Spider of the universe - Information

So don’t focus on the webs.
Focus on the spider.

This time it was ut’s comment on Green September: “Imagine all that money spent at the DOD to blast other people all over the world and they don't have enough employes and logistics to take care of Americans” which made me think, how stupid people act, how unbelievable un-intelligent it is to spend money for wars to kill and maim mothers and children far away instead of spending money to protect my house and the houses of my friends against floods and hurricanes here at home - so i remembered the gain function of intelligence.

I guess, many people think, that intelligence can grow and grow and grow and that the human race will survive every threat just by the power of its high tech game boys: the next invention will solve the problem, so don’t worry, be happy!

That’s simply not true.

Because sophisticated intelligence destroys information – like black holes do – it deletes the precondition for the success of intelligence (that’s by the way the reason why language was so important for the human evolution: the need to protect information).

You’re puzzled? Language is a tool for communication?

It is – but communication is “transport of information” between members of an information processing system and when the members start to destroy information, the group needs to protect it by increasing communication to survive. As we need now...

Still puzzled?

Then, World, may i introduce to you your mother, the creator of the generations?

Information - World.

World – information.

World, you know yourself, you know how knitted the web is connecting each small item with each other. You are son or daughter, mother or father, brother or sister, uncle or aunt. And even if you are all alone, you are part of a life chain which leads back to the beginning of life on Earth. But even the Earth is born, out of the chaos around a young sun, and even the sun is born, out of the chaos of dying suns, but even those suns were born soon after the universe was born in the big bang, creating the natural laws.

Seems, as if the galaxies can’t answer the question about infinity? So let’s look on the small side. Look on the cells in your body – complex manufactories of life, controlled by DNA and RNA, controlling cell and body with the chemistry build from those blueprints, a chemistry based on molecules based on atoms based on protons, neutrons and electrons, based on a particle zoo downwards to nearly not measurable quarks and a theory of multidimensional strings...

vanishing...

World, have you ever thought about the simple truth, that focusing on stability has limits? That for each and every stable thing in the whole universe there is a point of exactness, where stability vanishes away in facelessness, gets lost in Nirvana?

I see, you’ve heard from Heisenberg. His uncertainty relation was the first proof for the true nature of universe: You can’t measure positions and momentums together in any case, locations together with impulses forever, you can’t measure stability together with movement (change) with perfect exactness – either/or.

The experiments of physics demonstrate, that you can’t measure – and relate – everything, with an interesting aside (keyword “quantum eraser”): if you delete your previous measurement, you can measure the complementary observable. But that doesn’t explain, “why the ‘Teeny Tiny’ behaves like jelly which has to be taken with a spoon”. (Physics of information, p. 132).

Yet, there is another truth beyond the vanishing measurability, the loss of stability, of identity – the everlasting, ubiquitous, almighty quantum noise. As Stephen Hawkings told us, the quantum noise may even be able to destroy the greediest black hole.

But...

it can’t destroy information – at least not the whole information.

Hawking cracks black hole paradox
“After nearly 30 years of arguing that a black hole destroys everything that falls into it, Stephen Hawking is saying he was wrong. It seems that black holes may after all allow information within them to escape.”

There is something as mighty as the quantum noise...

information.

The “attribute” of the universe to be measurable, to have values – to have a name and a face, to have an identity, so to be recognized, remembered and related...

Yes, World, here the set comes into the mind:

And inside the set, you know, there is identity – therefore you can track movings, you can follow events, you can construct relations, you can map and store, retrieve and compare.
A set creates order in a random world.

You want to understand information?

Look at the set – it offers you the most characteristic property of anything, which is information: identity, measurability, because it creates reproducible uniqueness. The attribute, which makes elements belong to a set, which “parts the sea”, divides the world in inside and outside, remember? And inside the set, there exists some other attribute, allowing you to identify each element by distinguishing each element from every other, meaning nothing else than that this element is uniquely measurable in the whole universe.

But that isn’t the whole information...

Because we forgot that each and every state – in reality – has to be entered.

Values, faces, even identities may change – however, there’s a significant difference between values, faces, colors of hairs, numbers of electrons in atoms and the identity itself. While values may change without destroying the basic element, identity has to be stable, at least as long as the element exists.

So simply put both together – the set and the change of values of identities. You just have to take two set elements (e and w) and connect them by a “relation” (a well known mathematical construct):

e|w

And then do something, which is not very common in mathematics:

Change it.

Dissolve the relation by cutting off the link between the two set elements, holding one of the elements and then – link another set element to “the one”, replace w with w’. The unchanged element call “element of quality, e”, let it play the role of the stable part. It shall remain stable during all the changes you may now perform, cut relations and link new elements, cut and link new: the identity passing through different states e|w, e|w’, e|w’’, e|w’’’.

Now you can define the representation of that change (cut and replace), in the world of mathematics, just by a “transformation”, deleting and creating a temporary relation:

X(e|w) = e|w’

Boring?

So don’t focus on the webs.
Focus on the spider.

Yes, don’t look too eagerly at the set elements e, w, w’ – watch X.

What does it tell you? States can be entered and left – values can change like the color of your hair. In the youth it is dark, growing old it gets white.

Steps.

X can describe steps. While “e” is stable, “w" can change: from w to w’ to w’’, from dark hair to grey hair to white hair.

And the connection is “X”, in the case of human hairs the biological rules, how DNA and age creates colors of hairs.

It doesn’t really matter, what kind of set it is, to which e or w or w’ do belong. Because the creating power is “X”, not the set. If something in the universe is describable as set element, it can be an element of quality or values or both:

The relationship decides its nature, not the set.

Don’t forget that, because this offers you a freedom usual set mathematics can’t give.

Anything goes.

When there is an “X” which creates relationships, connections between one stable set element “e” and some other “w”s, the temporary relations exist, if we know something about the original sets – or not. Those “e”s and “w”s may belong to different sets or to the same set – the set doesn’t matter, it is only needed to provide identity, measurability, nothing else. And if the “w”s don’t belong to the same set – take the union of the set and call it “set of values”. If new “X” add new w’s to the element of quality, the set of value may grow: X decides, not an a-priori-definition of any set. (Physics of information, p. 127)

Now follow the steps on that set of values – from w to w’, from w’ to w’’, from w’’ to w’’’ – ways. X creates ways, paths because of the steps it makes.

Chaotic paths, starting somewhere, ending somewhere, crossing themselves...

Crossing themselves? What if the paths would be clear, well defined? If everytime, you reach w you know that just one X exists - to reach w’?

Than you would have a true “function” on the set of values, at least on the subset of the different “w”s reachable by some starting point w⁰. A function is a very useful tool in mathematics, World, i guess, you know.

So let us connect both.

The powerful function, able to describe quantum physics and social statistics – and the mighty information, inducted by “e”, “w” and “X”.

What does it need to make the paths of X a function? X has to be able to link every w of a given set of values to the element of quality and it has to be repeatable: everytime X reaches a value w, it has to connect the same value w’ to e. Than the way of the values on the set of values is a function.

Just an aside: this answers the question of Eugene Wigner about “The unreasonable effectiveness of mathematics in the natural sciences”, because it knits real changes in nature together with the mathematical tool “function”.

And interestingly, this set of all (repeatable and connecting) X of a given element of quality “e” forms a group, one of the basic preconditions for Noether’s Theorem, but that’s also just an aside.

Important is, that this set of X lets you know everything about the element of quality: How you can measure it (because it is a set element), which values it can has (because X connects it to the whole set of values), how those values can be measured (because each is a set element, too)...

and – most interesting – how e will behave in any situation. Because X is repeatable, you know, that reaching w does mean “reaching w’ in the next step” and because X is connecting and repeatable for every w, you know...

there can’t be randomness.

Predicting the future of e: with this set of (repeatable and connecting) X you have the full information about e, nothing can surprise you. That’s why this set is called “information regarding e”.

And because e or w or w’ needs nothing more than to be elements of sets, they can be everything. They just have to be identifiable and connected via repeatable temporary relations.

Like mother and son, father and daughter, husband and wife, Earth and Sun, proton and electron.

The element of quality can be simple or complex, it doesn’t matter – you just have to know how to identify it and how to identify it’s values and how to follow the change of values, creating a path of the set of values: a path which can be stored and mapped and remembered.

You’re not amazed, World?

Rethink it – complex elements of qualities can be anything identifiable, can be me and you, can be your city or my nation, can be the customer or the employer, can be the warmonger or the peacemaker. Anything goes, it just has to have a measurable identity.

And values? The same, just have to have a measurable identity, can be red hair or green hair, can be white skin or dark skin, can be nobleness or greed, can be stupidity or intelligence...

And here we are back to intelligence – and why and when it is able to destroy information. Because what does it need to destroy information? Think of X. You can destroy the connectedness or the repeatability or the identity – in any case you destroy information.

Still not impressed, World?

So imagine a railway. The train is the “element of quality” in our example, the stations are the “values” or “states”, where the train is reachable, and X is the diesel engine or the electric motor or maybe the little green men from the mars, pushing your train forward.

It doesn’t matter, how the divine force looks like which moves your train, because it doesn’t interest you or you are no engineer to understand it or you simply don’t know it.

The only thing you have to know is the number of the train, than you can look on the time table, (the “memory” or “knowledge”) and you know where to go. Because if the train reaches station w you knows it will leave for station w’, everytime you come according to plan.

And any accident destroys your information.

The train doesn’t come – your information “was wrong”, why? There was a tree on the railroad tracks, so the repeatability of the trains course was broken, because the full state of your time table does never include trees on tracks. “Reaching station w” is a quite useful description/mapping of the states of your system “train moving from a to b” to promise you to be able to leave for station w’ - if the states of reality don’t include trees or trucks or something else on the way of the train.

The wrong identity destroys your information, too.

You look for train x, but you mistake it for train y. So you leave the station w, but you will never reach w’. Instead of that, you’ll reach station “far away”.

Last but not least: the loss of connectedness destroys your information.

Your time table (plus map of the stations) tells you, that there is a bridge between two stations. But the bridge was wrecked by a storm, you can’t reach the station w’ any more. Your information, that you will be able to go to w’, if you can take the train at station w - was wrong.

That’s the problem of information processing systems in reality: they need to detect information by states and their relationships and have to store it to be able to find “identity” (objects) and “repeatability” (behavior) – they need intelligence (a detecting system) and knowledge (memory according to your detecting system “intelligence”)

But that’s another story and will be told another time...

One last remark: Because of the connectedness and the repeatability of information every known step of an interesting system helps you to detect more information about it, to understand it better - even if it is not exactly, what you want to know:

Bertrands Paradox:
the more you know about your problem, the better you can evaluate it – with the result, that your prognosis significantly betters, how this problem will develop.

That’s why Leo Trotzki was right: “Maybe i can find the truth by comparing the lies.”

And that’s why Riverbend compares the english and the arabian version of the Draft Constitution (Part I and II) to find the truth behind the words, to find the way, where her country will go – to predict the future.