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Talk:Algorithmic information theory

Issues
The following remarks pertain to the article Algorithmic Information Theory. The article as it stands has some issues that I would like to bring to discussion. I hope that some consensus can be reached about how to deal with them. Unlike classical information theory, algorithmic information theory gives formal, rigorous definitions of a random string..... is a point of view that is not universally shared, although it has been championed by Chaitin in popularizations of the area. It is well known that the AIT definition of random string is actually only asymptotically well defined, so the viewpoint that AIT does not give a formal definition of a random string is equally valid (and, among mathematicians I have spoken with, a common viewpoint). The issue is the lack of a canonical choice of a universal machine. CMummert 04:37, 16 June 2006 (UTC)
 * There are no references.
 * Komogorov complexity is an active research area in mathematics as well as computer science.
 * The statement
 * The definition of random infinite sequence has the same extent as the one given by Martin Lof, and this should be mentioned.

 * This is a stub. If you want to add more content or more references, feel free. However, it is a fact that classical information theory gives no definition of a random string or random infinite sequence (nor does it make any attempt, focusing as it does on random processes), whereas AIT does. Maybe there are those who don't like the definitions for aesthetic reasons, but they exist nonetheless, and have numerous applications in theoretical computer science, e.g.
 * the result of Allender et al (Power from Random Strings) that PSPACE ⊆ PR, where R is the set of Kolmogorov random strings
 * the incompressibility method to prove lower bounds such as the average case complexity of Heapsort as described in Li and Vitanyi (An Introduction to Kolmogorov Complexity and its Applicaions)
 * many, many others
 * The definition of a random string is formal, so long as one accepts that Turing machines are formal mathematical objects, and it is rigorous and robust, as the above mentioned results, and many others, do not depend on the choice of universal machine. If you are aware of results in pure mathematics that demonstrate that the definition of a random string or sequence is frail, please add these results. The notion that these definitions are robust to the choice of universal machine predates Chaitin. This robustness is due to the invariance theorem (Lemma 2.1.1 in Li and Vitanyi), first proven by Solomonoff in 1964. Finally, I'm afraid I don't understand your final point:

The definition of random infinite sequence has the same extent as the one given by Martin Lof, and this should be mentioned.
 * Is there another definition you are thinking of? (e.g. Schnorr randomness?) Pexatus 22:16, 17 June 2006 (UTC)

 * Yes the definition of a Komogorv random string is rigorous, but only once you have fixed some universal Turing machine (or universal prefix-free machine). There is no definition which in any canonical manner declares that particular finite strings are random while others aren't.  By uncanonical I mean that any fixed string is random with respect to some universal  machines and nonrandom with respect to other machines (by Kraft's theorem, any string can be given any Kolmogorov complexity).  For particular results that use the existence of random strings, such as the incompressibility method, the lack of canonicity is not important.  But it is important that the article doesn't claim that there is a way to canonically say that particular strings are random and others are not.  That is, the theory does not lead to an unambiguous answer to the question ''Is the string 10101010111 random?'
 * So the quote

Unlike classical information theory, algorithmic information theory gives formal, rigorous definitions of a random string.....
 * Should say

Unlike classical information theory, algorithmic information theory gives a formal, rigorous definition of a random string, although this definition requires a noncanonical choice of a universal Turing machine.
 * or something like that. I would like to come to a consensus on the talk page about the best way to phrase it before editing the article.

 * Kolmogorov complexity does give a canonical definition of a random infinite sequence, because any two universal machines give the same asymptotic complexities up to a constant. This definition of random infinite sequence gives exactly the same collection of random infinite sequences as the definition of a random infinite sequence due to Martin Löf, which says that a infinite sequence is random if it does not lie in any effective measure 0 set.  The fact that these two definitions agree is usually presented as part of the motivation for these definitions. CMummert 02:14, 18 June 2006 (UTC)

 * The way this is usually phrased in my research community (theoretical computer science) is that the Kolmogorov complexity of a string is well-defined up to a constant depending on the choice of universal machine. Maybe the sentence could be

Unlike classical information theory, algorithmic information theory gives a formal, rigorous definition of a random string. The set of random strings depends on the choice of the universal Turing machine used to define Kolmogorov complexity, but any choice gives identical asymptotic results, since the Kolmogorov complexity of a string is invariant up to an additive constant depending only on the choice of universal Turing machine.
 * All the results I know of are asymptotic, even when dealing with finite strings, since we are making claims about infinite sets of strings, OR they are statements about individual strings that begin with "There is a constant c such that...". For instance, in the example above from Allender et al, the set of random strings changes with the universal machine, but any of these sets has sufficient power to decide all of PSPACE in polynomial time. Therefore, even though there are an infinite number of ways to define the set of Kolmogorov random strings, every one of these definitions results in the exact same theory of algorithmic information, including finite string results. And there are those who believe that there is in fact a canonical universal machine, the one which requires the fewest bits to encode, and that this number is a fundamental constant of the universe every bit as important as the charge on an electron or Avogadro's Number.
 * The multiple equivalent definitions of random infinite sequences are discussed on the page for algorithmically random sequences. If you are going to edit this article, make sure you look at algorithmically random sequence and Kolmogorov complexity to make sure not to introduce too much overlap between the articles. Pexatus 02:52, 18 June 2006 (UTC)

A second quibble
The sentence that says Omega is a real number which expresses the probability that a random computer program will eventually halt. is not literally correct. There is no nontrivial measure on the set of programs, and thus there is no formal sense to the phrase 'random computer program'. What is true is that Omega gives the probability that a random infinite binary sequence has some initial string that is the index of a program that halts.

To see what is wrong with the phrase `random computer program' consider the supposed experiment in which a coin is flipped until the index of a valid program has been obtained, at which point the flipping stops. What if no such program is ever obtained? It can be shown that this is possible for any prefix free universal machine. Thus the coin flipping procedure is not a valid probability experiment. If you were to compute the conditional probability only relative to those infinite sequences that begin with the index of a program then the conditional probability you get would not, in general, be equal to Omega. It would be Omega divided by the measure of the set of infinite sequences that start with the index of a program. CMummert 02:20, 18 June 2006 (UTC)

 * The stuff about Chaitin seems to be hastily written. I'm sure this could be cleaned up (and references to other researchers besides Chaitin added). A better way to phrase that would be

Omega is a real number which expresses the probability that a self-delimiting universal Turing machine will halt when its input is supplied by flips of a fair coin.
 * The event space is the set of all infinite sequences that could be pre-placed on the input tape, and the event "U halts while reading the input tape supplied" is the event with probability Omega.

OK?
Here are slightly edited version extending Pexatus's proposed sentences. Are they OK with everyone? Unlike classical information theory, algorithmic information theory gives a formal, rigorous definition of a random string. (The set of random strings depends on the choice of the universal Turing machine used to define Kolmogorov complexity, but any choice gives identical asymptotic results because the Kolmogorov complexity of a string is invariant up to an additive constant depending only on the choice of universal Turing  machine.)

Ω is a real number which expresses the probability that a self-delimiting universal Turing machine will halt when its input is supplied by flips of a fair coin. Athough Ω is easily defined, it is impossible to determine infinitely many of its binary digits in any consistent axiom system; this result is similar to Gödel's Incompleteness Theorem in establishing the unprovability of certain statements in formal theories. Although the digits of Ω cannot be determined, many properties of Ω are known; for example, it is an algorithmically random sequence and thus its binary digits are equidistributed. From the point of view of computability theory, Omega is of the same Turing degree as the halting problem.

Pexatus: thanks for pointing out algorithmically random sequence. I would never have found it with that name. They are called 1-random reals in computability theory. CMummert 12:05, 20 June 2006 (UTC)

 * Looks good. I personally think that it is easier to see that Ω is uncomputable because access to it allows one to solve the halting problem, but since I'm not a logic guy, I guess I have a different notion of what is easy to see. I would remove the part about its digits being equidistributed (i.e., it is simply normal), as that might give the false impression that that is the definition of a random sequence. At some point, self-delimiting Turing machine should be given its own entry and linked from here. (a Turing machine with a read-only input tape whose read head may only move to the right, and which is defined such that its computation is invalid if the read head is not on the final character of the input sequence when the machine halts). Pexatus 18:35, 20 June 2006 (UTC)

 * Thanks for the feedback. I'll cut the equidistributed part (the whole clause starting with and thus). The Turing degree is the easiest way for me to see that Omega is uncomputable, as well, although I don't know any really easy proof.  CMummert 22:49, 20 June 2006 (UTC)

 * I edited the page using these suggestions as guidelines, since it's been two years and no action had been taken. - skeptical scientist (talk) 16:29, 9 July 2008 (UTC)

"Information" misleading, means compressibility?
The article now states "This use of the term "information" might be a bit misleading, as it depends upon the concept of compressibility."

Is this fair? I'm not sure if it does depend on compressibility. In the case of infinite strings, there are equivalent definitions using betting strategies and constructive null sets which make no mention of compressibility, and even in the finite case there is an equivalent definition using termgales. Furthermore, I think there are good reasons to use compressibility and information interchangeably, as different representations of the same piece of data should have the same information content, and no piece of data can contain more information than its most compact representation. The use of the term "information" may be misleading, but I think this has more to do with the distinction between "information" and "useful information" which is described elsewhere. skeptical scientist (talk) 14:38, 21 July 2008 (UTC)

Utility is an economical concept
IMHO, useful information refer to an economical concept, not a computer science one. First, there is a cost associated to processing information, and there is a trade off to make with space / time / energy. Kolmogorov Complexity is the minimum size, given you are willing to spend whatever amount of your time computing, it's an extrema of a space/time function. A random sequence could be seen as a fully (lossless) compressed one, therefore it cost time and energy to uncompressed it before using it somehow. The operation may be far from the optimal cost, so useless. Second, the information could have no utility because it can't be processed, like a text written in Chinese is useless to me alone. All of this utility consideration are relative to a context unrelated to the theory.77.192.56.161 (talk) 10:33, 19 October 2010 (UTC)a student

Lack of references
The last section, in particular the last paragraph needs references : "AC, AP, and AR are the core sub-disciplines of AIT, but AIT spawns into many other areas. It serves as the foundation of the Minimum Description Length (MDL) principle, can simplify proofs in computational complexity theory, has been used to define a universal similarity metric between objects, solves the Maxwell daemon problem, and many others." — Preceding unsigned comment added by 2A02:2788:925:E21B:91A9:A15:BAF:C904 (talk) 23:37, 17 February 2021 (UTC)

Scholarpedia
The Scholarpedia article on this topic was reviewed by Paul Vitanyi, which is sufficient to make it a notable and (at least when Vitanyi reviewed it) reliable resource. Thus, I have restored it as an external link. Kiefer.Wolfowitz (talk) 12:37, 10 February 2011 (UTC)

Other errors
There appear to be at least two outstanding errors in this article http://en.wikipedia.org/wiki/Algorithmic_information_theory

First,

'From this point of view, a 3000 page encyclopedia actually contains less information than 3000 pages of completely random letters'

is not completely true. In point of fact one can plot words or the sounds of a word made up of letters, to determine if said sounds represent actual language, versus pure jibberish. Therefore, written language cannot be said to contain random information, such as random letters. Even if you jumbled the letters of the encycopedia, then plotted their numbers, specific letters would occur periodically more often than others based on use in language, therefore they are not random.

Secondly,

'1100100001100001110111101110110011111010010000100101011110010110  presumably has no simple description other than writing down the string itself'

This above statement is also not entirely true. A program or algorithm can convert the binary numbers to octal, hexadecimal, base-10, or any other base numerical system, including expressing the above string of 1's and 0's in base 2^n groupings, for example. Such alternate representation can also be algorithmic expression of the binary string. — Preceding unsigned comment added by Contributions/ (talk) 14:14, 2 August 2013 (UTC)

title: Talk:Algorithmic information theory


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Talk:Soul theorem

I changed the part under the soul conjecture heading. I've read Perelman's paper, and am looking at it now, and I think he is proving the soul theorem in its full generality. Though he mentions the conjectural statement of Gromoll and Cheeger that pointwise sectional curvature anywhere in M is enough to send S to a single point, I do not know of a proof of this anywhere. Though I think it is possibly true, I'm not sure how to go about proving it, especially using the Sharafutdinov fibers as Perelman does. Hope I'm not missing something obvious. Cypa 04:23, 4 October 2005 (UTC)
 * You did not state Perelman's theorem and it makes no sense this way. I will revert in a few days if nothing will happen Tosha 16:40, 4 October 2005 (UTC)

 * Hey Tosha, its possible you're right, but i have the proof right here. Can you explain what part of the proof refers to local curvature restrictions?  From what I can tell, we are always dealing with global submersion equations onto S.  If you would like to state Perelman's thereom explicitly, then I can do that.  It comes in three parts, A, B, and C, and it is nothing but a slightly fleshed out version of the generalized soul theorem.  Part A, for example, explicitly states a nonnegative curvature assumption, not positive curvature.  I added the corollary because it is the stronger case of the statement that was originally quoted as the conjecture, the part that is known.  I thought it provided some insight, but we can remove it.  If I'm mistaken and Perelman is proving that any point with positive curvature collapses S to a point, then I would really appreciate knowing how.  Cypa 20:16, 4 October 2005 (UTC)

There are two things: soul conjecture and perelman's submersion theorem. second one imply first. it does not have sense to mention perelman's result without stating it. Tosha 00:28, 7 October 2005 (UTC)

 * I don't think so. I just reread the proof.  Are we talking about the same paper?  I'm reading "Proof of the Soul Conjecture of Cheeger and Gromoll" by Perelman.  The theorem is stated in 3 parts.  Part A says, assuming nonneg K, with Sharafutdinov map $$P\colon M\to S$$, then for x in S and normal vector v in the normal bundle of S, then at x $$P(\exp{tv})=x, \forall t\geq 0$$.  Part B is, for any geodesic l in S and v parallel along l, the correpsonding exponential map sends geodesics flows to minimizing geodesic flows.  And C says, the map P is a continuous Riemannian submersion (in fact a submetry) which has eigenvalues bounded by 1/injrad(S).  Since exp is just a surjective diffeomorphism here, it in no way follows (that i can see) that strictly positive sectional curvature sends u(0) to u(1), which is what would have to happen for your statement " but K > 0 at some point. Then soul of M has to be a point (or equivalently M is diffeomorphic to {\mathbb R}^n)" to hold ... no?  In fact, the usual bound on injrad makes it clear that the submersion does not send everything to a point.

 * I am concerned that the statement in the article is in fact wrong right now. Can you please explain yourself or I will have to rewrite the second section. Cypa 13:43, 7 October 2005 (UTC)

I do not think you should edit the article before you understand the statement. the formulated that statement implies that if soul is not a point then for any point there is a sectional direction with zero curvature. and therefore soul conjecture follows. Tosha 20:49, 7 October 2005 (UTC)

 * How? I'm not sure I even understand the sentence :"the formulated that statement implies that if soul is not a point then for any point there is a sectional direction with zero curvature. and therefore soul conjecture follows. "  Do you mean the formulation of that statement ...?  If so (and assuming by "that statement" you mean the statement of Perelmen's proof I provided above), then I don't understand.  Perelman only shows the cut locus for an arbitrary direction.  Again, please, just point to the part of the proof that you are talking about, or explain yourself coherently ... if it is my mistake, then I am sorry, but I cannot see it, and I am starting to think that you can't either.  If you are suggesting that $$P(\exp{tv})=x, \forall t\geq 0$$ implies zero curvature, I think not.  All it says is that the normal bundle is diffeomorphic pointwise.  Cypa 21:30, 7 October 2005 (UTC)

Look, I do not want to explain it. My point is: you should not edit page if you do not understand it. Tosha 22:45, 9 October 2005 (UTC)

 * Okay, well, I've looked into a bit more, refreshed some of the research I did several years back on the topic, and have come to the conclusion that you are just wrong. I would recommend Guijarro & Walschap's paper, "The Metric projection onto the soul" for help undertsanding Perelman's proof.  Perhpas you are confusing the 'soul with the pseudosoul of Yim's, see Yim, Distance nonincreasing retraction on a complete open manifold of nonnegative sectional curvature, Ann. Global Anal. Geom. 6 (1988), 191-206.  Here are some other references if you'd like to discuss ANY of them, I am game, as I have read them all:

G. Walschap, The Soul at infinity in Dimension 4, Proc. Amer. Math. Soc. 112 (1991), 563-567

G. Walschap, Soul-Preserving Submersions, Michigan Math Journal, 41 (1994), 609-617

I. Belegradek & V. Kapovitch, Finiteness theorems for nonnegatively curved vector bundles, Duke Math. J., 108 (2001), 109-134

I. Belegradek, Vector bundles with infinitely many souls, Proc. Amer. Math. Soc. 131(2003), no. 7, 2217-2221

V. Berestovskii & L. Guijarro, A Metric Characterization of Riemannian Submersions, Annals of Global Analysis and Geometry 18 (2000), pp.577-588:

J. Cheeger & D. Ebin, Comparison Theorems in Riemannain Geometry, North-Holland, New York, 1975

D. Gromoll & K. Grove, The low-dimensional metric foliations of Euclidean Spheres, J. Differential Geometry 28 (1988), 143-156

L. Guijarro and G. Walschap, Twisting and nonnegative curvature metrics on vector bundles over the round sphere, J. Differential Geometry 52 (1999), 189-202

L. Guijarro and G. Walschap, The metric projection onto the soul, Trans. Amer. Math. Soc. 352 (2000), 55-69

L. Guijarro & G. Walschap, Transitive holonomy group rigidity in nonnegative curvature, Math. Zeitschrift 237 (2001), 251-257

L. Guijarro, On the Metric Structure of Open Manifolds with Nonnegative Curvature, Pacific Journal of Mathematics, 196, No. 2, 2000 S. Kobayashi & K. Nomizu, Foundations of Differential Geometry, Interscience, New York, 1963

B. O'Neill The Fundamental Equations of a Submersion, Michigan Math. J. 13 (1966), 459-469

 * Mathematics is a complex subject full of nuances, and the soul theorem is an unusually nuance heavy theorem. I editted the page because I feared that the information was incorrect and thought it better to be safe than sorry -- that is, in providing false information to the WWW.  However, since you are incapable of defending your point of view with any facts, I feel forced to push mine, which I am fully willing to defend with many facts and a discussion of the pertinant mathematics when necessary.  I am sorry if editting the page out of turn offended you.  I appreciate all the work you've done here on wiki, and i admire you for staying with it.  However, I am now editting the page as I firmly believe that it is making an inaccurate and false statement about the Soul conjecture. Cypa 05:38, 10 October 2005 (UTC)

So, do you object that in the paper of Perelman, he (among other things) proved the following:

 * Suppose, M is complete and noncompact with sectional curvature $$K\ge 0$$, but $$K > 0$$ at some point. Then soul of M has to be a point (or equivalently M is diffeomorphic to $${\mathbb R}^n$$).

? Tosha 06:13, 13 October 2005 (UTC)

Yeah, I don't think he is proving that, and in fact I don't think it's even true (though it 'was' weakly conjectured by proxy in 1994) - due in part to recent results in the field (since 1998). So, the first example that is usually given in the soul theorem/conjecture is to think of a parabola P, take its umbilic; then because of the diffeomorphism of its injrad on the ambient space, the point S has no finite cut locus as its an extremal point in P. But now consider the hyperboloid of revolution H based at the origin in the upper half plane. Now, the diffeomorphism that covers the space is a compact set, namely the set of poles in H. Well, recall that there is volume bound on the metric by the injrad construction in Riemannian geometry. So a compact set, in particular, is not a point by the deformation retract and the corresponding constraints on the metric. So even though the curvature is strictly positive by construction at a collection of points, S is not a point. Now, this is purely intuitive, as much more needs to be said. For example, we may be able to use deformations and the splitting theorem to show that standard degree four polynomial embedded in $${\mathbb R}^2$$) can be reduced to a parabola, and thus has S=point. However, there is a well characterized volume growth bound on any M from above, with respect to the holonomy group of S.  So for an arbitrary degree n polynomial, it takes some work to show if S=point, and in general, by induction, is false.  The work of Perelman's is just an argument using the standard techniques - and skipping more than several steps - that shows that for an arbitry nonneg complete riemann manifold, the soul exists and is well characterized.  Namely, it is a C^1 Riemannian submersion.  Subsequent work has improved this to (1,1) Holder continuous in the general case, and C^2 in the special case.  The reason Perelman's work is noteworthy and exciting, is because it reduces the extremely complex soul theorem to a relatively transparent collection of basic algebraic tools. It is however somewhat vague about the nuances and details of the larger idea. Cypa 20:56, 15 October 2005 (UTC)

 * That is enough, as I stated before, I do not want to explain you anything, and from what you say it is clear that you are not able understand any mathematics. It would be better for everybody if you will NOT edit mathemetics in the future. Tosha 22:48, 15 October 2005 (UTC)

 * I am not a mathemetician but I have just read this talk page and am struck by the following. User:Cypa has gone to enormous lengths to discuss the article citing evidence, etc. User:Tosha is responding using the fallacy of argumentum ad verecundiam {argument from authority}. This isn't good enough, please try to resolve the dispute by properly explaining your position on this talk page.  Majts 23:53, 15 October 2005 (UTC)

Tosha, please stop being ridiculous. Surely there is SOMETHING you can say if you have such a refined understanding of the topic. Or perhaps you can explain where I am misunderstanding? MAthematics is based on evidence and facts. I am going to send this page to RFC. Cypa 23:01, 15 October 2005 (UTC)

 * Here Tosha, please see this paper: VOLUME GROWTH AND HOLONOMY IN NONNEGATIVE CURVATURE. I think if you read through this, this should clear up why the statement above is false.  Very vaguely, the reason for this bound, in an intuitive sense, is that the lipschitz condition along with the injrad condition sets bounds on how fast the surjective curvature in S can grow; so when you have alot of poles on a space, they aren't all necessarily going to collapse to a single S, since S can only take on curvature so fast.  Does that make sense? Cypa 23:33, 15 October 2005 (UTC)

I'm ready to explain anything to anybody who can unerstand something, but Cypa is not one of those. If you are doing math it should be clear from nearly any of his sentence. Tosha 05:23, 16 October 2005 (UTC)
 * That's not an adequate response. If it's that obvious, it will be easy for you to quickly state why any of Cypa's arguments are false. That would be good enough for me, but until then I will help keep the article reverted to Cypa's version despite the fact I have no understanding of the subject Majts 05:41, 16 October 2005 (UTC)

 * Majts, there is no arguments in Cypa's writing, and again please do not edit article which you do not undersand. read the papers then come back. Tosha 00:12, 17 October 2005 (UTC)

Tosha, what are you talking about? I have explained the parabola/hyperboloid example vaguely, because it is the first argument in the paper by Gromoll and Cheeger, and so I assumed you had some familiarity with it.
 * It is NOT an argument!

I am a mathematician by training, and these insults are merely ridiculous. I know quite alot about Riemannian geometry, differential geometry and algebraic topology - which is all that is really required to understand this theorem ... along with some elementary analysis.
 * Maybe you know enough, but you do not understand

Though initially I thought you perhaps had some insight into this subject that I might have missed, I am becomer more and more convinced that you don't even have an elementary understanding of what the soul theorem is.
 * Trust me I do

What is so strange is this hubris that seems to accompany it. I can assure you however that all of my sentences are based on direct referencing.
 * Which all unrelated

I am not writing from memory Tosha, I am looking at the proofs that sit right before me, and paraphrasing. So if my statements are wrong, then so are the theorems.
 * The fact that you have a paper in hand does not mean you understand it, I write from memory, but I do remember all prrofs

Another reason I am comfortable with my statements is because I have discussed many of these with my friends and colleges - professional mathematicians - on a daily basis.
 * professional mathematicians? hmmm

But all it takes is for you to point one issue out.
 * What do you want me to point out?

I will defend it with explanation and source material.
 * source is good only if you uderstand it

I could even have another mathematician or two enter into this discussion if you'd like. Really Sir, what is all this about? Why do you have no desire to reach an understanding? Cypa 01:15, 17 October 2005 (UTC)

''Once more my points: ''I claim, that my edition is correct, and your corrections make it more foggy and not that useful.
 * 1) Disussion page is NOT for getting help in math
 * 2) you should not edit page if you do not understand it

BTW, here is citation from MathSciNet (I hope you trust it)

''MR1285534 (95d:53037) Perelman, G. (RS-AOS2) Proof of the soul conjecture of Cheeger and Gromoll. J. Differential Geom. 40 (1994), no. 1, 209 212.''

''Let M denote a complete noncompact manifold of nonnegative sectional curvature with soul S. It is well known that if u is a vector tangent to S, and v is orthogonal to S, then the plane spanned by u and v has zero curvature. In a short geometric argument based on the second Rauch theorem, Perel0man shows that this is also true of the parallel translate of this plane along the geodesic in direction v. As a fundamental consequence, he obtains the existence of a Riemannian submersion from the ambient space onto S. This answers in particular a question asked some twenty years earlier by Cheeger and Gromoll: If the curvature is strictly positive at some point, then M is diffeomorphic to Euclidean space.''

Tosha 02:48, 17 October 2005 (UTC)

 * Alright, well, it seems clear that you are going to be unwilling to enter into a dialogue of any sort. I agree with Walschap's review paragraph.  The difference between what he has said, and the one sentence statement of Perelman's proof that you have provided, is one demonstrates an understanding of the larger field of statements, while the other is such a closed worded simplification of the idea, that it is misleading and approaches being just wrong.  I could try to explain this to you, but I am busy with other work, and this conversation is becoming redundant.  At least you provided a non-vacuous response this last time (by providing a quote of someone elses), so we're moving in the right direction.  You may not know this Tosha, but I have no way of knowing what your background is, or how much you know about the theorem or Riemannian geometry.  That IS the purpose of the discussion page, so that people can use logic and reason to reach mutual understandings.  I'm sorry you feel you're so talented that you don't need to explain yourself beyond insults and "because I'm right and I know it."  This approach is both childish and impossible to make sense of.  From the sum total of what you've said here, I can only conclude that English is clearly not your first language, that you think your very smart, and that you have very strong intransigence towards trying to understand any point of view that doesn't completely parallel your own.  Talk about content free dialogue.  Statements like: Trust me I do?  Okay Tosha, I trust you, you are the source of all mathematics on the web, and I'll just take your word for it.  But nonetheless, your going to have to flesh out the statement of Perelman's proof to the point where it demonstrates some understanding of the current state of the Soul Theorem, or I'm going to continue to revert to a more paultry, though less "foggy" version of the article.  Cypa 16:39, 17 October 2005 (UTC)

 * I have to say that I am bewildered by the discussion here. The discussion page is meant to improve the article. If somebody thinks that the article is wrong, this is the place to challenge it, and if the question is not satisfactorily answered, then it is all right to change the article. It is not enough to say that the article is correct, one should be prepared to give arguments for it. Of course, it would be too much to explain it to somebody who doesn't know any mathematics, but I've seen no evidence that Cypa would be somebody like that.
 * On the other hand, it is also not clear to me what Cypa's problem with the page is. Is the problem:
 * Perelman's article does not claim to prove that "if M is complete and noncompact with sectional curvature K ≥ 0, but K > 0 at some point, then the soul of M has to be a point (or equivalently, M is diffeomorphic to Rn)," OR
 * the article does claim to prove it but the proof is incorrect, OR
 * the article does prove it correctly, but it is misleading to summarize the statement like that?
 * The article says "Cheeger and Gromoll conjectured that the same conclusion [the soul is a single point] can be obtained under the weaker assumption that M contains a point where all sectional curvatures are positive", this is the only conjecture that I can find in the article so I assume that this is meant by the "Soul Conjecture", and Perelman claims that this is "an immediate consequence of Part (B)". The fact that this is accepted by the journal's referees and Walschap, writing for MathSciNet, is enough for me to believe that the proof is correct, at least unless arguments for the contrary are given.
 * So, what is going on here? -- Jitse Niesen (talk) 18:04, 17 October 2005 (UTC)

 * Thanks Jitse. Yeah, your right, what is going on here? Anyway, I'm going to rescind my complaint. There is nothing being accomplished here (and that is my own fault). Sorry for reducing myself to drivel. To vaguely clarify the original POV, I was trying to state something along the lines of option 3 above. Tosha the page is all yours. You've earned it. Cypa 23:40, 17 October 2005 (UTC)

Who proved what?
I am puzzled by this page, which I came to from a link on the Perelman page. That page states that he proved the Soul Conjecture. But this page states that Cheeger and Gromoll proved it. Whereas the Perelman citation on this page indicates that Cheeger and Gromoll conjectured it and that Perelman proved it. What is the correct story here???

Also, not having even heard of the Soul Conjecture before, I don't pretend to know anything about its proof. But I am having trouble seeing how the Soul Conjecture -- as stated on this page -- can hold for the simple case of, say, the surface z = x^2 + y^2 in R^3. I do not think this paraboloid P contains -any- compact submanifold whose normal bundle is diffeomorphic to P (not to mention a compact totally convex, totally geodesic submanifold whose normal bundle is diffeomorphic to P).

But if the condition of compactness is dropped, then it is easy to see that the modified statement would be true for P (using any complete geodesic through the vertex of P as the submanifold).Daqu 10:14, 5 March 2006 (UTC)

OOPS -- please disregard the last two paragraphs; I confess I did not think of a single point, as I should have.Daqu 10:26, 5 March 2006 (UTC)

"I am puzzled by this page, which I came to from a link on the Perelman page. That page states that he proved the Soul Conjecture. But this page states that Cheeger and Gromoll proved it. Whereas the Perelman citation on this page indicates that Cheeger and Gromoll conjectured it and that Perelman proved it. What is the correct story here???"Daqu 03:41, 22 March 2006 (UTC)
 * I wrote, however, *three* paragraphs and the first one is still unresolved:

 * There's a soul theorem and a soul conjecture. The article currently states the theorem was proven by Cheeger and Gromoll who conjectured the conjecture, which was proven by Perelman.  --C S (Talk) 04:50, 28 March 2006 (UTC)

Question
Why is it called the Soul Theorem? --Zhang Guo Lao 13:46, 24 August 2006 (UTC)

Minor error
In the paraboloid example, please remove the part "Not every point x of M is a soul of M, since there may be geodesic loops based at x", because it is obviously wrong: The normal bundle at any point-submanifold is diffeomorph to R^2, (which is diffeomorph to the paraboloid). 188.174.106.216 (talk) 12:43, 13 January 2014 (UTC)

Which part is incorrect? There are geodesic loops on the paraboloid (Clairaut's relation tells us that a geodesic travelling at an angle down the paraboloid will 'turn around' as the paraboloid narrows, then wind back upwards and meet itself eventually). Whether a point is a soul or not comes down (by definition) to whether it arises from the process of choosing a point, considering rays coming from it, constructing compact totally convex regions and then shrinking those down inductively. Points that are not souls can still have their normal bundle diffeomorphic to the whole space. It's just a matter of convention and definition that 'soul' means subspaces from this construction, not subspaces with the nice property of their normal bundles. 128.91.40.39 (talk) 15:46, 30 March 2016 (UTC)

title: Talk:Soul theorem


text:
A Present from the Past

A Present from the Past is a compilation album by the Swedish rock band The Soundtrack of Our Lives.

The album consists of tracks from B-sides and out of print EPs, as well as previously unreleased material.

title: A Present from the Past


text:
Talk:Tostig Godwinson

Image question
What's up with the book cover image? It's not portraying Tostig, so how is it useful? Everyking 04:26, 4 October 2005 (UTC)
 * Beats me. I didn't add it, but it breaks up the monotony. Adraeus 10:58, 5 October 2005 (UTC)

I wondered why the book cover was there. I suggest we remove it, and break the large paragraph down into more digestable snippets. MortimerCat 13:29, 28 August 2006 (UTC)
 * Removed the book cover, it looks to me like an advertisement. --Auximines 08:55, 25 September 2006 (UTC)

82.36.184.45 (talk) 16:36, 16 April 2008 (UTC)

wat is this??
"who had just concluded a long and inconclusive war with Denmark..."

concluded used badly

82.36.184.45 (talk) 16:36, 16 April 2008 (UTC) It was likely that Harold had exiled his brother to ensure peace and loyalty in the north. Secraser (talk) 00:53, 16 May 2010 (UTC)conjecture, prove it!

Can we improve this article?
In the section,  Earl of Northumbria and specifically in the third pararaph it says that Tostig was unpopular in Northumbria, and gives a number of reasons for this, away at court, heavy handed, employing expensive mercenaries, and consequently he is unable to raise local levies to go against the Scots raiders. Then at the bottom of the same paragraph it says that he was, "a major commander in these wars attacking in the north while his brother Harold marched up from the south." Okay, so where does he get the troops from to be, "a major commander" in Wales when he can't even raise local levies in his own backyard?

It's a rhetorical question, you are not supposed to answer the question directly. My point is that the article as wrtten suffers from credibility issues because of such obvious contradictions in its text, which has no inline citations in it at all. What we have here is not a bad start but you can't just put up a wall of self contradictory text, stick three book references on the bottom and consider that an encyclopedia article. Can I ask editors interested or knowledgeable about this subject to please revisit this article and make it more encyclopedic? Thank you.  Cottonshirt  τ   17:34, 24 June 2012 (UTC)

This really hasn't been written well. "After his death at Stamford Bridge, it is believed that his body was taken to France and buried at York Minster." Now how did they manage that neat trick. They took him to France then catapulted him into a grave in York Minster??? Khasab (talk) 14:07, 5 August 2014 (UTC)

Cannibalism
I don't see it in the article, and am wondering what weight is given to Henry of Huntingdon's claim that Tostig cut up servants of Harold and put bits of their bodies into a feast to be served to his brother. It seems this event is the basis for an inverse allusion involving the House of Atreus, in the anonymous Vita Aedwardi: “The Politics of Allusion in Eleventh-Century England: Classical Poets and the Vita Ædwardi.” England in Europe: English Royal Women and Literary Patronage, C.1000–C.1150, by ELIZABETH M. TYLER, University of Toronto Press, Toronto; Buffalo; London, 2017, pp. 135–201. JSTOR, www.jstor.org/stable/10.3138/j.ctt1whm96v.11. Accessed 22 July 2020. Shtove (talk) 01:33, 22 July 2020 (UTC)

name of battle with Edwin and Morcar
Does this battle where Tostig was defeated by Edwin and Morcar not have a name ? or a location ? thanks for info ... 82.11.163.59 (talk) 15:20, 10 April 2023 (UTC)

title: Talk:Tostig Godwinson


text:
Talk:Rodan

Untitled
I've seen it said that "Radon" was a British brand of soap and *that's* why the name was changed. Can anyone verify that such a thing exists? Ken Arromdee 04:26, 4 October 2005 (UTC)

Yes, Ive heard that too. Not sure of its credibility though.(219.88.54.53 08:09, 12 November 2005 (UTC))

It could also be that Radon is a hazardous chemical(IIRC). Maybe there's legal issues involved. Anguirus111 11:24 26 August 2005 (UTC)

Yeah do you guys agree it sounds stupid while in the English dub of Godzilla vs. MechaGodzilla II they said Radon not Rodan? they didn't even say ra-DON like it is pronounced they said RAH-don. I think it was dumb. Farts :D (talk) 04:07, 18 December 2013 (UTC)

 * I think that fact is fake since I look it up and there was No radons british soaps I assumed wikipedia thought there was a brithish Radan soap as along with a Spongeboy mop. Monster 1954 (talk) 16:43, 27 February 2024 (UTC)
 * well TBH Some dubs u cant think How their saying like are they saying Godziller or Godzilla and it the same problem with Ghidorah Is it Ghidrah or GHIDORAH Kamata kun overlord 2016 (talk) 14:50, 15 March 2024 (UTC)
 * Also they call anguirus angilas 174.34.4.27 (talk) 14:29, 7 May 2024 (UTC)

Rodan's beam
Rodan also has a limited breath weapon of its own, as seen in the 1956 movie

What?! Thanos6 10:10, 19 November 2005 (UTC)

Rodan can produce gusts from its beak. The monster equivalent of blowing, nothing that would qualify it has a beam or breath weapon. The only time Rodan gains a beam weapon is in the Heisei Godzilla film, "Godzilla vs. MechaGodzilla II".

When was Rodan in Family Guy?

Fair use rationale for Image:GojivRodan.jpg
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Please go to the image description page and edit it to include a fair use rationale. Using one of the templates at Fair use rationale guideline is an easy way to insure that your image is in compliance with Wikipedia policy, but remember that you must complete the template. Do not simply insert a blank template on an image page.

If there is other fair use media, consider checking that you have specified the fair use rationale on the other images used on this page. Note that any fair use images uploaded after 4 May, 2006, and lacking such an explanation will be deleted one week after they have been uploaded, as described on criteria for speedy deletion. If you have any questions please ask them at the Media copyright questions page. Thank you.

BetacommandBot 04:00, 7 November 2007 (UTC)

Mork and Mindy
In the fourth season, when Mork shows Mindy the egg he laid, he said he knew what he wanted to call the baby. Rodan. Later, however, the baby was named Mearth. GBC (talk) 05:53, 9 January 2008 (UTC)

A Commons file used on this page has been nominated for deletion
The following Wikimedia Commons file used on this page has been nominated for deletion: Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 11:54, 2 February 2019 (UTC)
 * Godzilla - PS4-PS3 - Ultimate mayhem (E3 Trailer) - Rodan v KG.png

What
Why is rodan the only Kaiju with his heisei design for the first thing people see All kaijus have their Showa era design with Kong Gamera and Godzilla being their first incarnation  Monster 1954 (talk) 17:06, 21 February 2024 (UTC)

title: Talk:Rodan


text:
Liang Zongdai

Liang Zongdai (Chinese: 梁宗岱) (1903–1983) was a Chinese poet and translator. Born in Baise, Guangxi, he went to Europe to study western languages in 1924. His translation of Tao Qian's poems into French was published by Lemarget, Paris in 1930, with a preface by Paul Valéry whom the young poet had visited at home in 1926.

He was one of the most popular "new poets" writing in free verse, after the May Fourth Movement in China. His most famous work is the non-fictional Poetry and Truth (詩與真). The title was borrowed from Goethe's autobiography Dichtung und Wahrheit.

Liang's translations into Chinese include poetry by Shakespeare, Blake, Rilke, and Valéry, as well as Montaigne's essays. His translation of Goethe's Faust was destroyed during the Cultural Revolution.

He was persecuted during the Cultural Revolution, and devoted the last part of his life to the study of Chinese medicine. He married three times. His last wife was a performer of Cantonese opera, who wrote a short memoir, recollecting her relationship with the poet.

title: Liang Zongdai


text: User talk:71.105.102.138

title: User talk:71.105.102.138


text:
User talk:Jimbo7676

Your edits to Broadgate and other articles have been reverted. Thanks for experimenting with Wikipedia. Your test worked, and has been reverted. Please use the sandbox for any other tests you want to do. Take a look at the welcome page if you would like to learn more about contributing to our encyclopedia. Thanks. -- Solipsist 04:27, 4 October 2005 (UTC)

title: User talk:Jimbo7676


text: User talk:82.35.90.197

title: User talk:82.35.90.197


text: Floristics

title: Floristics


text:
Stand-your-ground law

A stand-your-ground law, sometimes called a "line in the sand" or "no duty to retreat" law, provides that people may use deadly force when they reasonably believe it to be necessary to defend against certain violent crimes (right of self-defense). Under such a law, people have no duty to retreat before using deadly force in self-defense, so long as they are in a place where they are lawfully present. The exact details vary by jurisdiction.

The alternative to stand your ground is "duty to retreat". In jurisdictions that implement a duty to retreat, even a person who is unlawfully attacked (or who is defending someone who is unlawfully attacked) may not use deadly force if it is possible to instead avoid the danger with complete safety by retreating.

Even areas that impose a duty to retreat generally follow the "castle doctrine", under which people have no duty to retreat when they are attacked in their homes, or (in some places) in their vehicles or workplaces. The castle doctrine and "stand-your-ground" laws provide legal defenses to persons who have been charged with various use-of-force crimes against persons, such as murder, manslaughter, aggravated assault, and illegal discharge or brandishing of weapons, as well as attempts to commit such crimes.

Whether a jurisdiction follows stand-your-ground or duty-to-retreat is just one element of its self-defense laws. Different jurisdictions allow deadly force against different crimes. All American states allow it against prior deadly force, great bodily injury, and likely kidnapping or rape; some also allow it against threat of robbery and burglary.

A 2020 RAND Corporation review of existing research concluded: "There is supportive evidence that stand-your-ground laws are associated with increases in firearm homicides and moderate evidence that they increase the total number of homicides."

Canada
In Canada, there is no duty to retreat under the law. Canada's laws regarding self-defense are similar in nature to those of England, as they centre around the acts committed, and whether or not those acts are considered reasonable in the circumstances. Generally where retreat is available in the circumstances, the decision to stand your ground is more likely to be unreasonable. The sections of the Canadian criminal code that deal with self-defense or defense of property are sections 34 and 35, respectively. These sections were updated in 2012 to clarify the code, and to help legal professionals apply the law in accordance with the values Canadians hold to be acceptable.

A great deal of case law has emerged from different provincial superior courts regarding the interpretation of the elements of self-defense per ss. 34-35 of the Criminal Code. In Ontario, jurors are not permitted "...to consider whether an accused could have retreated from his or her own home in the face of an attack (or threatened attack) by an assailant in assessing the elements of self-defense.” In British Columbia, the leading case law of which predates the 2012 ss. 34-35 amendments, courts will permit juries to consider available lines of retreat in deciding whether an accused had no other option than to defend himself. However, the option of retreat is not considered a categorical exclusion from self-defense.

Alberta
The province of Alberta is unique among Canadian jurisdictions in affording civil immunity to occupiers who employ force, including lethal force, in defense of homes and other premises. In 2019, the Alberta legislature passed the Trespass Statutes (Protecting Law-Abiding Property Owners) Amendment Act, 2019, in response to rising rural crime, public concern with police inaction and several high-profile self-defense shootings the previous year. Especially influential was the case of Edouard Maurice, who wounded a trespasser and was served with a lawsuit after having criminal charges against him dropped.

The new Act amended the Occupiers Liability Act, 2000 and added the following sections:

(2) Where a trespasser is not a criminal trespasser, an occupier is not liable to the trespasser for damages for death of or injury to the trespasser unless the death or injury results from the occupier’s wilful or reckless conduct.

(3) Where a trespasser is a criminal trespasser, no action lies against the occupier for damages for death of or injury to the trespasser unless the death or injury is caused by conduct of the occupier that

(a)   is wilful and grossly disproportionate in the circumstances, and

(b)   results in the occupier being convicted of an offence under the Criminal Code (Canada) that is prosecuted by indictment.

(4) For the purposes of subsections (2) and (3), a trespasser is a criminal trespasser if the occupier has reasonable grounds to believe that the trespasser is committing or is about to commit an offence under the Criminal Code (Canada).

(5) For the purposes of subsection (3), an occupier is deemed not to be convicted of an offence until the period limited by law for the commencement of an appeal from the conviction has elapsed or the appeal taken from the conviction has concluded or been abandoned.

Czech Republic
There is no explicit stand-your-ground or castle doctrine provision in the laws of the Czech Republic; however, there is also no duty to retreat from an attack. In order for a defense to be judged as legitimate, it may not be "manifestly disproportionate to the manner of the attack".

England and Wales
The common law jurisdiction of England and Wales has a stand-your-ground law rooted in the common law defense of using reasonable force in self-defense.

In English common law there is no duty to retreat before a person may use reasonable force against an attacker, nor need a person wait to be attacked before using such force, but one who chooses not to retreat, when retreat would be a safe and easy option, might find it harder to justify his use of force as 'reasonable'.

Any force used must be reasonable in the circumstances as the person honestly perceived them to be, after making allowance for the fact that some degree of excess force might still be reasonable in the heat of the moment.

In the home, the householder is protected by an additional piece of legislation in which it is specified that force used against an intruder is not to be regarded as reasonable if it is 'grossly disproportionate' (as distinct from merely 'disproportionate' force, which can still be reasonable).

France
Like England and Wales, France has a stand-your-ground law rooted in the defense of using reasonable force in self-defense.

Under article 122-5 of French Criminal Code, a person who, faced with an unjustified attack on himself or another, at the same time performs an act required by the need for self-defense of himself or another, is not criminally responsible, unless there is a disproportion between the means of defense used and the seriousness of the attack. There is no duty to retreat before a person may use reasonable force against an attacker, nor need a person wait to be attacked before using such force, but one who chooses not to retreat, when retreat would be a safe and easy option, might find it harder to justify his use of force by the need for self-defense.

Any force used must be reasonable in the circumstances as the person honestly perceived them to be, after making allowance for the fact that some degree of excess force might still be reasonable in the heat of the moment. The person who performs the act is presumed to have acted in self-defense: 1° when repelling, by night, the entry by break-in, violence or trickery in an inhabited place; 2° when defending himself against the authors of robbery or looting executed with violence.

Germany
German law permits self-defense against an unlawful attack. If there is no other possibility for defense, it is generally allowed to use even deadly force without a duty to retreat. However, there must not be an extreme imbalance ("extremes Missverhältnis") between the defended right and the chosen method of defense. In particular, in a case in which firearms are used, a warning shot must be given when defending a solely material asset. If the self-defense was excessive, its perpetrator is not to be punished if he or she exceeded on account of confusion, fear or terror.

Ireland
Under the terms of the Criminal Law (Defence and the Dwelling) Act 2011, property owners or residents are entitled to defend themselves with force, up to and including lethal force. Any individual who uses force against a trespasser is not guilty of an offense if he or she honestly believes they were there to commit a criminal act and a threat to life. However, there is a further provision which requires that the reaction to the intruder is such that another reasonable person in the same circumstances would likely employ it. This provision acts as a safeguard against grossly disproportionate use of force, while still allowing a person to use force in nearly all circumstances.

The law was introduced in response to DPP v. Padraig Nally.

Italy
In 2019, the Italian senate passed a "legitimate defense" bill, protecting the right to self-defense for private citizens of Italy.

Poland
Stand-your-ground law applies to any kind of threat by an attacker that endangers the victim's safety, health, or life. The victim has no obligation to retreat, as said in a statement by the Supreme Court of Poland on February 4, 1972: "The assaulted person is under no obligation either to escape or hide from the assailant in a locked room, nor to endure the assault restricting his freedom, but has the right to repel the assault with all available means that are necessary to force the assailant to refrain from continuing his assault."

Section 2a of the Polish Penal Code introduced in 2017 codifies a limited castle doctrine, by excluding punishment if the defendant used excessive force while protecting one's home unless "exceeding the limits of necessary defense was gross".

If the self-defense was excessive, its perpetrator is not to be punished if he or she exceeded on account of fear or rage justified by the circumstances of the attack.

Laws

 * Thirty-eight states are stand-your-ground states, all but eight by statutes providing "that there is no duty to retreat from an attacker in any place in which one is lawfully present": Alabama, Alaska, Arizona, Arkansas, Florida, Georgia, Idaho, Indiana, Iowa, Kansas, Kentucky, Louisiana, Michigan, Mississippi, Missouri, Montana, Nevada, New Hampshire, North Carolina, North Dakota, Ohio,  Oklahoma, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, West Virginia, and Wyoming; Puerto Rico is also stand-your-ground.  Of these, at least eleven include "may stand his or her ground" language (Alabama, Florida, Georgia, Idaho, Kansas, Kentucky, Louisiana, Oklahoma, Pennsylvania, South Carolina, and South Dakota.) Pennsylvania limits the no-duty-to-retreat principle to situations where the defender is resisting attack with a deadly weapon.
 * The other eight states have case law/precedent or jury instructions so providing: California, Colorado, Illinois, New Mexico, Oregon, Vermont, Virginia, and Washington;  the Commonwealth of the Northern Mariana Islands also falls within this category.
 * Eleven states impose a duty to retreat when one can do so with absolute safety: Connecticut, Delaware, Hawaii, Maine, Maryland, Massachusetts, Minnesota, Nebraska, New Jersey, New York and Rhode Island. New York, however, does not require retreat when one is threatened with robbery, burglary, kidnapping, or sexual assault.
 * Washington, D.C. adopts a "middle ground" approach, under which "The law does not require a person to retreat," but "in deciding whether [defendant] reasonably at the time of the incident believed that s/he was in imminent danger of death or serious bodily harm and that deadly force was necessary to repel that danger, you may consider, along with any other evidence, whether the [defendant] could have safely retreated ... but did not." Wisconsin also adopts a "middle ground" approach, where "while there is no statutory duty to retreat, whether the opportunity to retreat was available goes to whether the defendant reasonably believed the force used was necessary to prevent an interference with his or her person."
 * There is no settled rule on the subject in American Samoa and the U.S. Virgin Islands.
 * In all duty to retreat states, the duty to retreat does not apply when the defender is in the defender's home (except, in some jurisdictions, when the defender is defending against a fellow occupant of that home). This is known as the "castle doctrine".
 * In Connecticut, Delaware, Hawaii, and Nebraska, the duty to retreat also does not apply when the defender is in the defender's place of work; the same is true in Wisconsin and Guam, but only if the defender is the owner or operator of the workplace.
 * In Wisconsin and Guam, the duty to retreat also does not apply when the defender is in the defender's vehicle.
 * Twenty-two states have laws that "provide civil immunity under certain self-defense circumstances" (Arizona, Arkansas, Colorado, Florida, Georgia, Idaho, Illinois, Kentucky, Louisiana, Maryland, Michigan, Montana, New Hampshire, North Carolina, North Dakota, Oklahoma, Ohio, Pennsylvania, South Carolina, Tennessee, West Virginia, and Wisconsin). At least six states have laws stating that "civil remedies are unaffected by criminal provisions of self-defense law" (Hawaii, Missouri, Nebraska, New Jersey, North Dakota, and Tennessee).

Controversy
Stand-your-ground laws are frequently labeled "shoot first" laws by opposition groups, including the Brady Campaign to Prevent Gun Violence. In Florida, self-defense claims tripled in the years following enactment. Opponents argue that Florida's law makes it potentially more difficult to prosecute cases against individuals who commit a crime and claim self-defense. Before passage of the law, Miami police chief John F. Timoney called the law unnecessary and dangerous in that "[w]hether it's trick-or-treaters or kids playing in the yard of someone who doesn't want them there or some drunk guy stumbling into the wrong house, you're encouraging people to possibly use deadly physical force where it shouldn't be used." A counterargument is that implementing a duty-to-retreat places the safety of the criminal above a victim's own life.

In Florida, a task force created by former Democratic state Sen. Chris Smith of Fort Lauderdale found the law to be "confusing". Those discussing issues with the group included Buddy Jacobs, a lawyer representing the Florida Prosecuting Attorneys Association. Jacobs recommended the law's repeal, stating that modifying the law would not fix its problems. In a July 16, 2013 speech in the wake of the jury verdict acquitting George Zimmerman of charges stemming from the shooting death of Trayvon Martin, Attorney General Eric Holder criticized stand-your-ground laws as "senselessly expand[ing] the concept of self-defense and sow[ing] dangerous conflict in our neighborhoods."

In 2014, Florida's legislature considered a bill that would allow people to show a gun or fire a warning shot during a confrontation without drawing a lengthy prison sentence. In 2017, there was a bill proposed in Florida's state legislature that would require the prosecution to prove that a defendant's use of self-defense was not valid. In 2018, the shooting of Markeis McGlockton led some civil rights activists and politicians to call for abolition of the statute.

Racial disparity
In 2012, in response to the Trayvon Martin case, the Tampa Bay Times compiled a report on the application of stand your ground, and also created a database of cases where defendants sought to invoke the law. The database included many cases that were not legally stand your ground, such as when the defender was in the home or had no safe opportunity to flee, so care must be taken in its evaluation in regards to stand your ground law. Their report found no racial disparity in Florida cases in which defendants claiming self-defense under the law are prosecuted, with Caucasian subjects being charged and convicted at the same rate as African American subjects, and results of mixed-race cases were similar for both white victims of black attackers and black victims of white attackers. Victims of African American attackers overall were more successful at using the law than victims of Caucasian attackers, regardless of the victim's race claiming self-defense, but analysis showed that black attackers were also more likely to be armed and to be involved in committing a crime, such as burglary, when shot.

A Texas A&M study found that when whites use the stand-your-ground defense against black attackers they are more successful than when blacks use the defense against white attackers. A paper from The Urban Institute which analysed FBI data found that in stand-your-ground states, the use of the defense by whites in the shooting of a black person is found to be justifiable 17 percent of the time, while the defense when used by blacks in the shooting of a white person is successful 1 percent of the time. In non-stand-your-ground states, the shooting of a black person by a white is found justified approximately 9 percent of the time, while the shooting of a white person by a black is found justified approximately 1 percent of the time. According to the Urban Institute, in Stand Your Ground states, white-on-black homicides are 354 percent more likely to be ruled justified than white-on-white homicides, even though they are more common by over 72 percent. The paper's author noted that the data used do not detail the circumstances of the shooting, which could be a source of the disparity. They also noted that the total number of shootings in the FBI dataset of black victims by whites was 25. A 2015 study found that cases with white victims are two times more likely to result in convictions under Florida's stand your ground law than cases with black victims, although the study did not exclude many cases that were not legally stand your ground under the law.

Effects on crime
A 2018 RAND Corporation review of existing research concluded that "there is moderate evidence that stand-your-ground laws may increase homicide rates and limited evidence that the laws increase firearm homicides in particular." In 2019, RAND authors published an update, writing "Since publication of RAND's report, at least four additional studies meeting RAND's standards of rigor have reinforced the finding that "stand your ground" laws increase homicides. None of them found that "stand your ground" laws deter violent crime. No rigorous study has yet determined whether "stand your ground" laws promote legitimate acts of self-defense.

A 2017 study in the Journal of Human Resources found that Stand Your Ground laws led to an increase in homicides and hospitalizations related to firearm-inflicted injuries. The study estimated that at least 30 people died per month due to the laws. A 2013 study in the Journal of Human Resources found that Stand Your Ground laws in states across the U.S. "do not deter burglary, robbery, or aggravated assault. In contrast, they lead to a statistically significant 8 percent net increase in the number of reported murders." A 2016 study in the Social Science Journal found that stand-your-ground laws were not associated with lower crime rates. A 2016 study in the Journal of the American Medical Association compared homicide rates in Florida following the passage of its "stand your ground" self-defense law to the rates in four control states, New Jersey, New York, Ohio and Virginia, which have no similar laws. It found that the law was associated with a 24.4% increase in homicide and a 31.6% increase in firearm-related homicide, but no change in rates of suicide or suicide by firearm, between 2005 and 2014. It noted that, "[c]ircumstances unique to Florida may have contributed to our findings, including those that we could not identify," and "[o]ur study examined the effect of the Florida law on homicide and homicide by firearm, not on crime and public safety". The study was criticized by researcher and gun rights advocate John Lott, for studying only one state and focusing on a narrow definition of effectiveness. Studies conducted by Lott’s Crime Prevention Research Center found that the loosening of restrictions on defensive gun use, including “stand your ground laws”, led to a decrease in crime overall. Self-defense law subject matter expert Andrew Branca was critical of the AMA study for not distinguishing between justifiable homicides and murder, and for relying solely on statutory laws while overlooking case law (i.e. Virginia) in determining the data set. The study's methodology was defended by Duke University professor Jeffrey Swanson for its use of other states as controls, saying "[t]hey look at comparable trends in states that didn't pass the law and don't see the effect.".

In a 2007 National District Attorneys Association symposium, numerous concerns were voiced that the law could increase crime. This included criminals using the law as a defense for their crimes, more people carrying guns, and that people would not feel safe if they felt that anyone could use deadly force in a conflict. The report also noted that the misinterpretation of clues could result in the use of deadly force when there was, in fact, no danger. The report specifically notes that racial and ethnic minorities could be at greater risk because of negative stereotypes.

A 2012 study examined whether a prominent Stand Your Ground shooting, Joe Horn shooting controversy, in 2007, which brought public attention to Texas' stand-your-ground law impacted crime. The study found that subsequent to the shooting, burglaries decreased significantly in Houston, but not in Dallas, over a 20-month period. A 2015 study found that the adoption of Oklahoma's stand-your-ground law was associated with a decrease in residential burglaries, but also that the law had "the unintended consequence of increasing the number of non-residential burglaries."

Florida's stand-your-ground law went into effect on October 1, 2005. Florida state representative Dennis Baxley, an author of the law, said that the violent crime rate has dropped since the enactment of the law, though he said there may be many reasons for the change. Others have argued that the law may lead to an increase in crime. Violent crime data for 1995 – 2015 has been published by the Florida Department of Law Enforcement.

title: Stand-your-ground law