User talk:Wmarkham

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[edit] "A Second Paradox", from Envelope paradox

(see talk page there...)

Bayes' theorem says that P(M=n|N=n) = P(N=n|M=n) P(M=n) / P(N=n) where
P(M=n) = q(1-q)^n
P(N=n) = (P(M=n) + P(M=n-1)) / 2
P(N=n|M=n) = 1/2
and similarly for P(M=n-1|N=n). Gdr 18:49, 2005 May 4 (UTC)
P(N=n) = P(M=n-1) P(N=n|M=n-1) + P(M=n) P(N=n|M=n), if n>0
= q(1-q)^(n-1) P(N=n|M=n-1) + q(1-q)^n (1/2)
= q(1-q)^(n-1) (1-P(N=n-1|M=n-1)) + (1/2) q(1-q)^n
= (1/2) q(1-q)^(n-1) + (1/2) q(1-q)^n
= (1/2) q (1-q)^(n-1)(1 + (1-q))
= (1/2) q (1-q)^(n-1)(2-q)

And P(N=0) = P(M=0) P(N=0|M=0) = q/2

P(M=n-1|N=n) = P(M=n-1) P(N=n|M=n-1) / P(N=n)
= q(1-q)^(n-1) (1/2) / ( (P(M=n) + P(M=n-1)) / 2)
= q(1-q)^(n-1) / (q(1-q)^n + q(1-q)^(n-1))
= 1 / ((1-q) + 1)
= 1 / (2-q)

P(M=n|N=n) = P(N=n|M=n) P(M=n) / P(N=n)
= (1/2) q(1-q)^n / ( (1/2) (P(M=n) + P(M=n-1)) )
= q(1-q)^n) / (q(1-q)^n + q(1-q)^(n-1))
= (1-q) / (1-q + 1)
= (1-q) / (2-q)

E(gain) = 2^(n-1) P(M=n-1|N=n) + 2^(n+1) P(M=n|N=n) - 2^n
= 2^(n-1) ( (1/(2-q)) + 4 (1-q) / (2-q) - 2)
= 2^(n-1) ( 1 + 4-4q - 2(2-q) ) / (2-q)
= 2^(n-1) ( 1 + 4 - 4q - 4 + 2q ) / (2-q)
= 2^(n-1) (1 - 2q) / (2-q)

When is E(gain) > 0? Exactly when 1-2q>0; q<1/2

[edit] intelligent design: notes on the intro

First, allow me openly admit that I have an agenda here. My main motivation in criticizing and messing with this article is to promote a better understanding of science. Proponents of ID claim that it is science. Practically all mainstream scientists claim that it is not. I want people to ask, "What things does that tell us about science?" Ideally, I would like this article to be as useful as possible to someone interested in answering that question. (Pure fantasy, yeah.)

Whether or not ID is religion, or religious in nature, is something that I care quite little about. Here is my opinion: it seems safe to say that individual advocates of ID support it for religious reasons, and like it or not, this implies that ID, as a movement, is religious in nature. However, the supporters claim that ID itself is not. I personally think that this article need not say any more than that. Although I understand that other people might care about the details of which proponents subscribe to which theologies, I do not. At any rate, there is a separate article on the movement. Political and social observations about it belong there.

Based on my experience trying to make changes a couple days ago, it looks like even ones that I think are innocuous will invariably offend somebody, on at least one side of the fence, if not both! There is no chance whatsoever that I would be allowed to remove any information from the article. The implicit consensus seems to be that a disorganized article that includes everyone's particular points of view (along with the associated churn as others try to censor those points of view that they disagree with) is better than a concise article that clearly shows where to find everyone's points of view.

For this reason, I am just going to dump some of my ideas for "improving" the introduction here on my talk page, including my rationales, and let others try to apply them to the article if they like. Feel free to skip ahead to my final proposal, and compare it with the one in the current article. In what ways, specifically, does the current article's introduction provide a better introduction to the topic?

(I started this more than a day ago, so it isn't exactly in synch with the current article.... It will probably continue to diverge.)

from the article:

controversial assertion that certain features of the universe and of living things exhibit the characteristics of a product resulting from an intelligent cause or agent.

Why would that assertion be controversial? In isolation, it seems vague, pointless and inane. (I take "certain features" to mean "there exist features".) I understand that ID additionally claims that ID "researches" are able to identify phenomena or structures for which there is no possible physical explanation. As if that weren't controversial enough, they proceed to identify particular phenomena for which there is an existing physical (at least partial) explanation, and claim that they know this explanation to be incorrect.

I can live with this as it stands, though, even with the word "controversial". After all, the manner in which they apply this idea certainly is controversial. At some point, however, I believe that someone needs to document exactly what the central claims of ID are, exactly what conclusions it draws are controversial, and why. I believe that proponents of ID should be responsible for presenting whatever its main premises and its most important results of ID are, including the wording. Quote from its leading proponents, if possible.

If there are, say, attacks on ID that do not apply (or not directly) to whatever statements were so important that they had to be placed up front, then treat these as pertaining to variants of ID. The variant should be described (by whomever feels the need to make the distinction) in a separate section, and criticisms of it can be described in a manner such that it is clear what they apply to.

Though publicly most ID advocates state that their focus is on detecting evidence of design in nature, without regard to who or what the designer might be, in statements to their constituents and supporters nearly all state explicitly that they believe the designer to be the Christian God.

This sentence needs to be simplified.

"does not constitute a research program within the science of biology"

Why is this statement needed? Would anyone claim, or mistakenly think that it does, from the rest of the intro?

"refered to popularly and in the media as Intelligent Design Theory"

It is also referred to, by the Discovery Institute, as the "theory of intelligent design". See http://www.discovery.org/csc/topQuestions.php#questionsAboutIntelligentDesign. This fact should not bother either side. ID's biggest proponent says it, and the very next point in the existing article casts questions over why anyone would call it such a thing. I don't mind documention of speculation about why they do call it this, as long as it is kept in a subordinate section. Within the intro, why bother accusing the populace and media of something, if ID proponents are the ones guilty of doing it?

it is not recognized as a scientific theory and has been categorized by skeptics as creationist pseudoscience [2]. The National Academy of Sciences...

A statement by a well-respected (both academically and politically) scientific organization about whether or not ID is science provides motivation for a much stronger and direct (IMO) statement than the statement about "categorized by skeptics" provides. With the current article, casual reader might, based upon the earlier mention of a "Cristian God", misinterpret this as characterizing the critics as, very specifically, those folks who are skeptical about that being's existence. Even when they present skepticism, the members of the NAS ought to be referred to as scientists. I haven't read it, but based on its title, Rosenhouse's document supports a statement about scientists, anyway.

Since the representatives of NAS are (by far) not the only critics of ID. Perhaps make it say "For example. the National...."

Critics argue that ID proponents find gaps within current evolutionary theory and fill them in with speculative beliefs, and that ID in this context may ultimately amount to the "God of the gaps" [4].

Both the Intelligent Design concept and the associated movement have come under considerable criticism. [5]

The intro has already established that the concept itself has come under such criticism. I would change this to something like, "the associated movement, as well, has come under considerable criticism". If someone actually wants to argue that NAS's statements don't constitute "considerable criticism", I think they need to explain why not.

This criticism is regarded by advocates of ID as a natural consequence of methodological naturalism

Personally, this is very telling of ID, since they seem to have provided a causal explanation that completely doesn't match the phenomenon being explained. If this claim is true, then someone should attribute it to a source! I suspect there was an edit mistake, and the statement is supposed to be something less ridiculous, like: "...a natural consequence of the adherence of critics to methodological naturalism."

I see two ideas there: critics adhere to methodological naturalism, and this adherence compels them to criticise. The first may be pigeonholing the critics, but I expect that many are not offended by this "accusation". If the claim about the reason for the criticism is worth describing, then I would say make explicit in the article what relationship between the critics and MN is claimed.

The second idea, even with my rewording, still shows a disconnect between the cause and the effect being described. I see no reason not to give the ID supporters that rope, if they want it. To see why, consider that this is like saying of Rosa Parks, "she's just objecting 'cuz she's black!" Even if ID could somehow produce better science than MN, that's just ad hominem. If you have a vindictive desire to see ID folks brought low, by all means, document the places where they argue in this manner.

Media organizations often focus on other qualities that the designer(s) in Intelligent Design theory might have in addition to intelligence, "higher power"[6], "unseen force"[7], etc.

Okay, but its not as if media organizations are doing science any more than ID "researchers"; these qualities are science exactly if they are testable. I say, move this somewhere else.

Putting it together:

Intelligent Design (or ID) is the controversial assertion that certain features of the universe and of living things exhibit the characteristics of a product resulting from an intelligent cause or agent. In some contexts, this intelligent cause is identified by ID proponents as being the Christian God.
Adherents of ID claim it stands on equal footing with the current scientific theories regarding the origin of life and the origin of the universe.[1] However, the claims that it makes have not been accepted by the mainstream scientific community, due to serious conflicts between the methodology that it proposes, and that of science. For example, the National Academy of Sciences has said that Intelligent Design is not science because its claims cannot be tested by experiment and propose no new hypotheses of their own.[2]
Further, despite being referred to as the theory of intelligent design by its major proponents, ID is not recognized as a scientific theory. To the contrary, it is categorized by skeptics as creationist pseudoscience.[3] ID proponents search for gaps within current evolutionary theory and fill them in with a supernatural explanation. Critics of this methodology refer to this explanation as the "God of the gaps" [4].
The associated movement has come under considerable criticism as well. [5] This criticism is regarded by advocates of ID as a natural consequence of a conflict between their methods and methodological naturalism, which precludes by definition the use of supernatural causes as scientific explanations. Proponents of ID descibe this as a systemic bias within the scientific community against proponents' ideas and research.

--Wmarkham 02:36, 7 September 2005 (UTC)