Essay on the General Theory of Relativity
or you could just add their logarithms:
It starts out as fairly unlikely that a woman has breast cancer - ourcredibility level is at -20 decibels. Then three test resultscomein, corresponding to 9, 13, and 5 decibels of evidence. Thisraises the credibility level by a total of 27 decibels, meaning thattheprior credibility of -20 decibels goes to a posterior credibility of 7decibels. So the odds go from 1:99 to 5:1, and the probabilitygoes from 1% to around 83%.
Just for fun, try and work this one out in your head. You don'tneed to be exact - a rough estimate is good enough. When you'reready, continue onward.
According to a study performed by Lawrence Phillips and Ward Edwards in1966, most people, faced with this problem, give an answer in the range70% to 80%. Did you give a substantially higher probability thanthat? If you did, congratulations - Ward Edwards wrote that veryseldom does a person answer this question properly, even if the personis relatively familiar with Bayesian reasoning. The correctansweris 97%.
The likelihood ratio for the test result "red chip" is 7/3, while thelikelihood ratio for the test result "blue chip" is 3/7. Thereforea blue chip is exactly the same amount of evidence as a red chip, justin the other direction - a red chip is 3.6 decibels of evidence for thered bag, and a blue chip is -3.6 decibels of evidence. If youdrawone blue chip and one red chip, they cancel out. So the of red chips to blue chipsdoes not matter; only the of red chips over blue chips matters. There were eight red chipsand four blue chips in twelve samples; therefore, four red chips than bluechips. Thus the posterior odds will be:
44which is around 30:1, i.e., around 97%.
The prior credibility starts at 0 decibels and there's a total ofaround 14 decibels of evidence, and indeed this corresponds to odds ofaround 25:1 or around 96%. Again, there's some rounding error,butif you performed the operations using exact arithmetic, the resultswould be identical.
We can now see that the bookbag problem would have exactly the same answer, obtainedinjust the same way, if sixteen chips were sampled and we found ten redchips and six blue chips.
What is the sequence of arithmetical operations that you performed tosolve this problem?
(45%*30%) / (45%*30% + 5%*70%)
Similarly, to find the chance that a woman with positive mammographyhas breast cancer, we computed:
The fully general form of this calculation is known as or
Given some phenomenon A that we want to investigate, and an observationX that is evidence about A - for example, in the previous example, A isbreast cancer and X is a positive mammography - Bayes' Theorem tells ushow we should ourprobability of A, given the X.
By this point, Bayes' Theorem may seem blatantly obvious or eventautological, rather than exciting and new. If so, thisintroduction has in its purpose.
So why is it that some people are so about Bayes' Theorem?
"Do you believe that a nuclear war will occur in the next 20 years?
General Theory of Relativity Essay Example for Free
general theory of relativity Essay - 863 Words | Major Tests
But most Kantian philosophers did not attempt to immunize Kant from anapparent empirical refutation by the general theory. Rather, theirconcern was to establish how far-reaching the necessary modificationsof Kant must be and whether, on implementation, anything distinctivelyKantian remained. Certainly, most at risk appeared to be the claim, inthe Transcendental Aesthetic, that all objects of outerintuition, and so all physical objects, conform to the space ofEuclidean geometry. Since the general theory of relativity employednon-Euclidean (Riemannian) geometry for the characterization ofphysical phenomena, the conclusion seemed inevitable that anyassertion of the necessarily Euclidean character of physical space infinite, if not infinitesimal, regions, is simplyfalse.
a specific metric theory of gravity, such as general relativity, ..
Following the experimental confirmation of the general theory in 1919,few Kantians attempted to retain, unadulterated, all of the componentsof Kant's epistemological views. Several examples will suffice toindicate characteristic “immunizing strategies” (Hentschel (1990). The Habilitationsschrift of E. Sellien(1919), read by Einstein in view of his criticism expressed in anOctober, 1919 letter to Moritz Schlick (Howard 1984, 625), declaredthat Kant's views on space and time pertained solely tointuitive space and so were not touched by themeasurable spaces and times of Einstein's empirical theory. The workof another young Kantian philosopher, Ilse Schneider, personally knownto Einstein, affirmed that Kant merely had held that the space ofthree-dimensional Euclidean geometry is the space in which Newton'sgravitational law is valid, whereas an analogous situation obtains ingeneral relativity. Furthermore, Einstein's cosmology (1917b) of afinite but unbounded universe could be seen as in complete accord withthe “transcendental solution” to the First Antinomy in theSecond Book of the Transcendental Dialectic. Her verdict was that theapparent contradictions between relativity theory and Kantianphilosophy disappear on closer examination of both doctrines (1921,71–75).