From dad12b76a49126551d011611bd40e6eb4788897f Mon Sep 17 00:00:00 2001 From: Youwen Wu Date: Sat, 19 Oct 2024 20:05:34 -0700 Subject: [PATCH] refactor: use typix and massively reorganize file system for innovation innovation --- .../by-course/phil-1/paper-1/package.nix | 30 +- .../digression-linear-algebra/main.typ | 165 ++++++++++ .../digression-linear-algebra/package.nix | 35 ++ .../digression-linear-algebra/refs.bib | 6 + 2024/flake.nix | 14 +- 2024/nix/lib/callTypstProject.nix | 16 + 2024/nix/lib/cleanTypstSource.nix | 18 ++ 2024/nix/lib/default.nix | 19 ++ 2024/nix/utils/default.nix | 0 2024/result | 1 + 2024/work/phil-1/paper-1-typix/.gitignore | 1 - 2024/work/phil-1/paper-1-typix/flake.lock | 99 ------ 2024/work/phil-1/paper-1-typix/flake.nix | 126 -------- 2024/work/phil-1/paper-1-typix/main.typ | 2 - 2024/work/phil-1/paper-1/main.pdf | Bin 451151 -> 0 bytes 2024/work/phil-1/paper-1/main.typ | 302 ------------------ 2024/work/phil-1/paper-1/package.nix | 49 --- 2024/work/phil-1/paper-1/prelude.typ | 21 -- 2024/work/phil-1/paper-1/refs.bib | 7 - 19 files changed, 278 insertions(+), 633 deletions(-) create mode 100644 2024/documents/by-name/digression-linear-algebra/main.typ create mode 100644 2024/documents/by-name/digression-linear-algebra/package.nix create mode 100644 2024/documents/by-name/digression-linear-algebra/refs.bib create mode 100644 2024/nix/lib/callTypstProject.nix create mode 100644 2024/nix/lib/cleanTypstSource.nix create mode 100644 2024/nix/lib/default.nix delete mode 100644 2024/nix/utils/default.nix create mode 120000 2024/result delete mode 100644 2024/work/phil-1/paper-1-typix/.gitignore delete mode 100644 2024/work/phil-1/paper-1-typix/flake.lock delete mode 100644 2024/work/phil-1/paper-1-typix/flake.nix delete mode 100644 2024/work/phil-1/paper-1-typix/main.typ delete mode 100644 2024/work/phil-1/paper-1/main.pdf delete mode 100644 2024/work/phil-1/paper-1/main.typ delete mode 100644 2024/work/phil-1/paper-1/package.nix delete mode 100644 2024/work/phil-1/paper-1/prelude.typ delete mode 100644 2024/work/phil-1/paper-1/refs.bib diff --git a/2024/documents/by-course/phil-1/paper-1/package.nix b/2024/documents/by-course/phil-1/paper-1/package.nix index f5cccee..1c9e4f7 100644 --- a/2024/documents/by-course/phil-1/paper-1/package.nix +++ b/2024/documents/by-course/phil-1/paper-1/package.nix @@ -2,10 +2,11 @@ pkgs, typstPackagesCache, typixLib, + cleanTypstSource, ... }: let - src = typixLib.cleanTypstSource ./.; + src = cleanTypstSource ./.; commonArgs = { typstSource = "main.typ"; @@ -25,25 +26,10 @@ let XDG_CACHE_HOME = typstPackagesCache; }; - # Compile a Typst project, *without* copying the result - # to the current directory - build-drv = typixLib.buildTypstProject ( - commonArgs - // { - inherit src; - } - ); - - # Compile a Typst project, and then copy the result - # to the current directory - build-script = typixLib.buildTypstProjectLocal ( - commonArgs - // { - inherit src; - } - ); - - # Watch a project and recompile on changes - watch-script = typixLib.watchTypstProject commonArgs; in -build-drv +typixLib.buildTypstProject ( + commonArgs + // { + inherit src; + } +) diff --git a/2024/documents/by-name/digression-linear-algebra/main.typ b/2024/documents/by-name/digression-linear-algebra/main.typ new file mode 100644 index 0000000..75a69df --- /dev/null +++ b/2024/documents/by-name/digression-linear-algebra/main.typ @@ -0,0 +1,165 @@ +#import "@preview/unequivocal-ams:0.1.1": ams-article, theorem, proof + +#show: ams-article.with( + title: [A Digression on Abstract Linear Algebra], + authors: ( + ( + name: "Youwen Wu", + organization: [University of California, Santa Barbara], + email: "youwen@ucsb.edu", + url: "https://youwen.dev", + ), + ), + bibliography: bibliography("refs.bib"), +) + += Introduction + +Many introductory linear algebra classes focus on _application_. In general, +this is a red herring and is engineer-speak for "we will teach you how to +crunch numbers with no regard for conceptual understanding." + +If you are a math major (or math-adjacent, such as Computer Science), this +class is essentially useless for you. You will learn how to perform trivial +numerical operations such as the _matrix multiplication_, _matrix-vector +multiplication_, _row reduction_, and other trite tasks better suited for +computers. + +If you are taking this course, you might as well learn linear algebra properly. +Otherwise, you will have to re-learn it later on, anyways. Completing a math +course without gaining a theoretical appreciation for the topics at hand is an +unequivocal waste of time. I have prepared this brief crash course designed to +fill in the theoretical gaps left by this class. + += Basic Notions + +== Vector spaces + +Before we can understand vectors, we need to first discuss _vector spaces_. Thus +far, you have likely encountered vectors primarily in physics classes, +generally in the two-dimensional plane. You may conceptualize them as arrows in +space. For vectors of size $>3$, a hand waving argument is made that they are +essentially just arrows in higher dimensional spaces. + +It is helpful to take a step back from this primitive geometric understanding +of the vector. Let us build up a rigorous idea of vectors from first +principles. + +=== Vector axioms + +The so-called _axioms_ of a _vector space_ (which we'll call the vector space +$V$) are as follows: + +#enum[ + Commutativity: $u + v = v + u, " " forall u,v in V$ +][ + Associativity: $(u + v) + w = u + (v + w), " " forall u,v,w in V$ +][ + Zero vector: $exists$ a special vector, denoted $0$, such that $v + 0 = v, " " forall v in V$ +][ + Additive inverse: $forall v in V, " " exists w in V "such that" v + w = 0$. Such an additive inverse is generally denoted $-v$ +][ + Multiplicative identity: $1 v = v, " " forall v in V$ +][ + Multiplicative associativity: $(alpha beta) v = alpha (beta v) " " forall v in V, "scalars" alpha, beta$ +][ + Distributive property for vectors: $alpha (u + v) = alpha u + alpha v " " forall u,v in V, "scalars" alpha$ +][ + Distributive property for scalars: $(alpha + beta) v = alpha v + beta v " " forall v in V, " scalars" alpha, beta$ +] + +It is easy to show that the zero vector $0$ and the additive inverse $-v$ are +_unique_. We leave the proof of this fact as an exercise. + +These may seem difficult to memorize, but they are essentially the same +familiar algebraic properties of numbers you know from high school. The +important thing to remember is which operations are valid for what objects. For +example, you cannot add a vector and scalar, as it does not make sense. + +_Remark_. For those of you versed in computer science, you may recognize this +as essentially saying that you must ensure your operations are _type-safe_. +Adding a vector and scalar is not just false, it is an _invalid question_ +entirely because vectors and scalars and different types of mathematical +objects. See #cite(, form: "prose") for more. + +=== Vectors big and small + +In order to begin your descent into what mathematicians colloquially recognize +as _abstract vapid nonsense_, let's discuss which fields constitute a vector space. We +have the familiar space where all scalars are real numbers, or $RR$. We +generally discuss 2-D or 3-D vectors, corresponding to vectors of length 2 or +3; in our case, $RR^2$ and $RR^3$. + +However, vectors in $RR$ can really be of any length. Discard your primitive +conception of vectors as arrows in space. Vectors are simply arbitrary length +lists of numbers (for the computer science folk: think C++ `std::vector`). + +_Example_. $ vec(1,2,3,4,5,6,7,8,9) $ + +Moreover, vectors need not be in $RR$ at all. Recall that a vector space need +only satisfy the aforementioned _axioms of a vector space_. + +_Example_. The vector space $CC$ is similar to $RR$, except it includes complex +numbers. All complex vector spaces are real vector spaces (as you can simply +restrict them to only use the real numbers), but not the other way around. + +In general, we can have a vector space where the scalars are in an arbitrary +field $FF$, as long as the axioms are satisfied. + +_Example_. The vector space of all polynomials of degree 3, or $PP^3$. It is +not yet clear what this vector may look like. We shall return to this example +once we discuss _basis_. + +== Vector addition. Multiplication + +Vector addition, represented by $+$, and multiplication, represented by the +$dot$ (dot) operator, can be done entrywise. + +_Example._ + +$ + vec(1,2,3) + vec(4,5,6) = vec(1 + 4, 2 + 5, 3 + 6) = vec(5,7,9) +$ +$ + vec(1,2,3) dot vec(4,5,6) = vec(1 dot 4, 2 dot 5, 3 dot 6) = vec(4,10,18) +$ + +This is simple enough to understand. Again, the difficulty is simply ensuring +that you always perform operations with the correct _types_. For example, once +we introduce matrices, it doesn't make sense to multiply or add vectors and +matrices in this fashion. + +== Vector-scalar multiplication + +Multiplying a vector by a scalar simply results in each entry of the vector +being multiplied by the scalar. + +_Example_. + +$ beta vec(a, b, c) = vec(beta dot a, beta dot b, beta dot c) $ + +== Matrices + +Before discussing any properties of matrices, let's simply reiterate what we +learned in class about their notation. We say a matrix with rows of length $m$, +and columns of size $n$ (in less precise terms, a matrix with length $m$ and +height $n$) is a $m times n$ matrix. + +Given a matrix + +$ A = mat(1,2,3;4,5,6;7,8,9) $ + +we refer to the entry in row $j$ and column $k$ as $A_(j,k)$ . + +=== Matrix transpose + +A formalism that is useful later on is called the _transpose_, and we obtain it +from a matrix $A$ by switching all the rows and columns. More precisely, each +row becomes a column instead. We use the notation $A^T$ to represent the +transpose of $A$. + +$ + mat(1,2,3;4,5,6)^T = mat(1,4;2,5;3,6) +$ + +Formally, we can say $(A_(j,k))^T = A_(k,j)$. diff --git a/2024/documents/by-name/digression-linear-algebra/package.nix b/2024/documents/by-name/digression-linear-algebra/package.nix new file mode 100644 index 0000000..1c9e4f7 --- /dev/null +++ b/2024/documents/by-name/digression-linear-algebra/package.nix @@ -0,0 +1,35 @@ +{ + pkgs, + typstPackagesCache, + typixLib, + cleanTypstSource, + ... +}: +let + src = cleanTypstSource ./.; + commonArgs = { + typstSource = "main.typ"; + + fontPaths = [ + # Add paths to fonts here + # "${pkgs.roboto}/share/fonts/truetype" + ]; + + virtualPaths = [ + # Add paths that must be locally accessible to typst here + # { + # dest = "icons"; + # src = "${inputs.font-awesome}/svgs/regular"; + # } + ]; + + XDG_CACHE_HOME = typstPackagesCache; + }; + +in +typixLib.buildTypstProject ( + commonArgs + // { + inherit src; + } +) diff --git a/2024/documents/by-name/digression-linear-algebra/refs.bib b/2024/documents/by-name/digression-linear-algebra/refs.bib new file mode 100644 index 0000000..ef367c4 --- /dev/null +++ b/2024/documents/by-name/digression-linear-algebra/refs.bib @@ -0,0 +1,6 @@ +@misc{chen2024digression, + author = {Evan Chen}, + title = {Digression on Type Safety}, + year = {2024}, + howpublished = {\url{https://web.evanchen.cc/upload/1802/tsafe-1802.pdf}}, +} diff --git a/2024/flake.nix b/2024/flake.nix index 426e999..593dc44 100644 --- a/2024/flake.nix +++ b/2024/flake.nix @@ -47,18 +47,24 @@ cp -LR --reflink=auto --no-preserve=mode -t "$out/typst/packages" "$src"/* ''; }; + typixLib = typix.lib.${system}; in let - inherit pkgs; - typixLib = typix.lib.${system}; + alexandriaLib = import ./nix/lib { + inherit pkgs typixLib typstPackagesCache; + }; + in { # checks = { # inherit build-drv build-script watch-script; # }; - packages.default = import ./documents/by-course/phil-1/paper-1/package.nix { - inherit pkgs typixLib typstPackagesCache; + legacyPackages = { + phil-1 = { + paper-1 = alexandriaLib.callTypstProject (import ./documents/by-course/phil-1/paper-1/package.nix); + }; + digression-linear-algebra = alexandriaLib.callTypstProject (import ./documents/by-name/digression-linear-algebra/package.nix); }; # apps = rec { # default = watch; diff --git a/2024/nix/lib/callTypstProject.nix b/2024/nix/lib/callTypstProject.nix new file mode 100644 index 0000000..83f5e0a --- /dev/null +++ b/2024/nix/lib/callTypstProject.nix @@ -0,0 +1,16 @@ +{ + pkgs, + typixLib, + typstPackagesCache, + cleanTypstSource, + ... +}: +package: +package { + inherit + pkgs + typixLib + typstPackagesCache + cleanTypstSource + ; +} diff --git a/2024/nix/lib/cleanTypstSource.nix b/2024/nix/lib/cleanTypstSource.nix new file mode 100644 index 0000000..9352b3b --- /dev/null +++ b/2024/nix/lib/cleanTypstSource.nix @@ -0,0 +1,18 @@ +{ pkgs, ... }: +src: +let + inherit (pkgs) lib; +in +lib.cleanSourceWith { + src = lib.cleanSource src; + filter = + path: type: + let + isTypstSource = lib.hasSuffix ".typ" path || lib.hasSuffix ".bib" path; + isImage = lib.hasSuffix ".png" path || lib.hasSuffix ".jpeg" path || lib.hasSuffix ".jpg" path; + isSpecialFile = builtins.elem (builtins.baseNameOf path) [ + "typst.toml" + ]; + in + type == "directory" || isTypstSource || isSpecialFile || isImage; +} diff --git a/2024/nix/lib/default.nix b/2024/nix/lib/default.nix new file mode 100644 index 0000000..4e43bfb --- /dev/null +++ b/2024/nix/lib/default.nix @@ -0,0 +1,19 @@ +{ + pkgs, + typstPackagesCache, + typixLib, +}: +let + defaultArgs = { + inherit pkgs typstPackagesCache typixLib; + }; +in +rec { + cleanTypstSource = (import ./cleanTypstSource.nix) defaultArgs; + callTypstProject = (import ./callTypstProject.nix) ( + defaultArgs + // { + inherit cleanTypstSource; + } + ); +} diff --git a/2024/nix/utils/default.nix b/2024/nix/utils/default.nix deleted file mode 100644 index e69de29..0000000 diff --git a/2024/result b/2024/result new file mode 120000 index 0000000..8a732bc --- /dev/null +++ b/2024/result @@ -0,0 +1 @@ +/nix/store/fv6y2dqv26lw4gzb2pf6ms5hyikpbkm9-typst \ No newline at end of file diff --git a/2024/work/phil-1/paper-1-typix/.gitignore b/2024/work/phil-1/paper-1-typix/.gitignore deleted file mode 100644 index fcfc4a1..0000000 --- a/2024/work/phil-1/paper-1-typix/.gitignore +++ /dev/null @@ -1 +0,0 @@ -result* diff --git a/2024/work/phil-1/paper-1-typix/flake.lock b/2024/work/phil-1/paper-1-typix/flake.lock deleted file mode 100644 index 88aaaeb..0000000 --- a/2024/work/phil-1/paper-1-typix/flake.lock +++ /dev/null @@ -1,99 +0,0 @@ -{ - "nodes": { - "flake-utils": { - "inputs": { - "systems": "systems" - }, - "locked": { - "lastModified": 1726560853, - "narHash": "sha256-X6rJYSESBVr3hBoH0WbKE5KvhPU5bloyZ2L4K60/fPQ=", - "owner": "numtide", - "repo": "flake-utils", - "rev": "c1dfcf08411b08f6b8615f7d8971a2bfa81d5e8a", - "type": "github" - }, - "original": { - "owner": "numtide", - "repo": "flake-utils", - "type": "github" - } - }, - "nixpkgs": { - "locked": { - "lastModified": 1729256560, - "narHash": "sha256-/uilDXvCIEs3C9l73JTACm4quuHUsIHcns1c+cHUJwA=", - "owner": "NixOS", - "repo": "nixpkgs", - "rev": "4c2fcb090b1f3e5b47eaa7bd33913b574a11e0a0", - "type": "github" - }, - "original": { - "owner": "NixOS", - "ref": "nixos-unstable", - "repo": "nixpkgs", - "type": "github" - } - }, - "root": { - "inputs": { - "flake-utils": "flake-utils", - "nixpkgs": "nixpkgs", - "typix": "typix", - "typst-packages": "typst-packages" - } - }, - "systems": { - "locked": { - "lastModified": 1681028828, - "narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=", - "owner": "nix-systems", - "repo": "default", - "rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e", - "type": "github" - }, - "original": { - "owner": "nix-systems", - "repo": "default", - "type": "github" - } - }, - "typix": { - "inputs": { - "nixpkgs": [ - "nixpkgs" - ] - }, - "locked": { - "lastModified": 1728290750, - "narHash": "sha256-piLZT8398O69hy0e3gX8hUWqSzbCslMCt10pT8d6c8E=", - "owner": "loqusion", - "repo": "typix", - "rev": "62d032735ad32a9a90225c06cb0857677fc753ee", - "type": "github" - }, - "original": { - "owner": "loqusion", - "repo": "typix", - "type": "github" - } - }, - "typst-packages": { - "flake": false, - "locked": { - "lastModified": 1729252723, - "narHash": "sha256-xdaQYNw1GApaJnXJO4WnUTNuYeRXisxIUSuAzVXFEW4=", - "owner": "typst", - "repo": "packages", - "rev": "9bcf190c85da91be6df9f5fc25a93ce5812489cc", - "type": "github" - }, - "original": { - "owner": "typst", - "repo": "packages", - "type": "github" - } - } - }, - "root": "root", - "version": 7 -} diff --git a/2024/work/phil-1/paper-1-typix/flake.nix b/2024/work/phil-1/paper-1-typix/flake.nix deleted file mode 100644 index d4bd532..0000000 --- a/2024/work/phil-1/paper-1-typix/flake.nix +++ /dev/null @@ -1,126 +0,0 @@ -{ - description = "A Typst project"; - - inputs = { - nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable"; - - typix = { - url = "github:loqusion/typix"; - inputs.nixpkgs.follows = "nixpkgs"; - }; - - flake-utils.url = "github:numtide/flake-utils"; - - typst-packages = { - url = "github:typst/packages"; - flake = false; - }; - - # Example of downloading icons from a non-flake source - # font-awesome = { - # url = "github:FortAwesome/Font-Awesome"; - # flake = false; - # }; - }; - - outputs = - inputs@{ - nixpkgs, - typix, - flake-utils, - ... - }: - flake-utils.lib.eachDefaultSystem ( - system: - let - pkgs = nixpkgs.legacyPackages.${system}; - in - let - typstPackagesSrc = "${inputs.typst-packages}/packages"; - - typstPackagesCache = pkgs.stdenv.mkDerivation { - name = "typst-packages-cache"; - src = typstPackagesSrc; - dontBuild = true; - installPhase = '' - mkdir -p "$out/typst/packages" - cp -LR --reflink=auto --no-preserve=mode -t "$out/typst/packages" "$src"/* - ''; - }; - in - let - inherit pkgs; - typixLib = typix.lib.${system}; - - src = typixLib.cleanTypstSource ./.; - commonArgs = { - typstSource = "main.typ"; - - fontPaths = [ - # Add paths to fonts here - # "${pkgs.roboto}/share/fonts/truetype" - ]; - - virtualPaths = [ - # Add paths that must be locally accessible to typst here - # { - # dest = "icons"; - # src = "${inputs.font-awesome}/svgs/regular"; - # } - ]; - }; - - # Compile a Typst project, *without* copying the result - # to the current directory - build-drv = typixLib.buildTypstProject ( - commonArgs - // { - inherit src; - XDG_CACHE_HOME = typstPackagesCache; - } - ); - - # Compile a Typst project, and then copy the result - # to the current directory - build-script = typixLib.buildTypstProjectLocal ( - commonArgs - // { - inherit src; - XDG_CACHE_HOME = typstPackagesCache; - } - ); - - # Watch a project and recompile on changes - watch-script = typixLib.watchTypstProject commonArgs; - in - { - checks = { - inherit build-drv build-script watch-script; - }; - - packages.default = build-drv; - - apps = rec { - default = watch; - build = flake-utils.lib.mkApp { - drv = build-script; - }; - watch = flake-utils.lib.mkApp { - drv = watch-script; - }; - }; - - devShells.default = typixLib.devShell { - inherit (commonArgs) fontPaths virtualPaths; - packages = [ - # WARNING: Don't run `typst-build` directly, instead use `nix run .#build` - # See https://github.com/loqusion/typix/issues/2 - # build-script - watch-script - # More packages can be added here, like typstfmt - pkgs.typstyle - ]; - }; - } - ); -} diff --git a/2024/work/phil-1/paper-1-typix/main.typ b/2024/work/phil-1/paper-1-typix/main.typ deleted file mode 100644 index 9083311..0000000 --- a/2024/work/phil-1/paper-1-typix/main.typ +++ /dev/null @@ -1,2 +0,0 @@ -= Lorem ipsum -#lorem(30) diff --git a/2024/work/phil-1/paper-1/main.pdf b/2024/work/phil-1/paper-1/main.pdf deleted file mode 100644 index f2d047b06e18e47754cb18b4a06fb87a2fed9e7c..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 451151 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Discounts - content in tables and the AI contribution statement. - ] - ], - ), -) - - -= Introduction - -The argument for Betting on God says that you should believe in God, regardless -of other evidence, purely out of self-interest. In this paper, I challenge this -argument by assessing the premise that believing in a particular God always -guarantees the greatest expected utility. - -The author's argument for belief in God #cite(supplement: [p. 38], -) goes as follows: - -#indented-argument( - title: "The Argument for Betting on God", - abbreviation: "BG", - [One should always choose the option with the greatest expected utility.], - [Believing in God has a greater expected utility than not believing in God.], - [So, you should believe in God.], -) - -BG1 should be uncontroversial. If you expect an action to bring you the most -utility (i.e. be the most useful), it's rational to do it. - -To justify BG2, the author uses a so-called "decision matrix" to compute the -expected utility of each combination of action and possible outcome. The -possible actions are placed on the rows, and the possible outcomes are placed -on the columns, except for the last column, which is the calculated expected -utility. At each intersection of a row and column, we place the utility we gain -from that combination of action and outcome. The expected utility for a given -action is computed by multiplying the utility of each action-outcome pair in -that row by the probability of the corresponding outcome occurring, and summing -up all of those values. - -Here is the decision matrix the author proposes on #cite(supplement: [p. 38], -) which gives the expected utility for believing or not -believing in God. - -#show table.cell.where(x: 0): strong -#show table.cell.where(y: 0): strong - -#figure( - caption: [Author's decision matrix], - align( - center, - table( - columns: (auto, auto, auto, auto), - table.header( - [], - [God exists ($50%$)], - [God doesn't exist ($50%$)], - [Expected utility], - ), - - [ Believe in God ], [$infinity$], [2], [$infinity$], - [ - Don't believe in God - ], - [1], - [3], - [2], - ), - ), -) - -Note that the numerical utility values themselves have no meaning, and they are -meant to be viewed relative to each other. Utility doesn't literally provide an -empirical measure of "usefulness" or "happiness." - -We assign the various finite utilities as we see fit, based on how much each -scenario benefits us. In the case where God does exist, and you believed in -God, then you are rewarded with an eternal afterlife of bliss and pleasure in -heaven. This reward is infinitely greater than any possible reward on earth, so -it has a utility of $infinity$. - -So, the expected utility for not believing is $0.5 times 1 + 0.5 times 3 = 2$, -and the expected utility is $0.5 times infinity + 0.5 times 2 = infinity$. If, -according to BG1, you should pick the option with greatest expected utility, -clearly you should choose to believe in God, because the expected utility is -$infinity$. - -The exact utilities don't matter much, since any finite utility you could gain -for atheism cannot possibly be greater than the infinite expected utility of -believing in God. Also, as the author points out on #cite(, -supplement: [p. 40]), the exact probabilities don't matter either since -multiplying them by $infinity$ still results in the expected utility of -$infinity$. - -I will show that the Argument for Betting on God fails because BG2 fails. In -section 2, I argue you cannot determine whether or not believing in God has the -greatest expected utility because the decision matrix approach fails when -possible outcomes involving infinitely negative utilities are introduced. In -section 3, I address a possible response to this objection. - -= Possibility of Infinite Suffering - -It is possible there are more gods than just the one that sends you to an -eternal afterlife for believing? The author partially addresses this in -#cite(, supplement: [pp. 43-44]), using the example of Zeus. -Zeus will only reward those who believe in him with an eternal afterlife of -pleasure. So, if you believe in the wrong god, you don't go to the afterlife. -The author concludes either believing in Zeus or the Christian God still has -expected utilities of $infinity$, while being an atheist does has a finite -expected utility. Therefore, it is still preferable to believe in _some_ god -that may grant you an eternal afterlife, although no argument is made for -_which_ god. - -However, this leaves out the possibility of gods who punish you for some -reason. For instance, suppose there exists an _Evil God_ who sends anyone who -believes in any god to hell for eternity, and does nothing to atheists. - -Let us modify our decision matrix to model an outcome where the Evil God -exists. - -#pagebreak() - -#[ - #set figure() - #figure( - caption: [Possibility of an Evil God], - table( - columns: (auto, auto, auto, auto, auto), - align: center, - table.header( - [], - [Correct god exists ($33.3%$)], - [No god exists ($33.3%$)], - [Evil God exists ($33.3%$)], - [E.U.], - ), - - [ Believe in some God ], [$infinity$], [1], [$-infinity$], [$?$], - [ - Don't believe in any God - ], - [2], - [3], - [4], - [4.5], - ), - ) -] - -We've added the new option to our matrix. For the sake of argument, let's say -each option has an equally likely outcome. Again, the exact probabilities don't -really matter when we're multiplying them by infinity. - -The utilities are mostly the same as before. Not believing in any god and the -Evil God existing is now the best case for the atheist since they avoided -infinite suffering. However, the theist now faces the possibility of the worst -case of all: eternal punishment for believing in the wrong god. If eternal -bliss in heaven has a utility of $infinity$, then it follows that we should -represent eternal punishment in hell with a utility of $-infinity$. - -There is a problem: how do we calculate the expected utility of believing in -god? We have $0.333 times infinity + 0.333 times 1 + 0.333 times -infinity$. -What is $infinity - infinity$? A naive answer might be 0, but infinity is not a -number in the traditional sense. It makes no sense to add or subtract infinite -values. For instance, try and subtract the total amount of integers -($infinity$) from the total amount of real numbers (also $infinity$) -#footnote[Famously, this infinity is "larger" than the infinite number of -integers in the sense of cardinality (G. Cantor). But subtracting them still -makes no mathematical or physical sense.]. Clearly, this notion is meaningless -and we cannot obtain a solution. So, we consider $infinity - infinity$ an -_indeterminate form_. So, the expected utility is now _undefined_. - -Consider the following Indeterminate Utilities argument: - -#indented-argument( - title: "The Indeterminate Utilities argument", - abbreviation: "IU", - [If the expected utility of believing in god is undefined, then we - cannot compare the expected utilities of believing in god or not believing - in god.], - [The expected utility of believing in god is undefined.], - [So, we cannot compare the expected utilities of believing in god or - not believing in god. - ], - [If we cannot compare the expected utilities of believing in god or - not believing in god, then we cannot determine if believing in god has a - higher expected utility than not believing in god. - ], - [So, we cannot determine if believing in god has a higher expected - utility than not believing in god. ], -) - -We just showed why the premise IU2 is true, and the conclusion IU5 is in direct -contradiction with BG2. So, if IU5 holds, then BG2 must fail. - -It's important to note that the Indeterminate Utilities argument doesn't say -that the _opposite_ of BG2 is true. It doesn't argue that the expected utility -of being an atheist is greater. In fact, it doesn't say anything about the -expected utilities, except that they cannot be compared. If they can't be -compared, then we can't say for certain which option has the higher expected -utility. Since BG2 claims that believing in god must have the higher expected -utility, it is a false premise. - -= Addressing Objections - -// == Believing in a god is still preferable to atheism -// -// One might argue that believing in a god that rewards believers is always -// preferable to atheism since you at least have the _opportunity_ to receive -// eternity in heaven. Perhaps there exists a god who punishes non-believers with -// eternal damnation. Then, even without the exact expected utility calculation, -// it's clear that the expected utility of believing in some god must be higher -// than believing in none as you stand to gain more. Either as a theist or -// atheist, you run the risk of eternal punishment, but you only have the -// opportunity to go to heaven by believing in some god rather than none. -// -// Fair, the possibility that you are punished for believing in the wrong god -// doesn't imply that you should be an atheist either. Indeed, there may be a god -// that punishes atheists. However, there could also exist a god who sends -// everyone to heaven regardless. Or perhaps they only send atheists to heaven. -// Either way, there is also the possibility of attaining the infinite afterlife -// in heaven by being an atheist, so it's still impossible to say that the -// expected utility of believing in god is must be higher. - -== The Evil God is not plausible - -One might argue that it is not plausible there is an Evil God who punishes all -theists, including their own believers. Many religions present a god that -rewards believers and at most punishes disbelievers. None of the major world -religions propose an Evil God who punishes all believers. It's much more likely -that a benevolent god exists than an evil one. - -I contend that it doesn't matter whether or not the Evil God is less plausible -than a benevolent god. Surely, if a rational atheist who is unconvinced by all -the world's scriptures can still concede that there is at least a non-zero -chance that some god exists, the rational theist should also concede that there -is a non-zero chance that the Evil God exists. All it takes is that non-zero -chance, no matter how small, because multiplying it by $-infinity$ still -results in the undefined expected utility. - -== Finite utilities - -One might argue that we can avoid using $infinity$ to ensure that all expected -utility calculations are defined. Instead, suppose that the utility of going to -heaven is just an immensely large finite number. The utility of going to hell -is likewise a very negative number. All of our expected utility calculations -will be defined, and given sufficiently large utilities, we should be able to -make a similar argument for believing in god. - -// The problem with this argument is that we now open our expected utilities up to -// individual subjective determination. A core feature of the previous argument -// involving infinite utilities is that they can effectively bypass numerical -// comparison. If, instead, finite utilities were used, then each person may -// assign different utilities to each possible outcome based on their own beliefs. -// Also, the probabilities are no longer irrelevant, so they must be analyzed as -// well. This greatly complicates the decision matrix. - -The problem with this argument is that infinity has a special property the -argument relies on. Namely, any number multiplied by $infinity$ is still -$infinity$, so the exact probabilities we set for the existence of God don't -matter. This is important for defending against the objection the author -mentions on #cite(, supplement: [p. 40]), that the -probabilities are possibly incorrect, since the numbers don't matter anyways. - -If, instead, only finite utilities were used, then the theist must contend with -the concern that the probabilities in the matrix are wrong. There could -conceivably exist a matrix with probabilities for a benevolent god and an Evil -God such that the expected utility of atheism is actually higher. The issue is -we cannot say for sure what the probabilities of the benevolent god and the -Evil God existing are. If we cannot know what the actual probabilities are, -then we cannot know the final outcome of our matrix. So, without knowing the -final outcome of the matrix, we still cannot determine whether or not believing -in god has greater expected utility, and BG2 still fails. - -#pagebreak() - -#[ - = AI Contribution Statement - - #quote[I did not use AI whatsoever in the writing of this paper.] -] diff --git a/2024/work/phil-1/paper-1/package.nix b/2024/work/phil-1/paper-1/package.nix deleted file mode 100644 index f5cccee..0000000 --- a/2024/work/phil-1/paper-1/package.nix +++ /dev/null @@ -1,49 +0,0 @@ -{ - pkgs, - typstPackagesCache, - typixLib, - ... -}: -let - src = typixLib.cleanTypstSource ./.; - commonArgs = { - typstSource = "main.typ"; - - fontPaths = [ - # Add paths to fonts here - # "${pkgs.roboto}/share/fonts/truetype" - ]; - - virtualPaths = [ - # Add paths that must be locally accessible to typst here - # { - # dest = "icons"; - # src = "${inputs.font-awesome}/svgs/regular"; - # } - ]; - - XDG_CACHE_HOME = typstPackagesCache; - }; - - # Compile a Typst project, *without* copying the result - # to the current directory - build-drv = typixLib.buildTypstProject ( - commonArgs - // { - inherit src; - } - ); - - # Compile a Typst project, and then copy the result - # to the current directory - build-script = typixLib.buildTypstProjectLocal ( - commonArgs - // { - inherit src; - } - ); - - # Watch a project and recompile on changes - watch-script = typixLib.watchTypstProject commonArgs; -in -build-drv diff --git a/2024/work/phil-1/paper-1/prelude.typ b/2024/work/phil-1/paper-1/prelude.typ deleted file mode 100644 index 226aa28..0000000 --- a/2024/work/phil-1/paper-1/prelude.typ +++ /dev/null @@ -1,21 +0,0 @@ -#set cite(style: "institute-of-electrical-and-electronics-engineers") -#set text(fractions: true) - -#let indented-argument(title: "", abbreviation: "", ..args) = [ - #set par(first-line-indent: 0pt) - - #pad(left: 12pt, smallcaps(title)) - - #let arg-numbering = (..nums) => nums.pos().map(n => ( - "(" + abbreviation + str(n) + ")" - )).join() - - #enum( - numbering: arg-numbering, - indent: 16pt, - tight: false, - ..args.pos(), - ) -] - - diff --git a/2024/work/phil-1/paper-1/refs.bib b/2024/work/phil-1/paper-1/refs.bib deleted file mode 100644 index 25f6815..0000000 --- a/2024/work/phil-1/paper-1/refs.bib +++ /dev/null @@ -1,7 +0,0 @@ -@book{Korman2022-KORLFA, - author = {Daniel Z. Korman}, - editor = {}, - publisher = {The PhilPapers Foundation}, - title = {Learning From Arguments: An Introduction to Philosophy}, - year = {2022} -}