Daily Archives: April 7, 2022

Quick Calculation 3.2

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A First Course in String Theory

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Verify that the gauge transformation (3.10) are correctly summarized by (3.21).

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Eq. (3.21):

\displaystyle{ \begin{aligned} A_\nu' &= A_\nu + \partial_\nu \epsilon \\ \end{aligned} }

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\displaystyle{ \begin{aligned} \left( A_0', A_1', ... \right) &= \left( - \Phi + \frac{\partial \epsilon}{\partial x^0}, A^1 + \frac{\partial \epsilon}{\partial x^1}, ... \right) \\ \left( -\Phi', {A^1}', ... \right) &= \left( - \Phi + \frac{1}{c} \frac{\partial \epsilon}{\partial t}, A^1 + \frac{\partial \epsilon}{\partial x^1}, ... \right) \\ \end{aligned} }

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\displaystyle{ \begin{aligned} \Phi' &= \Phi - \frac{1}{c} \frac{\partial \epsilon}{\partial t} \\ \left( {A^1}', {A^2}', {A^3}' \right) &= \left( {A^1}, {A^2}, {A^3} \right) + \left( \frac{\partial}{\partial x^1}, \frac{\partial}{\partial x^2}, \frac{\partial}{\partial x^3} \right) \epsilon \\ \end{aligned} }

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Eq. (3.10):

\displaystyle{ \begin{aligned} \Phi' &= \Phi - \frac{1}{c} \frac{\partial \epsilon}{\partial t} \\ \vec A' &= \vec A + \nabla \epsilon \\ \end{aligned} }

— Me@2022-04-07 07:05:29 PM

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2022.04.07 Thursday (c) All rights reserved by ACHK

C and Lisp

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numeromancer on Jan 25, 2010 [-]

In every art there is a dichotomy between the practical and the theoretical, and each has their fundamentals. In Comp. Sci., those two sets of fundamentals are these: sets of machine instructions, which come in several varieties; and lambda calculus, or one of the equivalent (by Church’s Thesis) formal systems. C and Lisp are similar in that they represent the first steps in each case to reach the other: C is a level above machine code, providing some abstraction and portability to the use of machine code, the fundamental elements of practical computing; lisp is a level above lambda calculus, providing a practical system for using functions, the fundamental elements of theoretical computing.

In short, mastery of C is concomitant with the ability to measure the cost of computation (sometimes, regardless of the value of it); mastery of Lisp is concomitant with the ability to measure the value of computation (sometimes, regardless of the cost).

Since C and Lisp lie on opposite borders of the universe of computation, knowing both will allow you to better measure the scope of that universe.

— Ask HN: Why does learning lisp make you a better C-programmer?

— Hacker News

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2022.04.07 Thursday ACHK

Circus

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drblast on Oct 27, 2010 | next [–]

Living with one child is like living with a demanding, but mostly reasonable, roommate who really likes spending time with you until she goes to bed early.

Having two or more children is like living in a circus where all the performers are deaf.

— Ask HN: How does having a baby change your life?

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2022.04.07 Thursday ACHK