The Road to Reality: A Complete Guide to the Laws of the Universe by Roger Penrose
My rating: 5 of 5 stars
In this amazing book, Roger Penrose looks for a very fundamental issue.
He is looking for a single metric to describe everything.
This is not a unit of reality, however, although this is how he poses the issue.
The problem with selecting a metric, as he shows us over and over, lies in how different metrics arise from localizations on various manifolds. As these metrics are extended beyond the localization, the very structure of these metrics will threaten to buckle. In many instances, the metrics (and their attendant relationships) will no longer be applicable. What this means, in the Kantian (and Badiouian sense) is that these relationships’s applicability will become “undecidable”. In some extreme cases, the relationships may even break down. For instance, black holes are a problem because the expressed relationships that emerge from physics experiments prove to be untenable in black holes (and the big bang) as these relationships decohere and infinities and zeros pop out everywhere.
This search for a metric leads Penrose to reject string theory as a viable relationship form. Each dimension is an extension of the 3 + 1 dimensions of space and time. For instance, gravity is a dimension, weak force is a dimension. Each dimension is an independent mathematical vector of a different “inertial” influence. Additionally, the mathematics of string theory, as well as other theories, proves to be too illusionary. As with post-structural critiques of modernism, Penrose points out that the consistency of string theory relies on theoretical supplements/signs that are attached onto the positions of various types in order to maintain coherency. For instance, superpartners, which have no physical correlative. In other words, the mathematical proliferation of dimensions as well as its immanent affects proves to be unweldly to Penrose because the coherence of the relationships are maintained by theoretical enforcement rather than any direct correlation of math and physical experimentation.
If Penrose was familiar with Badiou, Kant and Derrida, he would be able to recognize that the undecideability of supersymmetry and string theory result from these theoretical supplements. The supplements provide the missing pieces to cohere the theory, so physical experiments prove to be incomplete in their testing. As Penrose points out, string theorists in failing to find superpartners can always push the calibration of their theory to include these partners, just at higher energy levels, which can always lie beyond the ability of technology to generate.
In this sense, it seems to me that string theory and supersymmetry are antinomies of the Kantian variety. Penrose falls fault to this when he theorizes that Quantum Field Theory can be modified (rather than the Einstein’s general relativity) by changing the cut off metric. This is in line with all his discussions to “renormalize” the math so as to remove the variance accumulated by extending localized relations from beyond the area of origin on the manifold. We can always enforce a consistency of a given domain in two ways.
1. To provide a “superpartner” to supplement the terms, to keep phenomenon visible to one another within the domain, as a motion of immanence, as Derrida suggests.
Or.
2. To encapsulate a domain by limiting its identity to its other. From there, we can radically reduce the other to zero, thereby hiding the limitations of a domain, as with Moffe & Laulau with their Hegemony or as with Badiou with a basic atomic “cut” to center the domain as with Being and Event II.
Both of these strategies amount to the same kind of forced coherency by mapping a domain rigidly.
Penrose does offer his own favorite solution; his Twistor theory, which removes the need for extra dimensions beyond 3 + 1. Additionally, he considers this theory by collapsing all the different vector differences held cosmically in string theory into immanent relations that are founded on the very “knots” of space, so that the pre-space twistors contain the information that wider “vibrations” are meant to express. Both theories are incompatible in this regard because of their huge difference in scale.
And while Penrose admits that twistor theory adds nothing physically; that it’s just another way of viewing a situation mathematically, he also realizes the need for us to see things differently than we have.
It is this adherence to a particular view that causes all the problems in the first place. If you look at how these different views are constructed, you’ll see the mathematicians switch from one domain to another through various class equivalences whenever it suits them. When they need to express vectors they will jump to a manifold model, or a more generic (abstract) deformation of an algebra. In other words, we lack enough views. So we supplement the one we have in an attempt to normalize them.
Curiousier still is Penrose’s tiny discussion of consciousness in which he attempts to “renormalize” consciousness in terms of objective reduction. He theorizes that the waveform reduction that collapses due to quantum gravity may be at the seat of consciousness’s ability to complexly surject different sensory views into coherency. This suggestion is of the same kind as his forced synthesis of twistor theory. The satisfaction of trying to find a single metric, a single complex knot of relations that cannot be unraveled but contains all the “moves” is like a physicist trapped on a chess board recognizing the orthogonal formation of board, or as in Futurama the Professor discovering the smallest unit that constitutes the universe is the pixel.
In a real way, Penrose seeks to calibrate physics to the mathematical domain. He doesn’t want beautiful math that doesn’t apply, that is in excess of physics. This is why he creates that chart twice, in which the mathematical is the Truth of which the entirety of the physical is mapped; although mentality is generated from the physical and mathematical/Truth is generated from that.
The Platonic ideologue he insists on lies on the equivalence of function, on the purity of the sameness of process from point to point of the same type. Never-mind that the subatomic particles we find today are largely generated from artificial means. Penrose would assume as sameness of process that forces a universalization, but that is the way metaphysics and science both work, to equate different phenomenon as being identical based on narrow definitions of rational equivalence. This may work in some areas, but as we see, all relations are born locally, within a limited scope. Their extension cosmically creates the basis for which we start to see a degradation of relation qua variance (pollution, or various forces of form-fitting). After all, we can have no irrationality without first being able to posit a rational sheet of complete consistency.
Nonetheless, although this is a lengthy book it is still beautifully written. I wonder who Penrose’s audience is, for he approaches much mathematical complexity in such a short time, talking about basic principles like polynomials and trigonometry before jumping into Lagrangian manifolds and so on. Still, if you hunger for complexity and abstraction, here it is. Much of his explanations of very complex concepts are very clear, although at times we could use more handholding. His pictures are also very interesting and complement his point nicely.
Well worth the effort to read.
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