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Combined display of all available logs of Objective Mathematics. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).

• 17:28, 29 May 2025 Lfox talk contribs created page The block universe (temporary name) (Created page with "The aim of this essay is to argue against the metaphysical picture of the block universe. I'm writing this for people like Andrei, who recognize that there is some sort of contradiction with determinism, but have no clue how to reconcile it with what we know about physics. Maybe I should title it "the arrogance of modern physics." It's so ridiculous for them to say we know everything except for like dark matter and confinement and quantum gravity and times earlier than...") Tag: Visual edit
• 17:05, 24 May 2025 Lfox talk contribs created page Logic (Created page with "I think that set theory and formal logic need to be re-done rationally. This is a big project. I will list out some of my problems with formal logic below: == Material implication == <math>A \implies B</math> is held to equivalent to <math>\neg A \vee B</math>, so anything follows from a falsehood. This doesn't fit natural language reasoning. For example, suppose that it is not raining outside right now, and I say "if it were raining outside right now, then communism w...") Tag: Visual edit
• 19:17, 18 May 2025 Lfox talk contribs moved page Category theory to Category theory: abstracting mathematical construction (essay) without leaving a redirect
• 18:52, 18 May 2025 Lfox talk contribs created page File:Screenshot 2025-05-18 at 2.51.41 PM.png
• 18:52, 18 May 2025 Lfox talk contribs uploaded File:Screenshot 2025-05-18 at 2.51.41 PM.png
• 23:35, 14 May 2025 Lfox talk contribs created page Category theory (Created page with "In real life, and in particular, in mathematics, there are ''entities'' and ''actions''. We can consider types of entities. For example, let us consider two such types <math>X</math> and <math>Y</math>, where <math>X = \text{apples}</math> and <math>Y = \text{pie}</math>. There is a specific apple sitting in my fridge, There's an action of baking apple pie too broad Definition of a category '''Definition.''' A ''category'' <math>\mathcal{C}</math> consists o...") Tag: Visual edit: Switched
• 21:53, 12 March 2025 Lfox talk contribs created page Multiplication (Created page with "'''Multiplication''' is [TODO]") Tag: Visual edit
• 22:43, 9 February 2025 Lfox talk contribs created page Equivalence relation (Redirected page to Identity) Tags: New redirect Visual edit
• 19:37, 9 February 2025 Lfox talk contribs created page Identity (Created page with "'''Identity''' is a primary, axiomatic concept. It refers to the "this"-ness of an object, the fact that it is this and not that. Mathematics conceptualizes identity using the equals ("=") symbol. == Equivalence relations == Things can be identical in some respects, but not others. Standard mathematics formalizes this idea as follows. Let <math>S</math> be a set. An ''equivalence relation'' is a relation <math>\sim </math> on <math>S</math> satisfying three axioms...") Tag: Visual edit
• 02:32, 28 November 2024 Lfox talk contribs created page On the Electrodynamics of Moving Bodies (Created page with "In this article, I will explain Einstein's paper ''On the Electrodynamics of Moving Bodies''. My goal is not to do a historical investigation of exactly what Einstein thought. My goal is to justify special relativity == The problem == Einstein begins by noting the following problem: Maxwell's equations have a different interpretation in some reference frames than they do in others. He gives the following example, involving a magnet and a hoop of wire which are in mo...") Tag: Visual edit
• 19:58, 8 November 2024 Lfox talk contribs created page Against models (essay) (Created page with "In modern civilization, there are two perspectives on what science is. One perspective, which I will call the "identification perspective," is that the task of science is to identify facts of reality.")
• 04:14, 29 October 2024 Lfox talk contribs created page Perturbation theory (Created page with "== Solution to an equation == An equation is a stipulation that two things are equal. Sometimes equations have free variables. In such a case, we can say that a ''solution'' to the equation is an assignment of specific values to its free variables, such that the equation holds true. There are three types of solutions that an equation might have. === 1. Exact solutions === To have an exact solution is a bit of a vague concept. Characteristics of "exact" solutions *...") Tag: Visual edit
• 21:41, 15 October 2024 Lfox talk contribs created page Uncertainty (Created page with "== How do we measure continuous quantities? == First, set up some sort of "triangulation" of the space in which the continuous quantity can take values. For example, a ruler is a "triangulated" line. Typically some sort of quantitative system is chosen to keep track of the cells; e.g. for a ruler we count how many ticks there are. A measurement of a continuous quantity is simply an identification of which one of those intervals the continuous quantity lies inside. It's...") Tag: Visual edit
• 07:10, 6 October 2024 Lfox talk contribs created page Entropy (Created page with "We should proceed inductively, thinking about entropy in the way that it was initially thought of by people like Clausius, and only then proceeding to Boltzmann's explanation of it in terms of micro-states. == Original version == As background, we start with the fact that there is such a thing as heat, and such a thing as work. They have some interchangeability: You can turn heat into work via an engine (boil water to push a turbine up), and you can turn work into hea...") Tag: Visual edit
• 04:41, 6 October 2024 Lfox talk contribs created page On a Heuristic Viewpoint Concerning the Production and Transformation of Light (Created page with "These are my notes on Einstein's paper, On a Heuristic Viewpoint Concerning the Production and Transformation of Light, where he explains the photoelectric effect and founds quantum mechanics. I am reading the translation in ''The Dreams that Stuff is Made Of'' by S. Hawking. == Background == ??") Tag: Visual edit
• 04:27, 6 October 2024 Lfox talk contribs created page On the Law of Distribution of Energy in the Normal Spectrum (Created page with "These are my notes on a paper by Max Planck. I am reading the translation in Hawking's book, ''The Dreams that Stuff is Made Of''. == Background == I'm not completely clear on what a blackbody is. One definition: a blackbody is a body that can absorb or emit any frequency of wavelength. Another definition (Hawking's): a blackbody is the light produced by a glowing hot object. I think that the latter definition is better than the former, because it's clearer what it ref...") Tag: Visual edit
• 01:38, 6 October 2024 Lfox talk contribs created page Coordinate invariance: a manifesto (Created page with "What ''is'' a coordinate system? It is a way of assigning numbers to any point in a given region. The point of a coordinate system is that it allows us to quantitatively describe what is happening to an extended object (at each point of the object). [TODO that second sentence under-sells the value of coordinate systems.] Traditionally, a coordinate system is conceived of as a map <math>R \rightarrow \mathbb{R}^n </math> from the region <math>R</math>, to tuples of <mat...") Tag: Visual edit
• 15:08, 22 August 2024 Lfox talk contribs created page File:Geodesic vs 40th parallel .png
• 15:08, 22 August 2024 Lfox talk contribs uploaded File:Geodesic vs 40th parallel .png
• 05:24, 22 August 2024 Lfox talk contribs created page The Limits of Limits (Created page with "'''Essay prompt''': Is the idea of 'limit' indispensable? Neutral? A hindrance? I contend that ''some'' concept of limit is indispensable in mathematics, but that one must be very cautious in using standard mathematics' concept of limit. The focus of this essay is mainly negative. I criticize two common attitudes towards limits: the "empiricist" attitude, which believes in effect that we don't need limits at all, and the "rationalist" attitude (the attitude of modern...")
• 05:24, 22 August 2024 Lfox talk contribs deleted page Limits Limited by Reality (bad title)
• 05:22, 22 August 2024 Lfox talk contribs created page Limits Limited by Reality (Created page with "'''Essay prompt''': Is the idea of 'limit' indispensable? Neutral? A hindrance? I contend that ''some'' concept of limit is indispensable in mathematics, but that one must be very cautious in using standard mathematics' concept of limit. The focus of this essay is mainly negative. I criticize two common attitudes towards limits: the "empiricist" attitude, which believes in effect that we don't need limits at all, and the "rationalist" attitude (the attitude of modern...")
• 04:38, 22 August 2024 Lfox talk contribs created page File:Pictorial proof of geometric sum.png
• 04:38, 22 August 2024 Lfox talk contribs uploaded File:Pictorial proof of geometric sum.png
• 04:33, 22 August 2024 Lfox talk contribs created page File:Limit of circles.png
• 04:33, 22 August 2024 Lfox talk contribs uploaded File:Limit of circles.png
• 03:22, 21 July 2024 Lfox talk contribs created page Occam's razor (Created page with "Occam's razor is the principle that if a fact of reality admits multiple valid conceptual identifications, it is preferable identify it using concepts one already has. == Examples == === Kepler's law === Suppose you make some measurements and you find blahblahblah.[TODO] == The traditional concept == The traditional concept of Occam's razor is a mess. It says") Tag: Visual edit
• 03:00, 21 July 2024 Lfox talk contribs created page Limits (essay) (Created page with "'''essay prompt''': Is the idea of 'limit' indispensable? Neutral? A hindrance? I contend that some concept of 'limit' is indispensable in mathematics, physics, and beyond. I will make this case inductively, beginning with an exposition of the facts of reality that gave rise to the need for such a concept, and concluding with a proper definition of 'limit'. [TODO maybe also talk about invalid versions of the concept?] == Fact of reality 1: == The Earth is a sphere, bu...") Tag: Visual edit
• 17:22, 8 July 2024 Lfox talk contribs created page E (Created page with "'''e''' is the == Geometric interpretation == thumb|" A ray through the unit hyperbola ''x''² − ''y''² = 1 at the point (cosh ''a'', sinh ''a''), where ''a'' is twice the area between the ray, the hyperbola, and the ''x''-axis. For points on the hyperbola below the ''x''-axis, the area is considered negative" [TODO] <math>\cosh(a)</math> and <math>\sinh(a)</math> are the <math>x</math> and <math>y</...") Tag: Visual edit
• 17:20, 8 July 2024 Lfox talk contribs created page File:1920px-Hyperbolic functions-2.svg.png
• 17:20, 8 July 2024 Lfox talk contribs uploaded File:1920px-Hyperbolic functions-2.svg.png
• 17:25, 3 July 2024 Lfox talk contribs created page Limit (Created page with "The '''limit''' (of a Cauchy procedure) is the target which a Cauchy procedure approaches. [TODO ugh] == Examples == === Planes are the limit of increasingly large spheres === Work with 3 dimensional rectilinear coordinates, and consider some sequence of spheres, <math>C_1, C_2, \cdots </math> on the plane, where the sphere <math>C_n</math> is centered at <math>(0, 0, n) </math> and has radius <math>n</math>. Near the origin <math>(0,0,0)</math>, the sphere <math>C_n</...") Tag: Visual edit
• 16:26, 2 July 2024 Lfox talk contribs created page Magnitude (Created page with "A '''magnitude''' is a quantity with no restriction on how it can be divided into parts.<ref>Aristotle, ''Metaphysics'', Book V, Ch. 11-14</ref>") Tag: Visual edit
• 18:20, 19 June 2024 Lfox talk contribs created page Multitude (Created page with "'''Multitude''' is the quantity of a finite set. Synonyms for multitude are '''natural number''', '''whole quantity''', '''discrete quantity''', '''cardinality''', and the symbol <math>\mathbb{N}</math>; though all those concepts have different shades of meaning, Objective Mathematics uses them interchangeably. == Comparison == "Few" and "many" describe relative multitudes. == Counting == Counting is a process by which one identifies the isomorphism class of...") Tag: Visual edit
• 21:55, 27 May 2024 Lfox talk contribs created page Group (Created page with "[TODO defn] Consider a thing with some symmetry. A symmetry is a transformation of the thing which leaves it unchanged. Technically speaking, == Finite groups == == Infinite groups == == Notes == <references group="note" />") Tag: Visual edit: Switched
• 20:11, 25 April 2024 Lfox talk contribs created page Probability (Created page with "'''Probability''' is a quantitative method of exploiting the symmetry of a system to reach, with certainty, conclusions about aggregates of outcomes, even when each individual outcome is uncertain. The idea is that every context determines some small number <math>\epsilon > 0</math>, such that anything which will only happen with probability less than <math>\epsilon</math> is deemed ''impossible'' (IN THAT CONTEXT). There's an objection that it's "possible" to flip...") Tag: Visual edit
• 00:09, 23 April 2024 Lfox talk contribs created page Velocity (Created page with "The '''velocity''' of an object is the rate at which it moves. A particle is an entity considered as a point. == Specification == There is no such thing as the velocity of a particle at "an instant in time." But I want to specify a certain ''real'' measurement, which could actually be done, and which is the reality-based analogue of that notion. If one measures a particle and it is not moving (relative to me), then he can measure it at a certain position <math>x</m...") Tag: Visual edit
• 22:37, 22 April 2024 Lfox talk contribs created page Continuous (Redirected page to Continuity) Tags: New redirect Visual edit: Switched
• 20:13, 18 April 2024 Lfox talk contribs created page Real number (Created page with "I am not yet sure how to define real numbers. Many irrational numbers (e.g. <math>\sqrt{2}</math> and <math>\pi</math>) are in fact real, but the standard definition of the reals involves infinite nonsense. == Examples == Any fraction. Any algebraic number like <math>\sqrt{2}</math>. Pi e The output of the following computer program <code>digit(int i): if</code> <pre> digit(int i): if (suthaweou) return 0 </pre>") Tag: Visual edit: Switched
• 16:59, 18 April 2024 Lfox talk contribs created page Symmetry (Created page with "A '''symmetry''' is a change in perspective that renders a system unchanged. == Examples == [TODO picture] Imagine a square S with different sides (labels on each of its sides). You can rotate it, and you get a different square S'. But if you forget about the labels (omit the measurements of the labels), then S and S' are the same. This thing has a natural Z4 symmetry.") Tag: Visual edit
• 19:34, 10 April 2024 Lfox talk contribs created page Polynomial (Created page with "A '''polynomial''' is any function which obtains its result solely by some combination of: multiplying its inputs together, adding them together, or rescaling them. == Examples == The volume of a cube is a polynomial in its side length. Every linear transformation is uniquely associated to a polynomial called its characteristic polynomial. A computer program consisting of some number of <code>for</code> loops (and no recursion or <code>goto</code>...") Tag: Visual edit
• 05:18, 6 March 2024 Lfox talk contribs created page Information (Created page with "'''Information''' is a substance arranged in such a manner so as to convey knowledge to those who perceive it. [TODO is that right? It's consistent with saying "the words on this page are information" but not(?) with saying "the words on this page contain information." Information is not an irreducible primary, as some modern physicists think it is. Information presupposes the concepts of man and of knowledge. == Examples == Newspaper Brochure Wikipedia page Spe...") Tag: Visual edit
• 17:33, 14 February 2024 Lfox talk contribs created page Algorithm (Created page with "An '''algorithm''' is a sequence of simple tasks, steps, or operations that can be performed to compute values of a given function. == Examples == Schoolchildren learn algorithms for computing the sums, products, and ratios of numbers. There are algorithms to find the matrix resulting from the composition of two matrices. There can be no algorithm to compute whether two presentations generate the same group. == Time complexity == The time complexity of an alg...") Tag: Visual edit
• 04:12, 14 February 2024 Lfox talk contribs created page Coordinates (Created page with "A '''coordinate system''' is a system assigning a number (or tuple of numbers) to every point on an entity. The number (or tuple of numbers) assigned to a point is called the '''coordinate''' (or '''coordinates''') of the point. == Examples == Longitude and latitude are a coordinate system for the surface of the earth. If one picks two lines on a plane which meet at right angles, then one has implicitly chosen a Cartesian coordinate...") Tag: Visual edit
• 04:09, 14 February 2024 Lfox talk contribs created page Plane (Redirected page to Surface#Plane) Tags: New redirect Visual edit: Switched
• 02:51, 11 February 2024 Lfox talk contribs created page Existent (Created page with "An '''existent''' is an irreducible primary, and thus can only be defined ostensively. A circular definition of existent, which will help indicate what I'm talking about, is that it is "something that exists, be it a thing, an attribute or an action."<ref>Rand, Ayn. ''Introduction to Objectivist Epistemology''. Penguin, 1990.</ref> == Examples == Look at something around you. That is an existent. Consider one of its properties, like its shape or location or color. Tha...") Tag: Visual edit
• 19:41, 9 February 2024 Lfox talk contribs created page Zeno's Paradox (Created page with "'''Zeno's Paradox''' refers to<ref group="note">I call this Zeno's Paradox, but it is only loosely related to the historical Zeno. That is, I have made no attempt to conform to what Zeno himself actually said, or to understand what Zeno himself actually meant. Such historical questions are interesting, but not very relevant to Objective Mathematics.</ref> the following puzzle. To move any distance, one must first reach half the distance. After that, to close the remainin...") Tag: Visual edit: Switched
• 23:13, 2 February 2024 Lfox talk contribs created page Order (Created page with "A set <math>S</math> is said to possess an '''order''' (or, if necessary to disambiguate, a ''total'' order) if, for every pair of distinct elements <math>x,y \in S</math>, either <math>x</math> is ''before'' <math>y</math>, or <math>x</math> is ''after'' <math>y</math>, with respect to some order relation. Besides what Objective Mathematics means by "order," there are two other significant uses of the word. One refers to a command (an order) given to other people, as i...") Tag: Visual edit
• 04:18, 2 February 2024 Lfox talk contribs created page Nothing (Redirected page to Sets#The empty set) Tags: New redirect Visual edit: Switched
• 21:49, 30 January 2024 Lfox talk contribs created page Logicism (Redirected page to Formalism#Logicism) Tags: New redirect Visual edit: Switched