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8 episodes with partial derivatives
8 episodes with partial derivatives
12 episodes with partial derivatives
6 episodes with partial derivatives
28 episodes with partial derivatives
28 episodes with partial derivatives
2 episodes with partial derivatives
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Taking responsibility and partial derivatives, published by Ruby on December 31, 2023 on LessWrong. A common pattern for myself over the years is to get into some kind of interpersonal ~"conflict", feel mildly to extremely indignant about how the other person is at fault, then later either through confrontation or reflection, realize that I actually held substantial responsibility. I then feel very guilty. (When I say "conflict" I mean something broader, e.g. I mean to include cases where you're mad at your boss even if you never actually confront them.) I noticed this pattern some years ago such I did become skeptical of my indignation even when I couldn't yet see where I was responsible. Yet this led me to a feeling of frustration. How is it that I'm always at fault? Why can I never be justifiably indignant at someone else? I believe the answer to this can be explained via partial derivatives. It doesn't have to be explained via partial derivatives, but I think partial derivatives are this super great concept that's helpful all over the place[1], so I'm going to invoke it. See this footnote for a quick explanation[2]. Suppose we have a Situation in which there is a Problem. In the real world, any Situation is composed of a large number of parameters. The amount of Problem there is is a function of the parameters. And for any interpersonal situation, different parameters are controlled by the different parties involved in the situation. The needlessly mathematical Partial Derivative Model of Interpersonal Conflict says that for any nontrivial situation, likely both partners control parameters that have non-negligible impact on how much of a Problem there is. In other words, if you want to blame the other person, you'll succeed. And if you want to blame yourself, you'll succeed. I have been good at doing those serially, but might be a better model to them in parallel: see all the ways in which each of you are contributing to the amount of Problem. This isn't to say that always everyone is equally to blame. If someone runs a red light and hits your car, they're at fault even if you could have chosen to work from home that day. In many cases, it's less clear cut and I think it's worth tracking how each person is contributing. The asymmetry in the situation is that by definition you control the parameters you're in control of, so it's worthwhile paying attention them. If you can get over being Right and instead focus on the outcomes you want, you might be able to attain them even if you're compensating for the mistakes of the other person. (A note on compensating for the mistakes of the other person. This might get you the outcomes you want, but I think can be unhealthy or unbalanced. If I have a colleague who feels easily insulted and I do extra emotional work to avoid doing that, it might work, but it's imbalanced. I venture that imbalanced situations between adults and children, and [senior] managers and [junior] employees are okay, but between peers, you want balance. You want to be making and compensating for mistakes in equal measure, not one person enabling the flaws of the other. Possibly the best thing to do if you think someone is at fault and you're at risk of compensating for it, is it to go have a conversation with them about it - but do so in an open-minded way where you're open to the possibility you're more at fault than you realize.) Something to note is that while I've framed this is the Problem as a function of the parameters, as though we have a function evaluated at single point in time, in fact interpersonal situations have more of a "game" (in the game theory sense) element to them. The other person's behavior might be a response to your behavior and their models of you, your behavior might be a response to their behavior and your models of them, ...
Link to original articleWelcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Taking responsibility and partial derivatives, published by Ruby on December 31, 2023 on LessWrong. A common pattern for myself over the years is to get into some kind of interpersonal ~"conflict", feel mildly to extremely indignant about how the other person is at fault, then later either through confrontation or reflection, realize that I actually held substantial responsibility. I then feel very guilty. (When I say "conflict" I mean something broader, e.g. I mean to include cases where you're mad at your boss even if you never actually confront them.) I noticed this pattern some years ago such I did become skeptical of my indignation even when I couldn't yet see where I was responsible. Yet this led me to a feeling of frustration. How is it that I'm always at fault? Why can I never be justifiably indignant at someone else? I believe the answer to this can be explained via partial derivatives. It doesn't have to be explained via partial derivatives, but I think partial derivatives are this super great concept that's helpful all over the place[1], so I'm going to invoke it. See this footnote for a quick explanation[2]. Suppose we have a Situation in which there is a Problem. In the real world, any Situation is composed of a large number of parameters. The amount of Problem there is is a function of the parameters. And for any interpersonal situation, different parameters are controlled by the different parties involved in the situation. The needlessly mathematical Partial Derivative Model of Interpersonal Conflict says that for any nontrivial situation, likely both partners control parameters that have non-negligible impact on how much of a Problem there is. In other words, if you want to blame the other person, you'll succeed. And if you want to blame yourself, you'll succeed. I have been good at doing those serially, but might be a better model to them in parallel: see all the ways in which each of you are contributing to the amount of Problem. This isn't to say that always everyone is equally to blame. If someone runs a red light and hits your car, they're at fault even if you could have chosen to work from home that day. In many cases, it's less clear cut and I think it's worth tracking how each person is contributing. The asymmetry in the situation is that by definition you control the parameters you're in control of, so it's worthwhile paying attention them. If you can get over being Right and instead focus on the outcomes you want, you might be able to attain them even if you're compensating for the mistakes of the other person. (A note on compensating for the mistakes of the other person. This might get you the outcomes you want, but I think can be unhealthy or unbalanced. If I have a colleague who feels easily insulted and I do extra emotional work to avoid doing that, it might work, but it's imbalanced. I venture that imbalanced situations between adults and children, and [senior] managers and [junior] employees are okay, but between peers, you want balance. You want to be making and compensating for mistakes in equal measure, not one person enabling the flaws of the other. Possibly the best thing to do if you think someone is at fault and you're at risk of compensating for it, is it to go have a conversation with them about it - but do so in an open-minded way where you're open to the possibility you're more at fault than you realize.) Something to note is that while I've framed this is the Problem as a function of the parameters, as though we have a function evaluated at single point in time, in fact interpersonal situations have more of a "game" (in the game theory sense) element to them. The other person's behavior might be a response to your behavior and their models of you, your behavior might be a response to their behavior and your models of them, ...
An overview of Re70–Re76. Subscribe at: https://paid.retraice.com Details: Re70; Re71; Re72; Re73; Re74; Re75; Re76. Complete notes and video at: https://www.retraice.com/segments/re78 Air date: Sunday, 11th Dec. 2022, 11 : 00 PM Eastern/US. 0:00:00 Re70; 0:13:26 Re71; 0:14:27 Re72; 0:15:37 Re73; 0:16:51 Re74; 0:19:15 Re75; 0:21:03 Re76. Copyright: 2022 Retraice, Inc. https://retraice.com
Moving the airport to improve its value. Subscribe at: https://paid.retraice.com Details: two more guesses; the hand-math; the spreadsheet-math. Complete notes and video at: https://www.retraice.com/segments/re76 Air date: Saturday, 10th Dec. 2022, 11 : 00 PM Eastern/US. 0:00:00 two more guesses; 0:01:50 the hand-math; 0:17:48 the spreadsheet-math. Copyright: 2022 Retraice, Inc. https://retraice.com
Can we please just place an airport? Subscribe at: https://paid.retraice.com Details: a guess; calculating the objective function value; toil and explanation. Complete notes and video at: https://www.retraice.com/segments/re75 Air date: Friday, 9th Dec. 2022, 11 : 00 PM Eastern/US. 0:00:00 a guess; 0:02:44 calculating the objective function value; 0:06:23 toil and explanation. Copyright: 2022 Retraice, Inc. https://retraice.com
Bringing the algebra back down to numbers. Subscribe at: https://paid.retraice.com Details: two cities; distance; calculating the objective function. Complete notes and video at: https://www.retraice.com/segments/re74 Air date: Thursday, 8th Dec. 2022, 11 : 00 PM Eastern/US. 0:00:00 two cities; 0:06:33 distance; 0:10:30 calculating the objective function. Copyright: 2022 Retraice, Inc. https://retraice.com
The limits that define our gradient. Subscribe at: https://paid.retraice.com Details: our gradient equation; the partial derivatives. Complete notes and video at: https://www.retraice.com/segments/re73 Air date: Wednesday, 7th Dec. 2022, 11 : 00 PM Eastern/US. 0:00:00 our gradient equation; 0:13:01 the partial derivatives. Copyright: 2022 Retraice, Inc. https://retraice.com
Be in the math. Subscribe at: https://paid.retraice.com Details: the airport problem; the solution vector; the objective function; the gradient vector; the partial derivative. Complete notes and video at: https://www.retraice.com/segments/re72 Air date: Tuesday, 6th Dec. 2022, 11 : 00 PM Eastern/US. 0:00:00 the airport problem; 0:04:23 the solution vector; 0:08:44 the objective function; 0:16:18 the gradient vector; 0:21:56 the partial derivative. Copyright: 2022 Retraice, Inc. https://retraice.com
Put the airport problem first. Subscribe at: https://paid.retraice.com Details: the airport toy problem; a pile of numbers. Complete notes and video at: https://www.retraice.com/segments/re71 Air date: Monday, 5th Dec. 2022, 11 : 00 PM Eastern/US. 0:00:00 the airport toy problem; 0:09:32 a pile of numbers. Copyright: 2022 Retraice, Inc. https://retraice.com
The math of 'Local Search in Continuous Spaces'. Subscribe at: https://paid.retraice.com Details: placing three airports in Romania; gradient descent; struggling. Complete notes and video at: https://www.retraice.com/segments/re70 Air date: Sunday, 4th Dec. 2022, 11 : 00 PM Eastern/US. 0:00:00 placing three airports in Romania; 0:04:18 gradient descent; 0:09:05 struggling. Copyright: 2022 Retraice, Inc. https://retraice.com
This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.3: Extrema
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.3: Extrema
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 6.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.3: Extrema
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.3: Extrema
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Chapter 4.2: Partial Derivatives
Introduce application problems and show how to find first order partial derivatives and interpret the results. Use a website to demonstrate the wind chill temperature problem and Casio to check answers.
Show how to find second order partial derivatives of functions of two variables. Use a website to check the answers.
Introduce the definition of partial derivatives of functions of two variables. Use a website to demonstrate the partial derivatives. Show how to find the first order partial derivatives using the definition and rules of differentiation.
Show how to find first order partial derivatives of implicit functions of two variables. Introduce and show how to find second order partial derivatives. Use a website to check answers.
Herb Gross discusses Exact Differentials.
Herb Gross defines the Directional Derivative and demonstrates how to calculate it. Herb also emphasizes the importance of this topic in the study of Calculus of Several Variables
Herb Gross show how the Chain Rule is involved in finding some integrals involving parameters.
Herb Gross describes n-Dimensional Vector Spaces relating definitions to the concept of a mathematical structure.
Herb Gross introduces us to the traditional Calculus of Several Variables
Herb Gross shows examples of the Chain Rule for several variables.
extra practice
Computer Science: Introduction to Geometric Modeling (ECS178)
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