Mach: A Model Of The World Is Not The World


Ernst Mach, born in the the mid-1800s, witnessed:  the ascending atomic theory of matter, the proposal of Special Relativity theory, and the beginnings of that wild child of physics, quantum mechanics.  Yet he never much cottoned to these new-fangled notions.  Mach believed that a true scientist did not make speculations that outstripped his evidence.  Since atoms had yet to be observed, since the new Relativity theory was more of an interpretation than a fact, and since the crazy ideas of the nascent Quantum Physics were based largely on mathematical extrapolations and little direct evidence, he preferred to withhold judgment on these theories.

In this, Mach was going very much against the grain… This was the time that “theoretical physics” was taking off– a branch of physics that would ascend to great heights in the coming century.  However, in those days, many universities did not yet even offer classes on so-called “theoretical physics.”  Physics was supposed to be the hands-on science, dominated by experiments and devices.  But those days were quickly drawing to a close.  Physics was moving into the realm of abstraction, and Mach was not altogether happy at this.

Though Mach appreciated abstraction in its proper place, he felt that science was leaning too far in one direction of speculations.  One of the aims of his book, The Science Of Mechanics, is to provide a counterbalance to that mindset-tilting trend.  I want to make “a determined stand against the encroachments of speculative methods,” Mach declares within the pages of his impressive tome.

Mach believed that even the atomic theory as it existed in his day (and remember, there were different views contending with each other then, including J.J. Thomson’s “plum pudding” theory of the atom) was something “provisional” and merely “a mathematical model for facilitating the mental reproduction of facts.”

Mach, fully recognizing that there are two sides to science– the empirical and the logical– said that “my work is for good reason turned toward the empirical side,” and argued against the increasing over-emphasis on the other side, the side of broad abstractions based on narrow evidence and of mathematical interpretations instead of experimental results.  Experiment!, he advised.  Find how one thing affects another!  That is the job of the scientist.

“A competent view of the world can never be got as a gift,” he proclaims.  “We must acquire it with hard work”—  Not by armchair speculations, but by rolling up one’s sleeves and maybe even breaking a sweat.  “Physical science makes no investigation at all into things that are absolutely inaccessible to exact investigation,” says Mach.  “Where neither confirmation nor refutation is possible, science is not concerned.”  And going even further adds, “A thing that cannot be exhibited to the senses has no meaning in natural science.”  No one is warranted to extend principles “beyond the boundaries of experience.”  

We must resist the attraction to over-extrapolate from the evidence in order to provide a fuller and more satisfying explanation of events.  “The highest philosophy of the scientific investigator,” Mach tells us, “is precisely this toleration of an incomplete conception of the world.”  A true scientist does not make up fairy tales he wishes were true or that would help him fill-in the blanks of his picture of the world.  Of that which we do not know, one should not speak.

He extols Newton’s philosophy of “Hypotheses non fingo” (“Hypotheses I do not make”), saying that Newton’s brave willingness to admit his own ignorance and partial impotency in the face of a mysterious and overwhelming universe, “stamps him as a philosopher of the highest rank.”

In Mach’s view, a scientist’s job is to explore the relationships between observables, to see in what way and to what degree phenomena are (or are not) a function of one another.  Explanations as to WHY these relationships exist is not primary… others can argue over such non-provables.  Scientists, says Mach, should be “concerned only with the ascertainment of the interdependence of phenomena.”  Let us leave the metaphysical speculations to theologians and philosophers.  When a scientist concentrates on his core responsibility of observing and reporting, “all metaphysical obscurities disappear.”

One area Mach cites as an example of scientists allowing themselves to be carried away by speculation and by mathematical abstraction is the realm of extra-dimensions.  The case for 5th, 6th, and even higher levels of dimensions stem mainly from mathematical models.

“As mathematical aids,” says Mach, […] “spaces of more than three dimensions may be used” […] “but it is not necessary to regard them on this account as anything more than mental artifices.”  Yes, other dimensions may exist– who can prove that they don’t?– but, says Mach –perhaps with a forbearing smile– “I will not be ashamed of being the last to believe in them.”

“We must beware,” cautions Mach, “lest the intellectual machinery employed in the representation of the world” […] “be regarded as the basis of the real world.”


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