Is Diagrammatic Tensor Notation Widely Used in Mathematics?

  • Context: Undergrad 
  • Thread starter Thread starter Hill
  • Start date Start date
  • Tags Tags
    Notation Tensor
Click For Summary

Discussion Overview

The discussion revolves around the use of diagrammatic tensor notation as introduced by Roger Penrose, exploring its prevalence and acceptance within the fields of mathematics and physics. Participants examine the practicality, aesthetic appeal, and theoretical implications of this notation compared to traditional index notation.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants note that Penrose's diagrammatic tensor notation is not widely used, citing difficulties in typesetting and quality assurance of complex 2D representations.
  • Others mention that physicists may be more inclined to use such notations, while mathematicians generally prefer to avoid coordinate systems.
  • A participant references Cvitanović's "bird tracks" as a related system that addresses some practical issues of Penrose's approach.
  • There is a discussion about the distinction between abstract index notation and coordinate systems, with some arguing that abstract notation is not tied to specific coordinates.
  • Concerns are raised about the aesthetic and practical aspects of Penrose's notation, with some participants expressing a preference for more traditional representations.
  • Several participants share anecdotes about mathematicians' aversion to coordinate systems, suggesting that this aversion may vary by subfield within mathematics.
  • Some argue that while mathematicians may avoid coordinates, they still engage with concepts that involve tensor multiplication and traces.
  • There is a debate about whether the use of abstract index notation is palatable to mathematicians, with differing opinions on its acceptance.

Areas of Agreement / Disagreement

Participants express a range of views on the use of diagrammatic tensor notation, with no clear consensus on its popularity or practicality. Some agree that it is not commonly used, while others suggest that it may have niche applications in physics.

Contextual Notes

Limitations in the discussion include varying definitions of what constitutes "coordinates" and differing perspectives on the appropriateness of various notational systems across different mathematical disciplines.

  • #31
fresh_42 said:
How about Euclid?
I dont know. Can you show me a paper by him so that we can see?
 
Physics news on Phys.org
  • #32
I guess I could find one. But this isn't necessary. Euclid lived before Descartes and before analytical geometry was developed. Moreover, he undoubtedly was a Greek Geometer and as such had a completely different understanding than ours today. He didn't feel the necessity to determine a specific point from where he measured everything. (I would start to search for it in van der Waerden's oeuvre.)

Euclid is an example and one that doesn't use a circular argument.

Has anybody here ever wondered why nobody writes ##f_\alpha \in C(X)##? This is because index notation refers to finitely many components.
 
  • #33
Orodruin said:
Are you claiming mathematicians never multiply temsors together? Never have the need to take a trace or similar?
No, but they don't need abstract index notation to do it. Look at a mathematical differential geometry book and their use of this notation is infrequent.
 

Similar threads

Undergrad Dirac Notation for Vectors and Tensors (Neuenschwander's text ....)
  • · Replies 16 ·
Replies
16
Views
3K
Graduate Diagrammatic Notation for Tensors: Worthwhile Learning?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Diagrammatic Tensor Notation from the Beginning
  • · Replies 26 ·
Replies
26
Views
11K
Undergrad Is my use of Einstein notation correct in this example?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Symbol for matrix representative of a tensor
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Purpose of Tensors, Indices in Tensor Calculus Explained
  • · Replies 10 ·
Replies
10
Views
3K
Graduate How Do Indices Function in Tensor Notation?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad SR: GA Multivector vs. Tensor notation, Maxwell's equations
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Manipulation of 2nd, 3rd & 4th order tensor using Index notation
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Notation in Spivak's Calculus on Manifolds
  • · Replies 1 ·
Replies
1
Views
2K