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Comment by pmontra | Hacker News Reader

I like those articles too but I wish they include a short version with the major takeaways. In another industry that would be an executive summary. I don't always have the time to read all the story, so I end up fast reading it trying to find the important points and I'm never sure I really found them. In this case they seem to be the paragraphs after "Here’s an extremely rough cartoon version of the approach:"

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Traditional calculus is not well-suited to describing the behavior of particles at extremely small scales because it leads to infinite values in calculations: Traditional calculus is based on real numbers, which are continuous and can take on any value. However, at the subatomic level, particles behave more like waves than like particles with a definite position, and the value of some physical quantities, like energy, can become infinite at certain points, which makes the equations used in traditional calculus break down.

To overcome the issues with traditional calculus, alien calculus involves replacing the standard real numbers used in calculus with "fuzzy numbers" that represent probabilities instead of definite values. These fuzzy numbers allow the equations to describe the behavior of particles more accurately because they capture the uncertainty inherent in subatomic systems.

Alien calculus calculates the probability that particles will be in certain positions or states, rather than trying to determine their exact positions or states. This is because particles at the subatomic level are constantly in motion and their position or state cannot be precisely determined at any given moment. By using probabilities, alien calculus can provide a more accurate description of the behavior of particles at this level.

Wait, is this new? This is exactly how I'd assumed quantum calculations worked already

You are correct that the probabilistic nature of quantum mechanics has been known for many years. However, what is new in the approach of "alien calculus" is the use of a mathematical framework that replaces traditional calculus with a more probabilistic approach to avoid infinities and better describe the behavior of particles at the subatomic level. Alien calculus is a novel approach that aims to improve upon traditional methods and has shown promise in resolving some of the issues that arise in particle physics calculations

Thanks! Would you be aware of any kid-friendly sources that could be used to inspire students? Of the “We love calculus because it explains how a ball moves. Now let me show you something really cool!”

There is a nice discussion of quantum mechanics here - note you have to click to "reveal all steps" at the very bottom - https://mathigon.org/course/probability/randomness

Also check out https://ed.ted.com/search?qs=quantum+mechanics

Awesome - thanks!

Yeah the above comment and it's reply is exactly what I'd assume GPT-4 would reply if asked what "alien calculus" is ;) (the linked article isn't about this at all, it's about technical details of perturbation series in mathematics as they relate to non-perturbative treatments)

Product opportunity: an LLM based tool to summarize works ti a personally customizable level. An executive will want the societal implications without the math. A scientist will want the equations without the analogies or number of elephants in size. A lay reader mag want to know the number of elephants without those equations getting in the way.

Could be combined with the information bubble filter described in Stephenson’s Burn or Dodge in Hell.

https://kagi.com/summarizer/index.html?url=https%3A%2F%2Fwww...

Sometimes the fun is in the journey, not (only) the destination

And sometimes it's not. Sometimes the journey is miserable, and we only do it to get to the destination.

And of the authors who think "my journey will be worth the destination, because I can really write!", some large percentage of them overestimate their ability and/or our interest level.

There was a time when people had more time to read than they had things to read. At that time, writing in a way that expanded the text made sense. But now, there's an essentially infinite amount to read, and still only 24 hours in a day. That favors getting to the point in a hurry. On the internet, you have from 5 to 30 seconds to persuade me that your thing is worth reading. If in that time you don't persuade me that you're going to deliver enough value to pay back my investment of reading your thing, I'm on to the next tab.

That’s alright, not everything has to be catered to those with minimal time to read.

It's not exactly minimal time to read. It's too many other options to read. If you look at the number of things that people (or at least websites) suggest I read, I've got an average of less than a minute to give each one (and maybe less than a second).

So if I'm going to read your thing, you have to pay me back more than those others are going to. You have to hold my attention more than the promise of all those other things.

But you're right that people different tastes. Some people like long-form writing. The same dynamic is still true in their choices, though - they're just using a different filter to decide what's going to pay them back the most.

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