I have not read the article but I doubt the analogy was meant to be an exact explanation (thus the reason it is an analogy and not a mathematical definition).
But for those who are familiar with calculus the notion of holography is related to the mathematical ideas and formulations of Stokes Theorem (and in fact Calculus in total) [0][1]. :)
The holographic principle (iirc) is commonly discussed (in physics) in relation to / in terms of ADS/CFT duality[2]. Where the 'boundary' of some quantum gravity theory (such as formulated by a string theory) on anti-desitter (ADS) space is a conformal field theory which is equivalent to a real world quantum field theory (if in the correct number of dimensions).
As far as I understand it, it allows a way for string theorists to 'map' particular string theories (in a certain dimension) to an actual quantum field theory, using the ADS/CFT duality. In other words, it provides a possible key to doing real world physics with string-theoretic methods.
Some commentary from an actual physicist would be most welcome, though. :)
But for those who are familiar with calculus the notion of holography is related to the mathematical ideas and formulations of Stokes Theorem (and in fact Calculus in total) [0][1]. :)
The holographic principle (iirc) is commonly discussed (in physics) in relation to / in terms of ADS/CFT duality[2]. Where the 'boundary' of some quantum gravity theory (such as formulated by a string theory) on anti-desitter (ADS) space is a conformal field theory which is equivalent to a real world quantum field theory (if in the correct number of dimensions).
As far as I understand it, it allows a way for string theorists to 'map' particular string theories (in a certain dimension) to an actual quantum field theory, using the ADS/CFT duality. In other words, it provides a possible key to doing real world physics with string-theoretic methods.
Some commentary from an actual physicist would be most welcome, though. :)
[0] http://en.wikipedia.org/wiki/Stokes'_theorem [1] https://www.khanacademy.org/math/multivariable-calculus/surf... [2] http://en.wikipedia.org/wiki/AdS/CFT_correspondence