Which sentence contains more information: 'it snowed in January' or 'it snowed in July'.
Clearly big deal for the first sentence (technically it has low surprisal) but the second sentence is a very rare sentence and so has high surprisal and carries a lot of information. I might point out further that "you are reading some words" to show how low surprisal is as good as no information at all and we ignore it.
Of course to someone from abroad who has never seen snow both sentences are equally important because they are learning about snow. It is only when someone says we never get snow in the summer that the difference in information described above becomes apparent to the student.
So the information content depends upon the state of the receiver, and the state of the receiver is an historical feature. There is no absolute information content then independent of the environment or other information sources.
The Kolmogorov complexity which is measured by the smallest possible algorithm that produces a given set of data seems to be a search for an absolute information content. For example the Mandelbrot set can be produced by a very simple algorithm Z^2+C > 4 but most humans aren't very happy with that and like the picture. The picture is instructive to experts also because it shows the limit of the set - the famous apple man - which can't be deduced from the algorithm above. What is needed is a program to render that equation. The usual loops and graphics functions. What if there was hard coded graphics function:
M(complex c_position, double zoom)
For a given complex number and zoom it rendered the Mandelbrot set on the computer screen. Can't get much lower Kolmogorov complexity than that. But it is a cheat and just hides the real complexity. We need to put all the sub-calculations in to get a more realistic idea of the complexity.
But what if the algorithm produced the image in red and green and the receiver was colour blind. It would still fail to produce the apple man. And what if the receiver was blind all together and the algorithm had to drive a Braille printer which took up more coding space. The algorithm has to assume things about the receiver. I assume that Kolmogorov complexity refers to the ability of algorithms to produce sets of numbers rather than pictures and for any fixed set of numerically literate users it will be a relative measure where indeed there may be a smallest program that generates using a fixed minimum instruction set the required data. But peppered throughout the preceding description are the relative conditions of that measure. It is not absolute. No measure is absolute by definition because measuring involves providing a ratio against something else. That is pure SRH.
In passing SRH goes further to say that the ratio of something and itself is not 1 but undefined since no such comparison can be made meaningfully. One may argue that ruler A is 30cm long and a stick of wood the same length is 30cm long. One can then use the stick of wood to say that ruler A is 30cm long. But can you? What if ruler A was really 25cm long? We have correctly identified that the stick and the ruler are the same length. That is the ratio that we know. We can say that ruler A and the stick are the same length. We cannot deduce from this that ruler A has an "actual" length however, and then say that this imaginary actual length is the same as itself. We can only ever say that Ruler A and the stick are the same. If Ruler A becomes our standard then we have a system of measurement but that is a cultural and political point not a logical one - hence the pun on the word "Ruler"! This is why the ancient Greeks (being more truthful) were stuck with ratios and it took much later developments to develop the idea of actual Number. That is the crux of the problem... and ah ha as I get closer to Buddha's teachings I get closer to the SRH! Maybe SRH is just Anatta (non-self). The same argument works with humans. We find ourself in relations to other people, in relationships. We deduce from these relations that it is a relationship between "people" just as we incorrectly think that things being the same length means they have some intrinsic length outside the measurement. It follows as I was contemplating during writing the "Book of 7 Stories" for "my muse" that two rulers that have measured one another and been seen to be the same if they are then parted and sent into different universes can no longer be said to be the same! "My muse" did indeed depart for a different universe and I have wasted a long time trying to examine that measurement which I now see no longer exists. Indeed Death does win against those who believe they are together but maybe Riswey is learning the lesson of Elrus (that I confess I only vaguely grasped at the time of thinking out and sending to "my muse") that "we" really were never the same, and she never was "the One" because there were no people there to be measured and commensurated and so certainly no people to be linked by consumation. The relationship was what it was, the measurements, the similitude, existed while were together but once one of the rulers was broken the other ruler ceased to measure also. They say size matters, but how large am I? I need relationships to find that out and i will be a different size in each relationship... but all of human life is relationship because there is no ruler to exist out side of measurement. In days of old that density of meanings would fashion a poem but I'm off for a cup of tea now instead leave the blank page that follows to be the poem that measures what is said here.
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The absolute crux of this argument is that it is a mistake to say that something is the same length as itself!
A=B
B=C
C=A
Is correct, although I spent considerable time as a child looking for a "reason" why this was true. What is false is to then argue that:
A=A
The difference between this statement and the 3 above is that they are describing relationships "between" things. There is no relationship between A and itself, and if there was it is intrinsic and inaccessible to the outside world. We are inventing some internal property which we are saying is internally equal to itself as though this was meaningful. I will invent some internal quality called "sinustance" which all things have. Now I can say that A = A because they both share the same sinustance and so the sinustance is in direct relationship with itself. There we are I've proven the ontology of sinustance. But sinustance is completely made up as indeed is length when it is used to compare something to itself. The idea that the length of A=B means that A has some persistent quality "length" which exists after the measurement and which can then be used to put A in direct relationship with itself is exactly the same myth as sinustance. It is the basis of the materialist fallacy. A and B have length that comes from being measured, it wasn't there before and it isn't there afterwards. Shades of collapsing waveforms here, that become discrete when measured... I wonder if all that hokum is just an aberrations of models that are based upon old materialist thinking and maths rather than anything intrinsic to the data sets or "reality".
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