by: John D. Barrow, read in 2009
22 Group Theory seen as sets of possible changes.
33 "Of course we do not live in a ten- or eleven-dimensional space so in order to reconcile such a world with what we see it must be assumed that only three of the dimensions of space in these theories became large and the others remain 'trapped' with (so far) unobservably small sizes." I think this is an unnecessary and false assumption.
33 "One thing that we do know is that only in spaces with three large dimensions can things bind together to form structures like atoms, molecules, planets, and stars." This is an argument I haven't heard before. I would like more details because I doubt it.
35 "Lisa Randall and Raman Sundrum [argue] that the three dimensional space in which the strong, weak, and electromagnetic forces act only in that three-dimensional surface while the force of gravity reaches out into all the other dimensions as well."
36 This list of possibilities seems incomplete. It could be that both U and L exist and that the intersection of U and L is empty.
37 "...the next research programme would seek to understand why the laws of Nature, which allowed that, and no other, Universe to appear, do themselves exist and whether they could be different." Dr. Dick has answered this question.
49 The axioms of Set Theory
70 "...our universe is observed to expand at the same rate in every direction to within one part in 100,000.
72 The question of "What should be chosen first?" in terms of initial conditions and laws of nature seem analogous to the same question in terms of epsilon and delta in the definition of continuity in mathematics. Both raise the questions of "who is asking?"" And "who does the choosing?"
73 How is the spatial separation of A and B explained???
118 Relationship between the fine-structure constant and the gravitational-structure constant to known structures.
120 The unlikely production of abundant carbon in stars.
121 "...to suppose that life must result from the requisite mixture of chemicals is just the sort of teleological attitude that the biologists so rightly decry. There is no reason why life has to evolve in the Universe."
121 More details of coincidences in "The Anthropic Cosmological Principle" by John D. Barrow and Frank J. Tipler
122 "There exists a form of hierarchical structure in Nature which permits us to understand the way in which aggregates of matter behave without the need to know the ultimate microstructure of matter down to the tiniest dimensions....Fortunately, we do not need to know everything before we can know something."
125 "We observe there to exist three dimensions of space, but particle physicists have discovered that the most elegant and complete theories of elementary-particle processes,...predict that there are many more than three dimensions of space (perhaps a further six, or even another twenty-two in some cases). To square such a state of affairs with what we see, it is required that all but three of the dimensions of space be microscopically small." I say "baloney".
126 "The observations of unchanging constants tell us that if there are any extra-dimensions of space then today they are inert to fantastically high precision." I don't necessarily agree. Our measurements of those constants are measurements of the 3D + time manifestations of constants with greater scope. The manifestations in our 3D manifold may be constant while the greater cause may not, as you would expect in a manifold.
126 "An interesting point of principle emerges here. If there are additional dimensions of space, then the true constants of Nature are defined over the totality of the dimensions of space. Those that we see in three dimensions may not therefore be truly fundamental." As I said.
126 "If we exist in a manifold, the extra dimensions could also be large.
137 Proofs of the Prime Number Theorem
138 "We do not observe the laws of Nature; we observe their outcomes. Since these laws find their most efficient representation as mathematical equations, we might say that we see only the solutions of those equations not the equations themselves."
138 'quantizing' a problem is to show "how to generate a set of quantum equations (or laws) from the classical ones."
138 'symmetry breaking' "is responsible for the vast diversity and complexity of the real world."
140 Two forms of the argument from design. Neither one seems to cover the analog/digital form of the argument.
188 "The great unanswered question is whether there exists some undiscovered organizing principle which complements the known laws of Nature and dictates the overall evolution of the Universe...a true addition to what we know of Nature's laws". This question is answered for many mid-size systems. For computers and cars the answer is "mind". The question remains open for other mid-size systems, viz. organisms. Why not consider "mind" in this case too?
188 In looking for "a true addition to what we know of Nature's laws" I think he is looking in the wrong places and overlooking the obvious. Take Mars for example. The lowest entropy structure there are the rovers. Studying planets and ignoring rovers will never reveal the principle of mind.
190 Information processing also requires a mind unless you consider strictly analog behavior to be information processing.
191 Barrow's long term projects for the universe leave out a couple of possibilities: 1. The designer/programmer of his universal computer. The origination of this (these) computers is assumed to be human (like) minds. But why preclude future involvement? 2. Large extra dimensions. This would provide a place that would transcend and continue in spite of appearances and disappearances of 4D universes like ours. This is what I saw in the dentist's chair with the "Transfer of omniscience" modeled by a double pendulum.
192 "He who knows not and knows not that he knows not is a fool.
He who knows not and knows that he knows not is a child.
He who knows and knows not that he knows is asleep.
He who knows and knows that he knows is a wise man.
192 "A complete understanding of our observations of the Universe requires us to take into account those errors which are introduced by the act of observership." Yes. Like assuming that 4D is all there is on a large scale.
210 "The pre-established tripartite harmony between mind and mathematics and the physical world was supported by Hermite, who saw a metaphysical identity between the world of mathematics and physics that the mind shared in. Today, the notion of pre-established harmony seems little more than a disguised version of Platonism. Implicitly, it points to abstract mathematical notions that are the source both of our mathematical ideas and the mathematical aspects of the physical world. Both are reflections, albeit of differing intensity, of the mathematical blueprints that reside in the Platonic heaven." Penrose's three worlds.
212 Philosophies of mathematics: 1) Formalism, 2) Inventionism, 3) Platonic, or realism, 4) Constructivism, 5) Structuralism
220 "Tensors are defined by the fact that their constituent pieces change in a very particular fashion when their coordinate labels are altered in completely arbitrary ways."
234 Stephen Wolfram, Mathematica, and a grainy universe
240 Reasons why discrete mathematics will not suffice for a theory of everything.
242 Heinz Pagels' experience with intellectuals at a NY dinner party
244 Reasons why "soft" sciences don't lend themselves to computation
245 "prospective" properties, e.g. Beauty, Simplicity, Truth, are neither listable nor computable and require ingenuity and novelty to grasp.
245 "No non-poetic account of reality can be complete." This poetic or prospective world seems to be Penrose's "mental world", or my PC
246 "There is no formula that can deliver all truth, all harmony, all simplicity. No Theory of Everything can ever provide total insight. For, to see through everything, would leave us seeing nothing at all." Yes! That's my "transfer of omniscience"!!
©2009 Paul R. Martin, All rights reserved.