R.C. Smith

Over the summer break I set myself the task of reading through a fantastic recently published edition of the *Principia*. It has so far been immensely enjoyable. And, in the future, I do not doubt that I will dedicate an entire series of blog posts or essays to my working through Newton’s *Principia*.

In the meantime, with each new page I’ve been reminded of my personal appreciation for Newton. Growing up, Sir Issac Newton was one of my idols. I remember my first introduction to the name, Newton, when I was no more than six or seven years old. It was in science class and the initial introduction was basic. It was left simply that Issac Newton was an important historical figure, who contributed much to science. In that vein, the presentation was no different than when I was first introduction to Benjamin Franklin, Thomas Jefferson, or Galileo Galilei. Looking back, I wish there was more emphasis in the curriculum to explore these figures and the openness of scientific inquiry shared among them (and other notable historical thinkers). There are very basic lessons, I think, that can be learned about the force or principles of the modern scientific endeavor in the study of some of its most significant figures. One learns that it is not just the individual, himself, but an entire history of human thought and equiry leading up that eureka moment. But, importantly, at a young age there is much inspiration to be gleaned from the story of Newton, Galileo, Maxwell, Faraday (one of my favourite biographies), Friedmann, Wigner, Einstein, and on and on. They all evidence an energy and passion for discovery, and arguably also an incredibly creativity in thought. Important values=s in early education, I would be inclined to argue.

I think it is plausible that most scientists, whether your a young student like myself or a seasoned physicist or biologist or whatever, experience one or two “wow!” moments early on that help foster an interest in the pursuit of science. Mine directly relates to Newton.

Aside from revolutionizing physics by unifying all of mechanics in three laws of motion, my eureka moment (if I can call it that) relates to Newton’s discovery – or inventing – of calculus. The formulation of the law of universal gravity, the eventual development of newtonian field theory – these are all amazing feats in the history of human thought. But it was Newton’s discovery of calculus – needed to solve the equations Newtonian mechanics produced – that really cemented my love for both mathematics and physics. And I suppose, in a very direct way, this existential moment of all embracing and inspiring “wow!” that struck me when I was younger also owes a debt to Gottfried Leibniz.

Why? Well, admittedly, my introduction to calculus was first through Newton; but it was the eventual realization, as I frankly sought to piece together the history of the development of calculus and its first principles, as well as that of classical physics, where two profound facts hit me in a way that I’ll never forget. Understanding that the development of calculus as well as the concept of vectors was, in a deeply important way, absolutely vital to the mechanics of the time, when one studies the history of mathematics ideas in and around this period there is a very coherent, and certainly observable, logical consistency in the build up to the final result. Indeed, and to preface the following with one more remark: it was intentional that Newton’s inventing of calculus was described earlier as a “discovery”. In short: it is understood given the demands of the direction of the new mathematics that had emerged, that without calculus and vectors, the very idea of instantaneous velocity, which we kind of take for granted today, would have been very difficult. We had arrived at a point, in the history of mathematics and more broadly in the history of human thought, that what was required was a mathematics of change – a mathematics that account for change. This was demanded by Newtonian mechanics. But the “wow!” moment, if you will, is in how not only did Newton discover calculus and its relation to the scientific study of nature. Independent from Newton, Gottfried Leibniz also developed calculus! And together, they are both responsible for one of those special and key historical moments of realization, where, in the study of the history of science and of ideas, one is confronted with the special relation between the fundamental disposition of the systematic human pursuit in maths and science and the study of Nature.

That both Newton, given the demands of his mechanics, and Leibniz at a similar point in human history, both discovered calculus suggests that calculus was very much the next logical step.

Now, depending on where one sits with regards to the debates around nominalism and platonism, and the epistemological arguments about the knowledge of abstract objects, this realization may be met with great intrigue or a simple shrug. In the case of the latter, if you don’t think numbers exist, that they do not form an integral or constituent part of object reality, you might simply state that calculus needed to be invented according to the logic of the system within which modern thinking operations, and thus too that all mathematics is human invention. But, if you’re like me, and you see mathematics as a constituent part of reality reaching all the way back to the Pythagorean argument, then the development of calculus is nothing short of awe-inspiring, as it was not so much the need of invention, but the next step in the study of the nature of reality. Indeed, it becomes all the more arousing if one considers Archimedes method of exhaustion to calculate the area under a parabola (anticipating modern integration) as far back as 287–212 BC.

There are many similar events throughout the history of physics and mathematics, where the same solution, conclusion or development was arrived at by independent parties. Likewise, in physics, one could also add the number of times theory has predicted precisely future measurements (beyond the experimental capabilities of the time), or when two independent theories arrive at the same objective outcome. Physics is incredibly rich in inspiration in this regard. Whenever I come across new examples, it always deepens for me the idea of the objective.

As Albert Einstein once remarked, ‘the idea that truth is independent to human beings is something I cannot prove but something I think is basic’. ‘The problem’, stated Einstein, ‘is the logic of continuity’. Max Tegmark, celebrated cosmologist, would even go so far to say that mathematics* is* reality. And this seems to be the emerging consensus, but I’ll save the arguments toward those ends for another time.

In closing, it was in 1665 that Newton began to develop his ideas on calculus. ‘Fluxions’, as he called it, related very directly to Newton’s early study of the laws of motion. Though I know the textbook version of Newton’s Laws of Motion and Newtonian mechanics like the back of my hand, I am only now starting to read through the *Principia*. My drive toward first principles and has me eager to read *Opticks* and *Methodis Fluxionum *(calculus), the latter published posthumously.

As arguably the world’s greatest physics, to which the likes of more recent modern heroes owe like Maxwell or Einstein owe a great debt, Newton was known as a master scientists. What’s most fascinating about the man, since we’re on the subject, is that he also had an extremely energized private interest in religious and mystical pursuits. Apparently, he produced a thousand page manuscript on his own theological studies, as well as a significant collection of thoughts on things like alchemy. But in public, from what I understand, he would not partake in such wild speculation, which leaves me to wonder whether there was ever a tension between his standards of scientific practice and personal orthodoxy. It reminds a little bit of perhaps one of the more famous stories about Einstein.

I would say, personally, that Einstein is the most creative, critically inquisitive and challenging scientist to have existed. His entire career was based on challenging the status quo. But even Einstein suffered from a personal moment of fallibility with respect to the human vulnerability to orthodoxy. As Max Tegmark (2014, p. 43) recites:

Einstein himself realized that a static universe uniformly filled with matter [Newton’s laws] didn’t obey his new gravity equations. So what did he do? Surely, he’d learned the key lesson from Newton to boldly extrapolate, figuring out what sort universe

didobey his equations, and then asking whether there were observations that could test whether we inhabit such a universe. I find it ironic that even Einstein, one of the most creative scientists ever, whose trademark was questioning unquestioned assumptions and authorities, failed to question the most important authority of all: himself, and his prejudice that we live in an eternal unchanging universe.

To his credit, when further evidence emerged, Einstein admitted that adding this extra term in his equation to account for a static, eternal universe was his greatest blunder. It shows his remarkable character as an iconic scientist to admit to such a moment of prejudice, and critically analyze challenges toward that prejudice in an open and rational way. I like to think that, with all we now know, in our current moment of history, Newton’s response to challenges of his personal beliefs would have been the same.