User contributions

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• 03:29, 24 January 2020 (diff | hist) . . (+2,104)‎ . . N User:IssaRice/Poisson distribution ‎ (Created page with "Let X be the number of letters received in a day. If the letters arrive indenpendently blah blah blah, it should be clear that X has a Poisson distribution. Let's say you get...") (current)
• 05:42, 17 January 2020 (diff | hist) . . (+637)‎ . . N User:IssaRice/Linear algebra/Properties preserved under various operations to a matrix ‎ (Created page with "properties to discuss: {| class="sortable wikitable" |- ! Operation !! Preserved properties !! Properties not necessarily perserved |- | Elementary operation: swapping rows...")
• 09:11, 15 January 2020 (diff | hist) . . (+1,539)‎ . . N User:IssaRice/Linear algebra/Singular value decomposition ‎ (Created page with "the stupid textbooks don't tell you anything about SVD!!!! i think it's super helpful to look at all the ''wrong'' things one might say about SVD... we need to un-knot all tho...")
• 08:00, 15 January 2020 (diff | hist) . . (+247)‎ . . N User:IssaRice/Math resources I like ‎ (Created page with "* Terence Tao's notes and books * Tim Gowers's blog (especially intro logic) * Evan Chen's infinite napkin * mathematicalmonk's youtube videos * Vipul's notes * abstractmath.o...") (current)
• 07:51, 15 January 2020 (diff | hist) . . (+1,063)‎ . . N User:IssaRice/Linear algebra/Geometry of linear transformations ‎ (Created page with "There are various "geometric properties" that transformations can have, such as "[https://en.wikipedia.org/wiki/Isometry preserves lengths]", "[https://en.wikipedia.org/wiki/C...")
• 21:52, 14 January 2020 (diff | hist) . . (+1,403)‎ . . N User:IssaRice/Self-sampling assumption with large reference class in sleeping beauty ‎ (Created page with ""Unlike SIA, SSA ''is'' dependent on the choice of reference class. If the agents in the above example were in the same reference class as a trillion other observers, then the...")
• 00:05, 14 January 2020 (diff | hist) . . (+1,916)‎ . . N User:IssaRice/Convex function ‎ (Created page with "a function <math>f : \mathbf R \to \mathbf R</math> is often defined to be convex if <math>f(tx + (1-t)y) \leq tf(x) + (1-t)f(y)</math> for all <math>x,y \in \mathbf R</math>...") (current)
• 03:42, 8 January 2020 (diff | hist) . . (+736)‎ . . N User:IssaRice/Scoring rule ‎ (Created page with "how can we formalize the idea of a rule for scoring predictions? ==first pass== we can start with a list <math>s_1,\ldots,s_n</math> of statements. each statement makes a ye...")
• 10:34, 7 January 2020 (diff | hist) . . (+354)‎ . . N Quantities defined for a random variable that depend only on the distribution ‎ (Created page with "Some quantities defined for a random variable, such as expected value and entropy (as well as quantities defined in terms of those, such as variance), depend only...")
• 10:06, 7 January 2020 (diff | hist) . . (+84)‎ . . N User:IssaRice/Dual space of vector space of polynomials ‎ (IssaRice moved page User:IssaRice/Dual space of vector space of polynomials to User:IssaRice/Linear algebra/Dual space of vector space of polynomials) (current)
• 09:45, 7 January 2020 (diff | hist) . . (+1,527)‎ . . N User:IssaRice/Linear algebra/Dual space of vector space of polynomials ‎ (Created page with "Given a vector space <math>V</math>, its dual space <math>V'</math> is the set of all linear functionals <math>V \to \mathbf F</math>, i.e. all linear functions that "evaluate...")
• 05:40, 1 January 2020 (diff | hist) . . (+2,422)‎ . . N User:IssaRice/Generators and relations of dihedral groups ‎ (Created page with "problem II.2.5 (p. 57) in Aluffi's Algebra: Chapter 0. As suggested by the hint, take <math>x</math> to be a reflection through the center and some vertex, and <math>y</math>...")
• 02:39, 28 December 2019 (diff | hist) . . (+1,103)‎ . . N User:IssaRice/Linear algebra/Determinant as signed volume of transformation ‎ (Created page with " Let <math>f : \mathbf R^n \to \mathbf R^n</math> be some function (not necessarily linear) and let <math>\Omega \subseteq \mathbf R^n</math> be some region in space. we will...")
• 23:36, 18 October 2019 (diff | hist) . . (+1,748)‎ . . N User:IssaRice/Boundedness theorem for continuous functions ‎ (Created page with "There are two typical proofs of the boundedness theorem: * one uses just the least upper bound property * the other uses some sequences machinery (Bolzano-Weierstrass theorem...") (current)
• 22:11, 5 October 2019 (diff | hist) . . (+1,264)‎ . . N User:IssaRice/AI safety/Possibility of act-based agents ‎ (Created page with " "If a pre­dic­tor can pre­dict a sys­tem con­tain­ing con­se­quen­tial­ists (e.g. a hu­man in a room), then it is us­ing some kind of con­se­quen­tial­ist ma...")
• 21:58, 5 October 2019 (diff | hist) . . (+116)‎ . . N User:IssaRice/AI safety/List of critiques of iterated amplification ‎ (Created page with "{| class="sortable wikitable" ! Critique !! Links making this critique !! Paul's response !! Resolution status |- |}")
• 20:38, 4 October 2019 (diff | hist) . . (+291)‎ . . N User:IssaRice/AI safety/History of Paul Christiano's views ‎ (Created page with "https://www.greaterwrong.com/posts/9zpT9dikrrebdq3Jf/will-humans-build-goal-directed-agents/comment/JzYRLCdjxD2Cuqfgu -- i'd like to get the date ranges for each of these view...") (current)
• 08:13, 27 September 2019 (diff | hist) . . (+451)‎ . . N User:IssaRice/AI safety/Bostrom writing style ‎ (Created page with ""I think there is a possible culture where people say a bunch of inside-view things, and run with speculations all the time, and another possible culture where people mostly o...") (current)
• 20:59, 7 September 2019 (diff | hist) . . (+527)‎ . . N User:IssaRice/Implementation details in math ‎ (Created page with "ideas similar to software engineering's "implementation details" come up quite often in math, when we are constructing/defining certain objects: * constructing number systems...") (current)
• 20:52, 7 September 2019 (diff | hist) . . (+37)‎ . . N User:IssaRice/AI safety/Intelligence amplification ‎ (Created page with "https://nickbostrom.com/cognitive.pdf") (current)
• 03:44, 7 September 2019 (diff | hist) . . (+2,674)‎ . . N User:IssaRice/AI safety/Issa's stupid questions about AI safety ‎ (Created page with "* there's a bunch of different considerations that people talk about (like different takeoff scenarios, comparisons to nuclear arms control, etc.) and it's unclear to me how t...")
• 00:41, 6 September 2019 (diff | hist) . . (+236)‎ . . N User:IssaRice/AI safety/Whole brain emulation ‎ (Created page with "==Different kinds of WBE== * hi-fi * lo-fi ==Distinction between magically obtaining and the expected ways of obtaining== ==Timelines== * how many years to WBE under a "de...")
• 01:01, 3 September 2019 (diff | hist) . . (+115)‎ . . N User:IssaRice/AI safety/Asymmetry of risks ‎ (Created page with "https://www.greaterwrong.com/posts/aPwNaiSLjYP4XXZQW/ai-alignment-open-thread-august-2019/comment/moZS7T7gGYnTxkqDJ") (current)
• 00:56, 3 September 2019 (diff | hist) . . (+537)‎ . . N User:IssaRice/AI safety/Distribution of AI failures leading up to AGI ‎ (Created page with "'''Distribution of AI failures leading up to AGI''' refers to how many and how severe AI-related failures are, in the period leading up to AGI. Each "failure event" has sever...")
• 00:47, 3 September 2019 (diff | hist) . . (+117)‎ . . N User:IssaRice/AI safety/ ‎ (Created page with "Index of pages in this directory: {{Special:PrefixIndex/User:IssaRice/AI_safety/ | hideredirects=1 | stripprefix=1}}") (current)
• 22:47, 2 September 2019 (diff | hist) . . (+221)‎ . . N User:IssaRice/AI safety/Comparison of terms related to agency ‎ (Created page with "{| class="wikitable" ! Term !! Opposite |- | Agent || |- | Optimizer, optimization process || |- | consequentialist || |- | expected utility maximizer || |- | goal-directed, g...")
• 00:19, 1 September 2019 (diff | hist) . . (+548)‎ . . N Bellman equation derivation ‎ (Created page with "Bellman equation for <math>v_\pi</math>. We want to show <math>v_\pi(s) = \sum_a \pi(a \mid s) \sum_{s',r} p(s',r\mid s,a) [r + \gamma v_\pi(s')]</math> for all states <math>...")
• 01:54, 28 August 2019 (diff | hist) . . (+2,010)‎ . . N User:IssaRice/Two envelopes problem ‎ (Created page with "https://en.wikipedia.org/wiki/Two_envelopes_problem {| class="wikitable" ! Step !! Wikipedia !! Formal version |- | 1 || I denote by ''A'' the amount in my selected envelope....")
• 05:24, 20 August 2019 (diff | hist) . . (+1,270)‎ . . N User:IssaRice/Computability and logic/Motivation for encoding ‎ (Created page with "The idea of numbering things/encoding things comes up a lot in computability and logic, but many books don't really seem to discuss why we do this in the first place (the answ...")
• 18:09, 16 August 2019 (diff | hist) . . (+3,164)‎ . . N User:IssaRice/Lebesgue number lemma and Tao's proof that sequential compactness implies covering compactness ‎ (Created page with "One typical statement of the Lebesgue number lemma is the following: Let <math>(X,d)</math> be a metric space, and let <math>Y</math> be a subset of <math>X</math>. Let <math>...")
• 07:34, 15 August 2019 (diff | hist) . . (+1,927)‎ . . N User:IssaRice/Linear algebra/Deriving projection formula and equivalent formulas for dot product ‎ (Created page with "This is based on the symmetry argument given in https://www.youtube.com/watch?v=LyGKycYT2v0 Let <math>u</math> and <math>v</math> be vectors. We want to figure out how to pro...")
• 02:12, 14 August 2019 (diff | hist) . . (+652)‎ . . N User:IssaRice/Summary of counting techniques ‎ (Created page with "Let <math>A</math> be a set with <math>n</math> elements, and let <math>B</math> be a set with <math>m</math> elements. {| class="wikitable" ! Description !! Set representing...")
• 01:07, 14 August 2019 (diff | hist) . . (+1,737)‎ . . N User:IssaRice/Linear algebra/Equivalent statements for injectivity and surjectivity ‎ (Created page with "Let <math>A</math> be an <math>m \times n</math> matrix. {| class="wikitable" ! Injective !! Surjective !! Bijective |- | <math>A</math> is injective || <math>A</math> is sur...")
• 06:30, 10 August 2019 (diff | hist) . . (+1,411)‎ . . N Translating informal probability statements to formal counterparts ‎ (Created page with "(inspired by how Aluffi explains universal properties in ''Algebra: Chapter 0'') I think probability is one of the fields in math where people who have learned the subject of...")
• 04:12, 4 August 2019 (diff | hist) . . (+1,059)‎ . . N User:IssaRice/Pythagorean theorem, law of cosines, angle between vectors, and inner product ‎ (Created page with "There is something peculiar about the dependency of the following concepts in math: * Pythagorean theorem * Law of cosines * Angle between two vectors * Dot product * Inner p...")
• 03:59, 4 August 2019 (diff | hist) . . (+78)‎ . . N User:IssaRice/Stringing together relations ‎ (IssaRice moved page User:IssaRice/Stringing together relations to User:IssaRice/Stringing together relations and binary operations) (current)
• 03:28, 3 August 2019 (diff | hist) . . (+742)‎ . . N User:IssaRice/Stringing together relations and binary operations ‎ (Created page with "If <math>R</math> is a relation on a set <math>X</math>, and <math>x,y,z</math> are elements of <math>X</math>, we sometimes write <math>x \mathrel{R} y \mathrel{R} z</math> a...")
• 21:11, 31 July 2019 (diff | hist) . . (+771)‎ . . N Infinitely often and almost always ‎ (Created page with "Let <math>A_1, A_2, A_3, \ldots</math> be a sequence of events in some sample space <math>\Omega</math>. {| class="wikitable" |- ! perspective !! infinitely often !! almost a...")
• 05:26, 30 July 2019 (diff | hist) . . (+755)‎ . . N User:IssaRice/Linear algebra/Dual basis ‎ (Created page with "see p. 224 of https://terrytao.files.wordpress.com/2011/06/blog-book.pdf the following example is based on p. 115 of https://terrytao.files.wordpress.com/2016/12/linear-algeb...")
• 22:54, 29 July 2019 (diff | hist) . . (+1,480)‎ . . N User:IssaRice/Degree of polynomial ‎ (Created page with "Why is the definition of degree of polynomial what it is? First attempt: a polynomial like <math>a_n x^n + a_{n-1} x^{n-1} + \cdots + a_2 x^2 + a_1 x + a_0</math> should have...") (current)
• 05:38, 25 July 2019 (diff | hist) . . (+367)‎ . . N Lower semicomputable function ‎ (Created page with "A function <math>f : X \to \mathbf R</math> is lower semicomputable iff there exists a computable function <math>g : X \times \mathbf N \to \mathbf Q</math> such that: * for...")
• 20:00, 15 July 2019 (diff | hist) . . (+1,651)‎ . . N Shattering ‎ (Created page with "Let <math>\mathcal H</math> be a class of functions from <math>\mathcal X</math> to <math>\{0,1\}</math>, called a hypothesis class. Let <math>S = \{p_1, \ldots, p_n\} \subset...")
• 20:28, 12 July 2019 (diff | hist) . . (+651)‎ . . N User:IssaRice/Computability and logic/Rogers fixed point theorem using Sipser's notation ‎ (Created page with "Sipser's textbook presents the recursion theorem, but not the fixed point theorem. Here is one way to state the fixed point theorem using Sipser's notation. '''Theorem''' (Fi...")
• 07:24, 6 July 2019 (diff | hist) . . (+864)‎ . . N User:IssaRice/Isometry in metric spaces ‎ (Created page with "when playing around with metric spaces, one might notice that certain metric spaces can be "modeled" by other metric spaces. For instance, let <math>X = \{1,2,3\}</math> be a...")
• 07:09, 6 July 2019 (diff | hist) . . (+438)‎ . . N User:IssaRice/Construction of the real numbers ‎ (Created page with "something that i have seen clarified ''exactly once'' is why constructing the real numbers (for instance via dedekind cuts or equivalence classes of cauchy sequences of ration...")
• 04:24, 6 July 2019 (diff | hist) . . (+1,143)‎ . . N User:IssaRice/Adherent point and limit point ‎ (Created page with "Let <math>(X,d)</math> be a metric space, let <math>E</math> be a subset of <math>X</math>, and let <math>x_0\in X</math> be a point. * there exists a sequence <math>(x_n)_{n...")
• 03:42, 5 July 2019 (diff | hist) . . (+210)‎ . . N User:IssaRice/Subfield of math that is best for introducing proofs ‎ (Created page with "==Real analysis== Pros: Cons: ==Linear algebra== Pros: Cons: ==Abstract algebra== Pros: Cons: ==Computability and logic== Pros: Cons: ==Discrete math== Pros: Con...")
• 21:50, 27 June 2019 (diff | hist) . . (+531)‎ . . N User:IssaRice/Linear algebra/Linear transformation vs matrix views ‎ (Created page with "Given an <math>m\times n</math> matrix <math>A</math> we can define a linear map <math>T : \mathbf R^n \to \mathbf R^m</math> by <math>T(x) = Ax</math>. Given a linear map <m...")
• 00:46, 25 June 2019 (diff | hist) . . (+1)‎ . . N User:IssaRice/Logical inductor construction ‎ (Created page with ".")
• 00:09, 19 June 2019 (diff | hist) . . (+1,230)‎ . . N User:IssaRice/Computability and logic/Sipser's quine in Python ‎ (Created page with "Michael Sipser's ''Introduction to the Theory of Computation'' describes a quine using Turing machines. Here is an implementation of the machine ''SELF''. <pre>TAPE = "" de...")

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