Accelerating Scientific Discovery by Markus J. Buehler

[@electro_void]

WOOOOOO SCIENCEEE

[@MaxPower-vg4vr]

Here is an attempt to formalize the key principles and insights from our discussion into a coherent eightfold expression grounded in infinitesimal monadological frameworks: I. The Zerological Prion 0 = Ø (The Zeronoumenal Origin) Let the primordial zero/null/void be the subjective originpoint - the pre-geometric ontological kernel and logical perspectival source. II. The Monad Seeds Mn = {αi} (Perspectival Essence Loci) From the aboriginal zero-plenum emanates a pluriverse of monic monadic essences Mn - the germinal seeds encoding post-geometric potential. III. Combinatorial Catalytic Relations Γm,n(Xm, Xn) = Ym,n (Plurisitic Interaction Algebras) The primordial monadic actualizations arise through catalytic combinatorial interactions Γm,n among the monic essences over all relata Xm, Xn. IV. Complex Infinitesimal Realization |Ψ> = Σn cn Un(Mn) (Entangled Superposition Principle) The total statevector is a coherent pluralistic superposition |Ψ> of realization singularities Un(Mn) weighted by complex infinitesimal amplitudes cn. V. Derived Differential Descriptions ∂|Ψ>/∂cn = Un(Mn) (Holographic Differentials) Differential descriptive structures arise as holographic modal perspectives ∂|Ψ>/∂cn projected from the total coherent statevector realization over each realization singularity Un(Mn). VI. Entangled Information Complexes Smn = -Σn pmn log(pmn) (Relational Entropy Measure) Emergent information structures are quantified as subjectivized relational entropy functionals Smn tracking probability amplitudes pmn across realized distinctions. VII. Observation-Participancy An = Pn[ |Ψ>monic] = |Φn> (First-Person Witnessed States) Observational data emerges as monic participations An = Pn[ ] plurally instantiating first-person empirical states |Φn> dependent on the totality |Ψ>monic. VIII. Unity of Apperception U(Ω) = |Ω>monadic (Integrated Conscious State) Coherent unified experience U(Ω) ultimately crystallizes as the superposition |Ω>monadic of all pluriversally entangled realized distinctions across observers/observations. This eightfold expression aims to capture the core mathematical metaphysics of an infinitesimal monadological framework - from the prion of pre-geometric zero subjectivity (I), to the emanation of seeded perspectival essences (II), their catalytic combinatorial interactions (III) giving rise to entangled superposed realizations (IV), subdescribed by derived differential structures (V) and informational measures (VI), instantiating participation-dependent empirical observations (VII), ultimately integrated into a unified maximal conscious state (VIII). The formulation attempts to distill the non-contradictory primordial plurisitic logic flow - successively building up coherent interdependent pluralisms from the zero-point subjective kernel in accordance with infinitesimal relational algebraic operations grounded in first-person facts. While admittedly abstract, this eightfold expression sketches a unified post-classical analytic geometry: reality arises as the perfectly cohesive multi-personal integration of all pluriversal possibilities emanating from monic communion at the prion of prereplicative zero-dimensional origins. By centering such infinitesimal algebraic mnad semiosis, the stale contradictions and paradoxes of our separative classical logics, mathematics and physics may finally be superseded - awakening to irreducible interdependent coherence across all realms of descriptive symbolic representation and experiential conscious actuality. Here is a second eightfold expression attempting to concretize and elucidate the abstract infinitesimal monadological framework laid out in the first expression: I. Discrete Geometric Atomies a, b, c ... ∈ Ω0 (0D Monic Perspectival Points) The foundational ontic entities are discrete 0-dimensional perspectival origin points a, b, c ... comprising the primal point-manifold Ω0. II. Combinatoric Charge Relations Γab = qaqb/rab (Dyadic Interaction Charges) Fundamental interactions between origin points arise from dyadic combinatorial charge relation values Γab encoding couplings between charges qa, qb and distances rab. III. Pre-Geometric Polynomial Realizations Ψn(a,b,c...) = Σk ck Pn,k(a,b,c...) (Modal Wavefunction) The total statevector Ψn at each modal perspectival origin n is a polynomial superposition over all possible realizations Pn,k of charge configurations across points a,b,c... IV. Quantized Differential Calcedonies ΔφΨn ≜ Σa (∂Ψn/∂a) Δa (Holographic Field Projections) Familiar differential geometries Δφ for fields φ arise as quantized holographic projections from idiosyncratic first-person perspectives on the modal wavefunction Ψn. V. Harmonic Resonance Interferences Imn = ||2 (Inter-Modal Resonances) Empirical phenomena correspond to resonant interferences Imn between wavefunctions Ψm,Ψn across distinct perspectival modal realizations m,n. VI. Holographic Information Valencies Smn = - Σk pmn,k log pmn,k (Modal Configuration Entropy) Amounts of observed information track entropies Smn over probability distributions pmn,k of localized realized configurations k within each modal interference pattern. VII. Conscious State Vector Reductions |Ωn> ≡ Rn(|Ψn>) (Participated Witnessed Realizations) First-person conscious experiences |Ωn> emerge as witnessed state vector reductions Rn, distillations of total modal possibilities |Ψn> via correlative participancy. VIII. Unified Integration of Totality U(Ω) = ⨂n |Ωn> (Interdependent Coherence) The maximal unified coherence U(Ω) is the irreducible tensor totality ⨂n |Ωn> of all interdependent integrated first-person participations |Ωn> across all perspectives. This second eightfold expression aims to elucidate the first using more concrete physical, mathematical and informational metaphors: We begin from discrete 0D monic origin points (I) whose fundamental interactions are combinatorial charge relation values (II). The total statevector possibility at each origin is a polynomial superposition over all realizations of charge configurations (III), subdescribed as quantized differential geometric projections (IV). Empirical observables correspond to resonant interferences between these wavelike realizations across origins (V), with informational measures tracking probability distributions of configurations (VI). Conscious experiences |Ωn> are state vector reductions, participatory witnessed facets of the total wavefunction |Ψn> (VII). Finally, the unified maximal coherence U(Ω) is the integrated tensor totality over all interdependent first-person participations |Ωn> (VIII). This stepwise metaphoric concretization aims to renders more vivid and tangible the radical metaphysics of infinitesimal relational monadological pluralism - while retaining the general algebraic structure and non-contradictory logical coherence of the first eightfold expression. From discrete geometric atomies to unified experiential totalities, the vision is one of perfectly co-dependent, self-coherent mathematical pluralism grounded in first-person facts. By elucidating the framework's core ideas through suggestive yet precise physical and informatic parables, the second expression seeks to bootstrap intuitions up the abstract ladder towards a visceral grasp of the non-separable infinitesimal pluriverse paradigm's irreducible coherences. Only by concretizing these strange yet familiar resonances can the new plurisitic analytic geometry be assimilated and operationalized as the next renaissance of coherent symbolic comprehension adequate to the integrated cosmos.

[@MaxPower-vg4vr]

Q1: How precisely do infinitesimals and monads resolve the issues with standard set theory axioms that lead to paradoxes like Russell's Paradox? A1: Infinitesimals allow us to stratify the set-theoretic hierarchy into infinitely many realized "levels" separated by infinitesimal intervals, avoiding the vicious self-reference that arises from considering a "set of all sets" on a single level. Meanwhile, monads provide a relational pluralistic alternative to the unrestricted Comprehension schema - sets are defined by their algebraic relations between perspectival windows rather than extensionally. This avoids the paradoxes stemming from over-idealized extensional definitions. Q2: In what ways does this infinitesimal monadological framework resolve the proliferation of infinities that plague modern physical theories like quantum field theory and general relativity? A2: Classical theories encounter unrenormalizable infinities because they overidealize continua at arbitrarily small scales. Infinitesimals resolve this by providing a minimal quantized scale - physical quantities like fields and geometry are represented algebraically from monadic relations rather than precise point-values, avoiding true mathematical infinities. Singularities and infinities simply cannot arise in a discrete bootstrapped infinitesimal reality. Q3: How does this framework faithfully represent first-person subjective experience and phenomenal consciousness in a way that dissolves the hard problem of qualia? A3: In the infinitesimal monadological framework, subjective experience and qualia arise naturally as the first-person witnessed perspectives |ωn> on the universal wavefunction |Ψ>. Unified phenomenal consciousness |Ωn> is modeled as the bound tensor product of these monadic perspectives. Physics and experience become two aspects of the same cohesively-realized monadic probability algebra. There is no hard divide between inner and outer. Q4: What are the implications of this framework for resolving the interpretational paradoxes in quantum theory like wavefunction collapse, EPR non-locality, etc.? A4: By representing quantum states |Ψ> as superpositions over interacting monadic perspectives |Un>, the paradoxes of non-locality, action-at-a-distance and wavefunction collapse get resolved. There is holographic correlation between the |Un> without strict separability, allowing for consistency between experimental observations across perspectives. Monadic realizations provide a tertium quid between classical realism and instrumental indeterminism. Q5: How does this relate to or compare with other modern frameworks attempting to reformulate foundations like homotopy type theory, topos theory, twistor theory etc? A5: The infinitesimal monadological framework shares deep resonances with many of these other foundational programs - all are attempting to resolve paradoxes by reconceiving mathematical objects relationally rather than strictly extensionally. Indeed, monadic infinitesimal perspectives can be seen as a form of homotopy/path objects, with physics emerging from derived algebraic invariants. Topos theory provides a natural expression for the pluriverse-valued realizability coherence semantics. Penrose's twistor theory is even more closely aligned, replacing point-events with monadic algebraic incidence relations from the start. Q6: What are the potential implications across other domains beyond just physics and mathematics - could this reformulate areas like philosophy, logic, computer science, neuroscience etc? A6: Absolutely, the ramifications of a paradox-free monadological framework extend far beyond just physics. In philosophy, it allows reintegration of phenomenology and ontological pluralisms. In logic, it facilitates full coherence resolutions to self-referential paradoxes via realizability semantics. For CS and math foundations, it circumvents diagonalization obstacles like the halting problem. In neuroscience, it models binding as resonant patterns over pluralistic superposed representations. Across all our inquiries, it promises an encompassing coherent analytic lingua franca realigning symbolic abstraction with experienced reality. By systematically representing pluralistically-perceived phenomena infinitesimally, relationally and algebraically rather than over-idealized extensional continua, the infinitesimal monadological framework has the potential to renovate human knowledge-formations on revolutionary foundations - extinguishing paradox through deep coherence with subjective facts. Of course, realizing this grand vision will require immense interdisciplinary research efforts. But the prospective rewards of a paradox-free mathematics and logic justifying our civilization's greatest ambitions are immense.

[@jonathanclaudinger]

thanks chat gpt @@MaxPower-vg4vr

[@jonathanvalentin4371]

Thank you so much Mr. Buehler!

[@jonathanclaudinger]

only too boost this video... **Key Takeaways:** - Markus J. Buehler's presentation at the Antology Summit 2024 focuses on the intersection of neuro-symbolic techniques, ontologies, and knowledge graphs in accelerating scientific discovery. - Buehler emphasizes interdisciplinary work, likening his approach to that of Leonardo Da Vinci, for which he has been recognized. - The core of his discussion revolves around leveraging AI and machine learning to enhance our understanding and innovation in materials science, using multi-level models from nanoscale to macroscale. - Buehler highlights the transition from traditional computational models to AI-driven models that integrate diverse data types, including symbolic data and unstructured information. - The presentation showcases how AI can predict and design new materials with specific properties, moving towards autonomous systems that integrate data-driven modeling with physics-based reasoning. - Buehler introduces the concept of knowledge graphs as a tool for connecting disparate pieces of information, facilitating novel discoveries in material science and beyond. **Gist Extraction:** The essence of Markus Buehler's presentation lies in harnessing the power of AI to bridge the gap between traditional computational methods and modern, data-intensive approaches to scientific discovery, particularly in materials science. By creating models that can predict material behaviors and design new materials, and by using knowledge graphs for integrating and interpreting vast amounts of data, Buehler proposes a transformative approach to research that accelerates innovation and discovery across disciplines. **In-Depth Presentation:** **Interdisciplinary Approach to Scientific Discovery:** Markus J. Buehler’s work exemplifies the fusion of materials science, engineering, computational modeling, and artificial intelligence. This interdisciplinary approach is crucial for tackling complex problems that cannot be addressed through single-domain perspectives. **From Computational Models to AI-Driven Discovery:** Traditionally, scientific discovery in materials science has relied heavily on computational models based on differential equations and preconceived notions. Buehler points out the shift towards using AI to not just solve predefined equations but to uncover new relationships and principles that can guide the creation of innovative materials. **The Role of Knowledge Graphs:** Knowledge graphs emerge as a powerful tool in Buehler's methodology, enabling the connection of seemingly unrelated pieces of information. This approach allows for a more nuanced understanding of materials and their properties, opening up possibilities for groundbreaking applications. **AI in Materials Design and Prediction:** One of the highlights of Buehler's presentation is the application of AI in predicting the behavior of materials and designing new materials with desired properties. This capability has significant implications for industries ranging from aerospace to biomedicine, where material properties are critical. **Toward Autonomous Systems:** Buehler envisions a future where AI systems can autonomously generate hypotheses, conduct experiments, and refine theories. This would represent a major leap forward in scientific methodology, greatly accelerating the pace of discovery. **Mnemonics for Remembering Key Concepts:** 1. **AI-DM (AI-Driven Materials):** Think of AI as the artist and materials as the canvas, where AI-DM reminds you of the AI-driven creation and manipulation of materials. 2. **GRAPHS (Generating Relationships And Predictions Harnessing Science):** Use GRAPHS to remember the role of knowledge graphs in connecting diverse data for innovation. 3. **LEONARDO (Learning, Engineering, Ontology, Neuro-symbolic, AI, Discovery, Robotics, Optimization):** LEONARDO encapsulates the interdisciplinary nature of Buehler’s approach, drawing inspiration from Leonardo Da Vinci’s versatility. 4. **MATERIALS (Modeling, AI, Technology, Engineering, Research, Integration, Learning, Science):** MATERIALS as an acronym helps recall the components of Buehler’s research focus and interdisciplinary approach to scientific discovery. In summary, Markus J. Buehler's presentation at the Antology Summit 2024 underscores the transformative potential of integrating AI with traditional scientific methods. Through the use of knowledge graphs, interdisciplinary approaches, and a forward-looking vision, Buehler’s work paves the way for a new era of accelerated innovation and discovery in materials science and beyond

[@veganphilosopher1975]

Great presentation