Questioning the supremacy of mathematical formalism in understanding the universe

[Obvious Leo]

Spacetime physics is supremely self-correcting because almost any new observation can be mathematically tailored to fit the spacetime narrative.

"Mathematics can be used to prove ANYTHING"....Albert Einstein

"It is the THEORY which determines what the observer will observe".....Albert Einstein

Even an observation which flatly contradicts the spacetime narrative can always be formulated in such a way that it can be made to comply with it by brute mathematical force e.g quantum entanglement directly contradicts both SR and GR, which prompted Einstein to make this arresting proclamation:

"Spacetime must NEVER be regarded as physically real"....Albert Einstein

Einstein was adamant until his dying day that spacetime physics was only a mathematical representation of a physical model and not itself a physical model, which is a perfectly reasonable statement when viewed from the perspective of a philosopher of science. Notions such as an "expanding space" or a "curved space" must only be regarded as metaphorical statements because a space is nothing more than a mathematical co-ordinate system, not a physical entity which can perform physical work. Space has no physical properties and thus must only be regarded as a purely relational construct.

Mathematics is a gift that keeps on giving. Don't forget that exactly the same cosmological constant can be used to explain why the universe is expanding as well as why it isn't.

[surreptitious57]

Space has no physical properties and thus must only be regarded as a purely relational construct

Then is my very real perception of three dimensional space merely a product of my own imagination ?
Something which can not possibly exist in reality only because it can be mathematically represented ?

[Obvious Leo]

Then is my very real perception of three dimensional space merely a product of my own imagination ?

This is not my preferred form of language but as a philosopher of science my answer would be yes. My preferred way of saying it is that the Cartesian space is a cognitive construct only but I'll willingly grant that the logical positivists would cheerfully burn me at the stake for daring to suggest it. This is by no means as left-field a proposition as you might think because it forms the central plank of most of the major philosophies of both east and west, the great Persian philosopher/mathematicians defined space in this way, and both Gottfried Leibniz and Baruch Spinoza were adamant about it. In addition to this Kant based his entire "Critique" on it and it is effectively a canonical doctrine in cognitive neuroscience. The pre-Socratics were nothing if not a pragmatic lot and they were the masters of common sense logic. They reckoned that nothing could be defined as physically real unless it had physical properties, which is a bloody difficult argument to lay a glove on.

[surreptitious57]

The pre Socratics were nothing if not a pragmatic lot and they were the masters of common sense logic. They reckoned that no
thing could be defined as physically real unless it had physical properties which is a bloody difficult argument to lay a glove on

Space does have physical properties since it is composed of atoms though the Greeks did not know that. However they could still
have disproved their own argument by realising that it does not automatically cease to exist just because it appears to be empty

[Obvious Leo]

Space does have physical properties since it is composed of atoms though the Greeks did not know that. However they could still
have disproved their own argument by realising that it does not automatically cease to exist just because it appears to be empty

This is not a counter-argument to the "expanding" and "curved" spaces of spacetime physics. Empty space does not contain atoms or else it wouldn't be empty. The fact that interstellar space and even intergalactic space contain atoms is not germane to the point. For instance nobody suggests that atoms are responsible for gravity. In fact no physicist in the world will be able to offer you a physical mechanism for how gravity works because no such mechanism exists in spacetime physics. Everybody knows what gravity does but nobody knows how it does it and this has been an intractable problem for physics for a century.

[surreptitious57]

Empty space does not contain atoms or else it would not be empty. The fact that interstellar space and even intergalactic space contain
atoms is not germane to the point. For instance nobody suggests that atoms are responsible for gravity. In fact no physicist in the world
will be able to offer you a physical mechanism for how gravity works because no such mechanism exists in spacetime physics. Everybody
knows what gravity does but nobody knows how it does it and this has been an intractable problem for physics for a century

Empty space is not actually empty but is only perceived to be empty. Atoms cannot be observed at the classical
level so a space with nothing else in it is said to be empty. Since that is all the eye sees and the brain processes
But our senses cannot perceive all phenomena only some. This is also why we can only perceive a small fraction
of the light spectrum as most of that cannot be seen by the eye either. But that does not mean it does not exist

Mass is responsible for gravity because the greater the mass of an object is the greater its gravitational force of
attraction. And it has been known ever since Newton formulated it so there is no doubt or mystery about it now

[Obvious Leo]

You miss my point. Everybody knows that mass is responsible for gravity but nobody knows how it works. The best that physics can come up with is that a falling body follows the trajectory of a curved space, but this is a mathematical statement and not a physical one. In this respect spacetime physics is every bit as much an action at a distance model as the Newtonian physics it is predicated on.

This is what all the fuss and existential angst in physics is all about. I think it might have been Fred Hoyle who once responded to an audience question in this way when asked by a woman "What is Gravity?" I paraphrase from memory but Fred said something like this "Everybody knows what gravity does, madam, but nobody knows why it does it so nobody knows what gravity actually is.

This remains the case in theoretical physics right up till the present day and the quest for the holy grail of physics remains the same as the one it's always been since the publication of GR. What the fuck is gravity? Unfortunately physicists are no different from the rest of us mere mortals and thus tend to set too much store by their own eternal verities. In their hubris they've fallen for the three card trick of believing their own bullshit and thus they mistake their map for the territory it's intended to be mapping. This logical positivist stance has been their own undoing because it's caused them to overlook the elephant in the room of GR. Gravity is an expression of time because gravity and time bear a precise mathematical relationship to each other which is inversely logarithmic in its nature. Because they are two different ways of expressing the same thing gravity and time can be quantised equivalently but this interpretation can never be accommodated within the spacetime narrative because this narrative is founded on a fundamentally flawed a priori assumption, namely the constant speed of light.

Examine these two statements in terms of their logical consistency and thus their truth value.

1. the speed of light is a constant

2. the speed of light is only observed to be a constant because it is proportional to clock-speed.

Both of these statements will produce identical epistemic phenomena for the observer to observe but only one of them makes sense.

[surreptitious57]

Given enough time there is no reason why there cannot be a theory of quantum gravity which shall finally unite the four fundamental
forces. Now because it has not happened yet does not mean it will not happen at all because breakthroughs shall continue to happen
like they always have. Nothing is insurmountable if enough time and effort is applied to it. Just look at the towering achievements of
twentieth century physics. Today is rather apt since exactly a hundred years ago Einstein presented his theory of general relativity to
the world. And in another hundred years from now there may very well be another theory equally as profound if not actually more so

[Obvious Leo]

Given enough time there is no reason why there cannot be a theory of quantum gravity which shall finally unite the four fundamental
forces

I haven't the slightest doubt of it. However you'll see a man flying to Mars simply by flapping his arms long before you'll ever see such a unification model being accomplished within the spacetime paradigm. It is riddled with metaphysical flaws which are utterly insurmountable, even in principle. Thomas Kuhn and Paul Feyerabend were the two leading lights of 20th century science philosophy and both were adamant that the models of physics could only be unified by a paradigm shift in conceptualised thinking. What they meant was that it's not so much that there's something wrong with these models of physics, but rather that there's something wrong with the way we're thinking the world.

Try this for a different way of thinking the world.

The universe is not a place. It is an event which the observer merely perceives as a place.

[surreptitious57]

Thomas Kuhn and Paul Feyerabend were the two leading lights of 20th century science philosophy and both were adamant that the
models of physics could only be unified by a paradigm shift in conceptualised thinking. What they meant was that it is not so much
that there is some thing wrong with these models of physics but rather that there is something wrong with the way we are thinking the world

You say this as if it is some thing new yet it has existed for as long as civilisation has. For the history of science is littered with consciousness
raising overcoming false assumptions ever since we began to think about the natural world. So before Copernicus it was thought Earth was at
the centre of the solar system. Before Galileo it was thought heavy objects travelled faster through air when dropped than light ones. Before Newton light was thought to be composed of only one colour. Before Einstein time and space were thought to be absolute. So paradigm shifts occur on a regular basis and the next one shall be equally as profound as any of those I have referenced. So just be patient and it will happen

[Obvious Leo]

You say this as if it is some thing new yet it has existed for as long as civilisation has.

I'm only giving a very sketchy overview here but I'm certainly not claiming to be saying anything new. What I'm saying has constituted the backbone of mainstream philosophy for as long as philosophy has existed but what physics is doing in its logical positivist zeal is ignoring this.

Quantum gravity is a problem for physics but it's certainly not a problem for a philosopher of physics. Physics is entirely based on observation and Leibniz pointed out that inductive inference from observation is not a valid pathway to truth. An observation is an act of cognition and this is why Leibniz utterly rejected Newton's ontologising of the Cartesian space. It was Newton who established the methodology for mathematical physics and ever since Newton this has been the ruling ideology. What is observed is assumed to be that which is real but this is patently bollocks because all the observer can observe is raw information and it then becomes the role of his consciousness to construct this information into a coherent narrative of the world around him. Clearly the continuum of space and time is not such a coherent narrative because it leads to derivative models of the universe which are incompatible with each other and make no fucking sense. SR and QM are both background-independent models which lead to all manner of paradoxes and logical fallacies so GR is certainly a significant epistemic improvement because at least it operates in a dynamic background. However it still ontologises the Cartesian space and attributes physical properties to a mathematical co-ordinate system, so GR cannot possibly be a model of the real world either. However GR holds the key to the QM problem. The real universe doesn't need a background of any description to operate in because all the real world needs in order to be comprehensible is to conform to the universal doctrine of causality.

It all boils down to the problem of the observer and the early pioneers of 20th century physics were well aware of this fact even though they never satisfactorily resolved it. When we observe an object are we observing a physical thing that IS or are we observing an event which has already occurred in our own past? Since the speed of light is finite the answer to this question is a slam dunk but it represents a complete paradigm shift in the way we should think the world.

This logical positivist stance has been their own undoing because it's caused them to overlook the elephant in the room of GR. Gravity is an expression of time because gravity and time bear a precise mathematical relationship to each other which is inversely logarithmic in its nature. Because they are two different ways of expressing the same thing gravity and time can be quantised equivalently

This is quantum gravity.

[ittiandro]

Two people have asked you whether your concern would be addressed by differentiating science as descriptive versus explanatory. You have not yet responded adequately IMO. To be fair, you did respond to me when I made that point; but not in a way I could understand. You didn't seem to think there's a difference between description and explanation; when in fact there is all the difference in the world.

I have some difficulties in seeing how the distinction between description and explanation applies to science. Perhaps somebody should explain it. It would help the dialog.

Here below I’ll try to explain (and not merely..describe!) what I think of this distinction and WHY. At the end, I’ll reformulate my problem, to make sure it is properly understood.

There is a more or less overt view running through this forum that my problem is due to a misunderstanding, namely the faulty assumption that science should provide ultimate explanations, in terms of noumena, which, of course, it does and it cannot provide.

Science, the reasoning goes, only provides descriptions, not explanations, the implication being, as I understand, that when these descriptions are expressed in the mathematical language, this is all there is to them and we are not to look further for hidden “explanations”. Once I accept this, hopefully my problem would be solved.. Unfortunately the above mentioned distinction does not solve it. ..

In my opinion, this distinction, which I question, is true and meaningful ONLY if we take the word explanation to mean some kind of ultimate “ noumenal” reality. This is not, however, what I meant by this word.

That science is and should not be concerned with noumena is absolutely true, but this does not mean that explanations are outside its scope.

Higgs’ bosons and the mathematical models or equations supporting them, for instance, are indeed a DESCRIPTION of how reality works, but I can’t see how they cannot be ultimately seen also as an EXPLANATION.

I’m sure that Higgs himself does not consider his hypothesis as anything less than an explanation just as, similarly, scientists must view their hypotheses and the mathematical models conveying them as explanations of some kind, however imperfect they may be.

The primary and distinctive object of science, its ONLY object, is the description of the nexus of causality between phenomena, but inasmuch as this nexus is empirically validated and incorporated into a mathematically described hypothesis, this description becomes, ultimately, an EXPLANATION! Frankly, I can’t see any other way to put it!

Unless I can be proved wrong on this, my problem remains.

I’ll reinstate it briefly.
Most of the physicists’ work is done in the mathematical language, but in the end they are also able to formulate, on the basis of their mathematical constructs, inferences and, ultimately, hypotheses in the conventional conceptual language .

There is a shift between two different levels: the mathematical language and the conceptual everyday language. These languages are seemingly very different. What makes this shift possible? How can concepts be drawn, as they are, from the mathematical language?

Perhaps there is a sort of conceptual interface between the two levels, as if the mathematical language somehow already contained the conceptual seeds..
Kant, it will be remembered, had raised a similar question, although in a different context, when introducing the “schemata of reason” to explain the interaction, in the Understanding, between two entirely different entities: the A PRIORI categories of the mind and the A POSTERIORI sensations of sensible intuition ( experience).

Scientists must somehow be able to tap on this interface if if they are able, as they are, to transpose the mathematical constructs, at least the conclusions, into conceptual language. Could we do the same, without mathematics, if the authors of popular science books provided a "key", as it were, next to the mathematical constructs, enabling us not only to understand the conclusions.but also, as much as possible, the flow of reasoning, its links?

May be from the perspective of SCIENCE such questions can be scoffed at as unanswerable or outright meaningless, They may be relevant though from the perspective of Philosophy of Science,( if we keep in mind the difference between the two, a difference which is frequently overlooked ).

Ittiandro

[Obvious Leo]

How can concepts be drawn, as they are, from the mathematical language?

They can't, and herein lies the problem with logical positivism. The symbolic logic of mathematics as it is applied in physics depends on a conceptual narrative which must be specified in advance. For example Ptolemy conceived of a cosmology which placed the earth at the centre of the universe and he then proceeded to mathematically model his observations on the basis of this assumption. This worked. For 1400 years this model was adequate to predict eclipses etc and it offered a satisfactory explanation for most of the other celestial phenomena which could be observed without a telescope. It was ultimately superseded by Copernicus' heliocentrism but we fall into grave error if we thus assume that the Copernican model was in any sense "truer". It just worked better. After the refinements of Galileo, Kepler and Newton the Copernican model merely worked better because the mathematics were simpler and were able to explain a far larger class of observations. It was Bohr who pointed out that the model-building paradigm is all about "what works" and not about making truth statements about the universe. It's a pity that many of the media tarts in modern physics don't heed Bohr's advice to shut up and calculate.

It might be hard to imagine the horrendous mathematics needed but it would be perfectly possible to send a mission to Mars solely by using an updated version of Ptolemy's famous epicycles. It wouldn't be easy but there is no logical reason why this couldn't be done. However this wouldn't prove that the earth must be at the center of the universe because it is our stories of reality which specify our mathematical modelling of it, not the other way around.

[ittiandro]

How can concepts be drawn, as they are, from the mathematical language?

They can't, and herein lies the problem with logical positivism. d.

Thanks for your input.

You believe that concepts are not inferrable from mathematics, but that, on the contrary, they precede mathematics, as the necessary “ narrative” underlying its symbolic language.

To me, this is true in the case, for instance, of equations such as F=ma which refer to entities like Force, Mass and Acceleration , that are conceptually defined and empirically given,( either directly or, in some cases, inferred indirectly from their effects) . The same applies, I think, also to all the more complex equations of physics of this type.

These conceptually defined objects can be rightly said to supply the “narrative” which, translated into the symbolic language of mathematics, allows to establish the relationships between them , in the form of equations and, ultimately, to formulate laws describing (and why not explaining?) reality.

There are however cases, especially in theoretical physics, where it is hard to see a “conceptual narrative “supposedly preceding and giving life, as it were, to the mathematical constructs.

Indeed, notions like fractals, functors, curved space and the panoply of entities describing it, such as the Riemann curvature tensors and the like, seem to be of a purely mathematical or geometrical nature, drawing their validity more from a leap of the mind than from any empirical, conceptually defined narrative.

What is, for example, the “narrative” supposedly pre-existing Einstein’s field equations in G.R. , beyond the mathematical or geometrical entities which are presupposed in them?

In a way, all this looks somehow like a gigantic piece of circular thinking : we posit ( better “ invent” ) a “ narrative” made of objects, like tensors, curved space, etc , which are beyond empirical grasp (and may well be said, therefore, not to exist.) turn them into mathematical symbols, work out clever, logically consistent equations and then we re-translate the results into hypotheses which supposedly vindicate the original “ narrative” .

Even more challenging than these “philosophical” difficulties, however, is the fact that hypotheses seemingly resting on empirically thin air, like G.R. are increasingly shown to have predictive validity .

This is nothing short of a miracle and my profound respect, even the awe for Albert Einstein, abides.

Perhaps, in the end, we should heed N.Bohr’s exhortation to give up understanding and set what works as our intellectual horizon, the ultimate paradigm, as it were, in understanding the working of science and its interaction with mathematics.

Eugene Wigner once said :

“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning…. It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind's capacity to divine them.”

Perhaps he was right.

Ittiandro

[Obvious Leo]

You believe that concepts are not inferrable from mathematics, but that, on the contrary, they precede mathematics, as the necessary “ narrative” underlying its symbolic language.

Very much so, and this was very much the view of Gottfried Leibniz, a philosopher of mathematics of no minor fame. He used this argument by way of a cautionary warning when it came to an analysis of Newtonian physics, although it would also be unfair to suggest that Newton himself was unaware of this limitation imposed on his own methodology. Niels Bohr and Albert Einstein certainly understood it but the same cannot be said for many who followed in their footsteps. To put it bluntly mathematical physics cannot model what's going on in the universe. The best that it can do is model what the physicist thinks is going on in the universe, which leads to a serious problem of possible confirmation bias.

To me, this is true in the case, for instance, of equations such as F=ma which refer to entities like Force, Mass and Acceleration , that are conceptually defined and empirically given,( either directly or, in some cases, inferred indirectly from their effects) . The same applies, I think, also to all the more complex equations of physics of this type.

Exactly. F=ma is actually a statement of definition rather than the statement of a law of physics. It is the observer who frames his observations in this language of physical "laws". It works perfectly but these are purely epistemic constructs with no ontological currency.

There are however cases, especially in theoretical physics, where it is hard to see a “conceptual narrative “supposedly preceding and giving life, as it were, to the mathematical constructs.

What would you call the spacetime paradigm then? Is this not the conceptual narrative which has underpinned theoretical physics for the past century? With mixed success, I might add, since this conceptual narrative produces models which contradict each other. It's a good narrative for making laser-guided missiles and iPads but precious little use for explaining the universe.

Indeed, notions like fractals, functors, curved space and the panoply of entities describing it, such as the Riemann curvature tensors and the like, seem to be of a purely mathematical or geometrical nature, drawing their validity more from a leap of the mind than from any empirical, conceptually defined narrative.

Einstein himself repeatedly stressed throughout his life that the spacetime model was merely a mathematical representation of a physical model and not actually a physical model itself. Obviously this is true because when we refer to a notion such as a "curved space" we are not making a physical statement but a mathematical one.

"Space and time are modes in which we think, not conditions in which we exist"....Albert Einstein.

Kant would heartily agree with Albert on this point but the logical positivism which passes as an ideology for physics assumes that the cognitive map is synonymous with the physical territory. Since this assumption produces models which contradict each other as well as make no sense we are free to conclude that this ideology is bollocks. The spacetime narrative must be metaphysically flawed.

In a way, all this looks somehow like a gigantic piece of circular thinking :

Bingo. Have a chocolate, mate, because you've nailed the entire problem of physics, in my opinion. The model-building methodology is intrinsically tautologous and in this respect spacetime physics is no different from Ptolemy's geocentric cosmology. You start out with a story and then you tailor your observations and equations to conform to it. We now have a mathematical extravaganza of spectacular virtuosity which can tell us nothing about the universe we live in. The unification model which physics needs can never be found within the narrative it's defined for itself.

Eugene Wigner once said :

“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning…. It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind's capacity to divine them.”

Perhaps he was right.

I completely disagree with Wigner. I see no miracle here. I see the human mind modelling the patterns of order which he observes in nature in whatever way which works the best for him. These models make no truth statements whatsoever about the universe and if the human mind figures out a better way of modelling his world then he can simply chuck all his fancy equations in the bin to join Ptolemy's epicycles. Wigner's is a Platonist doctrine which depends on the notion of transcendent cause and should thus be anathema to a philosopher.