Some thoughts on the simplicity of the definition of sine function and association with quantum theory



March 3, 2007

I have just finished reading

  • Richard Dawkins The God Delusion
  • Marcus Chown The Never-ending Days of being Dead (Dispatches from the Front Line of Science)



It is good to see so much material carefully collected together exposing the absurdities of religion. I find it incomprehensible why the idea of a god should be appealing or helpful. Indeed from the point of view of the exciting mysteries of the existence of the universe the postulation of a god, and the associated faith, leads to a definite dead end because no further investigation can be made.


Of course, when Stephen Hawking used to say,  as the understanding of the Big Bang continued to develop, that physicists  would soon have a theory of everything, this was just as absurd. At least, though, new developments were made and he could change his mind. Disturbingly there will probably always be scientists who think they have reached the end of the search. It has always been my view that there can never be an end to understanding – as more is comprehended more questions will need to be asked.


Chown’s book gives fascinating insights into some aspects of this.


Dawkins exposes a mechanism as to how humans could  have evolved to a state where a religious requirement exists in their brains. Clearly, as for many other evolved conditions, some have it and some don’t. Could it evolve away?


He believes the world would be a better place without it but there are many other conditions, such as nationalism, racism or indeed   almost all group levels, that would allow conflict to develop between one group and another.


 I suspect that on an island where children are brought up without any mention of god, religion would probably eventually develop within the community and that particular kind of group would exist ready, perhaps, for conflict with another on another island or  to split into different parts, with the potential, again, for conflict.


Probably conflict is needed for human development, as in any nonlinear complexity problem one needs the balance between cooperation and conflict for greater complexity to arise.



Many exciting ideas from the edge of science here but I just mention two.




Incompleteness of Mathematics

There was a crisis in mathematics in the early 20th century.



The sentence in bold is not true 

or, just the sentence


I am lying


to see a puzzle.



Godel  was able to prove that mathematics must contain things that are true but which cannot be proved. This was a bit devastating for mathematicians.


Just a few years later Turing was able to show that there were things which could never be computed.


Currently, Chaitin has suggested that mathematics should be seen as a series of islands floating on a sea. Each island represent a robust mathematical edifice, such asalgebra, geometry, number theory all rising from a sturdy base of axioms. Each island can be connected by strong strands of reasoning. However surrounding these sturdy islands is an infinite, random collection of truths which cannot be proved and must themselves be axioms. They might form the rocks of other islands but, remember, cannot be proved. The axioms that we are used to are self evident to us because,  they are simple and can be related to our experiences of the world. The random ones require  creative intuition and may be further from the world but as understanding grows there will others to group with them which in turn will form new robust islands.


This is all rather pleasing and certainly matches in with an equivalent startling randomness in physics, in Quantum Theory.


Inertial Mass

A mystery from Newtonian Mechanics is the idea of inertial mass. From experiment
Newton found that  for a particle


   force = m * acceleration 

where m is just a constant of proportionality which he called the inertial mass and is associated with the particle itself.


It then turns out that this inertial mass is the same as the gravitational mass.


Hawkins has shown certain quantum results concerning behaviour at the edge of a Black Hole. This has led recently to a suggestion that inertial mass is not a property of the particle but a resistance set off by passage through the quantum vacuum.


February 22, 2007

testing mathtypetesting.docword testtingtesting word upload

February 20, 2007

Testing Latex: 

i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>


on new line \sqrt(x)=5


 Susan Blackmore Conversations on Consciusness, OUP 2005 


I ponder quantum uncertainty  I look ahead to the next conversation with Stuart Hameroff who considers consciousness to be quantum coherence in the microtubules of the brain. I think too of other physics. We talk of mass and time  etc but do we really know what they are? They are just mathematical entities. We must eventually get a mathematical theory of consciousness? 

Consciousness Quantum Effects and also meditation

I have been going on about the potential effects of Quantum Mechanics on consciousness. Here are some crucial sentences from a very exciting paragraph from the Sue Blackmore conversation with Stuart Hameroff concerning quantum effects on consciousness. 


Then what do you think happens to consciousness after death? Stuart:

When the quantum coherence in the microtubules is lost ….quantum information leaks out…….the quantum information….doesnt completely dissipate, but hangs together because of quantum entanglement. ….And because the universe at the Plank level is non-local, it exists holographically, indefinitely. Is this the soul? Why not? 


I have also been interested in meditation associations. Here a sample from a conversation with Stephen LaBerge who has worked significantly with lucid dreams. 


This implies that if we have these related kinds of illusion and you can wake up in a dream and say ‘Oh, but now I realize it’s a dream,’ you might be able to wake up in waking life in the same way- and have lucid living


Yes certainly. The religious, esoteric, religious traditions of enlightenment talk about that exactly, and lucid dreaming seems to be one of the best metaphors for what that enlightenment would be like.  


Susan Blackmore Conversations on Consciusness, OUP 2005 

There is an interesting chapter for the conversation with Thomas Metzinger. This deals with aspects of meditation and alerts to ramifications of consciousnes research on modes of media enetrtainment and the split in the world between metaphysical cultures and the western scientific ones.



Free Will Again

I have just been reading the conversation between Sue Blackmore (the collector of converstaions) and Susan Greenfield. Susan Greenfield was/is a Professor of Pharmacology with, currently,  interests in Anaesthesia and  Alzheimer’s and Parkinson’s diseases. They are discussing free will and the assumption that it does not exist. 

Susan has said:

……what do you do with criminal justice system? For example, if no one has free will it means that no one should be in prison. 

Sue has replied:

No it doesn’t because although you get rid of retribution you would still put people in prison in order to provide a deterrent for other people and in order to keep really dangerous ones off the streets – so some of the system would survive.  

…………….. I find this conversation quite extraordinary. If we do not have free will we cannot blame criminals but also we have no control over deciding on the criminal justice system.  As far as I am concerned the absence of  free will means that the universe unfolds, our neurons fire away, and we discover what the criminal code is and our sense of blame just arises from the neuronal activity . It is a kind of drama in which the audience is actually flowing along with it.  As I sit typing this it is part of the unfolding. If many people were persuaded in this unfolding that there was no free will, and the unfolding continued with a depressed population, which faded away to extinction as a result, that would be the drama continuing to unfold. I like the logic of no free will. However , of course , whilst living normal life and not thinking such thoughts, it does seem a strange mystery. When I am walking along a road with my wife, and a car driving far too fast passes by, we discuss the absurdity of such driving, as if it mattered. We discuss the absurdity of Bush and Blair and how wrong their way of thinking is.We talk to the dog and think what a fine specimen of an animal he is and how superior he is to any other dogs we know. And so on and so forth.  So why, if we have no control, do we bother? But we do simply because it all unfolds….. 


January 3, 2007


I have been reading


  • R.Penrose, The Road to Reality
  • D.Bohm, Quantum Theory
  • M.Frayne, The Human Touch
  • S.Blackmore, Conversations on Consciousness
  • B.Shine, The Infinite Mind

and am soon to read

  • R.Dawkins, The God Delusion


The Penrose has had to be, after an initial detailed start, a high level first view and I await the time to study it in much more depth taking on board every mathematical aspect. This should keep me going for a long time, I suspect.


The Bohm has put me back into a state of basic understanding of Quantum Theory that I once had back around 1963 at the end of my degree.


Frayne surprised me, in that, starting discussing the human  relationship with the world through the use of words, the discussions took the reader into the realm of consciousness. This book too will need a second study.  I have thus been led  into thinking more about consciousness with some very interesting reading currently from Blackmore’s book.


The book by Shine has exposed me to the approach of a medium to this field.


Intelligent Design

I have, too, recently been reading in the press about Intelligent Design and have begun to realise that I need to understand what this argument is about. I look forward to Dawkins on this.


My first thoughts follow, but bearing in mind that I have not read significantly about the topic.


It seems that there are some areas in Darwinian Evolution Theory for which a full argument cannot be found to explain. I have no problem with this and it becomes exciting that new developments or adjustments might be forthcoming.


Assuming that such areas of theory weakness do exist, ID seems to suggest that there should exist some conscious entities which have and do adjust the process from outside. I doubt that one could prove that such entities could not exist


Such outside entities seem also to arise in discussions on the existence of the universe. Again one can hardly prove that such things should not exist and being part of the  collection of things which exist we should be able to look forward to experiments to discover the properties of these entities, as yet another  set of phenomena in physics.


The trouble here, though,  is that investigation seems to stop her,e with the labelling of these things as gods . Why this should be so I don’t know. These entities are postulates and a curiosity of science and inquisitiveness would force investigation through experiment.


I would feel the same frustration if the ID designers marked a point at which study stopped.



The Blackmore book seems a good way of picking up current ideas on the topic through the recorded, and only lightly edited, conversations with a variety of experts.


A fascinating aspect is the great development of experiment and data collection that has recently taken place. A fruitful technique seems to be based on binocular rivalry. Each eye is exposed to a different image and it is found that only one can be experienced at a time. There is seemingly a means of separation between neuronal activity for conscious and subconscious effects. Using advanced brain observation techniques enables a close view of neurons active under conscious and unconscious states.


Suggestions are made by some that consciousness is just the state of certain neuron sets being active. I find this, personally, a fine idea – consciousness is just the state of activity of neurons deeply interconnected with other parts of the brain network.


It has also been suggested that consciousness is just another fundamental measurable of physics like mass, space, time, etc


Free Will is of course a topic in such discussions. Blackmore herself is happy to dispense with this.


On the whole I too feel comfortable with this view and must see life as mechanisms running onward and generating consciousness as they go, which one enjoys, or otherwise,  as they happen.


I get the impression that the study of consciousness awaits now much more experiment to correlate neuron behaviour with conscious experience and these will then help development of more detailed theories which can then predict and hence be testable.


As physics continues to develop with a variety of stuffs – space, time, mass, strings, consciousness, etc – the attempt will presumably be to use fewer and fewer stuffs. It does seem though, that there will always be some final stuff which can be used to explain all, except this stuff  itself.


What a wonderful mystery. As I walked the other day under a grey winter  sky, through leafless woods with the dog, what an amazing oddity! Neurons firing in my head, fewer perhaps in the dog’s head, none in the trees perhaps, all surrounded by space stuff and time stuff and mass stuff and consciousness stuff. How urtterly exciting and how feeble the idea of an-end-of-the- argument god.


Quantum Effects

I have considerable fascination for the possibility of quantum effects. The associated  uncertainty and ideas of quantum entanglement must be useful. I imagine a brain, with quantum processes, and associate that with free particles which interact with it, and through entanglement carry, in some way, knowledge of the brain’s  state throughout the whole universe!


How might quantum uncertainty relate to the unfolding of the life processes in which we discard free will?



I look forward to discussions in the Blackmore book on meditation.


January 3, 2007


Geometric Algebra

January 2, 2007

Over recent years I became interested in Clifford Algebra and this led me to material by Leo Dorst and Stephen Mann on Geometric Algebra. In the latter case the thrust being the scope for global computational algorithms for geometric objects.

In this weblog I plan to expose my growing understanding of GA in a set of fundamental and not very sophisticated observations.

Clifford Algebra introduction that I have used in teaching.

Geometric Algebra 1

An umbrella for scalar and vector prduct in 2D

Geometric Algebra 2

3D and Reflection

Geometric Algebra 3

Planes and their Dual

Geometric Algebra 4