jeremyscanvic

Another surprising place decibels pop up, pretty far from loudness related things, is in image comparison metrics. Peak signal-to-noise ratio is mean squared error normalized by a certain peak intensity and it is generally expressed in dB, i.e. as 10 log10(normalized mse). https://en.m.wikipedia.org/wiki/Peak_signal-to-noise_ratio

Edit: typo

I sympathize with your view and I dislike it as much as the next guy when people prove dubious points from poorly convincing stories, but here's how I view things: badly told stories are frustrating, and it is difficult to tell stories well.

The thing with (real) stories is they relate facts in a structured and somewhat neutral way (causality). This allows you, the reader, to learn things that are beyond the author's point. Essays, on the other hand, don't allow that as authors can (should) always leave out everything that does not support their point without compromising the text.

This reminds me of a talk that Leslie Lamport (author of LaTeX & prominent figure in the field of distributed computing) gave recently [1]. I remember him arguing that the difficult part in writing code is not to determine what code to write to compute something, but to determine what this something is in the first place. "Logic errors" are really about valid algorithms that end up computing the wrong thing - they're gonna compile, they're gonna run, but they won't do what you want them to do.

One example he gives is computing the maximum element in a sequence of numbers. This is something trivial to implement but you need to decide what to do with the obvious edge case: empty sequences. One solution is to return some kind of error or exception, but another is to extend what we mean by the largest element in a sequence the way mathematicians typically do. Indeed, the maximum function can be extended for empty sequences by letting max([]) := -infinity, the same way empty sums are often defined as 0, and empty products as 1. The alleged benefit of following the second approach is that it should lead to simpler code/algorithms, but it also requires more upfront thinking.

[1] https://www.youtube.com/watch?v=tsSDvflzJbc

A slightly tangential comment: integrating a continuous image on squares paving the image plane might be best viewed as applying a box filter to the continuous image, resulting in another continuous image, then sampling it point-wise at the center of each square.

It turns out that when you view things that way, pixels as points continues to make sense.

What a wild number system! That's very cool. Thanks!

I know that the irrationality of e can be proven using the theory of continued fractions or by showing that finite Taylor sums for e give out rational approximations that are too good for e to be rational. What you're saying does not ring a bell though. Can you elaborate on that? This sounds really interesting!

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The thing with mathematics is there are often many different ways to prove things leaving no universally agreed upon graph of true mathematical statements in terms of which helps proving which! That being said, you might want to check out ProofWiki [1], an online collaborative project featuring mathematical proofs consistently linked together.

[1] https://proofwiki.org/wiki/Main_Page

That's cool! Great work!

I was recently looking for a Linux alternative to LibreOffice Calc and couldn't find something that meets my needs (mostly CSV import/export, filtering and pivot tables). It's great to see this new contender showing up and even if it lacks major features what's there so far looks very good. This is promising! Congrats for the good work and best wishes for what's to come.

Great post! I didn't know about vmsplice(2). I'm glad to see a former ENSL student here as well!