Darwinism vs. mathematics in a post-modern world

WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT? Infinity – Max Tegmark Excerpt: real numbers with their infinitely many decimals have infested almost every nook and cranny of physics, from the strengths of electromagnetic fields to the wave functions of quantum mechanics: we describe even a single bit of quantum information (qubit) using two real numbers involving infinitely many decimals. https://www.edge.org/response-detail/25344

As should be needless to say, the preceding findings are very comforting to overall Christian concerns. Here is a video that goes over the preceding findings, and how they relate to Christian presuppositions, in a bit more detail

Double Slit, Quantum-Electrodynamics, and Christian Theism- video https://www.youtube.com/watch?v=AK9kGpIxMRM Double Slit, Quantum-Electrodynamics, and Christian Theism - paper https://docs.google.com/document/d/19lfxxHkkKOTSdfDKvhlKvBC5Fjl_x8dEUwzFqW8SeC0/edit

Four dimensional space was also mentioned in 'The Mathematics Of Higher Dimensionality' video. As was the necessity for Four-dimensional space in the formulation General Relativity also mentioned in the video:

Four-dimensional space - with 4-D animation: Excerpt: The idea of adding a fourth dimension began with Joseph-Louis Lagrange in the mid 1700s and culminated in a precise formalization of the concept in 1854 by Bernhard Riemann.,,, Higher dimensional spaces have since become one of the foundations for formally expressing modern mathematics and physics. Large parts of these topics could not exist in their current forms without the use of such spaces.,,, Einstein's concept of spacetime uses such a 4D space, though it has a Minkowski structure that is a bit more complicated than Euclidean 4D space. https://en.wikipedia.org/wiki/Four-dimensional_space animation https://upload.wikimedia.org/wikipedia/commons/5/55/8-cell-simple.gif

What was not mentioned in the  'The Mathematics Of Higher Dimensionality'  video is that special relativity is itself also based on a single four-dimensional continuum now known as Minkowski space. In fact, the higher dimensional nature of special relativity was a discovery that was made by one of Einstein math professors in 1908 prior to Einstein's elucidation of General Relativity in 1915.

Spacetime Excerpt: In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the definition of a spacetime interval that combines distance and time. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded. Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed that spacetime becomes curved in the presence of mass or energy.,,, Einstein, for his part, was initially dismissive of Minkowski's geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.[10]:151–152 Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime. https://en.wikipedia.org/wiki/Spacetime

Moreover, in the following video, starting at the 5:39 minute mark, you can see how these four dimensional spacetimes that undergird both special relativity and general relativity reveal two very different eternities to us.

Quantum Mechanics, Special Relativity, General Relativity and Christianity - video https://youtu.be/gKggH8jO0pk?t=339

The following video is also of related interest to mathematics as it relates to overall Christian concerns:

Gödel, Infinity, and Jesus Christ as the Theory of Everything - video https://youtu.be/x1Jw5Y686jY

Verse and Music:

Colossians 1:15-20 The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross. Touch The Sky (lyric video) - Hillsong UNITED - YouTube https://www.youtube.com/watch?v=y1RQciil7B0

bornagain77

January 13, 2018

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Here is a bit more information on the relationship between nature and the 'platonic world' of mathematics In the following video, the discovery of the higher dimensional nature of the square root of negative one, which is integral to quantum mechanics, and the discovery of higher dimensional geometry, which is integral to General Relativity, are discussed:

The Mathematics Of Higher Dimensionality - Gauss & Riemann - video https://www.youtube.com/watch?v=mxy3JhPRlV0

The history of the square root of negative one is particularly interesting to look at. Descartes had rejected complex roots and coined the derogatory term "imaginary" to describe the square root of negative one. Whereas, Gauss, who was the mathematician who finally clearly explained the higher dimensional nature behind the square root of negative one, suggested that complex magnitudes be called "lateral" instead of "imaginary" magnitudes since they represent a dimensional extension of the continuum. Gauss also proposed that complex magnitudes be awarded "full civil rights." The author further comments, in the language of Plato's allegory of the cave, complex numbers represent "forms" from a higher dimension casting "shadows" on the real number line.

Complex Magnitudes Excerpt: Descartes had rejected complex roots and coined the derogatory term "imaginary" to describe the square root of negative one, , but Leibniz thought that "The divine spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and non-being, which we call the imaginary root of negative unity." Gauss invented the "complex plane" (shown below) to represent these quantities. He suggested that complex magnitudes be called "lateral" instead of "imaginary" magnitudes since they represent a dimensional extension of the continuum. Gauss also proposed that complex magnitudes be awarded "full civil rights." In the language of Plato's allegory of the cave, complex numbers represent "forms" from a higher dimension casting "shadows" on the real number line. http://www.keplersdiscovery.com/ComplexNum.html

And in quantum mechanics, we find that the square root of negative one is necessary for describing the wave packet prior to measurement.

Why do you need imaginary numbers (the square root of negative one) to describe Quantum Mechanics? “Quantum theory needs existence of an x such that x^2= -1. The reason for this is that orthogonal function spaces, of dimension greater than 2, cannot exist otherwise. In fact the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement. Even the Canonical Commutation Relation doesn't need it. And nor do the eigenvalue equations. In those, any general scalar will do. But in the wave packet, you need an i.” - Steve Faulkner - Philosophy of Science, Logic, Epistemology https://www.researchgate.net/post/Why_do_you_need_imaginary_numbers_to_describe_Quantum_Mechanics2

What was not mentioned in the preceding video, or in the article, is that the wave function is also represented as being in an infinite dimensional Hilbert space:

Wave function Excerpt "wave functions form an abstract vector space",,, This vector space is infinite-dimensional, because there is no finite set of functions which can be added together in various combinations to create every possible function. http://en.wikipedia.org/wiki/Wave_function#Wave_functions_as_an_abstract_vector_space Why do we need infinite-dimensional Hilbert spaces in physics? You need an infinite dimensional Hilbert space to represent a wavefunction of any continuous observable (like position for example). https://physics.stackexchange.com/questions/149786/why-do-we-need-infinite-dimensional-hilbert-spaces-in-physics The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960 Excerpt: We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity.,,, The two theories operate with different mathematical concepts: the four dimensional Riemann space and the infinite dimensional Hilbert space, http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Here is an interesting quote about the 'profound role' of infinite dimensional Hilbert Spaces in quantum mechanics:

The Applicability of Mathematics as a Philosophical Problem - Mark Steiner - (page 44) Excerpt: The role of Hilbert spaces in quantum mechanics.. is much more profound than the descriptive role of a single concept. An entire formalism-the Hilbert space formalism-is matched with nature. Information about nature is being "read off" the details of the formalism. (Imagine reading off details about elementary particles from the rules of chess-castling. en passant-a la Lewis Carro;; in Through the Looking Glass.) No physicist today understands why this is possible. https://books.google.com/books?id=GKBwKCma1HsC&pg=PA44

Moreover, we find that this infinite dimensional Hilbert space takes an infinite amount of information to describe properly.

Explaining Information Transfer in Quantum Teleportation: Armond Duwell †‡ University of Pittsburgh Excerpt: In contrast to a classical bit, the description of a (quantum) qubit requires an infinite amount of information. The amount of information is infinite because two real numbers are required in the expansion of the state vector of a two state quantum system (Jozsa 1997, 1) http://www.cas.umt.edu/phil/faculty/duwell/DuwellPSA2K.pdf Quantum Computing – Stanford Encyclopedia Excerpt: Theoretically, a single qubit can store an infinite amount of information, yet when measured (and thus collapsing the superposition of the Quantum Wave state) it yields only the classical result (0 or 1),,, http://plato.stanford.edu/entries/qt-quantcomp/#2.1

bornagain77

January 13, 2018

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