Derivations based on string theory have a logically consistent foundation, but they only apply to special solutions in unrealistic world models, and they do not explain the simplicity and generality of the results inferred from the other methods[4, 5]… Even allowing for mights and mays, especially from such an accomplished scientist, it is hard to find an argument there. The usual singularity theorems, valid in 4dim asysmptotically flat space, are usually not taken to mean instability of flat space, or exclude it’s existence. Even if there is some hypothetical singularity thm. in higher dimesnion, why would it imply the non-existence of higher dimensional gravitational theory?

The Road to Reality : Roger Penrose : Free Download, Borrow The Road to Reality : Roger Penrose : Free Download, Borrow

To explore the process of pursuing mathematical truth, Penrose outlines a few proofs of the Pythagorean theorem. The theorem can be stated as such, "For any right-angled triangle, the squared length of the hypotenuse [math]\displaystyle{ c }[/math] is the sum of the squared lengths of the other two sides [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math] or in mathematical notation [math]\displaystyle{ a I believe that it is time for a Hard Nosed mathematician to have a look at this problem and provide some help to the Physic community! I was just reporting what Penrose says, and I’m not interested enough in this issue to spend my time on the details of this. In any case I don’t think Penrose has an air-tight argument against extra dimensions, because you can always claim that quantization solves the problem. The full conception of Plato's theory of forms was not limited to only mathematical notions. Mathematics was linked to the concept of Truth but Plato was also interested in the absolute idealized forms of Beauty and Good. Beauty plays an important role in many mathematical discoveries and is often used as a guide to the truth. Questions of morality are of less relevance in this context but are critical with respect to the mental world. Moral debates are outside of the scope of this book but must be considered as science and technology progress. Penrose notes that figure 1.3 has purposely been constructed to be paradoxical in the sense that each world is entirely encompassed by the next. He writes "There may be a sense in which the three worlds are not separate at all, but merely reflect, individually, aspects of a deeper truth about the world as a whole of which we have little conception at the present time."I’m not convinced that his exposition of fourier analysis would be easily graspible for the beginner, but I sure as hell enjoyed it! Not that this is necessarily what Pensrose means when he talks about collapse, though it is hard to tell precisely what he does mean.

The Road to Reality - Penguin Books UK

Penrose asks us to consider if the world of mathematics is in any sense real. He claims that objective truths are revealed through mathematics and that it is not a subjective matter of opinion. He uses Fermat's last theorem as a point to consider what it would mean for mathematical statements to be subjective. He shows that "the issue is the objectivity of the Fermat assertion itself, not whether anyone’s particular demonstration of it (or of its negation) might happen to be convincing to the mathematical community of any particular time". Penrose introduces a more complicated mathematical notion, the axiom of choice, which has been debated amongst mathematicians. He notes that "questions as to whether some particular proposal for a mathematical entity is or is not to be regarded as having objective existence can be delicate and sometimes technical". Finally he discusses the Mandelbrot set and claims that it exists in a place outside of time and space and was only uncovered by Mandelbrot. Any mathematical notion can be thought of as existing in that place. Penrose invites the reader to reconsider their notions of reality beyond the matter and stuff that makes up the physical world.

Just before a total eclipse of the Sun, the Moon is given a large velocity tangential to its orbit at mid-eclipse. Do the effects of relativity prevent the eclipse? Explain.

The Road to Reality: A Complete Guide to the Book Review: The Road to Reality: A Complete Guide to the

Is there any scientific paper, peer-reviewed and published, which supports the claim that (some) spacetimes of the KK form are classically unstable to small perturbations? In January, none other than Seth Lloyd weighed in with an initial proposal (submitted to Science) for an approach to quantum gravity, starting with general notions of quantum computation theory, and with strong correspondences to causal set theory (Sorkin, Dowker, and others):I got the book on Saturday, it should be in every physicist’s library. It reminds me of Klein’s various “Vorlesungen”– lectures, literally “readings”. One thing Peter may not have mentioned is the clever prologue, which I assume takes place in Atlantis 🙂 This book appeals on many levels, including the very “tominess” of it!

The Road to Reality - Wikipedia

Penrose’s point of view is that of a relativist, so his treatment of geometry, general relativity and classical field equations is the deepest and most detailed part of the book. But he also discusses quantum theory extensively as well as the various attempts to quantize gravity. Compared to the general relativity parts, his treatment of particle physics and quantum field theory is rather sketchy, but quite original. Real good review of Penrose’s book by Frank Wilczek in current (Feb 11) Science. Not Free, unfortunately. Says book is very interesting and challenging for beginners, but flawed at the highest level. The following might have been missed by the readers due to it having been posted a couple of days ago, but here it is (to humble ST people) I hope that this would serve as some kind of a signal also to Peter Woit, who has been continually censoring out my messages. This just to help the raise the level of discussion from what it is now. Why not entertain a similar possibility for the issues about the “observed” gauge groups, etc.? Do you really think such a point of view would render a theory based on the latter totally unpredictive?I got the book last july, it’s *very* impressive from a mathematical point of view (I can’t comment on the physics). As a general matter of philosophy though, I very much agree with Penrose’s point of view about Kaluza-Klein. You’ve got enough trouble dealing with the metric degrees of freedom of space-time. You’re just making things worse when you add in a dynamical metric for the fibers of your principal bundle or for some internal space. I think it was fairly obvious that the anonymous poster was talking about Penrose’s claims on the classical stability of KK spacetimes encountered in the string theory literature. I think it is legitimite to dwell on what the precise objection here is. I don’t think it is acceptable to show a tendency to sweep the issue under the rug if it turns out that this particular objection of Penrose’s turns out not to be so well-founded, but put flashing banners if there is the slightest possibility that it might be a valid objection. This is not how scientists should work, though unfortunately similar tendencies prevail in both the string theory camp and the anti-string theory camp. (Penrose’s objection *might* be well founded, I still don’t understand what the precise objection here is.) The literature contains several derivations of Hawking radiation, each with strengths and weaknesses. …