absolutely no relation to each other.  <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/58.179.98.125|58.179.98.125]] ([[User talk:58.179.98.125|talk]]) 03:25, 1 March 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

: This is a wikipedia article, not a research paper. It correctly reports what criticisms other physicists have made---there is even a citation showing you where this criticism was made. Just as a matter of interest, however, if the different parts have absolutely no relation to each other, and we are "in" one part, then presumably you agree with the criticism that the proposal is unverifiable, since we could never find any empirical evidence of the existence of the other, absolutely unrelated, parts. [[User:Dark Formal|Dark Formal]] ([[User talk:Dark Formal|talk]]) 05:24, 2 March 2008 (UTC)

:It is a "theory" in the philosophical sense: a reasoning mindset. Philosophical theories are not provable in the scientific sense, they work, or they don't. [[User:Rursus|Rursus]] dixit. ([[User talk:Rursus|<span style="color: red; background: #FFFF80"><sup>m</sup><u>bork<sup>3</sup></u></span>]]!) 21:13, 29 June 2010 (UTC)

::It is much more than just a philosophical theory. I argue it is a scientific theory. If you study the articles written on the topic by M.T., you'll see that there is math that goes with it, and some ways are suggested to test aspects of the theory. --[[User:IO Device|IO Device]] ([[User talk:IO Device|talk]]) 23:43, 29 June 2010 (UTC)

Folks, this page is not a physics or philosophy forum. It doesn't matter what any editor thinks of the subject, or what terms they think should be used -- all that matters is what terms ''reliable sources'' use. -- [[Special:Contributions/70.185.144.90|70.185.144.90]] ([[User talk:70.185.144.90|talk]]) 21:57, 27 October 2019 (UTC)

== Relation to Schmidhuber's ultimate ensemble ==

Apparently both [[Max Tegmark]]'s ensemble and [[Jürgen Schmidhuber]]'s ensemble of all computable universes were published in 1997. Their relation should probably be clarified. [[User:Discrepancy|Discrepancy]] ([[User talk:Discrepancy|talk]]) 20:50, 5 July 2008 (UTC)

: Only if there's a reliable source that does so. -- [[Special:Contributions/70.185.144.90|70.185.144.90]] ([[User talk:70.185.144.90|talk]]) 21:58, 27 October 2019 (UTC)

== Inadequate "Responses" section ==

The Criticisms section has three subsections.  The first two are criticisms and the third is entitled "Responses".  It's good to have a "Responses" subsection, but it needs to summarise Tegmark's answers to the two attacks.  It's unsatisfactory just to point the reader to Tegmark's book as if the article was a teaser campaign.  I suggest that somebody who has read the book gives a short precis here of the relevant arguments. [[User:Tommy Herbert|Tommy Herbert]] ([[User talk:Tommy Herbert|talk]]) 22:25, 11 December 2008 (UTC)

== The theory is well defined if you write it this way ==

The "Criticisms" section says: "Some argue that the "set of all mathematical structures" is not well-defined."

The [[Kolmogorov_complexity]] of the universe is 0, but the [[Kolmogorov_complexity]] of any part of the universe is more than 0. This means that if the universe was able to be converted to a form the computer would take as input, and if zip files were better optimized, then the universe would compress to a 0 byte zip file. This does not mean it could be represented as 0s and 1s or as a file at all. It means there is no total information because it all balances to 0. Many things decrease [[Kolmogorov_complexity]] as they get bigger. For example, "all integers" has more integers than "all integers except 107 and 30", but the [[Kolmogorov_complexity]] of "all integers except 107 and 30" is bigger. Similarly, if the universe includes all math structures, then that is very simple to describe: The [[Kolmogorov_complexity]] of the universe is 0. Also, the [[Kolmogorov_complexity]] of nonexistance is 0, which means if Max Tegmark's theory is true, then the universe does not exist. Its simple. [[User:BenRayfield|BenRayfield]] ([[User talk:BenRayfield|talk]]) 19:19, 5 March 2010 (UTC)
:Mathematical structures in the level-4 multiverse exist relative to other mathematical structures. What you're saying is that the KC of both existence and nonexistence is 0, and from that you're implying that existence==nonexistence, from which you imply nonexistence (this is a contradiction). I don't see the logic in your implications. --[[User:IO Device|IO Device]] ([[User talk:IO Device|talk]]) 03:19, 6 March 2010 (UTC)

:The KC of nonexistence is 0? Nonexistence isn't a thing, so how can it have a KC?[[User:Joncolvin|Joncolvin]] ([[User talk:Joncolvin|talk]]) 02:04, 24 April 2010 (UTC)

==Joke?==
Tegmark is known to produce elaborate intellectual jokes one time in ten or so. Funny enough, a few of them gain some considerable serious interest despite being jokes. Is this one of them? Just consider the sound of "MUH" and possibly also "TOE"... [[User:Rursus|Rursus]] dixit. ([[User talk:Rursus|<span style="color: red; background: #FFFF80"><sup>m</sup><u>bork<sup>3</sup></u></span>]]!) 21:17, 29 June 2010 (UTC)
:Are you kidding? You're practically defaming the man. MUH ain't a joke. Just consider the number of articles by him on the topic. --[[User:IO Device|IO Device]] ([[User talk:IO Device|talk]]) 23:41, 29 June 2010 (UTC)

:Perhaps more of a [[Shaggy dog story]] than a joke. And who cares how many articles X writes about X's idea? What counts is how many articles other experts (not popular media like New Scientist) write about X's idea.  [[Special:Contributions/84.177.47.244|84.177.47.244]] ([[User talk:84.177.47.244|talk]]) 19:33, 1 July 2010 (UTC)

Mathematical monism has been intuitively obvious to me since childhood. Rest assured that folks like Tegmark exist. Rather than projecting your nominalist's incredulity onto others, you should make an attempt at understanding a world-view that is clearly unnatural for the typical mammal. Expand your mind. [[Special:Contributions/75.139.170.90|75.139.170.90]] ([[User talk:75.139.170.90|talk]]) 08:32, 12 September 2015 (UTC)
:Intuition is not a reliable source of knowledge so say you intuitively knew it as a child means nothing. As has been said this is a philosophical theory not fact or science. Folks like Tegmark exist but that doesn't make them right. You need to expand your mind and not rely on intuition.[[Special:Contributions/2600:1700:1C80:5190:134:731B:172D:3A10|2600:1700:1C80:5190:134:731B:172D:3A10]] ([[User talk:2600:1700:1C80:5190:134:731B:172D:3A10|talk]]) 18:57, 5 September 2020 (UTC)

==Improving "Criticisms" Section==
{{anchor|round_1}}
The paragraph summarizing the three-way debate (Hut-Alford-Tegmark [http://arxiv.org/abs/physics/0510188]) is correct. It simply states the criticism made in section VI.A of that paper, in the paragraph beginning "Finally, the Fundamentalist describes himself as...". One way to improve this section of the WP article would be to also include summaries of the other criticisms made in that paper. And also criticisms from other papers. [[User:Dark Formal|Dark Formal]] ([[User talk:Dark Formal|talk]]) 22:08, 29 November 2010 (UTC)
:The "three-way debate" is fictional! The paragraph summarizing it obviously implies it's a real life debate in which two critics (rather than the two characters portrayed by his coauthors) were criticizing MUH, when (in fact of fiction) all the characters were speaking generally. See [[WP:SYN]].
:It is ''not'' acceptable for the structure of this article to be the lead followed only by criticism subsections. For clarity, does this article include ANY criticism that WASN'T in Tegmark's own paper? I'd suggest rather than heaping on more criticism, a first step would be to include the ACTUAL citations to Tegmark, (rather than Tegmark's citations), and to include Tegmark's replies to those criticisms (or to drop whatever's too obscure).—[[User:Machine Elf 1735|Machine Elf 1735]] ([[User talk:Machine Elf 1735|talk]]) 05:00, 30 November 2010 (UTC)
{{anchor|round_2}}{{unindent|:}}
''Dark Formal'': I have no idea what you mean. It is not fictional, it is a real debate, in print. The three authors explicitly say in the Introduction that each of them is the advocate of one of the positions in the debate. The criticisms of MUH in the paper are direct and explicit: did you read paragraph I pointed you to? If you are so worried about [[WP:SYN]] then we can easily rewrite the summary in this WP article using quotes from the Hut-Alford-Tegmark ("HAT") paper. Do you want me to do that?<br/>
I don't understand what you are trying to say in your second point. When you say "does this article include ANY criticism that WASN'T in Tegmark's own paper?" what are you getting at, and what do you mean by "Tegmark's own paper"? Since the HAT paper contains some of the few explicit published critiques of MUH it seems entirely reasonable to summarize it here. [[User:Dark Formal|Dark Formal]] ([[User talk:Dark Formal|talk]]) 02:56, 1 December 2010 (UTC)

:Yes, I did read it, that was the ''Math, Matter, or Mind'' ("HAT") abstract. That's not the article that I've been discussing however, (see [[:#MUH0704|below]] or [http://en.wikipedia.org/w/index.php?title=Mathematical_universe_hypothesis&diff=399851561&oldid=399663104 the citations you reverted]).
:No, it is not a real debate. Having "divergent views" makes for a protracted discussion, not a "vigorous debate" with "forceful critics". I'll explain:
:The coauthors are cooperating. They're working for a greater good.
:If any one of them were to actually "win", it would defeat the express purpose, of cautioning non-physicists to be "wary of any claim that modern physics leads us to any particular resolution of this circularity".
:So, that's just swell they're all looking out for one another, but:
:'''The goal of a ''real'' debate is to win.'''
:When you read the article I'm referring to, perhaps you'll agree that we do need to say where we got it {{small|[[WP:SAYWHEREYOUGOTIT]]}} I know ''I'' was more than a little annoyed to be directed to wade through a bunch of (mostly unrelated) cites, some without page numbers, only to find all of it Tegmark's article.
:So, if we're going to tell the reader what Tegmark said these other guys said, ''but'' you don't want his name repeated like a mantra, (fair enough, except for missing all the cites and assuming what? I'm some kind of Tegmark fanboy [cured]). I guess several criticisms could be consolidated into one section where it's made clear that Tegmark discusses them all in that particular article. 
:Here's what I had. I pushed Vilenkin out of this paragraph. If you think it's best, we can keep the part about [[Formalism (mathematics)]] and an axiomatic "Platonic ensemble" being "incompatible" per Gödel. However, Tegmark's spent a lot of time on that and his response is presumably not [curses foiled again]. If it's not a deal breaker for math, how is it a deal breaker for math + sassy math-based life forms? (i.e. might be too technical for non-mystics).
<blockquote><span id="TheSummary" class="citation">
{{small|{{gray|Tegmark, along with physicists [[Piet Hut]] and Mark Alford, coauthored a journal article in the format of a fictional debate which erupts between three characters who each approach physics from one angle, of either: Math, Matter, or Mind. In this [[Penrose triangle]]: {{nowrap|Math explains Matter,}} {{nowrap|Matter explains Mind, and}} {{nowrap|Mind explains Math.}} The authors explain that their intention was to caution the non-physicist, to beware of any claim that modern physics leads to ''any'' particular resolution of this circularity.<ref name='HTA'>{{cite journal |last1=Hut |first1=Piet |last2=Alford |first2=Mark |last3=Tegmark |first3=Max |year=2006 |title=On Math, Matter and Mind |journal=Foundations of Physics |volume=36 |issue=6 |pages=765-794 |doi=10.1007/s10701-006-9048-x |href=http://arxiv.org/abs/physics/0510188}}</ref>}}}}</span>
</blockquote>
: I think [[WP:UNDUE]] is a concern; it can't just be shooting fish in a barrel without begging the question of Tegmark's responses and why they were relegated to a short paragraph at the bottom when the article is about ''his theory''. I'm not game for trying to add replies myself, but I'd be satisfied with removing the POV visual cues introduced by section headers, (there's not that much text and there's no need for a subsection). 
::*Criticism
:::*Other criticism
:::*Response
:I want to point out, that the abstract does not once mention ANY of it, but I did find some Level IV and "Mathematical Multiverse" discussion at the end of the article. Per [[WP:SYN]], they're supposed to specifically address Mathematical universe hypothesis, but I think Level IV or "Mathematical Multiverse" will do in a pinch. 
:Here's the MMM ("HAT") abstract:
:<blockquote><span id="HAT_ABSTRACT" class="citation">{{small|{{gray|We discuss the nature of reality in the ontological context of Penrose's math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter can be explained in terms of math. Non-physicists should be wary of any claim that modern physics leads us to any particular resolution of this circularity, since even the sample of three theoretical physicists writing this paper hold three divergent views. Some physicists believe that current physics has already found the basic framework for a complete description of reality, and only has to fill in the details. Others suspect that no single framework, from physics or other sources, will ever capture reality. Yet others guess that reality might be approached arbitrarily closely by some form of future physics, but probably based on completely different frameworks. We will designate these three approaches as the fundamentalist, secular and mystic views of the world, as seen by practicing physicists. We present and contrast each of these views, which arguably form broad categories capturing most if not all interpretations of physics. We argue that this diversity in the physics community is more useful than an ontological monoculture, since it motivates physicists to tackle unsolved problems with a wide variety of approaches.}}}}</span></blockquote>
:The general one-liners for each stereotype are:
:#current physics has already found the basic framework for a complete description of reality, and only has to fill in the details...
:#no single framework, from physics or other sources, will ever capture reality...
:#reality might be approached arbitrarily closely by some form of future physics, but probably based on completely different frameworks...
:Tegmark is number 3, the mystic.
:You say: if I'm "so worried about [[WP:SYN]] then we can easily rewrite the summary in this WP article using quotes from the Hut-Alford-Tegmark ("HAT") paper." By summary do you mean the "Description" section? Because the lead is not something you've been reverting. Generally, I'd like it better if you did something ''in addition to'' as opposed to ''instead of''... Personally, I'd prefer that we make ( quite a few, if not all ) of that last set of reverted edits, and improve the article from that basis forward. Anyway, hopefully things will get cleared up if you take a good look through this article. It's the one that appears to be the source of the criticisms (which were used without attribution to Tegmark or his responses):
::*{{anchor|MUH0704}}[http://arxiv.org/abs/0704.0646 The Mathematical Universe (http://arxiv.org/abs/0704.0646)]
::<blockquote>{{small|{{gray|I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.}}}}</blockquote>
:—[[User:Machine Elf 1735|Machine Elf 1735]] ([[User talk:Machine Elf 1735|talk]]) 19:47, 1 December 2010 (UTC)
{{anchor|round_3}}{{unindent|:}}
''Dark Formal'': I agree that the paragraph on Tegmark's responses is inadequate and needs to be improved. But I don't see anything wrong with the article's current section structure with "criticism" followed by "response". There is nothing POV about that. Look at [[Keynesian economics]], for example, which also uses this structure. The article needs a better description of Tegmark's responses, not wholesale restructuring. I'd be happy to read Tegmark's response article, as you suggest, and give this a try, if it is OK with you.

Just because Tegmark attempts a response to his critics in one of his articles doesn't mean all the criticisms have to be placed in the frame of his response. The reader deserves to get a summary of and citations to those criticisms on their own terms, not filtered through one party in the debate. That's an elementary application of [[WP:NPOV]]. You are right that adding page numbers to the citations would be very helpful.

Who knows whether Tegmark's response article was the original source used by the authors of this page. That's irrelevant, because [[WP:SAYWHEREYOUGOTIT]] doesn't say you have to cite the first thing you ever read on the topic. It just says cite sources you have read. Then [[WP:NPOV]] implies that one shouldn't filter it through one party's account of the debate.

Concerning the HAT paper, I think you'd get a better picture by reading more of the paper beyond the abstract. You said "Tegmark is number 3, the mystic" but he is identified as the fundamentalist (see the introduction section) and his position is obviously MUH. Read section III.C where he lays it out explicitly, "self-aware substructures" and all. There is no [[WP:SYN]] involved in identifying HAT's "fundamentalist" position as MUH.
Also I think you'll find that the paper is clearly a debate. There are real (sometimes strongly-worded) criticisms and real responses, which is the definition of a debate. Your concerns are: (a) the goal of a real debate is to win and (b) the authors say they can agree on some some greater message that emerges from their debate. Neither of these proves that it isn't a debate. It's a debate where there may not be an obvious winner (isn't that usually the case with interesting and difficult questions?) and where the authors manage some very limited co-operation, agreeing on some greater message that emerges from their debate. They certainly don't agree on the point at issue here, which is the MUH (the "fundamentalist" position in the debate). [[User:Dark Formal|Dark Formal]] ([[User talk:Dark Formal|talk]]) 04:08, 3 December 2010 (UTC)

:'''Machine Elf 1735's reply to Dark Formal:'''
:You "agree the paragraph" is inadequate but "don't see anything wrong with the article's current section structure with 'criticism' followed by 'response'". Aside from being poorly structured, the repeated use of the word "criticism" visually reinforces the theory's lack of support. Rather than co-opting the article's structure, it's easy enough to cite a statement that Tegmark's theory hasn't been warmly received. That POV is, in fact, the ''dominate POV'', so there's no need to promulgate it via innuendo and lies of omission. Here is a copy of the [[Keynesian economics]] structure which you (inexplicably) believe uses this article's structure:
{{cot|Keynesian economics}}
<blockquote style="font-size:smaller;">
'''Keynesian economics'''
# Overview
# Precursors
## Schools
## Concepts
# Keynes and the Classics
## Wages and spending
## Excessive saving
## Active fiscal policy
## "Multiplier effect" and interest rates
# Postwar Keynesianism
## Main theories
# Criticism
## Monetarist criticism
## New classical macroeconomics criticism
## Austrian School criticism
## Methodological disagreement and different results that emerge
# Keynesian responses to the critics

'''Mathematical universe hypothesis'''
# Description
# Criticisms
## Definition of the ensemble
## Other criticisms
## Response
# See also
# References
# Further reading
# External links
</blockquote>
{{cob}}
:Criticism, which can sometimes be considered "constructive", should be integrated into the body of an article, when possible, to achieve a single NPOV perspective, rather than isolated POV perspectives. By established consensus, there is, ''arguably'', something wrong with it. Unless you can ''focus'' on why it cannot be done, then whereas 1) Tegmark himself [http://arxiv.org/abs/0704.0646 integrated the criticisms], and 2) all the criticisms are from that article, there's no reason to isolate Tegmark's responses in a single section at the bottom of the article. (Not that I'm game to provide them). I'm willing to compromise in so far as having most of the article appear as subsections under "Criticism" if that's satisfactory? "Other criticism" is not a viable subsection name under that section however.
:You say: "I'd be happy to read Tegmark's response article, as you suggest, and give this a try, if it is OK with you." If you still haven't read the main source, I can see this is largely a waste of my time and you show no concern in that regard. You don't need my permission to edit WP and in this instance, I've increasingly lost confidence in your ability to do so constructively.
:Not having read the source, you say: "Just because Tegmark attempts a response to his critics in one of his articles doesn't mean all the criticisms have to be placed in the frame of his response." However, '''all the criticisms''' are from that particular article and, far from "framing" them, omitting his responses (from this, the MUH article) and failing to cite his article as the (obvious) source would be pathetically incompetent or simply deceitful. As you can't be bothered to read the source, [[WP:AGF|you remain presumably unaware of this]], thank you. The remainder of the paragraph reflects that willful ignorance.
:Concerning the "HAT" paper, on which you fixate, I have read it, although not recently. Regarding the religious metaphors obscuring it, I stand corrected: Tegmark is '''not''' the so-called "mystic" but is, rather, portrayed as the "fundamentalist". (''What could have given me the "wrong" impression?'') Regardless of the article's contrivances, Tegmark's limited presentation of his theories demonstrates that the other two authors were willing to allow their article to serve as a vehicle for Tegmark. As I said, references to Level IV and Mathematical Multiverse might comply with [[WP:SYN]] but what's blisteringly "obvious" is that a metaphorical perspective '''most assuredly does not comply'''. Our protracted discussion over what constitutes a ''real'' debate has lost its relevance. Wikipedia ''wins''.
:I submit it's perfectly obvious to anyone who cares to [[WP:V]] that the contributor to ''this article'' failed to properly cite his or her true source and instead cited Tegmark's sources. (I hope this discussion is sufficient to suggest Tegmark's sources require further examination; I feel suggesting their contingent removal would have been quixotesque and besides ''I've verified them to a limited extent myself'', so I think they should remain.)
:I will once again add the appropriate inline references and strongly caution [[User:Dark Formal]] that repeatedly removing [[WP:RS]] citations, which they admit they haven't read, can be considered disruptive editing ([[WP:DISRUPT]]), with all that implies.—[[User:Machine Elf 1735|Machine Elf 1735]] ([[User talk:Machine Elf 1735|talk]]) 12:03, 3 December 2010 (UTC)
{{anchor|round_4}}{{unindent|:}}
''Dark Formal'': I have done as I said I would, and fleshed out Tegmark's responses to the criticisms, including citations (including section numbers to help readers to track them down) and direct quotes wherever possible. I have done the same for the criticisms themselves, for the ones I had access to. I can add more quotes soon. This should help to remove any appearance of [[WP:SYN|synthesis]]. I followed your suggestion of "having most of the article appear as subsections under 'Criticism'". I think it is obvious that [[WP:NPOV]] requires that the criticisms be presented on their own terms with quotes from their original authors, and not framed through Tegmark's quotations of them; equally it is important to include Tegmark's responses, which I have tried to do fully and fairly. I haven't yet found his response to the last criticism. You had a sentence or two about the testability of the theory in the Description section: that issue is now one of the subheadings in the "Criticisms and Responses" section. [[User:Dark Formal|Dark Formal]] ([[User talk:Dark Formal|talk]]) 20:56, 5 December 2010 (UTC)

:*You included a vague suggestion from Tegmark (2008) §VII that Vilenkin raises "other issues arising from Gödel's theorem". It seems Tegmark may have cited the wrong book by Vilenkin (failing [[WP:V]]). Unfortunately, I don't see where Tegmark clarifies what those issue might be vis-à-vis Gödel and Vilenkin. 
:*Likewise, the assertion attributed to Stoeger, Ellis, Kirchner (2006) fails verification. That paper discusses ''both'' testable and untestable hypotheses, (often quite generally), and I haven't found where it directly contradicts Tegmark's claim that MUH ''is testable'', or where it even discusses MUH specifically, (perhaps in passing?) So, unless I've missed it, your "response" from Tegmark is [[WP:SYN]], Tegmark does ''not'' respond to that paper directly. However, I have included part of your quote from Tegmark (2008) in part (b) of your response because it helps to clarify the kind of "probability distributions" to which he was referring in 1997. (Point (a) seemed vague and somewhat trivial or out of context however). 
:*I've restored the cited text which accurately describes the "HAT" paper. Stop removing it. I did include the issue brought forward '''''that the coauthors have raised'''''. Surprisingly, your "response" isn't even from Tegmark's "fundamentalist" character in that paper, it's from Tegmark (2008) §VII which doesn't seem to explicitly hearken back to "HAT"? I'm afraid it would seem to be [[WP:SYN]] once again, unless you could point me to the reference directly?
:*If anything, §VII would seem to be much more apropos to Schmidhuber, but you didn't mention it in that context? I included your dismissive "response" to Schmidhuber: that his objections are not a "show stopper". However, that could hardly be a fair summary of Tegmark's response, (even if MUH ''were'' comparable to string theory). 
:*If you've read Page (2006), which is available, you would surely realize that you've chosen a response which Page specifically anticipates and argues against. Tegmark can't defeat that argument by merely restating one of its premises. (Although he seems to take the argument much more seriously than I'd have thought it warranted.) I simplified Page's accusation to read "self-contradictory 'nonsense'" which was close to Page's own summary. I don't recall Page using your characterization of "partly contradictory", which I can verify if necessary, but considering your response on Tegmark's behalf is inadequate... and (perhaps taking after Tegmark) Page's "math" seems to achieve apotheosis prior to arranging its annihilation... perhaps it's just too technical for this article?
:*Finally, with the exception of "Definition of the Ensemble", your headers were POV in so far as they stated only the criticisms, and they were SYN in so far as they overstated the scope of the criticisms.
:I think that covers it. Let me know if missed anything or if I've been unclear. Thank you for trying to integrate some of my changes; much appreciated.—[[User:Machine Elf 1735|Machine Elf 1735]] ([[User talk:Machine Elf 1735|talk]]) 00:47, 6 December 2010 (UTC)
{{anchor|round_5}}{{unindent|:}}
''Dark Formal'': The majority of your changes consisted of removal of valid content. For example, all the description of Tegmark's explicit response to the Godel criticisms, in terms of CUH. Please contribute your own correct content, don't delete the fruit of other peoples hard work.

On specific points:
* Vilenkin's "other issues arising from Gödel's theorem". I agree it is vague. I was going to look it up when I got the chance. For now, I deleted it. 
* Stoeger, Ellis, Kirchner: that paper is about multiverse theories in general. It explicitly cites Tegmark's MUH paper as an example, and goes on to discuss the whole class of such theories. It is clearly criticizing the whole class (incl MUH) for untestability. I have modified the text to make that clear. I included Tegmark's explicit list of testable features of MUH because it is obviously (tautologically) relevant to this issue.
* I've restored the original text which accurately described the "HAT" paper. Stop removing it. It was in the article before you started editing it, and you have never shown that there is anything wrong with it. Just read the paper, it is obviously a real debate, with strongly-worded criticisms flung back and forth.
* Concerning the relevance of sec VII to Schmidhuber, feel free to add material saying so. The dismissive response to Schmidhuber is not mine, it is Tegmark's. If you can find a quote from him giving a better response, feel free to add it. Note that Tegmark explicitly identifies Godel-related criticisms as his motivation for that section (see VII.B) so it is appropriate to discuss sec VII as a response to the Godel-related criticisms.
* Concerning Page's criticism. Again you have taken correct (if incomplete) content and replaced it with something less clear and specific. How does it help the reader to learn that Page called Tegmark's theory "self-contradictory nonsense"? That's an insult, not a criticism. I quoted Tegmark's response directly. If it's weak, its weak. This is WP: we report what's out there.
* Headers: I made the subsection structure at your suggestion, remember? I have modified them trying to make them less POV. As I've said already, it is a violation of [[WP:NPOV]] to frame all the criticisms in terms of Tegmark's response to them. It also greatly reduces the readability of the Criticisms section. Let's stick with the subsectioned structure, which you agreed on before, and try to improve the content within it.
* Your version had a para about the "External Reality Hypothesis". It is probably inherited from old versions of the page. If you read Tegmark's response paper you'll realize that the ERH has nothing to do with responding to criticisms, it is just a way to derive the MUH. 

Please don't destroy the work that has gone in to this page. There is much that needs improvement, such as the "Consistency with our simple universe" section, which I haven't been able to verify. [[User:Dark Formal|Dark Formal]] ([[User talk:Dark Formal|talk]]) 01:38, 8 December 2010 (UTC)

''Dark Formal'': I've been working more on addressing your concerns. I gave a more appropriate quote from Page, skipping the Tegmark objection that (as you said) he had already anticipated. I included Tegmark's immediate response in the HAT paper to the Godel criticism. I rewrote the Vilenkin criticism (final subsection) using actual quotes from his book. I included his characterization of Tegmarks's response, but unfortunately he doesn't give a source for it so I can't get Tegmark's actual words on the topic. 
I am trying to get to the point where it is all solidly verified, and avoiding inadvertent [[WP:SYN]] by using direct quotes wherever possible.  [[User:Dark Formal|Dark Formal]] ([[User talk:Dark Formal|talk]]) 20:05, 8 December 2010 (UTC)

:'''Round 5 (response):'''
:*Per [[WP:TALKO]], I've added [[:Template:Unindent]]s, [[:Template:Anchor]]s and collapsed some of the information I had posted for ease of reference. With the ongoing and extended nature of the discussion, (hopefully drawing to a close soon), the threading may be unclear to the casual editor, as well being difficult to navigate. I'll briefly recap a few points I think bear repeating or explaining:
::*Comments prefaced with "''Dark Formal'':" are '''from''' rather than '''to''' [[User:Dark Formal|Dark Formal]].
::*The [[#TheSummary|"HAT" summary]] is verifiable by a glance at the [[#HAT_ABSTRACT|"HAT" abstract]]. We should disclose that the co-authors are play-acting a "religious" dispute, primarily for a ''non-physicist'' audience.
::*Mocking whole sentences ''verbatim'' (not as a quote) can easily mislead other editors scanning this page. (I've insisted on no more reverts of [[#TheSummary|"HAT" summary]]). Since I'm a "Destroyer", (which might be kinda bad-ass if it wasn't of fruit), I don't mind pointing out it demonstrates [[WP:IDHT]].
::*[[User:Dark Formal|Dark Formal]] and I started editing the article at about the same time, although his first 3 rounds consisted only in reverting edits I had been trying to make. This is only my second response subsequent to [http://en.wikipedia.org/w/index.php?title=Mathematical_universe_hypothesis&diff=400726227&oldid=400376220 his first "fruits"] at the start of [[#round_4]].
::*A one time IP in 2007 paraphrased material from Tegmark's Mathmatical universe ("[http://arxiv.org/abs/0704.0646 MU]") paper but ''did not cite Tegmark.'' Instead, the contributor ''cited Tegmark's own citations.'' The material consisted of Tegmark's ''descriptions of several criticisms of MUH,'' but did not include his responses, (as if the contributor had gathered various criticisms in the wild). From the paraphrasing, it's pretty obvious Tegmark's paper "[http://arxiv.org/abs/0704.0646 MU]" was the only source used, (for example, section five, V, parts E and F). This has been cleaned up, (there ''has'' been progress).
:::*[http://en.wikipedia.org/w/index.php?title=Mathematical_universe_hypothesis&diff=178818864&oldid=177578672 prev]''' {{small|22:41, 18 December 2007 [[Special:Contributions/86.7.219.67{{!}}86.7.219.67]] ([[User talk:86.7.219.67{{!}}talk]]) (2,974 bytes) EDSUM: (''Included refs to a sample of opposing views: this still needs expansion.'')}}
::*[[User:Dark Formal|Dark Formal]] wasn't exactly faced with an onerous burden in order to recover any work. He just reverted a fourth time and made a few changes. Here's the [http://en.wikipedia.org/w/index.php?title=Mathematical_universe_hypothesis&action=historysubmit&diff=401167494&oldid=400726227 diff], skipping my [[#round_4]] edit, and I didn't request #5 or #6:
{{Quote box |style=font-size:70%; |tstyle=font-size:100%; |title=01:28, 8 December 2010 |quote=::#'{{red|Inconsistency}} with Gödel's theorem'→'{{red|Consistency}} with Gödel's theorem'
::#'{{red|Self-contradictoriness}}'→'{{red|Coexistence of contradictory structures}}' 
::#'{{red|Inconsistency}} with our "simple universe"'→''{{red|Consistency}} with our "simple universe"'
::#Deleted the sentence, "{{red|Other issues arising from Gödel's theorem have also been raised by physicist [[Alexander Vilenkin]] [9].}}" [''sic''] because there don't seem to be "other issues" in that particular book which Tegmark cited, [[WP:V]].
::#"{{red|the MUH is not empirically testable, and therefore does not constitute a scientific theory. [10] [8]}}" [''sic'']→"{{red|multiverse theories in general [9] and the MUH in particular [8] are not empirically testable, and therefore do not constitute scientific theories.}}" [''sic''].
::#"{{red|that}}"→"{{red|it}}"}}

:*{{anchor|r5_cuh}}From your first batch of talk page posts [[#round_4]]:
::<blockquote>{{small|{{grey|"The majority of your changes consisted of removal of valid content. For example, all the description of Tegmark's explicit response to the Godel criticisms, in terms of CUH. Please contribute your own correct content, don't delete the fruit of other peoples hard work."}}}}</blockquote>
::<blockquote>{{big|{{grey|...}}}}</blockquote>
::<blockquote>{{small|{{grey|"Concerning the relevance of sec VII to Schmidhuber, feel free to add material saying so. The dismissive response to Schmidhuber is not mine, it is Tegmark's. If you can find a quote from him giving a better response, feel free to add it. Note that Tegmark explicitly identifies Godel-related criticisms as his motivation for that section (see VII.B) so it is appropriate to discuss sec VII as a response to the Godel-related criticisms."}}}}</blockquote>
:* As I said, I ''have'' found a better response for Schmidhuber, and I anticipate it will be used in lieu of yours, because your response fails [[WP:V]], (cited as section V.E of "[http://arxiv.org/abs/0704.0646 MU]"). I do not, as a matter of course, check up on your work, ''unless I have to''... Remember, I've said twice that I wasn't game to expand on Tegmark's responses. You might want to reflect on how ''the entirety'' of my edits in [[#round_4]] were regarding the issues that I listed, ''not'' some kind of rampage. Please consider that, from my perspective, you tend to leave me little choice and demonstrate little concern. The "CUH" is a ''what-if, an "exploration",'' which directly mentions Schmidhuber. As a ''second response'' for "the secularist", (reading more like a '''''result of''''' than a response...) it's much too tenuous to '''''insist''''' on responding from a different paper, based merely on Gödel, (which is ubiquitous), and which wasn't even a problem for Tegmark.
:*The second batch, 16 hours later, was much more ''reasonable'' and the changes were more substantial too, thank you. I'm given to understand you got logged off for a couple of them, (it happens). For our reference, here's some of the content items I'm concerned with:
::*Your proposed response on Tegmark's behalf to Schmidhuber's criticism (fails [[WP:V]]):
:::<blockquote>{{small|In response, Tegmark notes [2] (sec. V.E) that the measure over all universes has not yet been constructed for the String theory landscape either, so this should not be regarded as a "show-stopper".}}</blockquote>
::*An "exploration" of adding a Computable Universe Hypothesis ("CUH") "MU" section seven, (VII), page 20 (with clarification vis-à-vis exploration, acceptable as a response for Schmidhuber but [[WP:SYN]] as a ''second'' response to "the secularist"):
:::<blockquote>{{small|Tegmark's response [2] [''sic''] (sec. VII) is to suggest "drastically limiting the number of mathematical structures to be considered", by modifying the MUH to a much more restricted "Computable Universe Hypothesis" ("CUH") which only includes mathematical structures that are simple enough that Gödel's theorem does not require them to contain any undecideable/uncomputable theorems. Tegmark admits that this approach faces "serious challeges", including (a) it excludes much of the mathematical landscape; (b) the measure on the space of allowed theories may itself be uncomputable; and (c) "virtually all historically successful theories of physics violate the CUH".}}</blockquote>

<table><tr><td width="50%" valign="top">
{{Quote box |style=font-size:70%; |tstyle=font-size:100%; |title=01:28, 8 December 2010 |quote=<div>
Tegmark's response &lt;ref name="<span style="color: red; font-weight: bold;">Tegmark2008</span>"/&gt; (sec. <span style="color: red; font-weight: bold;">VII</span>) is to <span style="color: red; font-weight: bold;">suggest </span>"drastically <span style="color: red; font-weight: bold;">limiting </span>the <span style="color: red; font-weight: bold;">number of </span>mathematical structures <span style="color: red; font-weight: bold;">to be considered</span>", <span style="color: red; font-weight: bold;">by modifying </span>the MUH to a much more restricted "Computable Universe Hypothesis" (CUH) which only includes mathematical structures that are simple enough that Gödel's theorem does not require them to contain any undecideable/uncomputable theorems. Tegmark admits that this approach faces "serious challeges", including (a) it excludes much of the mathematical landscape; (b) the measure on the space of allowed theories may itself be uncomputable; and (c) "virtually all historically successful theories of physics violate the CUH".
</div>}}
</td><td width="50%" valign="top">
{{Quote box |style=font-size:70%; |tstyle=font-size:100%; |title=19:53, 8 December 2010 |quote=<div>
Tegmark's response <span style="color: red; font-weight: bold;">in </span>&lt;ref name="<span style="color: red; font-weight: bold;">HAT</span>"/&gt; (sec <span style="color: red; font-weight: bold;">VI</span>.<span style="color: red; font-weight: bold;">A.1</span>) is to "drastically <span style="color: red; font-weight: bold;">shrink </span>the <span style="color: red; font-weight: bold;">Level IV multiverse" so that it includes "only Godel-complete (fully decidable) </span>mathematical structures"<span style="color: red; font-weight: bold;">. In &lt;ref name="Tegmark2008"/&gt; (sec. VII) he gives a more detailed response</span>, <span style="color: red; font-weight: bold;">proposing a modification of </span>the MUH to a much more restricted "Computable Universe Hypothesis" (CUH) which only includes mathematical structures that are simple enough that Gödel's theorem does not require them to contain any undecideable/uncomputable theorems. Tegmark admits that this approach faces "serious challeges", including (a) it excludes much of the mathematical landscape; (b) the measure on the space of allowed theories may itself be uncomputable; and (c) "virtually all historically successful theories of physics violate the CUH".
</div>}}
</td></tr></table>

::* {{small|{{grey|Vilenkin's "other issues arising from Gödel's theorem". I agree it is vague. I was going to look it up when I got the chance. For now, I deleted it.}}}} 
:::* OK.
::* {{small|{{grey|Stoeger, Ellis, Kirchner: that paper is about multiverse theories in general. It explicitly cites Tegmark's MUH paper as an example, and goes on to discuss the whole class of such theories. It is clearly criticizing the whole class (incl MUH) for untestability. I have modified the text to make that clear. I included Tegmark's explicit list of testable features of MUH because it is obviously (tautologically) relevant to this issue.}}}}
:::*And yet, I found it unverifiable as you were using it at the time, and as modified. Please provide citations (with page numbers). I've summarized citation requests [[#CN|below]], thanks.
:::*It's not tautologically true that a testable feature is (a) "physics research will uncover mathematical regularities in nature"? I hope you realize I paid you a compliment regarding the other item (b) on that list.
::* {{small|{{grey|I've restored the original text which accurately described the "HAT" paper. Stop removing it. It was in the article before you started editing it, and you have never shown that there is anything wrong with it. Just read the paper, it is obviously a real debate, with strongly-worded criticisms flung back and forth.}}}}
:::*You didn't restore it the original text. I've responded at length to why I've deleted it, and regardless it's not not citeable, it's someone's editorial opinion and clearly yours too. You've been around long enough to know that when I started editing the article makes no difference; did that stop you from deleting any of my text that predates you? Have at it. I've told I've read the paper. Please see my citation requests: [[#CN]].
::* See [[#r5_cuh|here]] for "CUH".
::* {{small|{{grey|Concerning Page's criticism. Again you have taken correct (if incomplete) content and replaced it with something less clear and specific. How does it help the reader to learn that Page called Tegmark's theory "self-contradictory nonsense"? That's an insult, not a criticism. I quoted Tegmark's response directly. If it's weak, its weak. This is WP: we report what's out there.}}}}
:::*No, it wasn't correct. As you're probably now aware, it's a term used in logic and I quoted Page, like I said I did. Nonsense. Your response was inadequate and you fixed it in the second batch. You should also have stricken out many of these comments. What we do, is collaborate with each other. You made some mistakes and you fixed them. Well done. Moving on...
::* {{small|{{grey|Headers: I made the subsection structure at your suggestion, remember? I have modified them trying to make them less POV. As I've said already, it is a violation of [[WP:NPOV]] to frame all the criticisms in terms of Tegmark's response to them. It also greatly reduces the readability of the Criticisms section. Let's stick with the subsectioned structure, which you agreed on before, and try to improve the content within it.}}}}
:::*No, I said I was willing to compromised regarding the structure if you insist. I can't say I find it implausible that you remember something other than what's written on this page. Thank you for modifying them, I really appreciated that. [[WP:IDHT]], please don't your contrary assertions about "framing" ad nauseum. That's all been taken care of. Yes, I did agree: you're welcome.
::* {{small|{{grey|Your version had a para about the "External Reality Hypothesis". It is probably inherited from old versions of the page. If you read Tegmark's response paper you'll realize that the ERH has nothing to do with responding to criticisms, it is just a way to derive the MUH.}}}} 
:::*You mean the one it took you a week to read but didn't stop you from arguing? The one you had never even heard of? The one you're still playing [[WP:IDHT]] games about? ''That "response paper"?'' Shameless.

:*'''Responses to your second batch of posts''' (including few remarks on subsequent edits):
::*{{small|{{grey|I've been working more on addressing your concerns.}}}}
:::*Thanks, much appreciated.
::*{{small|{{grey|I gave a more appropriate quote from Page, skipping the Tegmark objection that (as you said) he had already anticipated.}}}}
:::*<div>Look good, I didn't want to pull any punches and I thought "nonsense" seemed less insulting than "inconsistent and inconceivable". In the future, it's good to include the page number inside the ref:<br><small><nowiki><ref>D. Page, "[http://arxiv.org/abs/hep-th/0610101 Predictions and Tests of Multiverse Theories.]" p. 14.</ref></nowiki></small><br>Section 4 is five pages long, and ''really'' not meant for non-physicists/mathematicians (o_O)</div>
::*{{small|{{grey|I included Tegmark's immediate response in the HAT paper to the Godel criticism.}}}}
:::*IMO, "the secularist" in "HAT", (Alford), was a bit of a shill and Tegmark is only too happy to discuss it. Even so, this article ''is'' about his theory, so I think it would be good to use his complete response in an extended quote because it also speaks to complexity issues. His #3 reference could be substituted, perhaps like this:
::::<div style="font-size:90%;padding-left:2em;border-left:solid 2px black;">My hypothesis is that only Gödel complete (fully decidable) mathematical structures have physical existence. This drastically shrinks the Level IV multiverse, essentially placing an upper limit on complexity, and may have the attractive side effect of explaining the relative simplicity of our universe. If you define mathematical structures as (equivalence classes of) models of axiom systems [{{big|*}}] then they are guaranteed to be Gödel-complete (consistent). Please note that although we conventionally use a Gödel-undecidable mathematical structure (including integers with Peano’s recursion axiom, etc.) to model the physical world, it is not at all obvious that the actual mathematical structure describing our world is a Gödel-undecidable one — lacking a theory of quantum gravity, we have certainly not found it yet. Even a world corresponding to a Gödel-complete mathematical structure could in principle contain observers capable of thinking about Gödel-incomplete mathematics, just as finite-state digital computers can prove certain theorems about Gödel incomplete formal systems like Peano arithmetic.<br>{{big|*}} {{small|''[http://arxiv.org/PS_cache/gr-qc/pdf/9704/9704009v2.pdf Is “the theory of everything” merely the ultimate ensemble theory?]'' page 5, part A}}<br><div style="padding-top:0.5em;">[[Max Tegmark]] [http://arxiv.org/PS_cache/physics/pdf/0510/0510188v2.pdf On Math, Matter and Mind], page 12, (with Piet Hut and Mark Alford)<br>{{small|Tegmark addresses Formal System fundamentals, symbols, rules for what strings are well-formed formulas and for what WFFs are theorems, and complete sets of theorems.</div>}}</div>
::*{{small|{{grey|I rewrote the Vilenkin criticism (final subsection) using actual quotes from his book. I included his characterization of Tegmarks's response, but unfortunately he doesn't give a source for it so I can't get Tegmark's actual words on the topic.}}}}
:::*I verified the material on page 203 and footnote 8 on page 222 material which you provided, it's all good... You tend to put cites at the beginning, that's fine. Putting them at the bottom usually works too. <s>I'd be willing to self-revert the {cn}, but I'm guessing you {cn}ed yourself by mistake?</s> 
::::*This evening, you've included a reference to "[http://arxiv.org/abs/0704.0646 MU]" part V. section B which certainly doesn't mention Vilenkin. It may well be related, (''it is a theory of '''everything''' after all''), but I would like to understand what ''exactly'' was ''not'' in Vilenkin, and which you had in fact sourced from "[http://arxiv.org/abs/0704.0646 MU]" part V section B (but forgot to cite). Also, why you placed the {cn} tag in a different spot.
::*{{small|{{grey|I am trying to get to the point where it is all solidly verified, and avoiding inadvertent [[WP:SYN]] by using direct quotes wherever possible.}}}}
:::* I agree that vocabulary can sometimes be an issue. However, so can context and omissions... Although you've agreed to include Tegmark's immediate reply to "the secularist's" comments in "HAT", (and drafted a version of that inclusion), I'm none-the-less still concerned that you seem to remain intent on using Tegmark's "exploration" of adding CUH to MUH, which is found in a later paper. As I've said, it seems to be appropriate for Schmidhuber, whom Tegmark mentions directly, but it's much too tenuous based merely on Gödel, which Tegmark didn't even see as being a problem. The string theory response to Schmidhuber, where ever it's from, ''is'' a quote, one that, IMO given Tegmark's "CUH" exploration, seemed disproportionately dismissive, even unrelated. As you indicated you were not interested in Tegmark's reply to Schmidhuber and invited me to enhance it, I'm willing to minimally address this problem by using the "CUH" material mentioning Schmidhuber. Furthermore, I'll do so in such a way that makes the "what if" nature of the "exploration" apparent. Finally, I'll remove the current discussion of "CUH" as a second response to "the secularist's" question.
::*However, I'll pass on this round of edits (except to restore the "HAT"[[#TheSummary]]).
::*{{anchor|CN}}I understand that the following are properly cited in your opinion, and I want you to know that I hear that. Please understand that I'm not asking for an explanation when I ask for citations. I'll still be needing them, even though you made adjustments. As you're aware, it's verifiability rather than truth that counts. So, there's no need to convince me that they're ''right,'' and there's only one way to convince me that they verify. Please excuse the repetition, but I'll need specific references, (by page number please) for each of:
:::# Stoeger, Ellis, Kirchner (2006), if MUH is said to be included in a certain class, and that class is said to be untestable, I'll need both page numbers if they're not on the same page. 
:::# The page number of "HAT" where "the secularist", Alford, states that MUH, "Mathematical Multiverse", or "Level IV" is an untestable hypothesis, (or an internal notation, with an additional page number on which that reference is resolved to one of the above). Please don't infer by this that I haven't reread it.
::* I'd like to make it clear that I ''am'' challenging the edits regarding MUH being untestable. If you like, you are certainly welcome to tag it with {cn} but I'll leave that up to you. (The version which I wrote, makes no such claim).
::* Finally, unless you can provide a policy based reason for reverting the [[#TheSummary]] regarding "HAT" (''On Math, Matter and Mind''), I expect you to stop removing it, (as ''I've'' said many times). In absence of such a reason, it's [[WP:TE]].
::* Thanks for your patience. I'll have a look at Jannes (2009) later. I'm concerned, of course, that once again '''you, yourself''' seem to be arguing with Tegmark, and again playing at pin-the-syn-on-the-donkey with the one article you might anticipate some resistance to... but I am looking forward to seeing how his hypothesis suffers from an "ism". Not necessarily an ad hominem I hope, but look no further than Aristotle if Platonism's the issue, (simpliciter, if not "radical"). De Caelo I, 10 ^_^* —[[User:Machine Elf 1735|Machine Elf 1735]] ([[User talk:Machine Elf 1735|talk]]) 11:15, 15 December 2010 (UTC)

''Dark Formal'' writes: To make progress we need to isolate issues that can be addressed one by one. Here are the issues that I could understand most easily. Let's try to settle them and then go on to the others.
* CUH: I agree that CUH ''seems'' appropriate to Schmithuber's scenario, but isn't that [[WP:SYN]]? Tegmark explicitly states that CUH is a response to the Godel objection. Does he say it is a response to Schmithuber? The thing that amazes me about Tegmark's response is that it is what you said it presumably wasn't, namely [curses foiled again]. He abandons MUH, making no attempt to defend it against Godel, and offers as an alternative CUH which he admits lacks the features that motivated MUH in the first place, since it no longer includes all of math, and in particular it does not include the kind of math that has been sucessful in describing nature! MUH, RIP!. 
* Including the long version of Tegmark's response in HAT to the Godel objection: I'm not against doing this, but it will make the Godel subsection rather long. We need to leave in the CUH material because that is his more fully considered response, which to his credit includes his admission that CUH is a big climb-down from MUH.
* Vilenkin section reference to "MU": The problem I was trying to fix is that Vilenkin says that Tegmark's solution is to weight the ensemble, but gives no citation. So I cited MU sec V.B because that is where Tegmark invokes weights to deal with the problem Vilenkin is complaining about. He says "The fact that our universe seems relatively simple has led many people to suggest that the correct measure somehow involves complexity. For instance, one could reward simplicity by weighting each mathematical structure by 2^−n ,where n is its algorithmic information content". Tegmark doesn't cite Vilenkin, he just says "many people" (they are as bad as each other, aren't they! Can we make [[WP:V]] a policy for all journals?), but he is explicitly talking about the same objection as Vilenkin's.
* Stoeger Ellis and Kirchner [http://arxiv.org/abs/astro-ph/0407329] on testability. On p2 they identify "Tegmark (1998,2003)" as one of the multiverse scenarios that they are discussing. Then at the start of sec 7 they say "The issue of evidence and testing has already been briefly mentioned. This is at the heart of whether an ensemble or multiverse proposal should be regarded as physics or as metaphysics.", then then a few lines below they say "... in the case of a true multiverse, there is not even the possibility of any indirect causal connection - the universes are then completely disjoint and nothing that happens in any one of them is causally linked to what happens in any other one (see Section 6.2). This lack of any causal connection in such multiverses really places them beyond any scientific support".
* testability in HAT: Before I try to defend it, I'd like to try to find a better citation and then defend that. As noted above, Stoeger is OK, but it would be good to have more.
* The policy-based reason for my reverting your summary of HAT is [[WP:V]]: your characterisation of the paper is not consistent with the content of the paper. For instance, in the conclusion they write  "Despite our similarities in research interests, knowledge and cultural background, we espouse conflicting views that we have termed fundamentalist, secular, and mystic." Seems clear it was a real debate. [[User:Dark Formal|Dark Formal]] ([[User talk:Dark Formal|talk]]) 03:39, 16 December 2010 (UTC)

Regarding Jannes: Gosh do we really have to quote this part of Jannes argument? I suppose NPOV requires it but objectively it is an incredibly weak argument. Essentially Jannes' argument is "Chipanzees /Orca's/dogs (snails?) can't do math, therefore math is at least partly a human invention". It's so silly nobody has even bothered to respond to it in a quotable publication, as far as I can tell. [[User:Joncolvin|Joncolvin]] ([[User talk:Joncolvin|talk]]) 06:45, 29 June 2011 (UTC)

:I was getting the impression it was something like that. Honestly, I couldn't be bothered to take it seriously. Nice to see you back.—[[User talk:Machine Elf 1735|<span style="text-shadow:#00FADE 0.05em 0.05em 0.07em;white-space: nowrap;font-family: Fraktur, Mathematica6, Georgia, sans-serif">Machine Elf <sup style="font-size:75%;font-family: Georgia, sans-serif">1735</sup></span>]] 01:13, 4 July 2011 (UTC)

This comment makes me think there is an additional structure: God. "It seems to introduce an additional mathematical structure, but all of them are supposed to be already included in the set" - any ideas? [[Special:Contributions/217.119.44.188|217.119.44.188]] ([[User talk:217.119.44.188|talk]]) 21:15, 7 January 2012 (UTC)
:God = math. But as Godel and Hilbert showed, there are limits to our knowledge of it. [[User:Joncolvin|Joncolvin]] ([[User talk:Joncolvin|talk]]) 10:04, 1 February 2016 (UTC)

{{reflist}}

== Stephen Wolfram :"A New Kind of Science" ==

Do you think they are related? --[[Special:Contributions/46.24.151.10|46.24.151.10]] ([[User talk:46.24.151.10|talk]]) 10:31, 31 March 2012 (UTC)
:I think ANKOS is more relevant to the fine tuning debate (Wolfram's systems require fine tuning to exhibit complexity) than MUH. That said, it is a nice illustration of how complexity can arise from very simple formal systems.[[User:Joncolvin|Joncolvin]] ([[User talk:Joncolvin|talk]]) 06:06, 12 February 2013 (UTC)
::@[[User:Joncolvin|Joncolvin]] Fine tune or salvational crosses? Evidences of countless crosses are undeniable. [[User:Tanengtiong0918|Tanengtiong0918]] ([[User talk:Tanengtiong0918|talk]]) 00:30, 2 December 2023 (UTC)
:@[[User:46.24.151.10|46.24.151.10]] No. Common sense tell us infinite physical energy and matters are impossible, and dimensions are limited in universes. There could be just this universe and the parallel one. Even the parallel one is just a hypotheses. Pseudo-science that is. [[User:Tanengtiong0918|Tanengtiong0918]] ([[User talk:Tanengtiong0918|talk]]) 00:26, 2 December 2023 (UTC)

== Russell K. Standish (2006) ==

From [[The Library of Babel#Influence on later writers]]:

:*[[Russell K. Standish|Russell Standish]]'s ''Theory of Nothing''<sup><nowiki><ref>http://www.hpcoders.com.au/nothing.html</ref></nowiki></sup> uses the concept of the Library of Babel to illustrate how an [[ultimate ensemble]] containing all possible descriptions would in sum contain zero information and would thus be the simplest possible explanation for the existence of the universe.  This theory therefore implies the reality of all universes.

This refers to a book by Standish from 2006 with the title ''Theory of Nothing'', described on the given website. Obviously his book does not precede Tegmark's hypothesis, but I wonder if it acknowledges Tegmark as precedent. The book seems to deserve mention here as supporting or possibly inadvertently recreating Tegmark's idea.
:Russel Standish' Theory of Nothing explicitly credits Tegmark as its inspiration. Much of it is based on discussions on the "everything" list, which was created to discuss Tegmark's Ultimate Ensemble[[User:Joncolvin|Joncolvin]] ([[User talk:Joncolvin|talk]]) 06:13, 12 February 2013 (UTC)

Considering the article where Standish is mentioned, Borges might deserve mention as possible inspiration for Tegmark. --[[User:Florian Blaschke|Florian Blaschke]] ([[User talk:Florian Blaschke|talk]]) 21:01, 22 May 2012 (UTC)

== Trying to say too much at once ==

The section {{section link|Mathematical universe hypothesis|Consistency with ancient/classical Pythagoreanism and Platonism, modern mathematical Platonism}} tries to say too much at once.  This leads to long, rambling and over-detailed sentences, which would take at least five minutes to disentangle – even for whomever may be fluent in this particular sub-field of philosophy, namely [[Mathematicism]].  Frankly, it's a nightmare to try to make sense of.  I wouldn't know how to paraphrase it accurately, being unfamiliar with Hockney's work (and not much inclined to become so, either).  For anybody willing to try, I suggest – as a ''tiny'' first step – replacing every "a/b" phrase by the more readable "a or b".  And good luck!  [[User:Yahya Abdal-Aziz|yoyo]] ([[User talk:Yahya Abdal-Aziz|talk]]) 13:33, 18 April 2017 (UTC)

:Actually, mathematicism is the general philosophical category that Tegmark's, Hockney's ('philosophical mathematics,' later renamed 'ontological mathematics') and preceding ancient/Classical & German Idealist MUHs he built on, and newer academic 'philosophical mathematics' (see new talk section) of basically same definition as his, are in. Oh well; even five years usually isn't enough to understand the theory, and supposedly difficult sentences (run-on size in USA English, but not so often in traditional UK English) are the last thing to worry about when it has even more difficult equations (and in relation to those, I haven't said enough at once.) My usage of slash is a technical (and maybe other?) writing convention in which the second word is a sub-category of the first, but not necessarily vice versa. The fact is I tried & succeeded to say things and then people who don't want so spend the five minutes are trying to read too much at once--[[User:Dchmelik|dchmelik]] ([[User_talk:Dchmelik|t]]|[[Special:Contributions/Dchmelik|c]]) 10:45, 11 May 2017 (UTC)

:yoyo: You mean "for ''whoever'' may be may be fluent ..." (not ''whomever'').

== philosophical mathematics ==
This Oxford University philosophy journal described (in 2015) a book by a PhD professor author using Mike Hockney's term ('philosophical mathematics') and basically same definition, for a forthcoming MUH: [https://academic.oup.com/mind/article-abstract/124/496/1332/962226/New-Foundations-for-Physical-Geometry-by-Tim New Foundations for Physical Geometry, by Tim Maudlin]  (Maudlin, Tim. New Foundations for Physical Geometry: The Theory of Linear Structures. Oxford University Press. 2014.) Others used the term at least since the 1960s in a different sense.--[[User:Dchmelik|dchmelik]] ([[User_talk:Dchmelik|t]]|[[Special:Contributions/Dchmelik|c]]) 10:50, 11 May 2017 (UTC)

== Translations ==

kin universes = a specific set of mathematically related univeses (study set theory and mathematical filters, they're are used in some theories of topological cosmogony) = a generation of univeses (that might be a subset though) = Greek: συμπαντογενεά, κοσμογενεά (note that cosmogony/creation of a universe is not cosmogeneration/mathematically related univeses which share some common cosmogonous topological properties (in topological algebra); they are different nouns)  <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2A02:587:410E:700:AC0C:14C4:8940:2AC1|2A02:587:410E:700:AC0C:14C4:8940:2AC1]] ([[User talk:2A02:587:410E:700:AC0C:14C4:8940:2AC1#top|talk]]) 03:30, 11 August 2019 (UTC)</small> <!--Autosigned by SineBot-->

== Tegmark's theory is not worth a Wikipedia article ==

Tegmark's Mathematical Universe Hypothesis is so utterly lacking in foundation that I find it absurd to even waste time discussing it.

It is absolutely inappropriate as the subject of a Wikipedia article, unless MGCH is also worth an article here (MGCH = Moon is Green Cheese Hypothesis).

== K. F. Sundman and his useless exact solution for 3-body problem not mentioned as counter-proof? ==

Dear Sirs,

I find it strange this article makes no mention of the [[3-body problem]], as the straightforward counter-proof of the Mathematical Universe Hypothesis?

Background info: in 1912, finnish astronomer [[Karl F. Sundman]] found the exact mathematician solution for generalized 3-body problem. It is an infinite series of complex variables, but has two main practical problems:

- It converges almost infinitely slowly, allegedly the slowest of all formulas found in any field of natural science thus far. Obtaining a result merely comparable with crude approximative solutions for the 3-body problem would still require calculation of 10**10**18 brackets and is infeasible.

- A solution, even if calculated, is only valid for point A in time, but contains zero useful or re-usable information for calculations for any point A+n or A-n in time. Thus the infinite series needs to be calculated over and over, ad nauseum to obtain orbit.

(Note that Sundman's work has been generalized to N-bodies during the 1980-90s by Qiudong Wang and L. K. Babadzanjanz, thus applicale to our observed Universe without reservations.)

Together, the above two problems make Math Universe Hypothesis impossible, because no object, be it small or large, can posses enough computing power (* footnote 1) to calculate its own orbital path - that is to solve the Sundman series over and over, within every Planck tick, which is the smallest timeframe that can be measured, at least to the precision of 1 Planck lenght, which is smallest deviation that can be measured.

If bodies subject to gravity cannot have sufficient computing power to solve their own orbital path equation Planck-exactly, then they need to rely on approximations to prevent wandering around aimlessly in space. In that case, with advanced astronomy equipment it would be possible to observe "jagged" movement of celestial bodies arising from approximative solutions accumulating errors, thus exposing our Universe as a "fake" simulation. That is obviously not the case however, so MUH is incorrect.

(* footnote 1) This fact of impossibility stems from the hard physical [[limits of computation]]: 0.018 eV (2.9 × 10**-21 Joule) / bit according to Landauer and  6 × 10**33 operations / second / Joule or 1.3563925 × 10**50 bits per second per kilogram accoring to Bremermann.
[[Special:Contributions/94.21.237.8|94.21.237.8]] ([[User talk:94.21.237.8|talk]]) 17:28, 15 December 2024 (UTC)

:I nearly deleted this per [[WP:NOTFORUM]], but I'll reply instead. However, I will not debate the issue you raise, and neither will any other editor. Talk pages are for discussions of improvement of the article, not for debating the subject itself Wikipedia does no original research. If you can find a secondary source that discusses the issues you have raised, we can include a summary of those sources in the article. We cannot critique the theory itself. That is not what an encyclopaedia is for. [[User:Sirfurboy|Sirfurboy🏄]] ([[User talk:Sirfurboy|talk]]) 18:50, 15 December 2024 (UTC)