Since I don't actually agree with that, I asked Professor Marks for some justification. He did not reply.
Three months later, I asked again. No reply (except auto-reply).
Now, six months later, I'm sending him another reminder.
Who thinks that he will ever send me a calculation justifying his claim?
Methinks he is like a weasel. No calculationsists to be forthcoming.
You see, it's a different kind of information.
I listen to the podcast ("so you don't have to"), and a few days ago they had a Dr. Donald E. Johnson as a guest, who said that what they're talking about is "functional" information. He didn't give any clues to how he defines that, but I'm sure Marks would say the same BS.
Maybe they took so much crap for their "complex specified information" that they had to change its name.
I'm happy if it's "functional information". I just want to see the calculation.
This sounds a tad like the debate in early Greek philosophy between the relativists (pre-Socratics) and the Platonists.
I'm curious what your calculation would look like to prove that they either contain the same information or that Mount Fuji contains more?
One of the subtleties of Shannon's original paper on information theory is in the second paragraph where he explicitly states that he's leaving out the semantic processing of the message by the receiver and just concentrating on the sending and receipt of the signal. (Put another way we can play the game telephone and you can hear and repeat the exact words I say, but concepts like double entendre and nuance may prevent you from understanding exactly what I meant to say. Shannon is leaving the second problem understanding out of the picture and solely working on the question of did you hear the words I actually said.) The way you're framing your question, it would appear that you're only focusing on the interpretation of the information after it's been received, in which case Shannon's information doesn't really have anything to say.
Now, to take a look at it from a purely mathematical standpoint within a Shannon framework, once could count the totality of the number of atoms and their states in Fuji and compare it to that of Rushmore and the one with more information is simply going to be the larger one.
If we're looking at photos of the two, then the one with more information is going to be the one that doesn't compress down as much under whatever compression algorithm we might choose. (ie, it won't have anything to do with the "information" contained in the faces and whose faces they are, which again is a semantic issue and not a mathematical one.)
I'm willing to bet he won't reply. Robert J. Marks, the second, is not writing these things for people who know information theory. He's only addressing the believers of his religion. In his face, they see a "scientist" whose word they will take for granted, for the same reason they take their bible's words for granted. As for your inquiries, they surely have a response: for them, you're the devil, and with the devil no serious christian should engage in communication.
I agree with you Mt. Rushmore contains less information (and lower entropy) than Mt. Fuji. In the same way that a royal flush contains less information than a random hand. Or, equivalently, an accurate description of Mt. Rushmore takes fewer bytes than an accurate description of Mt. Fuji.
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