Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

‘Alien calculus’ could save particle physics from infinities

quantamagazine.org

Post reply on HN
Print view View original

111–120 of 132 posts

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

#111

Post by froggychairs »

RugnirViking wrote: post #58
simonh wrote: post #17

Earlier quoted context omitted.

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

I’m very familiar with temperature and other parameters you can use to tweak output. They can take you decently far! GPT-2 can produce very coherent convincing output even today if you know what to tweak

Decoding methods also matter, and it’s a shame we aren’t given token probabilities (or any insight into model output) so we have more creative control over how to decode the output. Some of the better literature I’ve seen involving creative writing did have novel decoding methods

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

#112

Post by mathattack »

hammock wrote: post #80
rolenthedeep wrote: post #79

Earlier quoted context omitted.

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 tradi…

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!”

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

#113

Post by hammock »

mathattack wrote: post #112
hammock wrote: post #80

Earlier quoted context omitted.

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 tradi…

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

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

#114

Post by gus_massa »

simonh wrote: post #92
gus_massa wrote: post #48

Earlier quoted context omitted.

> The behaviour of _bosons_ is emergent from the behaviour of quarks. I think you mean > The behaviour of _hadrons_ is emergent from the behaviour of quarks. -- Anyway, back to your main idea, the problem is that most of the times the new underlaying theory is even worse than the original one > Newtonian mechanics is emergent from Relativity For Newtonian Mechanics you need only basic calculus. For General Relativity…

Yes Hadrons sorry. Posting in a hurry. >most of the times the new underlaying theory is even worse than the original one Oh quite. Macroscopic emergent behaviour is often apparently simpler than the underlying causes and is in some way a generalisation of them.

It's strange because from galaxies to protons/neutrons/electrons it looks like the underlying theory is simpler. But if you try to look inside the protons it gets nastier each time you go down in the ladder of theories.

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

#115

Post by criddell »

temp512345 wrote: post #38
criddell wrote: post #23

Earlier quoted context omitted.

I wish I understood it better, but you don’t have to go much below classical mechanics before I’m lost. But from what I’ve read, the deeper you go, the more it’s difficult to find something other than mathematics. When you ask what is a particle you find out it’s probably an excitation of a quantum field. So what is a quantum field if not a mathematical structure? Is there a physical reality to wave function collapse…

What do you mean something other than mathematics? It's just a language problem nothing else. Just because the English language lacks the descriptive power it does not mean those objects are "mathematical", just as a round ball is not "English" in it's nature just because you can describe it's properties and behavior using that language. A quantum field is just that, a field, it exists just as much as a magnetic fiel…

> It is an area of space where a specific "force" you might say has impact on objects that enter that area of space.

Aren't you describing a classical field?

As I understand it, a quantum field is essentially varying probabilities (the wavefunction).

> they produce consequences in the world

They don't produce consequences in the world, they are the world. You and I, we're excitations of a quantum field. We're of the wave function. The quantum field encodes all the information that is us.

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

#116

Post by mathattack »

hammock wrote: post #113
mathattack wrote: post #112

Earlier quoted context omitted.

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!

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

#117

Post by staunton »

nine_k wrote: post #104
staunton wrote: post #100

Earlier quoted context omitted.

Number of equations != How simple something is

Humans have a limited capacity of holding something before their "mind's eye", like 5-7 items. The simpler the equation is, the easier it is to understand and operate. Of course, it only works provided that the parts of the equation are well-understood, too. This way, the nabla symbol is very helpful in turning a group of (usually) 3 related PDEs into one pretty understandable one. Same for vector and matrix forms of…

Yes, good notation helps dealing with complexity. My point was that "number of equations" involved in a model or theory is not an objective measure of, really, anything.

Every system of equations can be written as "A = 0" for a suitable definition of A. That doesn't make it simple.

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

#118

Post by staunton »

simonh wrote: post #90
PartiallyTyped wrote: post #63

Earlier quoted context omitted.

You shouldn’t see mathematics as consistent because they are not. A system can be complete, meaning all true statements can be built based on axioms, but it cannot be sound leading to contradictions. Alternatively a system may be sound, but not all true statements could be derived. And finally there are statements impossible to prove because the proof is undecidable.

You’re quite right, which is why I described it as highly rather than completely or perfectly consistent. It’s an interesting question whether the physical world is perfectly or merely highly consistent. If it’s made of mathematics, it may be that it cannot be perfectly consistent. So if we ever find that it is perfectly consistent, that might be evidence that it isn’t made of mathematics. Most likely we’ll never be…

> whether the physical world is perfectly or merely highly consistent

What does that even mean? The physical world is not a formal system in any obvious sense.

Nor does "consistent" apply to mathematics, by the way, only to formal systems used/studied by mathematics. You cannot mathematically prove or disprove that mathematics is consistent or define precisely what that would mean because mathematics itself isn't rigorously defined. If you define it as "whatever mathematicians are doing", I guess it's in some sense inconsistent, since mathematicians often disagree.

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

#119

Post by staunton »

CyberDildonics wrote: post #47
strogonoff wrote: post #45

Earlier quoted context omitted.

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.

I reflected and I have no idea what you're talking about, since all you said was "physics is wrong" while giving no evidence.

I guess the intended meaning was that you chose your request ("apply what you say to a problem") based on certain philosophical criteria. I think that's actually a surprisingly valid point, given the original (downvoted) comment.

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

#120

Post by AnimalMuppet »

Ar-Curunir wrote: post #75
AnimalMuppet wrote: post #72

Earlier quoted context omitted.

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.

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.

Post reply on HN