 发现 ms@ms.lt +370 607 27 665 My work is in the Public Domain for all to share freely. 读物 书 影片 维基百科 Introduction E9F5FC Understandable FFFFFF Questions FFFFC0 Notes EEEEEE Software Upload 数学笔记 Complex numbers are more natural than real numbers or quaternions because complex numbers have simpler nondegenerate quadratic forms: {$Q(u)=u_1^2+u_2^2+\cdots +u_n^2$}. For we can insert a scalar {$i$} and that converts any minus sign into a plus sign. Jennifer Mather. The Case for Octopus Consciousness: Unity. https://www.mdpi.com/2673-4087/2/4/30 Spalio 4ta, 14:00 Lietuvos laiku, skaitys pranešimą Edinburgh Category Theory Seminar Posina Venkata Rayudu nLab: Sphere spectrum The sphere spectrum is the suspension spectrum of the point. The homotopy groups of the sphere spectrum are the stable homotopy groups of spheres. The sphere spectrum is the higher version of the ring Z of integers. See also: nLab: Suspension Laws of form Concatenation is "saying". Saying multiple times is the same as saying once. {$a^2=a$}. Cross is negating. It is crossing. Negating twice is identity. {$b^2=1$}. We can have a different kind of negating or a different kind of negated for which negating twice is reversal. {$c^2=-1$} Matematikos žinojimo rūmų sparnus sieja algebra veda iš centro į sąrašą analizė vedą iš sąrašo (indukcijos) į centrą (limitą) Apsikeičia - ar tai padalinimų ratas? Kiekviename sparne požiūriai prisideda +0, +1, +2, +3. Auxiliary loops in space-time are compatible with the rays in space-time, perhaps in this way the mind is compatible with the brain. That might be relevant for the hierarchy of agency. Consider a Clifford algebra with infinitely many generators {$a_i$} and {$b_j$} such that {$a_i^2=1$} and {$b_j^2=-1$}. How would different interpretations satisfy an eightfold periodicity? John Bolender. The Self-Organizing Social Mind. Consider the ways of constructing a 2x2 matrix by adding a generator {$a_i$} and then {$b_j$}, or alternatively, {$b_j$} and then {$a_i$}. Grammar of sociology in terms of a pattern language grounding concepts such as "generation", "the right biography", "class", "both agressors lose". Geometry arises on a vector space when we place a quadratic form on it, {$Q:V\rightarrow K$}. It gives a notion of length of a vector because {$Q(av)=a^2Q(v)$}, and also a notion of distance because there is a symmetric bilinear form {$B(v,w)=\frac{1}{2}(Q(v+w)-Q(v)-Q(w))$}. https://en.wikipedia.org/wiki/Cayley%E2%80%93Klein_metric Are there niine Cayley-Klein geometries? Try to undersand Morita equivalence in terms of irreducible representations. Equivalence up to isomorphism is relevant for "user requirements" as opposed to "material implementation". This is relevant for Bott periodicity. Wave function arises when two systems interact. As given by orthogonal Sheffer polynomials. In Lie group for rotations, SO(3), the bracket of [x,y] gives you z. In choice frameworks, such as the simplex, the center is the basis for geometry and the vertices are the basis for matter. Together can they ground general relativity? I dreamed of the grouping of examples from branches of mathematics by considering whether they involve, for example, aspects of mathematics, logic, semantics, and so on. Minkowski space. Time {$-t^2$} has us step out (thus reversing direction), space {$x^2+y^2+z^2$} has us step in. Why doesn't adding a pair of generators {$a_1 b_1$} to a Clifford algebra change it? Generators {$a_j$} for which {$a_j^2=1$} are experienced directly whereas generators {$b_j$} for which {$b_j^2=-1$} express the change in direction upon reflection, thus stepped out. Jane Loevinger's psychometrics = Maslow's hierarchy of needs. E8 is "worry about the needs of another". E9 is "be perfect". Do the generators of Clifford algebras which square to +1 and -1 encode, respectively, covariant and contravariant tensors? Differential equations for engineers Equality is inherently contradictory. Ivan. Was or was not regional politics helpful for potential democratic transition in Russia? Novosibirsk, Tatarstan. Partial knowledge forgetful functors fibrations, lenses Consciousness https://www.quantamagazine.org/what-a-contest-of-consciousness-theories-really-proved-20230824/ Fractal systems - fires, turbulences, hurricanes - model themselves and in that sense can leverage information. Counterquestions are a foundation for learnability. Each counterquestion defines a domain of new knowledge where we had no facts that we could rely on. Mind and Life Institute. Varela. Supporting contemplative research. https://www.mindandlife.org/events/summer-research-institute/ European Summer Research Institute. Buddhist. Nathaniel Virgo Modeling agency Improving a model of the environment = Bayesian prior. Controller gets new information and also the system changes over time. Don't care about the previous states, just the prior (t) and the current issue (t+1) Kalman filter: when the prior is a Gaussian then the posterior is also a Gaussian So only the means and variances need to be stored Bart Jacobs 2020: A channle based perspective on conjugate priors - this pops out of an adjunction Unifilar generator. A generator is unifilar if it is deterministic given output. They form a separate category. Forgetful functor: Unifilar Generator to Generator. In BorelStoch this has a right adjoint. Usually forgetful functor has a left (free) adjoint. A right adjoint of a forgetful functor is cofree. In this case the forgetful functor is forgetting both a fact about the objects and the morphisms. How does this relate to lenses? Strongly representable Markov categories are cool. Epistemic model and dynamical model. You want your model of the system to be unified. Supermaps - holes - contexts. Pragmatic approach. Context defines meaning. Robert Brandom. Making It Explicit. {$\textrm{Set}^{op}$} atomic boolean algebras. Map back into Set. Map back out PowerSet. Simplexes observe coordinate systems. df/dx = f. Can be expressed through the notion of infinity (Taylor series) {$e^x$}. Or through periodicity (trigonometry, Euler's equation) {$e^{ix}$} Jim in Oneonta. Adapt, improvise, overcome. Sheaf Representation of Monoidal Categories Monoidal Categories MonCat. Presheaf F: L->MonCat and Sheafs. Generalizing Stone's Theorem. Lax functor - may be relevant for allowing perspectives to be not associative yet related. Spivak and Kent: Ologs The volume of a unit sphere in n-dimensions goes up for small n, reaches a maximum at n=5, then goes down. https://en.wikipedia.org/wiki/Volume_of_an_n-ball https://julesh.com/2018/08/16/lenses-for-philosophers/ David Jaz Myers Eri Conformal and analytic is the same. Energy can be defined as the "separation constant" in Schroedinger's equation. If we can separate the wave function into a time dependent function and a position dependent function, then we can segregate the two sides of the equation so that one side depends on time, the other side depends on position, and both sides are constant, and that constant is the energy. Grothendieck. Structure and Form - or the Voice of Things Peter Scholze - condensed math Visual frameworks connects visualization with semantic contexts such as gravity. Note that gravity is based on a quadratic power law and yields the fivefold conics. Absolutism based on relativism is good. Relativism based on absolutism is bad. Objectivity based on subjectivity is good. Subjectivity based on objectivity is bad. The mind that does not know is based on the mind that knows and not the other way around. This is the rule of consciousness and the basis for morality. There is a gap between the quantum ether (the quantum foam) and the waves that propagate through it. Particles don't exist, particles are the medium. Waves exist in the medium. Threesome Vector bundles. Jimmy told me about vector bundles having a threefold sense: Data, gluing, and 3 sets coming together. This happens in 1 degree, 2 degrees, 3 degrees. Folk psychology. Daniel Dennett suggested studying this. Contact him. In the book on interpretations of quantum mechanics, there is the question of what is real. For example, in electromagnetism, the gauge can be adjusted by adding any gradient. This can change whether the change is transmitted by the speed of light or whether that speed is infinite and it happens instantaneously. But these two scenarios also raise the question of the reality of the "wiggle". What is real is a moral choice. Is the medium real? Or is the wiggling real? The wiggling creates the wave that moves across the medium. The medium is made of particles and anti-particles that appear from the foam. Explain why we get alternating signs for the boundary https://researchsemin The many-worlds interpretation of quantum mechanics and the Born rule Lev Vaidman (Tel Aviv University) ( view ) Mon May 22, 19:00-20:30 (7 days from now) Abstract: I will argue that the many-worlds interpretation is the best interpretation of quantum mechanics and discuss the status of the probability assignments in this deterministic theory.ars.org/seminar/AlgebraParticlesFoundations Applying a boundary map twice gives zero. Applying it twice removes two vertices, and this can be done in different orders, yielding different signs, canceling out. For the Snake Lemma, add a zero vector space before the first kernel and add a zero vector space after the last cokernel. Then we have the eightfold way with seven mappings. Can large language models work by simply transforming existing input - taken to be grammatical - to preserve grammaticality. Choice Frameworks A category with a zero object has semantic symmetry with regard to choice frameworks. A category without a zero object, but with initial objects and terminal objects which differ, such as the categories Set or Cat, have syntactic asymmetry. Introduction to Commutative Algebra Atiyah & Macdonald. Rings, ideals, modules, dimensions Looking at an ellipse in various ways yields all of the conic shapes. We can get a breaking at infinity. Thus this is a way to ground infinity. What about looking at a circle? We look through the point of the cone, which is where our eye is. Mobius transformations How are perspectives transformed? How are triangles mapped to triangles ? C.K.Raju. Time: Towards a Consistent Theory David Corfield's video. Colin McLarty: semiotics as the language of biology - logic in a biological key - trying to categorify this? Moebius transformations Emotional sphere Daniele Cuneo. The emotional sphere in the light of the Abhinavabharati He had 8 or 9 emotions including tranquility. https://en.wikipedia.org/wiki/Abhinavagupta One of his very important contributions was in the field of philosophy of aesthetics with his famous Abhinavabhāratī commentary of Nāṭyaśāstra of Bharata Muni Freedom House Report Fields Institute The Fields Institute. Workshop on the Applications of Topology to Quantum Theory and Behavioral Economics. Differentiation Algebra Abstract algebra. Dummit and Foote. Meditations by Marcus Aurelius Meditations by Renee Descartes On Liberty by John Stuart Mill Octavia Butler - Parable of the Sower, Parable of the Talents Cixin Liu - Trijų kūnų problema (Kitos knygos) Ursula Le Guin - The Left Hand of Darkness, Dispossessed A sum of particle clocks is like a prism operator (in the proof for singular homology that homotopic maps induce the same homomorphism for the homology groups) but without the minus signs. Wisdom Wisdom distinguishes everything and slack, what is whole and what is free, holisticity and laxity. Physics https://physics.stackexchange.com/questions/15082/how-did-feynman-derive-the-physics-of-medallion-vs-plate-wobble-rate Grad-Curl-Div Think of curl as surjection followed by injection. How does curl relate to local-global distinction at nLab ? https://mathinsight.org/curl_definition_line_integral curl in terms of line integrals https://en.wikipedia.org/wiki/Exterior_derivative#Gradient Exact sequence: Grad, Curl, Div Group theory Nathan Carter "Visual Group Theory" https://www.youtube.com/playlist?list=PLwV-9DG53NDxU337smpTwm6sef4x-SCLv Purcell. Electricity and Magnetism 90 degrees + 90 degrees can equal anything. But specifically can go from the diameter of a cube (standing on its vertex) to the vertex and back on the diameter to any point. But the same is true for 120 + 120. Quaternions act like a gauge - 3 dimensions are unspecified - but identified with the complex i. The Hilbert space that models the spin state of a system with spin 𝑠 is a 2𝑠+1 dimensional Hilbert space. And spin can be half-integered. Think of the Hilbert space as everything divided into 2s+1 perspectives. Simplicial sets Amplituhedron Lauren Williams - Combinatorics of the amplituhedron N. Arkani-Hamed, Lecture #1, Spacetime & Quantum Mechanics, Total Positivity & Motives - 09/03/2019 Causality Donald Davidson, On the Very Idea of a Conceptual Scheme. Proceedings and Addresses of the American Philosophical Association. Vol. 47 (1973 - 1974), pp. 5-20 (16 pages) Michael Friedman, Reconsidering logical positivism. 1999. Cambridge. Peter Machamer & Gereon Wolters, Thinking about causes: From Greek philosophy to modern physics. 2007. University of Pittsburgh. Bell's inequalities Richard Gill. Bell's theorem is an exercise in the statistical theory of causality Causal Set Theory Universal concepts such as universal confounders the confounder. Ambiguity is described by equations. Atmosphere has mass of 5.15×10^{18} kg Person breathes 10 tons of oxygen = 10,000,000 grams of oxygen in their lifetime 16 grams of oxygen has 6*10^23 atoms of oxygen 1 gram of oxygen has 0,375*10^23 atoms of oxygen (1) formulate a hypothesis, (2) deduce a testable consequence of the hypothesis, (3) perform an experiment and collect evidence, and (4) update your belief in the hypothesis. Modeling experience from old self to new self - Bayesian analysis - prior belief + new evidence = revised belief Jacobi polynomials have a notion of combinatorial space that may be relevant for thermodynamics as it relateswo disjoint sets malping into their union. Pearl seeing vs. Doing Homology sets up potential equivalences - they may be actual equivalences, which yield identities - or nonequivalences which are generators. Rotation accords with orientation (of a simplex) accords with an imaginary number i or j. Orientation is related to permutation as with the linearization for orthogonal polynomials. Causality Judea Pearl: The Fundamental Equation of Counterfactuals {$Y_X(u)=Y_{M_X}(u)$}. Relate to independent trials - throwing away a sheet of paper (a module). Choice Is Monty Hall problem related to quantum probability? Stephen Wolfram. The Concept of the Ruliad. Ravi Vakil: Main theme of mathematics - convert harder problems to linear algebra Ergodic theorem Chomsky: Successor function derives from the merge function applied unitarily to a single object. Parsing hierarchy Speculation: The difference in the measurements of the Hubble constant may relate to the history of the universe. Early in the universe the heavier particle families (in the parsing hierarchy) may have been predominant. And they may be the source of the megastructures of the universe. Field with one element Thomas noted the symmetry of {$x^0=1$}. Relate this to {$F_1$}, choosing one out of one, or none out of none. Schroedinger's cat Do the probabilities of a superposition evolve as per the phasor? Do they run through all possibilities between wavelengths? And does that mean that the decision of whether Schroedinger's cat is awake or asleep depends on the exact moment that we make the measurement? And what does that say about time? and superpositions? Is this a valid interpretation of superposition? http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf Fulton Curve Book Randomness How is randomness related to the Riemann Hypothesis? Forms of matter express geometry as uniformity and give rise to mass behavior even randomness. Entropy - physics is related to symmetry - Shannon entropy is related to information. And how does that relate to randomness? Symmetry breaking - choosing one possibility. From symmetry breaking randomness appears and information is constructed. Deterministic is replaced by irreversibility. Randomness as derived from a wall that allows for independent events, as with the other, or with transcendence. Randomness as lack of knowledge. Multiplying by quaternion j reverses angular momentum for electron. Is spin a clock? Like a particle clock? https://en.m.wikipedia.org/wiki/Zitterbewegung Seems to give behavior faster than the speed of light. Linear regression In multiple regression the constant {$b_0$} acts like free space, the initial compartment. The random variables are like compartments. Statistics Foundation of statistics is models. Distinguish the signal and the noise. Ignore the noise. Topology Heine-Borel theorem Proof of Heine-Borel theorem. Manya Raman-Sundstrom. A pedagogical history of compactness trivial tangent bundles on spheres? Hamiltonian is the sum of all the projections onto the energy eigenstates with the energies being the weights. Threesome Vector cross product is an example of the three-cycle. Study of variables Use of variable as an operator (or an action) as in https://en.wikipedia.org/wiki/Operational_calculus but also group multiplication, group action. Kervaire-Milnor formula {$\Theta = \Pi B$} where {$B=a_m2^{2m-2}(2^{2m-1}-1)B_{2m}/4m$} In the unfolding of math consider math as given by generators and relations the relations are equivalence classes https://neo4j.com Neo4J graph database management Richard Feynman. Negative probability. Dennis Stanton. An Introduction to Group Representations and Orthogonal Polynomials. Selcuk Bayin. Representation theory Tammo tom Dieck. Representation Theory. Generalized Linear Models J. A. Nelder, R. W. M. Wedderburn. Generalized Linear Models. 1972. Lattice 8 is special because {$\sqrt{8/4}=\sqrt{2}$} is the distance between neighbors but also the interspersed lattice in constructing the E8 lattice. 240 is the kissing number. {$128=dim(\mathbb{O}\otimes\mathbb{O}^2)$} Statistics http://stat.vadoveliai.lt/ Are the conditions for coverings the basis for completeness? Dobinski's formula relates Bell numbers and e. {$B_n=\frac{1}{e}\sum_{k=0}^{n=\infty}\frac{k^n}{k!}$} Gian-Carlo Rota. The Number of Partitions of a Set. 1964. Quaternionically differentiable is linear. 18.4 penrose. Hyperbolic length is one half of the rapidity it represents. Laws of physics are time-symmetric for particles traveling at the speed of light so time does not change Localization arises from local shielding by local interactions. That is what weakens global interactions which othwrwise exist. Complexity theory https://en.wikipedia.org/wiki/PCP_theorem Every decision problem in the NP complexity class has probabilistically checkable proofs Discourse https://en.wikipedia.org/wiki/Overton_window Window of political discourse: Unthinkable - Radical - Acceptable - Sensible - Popular - Policy Lambda Calculus Awodey. Topological Representation of the Lambda Calculus Study choice, probability, statistics. Physics First Person Physics In the Standard Model, fermions are not their own antiparticles, but in some theories they can be. Among other things, this involves the question of whether the relevant spinor representations of the groups Spin(p,q) are complex, real (‘Majorana spinors’) or quaternionic (‘pseudo-Majorana spinors’). The options are well-understood, and follow a nice pattern depending on the dimension and signature of spacetime modulo 8. Two reflections give you a rotation. So is a reflection the square root of a rotation? And does that relate to spinors? Bosons - real representations, fermions - quaternionic representations. Functions Richard Southwell describes how mathematical functions can be visualized by: (1) elements and arrows (2) Wiring diagrams (3) fibres (4) bouquets (5) graphs (6) ontology logs (7) categories Dirac's plate trick Plate trick Coxeter. Regular polytopes. Includes prehistory. Boole. Coxeter diagram {$D_n$} symmetry group of demicube: every other vertex of a hypercube. Is that related to a coordinate space? Combinatorially, can we flip the vectors of the demicube to get a coordinate system? Cube reflections given by vectors u, v, w from the center of the cube to the center of a face, the center of an edge, and the center of another edge. And the angles between the vectors are pi/2, pi/3 and pi/4. And the two edge midpoints are separated by pi/3 so rotating through six such edges gets you back. And that is the chain for the Dynkin diagram. Conjugation is an example of reflection. Finite field with one element Choosing one out of one: Driving on a winding road, each turn is a choice of one out of one. Whereas a fork is a choice of one out of two, a usual intersection is a choice of one out of three and so on. The 4 returns: natural return (value of landscape), economic return (restart agriculture), social return, humans return. Locality is the whole achievement of the continuum. Local means low overhead and the actual global time frame is even lower overhead. Locality arises with orthogonality, assumes measurement, observers, space time wrapper. Differentiation changes level. {$x^n$} number of levels of volatility, number of derivatives Spaces of states nLab: State Classical bit: line segment [0,1] Qubit: shaped like an American football {$\begin{pmatrix} a & b+ic \\ b-ic & d \end{pmatrix}$} Think of probabilities {$a, 1-a$} and mediator {$b \pm ic$}. We have {$a^2+b^2+c^2\leq a$} and {$a^2+b^2+c^2 = a$} for pure states. Rotate {$a-a^2$} from 0 to 1 around the a-axis. It is the MacMahon Master Theorem that unifies the angular momentum properties of composite systems in the binary build-up of such systems from more elementary constituents. Semilocally path connected avoids Zeno's paradox. Universal covering as naming schemes. Robert Gilmore. Group Theory. XIV. Group Theory and Special Functions. Relates Lie groups and orthogonal polynomials. Local - reversible, global (default) not reversible ("Not every cause has had its effects") Modeling Quantum Magic Rectangles: Characterization and Application to Certified Randomness Expansion Sean A. Adamson∗ and Petros Wallden and generalization of the magic squares How are games in game theory (with incomplete information, partial information) characterized by probability distributions. Charactization and application to certified randomness expansion In Cartesian categories you can copy and delete information. (John Baez - Rosetta Stone) How does that relate to Turing machine? Alytaus kredito unija Kapitalas 700,000 EUR, pelnas 43,000 EUR, paskolinta 4,600,000 EUR. Bose statistics - can't assign labels. Fermi statistics - can assign labels to particles. Information capacity is zero if probability is the same for all cases but also if one case is given 100%. Information transmission requires asymmetry. Otherwise you cannot define choice. Probability Kleisli categories and probability - 01 - The Giry monad Giry monad related to probability. Creating what you can feel certain about. (Continuity.) Building up levels of certainty through topological invariants. Stone's theorem: continuous implies differentiable "belt trick", aka the "Dirac scissors" or "Balinese candle dance When two events happen (the measurement of spins) there is a frame where one happens before the other. So if they are causally connected (as with spin measurements) there needs to be a distinguished frame. But that could be the frame in which they were initially entangled. So entanglement posits the existence of such a distinguished frame. Path integrals depend on the number of points in space, or the number of interactions. But my approach suggests that this number is actually given by the degree of x in the relevant polynomial. Quantum computing https://en.wikipedia.org/wiki/Probabilistic_programming probabilistic programming paradigm (quantum computing) Measurement based quantum computer vs gate based quantum computer lattice surgery https://en.wikipedia.org/wiki/Toric_code Quantum error correcting code topological quantum computer https://en.wikipedia.org/wiki/One-way_quantum_computer The Geometry of Semidefinite Programming Amelia: [The axiom of function extensionality is] inconsistent with many axioms of a more "computational" nature. For example, "formal Church's thesis" says that for any function N→N, there is a "program" (we call it a realizer) that realizes it. You can kinda see what goes wrong: this would be able to tell e.g. "λ x → x" and "λ x → x + 0" apart. You could imagine an assignment of realizers that sidesteps this, though, so to see that it's actually inconsistent takes slightly more work. Have all finite limits is equivalent to Having terminal objects Having a product for any pair of objects Having an equalizer for any pair of parallel arrows These are the building blocks for limits The 4th movement of Beethoven's Symphony No. 5. Conducted by Arthur Nikisch. Recorded in 1913. {$\alpha$} and {$\beta$} count ascents and descents and these are steps forwards or backwards in the unfolding of space (in time?) and so they may relate to John's picture of evolution taking us forward and backward in time. https://ww3.math.ucla.edu/dls/emily-riehl/ video about contractibility An isomorphism is a special morphism but truly it is a pair of morphisms that are inverses to each other. There may be many such pairs relating two objects but in each pair the inverses are unique with respect to each other. So it is similar to complex conjugation. Filmavimas OpenShot eksportuoti 30 fps nes iPhone filmuoja 30 fps Open Source Software to Thank: Linux, Ubuntu, OpenShot, Dia, GIMP Shot with an iPhone XS Max. Schuller on Stone's Theorem In physics, orthogonal polynomials relate what is necessary (top down) and actual (bottom up) as with string theory, questions and answers. The original spectral theorem: Look for subrepresentations such that S is a one-dimensional matrix eigenvalue. Induction argument. Classical (both x, p) and quantum (x). Bald and bankrupt Eastern Europe Wick's theorem - are operators of the same particles - propagator connects Evolution is indicated by learnability and also by sparse communication and natural differences between hierarchies, different orders of magnitude, allowing for a natural hierarchy of niches. Not only the laws of physics are sparse but also the states in nature are sparse. Rules of physics plus configuration space plus location within that space. Source of contradiction We are finite, our system is finite, but the Spirit is infinite dimensional Uncertainty principle - has to do with representations - representation adds a perspective - so that interferes with measuring certain things. Minimization operator mu - superhero - who clings to ledges and other such things and is stretched and blown by the wind. And the shape mu gives the shape of his body clinging to the left. https://en.wikipedia.org/wiki/%CE%9C_operator {$\mu$}-operator I had a dream that i was professor anthony zee... But in a quantum superposition. Was i z or not z ? Z or not z? ..... is there a third way? Yes but there is a fourth way .... Nevermind z here is m4w! A qubit specifies the relation between affirmation and negation of probabilities. In matrix form, it provides a complex number which is the coefficient that gets multiplied to the negation (in calculating the new affirmation) and whose conjugate gets multipled to the affirmation (in calculating the new negation). In classical bits, this coefficient is simply zero. Five zones of scattering can be thought of as Measurement establishes a quantity with regard to boundaries - it establishes the zone within which it is - identifies with a step in the algebra - whereas analysis demarcates the boundaries. Kojin Karatani, Sabu Kohso - Architecture as Metaphor_ Language, Number, Money (1995) semi-join lattice semilattice Quantum physics Duality Simplex Think of -1-cell as the center (of all things), the spirit. And think of 0-cell not simply as a point but as a 0-dimensional open arc (the point shell) with regard to that center (the spirit). The point shells are glued onto the spirit, and similarly, open arcs are glued onto point shells, and so on, inductively. In what sense are Feynman diagrams relativistic given that they have directions for time and for space? Instead of thinking of speed of light, think of a clock that doesn't tick, so that t=0 always. And this is the case for the quantum harmonic osciallator and for the particle-clocks with no steps. One {$\exists x$}, all {$\forall x$}, many {$\neg\exists x \wedge \neg\forall x$}. Bohm Pilot Wave, Thomas Spencer Relative invariance - more global than another Relate the three-cycle (taking a stand, following through, reflecting) to Kan extension as defined by filtering objects and morphisms, acting on them, and then taking the colimit or limit on that filter. https://en.wikipedia.org/wiki/Algorithmic_information_theory Gregory Chaitin = Shannon + Turing = Compression-Decompression as understanding. https://en.wikipedia.org/wiki/Cristian_S._Calude Philosophy of computation Life in life Thinking about the expansion of the universe as a reduction of density, by which the mass of particles becomes ever less important, by which we have an increase of entropy (becoming less deliberate). And we can reverse this by starting with an increase in entropy and arriving at the expansion of the universe. Matematika išplaukia iš (poreikių tenkinimo) algoritmų taikymo, vedančio iš duotybių į bendrybes. O tos bendrybės įkūnija, išreiškia tam tikrus prieštaravimus, juos paverčia sąvokomis, kurias galima mąstyti toliau. Pavyzdžiui, apskritimas iškyla iš begalinės simetrijos visom kryptim, arba iš virve aprėpto ploto maksimalizavimo. Information is what you learn. What you learn grows at the boundary, has the shape of the boundary. A shape can be thought of as being created by integrating over these boundaries as they increase. Tai-Danae Bradley: Information is on the Boundary Shannon entropy: the amount of surprise Prove that the matrix made up of eigenvectors diagonalizes a matrix. Potential energy source {$\frac{y}{2}$} (adding free cell) is in balance with kinetic energy source {$i\frac{\partial}{\partial y}$} (half-link) Santykis su Dievu yra atgarsis, kaip kad dalelytė turi santykį su savo lauku. Fizikos dėsnių raida yra pavyzdys Dievo įsakymo patobulinimo. Symmetry Observing symmetry requires breaking symmetry.
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