21. Infinite Ink: The Continuum Hypothesis By Nancy McGough History, mathematics, metamathematics, and philosophy of Cantor s Continuum hypothesis. http://www.ii.com/math/ch/

mathematics T HE C ONTINUUM H YPOTHESIS By Nancy McGough nm noadsplease.ii.com Overview 1.1 What is the Continuum Hypothesis? 1.2 Current Status of CH Alternate Overview Assumptions, Style, and Terminology 2.1 Assumptions 2.1.1 Audience Assumptions 2.1.2 Mathematical Assumptions 2.2 Style 2.3 Terminology 2.3.1 The Word "continuum" 2.3.2 Ordered Sets 2.3.3 More Terms and Notation Mathematics of the Continuum and CH 3.1 Sizes of Sets: Cardinal Numbers aleph c aleph 3.1.2 CH and GCH 3.1.3 Sample Cardinalities 3.2 Ordering Sets: Ordinal Numbers 3.3 Analysis of the Continuum 3.3.1 Decomposing the Reals 3.3.2 Characterizing the Reals 3.3.3 Characterizing Continuity 3.4 What ZFC Does and Does Not Tell Us About c Metamathematics and CH 4.1 Consistency, Completeness, and Compactness of ... 4.1.1 a Logical System 4.1.2 an Axiomatic Theory 4.2 Models of ... 4.2.1 Real Numbers 4.2.2 Set Theory 4.2.2.1 Inner Models 4.2.2.2 Forcing and Outer Models 4.3 Adding Axioms to Zermelo Fraenkel Set Theory 4.3.1 Axioms that Imply CH or GCH 4.3.1.1 Explicitly Adding CH or GCH 4.3.1.2 V=L: Shrinking the Set Theoretic Universe

22. Gaia Hypothesis What is the hypothesis of Gaia ? Stated simply, the idea is that we may have discovered a living being bigger, more ancient, and more complex than anything http://erg.ucd.ie/arupa/references/gaia.html

Gaia Hypothesis This will serve as an introduction to the Gaia hypothesis; It is a review (published in 1989) of James Lovelock's The Ages of Gaia What is the hypothesis of Gaia ? Stated simply, the idea is that we may have discovered a living being bigger, more ancient, and more complex than anything from our wildest dreams. That being, called Gaia, is the Earth. More precisely: that about one billion years after it's formation, our planet was occupied by a meta-life form which began an ongoing process of transforming this planet into its own substance. All the life forms of the planet are part of Gaia. In a way analogous to the myriad different cell colonies which make up our organs and bodies, the life forms of earth in their diversity coevolve and contribute interactively to produce and sustain the optimal conditions for the growth and prosperity not of themselves, but of the larger whole, Gaia. That the very makeup of the atmosphere, seas, and terrestrial crust is the result of radical interventions carried out by Gaia through the evolving diversity of living creatures. Encountering the Earth from space, a witness would know immediately that the planet was alive. The atmosphere would give it away. The atmospheric compositions of our sister planets, venus and mars, are: 95-96% carbon dioxide, 3-4% nitrogen, with traces of oxygen, argon and methane. The earth's atmosphere at present is 79% nitrogen, 21% oxygen with traces of carbon dioxide, methane and argon. The difference is Gaia, which transforms the outer layer of the planet into environments suitable to its further growth. For example, bacteria and photosynthetic algae began some 2.8 billions of years ago extracting the carbon dioxide and releasing oxygen into the atmosphere, setting the stage for larger and more energetic creatures powered by combustion, including, ultimately, ourselves.

23. Investor Home - The Efficient Market Hypothesis Investor Home The Efficient Market hypothesis and Random Walk Theory. http://www.investorhome.com/emh.htm

The Efficient Market Hypothesis An issue that is the subject of intense debate among academics and financial professionals is the Efficient Market Hypothesis (EMH). The Efficient Market Hypothesis states that at any given time, security prices fully reflect all available information. The implications of the efficient market hypothesis are truly profound. Most individuals that buy and sell securities (stocks in particular), do so under the assumption that the securities they are buying are worth more than the price that they are paying, while securities that they are selling are worth less than the selling price. But if markets are efficient and current prices fully reflect all information, then buying and selling securities in an attempt to outperform the market will effectively be a game of chance rather than skill. The Efficient Market Hypothesis evolved in the 1960s from the Ph.D. dissertation of Eugene Fama (link courtesy of Ibbotson Associates ). Fama persuasively made the argument that in an active market that includes many well-informed and intelligent investors, securities will be appropriately priced and reflect all available information. If a market is efficient, no information or analysis can be expected to result in outperformance of an appropriate benchmark "An 'efficient' market is defined as a market where there are large numbers of rational, profit-maximizers actively competing, with each trying to predict future market values of individual securities, and where important current information is almost freely available to all participants. In an efficient market, competition among the many intelligent participants leads to a situation where, at any point in time, actual prices of individual securities already reflect the effects of information based both on events that have already occurred and on events which, as of now, the market expects to take place in the future. In other words, in an efficient market at any point in time the actual price of a security will be a good estimate of its intrinsic value."

24. The Language Of Thought Hypothesis (Stanford Encyclopedia Of Philosophy) The Language of Thought hypothesis (LOTH) postulates that thought and thinking take place in a mental language. This language consists of a system of http://plato.stanford.edu/entries/language-thought/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free The Language of Thought Hypothesis First published Thu May 28, 1998; substantive revision Tue Jul 27, 2004 The Language of Thought Hypothesis (LOTH) postulates that thought and thinking take place in a mental language. This language consists of a system of representations that is physically realized in the brain of thinkers and has a combinatorial syntax (and semantics) such that operations on representations are causally sensitive only to the syntactic properties of representations. According to LOTH, thought is, roughly, the tokening of a representation that has a syntactic (constituent) structure with an appropriate semantics. Thinking thus consists in syntactic operations defined over such representations. Most of the arguments for LOTH derive their strength from their ability to explain certain empirical phenomena like productivity and systematicity of thought and thinking. 1. What is the Language of Thought Hypothesis? 2. Status of LOTH 3. Scope of LOTH 4. Nativism and LOTH ... Related Entries 1. What is the Language of Thought Hypothesis? S believes that P S hopes that P S desires that P S P P A S A s that P LOTH can now be formulated more exactly as a hypothesis about the nature of propositional attitudes. It can be characterized as the conjunction of the following three theses (A), (B) and (C):

25. The Sapir-Whorf Hypothesis These notes on the SapirWhorf hypothesis concerning linguistic relativity and determinism are from a book on The Act of Writing by Daniel Chandler. http://www.aber.ac.uk/media/Documents/short/whorf.html

The Sapir-Whorf Hypothesis Daniel Chandler Greek Translation now available Within linguistic theory, two extreme positions concerning the relationship between language and thought are commonly referred to as 'mould theories’ and 'cloak theories'. Mould theories represent language as 'a mould in terms of which thought categories are cast' (Bruner et al. 1956, p. 11). Cloak theories represent the view that 'language is a cloak conforming to the customary categories of thought of its speakers' (ibid.). The doctrine that language is the 'dress of thought' was fundamental in Neo-Classical literary theory (Abrams 1953, p. 290), but was rejected by the Romantics (ibid.; Stone 1967, Ch. 5). There is also a related view (held by behaviourists, for instance) that language and thought are identical . According to this stance thinking is entirely linguistic: there is no 'non-verbal thought', no 'translation' at all from thought to language. In this sense, thought is seen as completely determined by language. The Sapir-Whorf theory, named after the American linguists Edward Sapir and Benjamin Lee Whorf, is a

26. Hygiene Hypothesis: Are We Too "Clean" For Our Own Good? Cleanliness and lack of exposure to various microorganisms may be affecting our immune systems to the degree that we are losing out bodily ability to fight http://healthlink.mcw.edu/article/1031002421.html

Search Articles: search tips Please Take the HealthLink Survey Email this article Print this article Find related articles: By topic: Allergies/Asthma Children's Health Infections/Infectious Diseases Immune Disorders By keywords: immune response hygiene hypothesis Receive Health Link via email! Subscribe now >> Hygiene Hypothesis: Are We Too "Clean" for Our Own Good? Increased hygiene and a lack of exposure to various microorganisms may be affecting the immune systems of many populations - particularly in highly developed countries like the US - to the degree that individuals are losing their bodily ability to fight off certain diseases. That's the essence of the "hygiene hypothesis," a fairly new school of thought that argues that rising incidence of asthma, inflammatory bowel disease, multiple sclerosis and perhaps several other diseases may be, at least in part, the result of lifestyle and environmental changes that have made us too "clean" for our own good. "Medicine has a lot of history behind it related to why certain diseases are so widespread and certain diseases are not widespread," said

27. Evolution: Library: Hygiene Hypothesis Her hypothesis was that children growing up in the poorer, dirtier, and generally less healthful cities of East Germany would suffer more from allergy and http://www.pbs.org/wgbh/evolution/library/10/4/l_104_07.html

var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); Hygiene Hypothesis This segment from Evolution: "The Evolutionary Arms Race" features the work of Erika Von Mutius , who studies the relationship between early childhood exposure to microbes and later development of asthma and allergies. This clip details her latest work, examining whether exposure to livestock in farming communities provides the challenges necessary for the young immune system to grow strong. Credits: View in: QuickTime RealPlayer Resource Type: Video Format: QuickTime or RealPlayer Length: 3 min, 56 sec Topics Covered: Why Evolution Matters Backgrounder Hygiene Hypothesis: Millions of people suffer from the sneezing and wheezing of allergies and asthma, diseases that have suddenly become epidemic in some parts of the world. Initially, scientists blamed increasing air pollution for the surge in respiratory diseases. In the late 1990s, Dr.

28. Power Of A Hypothesis Test Applet (24-Mar-1997) This applet illustrates the fundamental principles of statistical hypothesis testing through the simplest example the test for the mean of a single normal http://www.stat.sc.edu/~ogden/javahtml/power/power.html

Power of a Hypothesis Test Applet This applet illustrates the fundamental principles of statistical hypothesis testing through the simplest example: the test for the mean of a single normal population, variance known (the Z test). The basic set-up of the test is this: using only n independent observations from a normal distribution with unknown mean (but known variance), the task is to decide whether to accept a null hypothesis for a specified value of , or to reject the null hypothesis in favor of some alternative hypothesis. In most applications, there are only three alternative hypotheses of interest: respectively, ``upper-tailed,'' ``lower-tailed,'' and ``two-tailed.'' The testing framework consists of computing a ``test statistic'' and then rejecting the null hypothesis if the appropriate condition is satisfied. In the order the alternative hypotheses are given above, the null hypothesis is rejected if where represents the upper critical point of the standard normal distribution. This hypothesis testing procedure is set up to give the null hypothesis ``the benefit of a doubt;'' that is, to accept the null hypothesis unless there is strong evidence to support the alternative. If

29. Definition: Hypothesis From Online Medical Dictionary hypothesis. statistics A supposition that appears to explain a group of phenomena and is advanced as a basis for further investigation, a proposition that http://cancerweb.ncl.ac.uk/cgi-bin/omd?hypothesis

30. Statistical Hypothesis Testing Significance level, null hypothesis, alternate hypothesis in statistical testing. http://www.ganesha.org/spc/hyptest.html

Ganesha.org Book promotion Levinson Productivity Systems, P.C. Lean Manufacturing and Lean Enterprise Henry Ford's Lean Vision Home ... Power Related pages Gage capability Manufacturing worker's role in quality Concept of variation in quality and SPC ISO 9000 ... Lean Manufacturing and Lean Enterprise Statistical Hypothesis Testing Information to accompany SPC Essentials and Productivity Improvement: A Manufacturing Approach NEW from Levinson Productivity Systems: Statistical Process Control Chart Simulator , designed to teach production workers how to read an interpret control charts in an hour or less. It also facilitates very rapid training in the concepts of variation and accuracy. It achieves this by using animated target and histogram (quincunx-style) figures in conjunction with control charts. The price is $50.00, which includes shipping and handling within the U.S.Download the instruction file (1 megabyte, Word document) for free. Hypothesis testing often confuses people but it is the keystone of most statistical applications. Every acceptance sampling test, designed experiment, and control chart* is a statistical hypothesis test. Statistical tests separate significant effects from mere luck or random chance.

31. THE HYPOTHESIS Key The nature of today s research is to prove a hypothesis false. Experiments are designed to falsify the hypothesis by yielding evidence (data) to http://www2.lv.psu.edu/jxm57/irp/hypothes.html

32. Introduction The Two Gospel hypothesis (2GH), formerly known as the Griesbach hypothesis, First given its name by Bernard Orchard, the Two Gospel hypothesis proposes http://www.colby.edu/rel/2gh/

A Web Site for the Two Gospel Hypothesis The Two Gospel Hypothesis (2GH), formerly known as the Griesbach Hypothesis, presents a comprehensive solution to the Synoptic Problem. First given its name by Bernard Orchard, the Two Gospel Hypothesis proposes that the Gospel of Matthew was the earliest gospel, that the author of the Gospel of Luke used the Gospel of Matthew as a source, and that the author of the Gospel of Mark wrote using both the Gospels of Matthew and Luke as sources. This page has been created to provide interested parties with basic information about this solution and its advantages. Links to detailed evidence and work in progress will be provided for those who wish to explore the solution further. We strongly recommend that you set your browser to view these pages at "full screen" configuration.

33. ZetaGrid - Verification Of The Riemann Hypothesis The verification of Riemann s hypothesis (formulated in 1859) is considered to be one of modern mathematic s most important problems. http://www.zetagrid.net/zeta/rh.html

Verification of the Riemann Hypothesis ZetaGrid Acknowledgement Performance characteristics Riemann Hypothesis Prizes Motivation News Statistics ... Links Why is Riemann's Hypothesis so important? The verification of Riemann's Hypothesis (formulated in ) is considered to be one of modern mathematic's most important problems. The last 140 years did not bring its proof, but a considerable number of important mathematical theorems which depend on the Hypothesis being true, e.g. the fastest known primality test of Miller. The Riemann zeta function is defined for Re( s )>1 by and is extended to the rest of the complex plane (except for s =1) by analytic continuation. The Riemann Hypothesis asserts that all nontrivial zeros of the zeta function are on the critical line (1/2+ it where t is a real number). To verify empirically the Riemann Hypothesis for certain regions and make it usable, in the first fifteen zeros of Riemann's zeta function t Participate in the verification of Riemann's Hypothesis! Today, we have better resources to verify or falsify Riemann's Hypothesis. First the high-speed computers, then the networks have increased the capacity of calculations. Now we want to go one step further by bundling up the resources into a grid network. Therefore, I invite all interested people to participate in the verification of the zeros of the Riemann zeta function for a new record. Before I have started with the computation on August 28, 2001, the hypothesis has been checked for the first 1,500,000,001 zeros. On October 27, 2001, J. van de Lune checked the hypothesis for the first 10 billion zeros. Up to now, it has been extended to the first 100 billion zeros which required more than 1.3

34. Whorf Hypothesis Whorf coined what was once called the SapirWhorf hypothesis, which is more properly referred to as the Whorf hypothesis. This states that language is not http://www.mnsu.edu/emuseum/cultural/language/whorf.html

The Whorf Hypothesis Examined The argument that language defines the way a person behaves and thinks has existed since the early 1900's when Edward Sapir first identified the concept. He believed that language and the thoughts that we have are somehow interwoven, and that all people are equally being effected by the confines of their language. In short, he made all people out to be mental prisoners; unable to think freely because of the restrictions of their vocabularies. An example of this idea is given in George Orwell's book 1984, in which he discusses the use of a language entitled "newspeak" which was created to change the way people thought about the government. The new vocabulary they were given was created to control their minds. Since they could not think of things not included in the vocabulary, they were to be zombies imprisoned by the trance of their language. Soon, Sapir had a student, Benjamin Whorf , who picked up on the idea of linguistic determinism and really made it his own. Whorf coined what was once called the Sapir-Whorf hypothesis, which is more properly referred to as the Whorf hypothesis. This states that language is not simply a way of voicing ideas, but is the very thing which shapes those ideas. One cannot think outside the confines of their language. The result of this process is many different world views by speakers of different languages. If the world view and behavior of people are affected so severely by the structure of their language, and languages have different structures, then is cross-cultural communication and understanding a realistic goal for the modern world? Whorf would have us believe that such barrier-free communication is almost impossible. However, does that explain current world trade agreements, joint business ventures with foreign companies or the emphasis on raising bilingual societies? Sure, not every word of communication between people of different language communities is expressed. But despite that fact, I believe that the substance of the messages are getting across. Using the universal languages of law and science, people from all over the world are working together with no major barrier because of differing mother tongues.

35. Hypothesis Definition - Dictionary - MSN Encarta The hypothesis of the big bang is one way to explain the beginning of the universe. That is what would logically follow if you accepted the hypothesis. http://encarta.msn.com/dictionary_/hypothesis.html

var s_account="msnportalencarta"; MSN home Mail My MSN Sign in ... more Hotmail Messenger My MSN MSN Directory Air Tickets/Travel Autos City Guides Election 2008 ... More Additional Reference Materials Thesaurus Translations Multimedia Other Resources Education Resources Math Help Foreign Language Help Project Planner ... Help Dictionary Find in Dictionary Thesaurus Translations A B ... See pronunciation key Search for " hypothes... " in all of MSN Encarta E-mail this entry Blog about this entry on MSN Spaces Download the MSN Encarta Right-Click Dictionary hypothesis WriteDictionaryPronObjectTag("152", "21", "http://images.encarta.msn.com/xrefmedia/sharemed/targets/audio/pron/a26/A2633000.mp3", "hypothesis"); hy·poth·e·sis hÄ« p³thəssiss plural hy·poth·e·ses noun Definition: theory needing investigation: a tentative explanation for a phenomenon, used as a basis for further investigation The hypothesis of the big bang is one way to explain the beginning of the universe. assumption: a statement that is assumed to be true for the sake of argument That is what would logically follow if you accepted the hypothesis.

36. Efficient Market Hypothesis (EMH) Efficient Market hypothesis (EMH) Definition of Efficient Market hypothesis (EMH) on Investopedia - An investment theory that states that it is impossible http://www.investopedia.com/terms/e/efficientmarkethypothesis.asp

Home Beginners Experienced Investors Active Traders ... Trading Efficient Market Hypothesis (EMH) An investment theory that states that it is impossible to "beat the market" because stock market efficiency causes existing share prices to always incorporate and reflect all relevant information. According to the EMH, this means that stocks always trade at their fair value on stock exchanges, making it impossible for investors to either purchase undervalued stocks or sell stocks for inflated prices. As such, it should be impossible to outperform the overall market through expert stock selection or market timing, and that the only way an investor can possibly obtain higher returns is by purchasing riskier investments. Although it is a cornerstone of modern financial theory, the EMH is highly controversial and often disputed. Believers argue it is pointless to search for undervalued stocks or to try to predict trends in the market through either fundamental or technical analysis. Meanwhile, while academics point to a large body of evidence in support of EMH, an equal amount of dissension also exists. For example, investors such as Warren Buffett have consistently beaten the market over long periods of time, which by definition is an impossibility according to the EMH. Detractors of the EMH also point to events such as the 1987 stock market crash (when the DJIA fell by over 20% in a single day) as evidence that stock prices can seriously deviate from their fair values. Arbitrage Behavioral Finance Fundamental Analysis Market Timing ... Index Investing: Index Funds - Learn how lower management fees boost the index fund''s popularity.

37. Ad Hoc Hypothesis An ad hoc hypothesis is one created to explain away facts that seem to refute one’s theory. Ad hoc hypotheses are common in paranormal research and in the http://skepdic.com/adhoc.html

Robert Todd Carroll SkepDic.com Click to order from Amazon Becoming a Critical Thinker by Robert T. Carroll ad hoc hypothesis pseudoscientists . For example, ESP researchers have been known to blame the hostile thoughts of onlookers for unconsciously influencing pointer readings on sensitive instruments. The hostile vibes, they say, made it impossible for them to duplicate a positive ESP experiment. Being able to duplicate an experiment is essential to confirming its validity. Of course, if this objection is taken seriously, then no experiment on ESP can ever fail. Whatever the results, one can always say they were caused by paranormal psychic forces, either the ones being tested or others not being tested. Martin Gardner reports on this type of ad hoc hypothesizing reaching a ludicrous peak with paraphysicist Helmut Schmidt who put cockroaches in a box where they could give themselves electric shocks. One would assume that cockroaches do not like to be shocked and would give themselves shocks at a chance rate or less, if cockroaches can learn from experience. The cockroaches gave themselves more electric shocks than predicted by chance. Schmidt concluded that "because he hated cockroaches, maybe it was his pk that influenced the randomizer!" (Gardner, p. 59) Ad hoc hypotheses are common in defense of the pseudoscientific theory known as biorhythm theory Astrologers are often fond of using statistical data and analysis to impress us with the scientific nature of

38. IngentaConnect Biblical Entheogens: A Speculative Hypothesis A speculative hypothesis is presented according to which the ancient Israelite religion was associated with the use of entheogens (mindaltering plants used http://www.ingentaconnect.com/content/berg/tmdj/2008/00000001/00000001/art00004

Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); Biblical Entheogens: a Speculative Hypothesis Author: Shanon, Benny Source: Time and Mind , Volume 1, Number 1, March 2008 , pp. 51-74(24) Publisher: Berg Publishers view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: A speculative hypothesis is presented according to which the ancient Israelite religion was associated with the use of entheogens (mind-altering plants used in sacramental contexts). The hypothesis is based on a new look at texts of the Old Testament pertaining to the life of Moses. The ideas entertained here were primarily based on the fact that in the arid areas of the Sinai peninsula and Southern Israel there grow two plants containing the same psychoactive molecules found in the plants from which the powerful Amazonian hallucinogenic brew Ayahuasca is prepared. The two plants are species of Acacia tree and the bush

39. New Left Review - Alain Badiou: The Communist Hypothesis What is the communist hypothesis? In its generic sense, given in its canonic Manifesto, ‘communist’ means, first, that the logic of class—the fundamental http://www.newleftreview.org/?view=2705

40. The Space Review: The Park Hypothesis May 30, 2006 Maybe they have isolated us for observation and study (the zoo hypothesis). Maybe they are waiting until our civilization reaches a certain http://www.thespacereview.com/article/629/1

The Park hypothesis by Michael Huang Tuesday, May 30, 2006 Bob Park will be remembered as a persistent human spaceflight critic, a leader of the anti-human-spaceflight movement. But he could also help solve one of the great space mysteries of all time: Do intelligent aliens exist, and if so, where are they? First, some background information. The Search for Extraterrestrial Intelligence (SETI) is challenged by an idea called the Fermi Paradox. Enrico Fermi thought that if intelligent alien civilizations existed, they would inevitably colonize the galaxy. Travelling slower than the speed of light, they would still colonize the galaxy in a relatively short time. And if our galaxy was colonized, we would know all about it. Fermi concluded that intelligent aliens do not exist. The Fermi Paradox drew a wide range of speculative hypotheses. Maybe intelligent aliens did exist, but they became extinct before they reached us. Maybe they have isolated us for observation and study (the zoo hypothesis). Maybe they are waiting until our civilization reaches a certain developmental stage (the sentinel hypothesis). Or could there be another explanation? If this is true, then aliens would be very difficult to detect. A robot probe is much harder to detect than worlds colonized by aliens. The communication between a robot probe and its homeworld would be a much weaker signal than the communication between a homeworld and its colonies. Aliens that resolved to stay on their home planet would leave a very small footprint on the galaxy, one easily overlooked.

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