Physics, Theoretical Understanding and the Limits of Human Knowledge/Understanding

Question

During an interview with Discover magazine, Roger Penrose makes the claim that a lot of the most theoretical physics, a la the physical theories that try to account for the discrepancies and contradictions between quantum mechanics and general relativity, leads to increasing nonsense, that flies in the face of the more observable features of the World (NB: I use this in both the sense of the reality around us, and a broader metaphysical sense) around us, consistent with the mathematics of a sensible theory.

I am struck by a certain sense that what he broached is a much deeper (meta-physical) question, one that concerns the limits of human understanding and knowing (and perhaps our ability to see it as such), especially as it related to the interpretation of physical data gleaned from experiments against the more (strictly) logical truths that arise out a consistent mathematical framework.

In one sense, we want these theories to make sense, to offer explanation for the way the World appears around us, even understanding that the actual mechanics and processes might be much more complicated or to a certain degree mysterious (not in the sense of nonsensical but apparently weird in contrast to what we observe with our "naked eye"). There are to my mind two things that fall out of this, one is whether we are coming to a ceiling with respect that we can make sense of what we can say is true mathematically, especially if the mathematics is completely coherent, as opposed to an adamant need to experimentally verify.

It is already known that certain hypotheses and experimental verifications are both incredibly difficult, technologically impossible or are otherwise theoretically barred based on the current models and estimations of what we need to set-up the experiment, etc. Conversely, the mathematics gets increasingly complicated and non-intuitive, becoming what appears to be further away from what is sensible according to the best know physical data, consistent with new results and what we already knew with less sophisticated theories.

So, a couple questions arise:

1. Are there simply limitations on what we may understand as meaningful and sensible because we lack the capacity to actually make sense of the results that we are getting?
2. What kind of theory do we end up with if we are prepared to simply settle for a theory that is completely sensible but within the bounds of the meaningful and sensible?
3. Does the abstraction of mathematics offer a via further up than experimentalists can even see/make sense of?

Answer 1

While there may be kenotic limits to human intelligence, I think the bigger error these days is the general disdain that many physicists and scientists have for philosophy, of all things. It is important to note that Einstein was very interested in philosophy, and this may well have influenced his genius. Michael Friedman argues this in Dynamics of Reason:

And even in the vastly more specialized climate of the twentieth century, scientists whose work has had a particularly revolutionary character have continued to be involved with fundamental philosophical problems as well. In the case of Albert Einstein, for example, there is a volume of the Library of Living Philosophers devoted to him (alongside of such figures as John Dewey, George Santayana, Bertrand Russell, Ernst Cassirer, Karl Jaspers, Rudolf Carnap, Martin Buber, C. I. Lewis, Karl Popper, Gabriel Marcel, and W. V. Quine), entitled Albert Einstein: Philosopher-scientist. (3)

Michael Polanyi's Personal Knowledge goes into some detail about Einstein and his philosophizing. He notes, for example, that the Michelson-Morely experiment did not particularly influence Einstein to come up with his theory of special relativity, as is often claimed. Einstein largely figured it out by philosophizing. This is lost on many scientists today. An example follows.

In my answer to Why do we tend towards discretizing things around and within us?, I quoted Massimo Pigliucci 2012-04-25 blog post Lawrence Krauss: another physicist with an anti-philosophy complex:

Lee Smolin, in his “The Trouble with Physics” laments the loss of a generation for theoretical physics, the first one since the late 19th century to pass without a major theoretical breakthrough that has been empirically verified. Smolin blames this sorry state of affairs on a variety of factors, including the sociology of a discipline where funding and hiring priorities are set by a small number of intellectually inbred practitioners. Ironically, one of Smolin’s culprit is the dearth of interest in and appreciation of philosophy among contemporary physicists. This quote is from Smolin’s book:

“I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today — and even professional scientists — seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historical and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is — in my opinion — the mark of distinction between a mere artisan or specialist and a real seeker after truth.” (Albert Einstein)

I agreed:

Note the "thousands of trees but has never seen a forest". This would be a preference to focus on particulars—an empiricist attitude—over and above a focus on universals—a rationalist attitude. I propose that Albert Einstein, Lee Smolin, and Massimo Pigliucci are correct: we need to find new, productive, holistic ways to think about science, ways which don't just discretize and reduce to basic elements.

Answer 2

Nonsense has always been a condition of science, as has sense. The two form a dialectic at several different levels and in different ways.

It requires much nonsense to produce a little new sense. We are the inheritors of a long history; of thought reflecting on itself. One recalls the long apprenticeship of mathematics through Babylonia today as mere data, as lacking sense; with Greece adding sense - that is proof; the same goes for astrology - the divination of futures, the coronation of kings through the movement of stars that even today casts a long shadow as mere nonsense until Galileo picked up his telescope.

This is the dialectic of intuition and technique. Every beginning is intuitive, and every ending saturated with technique. Beginnings are playful, endings totalising. Towards the end a backward look at beginnings becomes scornful. One has grown up and ones face is set to the future - towards an end.

This - the attitude of Janus. We are divided creatures having the capacity to look both ways. Assuming the posture of reverence to the past, the future is discounted. Assuming the posture of rapture towards the future, the past becomes a kind of nonsense. Being embodied creatures we cannot transcend this condition; rather we transcend it only to find ourselves in a new landscape whose contours resemble the old (the Nietzschian return).

Take the Langlands conjectures in Number Theory. Their development was not through logic, but through intuition. A new vision born. This is the reverse of the dialectic of intuition & technique. Through a long apprenticeship of technique, a long lonely march in making the abstract cohere and become sensible & sensual in the Understanding, Langlands achieves enough clarity of vision to have a vision. One must not confuse the formula for the thought.

Abstraction is the name of a certain magical strategy in mathematics amongst others. But this isn't the condition of mathematics to mathematicians. Rather it is making the invisible Sensible to the Understanding and Sensual to the Imagination (the Kantian perspective). One could point to Conways The Sensual Quadratic Form.

Isn't language abstract - can you hold a word? Being one of the conditions of our existence & essence this abstraction is concrete. But Number being not such a condition, when spiritualised it is vision, and materialised it is measure. Through measure - the ladder - to spirit and to vision (Wittgenstein)

The doxa and data of Babylonian mathematics, at its time, then a beautiful vision, operating under a materially signifying star lost now; thus nonsense - now.

To turn towards your first question - about the 'increasing nonsense' of the contradiction between QM & GR. There are deep differences between the two theories. Physicists assume that the unity of the world as it presents itself to us should be reflected in their theories. This of course is a metaphysical assumption. This may be actually true, but on the epistemological level, the world may be arranged as such that we can never realise it - that is through our physical theories. Verlinde remarked as much in an interview.

The 'nonsense' produced, is then thought operating intuitively; headway is made in certain directions, other directions prove false; bridges are built, torn down and built again.

One might point to Ashtekars New Variables in as unblocking an old path in the quantising of GR; causal nets as a new thought; TQFTs placing Feynman path integrals on a formal basis as solid achievements amongst others. Gravity thought thermodynamically is a new direction theorised by Padmanubhan & Verlinde; one recalls here Bekensteins application of thermodynamics to Black Hole physics and Hawkings later assertion of it. Chris Isham, Doering & others are exploring QM in the context of topos theory which are a generalisation of set theory whose logic is intuitionisitic. Further they may or may not have 'points', and what points there are may have shape - this is getting away from Euclids dictat of a point being a breadthless. Toposes have been arranged in a series whose infinite incarnation gives logic shape. This is known as homotopy type theory. Urs Scheiber is using this to synthesise vast swathes of mathematical physics into one coherent & consistent system. One also notes the introduction of inconsistent & paraconsistent methods in mathematics with slow seepage across the border to physics.

Much more 'nonsense' will have to be produced before some sense can be distilled. The Topologist Alexsandrov said at the beginning of Topology that he felt threatened by the immense production of topological papers until he realised that they were 'nonsense' meaning containing ideas of little significance by moving away from the mainline of mathematics. But one should recall that ideas that move away from the mainline may find their proper context for their full expression much later - for example Lord Kelvins theorising of Knots as a model for atoms, reducing atoms to pure geometry; or Brouwer reacting against Hilberts championing of the formal and infinite (Cantors Paradise) by retreating to the intuitive and constructive.

One should recall that Physics is a tradition with roots going back to Antiquity, and before; and with a future no less long.

One doesn't need a deep understanding of Modern Physics to understand that the world is mysterious. This has been the condition of men at most times. Most thinkers at most times have remarked on it. Only in a civilisation saturated with technique is this familiar and widely understood observation become unfamiliar, strange and bizarre.

It takes only a little thought to see that knowledge is infinite, that we are finite, and thus what we know though adding up to a great deal for us, is always at the beginning of the infinite. The simplicity of this thought has become a platitude, and like all platitudes have suffered the indignity of being ignored. This does not make it wrong but to really know it, one has to experience it. This what William Blake, the English Poet & Artist meant when he wrote in the Song of Experience, the Marriage of Hell & Heaven:

If the doors of perception are cleansed, everything will appear to man as it is, infinite.

Finally:

(1) are there simply limitations on what we may understand as meaningful and sensible because we lack the capacity to actually make sense of the results that we are getting?

Yes. When looked at the 'right way' this is always true. It is also very easy to forget this.

(2) what kind of theory do we end up with if we are prepared to simply settle for a theory that is completely sensible but within the bounds of the meaningful and sensible?

How can one work outside of the 'meaningful and sensible'? It is our horizon of thought as remarked by Wittgenstein in the Tractatus.

(3) does the abstraction of mathematics offer a via further up than experimentalists can even see/make sense of?

Yes; since mathematics is a tool, the more tools there are the better, the more efficient they are the better; but one shouldn't confuse mathematics for physical intuition, nor for thought or speculation. One should also recall that experimentalists do find things that are unpleasant suprises to the dreams of theorists - like the slow death of supersymmetry - or dark energy and matter. Remember experiment & theory form a dialectic. One shouldn't valorise one over the other. Human though it is.

Answer 3

1. Humans are necessarily limited in scope. This limitation allows us to have a certain functionality and place in the order of this world. As Noam Chomsky puts it, we are not angels. [Noam Chomsky lecture on the subject is in the link below]
2. This is an important question and one that relates to a revolution in logic within the 20th century. What your question ultimately implies is that many of our theories are based on limited foundations. Gödel's Incompleteness theorm tells us that within a formal system There is at least one statement you cannot prove. In plain English any distinct field of mathematics (geometry, set theory, algebra, etc.) are limited because there maybe several theorems that are not provable. Ergo, we come to the conclusion that the tools we are flawed but sufficient in the sense that we can still have some absolute truths.
3. The same can be said for any field that has an increasing growth of concepts and connections between those concepts. The idea that mathematics is not intuitive is simply a misconception. There are many books that describe how mathematics in it's core is graspable by any educated individual because at the core it models patterns. But since your question really pertains to physics, theoretical physics use mathematics to model concepts created by physicists. Therefore, an experimentalist would understand the applied mathematics but may not necessarily execute them.

Noam Chomsky - "The machine, the ghost, and the limits of understanding"

Answer 4

Are there simply limitations on what we may understand as meaningful and sensible because we lack the capacity to actually make sense of the results that we are getting?

Yes, down to earth, we are among the living people of a few billions, each with a limited capability of understanding and so the sum. Time wise, the sum will stop accumulating at some point. For over 100 years since Plank and Einstein, how much further have we advanced in fundamental understanding? If not much, the sign to reach a limit is apparent, just as a hyperbola approaches its axis. The flat opposite should have been supposed, i.e science breakthroughs must have been exponential over time due to increasingly sophisticated tools are newly created in number and pace (e.g with the help from computers and Moore's law).

whether we are coming to a ceiling with respect that we can make sense of what we can say is true mathematically, especially if the mathematics is completely coherent, as opposed to an adamant need to experimentally verify....Conversely, the mathematics gets increasingly complicated and non-intuitive... Does the abstraction of mathematics offer a via further up than experimentalists can even see/make sense of?

Math inherently has barriers you cannot pass, proved by Goedle's incompleteness theorem and his below more intuitive statement:

So the following disjunctive conclusion is inevitable: Either mathematics is incompletable in this sense, that its evident axioms can never be comprised in a finite rule, that is to say, the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems of the type specified . . . (Gödel 1995: 310).

NB: Goedle raised a very fine point about the Mind, but it's beyond the notion of knowledge and for another discussion, though very much relevant to R.Penrose's tendency.

What kind of theory do we end up with if we are prepared to simply settle for a theory that is completely sensible but within the bounds of the meaningful and sensible?

Well the best tool employable so far is Math and you see the limitation. There are a few candidates beyond science, first to start with metaphysics. I find the philosophy of C.S.Peirce on Semiotic and the relevant that are so distant to most others. Surprisingly it appears to be avoided or kept away.