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Mathematics – Unity in Diversity

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One of the things about math is that the more problems we look at the more we find a finite set of mathematical objects that can be generated in more than one way, observed in more than one context. These patterns recur in varying and apparently unconnected places.

Here are just a few of the “great ideas” and their specialised manifestations. Every area of maths and science displays them. Patterns that appear in separate domains, systems, phenomena and problems. I say apparently unconnected because, if anything, writing this article has made me realise how what the mystics say is so true: all is one and interconnected.

This list is of course vastly incomplete. After a while of coming up with more and more patterns you just say “right, that’s enough to make the point!” In fact I believe the one true exhaustive list of this kind is infinite. I have no idea for a proof or disproof of that ! Suggestions please.

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Written by Luke Dunn

April 14, 2010 at 4:02 pm

Living and nonliving cosmoses

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How many universes can there be ? and what is the ratio of life-producing-universes to (so called) fruitless ones ?

What was the first seed universe like ? What about other universes to ours ?

If ours is the only one then why life ? It seems so unlikely as a one off. Or are there many and living ones evolve among nonliving ones ? If a universe contained no consciousness then would it ever move out of a giant superposed state ? Could there be a multiverse which allocated the saved energy from a nonliving universe to a living one ?

IF THE PURPOSE OF A UNIVERSE AS INITIATED BY A CREATOR IS TO PERFORM A COMPUTATION, THEN HOW IS THE INPUT PROVIDED ? AND HOW THE OUTPUT YIELDED ?

Suggestion:

Input is given at commencement through settings of fundamental constants

Output is given in every successive state… each frame of the great movie is one vast output

Thus creator needs “reference dimensions” (the coiled up parts of the 11) to be able to inspect the details of each frame. In order to make use of this output the storage capability of the parent system must be huge but maybe “divine” beings can access that much power.

Yes I do honour Douglas Adams !

Here’s a diagram which shows a possible supercosmology of multiple created universes. Just for fun really but its nice to dream about possibilities.

supertime

Written by Luke Dunn

July 28, 2009 at 8:25 pm

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Arrows of Time

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The second law of thermodynamics states that entropy increases. Will this still hold if the universe starts to contract? Last I heard was that the heat death scenario might be the real one, but what if there was going to be a big crunch ?

I can easily imagine systems becoming more disordered with time, this is common sense, but its nearly impossible for me to imagine the opposite. Am I just prisoner of a mind that evolved in local conditions ? Is it part of some extended physical sensibility that order increasing is perfectly believable ?

If space is contracting then matter is being compressed into a smaller volume so presumably the 2nd law will change and say that order is increasing. One of the issues I have is that if space is contracting (at first) this implies that galaxies are moving together, but you could still imagine life on one planet of one star system in one galaxy where the contraction is not noticeable, and one’s imagination suggests that the second law will still mean disorder is locally increasing. Read the rest of this entry »

Written by Luke Dunn

July 28, 2009 at 7:56 pm

Paratime

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Paratime
Rudy Rucker speculated that there might be something called paratime, it works as follows…
States of a universe in time develop linearly, from start to end, with causes influencing the next frame of the movie so that each frame depends deterministically upon the previous. Let’s say you might assume a big bang, with increasing size, then maybe a contraction and eventual big crunch.
What if in some other perpendicular direction there was another development process where structures developed deterministically also, with more complexity building up as the paratime ticked away. I’ve done a very poor diagram below.
How could this be investigated ? it seems very hard but maybe there is a simulation that could be tried.
Consider a one dimensional cellular automaton which has a rule where one line of pixels generates a new line of pixels moving down the screen. the system starts with a random line of pixels and each new pixel in the next line is coloured black or white depending on the state of the three pixels above it. starting with a given pattern the output moves down the screen and generates a pattern like the one below with the triangles.
The neatest way to summarize a simple rule is shown in the last diagram.

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Written by Luke Dunn

July 28, 2009 at 7:01 pm

More on a Theory of the Living Universe

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The Theory of the Living Universe
Perhaps many theories of the universe are possible.
If several provide equal and maximal descriptive power then how might we group these possible theories?
I would suggest that each possible theory prioritises its starting facts in a different order. Looking at conventional modern physics it seems that the existence of life and consciousness have not been placed as primary facts which urgently need an explanation in a satisfactory theory.
Perhaps we could look at a possible list for conventional science as follows:
Energy exists
Matter exists in many forms
Start with these simple facts and build on up.
if anything seems too complex to include then ignore it
The theory of the living universe starts with a different set of suppositions :the primary need is to explain the existence of life and mind…
life exists
mind exists
start with these at highest priority to explain
work down to simpler systems as the need arises
Perhaps we then see a new role for “primitive” cosmologies and creation myths, they are inevitable stopping posts on the way to true understanding. Maybe each primitive notion is superseded but the developmental process of human understanding must honour each stage, just as to understand, say, Number Theory, its historical development must be understood.

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Written by Luke Dunn

July 25, 2009 at 4:42 pm

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A New Physics Of Life

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Physics traditionally studies dead matter. All our analysis of biological systems is a reductionistic one that aims to reduce the extreme complexity of living systems into a form that can be explained using the ordinary laws of physics as they apply to matter and energy. The vitalists thought that life consisted of an indivisible life essence but the whole lesson of reductionism is that once you chop things into sufficiently small parts all you can see is non-living systems.

In modern parlance we describe the appearance of complex behaviours in a system built from its component parts as emergence. Emergent qualities include such things as consciousness. A theory of the living universe would have to explain how complex emergent phenomena arise.

The emergent characteristics of a simple system like a living cell are a consequence of the microscale interactions of the particles composing it. However the richness and complexity of an emergent phenomenon such as the cell would be intractably complex to deduce by simply knowing about the physics of the particles that compose it. And yet at some level the potential for any kind of emergent phenomena must be present within the laws of physics. So we become suspicious that a theory of Everything which could be summarised in a short mathematical form would not indeed contain enough information to explain every kind of phenomenon in the universe – we need a law of emergence. Read the rest of this entry »

Written by Luke Dunn

July 22, 2009 at 12:52 pm