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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