Why did Dirac strongly pursue mathematical beauty?

  • #1
22
2
In everyday language, beauty is an emotional concept. How would you mix that with quantum physics and the mathematics behind it? Or is what he refers to as "beauty" is more like simplicity? I mean, I agree with the man, the Standard Model feels redundantly complex, but I feel like there is something big that I don't understand here.
 

Answers and Replies

  • #3
22
2
I don't get it.
 
  • #4
Stephen Tashi
Science Advisor
7,583
1,472
I don't get it.
At least @martinbn 's link makes it clear that Dirac thinks "beauty" is different than simplicity.

In everyday language, beauty is an emotional concept.
There are videos of interviews with Dirac. My guess is that he thinks Beauty is a subjective concept, but that it need not be emotional in the sense of producing powerful emotions.

Perhaps what Dirac has in mind is analogous to an complicated artwork where things fit together elegantly - something like a poster by Alphonse Mucha.

Of course to appreciate mathematical structures the way we comprehend Mucha poster, one would have to have Dirac's skill in seeing how all those structures fit together. Most of us get stuck in chapter 3 exercise 17 or some such place. We can see only one little curlicue at a time.
 
  • Like
Likes enter
  • #5
22
2
At least @martinbn 's link makes it clear that Dirac thinks "beauty" is different than simplicity.


There are videos of interviews with Dirac. My guess is that he thinks Beauty is a subjective concept, but that it need not be emotional in the sense of producing powerful emotions.

Perhaps what Dirac has in mind is analogous to an complicated artwork where things fit together elegantly - something like a poster by Alphonse Mucha.

Of course to appreciate mathematical structures the way we comprehend Mucha poster, one would have to have Dirac's skill in seeing how all those structures fit together. Most of us get stuck in chapter 3 exercise 17 or some such place. We can see only one little curlicue at a time.
Oh, so he was talking about the pieces fitting together and not powerful emotions. Now it clicked. Thanks!
 
  • #6
Demystifier
Science Advisor
Insights Author
Gold Member
11,357
3,970
For me, beauty in theoretical physics is a kind of simplicity. But not an apparent simplicity that everyone can see at first sight. It's a kind of hidden simplicity that you can see only when you dwell deeply.
 
  • Like
Likes Charles Link, bhobba, dlgoff and 3 others
  • #7
9,600
2,681
In physics beauty IMHO is when you see something so strikingly unexpected, simple and powerful in its explanatory power that you just sit there shaking your head. The paradigm of that often is given by the example of how Dirac came up with his equation, but for me the best example is Noether's Theorem:
https://curiosity.com/topics/emmy-n...mathematician-youve-never-heard-of-curiosity/

Have a look at the videos - one left me in stitches.

And if anybody asks me for a book on the beauty of physics I always say - Landau - Mechanics. If you do not see the true beauty in physics after reading that book then you are not meant to be a physicist :-p:-p:-p:-p:-p:-p:-p

Thanks
Bill
 
Last edited:
  • Like
Likes Charles Link
  • #9
pinball1970
Gold Member
722
736
Oh, so he was talking about the pieces fitting together and not powerful emotions. Now it clicked. Thanks!
He was a strange man apparently.
 
  • #10
Fra
3,193
176
The endavour (theoretical physics) where we from the apparently always changing complex observations of our environment, try to extract mathematical patterns that are timeless, and escape the superficial mess, is a kind of beauty as well as simplicity in the sense of data compression. Finding these timeless laws and invariants of the dynamics in nature, helps us control and predict the environment. And we can separate the timeless beauty from the not equally beautiful initial conditions. So we structure the total mess in one beautiful part, and blame the mess of unknown initial conditions. Probably a good way to reduce anxiety.

Its easy to be seduced by this method that served us very well so far. But it is not hard to see how extracting laws from processes that are easily monitored completely and repeated enough to get stable statistics, is different from the "gambling scenario" we face when trying to "guess" the corresponding "laws" for processes we observe only transiently or maybe only once.

/Fredrik
 
  • Like
Likes MathematicalPhysicist
  • #11
14,394
11,709
Beauty is in the eyes of the beholder.
I do not share this opinion. We are not talking about food, color or body shape. Or as I recently said in another thread about the same topic: A certain Lagrangian might be ugly, the principle (Noether) is not.

To me there is an objective beauty in the way we do physics or mathematics. This does not imply a scale by which it can be measured, unfortunately, but it doesn't make it subjective either.
 
  • Like
Likes bhobba
  • #12
Fra
3,193
176
Beauty is in the eyes of the beholder.
I can both agree and disagree with this depending what class of "beholders" we talk about, and what "beauty" is.

I do not share this opinion. We are not talking about food, color or body shape.
Assuming by "beauty" we mean the extracted timless laws and symmetries of the environment which the beholder interacts with, then I would say that beauty here is an inferred concept.

To me there is an objective beauty in the way we do physics or mathematics. This does not imply a scale by which it can be measured, unfortunately, but it doesn't make it subjective either.
The "beauty" is abductively inference from plenty of observations(=interactions) whilve evolving in the the environment in question, and the result of the inference necessarily depends on the inference machinery of the beholder (information processing and coding capacity), andn the result also forms the beholder.

In the everyday sense of science, the class of beholders are physicists, and indeed from that perspective the beauty is objective relative to the equivalence class of human scienctist beholders.

But as some symmetries, manifest themselves only at certain energy scale for example, not all observers will have the requirements for beeing to infer the symmetries from their perspective. This is merely one deeper way in which the beauty is still "subjective". By subjectivity here i dont mean a matter of PERSONAL opinon, but a matter of limits in the physical capability to infer and represent symmetries from their environment.

But energy scale is just one way this is effected, the inference machinery of an obserer may also differ in ways other than just energy scale, that IMO also are bound in physically constrain the possible inferences about beauty.

All this is to mer very relevant when you ponder about unification of laws, and how to explain the laws. How you think here probably explains your research direction as well.

/Fredrik
 
  • #13
MathematicalPhysicist
Gold Member
4,362
241
I can both agree and disagree with this depending what class of "beholders" we talk about, and what "beauty" is.


Assuming by "beauty" we mean the extracted timless laws and symmetries of the environment which the beholder interacts with, then I would say that beauty here is an inferred concept.


The "beauty" is abductively inference from plenty of observations(=interactions) whilve evolving in the the environment in question, and the result of the inference necessarily depends on the inference machinery of the beholder (information processing and coding capacity), andn the result also forms the beholder.

In the everyday sense of science, the class of beholders are physicists, and indeed from that perspective the beauty is objective relative to the equivalence class of human scienctist beholders.

But as some symmetries, manifest themselves only at certain energy scale for example, not all observers will have the requirements for beeing to infer the symmetries from their perspective. This is merely one deeper way in which the beauty is still "subjective". By subjectivity here i dont mean a matter of PERSONAL opinon, but a matter of limits in the physical capability to infer and represent symmetries from their environment.

But energy scale is just one way this is effected, the inference machinery of an obserer may also differ in ways other than just energy scale, that IMO also are bound in physically constrain the possible inferences about beauty.

All this is to mer very relevant when you ponder about unification of laws, and how to explain the laws. How you think here probably explains your research direction as well.

/Fredrik
The fact that we disagree is another instance of the statement:"Beauty is in the eyes of the beholder".
 
  • #14
MathematicalPhysicist
Gold Member
4,362
241
Also in physics if we have two theories that predict the same numerical values, which theory to choose is a matter of personal taste.
 
  • #15
Stephen Tashi
Science Advisor
7,583
1,472
The topic of the thread is (supposedly) Paul Dirac's opinions. So we shouldn't began expounding our own opinions - except as they are opinion's about Paul Dirac's.
- That's my opinion!
 
  • #17
9,600
2,681
The fact that we disagree is another instance of the statement:"Beauty is in the eyes of the beholder".
If you believe that after reading Landau - Mechanics then it might have some validity IMHO. But I do not know of any mathematician/physicist to which that applies.

If one posts here please explain, with references from that book, why - eg why its proof of the existence of mass, and that its positive, does not strike you as beautiful. When I read it and other parts of that book, at times too numerous to mention it was like a thunderbolt of lightning struck me. From a review on Amazon:

If physicists could weep, they would weep over this book. The book is devastatingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages. I first came across Landau's mechanics many years ago as a brash undergrad. My prof at the time had given me this book but warned me that it's the kind of book that ages like wine. I've read this book several times since and I have found that indeed, each time is more rewarding than the last.The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underly every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophistication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.

IMHO that says it all. Symmetry lies at the very foundations of physics - along with QM, which off course is what the symmetries are often applied to.

Thanks
Bill
 
  • Like
Likes martinbn
  • #18
9,600
2,681
The topic of the thread is (supposedly) Paul Dirac's opinions. So we shouldn't began expounding our own opinions - except as they are opinion's about Paul Dirac's.
- That's my opinion!
Fair enough.

Their have been papers and books written on it, but I do not have access to them. I do have access to a review of one:
https://www.ams.org/notices/200303/rev-faris.pdf

What I do have access to is the following:
https://physicsworld.com/a/strange-genius-the-life-and-times-of-paul-dirac/

It was a teacher, Peter Frazier, that instilled the beauty of math and physics into Dirac through protective geometry.

His opinions on physics overall are not necessarily about beauty - he certainly believed in, and used it in his development of theories (the beauty of it) but that doesn't seem to be the core of his view of physics which he espoused to his friend Heisenberg:
http://philsci-archive.pitt.edu/1614/1/Open_or_Closed-preprint.pdf

BYW Dirac's view is mine as well. Physics is not done in the way Kuhn says - its done in the slow methodical progress Dirac thought - of course that pace varies a bit - but its not the paradigm shifts of Kuhn. Although not stated in the article that progress was, because of his beliefs, guided heavily by beauty.

Thanks
Bill
 
Last edited:
  • #19
MathematicalPhysicist
Gold Member
4,362
241
If you believe that after reading Landau - Mechanics then it might have some validity IMHO. But I do not know of any mathematician/physicist to which that applies.

If one posts here please explain, with references from that book, why - eg why its proof of the existence of mass, and that its positive, does not strike you as beautiful. When I read it and other parts of that book, at times too numerous to mention it was like a thunderbolt of lightning struck me. From a review on Amazon:

If physicists could weep, they would weep over this book. The book is devastatingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages. I first came across Landau's mechanics many years ago as a brash undergrad. My prof at the time had given me this book but warned me that it's the kind of book that ages like wine. I've read this book several times since and I have found that indeed, each time is more rewarding than the last.The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underly every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophistication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.

IMHO that says it all. Symmetry lies at the very foundations of physics - along with QM, which off course is what the symmetries are often applied to.

Thanks
Bill
Proof of the existence of mass?
Well, mass like charge like length like time are the basic constituents of any physics; what is more basic than mass?
I mean if you prove that mass exists you must have something else that entails it.

Then what's more basic than mass?

No, I haven't read Landau's and Lifshitz due to lack of time.
 
  • #20
9,600
2,681
I mean if you prove that mass exists you must have something else that entails it.
Yes something else goes into it. The beauty is what that something is. Its the two axioms of QM as per Ballentine plus symmetry. Those two axioms lead to the Principle Of Least Action. Now Landau has an argument you can read on page 6 but its actually easier to do in relativity. The form of the free Lagrangian must be invariant. The only such Lagrangian is the proper time or proportional to proper time dτ so the action is S = ∫mdτ. m by definition is called the mass. In the Classical Theory Of Fields Landau also gives that derivation. But Landau, while beautiful, is quite terse. A better place to examine it is believe it or not a book on String Theory - A First Course In String Theory - Zwienbach - Chapter 5.

How did mass come out of it - that's the beauty of physics.

Thanks
Bill
 
  • Like
Likes Demystifier

Related Threads on Why did Dirac strongly pursue mathematical beauty?

Replies
3
Views
2K
Replies
5
Views
1K
Replies
18
Views
2K
  • Last Post
Replies
1
Views
4K
Replies
5
Views
3K
  • Last Post
Replies
3
Views
863
Replies
2
Views
726
Replies
4
Views
2K
Top