I really appreciate how writers at Quanta turn extremely complex and dry topics into a pleasurable read by mixing simple analogies with history. I really admire the skill it takes to break down these topics and make them fascinating for someone with no understanding of them, such as me.
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:"
‘Alien calculus’ could save particle physics from infinities
71–80 of 132 posts
Re: ‘Alien calculus’ could save particle physics from infinities
#72Earlier quoted context omitted.
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:"
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.
Re: ‘Alien calculus’ could save particle physics from infinities
#73Using different math approach is super fruitful. For example, alternating current in presense of capaciators and induction coils is well handled by switching to imaginary (complex) resistance/current/voltage calculation, and transition processes in electric chains are handled by operational calculus. If we used differential equations to solve these, which indeed look natural for these tasks, we will not be able to ac…
> If we used differential equations to solve [RC networks], we will not be able to accomplish any calculations without a PhD.
That's overstating the argument[1]. In fact "differential equations" are naturally abstractable too. Decades and decades of workaday electrical engineers have been writing SPICE models successfully. The fact that one abstraction looks like "math" and the other "software" is just an aesthetics thing.
That's not to say that there's no point in teaching complex impedance. There absolutely is. But abstraction works in mysterious ways and some abstractions are more "beautiful dead ends" than others.
[1] Also needs to be mentioned that linear RC networks are a pretty small subset of the actual problem that needs solving. Transistors are kinda important too.
Re: ‘Alien calculus’ could save particle physics from infinities
#74Looks like the three Jean Écalle books mentioned in the article are available (legitimately) online:
https://www.imo.universite-paris-saclay.fr/~jean.ecalle/publ...
Unfortunately, as mentioned in TFA, they are in French, which makes them less than ideal for anyone who doesn't read/speak French. I wonder if these will ever see an English translation?
Short of that, I wonder how well it would work to try to read through it using ChatGPT or something to translate the prose bits.
Re: ‘Alien calculus’ could save particle physics from infinities
#75Earlier quoted context omitted.
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 t…
That’s alright, not everything has to be catered to those with minimal time to read.
Re: ‘Alien calculus’ could save particle physics from infinities
#76Earlier quoted context omitted.
Sarcasm aside. Even the output from GPT-4 is quite bland and generic. Very good for performing tasks (I.e convert a blob of text into a knowledge graph or generate X code), but quite awful at the elegant prose we see at play Wonder how long before that’s solved. Hard to believe training on such large swathes of the web doesn’t result a compressed generic representation of language within its weights.
It seems like there’s a tension. On the one hand generating the most likely sequence of tokens maximises the chance the response will make sense and be relevant. On the other hand it also guarantees you will get the most bland and unimaginative response.
Counterargument: "explain linked lists in the style of edgar allan poe"
Re: ‘Alien calculus’ could save particle physics from infinities
#77I really appreciate how writers at Quanta turn extremely complex and dry topics into a pleasurable read by mixing simple analogies with history. I really admire the skill it takes to break down these topics and make them fascinating for someone with no understanding of them, such as me.
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:"
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.
Re: ‘Alien calculus’ could save particle physics from infinities
#78Earlier quoted context omitted.
It's related in the sense that the vanilla attempts to quantize gravity lead to infinities as described in the article. But the nature of these infinities is more troubling in the case of quantum gravity than those found in the rest of the theories that compose the Standard Model. Infinities appear very early in the series expansion of quantized gravity, at second order of the series expansion for the free theory. An…
I recall reading a book on String Theory in the late 1990s edited by Ed Witten where he mentions the problems with physics and the limits of mathematical techniques. It's long ago so I can't paraphrase his words accurately but he did so with such eloquence that I've long remembered the fact. He pitched the problem in terms of both existing physics and of new '21st Century' ideas inklings of which had somehow trickled…
He pitched the problem in terms of both existing physics and of new '21st Century' ideas inklings of which had somehow trickled down into the 20th Century and that physicists needed new mathematics to deal with them (I hope I've not mangled his words too much).
It has definitely been said that "String theory is part of 21st-century physics that fell by chance into the 20th century.". I can recall seeing variations of that quote in a few different books over the years. Interestingly though, a quick Google search (maybe I should have asked ChatGPT?) shows attributions to both Witten and Daniele Amati. So I'm not sure who said that particular bit first.
Re: ‘Alien calculus’ could save particle physics from infinities
#79Earlier quoted context omitted.
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:"
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…
Wait, is this new? This is exactly how I'd assumed quantum calculations worked already
Re: ‘Alien calculus’ could save particle physics from infinities
#80Earlier quoted context omitted.
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…
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