One of the major difficulties in studying electricity, especially when compared to many other physical phenomena, is that it cannot be observed directly by human senses. We can manipulate it to perform various tasks and see its effects indirectly, like the ionized channels formed during lightning strikes or the resistive heating of objects, but its underlying behavior is largely hidden from view. Even mathematical descriptions can quickly become complex and counter-intuitive, obscured behind layers of math and theory. Still, [lcamtuf] has made some strides in demystifying aspects of electricity in this introduction to analog filters.

The discussion on analog filters looks at a few straightforward examples first. Starting with an resistor-capacitor (RC) filter, [lcamtuf] explains it by breaking its behavior down into steps of how the circuit behaves over time. Starting with a DC source and no load, and then removing the resistor to show just the behavior of a capacitor, shows the basics of this circuit from various perspectives. From there it moves into how it behaves when exposed to a sine wave instead of a DC source, which is key to understanding its behavior in arbitrary analog environments such as those involved in audio applications.

There’s some math underlying all of these explanations, of course, but it’s not overwhelming like a third-year electrical engineering course might be. For anyone looking to get into signal processing or even just building a really nice set of speakers for their home theater, this is an excellent primer. We’ve seen some other demonstrations of filtering data as well, like this one which demonstrates basic filtering using a microcontroller.

An elegant new equation identifies the surprisingly orderly, mathematical way in which things break, shatter, and fall apart.

With just a friend, a phone, and a few Lego bricks, you can accurately measure the size of our planet.

You have that slide rule in the back of the closet. Maybe it was from your college days. Maybe it was your Dad’s. Honestly. Do you know how to use it? Really? All the scales? That’s what we thought. [Amen Zwa, Esq.] not only tells you how slide rules came about, but also how to use many of the common scales. You can also see his collection and notes on being a casual slide rule collector and even a few maintenance tips.

The idea behind these computing devices is devilishly simple. It is well known that you can reduce a multiplication operation to addition if you have a table of logarithms. You simply take the log of both operands and add them. Then you do a reverse lookup in the table to get the answer.

For a simple example, you know the (base 10) log of 10 is 1 and the log of 1000 is 3. Adding those gives you 4, and, what do you know, 10⁴ is 10,000, the correct answer. That’s easy when you are working with numbers like 10 and 1000 with base 10 logarithms, but it works with any base and with any wacky numbers you want to multiply.

The slide rule is essentially a log table on a stick. That’s how the most common scales work, at least. Many rules have other scales, so you can quickly, say, square or cube numbers (or find roots). Some specialized rules have scales for things like computing power.

We collect slide rules, too. Even oddball ones. We’ve often said that the barrier of learning to use a slide rule weeded out many bad engineers early.

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions.

But now Google’s DeepMind team has built AlphaProof, an AI system that matched silver medalists’ performance at the 2024 International Mathematical Olympiad, scoring just one point short of gold at the most prestigious undergrad math competition in the world. And that’s kind of a big deal.

True understanding

The reason computers fared poorly in math competitions is that, while they far surpass humanity’s ability to perform calculations, they are not really that good at the logic and reasoning that is needed for advanced math. Put differently, they are good at performing calculations really quickly, but they usually suck at understanding why they’re doing them. While something like addition seems simple, humans can do semi-formal proofs based on definitions of addition or go for fully formal Peano arithmetic that defines the properties of natural numbers and operations like addition through axioms.

Read full article

Comments

© Hill Street Studios