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38+ teosta 8,850 jäsentä 100 arvostelua 15 Favorited

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Born in England, the son of a geneticist, Roger Penrose received a Ph.D. in 1957 from Cambridge University. Penrose then became a professor of applied mathematics at Birkbeck College in 1966 and a Rouse Ball Professor of Mathematics at Oxford University in 1973. Penrose, a mathematician and näytä lisää theoretical physicist, has done much to elucidate the fundamental properties of black holes. With Stephen Hawking, Penrose proved a theorem of Albert Einstein's general relativity, asserting that at the center of a black hole there must evolve a "space-time singularity" of zero volume and infinite density, in which the current laws of physics do not apply. He also proposed the hypothesis of "cosmic censorship," which claims that such singularities must possess an event horizon. In 1969 Penrose described a process for the extraction of energy from a black hole, as well as how rotational energy of the black hole is transferred to a particle outside the hole. In addition, Penrose has done much to develop the mathematics needed to unite general relativity, which deals with the gravitational interactions of matter, and quantum mechanics, which describes all other interactions. (Bowker Author Biography) näytä vähemmän
Image credit: Roger Penrose at Festival della Scienza Oct 29 2011


Tekijän teokset

Shadows of the Mind (1994) 930 kappaletta
The Nature of Space and Time (1996) 724 kappaletta
Quantum Physics of Consciousness (2011) — Avustaja — 15 kappaletta
Oxford en Cambridge (1950) 12 kappaletta

Associated Works

What Is Life? : With Mind and Matter and Autobiographical Sketches (1992) — Esipuhe, eräät painokset849 kappaletta
The Oxford Book of Modern Science Writing (2008) — Avustaja — 802 kappaletta
Six Easy Pieces and Six Not-So-Easy Pieces (1963) — Johdanto, eräät painokset395 kappaletta
White Mars (1999) 201 kappaletta
'Nature and the Greeks' and 'Science and Humanism' (Canto original series) (1996) — Esipuhe, eräät painokset89 kappaletta
Explaining Consciousness: The Hard Problem (1997) — Avustaja — 82 kappaletta
The Nature of Time (1986) — Avustaja — 41 kappaletta
Coffee with Einstein (Coffee with...Series) (2008) — Esipuhe — 33 kappaletta

Merkitty avainsanalla




Chapter 4. A complex number is of the form a ib, where i is an imaginary number, the square root of -1. All regular rules of algebra apply to complex numbers, and it turns out that they govern the behavior of the universe at the tiniest scales. Very good. Illustration of the use of complex numbers in the convergence and divergence of power series, where for ex. 1 x^2 x^4 x^6 ... = (1-x^2)^-1. Manually adding up some number of partial sums converges to the "answer" only where |x|1, adding partial sums diverges from the "answer" (1 2^2 2^4 2^6 ...=(1-2^2)^-1 = -1/3... say what???). Same convergence/divergence issue for (1 x^2)^-1, where |x|=1 is also the point of difference. We see why when we make use of the complex number plane, where real number x is a particular case of z=x iy where y=0. Or at least we should, I don't quite follow this voodoo, which results in the same "circle of convergence" for those 2 functions using different sets of points along the outer edge of the circle: one set is on the x axis, 1 and -1, the other on the y axis, i and -i. The point however seems to be that using concept of complex numbers and the complex number plane (where y axis is in units of i, and 2 2i = 2 units right, 2 units up from 0) provides insight into behavior of real numbers. The famous Mandelbrot Set lies in the complex plane, where the dark parts of the image are where an iteration of a complex number function does not diverge.

Chapter 3. Numbers in the physical world. Only in the last century is it evident that the set of integers, including negative numbers, have direct physical relevance, with discovery that protons made up of 3 quarks, one of which has negative charge. Unclear if system of rational numbers has any physical relevance; perhaps in quantum mechanical probabilities, where there's a finite number of possibilities.

Chapter 2. Hyperbolic geometry, illustrated by Escher in this conformal representation in Euclidean perspective. Is the shape of the universe hyperbolic rather than flat (Euclidean), such that a familiar square does not exist on the cosmological scale? Penrose suspects so. He's wrong; according to more recent (2013) discoveries, the universe is indeed flat. A massive cosmological sized square could be drawn through our universe with 4 parallel sides and 4 right angles. Whew.

Chapter 1. The author's prejudices. A portion of each world encompasses the entirety of another world. Most importantly for this book, not all mathematics is relevant to the physical world, but all action in the physical world is governed by mathematical law.
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Merkitty asiattomaksi
lelandleslie | 32 muuta kirja-arvostelua | Feb 24, 2024 |
I enjoyed the first few chapters on computation/algorithms. The physics chapters however moved way too quickly for my comprehension. The last two chapters where he finally gets around to drawing everything together into his thesis are pretty unconvincing.
Merkitty asiattomaksi
audient_void | 26 muuta kirja-arvostelua | Jan 6, 2024 |
A really excellent book, explaining how conscious understanding is beyond something that is computable, and exploring how this might arise from the physical world of atoms, electrons and quantum mechanics, and whether there may be some link with the so-called “measurement problem”. Just brilliant.
Merkitty asiattomaksi
jvgravy | 6 muuta kirja-arvostelua | Dec 22, 2023 |
I managed to understand (mostly) approximately the first half of the book, but couldn't keep up when Penrose dipped into conformal space-time diagrams. I really liked the opening discussion on entropy and the explanation that early entropy was very special. In a sense the entropy was very low, which is why it can keep increasing, but also that as the universe was very hot at first that the entropy was as high as it could be. Only recommended for students of general relativity and cosmology!
Merkitty asiattomaksi
jvgravy | 11 muuta kirja-arvostelua | Nov 23, 2023 |



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