"The Art of Insight in Science and Engineering: Mastering Complexity" by Sanjoy Mahajan.
It beautifully treats estimation and problem solving techniques, illustrated by examples from science and engineering. Instead of aiming for a complete, thorough and accurate treatment of problems, its goal is to teach shortcuts to sacrifice some accuracy for much reduced effort. This is a refreshing change to academia where rigor is often pursued at all cost. But in the real world rigor rarely matter, and simplifications are almost always worthwhile, especially initially since we can always refine models if required.
I first read it as an undergraduate and use the estimation and problem solving techniques from it almost daily. Though well hidden, the pdf is available for free on the website of the publisher.
Yes, it can easily correspond to a BPF, for example when trying to track a sinusoidal signal, say the AC line frequency. Then you can be reasonably certain that it will be near 50 Hz (or 60 Hz), and the resulting Kalman filter will be a sharp band-pass filter centered around that (when neglecting higher harmonics).
The 4th derivative is quite important for good motion control where it is usually called 'snap'. Specifically, it is relevant both for feedforward control design [1] and trajectory planning [2]. As shown in the latter, it is advantageous to design trajectories based on segments of constant snap. Consequently, also including 'snap' in the feedforward signals makes the achieved position profiles notably smoother.
“So what” is otherwise known as why. And it often flows better if you put it before the what – why is it that you’re doing the what and why should I care?
Another good writing tip: replace every “and then” transition with a “and that’s why” or “and despite that” transition
It's valuable to phrase it as "so what" rather than as "why", because people without focus in all fields end up writing only "why the thing being analyzed happened" and not "why this analysis/suggestion/whatever matters". The problem with "why" is that "why"ing the wrong thing ends up just being an extension of the "what". Or at least be up front and clear and say in its entirety "why you need to stop whatever else you are doing right now and listen to me". Writing advice can improve itself by careful attention to writer failure modes.
> And it often flows better if you put it before the what
Indeed. You want to quickly convince the reader to stick around. But often you need to give a little background first, so really it becomes "what, so what, what for real, how, etc"
These are often different. "Why" is often interpreted to mean why the author did it, while "So What?" or "Why Should I Care?" is why the audience should care and continue reading.
I am not sure “so what” equates to “why” in my mind. “Why” tells the cause of the “what”. “So what” explains the reason one should care about the “what”.
Announcements where personality has been deliberately injected seem to have a habit of beginning with a pithy-but-vague mission statement, immediately followed by “that's why” and then an unwelcome operational detail:
> Here at {company} we know you value {vague nice thing like fairness or something}. That's why we're sunsetting our 64 petaquux widgets, and transitioning all of our customers over to our popular 32 petaquux widgets, in order to enhance your experience.
If you believe what you're saying but you're struggling to articulate it, borrowing a form can help you along, but you really can't manufacture genuinely persuasive writing.
> replace every “and then” transition with a “and that’s why” or “and despite that” transition
The creators of South Park give the same advice for writing fiction: every two beats in your story should be linked not by an "and" but by a "but" or "therefore".
what you're describing is Rolfe's reflective model in the pedagogical literature.
You're missing the 3rd step, which is "Now What?"
Example:
What:
- What happened?
- What was your role in the situation?
- What were you trying to achieve?
- What actions did you take?
- What surprised you?
So what:
- So, what have you learnt?
- So, what was the importance of this learning?
- So, what more do you need to know about this?
- So, what broader issues have arisen from the situation?
Now what:
- Now, what could you do to enhance/improve the outcome?
- Now, what might you do to repeat this success in the future?
- Now, what might be a consequence of your chosen course of action?
For electronics, my vote goes to various spectacular application notes from the electronics industry that have stood the test of time. In comparison to the usual literature (textbooks, papers, etc.), these are often laser-focused on helping the user, often at a holistic level, including practical issues. This is a rare case where the incentives of the readers and producers are well aligned:
In order to sell their products, manufacturers need to teach their prospective customers enough to use their products adequately. If a product is good, but a customer makes (potentially silly) mistakes in using it, both the customer and the manufacturer lose -- which is exactly what application notes are intended to counteract.
# Example 1: Old HP application notes
Quote:
"In a real sense, Hewlett-Packard sold MEASUREMENTS as well as products. According to one marketing professional, when you go to a hardware store to buy a 5mm drill bit, what you really want is a 5mm hole. So, likewise, as HP developed their massive line of innovative measurement instruments, the customers often had to be educated in the newer processes of the new measurement techniques, permitted by the newest product."
I'm too young to have experienced the heyday of HP as a test & measurement company, but they produced spectacularly good material. Many of their application notes introducing the fundamentals of a field such as spectrum analysis, signal analysis, modal testing etc. remain excellent introductions even today, despite being decades old and thus predating my birth. I've thoroughly enjoyed the following ones (amongst others):
# Example 2: LTC application notes, especially by Jim Williams
A big chunk of my electronics knowledge comes from data sheets and application notes. The application notes by Jim Williams (RIP) stand out to me. Jim obviously was very gifted, but always sides with the (probably much less skilled) reader, making complicated material accessible. He always retains a holistic picture, and also addresses many practical aspects one can easily stumble upon. He does it all with a minimum of math, a maximum of intuition, and a great sense of humour.
While there are many dozens of application notes by him, I particularly like the following one:
>> I tried to define the integration operator in terms of e^x. The 1 + x/N needed to be one "infinitesimal" iteration of integration, that adds an extra infinitesimal rectangle to the area. But it didn't seem to work out.
You're close! This can indeed be done properly and is then called the Euler-Maclaurin formula. For this, you define the "shift to the left by n operator" e^(nD) where D is the differentiation operator d/dx.
You then always take the current value of f(x), multiply it by the small shift n to get the first rectangle. Then you shift to the left by n, i.e. to e^(nD)*f(x) = f(x+n), multiply that by the small shift n to get the next rectangle etc.
The book "street-fighting mathematics" [1][pdf] has a very hands-on and playful derivation of this in chapter 6.3.
Gunter Stein's inaugural Bode prize lecture from 1989 titled "Respect the Unstable" [0]. In this talk, he uses a minimum of mathematics to clearly demonstrate the fundamental (and inevitable!) trade-offs in control systems design. He effortlessly makes the link between his (in)ability to balance inverted rods of various lengths on his palm (with shorter rods being harder to balance) to why the X-29 aircraft was almost impossible to control and why Chernobyl blew up.
The fundamental message is extremely important and the derivation is so crystal clear that it is simply marvelous to watch him present it. I like it so much that I re-watch it about once a year.
Same for me. The book and its tools are extremely empowering. In general, anything from Sanjoy Mahajan (the author) is extremely insightful:
-Street Fighting Mathematics
-The Art of Insight in Science and Engineering
-Lecture notes on signals & systems (a bit harder to find)
-Lecture notes on thermodynamics (real-world insights rather than endless manipulations of weird partial derivatives)
Afaik he is currently working on a textbook on mechanics.
You can consider it as such, yes. The main difference is that whereas street fighting mathematics was focused more on the mathematical side, this book focuses more on physics. However, the spirit and bold worry-free approach is exactly the same.
Note: The draft linked in the title [1] has been superseded by the finished book [2] (free pdf download here [3]), which is even better!
This is probably the most useful book I have read during my studies in physics and I highly recommend it to everybody with some technical interest because it focuses on teaching general and useful tools (using science and engineering examples (mainly physics)).
During the first years of my studies I did reasonably well, but it always felt like I was just manipulating symbols on paper, and the results didn't mean much to me -- it was all just theory (and if the results would have come out some other way I probably would have believed that too). This book taught me how to be reckless and throw away unnecessary complexity in order to make said theory simple enough to apply it easily to real-world problems, which suddenly made my theory knowledge much, much more useful (previously it was mainly good for passing exams). Now, during my PhD I still use the methods from the book almost daily!
Compared to the earlier book draft [1] that has been floating on the web for many years, the final book is much improved, mainly because it focuses on general tools rather than specific physics topics. However, if you want to have a quick demonstration of how powerful the methods from the book are, I'd recommend to read chapter 9.3 about waves in [1], which unfortunately only partially made it into the final book. Within a few pages you quickly derive all the properties of waves in different regimes and draw practical conclusions such as the speed limit for boats, the speed of tsunamis, why bugs walking on water don't generate waves, etc!
The author of the book Sanjoy Mahajan also has a very entertaining book and online course titled "Street Fighting Math" [0]. Previous discussions on HN about the book [1, 2, 3].
It beautifully treats estimation and problem solving techniques, illustrated by examples from science and engineering. Instead of aiming for a complete, thorough and accurate treatment of problems, its goal is to teach shortcuts to sacrifice some accuracy for much reduced effort. This is a refreshing change to academia where rigor is often pursued at all cost. But in the real world rigor rarely matter, and simplifications are almost always worthwhile, especially initially since we can always refine models if required.
I first read it as an undergraduate and use the estimation and problem solving techniques from it almost daily. Though well hidden, the pdf is available for free on the website of the publisher.