What was a problem with Newton's Principia

Newton's biggest mistake was to deliberately write complicatedly

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In 1987 the physics student Robert Garisto of the University of Chicago discovered a mistake in one of the most influential works of science: the book Philosophiae Naturalis Principia Mathematica by Isaac Newton, published 300 years earlier.

What Newton announced to the world in this book was, so to speak, only justified by modern natural science. It was about much more than "just" the formula for calculating the force of gravity. It was not for nothing that he called the third volume "De mundi systemate", ie the "system of the world". Indeed, it was unprecedented work in its generality.

Universal breakthrough

Newton not only showed that one could mathematically calculate the gravitational force acting between two objects. His really great achievement lay in demonstrating the universality of this force. The same laws that determined the movement of the heavenly bodies in the universe also applied to the fall of an apple or the flight of a cannonball. The same force was responsible for the tides, the shape of the earth, and the sway of the earth's axis. Isaac Newton showed the world that the cosmos is determined by universal laws of nature - and that it is possible to describe and apply these laws mathematically.

For this achievement he is rightly considered one of the greatest scientists of all time. But that doesn't change the physics student's findings from 1987: Newton had miscalculated. To demonstrate the effectiveness of his theory, Newton calculated, among other things, the mass and density of the planets. Astronomical observation data were necessary for this; including the apparent size of the earth as viewed from the sun. According to Newton, this value was 10.5 arc seconds, but he used 11 arc seconds in his calculation.

Undiscovered for centuries

Probably Newton had simply written down a wrong number somewhere on his calculations, or mixed up two numbers. And this mistake probably ended up unnoticed in the final version of the book. That is neither particularly unusual nor reprehensible. You will hardly find a book that does not contain typographical or typographical errors. Other than that, Newton's mistake wasn't particularly tragic. His great discoveries and his impressive description of the cosmos are not influenced by this (and furthermore, thanks to the much better instruments today, we know that the correct value is neither 10.5 nor 11 arcseconds, but 8.8 anyway).

The really remarkable thing about the episode about the physics student who found a calculation error in Newton's work is something completely different: namely, the fact that the error went undetected for 300 years. Even if it is only a minor careless mistake, one should actually assume that such an epoch-making work has been read by so many people over the course of time that all errors had to be noticed long ago.

This is exactly the case with the "Mathematical Foundations of Natural Philosophy" - at least not to the extent that it would be appropriate to the meaning of the work and as it applies to similarly influential books.

Charles Darwin's "Origin of Species," for example, is still everywhere in bookstores, and new editions and translations are still appearing to this day. Even if biology has developed massively since then and much of Darwin's work is out of date, his book is still an interesting and exciting read.

"Little Mathematical Bumblers"

Isaac Newton's theories, on the other hand, are taught in school and at university, but hardly anyone reads the original text of the Principia Mathematica. This is mainly due to the fact that Newton's book is hardly readable and should never be readable. "Those who are not familiar with the basics have a hard time understanding the strength of the arguments or shedding the prejudices they have been accustomed to for many years. To avoid debates that might ensue, I have chosen to to reduce the content of the book to the mathematical theorems intended to be read by those who have already studied the basics sufficiently. " Newton himself writes this in the introduction to the third volume of his work.

Newton was known for not taking criticism. That is why he was reluctant to publish his work and if so, then, as in this case, in a way that scares off as many readers as possible. The natural philosopher William Derham wrote in a letter from 1733 that Newton had told him that he had made his book "purposely tangled" in order to avoid "small mathematical bunglers" from picking on it. Indeed, Newton's work is much more complicated than it needs to be. With the mathematical and physical knowledge that Newton had laboriously acquired, it could have been formulated much more simply. But Newton did not want to be understood - and that is why one of the most important works of science remained (and remains) inaccessible to the vast majority of people for centuries.

Bad example

This is exactly Newton's real error, which this whole story is about, not the simple calculation error (of which there are a few more in his book), but the failure to formulate his revolutionary ideas in a way that accessible to everyone - and not just to those struggling through the confused mathematical language of his work.

Of course, as time has passed, many others have seized the opportunity to make Newton's theories commonplace. But with his disdain for what we call "public relations" today, Newton can only serve as a bad role model for all researchers. The most ingenious discovery is worthless if it is not communicated. That is even more true today than it was then.

We now live in a world that has never been more shaped by the findings of research and technology. We should strive to understand the world in which we live. Failure to understand leads to ignorance, and that leads to a lot of problems. Communication in research is just as important as research itself, which is why it should be just as important in the scientific community. That this is still not the case is just as irresponsible as Isaac Newton's self-imposed incomprehensibility. (Florian Freistetter, May 29, 2018)