Quote from: iamnotback on March 02, 2017, 02:27:31 PM

Quote from: dinofelis on March 02, 2017, 08:41:09 AM

the "entropy of the universe" (which is an ill-defined concept)...

That is what I've been trying to tell you. (not ill-defined, rather unbounded)

It really is ill-defined, and in as much as you'd like to estimate it, you'll probably end up with 0. Yes, zero. Like the total energy content of the universe is also most probably zero, in as much as that even could have a meaning.

Most people talking about the "entropy of the universe" talk about the "entropy of the REST OF THE UNIVERSE with respect to an observer inside that universe". But there's a subtle difference between what one would call the entropy of the universe (with respect to an "outside observer" Huh

hence ill defined) and the "entropy of the rest of the universe".

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As if memory capacity is the entropy of the Internet (and which memory specifically?). Since when was the Internet an isolated system and not entangled with the user's lives?

That really doesn't matter. My cup of hot water is also entangled with the rest of the universe, but that doesn't increase its entropy with respect to me.
The "states of the internet" is the number of different states the internet can be in, and that is limited to the technical capacity of that system. If we limit ourselves to the *digital states* (and not to, say, the heat in a micro processor - like I'm not taking into account the nuclear states when accounting for the entropy of my cup of coffee) of the devices that make up the internet: the nodes, the network devices and so on, their digital state is entirely determined by all bi-stable digital components, essentially memory bits (and a few register bits in processor units and FPGA). If you know every single state of every single bi-stable circuitry of every device that makes up the internet, then you know the entire state of the internet. That's equivalent to me knowing the quantum state of the entire set of molecules making up my hot cup of water: i'd know the microstate of my hot water. The IGNORANCE of that microstate is what makes up the entropy I have about that cup of hot water, and the IGNORANCE I have of the state of every bistable state of every component of the internet is what makes up the entropy I have about the internet.

My rather secure guess is that the internet doesn't have 10^25 bistable circuits. It would mean about 10 billion devices with each a Petabit memory state. We aren't there yet (in a few years we will maybe).

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Someone posts something to Facebook shares with a friend who is talking about and hours later posts something back to the Internet. The offline surprises are not included in the entropy of the Internet?

No, of course not, not any more than the swimming of a whale, which is entangled with every molecule in my cup of hot water for historical reasons, increases the entropy of my cup of coffee. Because that's exactly what entropy is about: my ignorance of *just the cup of water*, and NOT its environment.

The posts only contain at most the amount of bits that are needed to download the page (in compressed format). And they were already taken into account by counting the empty bits on the page's server's hard disks. So someone posting some stuff on the internet doesn't really increase its entropy. A technician adding a few more disk units in a data center, does.

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How did you decide where to draw this arbitrary border around what is the Internet? Can you define this border unambiguously (be careful!)?

Ah, if you call "the internet" all of physical spacetime between here and Andromeda, of course we're talking about different stuff. I'm talking about all the data that is available to be transferred and stored by all nodes with an internet connection.
Now, of course, you can say, there are sensors connected to the internet, so they bring in an "unbounded amount of entropy". No, not really. When that camera takes a picture, say, of 8MB, then these 8 MB are available and are entropy to you if you didn't know the picture. But if at the next instant, the camera takes a new picture, the previous one is gone. There's still 8 MB of entropy because of that camera. If the previous picture wasn't STORED, and made available for download, the new pictures don't add entropy. If you are looking at each picture, you get 8 MB of information THROUGH the internet. But each time that picture gets refreshed, and not stored (nor on the camera side, nor at a cache site, nor at your side) on an internet-connected device, the internet's entropy doesn't increase. In fact, when the camera takes the picture, its entropy rises (for you) with 8 MB. When you look at it, you receive 8 MB of information, and hence the internet's entropy LOWERS with 8 MB wrt you. When the camera takes a new picture you haven't seen yet, the internet's entropy rises again with 8 MB. When you look at it, it lowers again with 8 MB. Etc.

This is like a telephone wire. The (digital) state of the wire is 1 bit at a time. Whole conversations can go through a telephone wire. But the state of the wire is at most 1 bit. When you haven't received the bit yet, it has 1 bit of entropy. When you read it out, it has 0 bit of entropy, until the transmitter puts another bit on it. Etc...

The internet, as defined by all the devices connected to it and their digital states, has less entropy than my cup of hot water.

A sensor, looking at the entire universe, has only the entropy of the data it has at a certain point in time, while you didn't look at it. From the moment you know the data, its entropy falls back to zero, until the next (unknown) data are taken.