A best-fit analysis of the facts and circumstances related to the death of JonBenet Patricia Ramsey
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B = ( x1, y1, z1; x2, y2, z2; x3, y3, z3 ) ( a, b, c ) B = axi + byj + czk But this is truly oversimplified because, for one thing, we’re using 3 spatial dimensions, which makes perfect sense in regular, Cartesian geometry (in the real world there are 3 dimensions, x, y and z). But in our case, each dimension has a more abstract meaning. Each dimension is what is called a “degree of freedom”. Let us explain. Suppose we find that the temperature on the Ramsey property outside the house at 7 a.m. on 26 December, 1996 turns out to be materially relevant to the case. Then we find the temperature as recorded at that time from the national weather service, noting that this recording was done at the Boulder airport and not on the Ramsey property. We also note that all measurements have a margin of error, a range of values indicating that the true value may fall anywhere within that range. So, to construct temperature as a “degree of freedom” we estimate the possible variation in temperature created by the error introduced by measuring the temperature at a location not exactly identical to the Ramsey property (it was measured at the airport 5 miles away). We then add in the margin of error for the measuring device. Now we know this with nearly 100% certainty: the temperature measured by the national weather service was r. The minimum actual temperature, based on those variations mentioned, would come out to be r – s, s being the ½ that variation. Then the highest value for temperature would be r + t, t being ½ the variation. Therefore, the outdoor temperature on the Ramsey property is not an exact number but lies on an open interval (r – s, r + t). Now, consider the infinite number of real numbered values we could identify on that interval. That is called a degree of freedom. Now, let’s take the entire heap of evidence released into the public domain for the entire JonBenet Ramsey case. Next, whittle it down using the 25 standing criteria. What is left is the set of all degrees of freedom for the best-fit tensor. And this is identical, as we noted, to the number of dimensions, or order, of the tensor. Let that value be n. Then the tensor we are constructing is order n. The object of the calculation here is to solve for the exact value of each n. such that some operator p will result in a geometric fit. Now, given all those infinite values and the billions of calculations we’re potentially talking about, the problem seems intractable. That’s where tensors come in. They dramatically reduce the complexity of the calculation by treating the problem as a geometric problem that has certain common properties, such as a Pythagorean theorem, for example. Once we know the correct value for each n, we can use those points to identify a point in “space”, in this case an n dimensional space. That creature is a type of tensor called a Hilbert Space (often used in Quantum Field Theory for the same reasons indicated). So, for our best-fit analysis, we will construct a Hilbert Space, call it: H = (|v|1, |v|1 … |v|n; |v|2, |v|2 … |v|n; |v|3, |v|3 … |v|n … |v|n |v|n … |v|n) (p1, p2 … pn). The finger of guilt as it points to the parties responsible is the “ray” v. The way these tensors help us solve complex problems so readily is because they take a “vector”, v, and rotate it about the origin through the Hilbert Space into a new location. That new location gives you the answer you’re seeking – the identity of p. A vector results when we take a value for, say, x, y and z, and then see at what point in space that points. Drawing a line from the origin to that point is a vector; a mathematical object with the key properties of magnitude (length) and direction (just to make themselves feel smarter, they decided to call vectors in Hilbert spaces by yet another name, called “rays” - whatever). So, there is a rather large set of p ‘values’ we’ll be implicitly discussing herein. Note that whenever we identify a item of evidence satisfying the 25 Standing Criteria, the process by which we generate its most probable implication is a p value. So, each such item of evidence, we’ll solve for a pn and place it in the tensor. The Sick Carnival Begins JBR was murdered sometime on December 25 or 26, 1996. Her body was found by her father, John Ramsey (JR), in the early afternoon on 26 December, 2006 in the “wine cellar” depicted in the images that follow. This room is perhaps better described as a concrete pillbox in that it has no windows, is mostly concrete and is below grade. Moisture problems were evident by mold growth on the floor, indicating that moisture content was likely to affect estimates of time of death due to its relevant deviance from ambient humidity. Having noted that, the typical dew point in Boulder Colorado in winter is very low. According to the parents, the family, which included JBR, JR and the mother, Patsy Ramsey (PR) and her elder brother Burke Ramsey (BR), aged 9 – almost 10 – attended a Christmas party at the neighbor and friend’s house of Fleet White (FW). According to JR and his wife PR, the family left the party around 9 p.m., stopping by another neighbor’s house and dropping off some presents. Upon arriving home, JBR, the parents agree, was asleep and JR carried her from the car, through the garage and into the home, up the spiral staircase and to her bedroom one floor up. According to JR and PR, she did not wake up that night as far as they knew. BR retired to his room where JR states he read to him before he went to sleep, he estimates, around 10:30 that evening, the 25th of December. According to both JR and PR, none of the family members ventured into the family breakfast room, had a snack there, or placed any dishes in that room. When police arrived the next morning, according to police, the light in the family breakfast room was off. This was before sunrise. According to the parents, JR went to bed first and PR last, both of them going to sleep about 11:00 p.m. that evening. According to PR, she awoke at approximately 5 a.m. and donned the outfit she was wearing the night previous. She then proceeded in two possible directions, depending on which witness you choose to believe. One witness says she stated that she went first to JBR’s room and noticed that JBR was not present. She then proceeded on her usual path to the kitchen by taking the spiral staircase and upon reaching the first floor, saw a three page note on the lower steps. In a deposition she claimed that she first went down the spiral steps, found the note and read it, then raced up to JBR’s room to see if she was present. Whether this was a mistake or deception cannot, on the basis of this information alone, be ascertained due to lack of knowledge of her state of mind. I therefore dismiss it from a best-fit analysis. Shortly after reading the note, PR claimed, she woke up JR and then proceeded to call 911. Here is the unenhanced recording of that call. To be precise, this is the 911 cassette recording that was “cleaned”; that is, known mechanical sounds were removed but nothing was “enhanced” in the sense of bringing anything out. Numerous claims regarding previously unknown voices on this recording have been claimed. It is significant to note that PR apparently set the receiver down during the call thinking she had hung up the phone. But she had not. The supposed voices are heard after the point at which PR thought she had hung up. I’ve obtained several different “enhanced” versions of this recording and I can hear not a single indication of any out of place noises on the tape, much less any sounds from which speech can be heard. For this reason, I dismiss this evidence for the purposes of a best-fit analysis. For the sake of completeness we note that another enhancement, apparently of the highest quality yet achieved, was performed by Aerospace Corporation for the Boulder City Police Department. This enhancement is considered Grand Jury evidence and has therefore been withheld from public disclosure. Transcripts of this enhancement, as best as can be determined, could strongly alter the probabilities we’ll be discussing. Various witnesses seem to concur that the sounds heard indicate the following background conversation: BR: “Please what do I do?” JR: “Its none of your business. Go back to bed. We’re not speaking to you” BR: “but what did you find?” [emphasis in original]
The main floor kitchen is shown here. Pineapple was kept in the reefer behind the insulated door just left of center. Safety considerations should preclude operation of this door by a six year old child. Directory: 2012 2012 -> The Case Against the nypd’s Quota-Driven ‘Broken Windows’ Policing What Is It? 2012 -> Annual InStructional unit plan 2012 -> University of Hawai‘i Maui College dental assisting program review october 21, 2013 2012 -> Committee on the rights of the child the rights of all children in the context of international migration 2012 -> Background on the Haitian Earthquake 2012 -> The Collected Wisdom of Science Olympiad Coaches 2012 -> Federal Communications Commission fcc 12-81 Before the Federal Communications Commission 2012 -> Aa and na members Dying from Tobacco 2012 -> [Baby Crying] 01: 04 [Ching Download 5.45 Mb. Share with your friends:
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