EVEN PHYSICISTS ARE AFRAID OF MATHEMATICS! But the Paradoxes of “Knowledge” May Require Knowing What We Mean by ‘KNOWING”

14991786_1889143401313680_6122259088693183352_nThis is a problem in Biology and Neuroscience as well.


They say, “This is an important issue because it shows there could be a disconnection between mathematical theory and experimental work. This presents a potentially enormous barrier to all kinds of scientific progress.”

“We have already showed that biologists are put off by equations but we were surprised by these findings, as physicists are generally skilled in mathematics.”

By performing a systematic analysis of the citation counts of papers published in one of the leading journals in physics covering all its disciplines, we find striking similarities with distribution of citations recorded in biological sciences.

Read more at: http://phys.org/news/2016-11-physicists-mathematics.html#jCp

Deeper than it appears, also, insofar as we believe that what we call “thought” is really embodied in and progresses through mathematical structures that express how the rules and workings of our “models” can unfold.

The deepest intuitions of which we, as scientists are capable arise, as we can see from Einstein’s sharing with us, in a manner beyond and far more fundamental than our language….and then only do they come to expression via the hard work of mathematical puzzlement and solution that arises from those intuitive beginnings. And those beginnings are NOT ‘verbal” but are in some way akin to what Einstein called “muscle events’ or “kinaesthetic” when they arise.

The talk that accompanies the work of science that is etched in mathematics is merely just that, “talk”. I is riddled with attempts to make it be consistent with our ordinary language intuitions that we have inherited and which have been passed along from far more primitive times.

Quantum physics is a great example of this discordance. The mathematics of the theory of quantum physics, seems to work (albeit there are a few patches here and there that seem be ad hoc improvisations), but the achievements of quantum physics when it is guided by its mathematics formulations is incredible and impressive.

Yet at the same time it continues to befuddle and perplex those who seek to talk about it in ordinary language, rooted in so called “intuitions” that are truly not our deepest intuitions, but merely the way we have been trained to traffic and constrain the flow of that intuition down the highways and byways of highly inadequate ordinary language.

Nobel Laureate Weinberg thinks there’s a need for a new chapter in the quantum story is that those who think everything is fine with quantum mechanics take different sides in the debates about it.

Why quantum mechanics might need an overhaul

“It’s a bad sign in particular that those physicists who are happy about quantum mechanics, and see nothing wrong with it, don’t agree with each other about what it means,” Weinberg says.

Weinberg thinks “there might be something beyond quantum mechanics, a deeper theory that introduces probabilities at a fundamental level, rather than requiring a human to make measurements to get the probabilities to show up. And there is a line of research attempting to generalize quantum mechanics along those lines. But so far a compelling theory that succeeds in generalizing quantum mechanics does not exist.”

Perhaps a replacement for today’s quantum theory will come together any time now. Or perhaps not. “Maybe it’s just the way we express the theory is bad,” Weinberg says, “and the theory itself is right.”

The Illustrious John Bell, in a volute titled Speakable and Unspeakable in Modern Physics,( http://philpapers.org/rec/BELAM ) brings us to the notion of FAPP…which is “For All Practical Purposes” when he writes, about “why bothering”

“Perhaps the most distinguished of the ‘why bother?’ers has been Dirac He divided the difficulties of quantum mechanics into two classes, those of the first class and those of the second. The second- class difficulties were essentially the infinities of relativistic quantum field theory. Dirac was very disturbed by these, and was not impressed by the ‘renormalisation’ procedures by which they are circumvented. Dirac tried hard to eliminate these second-class difficulties, and urged others to do likewise.

The first-class difficulties concerned the role of the ‘observer’, ‘measurement’, and so on. Dirac thought that these problems were not ripe for solution, and should be left for later. He expected developments in the theory which would make these problems look quite different. It would be a waste of effort to worry overmuch about them now, especially since we get along very well in practice without solving them.

Dirac gives at least this much comfort to those who are troubled by these questions: he sees that they exist and are difficult. Many other distinguished physicists do not.

It seems to me that it is among the most sure-footed of quantum physicists, those who have it in their bones, that one finds the greatest impatience with the idea that the ‘foundations of quantum mechanics’ might need some attention. Knowing what is right by in- ‘measurement’stinct, they can be- come a little impatient with nitpicking dis- tinctions between theorems and assump- tions. When they do admit some ambiguity in the usual formula- tions, they are likely to insist that ordinary quantum mechanics is just fine ‘Fo all PRACTICAL PURPOSES = FAPP (caps by Bell)’.

In neuroscience the same is true. There is a refusal to consider mathematics as more than a tool or device for measurement but never a delving into the foundational notion of mathematical structures to guide the enterprise of neuroscience

What this means is that we don’t confront and tackle our own thought by means of the employment of mathematical reasoning…and treat mathematics on a limited game board where the moves are predetermined by outdated and primitive intuitions which infest our ordinary language.

Instead we might consider how it is that our thoughts are put together, and what the underlying “models” of our thinking might offer us, if we treated them with the same respect and wonder that mathematicians treat their own systems.

In the realm of physics, Bell says, ‘Here are some words which, however legitimate and necessary in application, have no place in a formulation with any pretension to physical precision: system, apparatus, environment, microscopic, macroscopic, reversible, irreversible, observable, information, measurement.”

The concepts ‘system’, ‘apparatus’, ‘environment’, immediately imply an artificial division of the world, and an intention to neglect, or take only schematic account of, the interaction across the split. The notions of ‘microscopic’ and ‘macroscopic’ defy precise definition. So also do the notions of ‘reversible’ and ‘irreversible’.

We add that In both theoretical physics and neuroscience we have an intrinsic and analogous slovenliness in the drawing of boundaries between such notions as the “observer”, whatever in the world that entity might be, and apparently mundane “measurement” on the one side and mysterious and ennobled “consciousness” on the other.

This is not much different from the positioining in neuroscience of some sort of “perceptual encounter” of the person with the world that is exceedingly sloppily positioned between “sensory process’ on the one side and a true magical and inpenetrable notion “cognition” as providing the backdrop.

In both sciences they cannot seem to get beyond a rootedness in rather primitive notions of “knowing” that consider knowing to be no more than an archaic and somewhat magical “relation” between an “observer” and some “reality beyond that observer. That is truly a primitive notion. But it is what happens when we rely on our ordinary language intuition to guide us

“We accept reality so readily perhaps because we sense that nothing is real”…said the poet, Borges. We tend to agree with him but only in the sense that to the degree to which we use the word “reality in both parts of his statements that concept itself is insufficient and itself needs to be transcended. That does not means to us mean that “reality” as such needs to be mystically transcended.

According to Bell, “Einstein said that it is theory which decides what is ‘observable’. I think he was right – ‘observation’ is a complicated and theory-laden business. Then that notion should not appear in the formulation of fundamental theory. Information? Whose information? Information about what? On this list of bad words from good books, the worst of all is ‘measurement’. It must have a section to itself.

When we look at the current ostensible “predicament “of quantum physics, we actually find it no less crudely primitive that the most tedious puzzlements over the brain and the mind and the world outside our eyes and ears.

The resulting perplexity arises, despite the fact that the mathematics somehow and surely ‘works’ and helps technology to achieve wonders, because they cannot seem to get beyond a rather simplistic question: Do the equations of quantum physics and its “waves’ and their “collapse” reflect something about the “reality” outside the “observer”…OR…on the other hand, to they reflect only something about the limitations of the knowledge to which that “observer” might be privy.

If we look closely at what Weinberg says…we can almost instantly translate it, as fast our eyes skip over the words into equivalent statements about what we see to be the ‘hard problem” of neuroscience. And talk about the real person’s “minding brain” and how it relates to the world just as easily as he speaks of some collective “knowing’ of the “reality’ that is presumably “out there” for us ‘now’, of course presuming that we have coherent notions of ‘there’ and ‘now”…

Attempts to explain fall into two broad categories, Weinberg said: “instrumentalist” and “realist.” Instrumentalists contend that the wave function is merely a tool for calculating the results of experiments — there’s no way to know anything more about reality. Devotees of the realist approach contend that the wave function is a real thing out in the world, evolving over time, and at a fundamental level it is responsible for what’s really happening.

Weinberg finds the instrumentalist view unattractive. It’s “so ugly to imagine that we have no knowledge of anything out there — we can only say what happens when we make a measurement,” he says. “The instrumentalist approach takes the attitude that we just don’t know what’s going on out there.”

On the other hand, the realist view does say what’s going on “out there,” but at the cost of enormous complexity, in the form of a countless number of independent streams of reality.

We have to ask here, ” what is the underlying intuitive structure that compels us in modern physics, not less than in neuroscience to speak of such an odd entity as ‘the observer” and an even odder entity which we call ‘reality”? The choice is not “between the two, but to understand how that ‘choice” appears to be our only choice.

As Bells reminds us, the concept of ‘measurement’, in the fundamental axioms of quantum mechanics, is that it anchors there the shifty split of the world into ‘system’ and ‘apparatus’.

And then there is the problem ” that the word comes loaded with meaning from everyday life, meaning which is entirely inappropriate in the quantum context. When it is said that something is ‘measured’ it is difficult not to think of the result a s referring to some preexisting property of the object in question.

When one forgets the role of the apparatus, as the word ‘measurement’ makes all too likely, one despairs of ordinary logic – hence ‘quantum logic When one remembers The role of the apparatus, ordinary logic is just fine.

In neuroscience and biology there is a sadly dismissive view of mathematics as fine enough, convenient. and some sort of notational or measurement contrivance. However the thinking that guides neuroscience is primitive barbarism that goes back hundreds of years in its utter lack of wit, wisdom, insight or cogency.

We might as well have gathered a collection of old wives to tell us their tales with the help of modern technology to try to quantify their gossiping.

Truthfully, we suspect that, as this article points out, much the same is true today of the physicists who are toiling in the mines but not interested in delving into the deepest re structuring of their own theories.

That is, in fact why we have devoted so much of our energies on a Page devoted to the science of the Minding Brain to the quandaries facing theoretical physics an its mathematical foundations.

Weinberg would prefer a deeper treatment of the problems

The current puzzlement in theoretical physics is not at all a sophisticated sort of puzzlement…but almost aboriiginal in its primitive nature That “model “is one that has been with us for thousands of years….And there is no reason to believe that the solution to the perplexity of theoretical physics today will be arise from a multiple choice of “either/or’ one of these two arbitrary and truly uninteresting alternatives.

The really interesting question to us is, rather, how it is that this modeling which we find ourselves doing, between an “observer” and “a reality”, both of which are murkier than murky concepts, can itself be understood, not as defining the game board on which our moves of thought must be made, but instead to reflexively investigate how this model itself arises from a level of thought outside that ‘box” or that game board.

“There’s always a third possibility,” as Weinberg said, “that’s there’s something else entirely, that we’re going to have a revolution in science which is as much of a break with the past as quantum mechanics is a break from classical physics. That’s a possibility. It may be that a paper from a graduate student tomorrow morning will lay it out. By definition I don’t know what that would be.”

However the above cited research on the apparent avoidance of mathematics use in cited publications tells us “The idea that a lack of training in reading/doing mathematics is responsible for the lack of citations seems not to be true since data reflecting habits of a broad community of physicists displays similar trends as those found in publications by biologists.”

We feel that it is the reluctance to confront the prospect of the mathematics considerations often leading to questions that are not easily put or offer easy, though incoherent attempts at answers via ordinary language.

Perhaps the attention ought to be less to puzzling over whether the functional mathematics of quantum physics fits either the “state of reality” or the ‘state of the observer”, but instead perhaps to aim the insight of mathematics as it reflects back upon itself to the question of whether the mathematics refers to the relation between the speak of science for whom both “the reality and the measuring observer somehow responsible for measuring ‘IT” seem to occupy place in a relation to each other about which science seems to “speak”

Maybe what is needed is an examination of the implicit “axioms” in the system rather than an endless quest to rationalize the calculations in accordance with common intuitions

That is how mathematics has grown so incredibly over the years, by means of considering the very elements of mathematics itself, it has reflexively spiraled outward to all sorts of wisdom and insight as to the nature of the mathematical structures with which it began.

What quantum physics makes quite clear..and which physics prior to that did NOT…is that physics (despite its own blithe assumptions) has never simply presented us with a pictorial rendering of states of affairs that are the “landscape” being painted for us.

On the contrary, physics has always implicitly been predicated on some such implicit ‘model” which entails a contrivance as an “observer” as being part of its formulation….although not necessary…..if other modes of grasping the ‘knowledge” paradigm itself are explored and certainly as paradoxically riddled as is “he picture of a painter painting a picture of a painter painting a picture and so on….”

This ‘observer “concept and the confusion between this ‘surrogate” contrivance and the ostensible “cbserving” of the scientist presenting his papers and theory has always been a cause of misery. Einstein had to point it out to remediate classical physics and introduce a clarification of the observer as not outside the time of any inertial frame.. Zeno, centuries prior used that confusion to torment the Aristotelian view of motion, by confusing the person confronting with his paradox with the viewpoint of an observer in the time frame of the moving “arrow”..

Why can’t the mathematics of the wave equations be interpreted as emerging from the a different “model”..one in which the person doing the “talking about science” in those publications is actually a third element insofar as the “story teller” must be included as well as the actors in his story”..the “observer” of which he speaks to us and something which that “observer” seeks to observer, the “reality”. There is triad of relations that looms in physics (and indeed in neuroscience as well, whether the implicit homunculus observer is always inferred) the three way “relation” among the speaker in science who writes to us about what has been done, and the characters in the drama that he portrays for us by that speaker; the engagement of the “observer who measures” and the “reality which is measured”.

Could it be that this more complex narrative is the one which the mathematical equations may be interpreting as somehow expressing, rather than the dichotomous rudiments in the arena between observer and reality.

It may really be a question in the end of what we mean when we speak of “knowing” and that the issue is “not” the ‘KNOWING”…but the “speaking of such a mysterious almost occult process as ‘knowing’, per se.

And that is where mathematics can likely be the most help in the manner in which it reflects back upon its operations and allows us to move on to further perplexities that always await.

Roger Penrose puts the ‘hard problem” of quantum physics this way, as having two parts : One is the evolution of a quantum system, which is described extremely precisely and accurately by the Schrödinger equation. That equation tells you this: If you know what the state of the system is now, you can calculate what it will be doing 10 minutes from now. However, there is the second part of quantum mechanics—the thing that happens when you want to make a measurement.”

“It appears, he says, ‘ that the current way of interpreting the results of an actual measuring are interpretable in more than one way. So, the question of “probablitily” arises as Instead of getting a single answer, you use the equation to work out the probabilities of certain outcomes. The results don’t say, “This is what the world is doing.” Instead, they just describe the probability of its doing any one thing.: This is considered to be either an odd aspect of that external “reality” or an odd limitation on the observing abilities of the ‘observer ”


Dirac has famously described the situation of “knowing’ in quantum physics as follows” I can describe the situation by comparing it to the game of chess. In chess, we have various chessmen, kings, knights, pawns and so on. If you ask what chessman is, the answer would be that it is a piece of wood, or a piece of ivory, or perhaps just a sign written on paper, or anything whatever. It does not matter. Each chessman has a characteristic way of moving and this is all that matters about it. The whole game of chess follows from this way of moving the various chessmen.”

As one quantum researcher has said ‘“A theory of reality must not only explain reality, but also knowledge about that reality because knowing reality is part of reality.” (Ashish Dalela, Quantum Meaning: A Semantic Interpretation of Quantum Theory)

Penrose concludes, ” it seems to me that we must make a distinction between what is “objective” and what is “measurable” in discussing the question of physical reality, according to quantum mechanics. This reconsideration of the meaning of what is ‘objective” to us means that the very idea of ‘knowing’ must be re modeled and not in terms of some measuring by an observer of some “reality to be measured..

However that raises the question for us of if and when we examine the underlying axioms by means of which the system is defined….That its essentially what we mean by looking just a bit more closely the decisions of choosing upon which manner of chess board to exercise our gambits when we come up against some of the perplexities we see today.

Mathematics and the wisdom and “knowledge” it provides seems to be different from other sorts of “knowledge” that is the main content of other disciplines. Does physics need to consider just what sort of ‘chess board” it is playing on.

Mathematics seems to be devoted to knowing itself, and not to describing the “reality” of the outside world as if that ‘reality ‘were patterned perfectly for our mathematics to discover, and not to describe the knowing of some measuring observer standing before that reality traing to “know it’. Instead math reflects back on itself and the more deeply we pursue it to more we know about what we have just done.

Clearly what this means is that the “knowing” that arises during the course of mathematics relies upon another “modeling’ of what is to “know’ rather than the ancient one that guides modern physics, even today.

Today, there is a notion called “Model-dependent realism” coined by Stephen Hawking  in his 2010 book, The Grand Design  (It claims that it is meaningless to talk about the “true reality” of a model as we can never be absolutely certain of anything. The only meaningful thing is the usefulness of the model.  They add, ” it is pointless to ask whether a model is real, only whether it agrees with observation”

It seems that while there is a recognition here that we are dependent on our ‘models” by mans of which to “know”, that these models are still each dependent in some way on some externality that we seek to know via those “models’. This  theory of Hawking’s states that when several models overlap in describing a particular subject, multiple equally valid “realities” exist’

This point of view seems to be a bit pessimistic in mood in that i  all we can know about “reality” consists of networks of world pictures that explain observations by connecting them by rules to concepts defined in models. They ask,  Will this sequence eventually reach an end point, an ultimate theory of the universe, that will include all forces and predict every observation we can make”  The “theory of everything” may not be reachable…but for the very fact, we say, because there it does not make sense to consider that there may be” such an ‘EVERYTHING” about which a theory should concern itself.

But that too does not mean that we must consider, while still constrained to a notion of ‘reality, we can make ourselves feel better at ease by simply saying that  “the cosmos does not have just a single existence, or history, but rather that every possible history of the universe exists simultaneously” and “that the observable universe in which we seem to live doesn’t exist independently, apart from anything else, but is one member of an enormous collection of physically real universes”

However, the ‘model” in which they themselves are speaking to us and sharing their wisdom is one with an ancient metaphysics which they do not take into account, that of the “observer talking about an observer who is measuring some reality”  And all that seems to be achieved here is that “there are multiple realities” posited instead of one reality.

Hawking himself manages to speak about this matter in a full circle when he gives us his implicit idea of just what it might mean for the “observers” of science to be so ‘limited” in their access to that “reality” beyond their reach, with an ad hoc theory of neuroscience of his own, “our brains interpret the input from our sensory organs by making a model of the outside world. We form mental concepts of our home, trees, other people, the electricity that flows from wall sockets, atoms, molecules and other universes. These mental concepts are the only reality we can know. There is no model-independent test of reality.”

Of course, he would say that. That is precisely the implicit and antediluvian model of human cognition and the very notion of ‘knowing’ within which his talk of scientific modeling and “knowing” via that more sophisticated modeling is taking place. In the end, Hawking is unwittingly involved in a tacit metaphysics and epistemology here, just as most of those engaged in science today.

And as we surprise ourselves at the end of this post, is the fact that both neuroscience and theoretical physics today, don’t attend nearly enough to truly knowing what they mean by “knowing’ and they fuss much too much about the vagaries of the term as it plays out in a narrow arena that ought itself to be attacked as a problem to be resolved.

We are inclined here to quote from an insightful recent review by P.M.S.Hacker (http://info.sjc.ox.ac.uk/scr/hacker/DownloadPapers.html   of Wittgensteins radical ideas on the nature of mathematics and just what it does for us when formulate its beguiling expressions Hacker  quides us to Wittgenstein in the following way, “we should think through the consequences for our conception of mathematical propositions of the idea that they are rules, belonging to systems of rules, rather than true descriptions,” he say.

What we are dealing with here in those mathematical formulations that enable quantum physics to do so much but about which it can say so little that it intuitively compehensible, is that mathematics is not a body of  instrumental rules subservient to an independently given end….its expressions are ” norms of representation in the guise of super-physical descriptions of the scaffolding of the world……

What are  ‘held  to be descriptions of necessities in re are at best expressions of our forms of representation in the guise of descriptions or grammatically related to our forms of representation and our forms of transformation of expressions. 

For the world has no necessary structure – that is, contrary to the pronouncements of meta-physicists, there is no such thing as the necessary structure of the world’…..far from describing the scaffolding of the world, these norms of representation are grammatical propositions that constitute the scaffolding from which we describe the world in empirical propositions.”

Long ago, Leibniz who was both quite a mathematician and quite a philosopher, said:

“Without mathematics we cannot penetrate deeply into philosophy.

Without philosophy we cannot penetrate deeply into mathematics.

Without both we cannot penetrate deeply into anything.”

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