If anyone is interested, I put some ideas about infinite sets up at my website:
https://sites.google.com/site/ralphthewebsite/ and the abstracts of the two papers are below. There are also some ideas on why things exist and why is there something rather than nothing. Thanks! Roger Infinite Sets: Experimental Artifacts Are Produced by the Infinite Set- Infinite Subset Size Comparison Method Thought Experiment Abstract This paper discusses the mathematical method for comparing the relative size of a single infinite set (say, the set of all positive integers) with one of its subsets (say, the subset of all even integers). Suppose one does a thought experiment in which one starts with a single infinite set N of all the positive integers and in which the goal is to determine the number of even integers relative to all the integers, within the context of this single set. That is, the single, original set in this thought experiment is the "experimental" system being studied, and the results obtained should accurately reflect what is occurring in this system. Traditionally, this size comparison is done by extracting the evens as a separate subset and then pairing off its elements one-to-one with those of the original set in order to show the counterintuitive result that the evens and the total positive integers are the same size, as opposed to the intuitive view that there are only one-half as many evens as total positive integers. I suggest that while this is a thought experiment, it is still an experiment and should follow the rules for good experimental method. But, it doesn't. By extracting the evens out and putting them into a separate subset, this dramatically alters the original single set system and leads to the result that there as many even integers as total integers. By definition, this is an experimental artifact. It is identical to extracting the nucleus from a cell and then studying the nucleus and remaining parts of the cell in isolation and assuming that the results obtained are the same as in the original intact cell. They are not. Many have argued that mathematics is not a science and that thought experiments are not "real" experiments and therefore that experimental method and artifacts don't matter, no matter how counterintuitive the results. If this is acceptable to mathematicians, fine. But, unfortunately, the mathematics of infinities plays a major role and causes major problems in physics, which is a real science, and which should require the following of proper experimental techniques, especially in its logical foundations. I suggest that a re-examination of the use of the mathematics of infinities in physics is greatly needed and that it would pay major dividends. ~~~~~~~~~~~~~~~ Infinite Sets: The Appearance of an Infinite Set Depends on the Perspective of the Observer Abstract This paper discusses how an infinite set would appear to different observers and how this applies to both physics and mathematics. Consider a set, N, defined as containing an infinite number of discrete, finite-sized elements such as balls. Any one of these balls can be defined as an internal observer, O. The balls extend outward in infinite numbers relative to any location and orientation of any internal observer O. That is, wherever O is in the set and in whichever direction O is “looking”, the elements of the set extend without bounds the same potentially infinite distance in all directions relative to O. To observer O, set N appears as a potentially infinite space composed of discrete, finite-sized elements. Now, consider a hypothetical second observer, P who is outside the same set N and whose size relative to internal observer O is actually infinite. That is, P is of the same size “scale” as the entire set N, which is actually infinite relative to O. To observer P, set N appears as a finite-sized object containing a smooth, infinitely divisible internal space. The implications of these differing views of the same set depending on the reference frame of the observer are discussed for both mathematics and physics. On Aug 15, 12:45 am, sadovnik socratus <is.socra...@gmail.com> wrote: > I want to go back to my message > ‘Does an Absolute Infinite Frame of Reference exist?’ > and understand the situation better and deeper. > ===========.. > 1 > ‘ 90% or more of the matter in the Universe is unseen / dark’ > and the % of the visual matter in the Universe is few. > In other words: we have two (2) parallel Worlds – > Vacuum and Material / Physical. > Question: > What is interaction between these two ( 2) different Worlds? > 2. > In the early existence of Universe its temperature was > T=2,7K -- > T=0K. We live on the warm planet Earth. > Question: > How from the Kingdom of Coldness (T=2,7K -- > T=0K ) > the beautiful Earth was created? > 3. > The Vacuum is not empty space. > Dirac wrote that ‘ virual particles – antiparticles ‘ live there. > The astrophysics write that ‘ dark matter/ energy’ exists there. > Question: > How can the ‘ virual particles – dark antiparticles ‘ become real? > 4. > According to QED Electron in interaction with vacuum has > infinite parameters ( energy, mass …etc ). > First : it means that the Vacuum also has infinite parameter > or parameters. > Second: How in the Nature this infinite electron can have > real local physical parameters? > 5. > In 1928 Dirac wrote that every elementary particle with > positive energy (+E=Mc^2 ) has its antiparticle with > negative energy (–E=Mc^2). > But in my opinion the first man who wrote about antiparticles > was Sommerfeld. In 1916 he wrote two ( 2 ) formulas for electron. > The formula of electron as: -e=h*ac and the formula of its > antiparticle as: +e=h*ac. > Question: > What is interaction between +e=h*ac and : -e=h*ac ? > What is interaction between +E=Mc^2 and –E=Mc^2 ? > Why sometimes E= Mc^2 can behavior as a ‘rest’ particle > and sometimes can be ‘active’ and can destroy cities like > Hiroshima and Nagasaki ? Why E= Mc^2 is so strange? > My conclusion: > The answers to these questions can be get only through > understanding the Vacuum. > ===. > I.S. > =====================… -- You received this message because you are subscribed to the Google Groups "Epistemology" group. To post to this group, send email to epistemology@googlegroups.com. To unsubscribe from this group, send email to epistemology+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/epistemology?hl=en.
