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‘Alien calculus’ could save particle physics from infinities

quantamagazine.org

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Re: ‘Alien calculus’ could save particle physics from infinities

#51

Post by mcabbott »

pvitz wrote: post #6
JPLeRouzic wrote: post #4

Earlier quoted context omitted.

I am not a scientist, is this Alien calculus akin (somehow) to a derivative?

The capital delta acts like a "normal" derivative if you want to say so. In eq. 4, you can see the product rule which is one of the most defining features for any sort of calculus. However, I must admit that this summary will take me a lot of time to digest...

Yes, it obeys enough algebraic laws that calling it a derivative is useful.

But I don't think there's any underlying notion of small changes to something continuous. It is not the slope of some smooth function.

Re: ‘Alien calculus’ could save particle physics from infinities

#52

Post by esperent »

evanb wrote: post #39
esperent wrote: post #30

Earlier quoted context omitted.

> It turns out Newtonian mechanics is emergent from Relativity. However relativity is far more complex than Newtonian physics.

The kinds of physical influences that are allowed in Newtonian physics are more general than those allowed in relativity. Relativity requires physics to satisfy constraints . Which is more complex depends on what you mean. There are fewer laws in the possibility space of generally-relativistic physics than Newtonian physics. So, which metric is more important? Less pleasant calculations or a larger search space? Your…

> most physicists would come down on the other side of the issue.

What's your reason for saying this? I'm more on the mathematical side of things so I don't know that many physicists. But it's been my understanding that equations that are extremely difficult to solve, impossible to solve except numerically, or involve infinities that can't be explained, are a major pain point for physicists. I mean, that's the entire premise of this article.

Re: ‘Alien calculus’ could save particle physics from infinities

#54

Post by tsimionescu »

strogonoff wrote: post #45
CyberDildonics wrote: post #41

Earlier quoted context omitted.

Can you give an example of your philosophy physics being applied to a real world problem?

What do you mean by “philosophy physics”? Apart from that, I hope upon some reflection you realize that your sentence is an illustration of my point.

Your claiming that there exists some simpler physical theory that could be derived from philosophy.

You should be able to back up your claim by showing some example (not fully worked out, just some idea) of a philosophy-inspired physical theory that is simpler than current theories but more or less as precise in its measurable predictions of what will happen next in sine physical system.

Re: ‘Alien calculus’ could save particle physics from infinities

#55

Post by eternalban »

esperent wrote: post #52
evanb wrote: post #39

Earlier quoted context omitted.

The kinds of physical influences that are allowed in Newtonian physics are more general than those allowed in relativity. Relativity requires physics to satisfy constraints . Which is more complex depends on what you mean. There are fewer laws in the possibility space of generally-relativistic physics than Newtonian physics. So, which metric is more important? Less pleasant calculations or a larger search space? Your…

> most physicists would come down on the other side of the issue. What's your reason for saying this? I'm more on the mathematical side of things so I don't know that many physicists. But it's been my understanding that equations that are extremely difficult to solve, impossible to solve except numerically, or involve infinities that can't be explained, are a major pain point for physicists. I mean, that's the entire…

This could the universe's way of telling us that knowledge requires work, mathematically speaking.

Re: ‘Alien calculus’ could save particle physics from infinities

#56

Post by maroonblazer »

simonh wrote: post #17
froggychairs wrote: post #16

Earlier 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.

I've only explored ChatGPT in the most cursory way, but wouldn't this be a function of the prompt it's given?

E.g. "Summarize this idea in a way that uses novel comparisons to everyday phenomena. The target reader is someone who doesn't have domain knowledge of the field...etc."

Or something like that.

Re: ‘Alien calculus’ could save particle physics from infinities

#57

Post by notorandit »

One sentence from Wikipedia:

> "Resurgent functions" are divergent power series whose Borel transforms converge in a neighborhood of the origin and give rise, by means of analytic continuation, to (usually) multi-valued functions, but these multi-valued functions have merely isolated singularities without singularities that form cuts with dimension one or greater.

Cool!

Re: ‘Alien calculus’ could save particle physics from infinities

#58

Post by RugnirViking »

simonh wrote: post #17
froggychairs wrote: post #16

Earlier 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.

that's exactly why it doesnt generate the most likely sequence of tokens! They are chosen at random based on the probabilities assigned by the model, so there is a chance of unusual output. In the API you can tweak the "temprature" which weights this towards more novel output

Re: ‘Alien calculus’ could save particle physics from infinities

#60

Post by Ar-Curunir »

pmontra wrote: post #34
omeysalvi wrote: post #9

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:"

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