4 ms·

How Symmetry Shapes Laws of Physics [video]

34 points by treefire86 11y ago

noobermin 11y ago
We can thank Emmy Noether[0][1] for our current understanding of symmetries and for how today we view such symmetries as being or underlying the fundamental laws of physics. [0] http://arstechnica.com/science/2015/05/the-female-mathematician-who-changed-the-course-of-physics-but-couldnt-get-a-job/1/ http://arstechnica.com/science/2015/05/the-female-mathematic... [1] previous HN discussion: https://news.ycombinator.com/item?id=9606497 https://news.ycombinator.com/item?id=9606497
- naringas 11y ago
  I'm extremely curious about the notions/concepts of symmetry in a more mathematical sense, but from a philosophical perspective. I preliminarily believe that symmetries may be related to the notion of novel information.
  - Retra 11y ago
    Sure, that's not unsurprising. Information symmetries are fundamental to how you distinguish between states -- so much so that you could probably just define information to be the manifestation of observational asymmetries.
    - williamjennings 11y ago
      Information already has a precise, functional definition in the context of mathematics, machine learning, and AI. It is the number of bits necessary to encode a message, and that is the most essential aspect of coding theory. I would suggest reading the original works of Claude Shannon to become enlightened about how the word 'information' is used in the context of math, electrical engineering, and computer science. The manifestation of observational asymmetries absolutely must be equivocal to the asymmetry of manifest observation. Therefore, the format of an observation is manifest via the symmetry of a relation under a set of attributes. Thusly, the asymmetry of observations is a point measurably manifested by the difference in attributes. That allows for the derivation of: a union operation over the observations; an intersection operation over the asymmetries; and a manifest closure property. This is how one may define points of 'data' in the sense that is absolutely congruent with the terms database, big data, or data science. Information Theory and Relational Algebra have some overlap, but they are not completely intertwined. The subjects of Abstract Algebra and Information Geometry are there at the intersection, but they still too terminologically distinct to be taught in tandem. The former subject is still best learned in French; whereas the latter subject is still best learned in Japanese. It is possible for one to teach themselves these subjects by machine translation, if they have a deep understanding for the grammar and history of each language. Deep learning of this sort is a kind of meditative activity, the type of which is only available to the most erudite thinkers.
      - renox 11y ago
        > Information already has a precise, functional definition in the context of mathematics, machine learning, and AI. It is the number of bits necessary to encode a message, Precise?? You're joking right? Given that the number of bits necessary to encode a message is highly depending on the way your message is interpreted.. If your bits are interpreted as either black or white, I need only 1 bit to send a message indicating a color, if your bits are ASCII strings I need more bits to send the same information..
        williamjennings 11y ago
        >Precise?? You're joking right? Given that the number of bits necessary to encode a message is highly depending on the way your message is interpreted.. The interpretation is not the language. If a message consists of words, or is mapped thereof; then there is an exact number of bits necessary. >If your bits are interpreted as either black or white, I need only 1 bit to send a message indicating a color, if your bits are ASCII strings I need more bits to send the same information.. It seems like you are not familiar with the definition of bits. It is the binary measure implicit to boolean algebra. Bits are not specifically ASCII strings, because the former is a subset of the latter's characters.
  - agumonkey 11y ago
    My main interest in symmetries is the equivalence under transformation view. Especially how do you recognize composed transformations / abstractions from new information.
TTPrograms 11y ago
Symmetry can also be very useful in the context of programming. In particular I find loop invariants to be a very useful tool when building convoluted looping algorithms - I'd guess you could formulate a similar symmetry for recursive algorithms.

34 points by treefire86 11y ago

We can thank Emmy Noether[0][1] for our current understanding of symmetries and for how today we view such symmetries as being or underlying the fundamental laws of physics. [0] http://arstechnica.com/science/2015/05/the-female-mathematician-who-changed-the-course-of-physics-but-couldnt-get-a-job/1/ http://arstechnica.com/science/2015/05/the-female-mathematic... [1] previous HN discussion: https://news.ycombinator.com/item?id=9606497 https://news.ycombinator.com/item?id=9606497

naringas 11y ago
I'm extremely curious about the notions/concepts of symmetry in a more mathematical sense, but from a philosophical perspective. I preliminarily believe that symmetries may be related to the notion of novel information.
- Retra 11y ago
  Sure, that's not unsurprising. Information symmetries are fundamental to how you distinguish between states -- so much so that you could probably just define information to be the manifestation of observational asymmetries.
  - williamjennings 11y ago
    Information already has a precise, functional definition in the context of mathematics, machine learning, and AI. It is the number of bits necessary to encode a message, and that is the most essential aspect of coding theory. I would suggest reading the original works of Claude Shannon to become enlightened about how the word 'information' is used in the context of math, electrical engineering, and computer science. The manifestation of observational asymmetries absolutely must be equivocal to the asymmetry of manifest observation. Therefore, the format of an observation is manifest via the symmetry of a relation under a set of attributes. Thusly, the asymmetry of observations is a point measurably manifested by the difference in attributes. That allows for the derivation of: a union operation over the observations; an intersection operation over the asymmetries; and a manifest closure property. This is how one may define points of 'data' in the sense that is absolutely congruent with the terms database, big data, or data science. Information Theory and Relational Algebra have some overlap, but they are not completely intertwined. The subjects of Abstract Algebra and Information Geometry are there at the intersection, but they still too terminologically distinct to be taught in tandem. The former subject is still best learned in French; whereas the latter subject is still best learned in Japanese. It is possible for one to teach themselves these subjects by machine translation, if they have a deep understanding for the grammar and history of each language. Deep learning of this sort is a kind of meditative activity, the type of which is only available to the most erudite thinkers.
    - renox 11y ago
      > Information already has a precise, functional definition in the context of mathematics, machine learning, and AI. It is the number of bits necessary to encode a message, Precise?? You're joking right? Given that the number of bits necessary to encode a message is highly depending on the way your message is interpreted.. If your bits are interpreted as either black or white, I need only 1 bit to send a message indicating a color, if your bits are ASCII strings I need more bits to send the same information..
      - williamjennings 11y ago
        >Precise?? You're joking right? Given that the number of bits necessary to encode a message is highly depending on the way your message is interpreted.. The interpretation is not the language. If a message consists of words, or is mapped thereof; then there is an exact number of bits necessary. >If your bits are interpreted as either black or white, I need only 1 bit to send a message indicating a color, if your bits are ASCII strings I need more bits to send the same information.. It seems like you are not familiar with the definition of bits. It is the binary measure implicit to boolean algebra. Bits are not specifically ASCII strings, because the former is a subset of the latter's characters.
- agumonkey 11y ago
  My main interest in symmetries is the equivalence under transformation view. Especially how do you recognize composed transformations / abstractions from new information.

TTPrograms 11y ago

Symmetry can also be very useful in the context of programming. In particular I find loop invariants to be a very useful tool when building convoluted looping algorithms - I'd guess you could formulate a similar symmetry for recursive algorithms.