10 Nov 2006
See “Conspiracies” , “Lies” , et al in http://andreswhy.blogspot.com/
After some discussion with Eben Swart , it seems that I have not clarified the concept of the Universum sufficiently .
The Universum is everything .
It includes all possible delineated things , but also the non-delineated things .
The problem is to represent non-delineated things in terms that a brain built from delineated blocks ( atoms and molecules) can understand .
An infinite series is one way of describing non-delineated things . If the series converges , we can talk about e or pi (for example) as if they are delineated entities , but in reality they are fuzzy and non-delineated .
The basic concept is Taking the Limit , the heart of calculus .
The Venn diagram is another tool to show an abstract of the logical elements . Notice the definition of a set : it is by definition comprised of identifiable elements
A Venn diagram can thus be drawn encircling all the delineated systems ,. . The number of delineated systems need not be infinite (see below) but the non-delineated systems lie in an infinity outside . Delineated systems are bounded inside our Venn diagram , but the Universum is not bounded ouside .
In other words , draw a Venn-circle on sheet of paper . Inside the circle represents all the possible delineated universes .
You cannot have a Venn-boundary outside this , since if you could , it means that defineable elements exist outside the circle , which is a contradiction . The sheet of paper stretches to infinity on all sides .
This is the heart of this argument .
We know that we have at least one logical mechanism whereby an entity inside the Venn-boundary can draw in a non-delineated “something” into the delineated boundary : infinite series like e or pi as discussed above .
If one such process is possible , then an infinity of such processes are possible . The proof is easily seen in the proliferation of complexity inside the Venn-diagram boundary as “things” outside the boundary is brought inside . The outside is by definition infinite , so as “things” outside the Venn-boundary is drawn in , the Venn-boundary expands .
The outside of the Venn-boundary still remains infinite . Only if processes inside the boundary goes to infinity do we approach the concept of Singularity .
Time is the simplest thing . (Honours to Clifford Simak)
Anything increasing the complexity of identifiable things inside the Venn-boundary will create time-layers .
ie Venn-inside (at time t) + “outside” = Venn-inside (at time t+1)
The Venn-inside thus changes by virtue of it’s complexity .
It defines the time .
By definition , any time–reversals would require some very complicated operations (only possible when the system inside the Venn-boundary is very complex .)
Time-flow is thus created .
The complexity inside the Venn-boundary increases between an upper boundary of exponential increase and a lower boundary of fibonacci increase .
Time is created by denser layers of delineated things inside the Venn-boundary . (ie “faster”) . Things happen quicker . Events not perceived before become measurable .
An interesting corollary is “pockets” . Over a certain threshold rate of change , the system cannot propagate change fast enough throughout the whole system . Pockets of fast change gallop to the Singularity (ie infinite change) . Other pockets that reject alterations change slower or move into attractor lines that does not lead to Singularity .
The first pocket that goes infinite (ie into the singularity) sets the conditions for all others in same universe . There is thus only one Singularity per universe . We are talking about (Type III +) time traveling civilizations .
Why does non-altruistic civilizations fail?
Successful time-travelling non-altruistic civilizations will set up interference waves with their predecessors in time that will cancel themselves out . If they are not time-travelling , they are not sufficiently deep into the singularity .
Survivors must thus have a high degree of altruism .
But good things in the long-run has this tendency to be horrible in the short-run (ask any school-child).
See Monroe (Google Monroe Institute) to see the result of many Universes of this altruistic type .
The real world.
What this means in the real world if you add a time dimension , is that bootstrapping is possible (as seen in our socio-economic systems) .
You can also mine the non-delineated systems for useful things , thereby bringing them into the Venn-boundary of delineated things .
This is also called quantum-physics .
The complex observer plays an important part in the process .
Actually , the process of observing (ie pulling in “things” from outside the Venn-boundary ) becomes more and more dominant as the singularity is approached .
Why a two-dimensional Venn-diagram instead of other dimensions?
Why can this be represented on a 2-dimensional Venn diagram ?
Because 3 dimensions are the necessary sufficient minimum number of dimensions to have contiguity (I cannot put this simpler : if you cannot see it , too bad.)
(The four-colour theorem in 2 dim is equivalent if you define the difference between colours as a dimension)) . Any such 3-dim system can be mapped onto a 2-dim system . The general expression for people looking for an explanation in delineated terms is x(n) = function of(x1,x2,x3,…,x(r) ..etc , r
A delineated statement is when you talk about something defined as separate from something else . For example integers , points , mother , novels , computer programs , anything that can be expressed as separate . Any axiomatic system has to be delineated . Human information processing utilizing the brain cannot operate except in discrete , delineated terms . Even changing levels in neuro-transmitter concentrations change one molecule at a time .
Aristotelian Systems .
Aristotle postulated that A combined with everything not-A must be the Universum . This looks reasonable , but the hidden axiom is that A must delineated , ie that we can make sense to talk about A separate from anything else .
In 1906 Russell et al in “Principia Mathematica” proved rigorously that
A and not-A is smaller than the Universum . As you suspect , the crucial point is the definition of delineation .
A crude proof :
Consider a coffee table . A leg of the table is definitely not-the-table . So we wield Occam’s Axe ( Occam’s Razor is for smaller problems) and chop off the leg . But now the table is no longer a table . So , we have an internal contradiction . Purely logically , the leg is both part and non-part of the table .
This was further illustrated in Godel’s theorem . He proved that that any mathematical system incorporating the standard rules of arithmetic has true statements that cannot be derived from the axioms . This is commonly (and mistakenly ) taken as proof that certain things cannot be proven . This as result of the infinity axiom (ie a number plus 1 is never equal to a previous number ).
If the axiom is changed to “number plus 1 is equal to a previous number” , the proof breaks down , but unfortunately it then requires an extra axiom (the number where the system loops back , or equivalent the radius of the number line.) Since the radius of the new number-line can take infinite values , it means that you can prove anything , but you will require at least one extra assumption . And the extra assumption can take on an infinity of values . This is why our Universe is inherently 2-dimensional : from Heisenberg’s uncertainty principle to the distribution of primes , the unit seems to be a product . If we try to explain everything by only one factor , we end up having to take into account a concomittant factor which can take a large number of values ( ie a product , whether smooth or discrete )
Experimental proof .
TV’s , computers , phones , all modern electronics operate on quantum systems .
At the heart lies the universum.