Let us examine a bit more closely Synge’s picture of physics as

*bricolage*, where theories have the intellectual status of just-so stories, and are really little more than pragmatic techniques, or tools -- Newtonian mechanics and relativistic mechanics each useful in its own sphere, like screwdrivers and spoons, but of little interest in their own right. Now, this is not to knock the status of a toolkit -- my respect for competent carpenters and electricians borders on reverence -- but fundamental physics is not like that.
Synge presents the Newtonian view as having not been replaced or refuted by relativity; it rules as before in its own realm. Newton’s good for some things, Einstein for others, and Wiccan no doubt for others still. But this view assumes a confusion. For it is not the case that Newtonism and relativity are independently valid in their own way but incompatible; rather, Newtonism is the limiting case of relativity, in a way very familiar in mathematics; its continued use in everyday life is simply a calculational convenience, a shortcut. To continue the tool metaphore: Einstein and Newton are not like screwdriver and pliers, but like a hammer, and an old shoe

*used*as a hammer, good enough for the task at hand.
Furthermore, it is a good thing, not a bad thing, when initially separate paths converge. If you only know one way to climb a thing, perhaps it is only a Potemkin mountain -- a paper-maché façade, hollow behind the north slope. It is quite a relief -- and an ontological ratification -- to meet another mountaineering party that has scaled up the other side.

The reader may be familiar with the story of how Schrödinger and Heisenberg separately found Rome by different roads. Let George Gamow tell it, in

__Thirty Years that Shook Physics__(1966), p. 3:
The simultaneous appearance of Schrödinger’s and Heisenberg’s papers in two different German magazines … astonished the world of theoretical physics. These two papers looked as different as they could be, but led to exactly the same results concerning atomic structure and spectra.

We are, in hindsight, not overly surprised by this, since by now we most of us accept that there is something there at the quantum level, something real, something other than subjective, to be described. It is describable by two quite different mathematical approaches, much as our peak may be scaled by walking up the north face or rappelling up the southern cliffs. Nor is such ‘duplication of effort’ a waste of time, for in this instance, not only the factual success, but even the approaches themselves retained their usefulness -- for determining energy levels, Schrödinger’s wave mechanics was calculationally more convenient; and Heisenberg’s matrix methods had the edge when it came to calculated the intensities of the radiated frequencies. Or, alternately, P.A.M. Dirac,

__The Principles of Quantum Mechanics__(4^{th}edn. 1958), p. viii:
Quantum mechanics … is known under one or other of the two names ‘Wave Mechanics’ and ‘Matrix Mechanics’, according to which physical things receive the emphasis in the treatment, the states of a system or its dynamical variables.

And (p. 115):

The Schrödinger form is the more useful one for practical problems, as it provides the simpler equations. … Heisenberg’s form for the equations of motion is of value in providing an immediate analogy with classical mechanics.

Or again (R. F. Streater & A. S. Wightman,

__PCT, Spin & Statistics, and All That__(1964), p. 4):
Throughout this book, states will be described in the Heisenberg picture of quantum mechanics. The Schrödinger picture is much less convenient for the description of a relativistic theory, because it treats the time coordinate on a very different footing from the space coordinates.

And:

P.A.M. Dirac,

__The Principles of Quantum Mechanics__(4^{th}edn. 1958), p. 311:
The Schrödinger
picture is unsuited for dealing with quantum electrodynamics, because
the vacuum fluctuations play such a dominant role in it. … They get
bypassed when one uses the Heisenberg picture, and one is then able to
concentrate on qualities that are of physical importance.

Dr. Matrix |

Dr. Wave |

Approaching an abstract but genuine reality from two different theoretical complexes has its counterpart in different experiments, or different means of calculation, strengthen each other when they arrive at the same result. Thus Einstein, in his annus mirabilis of 1905, when not inventing Relativity, found it worth his while to “develop theoretically three independent methods for finding Avogadro’s number.” (Abraham Pais,

__Subtle is the Lord__(1982), p. 55.) It was worth his while because, independently of our endeavors, this number is indeed*there*.
Summarizing: For epistemology, the fact that two or more radically different approaches each manages to describe the phenomenon of interest, reassures us that we really do have our arms around this thing. The lesson goes over, I would submit, in cases where what is being described is nothing so tangible as an atom (which Rutherford reportedly saw in front of his face as plainly as a spoon), but rather a four-manifold, or a simple Lie group.

~ ~ ~

Afterword.

I recently happened across the following curious passage:

The algebras G_2, […] E_8 are called

*exceptional*. In 1945, Chevalley remarked that the existence of these algebras is**a brutal act of Providence**which we must accept blindly. Perhaps this should be revised today to assert that the source of these algebras is the wisdom of the Deity in allowing the Cayley numbers to exist.
-- Irving Kaplansky, “Lie Algebras”; in: T. L. Saaty, ed.

__Lectures on Modern Mathematics__, vol. I (1963), p. 126
~ ~ ~

There’s one further type of brane
in M-theory that is really
surprising. This brane is

**the edge of spacetime**. … The photons at the edge of spacetime participate in supersymmetric**E**gauge theory._{8}
-- Steven Gubser,

__The Little Book of String Theory__(2010), p. 95
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