jrspriggs

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  1. Where do Photon's come from?

    kenstauffer: You asked "Where are the photons coming from? ... Will a particular closed system ... run out of photons?". There is no reason to believe that the photons exist in any form before they are emitted. There is no evidence that a system will ever run out of photons.
  2. The so-called "infinity" in mathematics

    ADS: I did not intend to insult you or to start an argument with you. I was merely trying to answer a question from Stephen. Since your essay is a rather large subject in itself and not quite on the topic of this thread, I would suggest that, if you really want my comments, you start a new thread specifically on your essay. You said "The concept of infinity is metaphysically invalid because it attempts to describe an existent (e.g., an attribute) as existing, but as nothing in particular. But, since to be is to be something, infinity is at war with the Law of Identity and reality, and is therefore metaphysically impossible.". In isolation, this appears to me to mean: The universe is an existent and thus has a specific identity. One of its attributes is the number of particles in it. If that attribute had the value infinity, then it would not have a value. That is forbidden by the law of identity. The conclusion is that the number of particles is finite. First, I do not regard an infinite number as undefined, so the argument does not convince me. Second, my interpretation seems to be at variance with other things in your essay which imply that the attribute does not exist. Tom Rexton: In Stephen Speicher's Post #2, he responded to martjoh's statement "It is a fact that infinity is an invalid concept." by saying "Yes, as a metaphysical existent, without a doubt.". What is being excluded from the category "metaphysical existent"? Stephen Speicher: I was merely trying to clarify how the things you were saying appear to me, so that you can correct my misunderstandings. You said "... 'infinity', in the metaphysical sense, as an actual physical existent, is invalid.". Scare quotes around "infinity", I presume. Certainly, I agree that Aleph-null (the smallest infinite cardinal, to be specific) does not exist as a material object. Neither does any other number, including finite numbers. I do not think that I said the opposite. You said "The finite, meaning that which has definite limits, has referents in physical reality, namely all the attributes, relationships, actions, etc. of things that physically exist. In contrast, the infinite has no referents in physical reality, but it exists as a potential of a process, a concept of method.". Are you not simply begging the question? You asked "... what is your specialty?". My major was Mathematical Logic and the Foundations of Mathematics. My minor was Topology.
  3. TEW, Gravity and Objective Reality.

    Stephen Speicher: You said "This will be big news to Einstein scholars.". This is argument by intimidation. Who are the scholars who say the opposite? You said "... you will have no difficulty then producing a quote from Einstein's extensive writings in which Einstein interprets gravity as spacetime curvature.". Most of Einstein's direct writings are in German which I do not read. And although his writings are extensive, I only have two books by him in my possession. Further, in them he implicitly assumes the applicability of Riemannian Geometry rather than explaining why he choose to use it. His focus is on developing the equations and their consequences. What I said was what I understood to be common knowledge. None the less, on page 117 of "The Principle of Relativity", a collection of papers by A.Einstein, H.A.Lorentz, H.Weyl, and H.Minkowski, Einstein said "In the general theory of relativity, space and time cannot be defined in such a way that the differences of the spatial co-ordinates can be directly measured by the unit measuring rod, or differences in the time co-ordinate by a standard clock.". On page 170, he says "It further follows that G (apart from a constant factor) must be equal to the scalar of Riemann's tensor of curvature; because there is no other invariant with the properties required for G.". Both of these quotations are translations from German. And one must read between the lines to see the implicit endorsement of the idea that space-time is curved.
  4. TEW, Gravity and Objective Reality.

    Let me begin by saying that I am not yet familiar with TEW, so my comments will be exclusively from the point of view of the standard understanding of the General Theory of Relativity. Alpha (Post #1): You asked "Does gravity affect the length of material objects, i.e.: does an object shrink in length when put in a place of high gravity, such as a huge star?". It is all relative (joking). It depends on what you mean. GTR says that STR holds to the first approximation in a small free-falling frame of reference. If both the objects measured and the instruments measuring them are in close proximity to each other and in free-fall and not distorted by external forces other than gravity, then you will get the same result that you would get if you were far away from the star. That is, the answer would be NO CHANGE. But if you try to set up a global coordinate system around the star, then the curvature of space-time forces you to make compromises. I will assume that the star is spherically symmetric and static (not growing or shrinking or whatever) and that you set up a coordinate system which is as symmetrical as possible. This leads to the Schwarzschild solution outside the star. In that case, clocks near the star would run slower than clocks far away, if they are in free-fall (but instantaneously at rest). And a vertically oriented rod would appear to be shorter in the sense that the circumference of a great-circle around the star would increase by less than 2*pi*(length of rod) when raised from the bottom of the rod to the top. Stephen Speicher (Post #2): You said "In general relativity (GR), many of the effects directly affect the objects themselves.". Not really. Gravity (curvature) does not change the structure of things in a small locality. What it changes is how those localities fit together into an extended space-time. You said "Gravity is a different phenomena in kind, which is one reason that it took Einstein a full ten years after his discovery of SR, to formulate the field equations of GR.". When STR was introduced, Maxwell's equations for electro-magnetism fit right in without any difficulty. But Newton's equations for gravity could not be made consistent with STR. After much thought, Einstein realized that the equivalence principle was the essence of gravity and that it implies that gravity is actually curvature of space-time itself rather than merely another material field in space-time. Consequently, he began to study Riemannian geometry (the geometry of curved spaces where the curvature varies from place to place). Riemannian geometry is quite complicated in four dimensions. And he had to decide which function of the curvature was to be set proportional to the stress-energy tensor of matter which is the source of the gravitational field. That is what took so long. Alpha (Post #3): You asked "... can gravity decrease the speed of light in the GTR?". As measured locally, NO. Relative to a global coordinate system, YES. Stephen Speicher (Post #4): You said "... falling feet first into a neutron star ... you experience an elongation in the direction of motion and a compression in the transverse directions.". Correct.
  5. The so-called "infinity" in mathematics

    Stephen Speicher: You said "... we isolate this fact by establishing a sub-category under the more general heading of concepts of consciousness, and we label this sub-category concepts of methods.". You said that infinity is a concept of method. And you said concepts of methods are concepts of consciousness. Consciousness is part of existence, so concepts of consciousness are concepts of existence, i.e. concepts (without qualification). Thus concepts of methods are concepts. But you said that infinity is an invalid concept. This appears to be a contradiction. Also do you consider finite numbers like 27 to be concepts of methods? If not, then why the distinction between the finite and the infinite? You said "You might enjoy reading this essay. Let us know what you think.". The essay begins with "The Unbounded, Finite Universe The Integration of 'Finite' and 'Unbounded' The question is commonly asked as follows: is the universe finite or infinite? Since the infinite is the impossible, the latter choice is rightly dismissed. ...". Sorry, but it seems like nonsense to me. And it assumes the impossibility of infinity without proof in the second sentence and in several other places thereafter. You said "... here is a nice little tidbit for you.". Thank you for the information about automorphism towers of groups. Group Theory is not my specialty, so I had not heard of it.
  6. The so-called "infinity" in mathematics

    Stephen Speicher (Post #2): You said "[infinity is an invalid concept] ... without a doubt.", and "[infinity in mathematics] ... is a concept of method, representing a potential, not an actual.". Why is it necessary to distinguish between concepts of method and concepts? Currence (Post #11): You said "... infinity is not real because it is not a thing ...". The number 27 is not a thing either. Is it unreal? Stephen Speicher (Post #12): You said "[Dr. Binswanger] ... argues that the infinite is an invalid concept, in that counting numbers lose their meaning beyond a certain range; a range beyond which we cannot physically represent a number, and it therefore becomes meaningless, and a range by which our own epistemologies can sensibly grasp, by whatever notation, the limited, as opposed to the unlimited. In addition, there is also a physically practical limit beyond which we cannot even represent numbers in any notation. There will be some point which is reached where there are not even enough particles in the universe where the most compact notation could denote and delimit a number. (Any errors in this representation are my own.) The conclusion, then, is that the number system is not even potentially infinite.". It is true that there cannot be an infinite number of discrete objects within a finite volume of space at one time. But as far as I know, there could be and probably is an infinite amount of space containing an infinite amount of matter. Any argument against infinity based on how much a human being can grasp conceptually is invalid, because existence is primary, not consciousness. Currence (Post #16): You said "I'm not about to say the universe has an infinite amount of particles ...". But then you do say it in other words -- "... imagine a sphere increasing in size from one point in space. In my opinion, the sphere would continue to increase in size without ever not being able to increase in size or ever touching particles it had already touched; that is, at no point in time would it not have new particles to touch.". You say "Maybe the word 'limitless' is appropriate ...". "Infinite" literally means without ("in") end ("fin"). "Limitless" literally means without ("less") end ("limit"). kenstauffer (Post #18): You said "... the diagonalization method is valid, but does not show that one infinite set is larger than another infinite set, but rather shows that one set is countable versus not countable.". The uncountably infinite is larger than the countably infinite. This is because we DEFINE a set to be larger than another set if the second set can be mapped one-to-one into the first but not the other way around. This is true of your example. You said "The set of integers is really an algorithm for churning out symbols in an ordered way from the previous symbol.". If you want semantic precision, I would call that a representation or system of notations for the integers. Stephen Speicher (Post #24): You said "First, speaking as moderator, please include enough context in your posts to make clear to whom or to what you are responding.". I thought it was understood that if I do not specify a person, then I am addressing the topic generally and not any specific person. I was bothered by the hostile tone of the thread generally towards infinity. Notations for infinite numbers (transfinite ordinals) was my favorite subject at graduate school. You said "There are physical existents and mental existents ...". Are you saying that there cannot be any other kind of existents? Why cannot relationships among things (including sets as unary relations) be considered to exist, with numbers as relationships of a higher type (relationships among relationships)? If infinity merely existed in the purely psychological sense and did not correspond to anything in reality, then why would the methods work so reliably (when used correctly)? You said "... speaking as moderator, on THE FORUM we do not permit speculation as to member's motives.". I am sorry. Stephen Speicher (Post #25): You said "... the way to avoid the emoticon problem ... is to uncheck the 'Enable emoticons?' ...". Yes. I just forgot to preview my message to make sure that there were no problems. And thank you for deleting my corrupted message.
  7. The so-called "infinity" in mathematics

    Excuse me, my previous message was messed up by the emoticons. If it were actually the case that infinite numbers "do not exist", then I would expect the assumption that they do exist which is regularly used by mathematicians to lead to a contradiction. But it has not, as far as I know. Similarly, if it were actually the case that sufficiently large finite numbers "do not exist", then I would expect ultra-finitism to be the mathematical mainstream rather than a back-water. As for complex numbers, these are as real as points on a plane. Consider x+iy to be the point (x,y). Then addition of complex numbers is the same as vector addition in the plane. To multiply (a, by (c,d), imagine making a copy of the plane and stretching it out and rotating it so that the unit (1,0) of the second plane lies on top of (a, [and (0,0) on (0,0)], then (c,d) will lie on top of the product. What is the point of denying the existence of numbers in consistent number systems? Are you looking for an excuse to avoid learning the mathematics?
  8. What is reason?

    Soulsurfer: You asked "How does one promote the concept of reason without also catalyzing the spread of rationalism?". Well, I would not say "Be rational." or "Use reason." because, as you pointed out, most people would not know what that meant. You should teach by example. Be rational in your own actions, speech, and writing. Point out when others are being irrational, if they want your opinion. I think that the key lesson people need to learn is to recognize contradictions and learn how to escape from them. Contradictions are not always as blatant as "A and not A". A key sign of a contradiction is when one thinks that one has enough information to make a decision but is still confused about what that decision should be. You should verify that you have in fact reached a contradiction. Then you must identify which premise or inference is faulty and expunge it from your thinking.