Archive for the ‘Roger Penrose’ Category

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Sunday, January 18th, 2009

No prescription tramadol online, If a religion is defined as a system of thought which requires belief in unprovable truths, then mathematics is the only religion that can prove it is a religion!

via Paul Davies, The Mind of God, Penguin Books, 1992.

If mathematics describes the universe, it must describe a universe which contains mathematics, The Drug Tramadol, and therefore, Non Prescription Tramadol, itself. Self-reference in mathematics is not merely esoteric, it's fundamental, Ultram Medicine, and nowadays quite commonly understood. Purchase tramadol online cheap, In fact, self-reference of formal systems is ubiquitous in computer science: one can write a program in a language X, that can compile and execute other programs in language X, Companies That Make Tramadol, including itself.  Recursion on all kinds of scales appears everywhere in computer science; languages such as LISP are built around it.

Look again at the Penrose diagram, it seems a reasonable approach to the problem of fundamentalism is to apply a scientific (evolutionary) viewpoint to its existence.  Instead of addressing our species' reluctance to evolve with outrage, let's understand and accept it as a part of the same natural system that brought us here in the first place.  Let's turn the system on itself.

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Friday, May 16th, 2008

Order tramadol online cheap, Quantum physics, on the other hand, seems more resonant with those residual dualist hankerings, perhaps by holding out the possibility that scientific realism and objectivity melt away in that domain, or even that thoughts and feelings are, in the end, the fundamental properties of the universe. Explanation of something as special as what makes me me, should really involve, the feeling is, something more "deep" and mysterious and "other worldly" than mere neurons. Perhaps what is comforting about quantum physics is that it can be invoked to 'explain' a mysterious phenomenon without removing much of the mystery, quantum physical explanations being highly mysterious themselves.

Now we are not for a moment suggesting that anything like this is behind Penrose's work, and whether our diagnosis is right or wrong has no bearing whatever on the strengths and weaknesses of his arguments. It may, however, Sniffing Ultram, help explain why the very possibility of a quantum physical explanation is often warmly greeted, whereas an explanation in terms of neurons may be considered "scary", "degrading" and even "inconceivable". Why should it be less scary, reductionist or counter-intuitive that "me-ness" emerges from collapse of a wave function than from neuronal activity?

Nothing we have said in this paper demonstrates the falsity of the quantum-consciousness connection. Our view is just that it is no better supported than any one of a gazillion caterpillar-with-hookah hypotheses.


-- From Gaps in Penrose's Toilings [a play on Penrose tiling] by Rick Grush and Patricia Smith Churchland, Philosophy Department, UCSD, order tramadol online cheap.

Yeah, that Caterpillar-with-Hookah didn't really have anything helpful to say:

The Caterpillar and Alice looked at each other for some time in silence: at last the Caterpillar took the hookah out of its mouth, and addressed her in a languid, Online tramadol online, sleepy voice.

`Who are YOU?' said the Caterpillar.

This was not an encouraging opening for a conversation. Alice replied, rather shyly, `I--I hardly know, sir, just at present-- at least I know who I WAS when I got up this morning, but I think I must have been changed several times since then.'

`What do you mean by that?' said the Caterpillar sternly. `Explain yourself!'

`I can't explain MYSELF Order tramadol online cheap, , I'm afraid, sir' said Alice, `because I'm not myself, you see.'

`I don't see,' said the Caterpillar.

`I'm afraid I can't put it more clearly, Ultram Euphoria,' Alice replied very politely, `for I can't understand it myself to begin with; and being so many different sizes in a day is very confusing.'

`It isn't,' said the Caterpillar.

`Well, perhaps you haven't found it so yet,' said Alice; `but when you have to turn into a chrysalis--you will some day, you know--and then after that into a butterfly, I should think you'll feel it a little queer, 100 Tramadol Free Shipping, won't you?'

`Not a bit,' said the Caterpillar.

`Well, perhaps your feelings may be different,' said Alice; `all I know is, it would feel very queer to ME.'

`You!' said the Caterpillar contemptuously. `Who are YOU?'

Which brought them back again to the beginning of the conversation. Alice felt a little irritated at the Caterpillar's making such VERY short remarks, and she drew herself up and said, very gravely, 100mg Buy Tramadol, `I think, you out to tell me who YOU are, first.'


-- From Alice's Adventures in Wonderland, Lewis Carroll.

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Sunday, April 6th, 2008

While New Atheist Ordering tramadol no prescription, views (espoused by Dawkins, Daniel Dennett, Sam Harris, et al.) tend to focus on the field of evolutionary biology, the sphere of physicists and mathematicians seems to have a much more nuanced view of the relationship between science and metaphysics. In particular, mathematics stands distinct from science per se in that it does not make specific verifiable claims of empirical fact (much of mathematics does not directly relate to the physical world at all); rather, it provides a formal structure, a framework, by which we can communicate and generalize abstract notions. In some sense, these decontextualized abstract notions themselves can be said to have an existence independent of physical manifestation and our ability to perceive them. These three ideas - abstract (Platonic/mathematical) ideal, imperfect manifestation in physical reality, and the human mind's perception of pattern in the physical world and transference of physical phenomena into abstract ideals - lie at the foundation not only of mathematics, but true religion as well.

In the first chapter of his excellent The Road to Reality, Sir Roger Penrose introduces a diagram illustrating this threefold relationship:

The Penrose Trinity

Plato made it clear that the mathematical propositions -- the things that could be regarded as unassailably true -- referred not to actual physical objects (like the approximate squares, triangles, circles, spheres, Tramadol Line, and cubes that might be constructed from markers in the sand, or from wood or stone) but to certain idealized entities. He envisaged that these ideal entities inhabited a different world, distinct from the physical world, ordering tramadol no prescription. Today, we might refer to this world as the Platonic world of mathematical forms....

This was an extraordinary idea for its time, and it has turned out to be a very powerful one.... It tells us to be careful to distinguish the precise mathematical entities from the approximations that we see around us in the world of physical things. Moreover, it provides us with the blueprint according to which modern science has proceeded ever since. Ordering tramadol no prescription, Scientists will put forward models of the world -- or, rather, of certain aspects of the world -- and these models may be tested against previous observation and against the results of carefully designed experiment....

If the model itself is to be assigned any kind of "existence", then this existence is located within the Platonic world of mathematical forms. Of course, one might take a contrary viewpoint: namely that the model is itself to have existence only within our various minds, rather than to take Plato's world to be in any sense absolute and "real". Yet, there is something important to be gained in regarding mathematical structures as having a reality of their own. For our individual minds are notoriously imprecise, unreliable, Tramadol 120, and inconsistent in their judgments....

Thus, mathematical existence is different not only from physical existence but also from an existence that is assigned by our mental perceptions. Yet there is a deep and mysterious connection with each of those other two forms of existence: the physical and the mental, ordering tramadol no prescription. [In the figure above] I have schematically indicated all of these three forms of existence -- the physical, the mental, and the Platonic mathematical -- as entities belonging to three separate "worlds", drawn schematically as spheres. The mysterious connections between the worlds are also indicated, where in drawing the diagram I have imposed upon the reader some of my beliefs, or prejudices, concerning these mysteries.

It may be noted, with regard to the first of these mysteries -- relating the Platonic mathematical world to the physical world -- that I am allowing that only a small part of the world of mathematics need have relevance to the workings of the physical world.... Likewise, in relation to the second mystery, whereby mentality comes about in association with certain physical structures (most specifically, healthy, Online tramadol without prescription, wakeful human brains), I am not insisting that the majority of physical structures need induce mentality.... Ordering tramadol no prescription, Finally, for the third mystery, I regard it as self-evident that only a small fraction of our mental activity need be concerned with absolute mathematical truth. ... These three facts are represented in the smallness of the base of the connection of each world with the next, the world being taken in a clockwise sense in the diagram. However, it is in the encompassing of each entire world within the scope of its connection with the world preceding it that I am revealing my prejudices....

On this view, everything in the physical universe is indeed governed in completely precise detail by mathematical principles....


In William Blake's Newton, we see this very same threefold mystery: Here, the man emerges from the earth and produces a representation of the geometry (γεωμετρία; geo = earth, metria = measure) of which the earth is made.


Blake’s Newton


Newton (1795) by William Blake


Likewise, we can easily see the Platonic significance of the Christian trinity as well.

Medieval trinity illumination (origin unknown)


Handcolored woodcut, ca, ordering tramadol no prescription. 1500, origin unknown


Here, the Holy Trinity of Christianity is presented as a triangle: Father (Pater, which might stand for "earth"), Son (Filius, Smoke Tramadol, "man"), and Holy Spirit (Spiritus Sanctus, "platonic ideal") in an triangular relationship, three equal and essential parts of God. The connections between them ("non est") assert the independence of the parts, while their connections to the center ("est") assert their importance in the integral whole. We might say also that the human conception of mathematical truth is not the truth itself; that manifestation in the physical world is not the Platonic form; and that the physical world consists of much more than human minds. But the relationship remains the same: timeless, illustrated through myriad imperfect forms, this knowledge has been transmitted from ancient (pre-scientific) times to us today, and we continue to find new manifestations of the Trinity. There's a lot more to be said here; this touches upon the significance of mythology, sacred geometry, and mysticism: these have always been vehicles by which humans could codify and transmit eternal truths. We may use science to perceive the details, but we use religious/mythological and mathematical abstraction to incorporate, Paypal tramadol online, generalize, and interpret this knowledge.


In this way, true religious/spiritual knowledge does not properly occupy the space of empirical scientific knowledge, but rather serves as a counterpart to abstract mathematical knowledge, existing the the Platonic (meta) realm, rather than making specific claims of empirical truth in the physical realm.

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