2034: Equations - Revision history

92.23.2.208: Undo revision 402119 by 104.225.177.124 (talk) Revised undo to make comment as intended. The end of a "< ! - -" tag is not a "- - ! >" but a "- - >" one... minus spaces (justincase!)

2025-12-19T22:18:58Z

Undo revision 402119 by 104.225.177.124 (talk) Revised undo to make comment as intended. The end of a "< ! - -" tag is not a "- - ! >" but a "- - >" one... minus spaces (justincase!)

104.225.177.124: I'm just going to put this here. S_g=\frac{-1}{2\bar{\varepsilon}}ið\hat{\big(}\xi_0\overset{\circ}{+}\rho_\varepsilon\rho_\text{v}^\text{abc}\cdot\eta_0\hat{\big)} (why did that end the article there)

2025-12-19T16:51:37Z

I'm just going to put this here. S_g=\frac{-1}{2\bar{\varepsilon}}ið\hat{\big(}\xi_0\overset{\circ}{+}\rho_\varepsilon\rho_\text{v}^\text{abc}\cdot\eta_0\hat{\big)} (why did that end the article there)

97.64.62.188: a

2025-12-19T16:45:12Z

172.71.195.24: /* Explanation */ ¬HeAt

2025-03-28T19:34:54Z

‎Explanation: ¬HeAt

172.70.85.133: /* Explanation */ Dealt with the MathML/TeX display error by inserting the direct unicode symbol. If it doesn't work for everyone, it should at least start working for many.

2024-11-06T22:53:59Z

‎Explanation: Dealt with the MathML/TeX display error by inserting the direct unicode symbol. If it doesn't work for everyone, it should at least start working for many.

172.69.6.182: Some minor stylistic changes

2024-10-01T09:27:44Z

Some minor stylistic changes

172.70.114.28: wording change

2024-09-16T00:17:28Z

wording change

162.158.159.192: expanded gauge theory section

2024-09-16T00:16:09Z

expanded gauge theory section

ConscriptGuide at 23:02, 12 August 2024

2024-08-12T23:02:19Z

172.70.210.249: /* Explanation */

2024-08-01T04:30:23Z

‎Explanation

@@ Line 36: / Line 36: @@
 Quantum gravity uses mathematical {{w|Group (mathematics)|groups}} denoted by uppercase letters, as shown. {{w|Special unitary group|SU(2)}}, {{w|Unitary group|U(1)}}, and {{w|Unitary group|U(2)}} are all well-studied groups, though 'SU(U(2))' makes no sense.  The lack of relator means this expression isn't an equation, but an expression.
-:[[File:All gauge theory equations.png]]
+:[[File:All gauge theory equations.png]] <!-- So far, I have S_g=\frac{-1}{2\bar{\varepsilon}}ið\hat{\big(}\xi_0\overset{\circ}{+}\rho_\varepsilon\rho_\text{v}^\text{abc}\cdot\eta_0\hat{\big)}. -->
 ;All {{w|gauge theory}} equations
 Gauge theory is a subset of quantum field theory. Because the objects in gauge theory carry a lot of symmetry information, they tend to have a lot of indices and twiddly annotations. Shorthand, such the {{w|Feynman slash}}, is also very common. Although most of the symbols used here do not have specific meanings in gauge theory, &xi; corresponds to the {{w|Gauge fixing#Rξ gauges|Rξ gauges}} in quantum electrodynamics, and the  "abc" superscript is reminiscent of a {{w|structure constant}}.

@@ Line 36: / Line 36: @@
 Quantum gravity uses mathematical {{w|Group (mathematics)|groups}} denoted by uppercase letters, as shown. {{w|Special unitary group|SU(2)}}, {{w|Unitary group|U(1)}}, and {{w|Unitary group|U(2)}} are all well-studied groups, though 'SU(U(2))' makes no sense.  The lack of relator means this expression isn't an equation, but an expression.
-:[[File:All gauge theory equations.png]] <!-- So far, I have S_g=\frac{-1}{2\bar{\varepsilon}}ið\hat{\big(}\xi_0\overset{\circ}{+}\rho_\varepsilon\rho_\text{v}^\text{abc}\cdot\eta_0\hat{\big)}. --!>
+:[[File:All gauge theory equations.png]]
 ;All {{w|gauge theory}} equations
 Gauge theory is a subset of quantum field theory. Because the objects in gauge theory carry a lot of symmetry information, they tend to have a lot of indices and twiddly annotations. Shorthand, such the {{w|Feynman slash}}, is also very common. Although most of the symbols used here do not have specific meanings in gauge theory, &xi; corresponds to the {{w|Gauge fixing#Rξ gauges|Rξ gauges}} in quantum electrodynamics, and the  "abc" superscript is reminiscent of a {{w|structure constant}}.

@@ Line 36: / Line 36: @@
 Quantum gravity uses mathematical {{w|Group (mathematics)|groups}} denoted by uppercase letters, as shown. {{w|Special unitary group|SU(2)}}, {{w|Unitary group|U(1)}}, and {{w|Unitary group|U(2)}} are all well-studied groups, though 'SU(U(2))' makes no sense.  The lack of relator means this expression isn't an equation, but an expression.
-:[[File:All gauge theory equations.png]]
+:[[File:All gauge theory equations.png]] <!-- So far, I have S_g=\frac{-1}{2\bar{\varepsilon}}ið\hat{\big(}\xi_0\overset{\circ}{+}\rho_\varepsilon\rho_\text{v}^\text{abc}\cdot\eta_0\hat{\big)}. --!>
 ;All {{w|gauge theory}} equations
 Gauge theory is a subset of quantum field theory. Because the objects in gauge theory carry a lot of symmetry information, they tend to have a lot of indices and twiddly annotations. Shorthand, such the {{w|Feynman slash}}, is also very common. Although most of the symbols used here do not have specific meanings in gauge theory, &xi; corresponds to the {{w|Gauge fixing#Rξ gauges|Rξ gauges}} in quantum electrodynamics, and the  "abc" superscript is reminiscent of a {{w|structure constant}}.

@@ Line 30: / Line 30: @@
 :<math>CH_4+OH+HEAT\rightarrow{}H_2O+CH_{2}+H_2EAT</math>
 ;All {{w|chemistry}} equations
-Chemistry equations use formulas of chemical compounds to describe a chemical reaction. Such equations show the starting chemicals on the left side and the resulting products on the right side, as displayed. Sometimes such an equation might optionally indicate that an {{w|activation energy}} is required, for the reaction to take place in a sensible timeframe, e.g. by heating. A reaction requiring heating is usually indicated by a Greek capital letter Delta (''&Delta;'') or a specified temperature above the reaction arrow, however this comic uses the "+ HEAT" term on the left side instead. The joke is that Randall interprets "HEAT" to be another chemical, possibly the nonsensical helium-monastatide, which reacts with Hydrogen (H) to H<sub>2</sub>EAT, which is nonsensical, as heat is transferred energy here, not added matter. Regardless of this, Randall gets the {{w|stoichiometry}} of this equation correct, with the same number of all types of 'atoms' on each side of the equation.
+Chemistry equations use formulas of chemical compounds to describe a chemical reaction. Such equations show the starting chemicals on the left side and the resulting products on the right side, as displayed. Sometimes such an equation might optionally indicate that an {{w|activation energy}} is required, for the reaction to take place in a sensible timeframe, e.g. by heating. A reaction requiring heating is usually indicated by a Greek capital letter Delta (''&Delta;'') or a specified temperature above the reaction arrow, however this comic uses the "+ HEAT" term on the left side instead. The joke is that Randall interprets "HEAT" to be another chemical which reacts with Hydrogen (H) to H<sub>2</sub>EAT, which is nonsensical, as heat is transferred energy here, not added matter. Regardless of this, Randall gets the {{w|stoichiometry}} of this equation correct, with the same number of all types of 'atoms' on each side of the equation.
 :<math>SU(2)U(1)\times{}SU(U(2))</math>

@@ Line 22: / Line 22: @@
 :<math>\frac{\partial}{\partial{t}}\nabla\!\cdot\!\rho=\frac{8}{23}\int\!\!\!\!\int\!\!\!\!\!\!\!\!\!\subset\!\!\supset\rho\,{ds}\,{dt}\cdot{}\rho\frac{\partial}{\partial\nabla}</math>
 ;All {{w|fluid dynamics}} equations
-Fluid dynamics equations often involve copious use of vector calculus operators. It's common in field theories like fluid dynamics and electromagnetism to represent equations of motion using multidimensional operators, like the <math>\nabla</math> and closed contour integral <math>\oint</math> which appear here. The fraction 8/23 is a comically weird choice, but various unexpected fractions do pop up in fluid dynamics. The ds and dt go with the double contour integral (s is probably distance, t is time), but the derivative with respect to <math>\nabla</math> at the end is very much a joke and not allowed.
+Fluid dynamics equations often involve copious use of vector calculus operators. It's common in field theories like fluid dynamics and electromagnetism to represent equations of motion using multidimensional operators, like the <math>\nabla</math> and closed contour integral ∮ which appear here. The fraction 8/23 is a comically weird choice, but various unexpected fractions do pop up in fluid dynamics. The ds and dt go with the double contour integral (s is probably distance, t is time), but the derivative with respect to <math>\nabla</math> at the end is very much a joke and not allowed.
 :<math>|\psi_{x,y}\rangle=A(\psi)A(|x\rangle\otimes|y\rangle)</math>

@@ Line 14: / Line 14: @@
 :<math>E=K_{0}t+\frac{1}{2}\rho{}vt^2</math>
 ;All {{w|kinematics}} equations
-Most kinematics equations tend to make heavy use of constants, addition, powers, and multiplication. This specific equation resembles the actual kinematics equation d = vt + 1/2at^2, but replaces a (acceleration) with v (velocity) times <math>\rho{}</math> (density) and replaces velocity with "K<sub>0</sub>", which is not a term used in kinematics.
+Most kinematics equations are polynomials, usually at most quadratic, and are often integral quantities (corresponding to the 1/2 t^2 term). This specific equation resembles the actual kinematics equation d = vt + 1/2at^2, but replaces a (acceleration) with v (velocity) times <math>\rho{}</math> (density) and replaces velocity with "K<sub>0</sub>", which is not a term used in kinematics.
 :<math>K_{n}=\sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)(i+e^{\pi-\infty})</math>
 ;All {{w|number theory}} equations
-Randall jokes about how number theory often involves the use of summations. The use of ''&pi;'' as an integer variable in the double summation is a joke, as ''&pi;'' is essentially always used for the well-known constant 3.14159..., not a variable. The use of ''i'' as a summation variable '''is''' common, though it can also be confused with the imaginary unit &radic;-1. The constants ''e'', ''i'', and ''&pi;'', as well as the theoretical upper bound <math>\infty</math>, often appear in number theory equations.
+Number theory is the study of the integers and their properties. Randall jokes about how this often involves the use of summations over integers. The subscripts are indices, but the use of ''&pi;'' as a summation index is a joke — ''&pi;'' is almost always used for the well-known constant 3.14159..., not a variable. The use of ''i'' as a summation variable '''is''' common, but the joke is that when it appears along with the constant ''e'', as it does here it usually represents the imaginary unit &radic;-1. As well, the constant ''e'' is out-of-place in a field like number theory — it's more closely related to fields like calculus/analysis. The use of the symbol <math>\infty</math> as a literal is also a joke.
 :<math>\frac{\partial}{\partial{t}}\nabla\!\cdot\!\rho=\frac{8}{23}\int\!\!\!\!\int\!\!\!\!\!\!\!\!\!\subset\!\!\supset\rho\,{ds}\,{dt}\cdot{}\rho\frac{\partial}{\partial\nabla}</math>
 ;All {{w|fluid dynamics}} equations
-Fluid dynamics equations often involve copious integrals, especially those over closed contours as done here, which are often the main telling factors of those equations to an outsider. The time derivative and gradient operator <math>\nabla</math> are common in fluid dynamics, mostly via the Navier-Stokes equation, and the fluid density <math>\rho</math> is one of the functions of central importance. The fraction 8/23 is a comically weird choice, but various unexpected fractions do pop up in fluid dynamics. The ds and dt go with the double contour integral (s is probably distance, t is time), but the derivative with respect to <math>\nabla</math> at the end is very much not allowed.
+Fluid dynamics equations often involve copious use of vector calculus operators. It's common in field theories like fluid dynamics and electromagnetism to represent equations of motion using multidimensional operators, like the <math>\nabla</math> and closed contour integral <math>\oint</math> which appear here. The fraction 8/23 is a comically weird choice, but various unexpected fractions do pop up in fluid dynamics. The ds and dt go with the double contour integral (s is probably distance, t is time), but the derivative with respect to <math>\nabla</math> at the end is very much a joke and not allowed.
 :<math>|\psi_{x,y}\rangle=A(\psi)A(|x\rangle\otimes|y\rangle)</math>

@@ Line 35: / Line 35: @@
 ;All {{w|quantum gravity}} equations
 Quantum gravity uses mathematical {{w|Group (mathematics)|groups}} denoted by uppercase letters, as shown. {{w|Special unitary group|SU(2)}}, {{w|Unitary group|U(1)}}, and {{w|Unitary group|U(2)}} are all well-studied groups, though 'SU(U(2))' makes no sense.  The lack of relator means this expression isn't an equation, but an expression.
 :[[File:All gauge theory equations.png]]
 ;All {{w|gauge theory}} equations
-Gauge theory is a subset of field theory. Most gauge theory equations appear to have many strange-looking constants and variables with odd labels. However, almost none of the symbols used here are found or applicable to gauge theory.
+Gauge theory is a subset of quantum field theory. Because the objects in gauge theory carry a lot of symmetry information, they tend to have a lot of indices and twiddly annotations. Shorthand, such the {{w|Feynman slash}}, is also very common. Although most of the symbols used here do not have specific meanings in gauge theory, &xi; corresponds to the {{w|Gauge fixing#Rξ gauges|Rξ gauges}} in quantum electrodynamics, and the  "abc" superscript is evocative of a {{w|structure constant}}.
 :<math>H(t)+\Omega+G\!\cdot\!\Lambda...\begin{cases}...>0\mathrm{\ (Hubble\ model)}\\

@@ Line 87: / Line 87: @@
 {{comic discussion}}
+[[Category:Comics with lowercase text]]
 [[Category:Science]]
 [[Category:Physics]]