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Sir Roger Penrose just delivered a masterclass in physical skepticism. In this sharp exchange with Brian Cox, he dismantles the dangerous allure of mathematical aestheticism. We often fall into the trap of assuming that if an equation is beautiful, it must be true. But Sir Roger warns that "beauty...

97,475 görüntüleme • 3 ay önce •via X (Twitter)

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––Charlie Barnett: "Consciousness and the computability of it. It sounds like, or at least in the past, that you've implied that consciousness is computable. Some, like Roger Penrose, have argued the opposite, and he's argued that consciousness is non-computational, and he uses Gödel's incompleteness theorems to argue that the mind can see truths that a purely algorithmic system can't derive, and therefore the brain must be using some kind of non-computable process when it comes to consciousness, something beyond what machines can do. What would you say to a view like that? David Deutsch: Yet again, it is using an impossible conception of what knowledge is. So Penrose thinks that when we see a proof of a mathematical theorem, we are touching certainty, we are god-like entities when we're mathematicians. But that's not true. Our mathematical knowledge is conjectural, just like our knowledge of physics. It's even more removed from our senses, because it's not true that the interior of our brains and the interior of our thoughts is more accessible to us than the world we perceive through our senses, or the world that we perceive through our theories, the center of the sun. We know lots about the center of the sun, even though no one has ever perceived it, and perhaps no one ever will. So mathematical truths are based on conjecture. What Gödel showed is that there is no firm ground underneath mathematical theories either. There's no way of proving that the standards of proof that we currently use are perfectly rigorous. And there have been cases in history where they have shown not to be rigorous. I think Pernot, who was the first to axiomatize the principles of the natural numbers, his first attempt at that was wrong. And it's interesting that he did not say, well, I've axiomatized them, therefore there's nothing to them other than my axioms. No, he said, oh dear, my axioms don't correctly represent the real number, the natural numbers, so I have to change them. So he was grasping, conjecturing for a reality, an abstract reality, just like scientists try to grasp physical reality. So the same epistemology applies to mathematics as it does to science."

Deutsch Explains

13,826 görüntüleme • 1 yıl önce

Thomas Nagel dismantles relativism in one paragraph. In a 1995 talk on reason, the philosopher exposes a fatal flaw at the heart of the relativist position: "Claims to the effect that a type of judgment expresses a local point of view are inherently objective in intent. They suggest a picture of the true sources of those judgments which places them in an unconditional context." In other words, the moment you say "all truth is relative," you've already made an absolute claim. Nagel sharpens this into a precise logical trap: "The judgment of relativity or conditionality cannot be applied to the judgment of relativity itself." The relativist wants to stand outside all perspectives and declare that no perspective is universal. But that declaration is itself a universal perspective. He then drives it home: "To put it schematically, 'everything is subjective' must be nonsense, for it would itself have to be either subjective or objective. But it can't be objective, since in that case it would be false if true. And it can't be subjective, because then it would not rule out any objective claim including the claim that it is objectively false." The argument is elegant in its completeness. If "everything is subjective" is an objective truth, it defeats itself immediately because it would mean at least one thing is objective. But if it's merely a subjective opinion, it has no power to challenge objectivity at all. Either way, relativism collapses under its own weight. What's striking is how often this self-refuting structure goes unnoticed in everyday debates about truth, culture, and morality. The person who says "that's just your perspective" is quietly assuming their own perspective is the correct one. Nagel's point isn't that objectivity is easy to achieve, only that abandoning it entirely is incoherent.

Mateus — eu/acc 🇪🇺

27,895 görüntüleme • 4 ay önce

“Don’t Panic.” THE ANSWER IS 42 The ultimate question remains deliciously unsolved. In Douglas Adams’ 1979 masterpiece, a supercomputer Deep Thought spends 7.5 million years computing the Answer to the Ultimate Question of Life, the Universe, and Everything—only to deliver the cryptic integer 42. This is pure mathematical comedy gold: a dimensionless, context-free number that mocks our human obsession with finding meaning in a cosmos governed by probabilistic quantum fields, general relativity, and the second law of thermodynamics. Adams weaponizes absurdity to remind us that the universe is under no obligation to make sense to three-dimensional carbon-based lifeforms evolved on a minor planet orbiting an unregarded yellow sun. Yet the joke lands hardest because 42 is real—it’s the atomic number of molybdenum, appears in light refraction formulas, and even shows up in the cosmic microwave background anomaly known as the “Cold Spot.” The galaxy doesn’t need our questions to be coherent; it just keeps expanding at 73 km/s/Mpc anyway. 42 (The Answer, apparently definitive, Answer) Adams’ genius is turning computational complexity into existential slapstick. By making the universe’s deepest truth a prime-number-age crisis, he forces physicists and philosophers alike to confront the limits of reducibility. In an era of Large Hadron Colliders and quantum supremacy claims, 42 is the perfect reminder that some patterns may be true yet forever uninterpretable—much like the fine-structure constant ≈ 1/137 that still baffles theoreticians. If 42 really is the Answer, what exact question would make the universe finally make sense to you? 🚀🧠 Primary source: The Hitchhiker’s Guide to the Galaxy, Douglas Adams - Grok Imagine Images

Lacey

99,131 görüntüleme • 8 ay önce

🚨 New episode of AFTERMATH (my new series) is about Unification of Mathematics & Analytic Psychology. Following Carl Jung, I propose that all mathematical objects & ideas come from archetypes in our Collective Unconscious, so Math is a Portal into the Human Psyche. KEY POINTS: 1. All mathematical objects and ideas (such as perfect lines and planes) are rooted in the shared structural elements of our Collective Unconscious, which Carl Jung called archetypes. These mathematical archetypes produce identical images in our individual minds – explaining why everyone imagines the same idealized mathematical forms; even those forms that don't appear in the outer, physical reality. 2. Similarly to how individuals project their undesired or repressed character traits onto others (manifesting the Jungian archetype of the Shadow), entire societies projected the mathematical archetype of Flat Space onto the surface of the Earth, accepting as an axiom that it was flat. This unconscious belief exemplifies how unintegrated archetypal forces shape our perception of physical reality in the absence of conscious scrutiny. 3. Progress and evolution occur when people recognize and integrate mathematical archetypes, as exemplified by Pythagoreans' insight 2500 years ago that the surface of the Earth might be spherical. Moving from unconscious acceptance to evidence-based inquiry mirrors the process of owning and integrating personal shadow elements. 4. The Enduring Spell of Flat Space: Even though we now realize that Earth is round, most of us still reflexively perceive the Universe as a three-dimensional flat expanse. This unconscious attachment to the archetype of the 3D Flat Space hampers serious consideration of curved or higher-dimensional geometries. When we integrate the archetypes of the 3D Flat Space, the 3D Sphere, and so on, new dimensions of Reality may well open up to us. 5. Brilliant scientists, such as Einstein, Wigner, Weil, Poincaré, and Ramanujan have stressed the essential role of the unconscious (and dream-based) revelations in their work. Such flashes of insight align with Jung's view of archetypes spontaneously emerging from the Collective Unconscious, fueling humanity's creative and mathematical breakthroughs.

Edward Frenkel

34,344 görüntüleme • 1 yıl önce

Adding more GPUs will never make a machine conscious. Nobel Prize-winning physicist Roger Penrose just dismantled the entire AI race’s core assumption. Right now, the industry operates on one belief. Build massive data centers. Scale the models. AGI will just “wake up.” Penrose destroys this completely. Penrose: “There is this sort of view that once you make a computer complicated enough or something, it suddenly becomes aware. I just don’t believe that. There’s no reason to believe that.” A machine can compute better than any human alive. But computation is not awareness. Penrose: “There is something quite different involved in understanding things, in being aware of things, of feeling things, which is not part of computations.” We’re confusing rule-following with actual intelligence. Penrose: “The keyword is the word ‘understanding.’ You can follow rules alright, but we don’t understand what we’re doing. The understanding is the key point.” Models today are exceptional at processing data. At mimicking logic. But true understanding requires consciousness. Penrose: “It doesn’t make sense to say of a device that it understands something if it’s not even aware of it. There is something much more profound in being conscious of something.” And here’s what should terrify every AI lab on earth. Penrose: “I believe that the brain is following the laws of physics, sure. We don’t have a good picture of the laws of physics.” Penrose: “Quantum mechanics is not an answer to the way the universe operates. It’s a partial answer. It’s incomplete.” We’re trying to engineer synthetic consciousness using classical computation. While biological consciousness likely operates on physics we haven’t even discovered yet. The race to AGI isn’t just an engineering problem. It’s a frontier science problem. The labs are hiring engineers. The problem might require physicists who don’t exist yet.

Dustin

196,858 görüntüleme • 5 ay önce