Showing posts with label Bertrand Russell. Show all posts
Showing posts with label Bertrand Russell. Show all posts

Monday, February 10, 2025

Spin Chronicles Part 45: positive domination

For some reasons I consider the concept of state on a *-algebra as important. I wrote a whole post on the subject, with a Theorem, its detailed proof, and with exercises for the Reader. I also wrote a long introduction. Then I have made one wrong click, and all was gone. Well, not all, the introduction has been preserved, since I have already managed to copy it to the blog. But introduction is just words. All the hard stuff, all formulas, are gone. So I decided to ask the I Ching oracle for advice. I Ching told me:

"Thunder and wind symbolize Duration,

The superior man stands firm

Without changing direction."

Fine. I stand firm. Will not change direction. But will provide a theorem, and skip the proof. The proof is lengthy, but not difficult. There will be no harm in skipping it. Maybe it will even be good. No distraction. So, first the beginning of the Introduction. The rest of the introduction will be at the end.

Introduction Part 1

 In this post, we will delve deeper into the concept of states on *-algebras. States are fundamental in physics, serving as a crucial link between the abstract formalism of algebra and the concrete realm of empirical measurement. They transform abstract algebraic elements into numbers, which we then interpret as experimental values. In this way, states act as a bridge between the invisible, abstract structures of theoretical physics and the tangible, measurable phenomena of the observable world. But this raises a profound and provocative question: Are states themselves "visible"? Or, more precisely, do they belong to the realm of the measurable, or do they reside in a liminal space between the abstract and the concrete?

This question is not merely technical; it is deeply philosophical. It forces us to confront the nature of representation, measurement, and the limits of human knowledge. States, in their role as mediators, challenge the boundary between the intelligible and the sensible, between what can be thought and what can be experienced. To ask whether states are "visible" is to grapple with the very nature of reality and our capacity to comprehend it. It is a question that mingles different levels of description—mathematical, physical, and metaphysical—in a way that is both illuminating and perilous. Such questions are logically treacherous, reminiscent of the paradoxical barber who shaves only those who do not shave themselves. They expose the fragility of our conceptual frameworks and the limitations of language itself.



Let A be a finite-dimensional *-algebra with unit 1. Let f be a state on A, and let H be the Hilbert space of the GNS construction with cyclic vector Ω for a representation π (which previously we have denoted by ρ).


Definition. If f1 is a positive functional on A, we say that f1 is f-dominated if there exists a constant λ>0 such that

f1(a*a) ≤ λ f(a*a) for all a in A.

We say that f1 is f-absolutely continuous if f(a*a)=0 implies f1(a*a) = 0.

It is evident that every f-dominated functional is f-absolutely continuous. (can you see it?) The converse is not immediately evident. But it will be seen from the following theorem that I adapt from the monograph by Naimark.

Here is the original theorem:

Let H be the Hilbert space of the GNS construction with cyclic vector Ω for a representation π (which previously we have denoted by ρ).

TheoremLet f1 be a positive functional on A that is f-absolutely continuous. Then there exists a unique positive operator B in the commutant π(A)' of π(A) such that

f1(a) = (Ω,π(a)BΩ).         (1)

Conversely, every such B determines, by (1) a positive functional  f1 that is f-dominated.

Proof. Gone with the wind.

In a future post we will use this theorem to prove that a GNS representation is irreducible if and only if f is a pure state.

Introduction Part 2


Yet, it is precisely these kinds of questions that I find most compelling. They reveal the boundaries of our understanding and force us to confront the inadequacy of communicable language when grappling with the ineffable. By asking such questions, we quickly come to realize how constrained our knowledge is when confined to the tools of language and logic. Language, as a system of symbols, is inherently limited in its ability to capture the full depth of abstract thought and the complexity of reality. It is a filter through which we attempt to convey the inexpressible, but it inevitably falls short.

This tension between the communicable and the ineffable is at the heart of both science and philosophy. States on *-algebras, as abstract entities that give rise to measurable quantities, embody this tension. They are both a product of human thought and a reflection of an external reality that exists independently of our conceptual frameworks. In this sense, they invite us to consider the nature of existence itself: Is reality fundamentally mathematical, as some physicists and philosophers suggest? Or is mathematics merely a tool, a language we have invented to describe a reality that ultimately transcends it?

These questions are not merely academic; they have profound implications for how we understand the universe and our place within it. They challenge us to think beyond the limits of our current knowledge and to embrace the uncertainty and ambiguity that come with exploring the unknown. By engaging with such questions, we not only deepen our understanding of states on *-algebras but also confront the very nature of knowledge, reality, and the human condition. And in doing so, we may come to appreciate the beauty and mystery of a universe that is far more complex and enigmatic than our language and logic can ever fully capture.

Friday, April 12, 2024

Why? The Purpose of the Universe - Part Seven

 


By Laura Knight-Jadczyk

In the previous post, we looked at Philip Goff’s take on “Cosmic Purpose Without God”.  He covered Non-Standard Designers, Teleological Laws, and left Cosmopsychism dangling. But we ended with a hint as to the direction he was going:

Teleological laws are the most parsimonious accounts of cosmic purpose.  They simply accept the brute existence of cosmic purpose without feeling the need to postulate any deeper explanation of it.  On the other hand, the deeper explanation of cosmic purpose provided by non-standard designer hypotheses is an attractive feature.  We arguably have a tie here, with one theory ahead in terms of parsimony, the other ahead in terms of explanatory depth.  The idea would be to find a way of securing the extra explanatory depth but with minimal cost in terms of postulating extra entities.

Fortunately, there is such a theory: rather than postulating a supernatural designer, we can instead ascribe mentality to the universe itself. 

And so, in the next chapter, we enter “A Conscious Universe”.  Goff warns us that this is a view that was once laughed at, is wildly controversial, and yet, nowadays, is being taken quite seriously. How did this happen?  The following is gleaned from Goff’s discussion.

Bertrand Russell, in the 1920s, was considering the fact that our most fundamental science, physics, is purely mathematical.  The math has changed and become more complex and abstract over time, but it’s still basically mainly equations that describe the mathematical structure of our reality.  This is apparently due to the fact that Galileo made the decision that ‘natural philosophy’ must take a purely mathematical form.

This isn’t of much use to a philosopher.  And so, quite a number of them, inspired by Bertrand Russell, are positing that consciousness is what underlies the mathematical structures of physics. 

The standard form of this view is that, at the fundamental level of reality, there are networks of very simple conscious entities that behave in simple, predictable ways and have rudimentary experiences. 

The idea is, then, that what we call mathematical structures are just descriptions of the interactions and patterns of these micro-entities and their rudimentary behaviors and experiences.  These patterns and structures are what we call ‘physics’.  The micro-entities reveal their consciousnesses in ‘mass’, ‘spin’, and ‘charge’. And so, the view of the Russellian panpsychists is that physics emerges from consciousness. And, if this view is the right one, what you are doing when you are doing physics is simply studying the behavior of very, very simple conscious entities.

And of course, here we see the basis of Goff’s “Pan-Agentialism” wherein matter is inherently disposed to respond rationally to reality.  Particles have ‘conscious inclinations’ even if their behaviour is imposed on them by Pilot Waves, according to Goff, thus casting doubt on the idea that matter is ‘inherently disposed’ to anything in its responses.

Goff reports that Sabine Hossenfelder doesn’t like this idea because the Standard Model of particle physics, (best model of the 25 kinds of fundamental particles), predicts behavior based on physical properties, i.e. mass, spin and charge.  If you add non-physical properties such as consciousness, then you lose control of your ability to predict behavior.  She declares that if particles were conscious, then their consciousness would show up on the behavior and physicists would easily be able to spot it.

Goff points out the Hossenfelder obviously does not understand the panpsychist hypothesis and she is interpreting panpsychism in dualistic terms, i.e. as if the particle has physical properties – mass, spin, and charge – and additional properties of consciousness.  She assumes that the micro-level consciousness proposed by the panpsychist exists at the level of the most basic mathematical structures.  The panpsychists, however, are actually concerned with the reality that underlies the mathematical structures. Goff’s view of the matter is:

… panpsychism offers the best solution to the mind-body problem, the philosophical challenge that arises from the fact that we access objective reality in two very different ways: perception and introspection.  In perception we access the physical world through our senses, something we’ve learnt to do more accurately and precisely through science.  Through introspection we access consciousness, via our immediate awareness of our feelings and experience. 

The problem is, of course, how to bring consciousness and the physical world together into a single unified theory of reality?  There are three main philosophical solutions to the problem:

1. Materialism:  The physical world is fundamental, and consciousness arises from physical processes in the brain.

2. Panpsychism: Consciousness is fundamental, and the physical world arises from more fundamental facts about consciousness.

3. Dualism: Both consciousness and the physical world are distinct but equally fundamental aspects of reality.  Contemporary ‘naturalistic’ dualists like David Chalmers postulate special ‘psycho-physical’ laws of nature to hook consciousness up to the physical world.

Goff notes:

In terms of materialism, nobody has ever made the slightest progress on its central explanatory task of explaining how we can get consciousness out of purely physical processes in the brain.  Moreover, I think there are good arguments that show that such a thing cannot be done in principle.

That is a useful point, but for me, the even bigger problem is actually the converse:  how can anyone possibly explain the existence of a single particle at all… a single grain of sand?  Where did the stuff of the Universe come from?  Especially considering the Standard Model of Physics and its ‘Big Bang’! If the physical world is fundamental, what made it?  Where did the ‘stuff’ come from and how?

Goff then states the most obvious thing of all:  “The mathematical structures of physics cannot produce consciousness, but consciousness can produce the mathematical structures of physics.”  That, right there, makes the materialists/physicalists shudder in horror! 

The Dualist option is problematical because it leads to positing two distinct entities when one should do (Ockham’s Razor) and, again, cannot explain the existence of matter in any coherent way.

In any event, Goff concludes (after a brief foray into neuroscience that need not detain us), that:

Our choice is between a philosophical explanation nobody’s ever managed to make sense of (materialism) and a philosophical explanation we know how to make sense of (panpsychism).  Once the options are correctly understood as philosophical – rather than scientific – rivals, there is, to my mind, an obvious winner.

Goff next brings in the ‘combination problem’, or the challenge of figuring out how many conscious particles come together to form a complex system which has its own unified consciousness. He considers that this problem is of concern only to those who advocate very reductive forms of panpsychism. Goff himself argues for a hybrid of reductive and non-reductive views; he distinguishes between conscious experiences and the ‘I’ that has the conscious experiences.  Goff’s “‘I’ is more than the sum of its parts, but its conscious experiences are ‘inherited’ from streams of consciousness at the level of fundamental physics.”

Are you confused by that?  I am.  Goff appears to want to have his cake and eat it too.  He doesn’t like materialism, and yet he continues to try to argue for a hybrid form of it.  He didn’t tell us anything about where his favored Pilot Waves come from, nor what foundation gives particles ‘agency’.  He appears to propose that a bunch of particles with this ‘agency’ jostle about guided by pilot waves and over vast expanses of time, eventually form consciousness with an ‘I’ somehow.  This consciousness then has the ability to make choices against what it wants itself and what it knows to have value; and all in the frame of Darwinian evolution. Because, of course, if there is a designer s/he is limited somehow to just getting the ball rolling.

Goff goes on to say:

Even if human consciousness ends up being utterly irreducible, it’s still better to be a panpsychist than a dualist.  Panpsychism earns its keep through its reduction of the physical world to consciousness.  If it can also reduce human consciousness to particle consciousness, whether partially or wholly, then that’s a bonus: the more we can reductively explain, the simpler our basic theory of reality.

That is to say, Goff’s Panpsychism pretty much says that the complex consciousness of a human (or animal) brain is built up out of, or emerges from, the consciousness of particles with agency guided by Pilot waves.  Goff says nothing about where the particles, the agency, or the pilot waves come from.

He notes that many theoretical physicists think that the fundamental building blocks of reality are not particles at all but rather universe-wide fields in which particles are simply local vibrations within those fields. That is, some fundamental form (or forms) of consciousness underlie these universe-wide fields and that a fundamental mind is the origin and bearer of those fields.  This hypothesis is known as Cosmopsychism.

Goff’s view of this hypothesis is that the consciousness of the universe is just some kind of huge meaningless mess.  “The kind of experiential understanding enjoyed by human beings is the result of millions of years of evolution, but the consciousness of the universe has not been shaped by the pressures of natural selection.” 

Again, Goff is trying to have his cake and eat it too.

Goff doesn’t think that a “meaningless mess” consciousness of the universe can explain the consciousness of beings nor the Fine Tuning of the universe.  So he tries to wrangle that problem that simply wouldn’t exist if he would make a different assumption. Goff presses on with his “meaningless mess” universal consciousness, proposing something like the ‘agency’ of particles in his pan-agentialism:

…replace the picture of a universe of messy meaningless experience, blundering from one moment to the next, with a view of the universe as something that recognizes and responds to considerations of value.  On the view we can call ‘teleological cosmopsychism', the universe is essentially driven to try to maximized the good. […]

Many philosophers postulate impersonal causal powers to explain the behavior of the universe.  But it’s equally consistent with observation to suppose that the universe’s drive to maximize value is running the show.

Or is it?  Doesn’t this lead straight back into the problem of evil?  If the universe is trying to maximize the good, how do we explain the terrible things that happen within it, at least on the planet we live on? Also, how do we think about the laws of physics on this picture?  If the universe is driven by a compulsion to maximize the good, shouldn’t there just be one law of physics, … ‘Do Your Best’?

We can kill both of these birds with one stone.  On teleological cosmopsychism, the laws of physics record the limitations of the universe.  Each moment, the universe is pushing to maximize the good, but under quite severe constraints as to what it is able to do.  As with the Limited Designer Hypothesis… it’s not that something outside of the universe is limiting the universe.  It’s just a primitive fact about the universe that it is able to do some things but not others.

Here I simply must comment.  Goff keeps talking about ‘good’ but he never discusses the fact that there can be many perspectives and what is ‘good’ to one perspective, is ‘evil’ to another.  He talks about morals, but what morals?  Whose morals?  What is moral in one culture, can be deeply immoral in another culture.  From the perspective of Goff’s beloved Darwinism, killing is a great moral good as long as it is the weak and stupid that are killed off and the strong and intelligent survive. The very thing that Goff most hates – suffering – about our reality, is in-built into the theory he is fighting so hard to conserve with his feats of philosophical legerdermain.


Getting toward the end of this discussion, Goff decides that the teleological cosmopsychist can propose that the universe fine-tuned itself. That is, teleological cosmopsychism is extremely parsimonious. Goff writes:

We know, or so I would argue, that there must be something underlying the mathematical structures identified by physics, otherwise our universe would contain no consciousness.  And we know there must be something that drives the predictable behavior of the universe.  It’s certainly possible that the fundamental level of reality is wholly impersonal and non-conscious.  But the alternative hypothesis of a universe responding to value under limitations recorded by the laws of physics is empirically indiscernible and no less parsimonious.

So Goff proposes that during the first split second of time, the universe fine-tuned itself because the universe must have been aware of future possibilities, and to account for this, we can attribute to the universe conscious awareness of the full consequences of each of the options available in that instant of time. And he then “cheekily” (his word) borrows the multiverse theory which he previously discarded, and which he now tries to slide in with a twist of Ockham’s razor; again, most confusing.

Goff next brings his pan-agentialism together with teleological cosmopsychism, and is quite satisfied with the results.  He writes:

If we stripped away the Bohmian mechanics, we could bring together pan-agentialism and cosmopsychism by identifying the universe with a universe-wide field, with the result that the universe will behave in a predictable way because the universe is conscious but lacks experiential understanding, and so inevitably acts through the basic rational response: do what you feel like doing.  But, contrary to the teleological form of cosmopsychism, this would not be a view on which the universe is maximizing the good; it’s just doing what it feels like doing.  […]

…we need to identify the cosmic fine-tuner with the wave function itself.  On the resulting view, the wave function is a conscious entity that is aware of the complete future consequences of the options available to it, and acts by choosing the best one.  During the Planck Epoch, the best option available to the wave function was to put itself in a state whereby the universe would become life-permitting.  The apparently mechanical behavior of the wave function thereafter reflects the limited options available to it. […]

On teleological cosmopsychism we start with rational matter, as particles and the wave function are themselves rationally responsive material entities.  The wave function then fine-tuned itself in order to allow mater to reach a greater realization of its rational nature. 

And there you have it, Glory Be!  Goff declares that the fit between fine-tuning and matter is not a coincidence! 



Goff has a twisty sort of brain.  I normally wouldn’t make the following discursus, but this problem is too big to just sweep under the rug.  The way Goff works through problems reminds me of a passage in Lobaczewski’s “Political Ponerology”:

Unconscious psychological processes outstrip conscious reasoning, both in time and in scope, which makes many psychological phenomena possible: including those generally described as conversive, such as subconscious blocking out of conclusions, the selection, and, also, substitution of seemingly uncomfortable premises.

We speak of blocking out conclusions if the inferential process was proper in principle and has almost arrived at a conclusion and final comprehension within the act of internal projection, but becomes stymied by a preceding directive from the subconscious, which considered it inexpedient or disturbing. This is primitive prevention of personality disintegration, which may seem advantageous; however, it also prevents all the advantages which could be derived from consciously elaborated conclusion and reintegration. A conclusion thus rejected remains in our subconscious and in a more unconscious way causes the next blocking and selection of this kind. This can be totally harmful, progressively enslaving a person to his own subconscious, and is often accompanied by a feeling of tension and bitterness.

We speak of selection of premises whenever the feedback goes deeper into the resulting reasoning and from its database thus deletes and represses into the subconscious just that piece of information which was responsible for arriving at the uncomfortable conclusion. Our subconscious then permits further logical reasoning, except that the outcome will be erroneous in direct proportion to the actual significance of the repressed data. An ever-greater number of such repressed information is collected in our subconscious memory. Finally, a kind of habit seems to take over: similar material is treated the same way even if reasoning would have reached an outcome quite advantageous to the person.

The most complex process of this type is substitution of premises thus eliminated by other data, ensuring an ostensibly more comfortable conclusion. Our associative ability rapidly elaborates a new item to replace the removed one, but it is one leading to a comfortable conclusion. This operation takes the most time, and it is unlikely to be exclusively subconscious.

That passage in PP reminds me of a passage in Barbara Oakley’s book “Evil Genes”:

A recent imaging study by psychologist Drew Westen and his colleagues at Emory University provides firm support for the existence of emotional reasoning. Just prior to the 2004 Bush-Kerry presidential elections, two groups of subjects were recruited - fifteen ardent Democrats and fifteen ardent Republicans. Each was presented with conflicting and seemingly damaging statements about their candidate, as well as about more neutral targets such as actor Tom Hanks (who, it appears, is a likable guy for people of all political persuasions). Unsurprisingly, when the participants were asked to draw a logical conclusion about a candidate from the other - "wrong" - political party, the participants found a way to arrive at a conclusion that made the candidate look bad, even though logic should have mitigated the particular circumstances and allowed them to reach a different conclusion. Here's where it gets interesting.

When this "emote control" began to occur, parts of the brain normally involved in reasoning were not activated. Instead, a constellation of activations occurred in the same areas of the brain where punishment, pain, and negative emotions are experienced (that is, in the left insula, lateral frontal cortex, and ventromedial prefrontal cortex). Once a way was found to ignore information that could not be rationally discounted, the neural punishment areas turned off, and the participant received a blast of activation in the circuits involving rewards - akin to the high an addict receives when getting his fix.

In essence, the participants were not about to let facts get in the way of their hot-button decision making and quick buzz of reward. "None of the circuits involved in conscious reasoning were particularly engaged," says Westen. "Essentially, it appears as if partisans twirl the cognitive kaleidoscope until they get the conclusions they want, and then they get massively reinforced for it, with the elimination of negative emotional states and activation of positive ones." {...}

Ultimately, Westen and his colleagues believe that "emotionally biased reasoning leads to the 'stamping in' or reinforcement of a defensive belief, associating the participant's 'revisionist' account of the data with positive emotion or relief and elimination of distress. 'The result is that partisan beliefs are calcified, and the person can learn very little from new data,'" Westen says. Westen's remarkable study showed that neural information processing related to what he terms "motivated reasoning" ... appears to be qualitatively different from reasoning when a person has no strong emotional stake in the conclusions to be reached.

The study is thus the first to describe the neural processes that underlie political judgment and decision making, as well as to describe processes involving emote control, psychological defense, confirmatory bias, and some forms of cognitive dissonance. The significance of these findings ranges beyond the study of politics: "Everyone from executives and judges to scientists and politicians may reason to emotionally biased judgments when they have a vested interest in how to interpret 'the facts,'" according to Westen.

My point is that Goff seems to be very attached to a materialist view of reality, while trying to argue for some form of consciousness that is above and beyond materialism.  Sort of like the “participation prize” that kids are given nowadays for just showing up and making half-hearted efforts.  He argues that the Universe has purpose and next, he is going to tell us how to “Live with Purpose” based on his twisted, bizarre reasoning. But, that’s the next post.

Thursday, March 9, 2023

Questions About Science: Is Science rational?

 Science is supposed to be rational. But how can science be rational if it is done by scientists who often behave in an irrational way?

To start with let us touch here, briefly, the problem of Science vs. religion – we will discuss it in detail later on. The difference between these two domains is examined by Bertrand Russell in his “Religion and Science”.


The book, "Understanding Science and Religion" would be of a similar size.


Science is Bottom Up

In Science we start from observations, from data, and then we build general rules, or principles that are supposed to explain these data and predict new data. Once in a while, when new data are acquired, or when a new insight into their interpretation appears, our old explanations do not suffice, and a revision of general principles is needed. That is, in short, how Science is done, or how it is supposed to work. One can say that Science is built bottom-up, from a large number of observations to a unified theory.

Religion is Top Down

Religion, on the other hand, is constructed top-down, from general principles, by deduction, reasoning and interpretation, to simple rules that are to be applied in everyday lives. Once in a while the reasoning is revised and religious practices change, but the starting principles remain essentially unchanged. As Russell sums it up:

A religious creed differs from a scientific theory in claiming to embody eternal and absolutely certain truth, whereas science is always tentative, expecting that modifications in its present theories will sooner or later be found necessary, and aware that its method is one being logically incapable at a complete and final demonstration.

He notices also another important difference between religion and Science:

The conflict between theology and science was quite as much a conflict between authority and observation. The men of science did not ask that propositions should be believed because some important authority had said they were true; on the contrary, they appealed to the evidence of the senses, and maintained only such doctrines as they believed to be based upon facts which were patent to all who chose to make necessary observations.


Religion and Science in Society

Religion and Science also had different functions in society. One of the functions of religion was clearly pointed out in an old treatise “History ofthe Conflict between Religion and Science” by John William Draper, professor at the University of New York and the author of “A Treatise on Human Physiology”. He wrote in 1875:

A few years ago, it was the politic and therefore the proper course to abstain from all allusion to this controversy, and to keep it as far as possible in the background. The tranquility of society depends so much on the stability of its religious convictions, that no one can be justified in wantonly disturbing them.

How is the situation different today? Religion is still a convenient tool for maintaining the tranquility of society, but, in the meantime, Science, industry and technology have provided other efficient means. Nowadays we have drugs and other chemicals, globally controlled media, Artificial Intelligence,  and psychological techniques – they are all at the disposal of those whose aim is to tranquilize society. Thus, religion is no longer needed by science and perhaps this is one of the reasons for the increasing conflict?

Are All Scientists Rational?

After this digression let us come back to the question of whether or not scientists can be rational? After all, just acquiring the status of being a scientist does not mean that a person is no longer subject to all the foibles of being human.



Rationality requires abandoning the blind attachment to any authorities. Religion, on the other hand, rests on authorities. Can these two different modes of thinking be separated in an individual?






Coming next: The Taboo of Subjectivity



Biolocation

  On Tuesday, December 23, Vlad Zhigalov (see e.g. here ) had a talk at the " Temporology " seminar hosted at Omsk.  He spoke abo...