The holographic principle states that all the information contained within a region of space can be determined by the information on the surface containing it. Mathematically, this means the volume of space can be represented as a hologram of the surface, hence the idea’s name.
I find this extremely hard to accept. His simplified example -- a hotel doorman can know the number of people entering and leaving, hence the surface (doorman) can encode information about the volume (hotel) -- does not help. For the doorman/surface to know everything about the volume/hotel, she would require (1) to have been continuously present from the inception of the volume and (2) to have some means or medium of encoding the information about everything that entered or left the volume. Such a recording medium itself has to be error-free and persistent, and it would seem to me must itself have nonzero volume -- which creates an infinite regress of a recording surface on the recording surface of the...
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. :)
My "aha" moment for that one was when I read Terry Pratchett's first Discworld Novel, "The Colour of Magic", I guess when I was about 12 or so. First I laughed my head off at this ridiculous word and then, from the context, I worked out what it meant. A lesson I've never forgotten, as I'm sure this one will be for you...
Duality is a connection between two things where the properties of one defines the properties of the other.
Here's what comes up in Google:
1. the quality or condition of being dual.
"the novel's deep duality about human motive"
2. an instance of opposition or contrast between two concepts
or two aspects of something; a dualism.
"the photographs capitalize on the dualities of light and
dark, stillness and movement"
Also, if you look at the Wikipedia entry on Duality, just in physics, there are many kinds of duality just under physics alone. I'm not so sure this line from the article makes it past the level of "physics woo." It might be better if the article tried to talk more directly about Holographic duality, instead of trying to raise the term "duality" on a pedestal like it's some sort of Marvel Comics embodiment of "cosmic fundamentals."
It's not physics woo; the way the OP's using "duality" is common among mathematicians and physicists. The different types of duality listed in the physics and math sections of the Wikipedia article you linked to are thought of, by typical practitioners in these areas, as all being instances of a more general phenomenon. That's why these various things end up being called dualities.
That generic kind of duality is well described in the first sentence of [1], and the OP's explanation of a duality as "a connection between two things where the properties of one defines the properties of the other" is pretty obviously an attempt to convey, to a lay audience, that sense of duality.
At least within mathematics and physics, 'the properties of one defines the properties of the other' is a pretty good explanation of what's meant by 'duality'. Looking at that wiki list it explains all of the dualities I'm familiar with except (maybe?) the wave-particle duality.
The crazies are certainly out in force on the article's comments section... Any mention of quantum physics seems to bring them out, I guess because to the layman "quantum" == "magic"
I find this extremely hard to accept. His simplified example -- a hotel doorman can know the number of people entering and leaving, hence the surface (doorman) can encode information about the volume (hotel) -- does not help. For the doorman/surface to know everything about the volume/hotel, she would require (1) to have been continuously present from the inception of the volume and (2) to have some means or medium of encoding the information about everything that entered or left the volume. Such a recording medium itself has to be error-free and persistent, and it would seem to me must itself have nonzero volume -- which creates an infinite regress of a recording surface on the recording surface of the...
Maybe somebody can clarify?