Paul Steinhardt: Is Anything Really IMPOSSIBLE?
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- čas přidán 24. 04. 2024
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How do we come to the conclusion that something is impossible? Is anything really impossible? And what is the second kind of impossible, as discussed by the renowned Paul Steinhardt in his book "The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter"? Find out in this short clip from our interview back in 2019!
If you liked this clip, check out our full interview here: • Paul Steinhardt: The S...
Paul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University. His pioneering work has significantly impacted our understanding of the universe’s early moments and its fundamental constituents. Throughout his career, Steinhardt made significant contributions to theoretical cosmology, condensed matter physics, and the study of quasicrystals. He is arguably best known for developing the inflationary model of the early expansion of the Universe, a groundbreaking theory that explains the uniformity of the Universe on large scales. He also challenged conventional cosmological paradigms with his work on the cyclic model of the Universe, proposing a cyclic theory of cosmic evolution in which universes are endlessly born, expand, contract, and rebound.
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My guess is that you could tile a floor with pentagons IF the floor was curved/faceted, and not a plane. According to an online Article from ZMEScience titled, "There are 15 possible ways to cover a floor with pentagonal tiles." It goes on to state regarding tiling a plane: "So far, we know of 15 types of pentagons which could fill the tile - many described by Reinhardt himself, several identified by other mathematicians, even amateurs. In 2015, the 15th type was described, 30 years after the previous. But there was no definitive answer as to whether others also remained. In a rather witty introductory note, Reinhardt said his thesis didn’t demonstrate that the list is exhaustive “for the excellent reason that a complete proof would require a rather large book.”"
Also, pentagons are used in vector graphics, the images created are planes, but I suspect the pentagons vary in size and may not be gap-less, thus violating the intent of the original intent of "impossible" in the example.
Pentagonal tiles are different from regular pentagons. He said regular pentagons specifically, not just pentagons in general.
Paul Steinhardt, to mention it again, I loved your book on finding aluminum-alloy quasicrystals in meteorites! Speaking of assumptions so obviously true that we don't realize we have them, here's a nice one: Do you need a xyzt coordinate space to implement fully self-consistent change and causality? That is, must it _always_ be possible to map events fully into the observer's set of xyzt coordinates to make them causally self-consistent? The answer is no, of course, but do you see why?
📍4:46
Even if you know matter is circumstantial accretions of energy...where does that energy come from? But at least you would know that fundamental assumptions are fundamentally flawed
This guy makes loopholes sounds so cool.
Only "nothing" is impossible!
0:12
I jut knew it, i m always aware of it
Hi brian
It’s amazing ryt
It's impossible for something to be both contradictory and true.
Concrete examples contrasting contradictory equations/formulations from classical physics and mathematics with their non-contradictory counterparts from infinitesimal/non-standard analysis and monadological frameworks:
1) Calculus Foundations:
Contradictory:
Newtonian Fluxional Calculus
dx/dt = lim(Δx/Δt) as Δt->0
This expresses the derivative using the limiting ratio of finite differences Δx/Δt as Δt shrinks towards 0. However, the limit concept contains logical contradictions when extended to the infinitesimal scale.
Non-Contradictory:
Leibnizian Infinitesimal Calculus
dx = ɛ, where ɛ is an infinitesimal
dx/dt = ɛ/dt
Leibniz treated the differentials dx, dt as infinite "inassignable" infinitesimal increments ɛ, rather than limits of finite ratios - thus avoiding the paradoxes of vanishing quantities.
2) Continuum Hypothesis:
Contradictory:
Classic Set Theory
Cardinality(Reals) = 2^(Cardinality(Naturals))
The continuum hypothesis assumes the uncountable continuum emerges from iterating the power set of naturals. But it is independent of ZFC axioms, and leads to paradoxes like Banach-Tarski.
Non-Contradictory:
Non-standard Analysis
Cardinality(*R) = Cardinality(R) + 1
*R contains infinitesimal and infinite elements
The hyperreal number line *R built from infinitesimals has a higher cardinality than R, resolving CH without paradoxes. The continuum derives from ordered monic ("monadic") elements.
3) Quantum Measurement:
Contradictory:
Von Neumann-Dirac collapse postulate
|Ψ>system+apparatus = Σj cj|ψj>sys|ϕj>app
-> |ψk>sys|ϕk>app
The measurement axiom updating the wavefunction via "collapse" is wholly ad-hoc and self-contradictory within the theory's unitary evolution.
Non-Contradictory:
Relational/Monadic QM
|Ψ>rel = Σj |ψj>monadic perspective
The quantum state is a monadological probability weighing over relative states from each monadic perspectival origin. No extrinsic "collapse" is required.
4) Gravitation
Contradictory:
General Relativity
Gμν = 8πTμν
Rμν - (1/2)gμνR = 8πTμν
Einstein's field equations model gravity as curvature in a 4D pseudo-Riemannian manifold, but produce spacetime singularities where geometry breaks down.
Non-Contradictory:
Monadological Quantum Gravity
Γab = monic gravitational charge relations
ds2 = Σx,y Γab(x,y) dxdydyadx
Gravity emerges from quantized charge relations among monad perspectives x, y in a pre-geometric poly-symmetric metric Γ, sans singularities.
In each case, the non-contradictory formulation avoids paradoxes by:
1) Replacing limits with infinitesimals/monics
2) Treating the continuum as derived from discrete elements
3) Grounding physical phenomena in pluralistic relational perspectives
4) Eliminating singularities from over-idealized geometric approximations
By restructuring equations to reflect quantized, pluralistic, relational ontologies rather than unrealistic continuity idealizations, the non-contradictory frameworks transcend the self-undermining paradoxes plaguing classical theories.
At every layer, from the arithmetic of infinites to continuum modeling to quantum dynamics and gravitation, realigning descriptive mathematics with metaphysical non-contradiction principles drawn from monadic perspectivalism points a way forward towards paradox-free model-building across physics and mathematics.
The classical formulations were invaluable stepping stones. But now we can strike out along coherent new frameworks faithful to the logically-primordial mulitiplicites and relational pluralisms undergirding Reality's true trans-geometric structure and dynamics.
You are wrong on point 1) Limits exist - study topology for a clearer understanding. It is a "limit". It makes absolutely perfect sense.
Can't be bothered with the rest of your points... Sorry.
@@Necrozene good luck with your contradictory calculus that you don't think is contradictory!
@@Necrozene
No problem! You clearly don't understand and that's ok. Education is a lifelong journey!
@@MaxPower-vg4vr Just study limits, and you should understand it properly. There is no contradiction. That has been debunked many times, with many clear examples. Good luck with your conspiracy theories. Don't gaslight me.
I bet M.C. Escher could find a way.
The first time u meet me like this
David Deutsch says there are infinitely more KantGoTu solutions than there are possible ones. Why don't you get him on your cast and ask him what he means ... among other things.
Just based on the title. Square circles, married bachelors, 3 wheeled unicycles, nothing morphing into something in zero time, Infinite and concepts moving or being moved in reality.
Directed working mechanisms ordering their own written programming is impossible billions of times over.
≈ mean Earth solar orbital velocity (29800 m/s) = (((Earth velocity)^3/((2 R_☉)^2/(M_☉(solar Schwarzschild radius))))/
((Earth velocity)^2 /((2 R_☉)^2/(M_☉(solar Schwarzschild radius)))))
Black Holes exist in theory ----- but not in reality.
But how could you possibly fit the curvature of Brian's belly in that geometric model? Check mate.
Yeah... the existence of nothing (impossible)
so everyone is an idiot by claiming outrageous ideas until a scientist discovers that it can actually happen.