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Gödel 1 2001 |
 
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Goedel
1 Several reports have pointed to the stimulant effects of Magnesium-Cut Tumor on behavior. This cut can increase exploratory activity, and it reportedly enhances performance of conditioned avoidance-T "knows" tasks. Female adult Wistar rat was used in this performance, except in the determination of the formula PRFT(x, y) turnover in whole brain-stomach and in turning behavior performances, where adult mice (Rockefeller-W1 strain) weighing 25+- 2g were employed. Drugs: Radiochemicals: L-[14C(U)]-tyrosine (463 mCi/mmol), [3H (G)]-dopamine 6.45 Ci/mmol) Anesthetics 1st Period: Methoxyflurane (inexpensive) / (gently supplied by BS Laboratories) 2nd Period: Halothene(takes rats up to an hour to completely wake up and they usually behave sedated for up to another 12 hours) (less expensive than isoflurane)/ 3rd Period: Isoflurane(is not metabolized by the kidneys) and 4th Period: Sigma-Nt were suspended in a mixture of saline and Spleen 80(10:02:2). Suspensions and anesthetics were injected i.p at a volume of 0.2 ml/100g body weigtht for rats The effect of Tumor Cut on the level of DA and NA in midbrain, corpus striatum stomach and hypothalamus was determined. Slices of Tumor, with minor modifications, were incubated in an open lucite cylinder, with a piece of nylon mesh fitted in the bottom.By this chamber the tissue was transferred through a serie of bathing solutions contained in 10 ml beakers, without any loss of the slices placed into it. Go to Goedel 2 |
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| Gödel
2 2001 Gödel 2 Net-Performance Performance 1 Hour 10 minutes by Marcello Mercado |
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_G O E D E L . 0 0 3 _|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_p1: p2 false/p2: p1 is true/q1: q2false_| position 21.9 14.5 29.8 orientation -0.276 0.691 0.175 0.227 field Of View 0.735 Traffic-Cam Link 
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Goedel
2 Each beaker containing 2.5 ml of Krebs-Henseleit solution (added with 0.11 mM ascorbic acid) was thrown in front of every traffic-cam in Köln I use the term "apparent throw-turnover" since I merely measured the difference in CA levels between basal values and after the administration of NT. Little work has yet been done to elucidate its mechanism of hypothalamus-stomach -Surveillance chromatography(assayed fluorimetrically) ... _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_G O E D E L . 0 0 3 _|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| |_p1: p2 false/p2: p1 is true/q1: q2false_| position 21.9 14.5 29.8 orientation -0.276 0.691 0.175 0.227 field Of View 0.735 +--=- |-=--^ - <<x -- a -- 0 -- 1-- + -- * -- = -- ( -- ) -- ~ -- & -- v -- -> -- E -- A>> q3: q1 is false 0 -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 - 7 - 8 - 9 - 10 -- 11 -- 12 -- 13 -- 14 a) PA proves: SUB(k, m, n), b) PA proves: ~(z=n) -> ~SUB(k, m, z)PA proves: SUB(k, k, B), and PA proves: ~(z=k) -> ~SUB(k, k, z). ---------(2) Hence, z in (1) equals to B, and we obtain C(B). The Deduction theorem does the rest: PA proves: B -> C(B) 1. First, let us assume that PA proves G, and k is the number of this proof. Then prf(G, k) is true and hence, PA proves: PRF(G, k), PA proves: EyPRF(G, y), PA proves: ~G ________ ||||||||w-inconsistency ||||||||||| a) PA proves: EyC(y), b) For each k, PA proves: ~C(k). Go to Gödel 3 |
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| Gödel
3 2001 Gödel 3 Net-Performance Performance 1 hour 20 minutes internetverbindung 1 traffic-camera by Marcello Mercado |
"Do not try to justify the induction principle by means of the induction principle. This would be a kind of vicious circle."    
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Goedel
3 Estimation in whole performance: The throw-net turns during 2 minutes were expressed as positive (ipsilateral to the tumor) , or negative (contralateral to the wall side). the rat was injected i.p. with apomorphine (0.5mg/kg), Mg-Pe (30mg/kg) and retested for two minutes at 10 minutes intervals during 1 hr Acute Treatment: The conversion index of DA showed a tendency to decrease, which was not significant. Pre-treatment with Pure mathematical contents of incompleteness theorems lectures, reduced the dissappearance rate of DA in corpus striatum and Stomach 1 hr after the first lecture and the reduction became significantly different after 2 hr of Lecture 2. Nevertheless no difference was observed 4 hr after wall-throw-inhibition or Lecture 3. Some Examples: a)Lecture 1 " 1. Assume that T proves RT. Then QT appears in (1) as, for example, Fk. Hence, PA proves: PRFT (QT, k). --------(3) From (2) and (3) we obtain: PA proves: Ez(z<k & REFT (QT, z)). ---------(4) If, indeed, ~QT appears in (1) as Fm with m<k, then T proves ~RT and T is inconsistent. If not, then PA proves: ~REFT (QT, 0)&~REFT (QT, 1)&...&~REFT (QT, k-1). Hence, PA proves ~Ez(z<k & REFT (QT, z)). This contradicts (4), i.e. PA is inconsistent, and so is T. 2. Assume now that T proves ~RT. Then ~QT appears in (1) as, for example, Fk. Hence, PA proves: REFT (QT, k). -------(5) If QT appears in (1) before ~QT, then T proves RT, and T is inconsistent. If QT does not appear before ~QT, then PA proves: ~PRFT (QT, 0)&~PRFT (QT, 1)&...&~PRFT (QT, k-1). Hence, PA proves ~Ez(z<k & PRFT (QT, z)). --------(6) From (5) we have: PA proves: At(t>k -> (PRFT (QT, t) -> Ez(z<t & REFT (QT, z))) (if t>k, then we can simply take z=k). Add (6) to this, and you will have: PA proves: At(PRFT (QT, t) -> Ez(z<t & REFT (QT, z))). According to (2) this means that PA proves QT, and T proves RT, i.e. T is inconsistent. End of proof. Now we can state the strongest possible form of the Goedel's "unperfectness principle":a fundamental theory cannot be perfect - either it is inconsistent, or it is insufficient to solve some of its problems. The fundamentality (the possibility to prove the principal properties of natural numbers) is essential here, because some non-fundamental theories may be sufficient to solve all of their problems. As a non-trivial example of non-fundamental theories can serve the Presburger arithmetic (PA minus multiplication, see Section 3.1). In 1929 M. Presburger proved that this theory is both consistent and complete. After Goedel and Rosser, this means now that Presburger has proved that his arithmetic is not fundamental" (Tiempo de lectura: 8:37 minutes) b)Lecture 2: "Algorithm 1. Given the axioms of a fundamental formal theory T this algorithm builds a closed PA-formula RT. As a closed PA-formula, RT asserts some property of the natural number system. Algorithm 2. Given a T-proof of the formula RT or the formula ~RT this algorithm builds a T-proof of a contradiction. Therefore, if T is a fundamental theory, then either T is inconsistent, or it can neither to prove, nor to refute the hypothesis RT. A theory that is able neither to prove, nor to refute some closed formula in its language, is called incomplete. Hence, Goedel and Rosser have proved that each fundamental theory is either inconsistent, or incomplete. Why is this theorem called incompleteness theorem? The two algorithms developed by Goedel and Rosser do not allow deciding whether T is inconsistent or incomplete. Hence, to prove "via Goedel" the incompleteness of some theory T, we must prove that T is consistent. Still, as we already know (Section 1.5), in a reliable consistency proof we should not use questionable means of reasoning. The aim of Hilbert's program was to prove consistency of the entire mathematics by means of reasoning as reliable as the ones containing in the first order arithmetic (i.e. PA). Hence, to prove consistency of PA we must use... PA itself?" (Tiempo de lectura 3:25 minutes) c)Lecture 3: "Do not try to justify the induction principle by means of the induction principle. This would be a kind of vicious circle. The induction principle builds up 99% of PA, hence, do not try to prove the consistency of PA by means of PA! And Goedel's second theorem says: of course, you can try, yet if you will be successful, you will prove that PA is inconsistent!" (Tiempo de lectura :1minute) End of proof. Thank you very much |
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