[e2e] [SPAM] Re: a means to an end
David P. Reed
dpreed at reed.com
Wed Nov 12 18:16:11 PST 2008
To your last question: this is relevant, because you asserted without
qualification or caveat that ALL information (except for odd things like
my majority example) *has a location*. That's just plain false. Some
systems, by convention, are organized so that they store a piece of
information in a single unique storage "bin" (a physical device, a time
slot, an addressable magnetic domain, ...). But that is a convention of
a designed organization or descriptive frame of reference, and hardly a
"law of nature". In fact it is just a design choice. Even in trivial
case of an RSA encrypted 32-bit word of data, stored in a 32-bit
container, the "first bit" of data is not localized, but is smeared into
the whole word.
So saying that "all information is located" and therefore deriving that
access of information requires "first finding its unique location" is
JUST a choice of design. But it is not the only choice. You can talk
about information that inherently has NO location, and doing so has
benefits to the designer and the design space he works in. (as is the
case with Van's work).
In networking, it is worth thinking about this, because by abusing
yourself of the notion of information being in a location, you can make
better choices. Just look at "network coding" as one example - Dina
Katabi and Crowcroft showed that in practice de-localizing information
has many advantages. Or as a different example, consider the work of
Trachtenberg, Minsky and Zippel on distributed set reconciliation.
Information flows between containers in a manner that is diffused in
space and time. Or look at a hologram or FFT - again information
loses locality, with many benefits.
Information may have a *name* - that is one of the points of my (now
old) Ph.D. thesis, and in practice it is often the case that any
information of interest must have an "effective computation" that can
make a decision based on it. B ut even the "effectively computable"
notion of information is NOT complete. There can be information that is
not "effectively computable" - that's the whole point of Goedel's work.
Note: We can also discuss physics if you like - I spend a lot of time
thinking about the physics of information and information theory, so I'm
happy to discuss it with you. Thoughh it perhaps is less relevant to e2e.
But in fact, it is not the case that in modern physics information needs
must have a location, either. You can try to approximate "localized
information" in physics, but then you end up with laws that cannot
describe all possible experiments. (In fact, the recent resolution of
some of the paradoxes of black-hole information has been possible
because Hawking admitted that information need not have a location - in
essence, though the math is subtler than that).
One of the problems with location in physics is that in most late 20th-
early 21st century physical theories, there is no such thing as a
"location" that is independent of the stuff that is in it. The
boundaries of space themselves don't exist independently of their content.
Of course when you take physics classes in school, the *problem sets*
simplify reality to cases where information is localized. Surely you
realize that problem sets are designed to teach, and not to represent
the entirety of reality?
touch at ISI.EDU wrote:
> Quoting "David P. Reed" <dpreed at reed.com>:
>> You should be careful. If the mole of gas is embedded in a larger
>> system, its information is not separable from the larger system's
>> information because there is no isolation.
> If you're talking about its temperature, that is defined as its average kinetic
> energy, which has no relationship to the environment in which it exists.
> However, intrinsic values like temperature are not in of themselves
> "information"; e.g., the mass of an electron is not "information" per se, but
> it can be information to an entity to whom that value is not known. Information
> is defined over a set of possible states, as the difference between the number
> of actual states vs. the number of possible. In this case, it's the number of
> possible temperatures vs. the actual temperature. Again, none of this is
> related to the system in which the gas resides.
> That's not to say that there are not measurements that are related to the
> environment of the system, but this isn't one of them. Or are you running
> towards the Liouville Theorem, regarding aggregate information and its
> conservation in a closed system?
> Why, however, is this relevant?
>> Joe Touch wrote:
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>>> David P. Reed wrote:
>>>> No, information is not the uncertainty in the outcome of an event (not
>>>> least because that puts information as a "future" thing). It's related
>>>> to the number of possible states of a system as a whole. Decomposing
>>>> the state of a system into the state of parts (needed to assign a
>>>> location to some piece of information) must be done carefully, because
>>>> the states of parts may have invariant relationships, which reduce the
>>>> number of states, and create the illusion of information where there is
>>> There are numerous definitions of the term. Let's use your proposed one:
>>> "related to the number of possible states of a system"
>>> Both the system and the states are represented physically, and thus have
>>> a location.
>>>> E.g.: the states of atoms that make up a one-bit storage cell typically
>>>> are highly correlated. Thus the cell contains a single bit of
>>>> information, whereas the individual atoms contain no bits (or more
>>>> properly, they contain contingent information, of the sort that the
>>>> "majority" talks about).
>>>> Similarly, the "temperature" of a mole of gas expresses a bounded number
>>>> of bits of information, and that information is neither an event nor a
>>>> place, and is not independent of the "pressure" and "volume" of the gas,
>>>> each of which is dependent on the other.
>>> The gas has a location. I never said that a bit correlated to an atom or
>>> a *point* in space.
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