[FilipBjoerner]

Two days ago, Jason Gibson released this video: The Derivative – The Most Important Concept in Calculus. In it, he says that the derivative is the same as “the rate of change.”

In his videos on various topics, he takes key concepts seriously. 

This video is part 1 on the topic.

/sb

[Harry Binswanger]

Re: Filip Bjoerner’s post 104585 of 3/19/25

Why are you recommending this? It’s poorly taught and has no original philosophic content.

I do like his use of “rate of change” and his attempt to de-mystify calculus. But he talks too fast and violates the hierarchy repeatedly.

A great example of a bad example comes right at the beginning:

In order to understand conceptually what a derivative is, we are going to talk about everyday life: position of a particle . . .

Hilarious. But not in a good way.

He does then give some actual, everyday examples, “position of a car, position of an airplane.” But it is too late. And he never (in what I heard) returns to the case of the car or the airplane.

It’s hard to parody this, but I’m going to try.

In order to understand conceptually what capitalism is, we are going to talk about everyday life: renegotiating the terms of a proposed merger of two investment banking firms.

Philosophically, he gives us an (incomplete) exposition of the traditional theory of limits, then tells us if we have any unclarity about it, re-watch that segment 5 times. I kid you not.

I will start a new thread of my conceptualization of the derivative.

*sb

[FilipBjoerner]

Re: Harry Binswanger’s post 152739 of 3/20/25

This video is philosophically uninteresting. However, it should be of interest to some of the Objectivists who appreciate the work of Leonard Peikoff and David Harriman, and who do not already have a good knowledge of mathematics or physics. I probably should have written something in the initial post about how we are never too old to learn mathematics and that Gibson is a good alternative for those of us who appreciate baby steps. None of us need to watch any particular video by Jason Gibson. But YouTube is a goldmine and none of us are too old to learn something new.

Gibson almost always assumes that his listeners have very little prior knowledge. He treats things simply. In his own words, he often talks in his videos about “baby steps” and “manageable chunks,” and he rehearses and chews, and builds up bits of knowledge around central key concepts.

I disagree with you, Harry, that it was bad of Gibson to say that you can watch his video five times, because any of us can do so if we want to. However, I have a few minor objections. It is that in the first diagram he talks more about positions instead of distances. And it is that the curve in a distance-time diagram is velocity and that the curve in a velocity-time diagram is acceleration. But, I forgive him because his intention is to simplify and focus on small baby steps.

I look forward to reading your conceptualization of the derivative.

/sb

[Harry Binswanger]

Re: Filip Bjoerner’s post 152747 of 3/21/25

I disagree with you Harry that it was bad of Gibson to say that you can watch his video five times

I didn’t mean he shouldn’t point that this is often a good thing to do. I meant that he was saying this because his explanation was quite inadequate.

I’ve been working on my conceptualization of the derivative for about 10 hours now. I hope I found I have to represent the background, which will be part I.

?sb

[Rabbit01]

Re: Filip Bjoerner’s post 104585 of 3/19/25

I think this video does not do a good job of explaining derivatives.

It really is messy how it is explained and I think a student would be simply overwhelmed and still feel like he doesn’t understand anything.

I will explain my view in the following paragraphs and present an alternative at the end of my post:

He begin with immediately just putting values on the board without explaining how he got them.

I dislike this approach since this is overwhelming to the student. Remember, the student has no concept of the derivative before this video.

Not only this, but also talking about the derivative as if it were obvious, without showing why, is bad. I don’t see how this is a good practice.

Furthermore, Mr. Gibson immediately plotted the double derivative without explanation. This can be overwhelming. The student doesn’t even know what the first derivative is and how to compute it.

Gibson immediately starts using multiple notations like p'(t) and dp/dt without explaining what it all means. Then he starts using p dot out of nowhere, without explaining the proper context of using such derivative notation.

Gibson is also using p(t) for position, when most students only know x and y graphs by this point. This is not great. P(t) feels abstract, x(t) not. P(t) could be in 3D, x(t) is not.

He continues to using many notations when the student still doesn’t really know what the derivative is or how to calculate it by himself.

He motivates this messy explanation by saying this is the concept of derivatives. How? He just wrote down some extremely abstract things. Again the student might feel as if this were incomprehensible like Cthulhu.

Then he moves on to the definition of a derivative. He immediately shows two formulae and proclaims that they are the same. They sort of are but then why show two? There is no reason for it. Again, this overwhelms the student.

Remember that the student is still thinking about all the previous concepts shown in the video and then he writes down two equations and proclaims that they are the same.

He also talks about df/dx or df/dt but not other variables

This notation (df/dx) can be interpreted as the derivative in the direction of x or t (df/dt) or y (df/dy) or any other variable but only in that direction. Which helps students when they get to partial derivatives.

But he doesn’t really touch it. Which is weird because he started so abstractly. He can easily show it but using multiple variables or using 3D plots of 2D lines.

He talks about the temperature over a metal bar, which is a complete departure from positions/location. Although interesting, this should be reserved for another lecture. It might simply be too much.

Around 58:00, he starts with discreet derivatives. However, that is how he should have started, so that he can show that when your step size is small enough, you get the derivative.

But then he shows it as a discontinuous function. Suddenly going from continuous to discontinuous when not even computing continuous functions is horrible to the student.

Mainly because Gibson doesn’t use the formula of the derivative throughout the video. I don’t know why he does this. Again he started with just noting down some derivatives and plotting them. However, he doesn’t even show HOW he did that.

Why doesn’t he show how he gets 2*t from t^2?

How is this teaching the derivative to students? 

I hope that you see how bad this video really is.

Also, Dr. Binswanger’s example is very fitting to show the quality of that video.

If Gibson’s videos are all like this, then I would never recommend his channel to anyone.

I would suggest an alternative by Eddie Woo. It is not perfect but better than Gibson’s video.

https://youtube.com/playlist?list=PL5KkMZvBpo5DwIsDKWdHYmkRZmXMi1mE8&si=zOLCyjRV9x6txsDM

Or Kahn’s academy.

/sb

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