Maths, science, culture and religion

Friday, January 06, 2017

An Extension of Penrose's three worlds diagram


Penrose's view — see e.g. Roger Penrose, The Road to Reality, a Complete guide to the Laws of the Universe (Alfred and Knopp 2005) — of the relation between the mental, mathematical and real (physical) worlds

 

My extension of Penrose's diagram as a view of the total (or Ultimate) reality (including, but not reducible to, the physical:


No evidence that conscience could be fully understood in terms of computational models.

No evidence only expert opinion  can be extracted from the 54 pages of the first chapter “Consciousness and Computation” in Roger Penrose’s book “Shadows of the Mind - a Search for the Missing Science of Consciousness” (OUP 1994), summarised in the Preface thus: 

  • My case has two distinct strands to it. One of these is essentially negative, in that I argue strongly against the commonly held viewpoint that our conscious mentality - in all of its various manifestations - could, in principle, be fully understood in terms of computational models. The other strand to my reasoning is positive in the sense that it represents a genuine search for a means - within the constraints of the hard facts of science - whereby a scientifically describable brain might be able to make use of subtly unknown physical principles in order to perform the needed non-computational action”.

Note that Penrose is a distinguished mathematical physicist and atheist. And that in spite of his search, he does not explicitly claim that science will be able to EXPLAIN consciousness (as e.g. it can explain the movement of the planets). 

When he writes that “scientifically describable brain night be able to make use of subtly unknown physical principles in order to perform the needed non-computational action” this is a personal belief not very different from that of the theist who can make use of other (albeit non-physical) principles —namely of his/her faith —- that in his/her mind can play the role of Penrose’s “non-computational action”. 

My personal belief is that science might be able to better and better approximate the function of consciousness by some “non-computational actions” but never be able  to fully explain it like it can some phenomena from the physical world.

Of course, there are many definitions of consciousness.They are usually tailor-made to exhibit the quality that distinguishes humans from non-human animals and other life forms. 

Penrose, for instance, devotes the whole of his Section 1.12 to a discussion of the terms awareness, understanding, consciousness and intelligence as he understands them. I cannot reproduce the lot here, only quote this (p.39)

  • “‘(U)nderstanding requires ‘awareness’. Awareness I take to be one aspect - the passive aspect - of the phenomenon of consciousness. Consciousness has an active aspect also, namely the feeling of free will … the passive having to do with sensations (or ‘qualia’) … I take these to be two sides of a single coin.” 

In particular, we speak of artificial intelligence (where computers come into play) not artificial consciousness or awareness. 

I also remember, from somewhere else, a definition of consciousness as “awareness of being aware”, i.e  the capability of capability of "being aware of bewing aware". In this sense apparently non-human animals are aware (of their environment) without being aware of their awareness.

I fail to see how it is relevant to Penrose’s (or other scientist’s) approach to the complicated (and rather ambiguous in scientific terms) concept of human consciousness (and awareness). In particular, how the “elementary biological function” that you associate with all sorts of living organisms (apparently including carnivorous plants) can be identified with what is referred to as 


Apparently it is this “awareness of being aware” that one associates with the Latin cogitare, an activity — leading to all sorts of philosophical, artistic and scientific achievements, i.e. reactions to the environment — that only humans (human animals if you like) are known to be capable of.

Tuesday, March 05, 2013

Einstein on mathematics and physics applied to religion

Einstein’s famous aphorism “as far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality” 

could be paralleled by “as far as religious symbols (and norms) refer to observable reality (and rules that can be enforced) they are not certain; as far as they are certain they do not refer to observable reality (and rules that can be enforced).”

Monday, December 24, 2012

Stop abusing science as a rhetorical bludgeon


Some (e.g. Richard Dawkins) think 

“it is time to leave superstition behind and embrace the beauty and challenges of the world without supernatural beings. We … use critical thinking to overcome religious fundamentalism, intolerance, and human suffering.”

Others think that it is rather time to leave behind slogans and clichés based on 19th century philosophy of science and embrace the insipartion and challenges coming from the interrelation of new physics and metaphysics, without a priori materialist (metaphysical) restrictions. Because, as J. W. Goethe put in his ‘Faust’, 

“True, human beings may abound
Who growl at things beyond their ken, 
Mocking the beautiful and good,
And all they haven't understood”

It is time to stop misusing science as a a rhetorical bludgeon against this or that world-view, and instead use critical thinking to overcome intolerance towards other world-views - theist or atheist - (and human suffering often resulting thereof). 

Sunday, November 07, 2004

The objective and subjective in maths and religion

If you can accept the existence of an independent mathematical world (as many mathematicians, the so-called Platonists, do), which nevertheless somehow interacts with both the physical and the mental world, then it is easier for you to accept the existence of an independent Transcendent (spiritual) world of (Christian) religion which somehow interacts with both our physical and mental worlds.

The question is not whether a mathematician invents or discovers mathematics; the question is in what relation are these two complementary aspects of his/her activity. The question is not whether what a Christian believes in has an objective existence or is purely a product of his/her mind; the question is in what relation are these two complementary aspects of his/her faith.

The roles of maths and religion

There are similarities between the role of mathematics in science (physics) and that of religion in culture.
Mathematics was the abstract perspective which helped to understand (and partly resolve) the crisis in physics at the beginning of the last century; Christian religion could similarly provide an (abstract) perspective through which one can obtain a better insight into our present crisis of (Western) culture and (cultural) globalisation.

The two not-so-obvious worlds

The world of mathematics exists on its own and is mysteriously related to the “real” world and to human mind; the same can be said about the (Christian) spiritual world.
Mathematics not only helps to understand the physical world through mathematical models but it could inspire an understanding of the relation between cognitive models of reality presented by science and (Christian) religion respectively.

Thursday, November 04, 2004

Compatible interpretations

It is not true that religion and science are on a collision course.
It is not true that religion and science are mutually irrelevant.

It is true that some interpretations of religion and some interpretations of science are on a collision course.
It is true that "uninterpreted" religion and "uninterpreted" science are mutually irrelevant.