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Dru

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Everything posted by Dru

  1. if its this weekend forecast is not looking great for a 4 day trip on the west side so head east, you might have to give up on a glacier to stay dry though.
  2. Re: Loyalty to your comrades or doing the right thing People are saying Kerry sold out his soldier brothers-in-arms by coming home and criticizing the war. Isn't that a good quality for a President, not being loyal to a flawed idea just because your close friends are, but having the candour to stand up for what you believe is right even if it means alienating your friends? Compare to Bush stacking the deck with his ex-oil business cronies?
  3. Ants FAQ
  4. The significance of Russell's paradox can be seen once it is realized that, using classical logic, all sentences follow from a contradiction. For example, assuming both P and ~P, any arbitrary proposition, Q, can be proved as follows: from P we obtain P Q by the rule of Addition; then from P Q and ~P we obtain Q by the rule of Disjunctive Syllogism. Because of this, and because _nodder theory underlies all branches of mathematics, many people began to worry that, if _nodder theory was inconsistent, no mathematical proof could be trusted completely. Russell's paradox ultimately stems from the idea that any coherent condition may be used to determine a _nodder. As a result, most attempts at resolving the paradox have concentrated on various ways of restricting the principles governing _nodder existence found within naive _nodder theory, particularly the so-called Comprehension (or Abstraction) axiom. This axiom in effect states that any propositional function, P(x), containing x as a free variable can be used to determine a _nodder. In other words, corresponding to every propositional function, P(x), there will exist a _nodder whose members are exactly those things, x, that have property P.[3] It is now generally, although not universally, agreed that such an axiom must either be abandoned or modified.[4] Russell's own response to the paradox was his aptly named theory of types. Recognizing that self-reference lies at the heart of the paradox, Russell's basic idea is that we can avoid commitment to R (the _nodder of all _nodders that are not members of themselves) by arranging all sentences (or, equivalently, all propositional functions) into a hierarchy. The lowest level of this hierarchy will consist of sentences about individuals. The next lowest level will consist of sentences about _nodders of individuals. The next lowest level will consist of sentences about _nodders of _nodders of individuals, and so on. It is then possible to refer to all objects for which a given condition (or predicate) holds only if they are all at the same level or of the same "type." This solution to Russell's paradox is motivated in large part by the so-called vicious circle principle, a principle which, in effect, states that no propositional function can be defined prior to specifying the function's range. In other words, before a function can be defined, one first has to specify exactly those objects to which the function will apply. (For example, before defining the predicate "is a prime number," one first needs to define the range of objects that this predicate might be said to satisfy, namely the _nodder, N, of natural numbers.) From this it follows that no function's range will ever be able to include any object defined in terms of the function itself. As a result, propositional functions (along with their corresponding propositions) will end up being arranged in a hierarchy of exactly the kind Russell proposes. Although Russell first introduced his theory of types in his 1903 Principles of Mathematics, type theory found its mature expression five years later in his 1908 article, "Mathematical Logic as Based on the Theory of Types," and in the monumental work he co-authored with Alfred North Whitehead, Principia Mathematica (1910, 1912, 1913). Russell's type theory thus appears in two versions: the "simple theory" of 1903 and the "ramified theory" of 1908. Both versions have been criticized for being too ad hoc to eliminate the paradox successfully. In addition, even if type theory is successful in eliminating Russell's paradox, it is likely to be ineffective at resolving other, unrelated paradoxes. Other responses to Russell's paradox have included those of David Hilbert and the formalists (whose basic idea was to allow the use of only finite, well-defined and constructible objects, together with rules of inference deemed to be absolutely certain), and of Luitzen Brouwer and the intuitionists (whose basic idea was that one cannot assert the existence of a mathematical object unless one can also indicate how to go about constructing it). Yet a fourth response was embodied in Ernst Zermelo's 1908 axiomatization of _nodder theory. Zermelo's axioms were designed to resolve Russell's paradox by again restricting the Comprehension axiom in a manner not dissimilar to that proposed by Russell. ZF and ZFC (i.e., ZF supplemented by the Axiom of Choice), the two axiomatizations generally used today, are modifications of Zermelo's theory developed primarily by Abraham Fraenkel. Together, these four responses to Russell's paradox have helped logicians develop an explicit awareness of the nature of formal systems and of the kinds of metalogical and metamathematical results commonly associated with them today.
  5. they rock
  6. Quark
  7. The word sheath has a number of related meanings in English. In general usage, a sheath is any protective covering that fits closely around the object to be protected. A sword's sheath is called a scabbard. A sheath (synonym: jacket) is the outer covering or coverings of a communications or power cable. It is made of tough material, often plastic, that is resistant to environmental hazards such as abrasion, liquid intrusion, solar radiation, etc., and is used to protect cable components such as optical fibers or metallic conductors that transport the signal or power. There may be more than one sheath surrounding a given cable. For example, some cable designs use an inner sheath surrounded by metallic armor, over which is an outer sheath. (Source: Federal Standard 1037C) Sheath leaves are a type of leaf characteristic of some monocotyledonous plants, especially grasses. Sheath leaves are typically long, narrow, and triangular in shape. The leaf veins are parallel. The main characteristic is a basal part (the sheath) that clasps the stem or culm for some distance above the leaf origin (node). An example of a plant with sheath leaves is maize. A sheath is another word for condom. A penis sheath is traditional clothing in New Guinea, worn without other clothing, tied in upward position (image: http://www.trekearth.com/gallery/Asia/Indonesia/photo12474.htm)
  8. Dru

    W00t!

    Kelly didn't tell me. I'm more impressed with the no water for 2 days thing. This is right up there with that Croft/Anker 8000' pillar in-a-day 5.11 simulclimb near K7. Which I have STILL never seen any pictures of were they in a TNF catalogue or somethin'
  9. Stuffed Camel 1 whole camel, medium size 1 whole lamb, large size 20 whole chickens, medium size 60 eggs 12 kilos rice 2 kilos pine nuts 2 kilos almonds 1 kilo pistachio nuts 110 gallons water 5 pounds black pepper Salt to taste Skin, trim and clean camel (once you get over the hump), lamb and chicken. Boil until tender. Cook rice until fluffy. Fry nuts until brown and mix with rice. Hard boil eggs and peel. Stuff cooked chickens with hard boiled eggs and rice. Stuff the cooked lamb with stuffed chickens. Add more rice. Stuff the camel with the stuffed lamb and add rest of rice. Broil over large charcoal pit until brown. Spread any remaining rice on large tray and place camel on top of rice. Decorate with boiled eggs and nuts. Serves friendly crowd of 80-100. Shararazod Eboli Home Economist, Dammam, Saudi Arabia
  10. a giant cornice!
  11. Dru

    Watered down...

    ya but give me 24 years!
  12. No what I'm saying is that if you can't build a bomber anchor either from cams,nuts,pins, bolts, slung trees etc dont fix a line. And if you can then why are you asking the question?
  13. Dru

    Watered down...

    Coast Mountains---->Cascades
  14. I wouldn't fix the bottom until you have the top fixed, just have someone belay you till then. Why? Pitons? Do you lead climb? The question makes it sound like you don't know much about placing gear. Just tie off to a bomber anchor. If you cant get a bomber anchor dont fix the line.
  15. Upon completing my morning routine I noticed a fried mushroom floating in the bowl. I know corn does this but its the first time I have seen a mushroom complete the Northwest Passage unscathed
  16. Yeah in July and August you should be flying in to the unclimbed 2000 to 5000 foot rock routes in the Coast Mts not scrambling up loose choss in the Rockies.... Oh wait. Forget that. There is no unclimbed rock in the Coast Mts. The Rockies are the home of North American alpinism. Stay there. Climb there. Embrace your inner choss.
  17. Dru

    Bad Photo Contest

    super bad
  18. Dru

    Watered down...

    trask---->catbirdseat
  19. I would rather see another informal ice fest like last year than a formal one with clinics and stuff. Except that you seem to get more free swag at the formal ones. The big problems seems to be that when you pick the date months in advance it often coincides with a warm spell. With an informal one you can just say "OK it's this weekend, show up" 3 days beforehand and it all works!
  20. There are people talking about snow in *The Freshiezone*
  21. With beer goggles on you think you can do any crack
  22. Dru

    Who is it?

    lance armstrong
  23. It's the anti-Bachy! stupid webcam that pi wont link to using img tags
  24. Dru

    W00t!

    Trango SW ridge!
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