Gottfried Leibniz: His crazily intriguing metaphysics and the breadth of his grand vision

The great philosopher, mathematician, physicist, universal genius and all-around badass was centuries ahead of his time – how his ideas helped to shape my own fictional mythology

J. Wes Ulm

Spoiler Potential: Mild-to-Moderate

Since Leibniz’s metaphysics did inspire a good deal of the core mythology in Echoes of the Mystic Chords and its successor novels, there is some potential for spoilage in regard to the themes that are introduced especially in Books 2 and 3. That being said, since these are novels and works of fiction after all, Leibniz’s concepts are worked intricately into the plot and its suspense rather than laid out as topics in a treatise, so their presence is subtle rather than overt. If you’re sensitive to any spoilage on the story, you may want to halt here and hold off on reading until after you’ve started on Book 2 in the trilogy. Otherwise dive right in, though as an FYI, this particular pseudo-interview does get a bit technical and historical about three questions in.

Q: Wes, throughout your pre-publication releases you’ve sprinkled in references to the mathematician and philosopher Gottfried Leibniz as an inspiration, and Echoes of the Mystic Chords after all is Book 1 of The Leibniz Demon Trilogy. Most people, if they’re familiar with Leibniz at all, connect him to the invention of calculus, which (considering all the tortures so many of us endured in that class) hardly seems like inspirational fodder for a thriller/mystery novel.

Wes: Leibniz was That Calculus Guy, yes – more specifically, the innovator of the form of calculus (with its fraction-like derivative statements and integral expressions) that engineers, economists, scientists, and just about everyone else uses today. But Leibniz was more than this, much, much more. It was Leibniz who essentially came up with the concept of the function and variable that are ubiquitous from the first day of Algebra I in middle school, so in essence just about all the math we learn today, not only calculus, taps into the formalism and structure that Leibniz pioneered. He was a ridiculously prolific inventor, that rare bird who’s as nimble with things practical and mechanical as he is with all things theoretical and conceptual. Leibniz was quite possibly the world’s greatest polymath, an original genius with imaginative contributions in everything from library science to law, diplomacy, and political strategy. Yet all this is merely the appetizer, because Leibniz’s mind-blowing coolness and badassery emerge most markedly with his philosophy and his seminal role in the foundations of computer science and technology. Moreover, his metaphysics opens a portal into some thoroughly mind-blowing explorations of ancient riddles involving the soul, the nature of existence, and consciousness (which, for the sake of spoiler-avoidance, I won’t be delving into much here).

Q: For the benefit of anyone taking a cursory browse at this essay, could you distill whatever made Leibniz’s philosophy so intriguing – and inspiring – down to a short version before digging deeper?

Wes: Here’s the abridged version, or my best stab at it: Leibniz’s metaphysics was all about uncovering a kind of universal language or logic at the heart of how things in our world interact. And Leibniz wasn’t thinking small: To him, this “universal medium” would cover not only the back-and-forth between inanimate particles but also cells and biological systems, all the way up to people and their thoughts and emotions. Leibniz was a Rationalist at heart, and he believed that both interlocking physical systems and human interaction were characterized by meaningful logical structures that had the capacity (almost magically, based on what they knew in Leibniz’s day) to evolve and innovate. In fact, Leibniz posited that at the core of the natural world were little quanta called “monads” – in essence, “atoms of logic and information” that, governed by logical rules (themselves feeding back and evolving) would give rise to the physical world as well as the information-rich tapestry we see today. Leibniz’s metaphysics was on the one hand well-defined and semiotically precise (I’ll get to what this means below), but on the other full of richness, surprise, imagination, creativity, even a sense of magic when you delve into it. This is necessarily a simplification of what he was about, but when you take stock of Leibniz’s discoveries and ambitions, you enter a world teeming with fertile material for fiction and other creative efforts, one that links up with dozens of fields and phenomena. As I hinted at above, Leibniz’s philosophy also led to specific, practical developments in many other realms, including the nucleus of what we today call computer science – on both the hardware and software sides.

Q: Computer science? Hardware and software? But wasn’t Leibniz hanging out around, oh, the 1600s or so? Seems a bit early for a computer pioneer.

Wes: The 17th century was a remarkable little high-water mark in the history of computing, and a bit of a historical anomaly. It hosted three way-ahead-of-their-time geniuses who laid the foundations of computers – which are logical manipulation engines at heart -- that weren’t really built upon until two centuries later, in the mid-1800s. Leibniz’s countryman, the German engineer Wilhelm Schickard, and especially the French physicist and mathematician Blaise Pascal (a universal genius and polymath in his own right) were the first to build calculating machines and arithmetic engines, the precursors of modern desktops, laptops, and tablets. Pascal’s’ device was sheer, 200-proof awesomeness in its trailblazing innovation, and it inspired Leibniz to build his own calculating machine – the so-called Stepped Reckoner – which was remarkably advanced for its own time and well into the future..

Q: But you’re talking about the hardware here. You were saying Leibniz was also a “proto-computer scientist” – an early software engineer of sorts. Why?

Wes: Guess we’re starting in on the “long version” of Leibniz’s philosophy here, but to dig deeper into the mind-blowing things he was getting at, it’s essential to understand just why he was at the forefront of innovation in so many distinct domains, computing being one of the most significant. As the renowned computer scientist and author Martin Davis has eloquently put it: Computers are “engines of logic,” in fact the very field of computer science itself was an outgrowth of mathematics, specifically the sub-discipline of mathematical logic. Davis’s own brilliant book on the history of computing – The Universal Machine (can’t recommend it highly enough) – kicks off with Leibniz as the starting point for what we now call computers and computer science.

Q: How so?

Wes: Think about it this way. The modern computers and data networks we use all the time today, both the hardware and the software, ultimately stem (directly or not) from answers to an esoteric-sounding question in mathematical logic called the Entscheidungsproblem, or “decision problem.” It was posed by an early 20th-century mathematician named David Hilbert, and Hilbert’s work was closely linked to investigations by other mathematicians and logicians – Georg Cantor, George Boole, Gottlob Frege – into the foundations of mathematics and logical thought itself. There were parallel developments in early computer hardware by Jacquard, Babbage, and Lovelace, but in any case, all of these innovators and their incremental progress trace back to the pioneering work of a single towering figure from the 1600’s.

Q: Gottfried Leibniz.

Wes: Precisely. Leibniz was the first to comprehensively appreciate – and formulate – the mini-universe of concepts at the core of systematic logical reasoning and evaluation, and thus of computation (and the extra problem-solving mojo it gives us) as a discipline. Things like truth tables and what we’d today call algorithmic workflows and automated problem-solving, as well as functional programming – a natural offshoot of Leibniz’s mathematical investigations into functions and variables – and even binary code as a keystone of the computation process.

Q: Binary code? All the way back in the 1600’s? How did Leibniz stumble onto that?

Wes: Leibniz’s fascination with binary arithmetic stemmed from his parallel engagement with the Chinese I Ching and yin-yang notions – a classic example of the non-linear, discipline-hopping creativity that framed so much of his work. The upshot is that these meandering investigations led Leibniz to propound the conceptual nucleus (logical progression, workflow, formal axiomatic systems, semiotics) of what we today call computer software and information theory. (The books by Martin Davis and Gregory Chaitin – as well as an insightful journal article by Daniel R. Lande – do a great job of laying out and explaining this history.) For now, the take-home message is that Leibniz was the original architect of much of the conceptual infrastructure that underlies systematic logical processing and its practical realization in the form of computers. Especially through his semiotics, which proved crucial in laying the groundwork for better computational devices and mathematical advances. This was pivotal both for Leibniz’s watershed work in computational logic and – where my interest was stirred – in his astonishingly imaginative metaphysics.

Q: Semio – what?

Wes: Semiotics is a sub-discipline of philosophy, linguistics, and logic that focuses in on signs and symbols, what they mean, how they’re interpreted, and how they’re manipulated. (Charles Sanders Peirce, for those who are interested, was perhaps the most accessible philosopher to specialize in this.) This may seem pretty dry and esoteric at first, but in fact the seeming magical powers of our computers today derive largely from their ability to interpret and manipulate symbolic logic. For those with a comp-sci background, “semiotic manipulation” is basically what Alonzo Church and Alan Turing were getting at with the lambda calculus, the Turing machine, and the Church-Turing hypothesis, all bedrocks (from the 1930s) of modern computer science. As a quick-and-dirty explanation, their work was geared to more-or-less describe what any computer is at heart: a machine for inputting, processing, and manipulating symbols based on (programmable) logical rules. Church and Turing’s work was based on the groundbreaking discoveries of Kurt Gödel on the phenomenon known as recursion (a powerful operation which in effect bridges mathematical logic to the “guts” of modern computers). Gödel – an original genius in his own right and basically the father of modern computer science – in turn based his own discoveries on previous work in formal logic by Frege, Hilbert, Boole, Carnap, and Cantor, and all these strands, in turn, lead right back to Leibniz.

Q: To Leibniz’s semiotics?

Wes: More than that – to Leibniz’s grand ambition, something that has tremendous implications for us and our society far beyond even the enormous impact of modern computers. I was hinting at this in the abridged version above, but this is part of what makes Leibniz so intriguing and forever relevant – even in our modern world, where if anything his significance is even greater. Leibniz’s metaphysics was intimately bound up in his semiotics. More than any other mathematician, physicist, or logician, Leibniz placed a heavy emphasis on high-precision signs, symbols, and formalism, with a clear illustration of the formal rules governing the manipulation of those signs and symbols. It’s one of the reasons that scientists and engineers today use Leibniz’s formalism in calculus rather than that of Isaac Newton (who independently developed calculus at about the same time) – the flow of logical arguments in Leibniz-speak is both easy-to-follow and rigorous.

Q: But how does this semiotics, and Leibniz’s metaphysics more broadly, relate to the physical world – the things that we encounter and take in outside specialized areas like math or computer science?

Wes: Leibniz quickly grasped that physical phenomena and even human interactions could also be explained on the basis of these subtle interactions involving such signs and symbols – of codes, in essence, filled with layers of underlying significance. This notion may seem subtle and more than a little arcane, but in fact it has all manner of mind-teasing ramifications. In effect, this perspective allows one to recapitulate phenomena we generally conceive of as strictly material or mechanical – even physical laws or processes – in terms of the meaningful interfacing of information-bearing “packets” of logic. This is at the heart of all kinds of intriguing investigations in areas outside of computer science per se, such as biosemiotics (reformulating biological interactions in terms of Peircean semiotics, one of my own professional interests) as well as digital physics and physical information theory.

Q: Digital physics? Physical information theory?

Wes: They’re sub-disciplines merging physics, computer science, and mathematical logic, pioneered in the mid-20th century by Konrad Zuse, the inventor of the modern computer. Zuse was directly influenced by Leibniz in his grand venture of building the Z1 through Z3 models (the first Turing-complete programmable computers) in the late 1930s, as well as in Zuse’s establishment of the first programming language (Plankalkül) and his implementation of binary switches. Zuse, like Leibniz, embraced the challenge of computation from both the hardware and software sides, but even more intriguingly, Zuse also appreciated the significance of Leibniz’s concepts and semiotics far outside the realm of computation itself.

Q: In what way?

Wes: To restate the point above about Leibniz’s semiotics – he had a conception of the physical world, with its physical laws and phenomena, as expressible equivalently in the form of logical laws and relationships. Zuse then took up and ran with this idea three centuries later, to formally conceptualize nature itself as an evolving web of these logical relationships. In turn, Zuse’s Leibnizian trailblazing has been taken up by a handful of modern authors, such as Stephen Wolfram, Lee Smolin (applying it to questions of quantum gravity and other domains of theoretical physics), and Gregory Chaitin (with a focus on computational and algorithmic complexity). Their work, collectively, provided a wealth of material for me in crafting the mythology for Echoes of the Mystic Chords and the trilogy. That’s because things get really interesting when you take another leap and extend these Leibnizian-Zusian notions even further, from the realm of physical processes and into the deep well of human experience, thought, and emotion – prime thematic territory, across millennia, for literature and art in general.

Q: But it would seem like Leibniz’s work on a code of formal logic, governed by specific rules, would be restricting rather than conducive to creativity and imagination.

Wes: Just the opposite, at least in the way that Leibniz conceived these formal structures and the semiotics he devised for them. As these “codes” underpinning our physical world interact with each other and rearrange themselves, they give rise to higher structures, cognition, and eventually a phenomenon we’d recognize as creativity. That’s the beauty of Leibniz’s conceptual umbrella, the way it can flexibly stretch to cover emergent macroscopic phenomena and even human thought as seamlessly as hard-core mathematical logic and physics. Leibniz was undoubtedly focused intensively on precision and rigorous definitions, which are crucial for calculus and the mathematical terms that Leibniz specified in his work. But to him, these weren’t rigid, immutable, dogmatic properties – they were capable of recursive change and evolution.

Q: “Recursive”?

Wes: Recursion, in the 25-words-or-less version, essentially means that a function, statement, or process feeds back upon and alters itself. While recursion has a basis in logic, it also carries a sort of mystical quality to it since it’s a feature of our natural world that allows complexity to arise from simple structures. (Recursion was the bread-and-butter of Douglas Hofstadter’s book Gödel, Escher, Bach – about how consciousness arises from unconscious components in the brain, and how computer science, mathematics, and music are linked by recursive processes.) As I alluded to above, recursion is at the heart of the logical motors that power our modern computers. In fact the Turing Machine and lambda calculus, in computer science, are simply tangible models of mathematical expressions called recursive functions (as Gödel detailed a few years before them), and it was Leibniz who first developed the notion of logical structures with the power of recursion. Leibniz understood that, in his formal system, the logical rules governing the interaction of phenomena didn’t have to be set in stone – they could grow and evolve themselves based on feedback from the very systems they were governing. This in turn would lead to ever more novel and innovative structures, including what we call emergent properties – totally new features of a complex system that can’t be conceptualized at simpler levels.

Q: But how specifically does all this food for thought from Leibniz get transformed into a work of fiction? What’s the creative inspiration, the kindling for the story as it were?

Wes: Leibniz’s grand synthesis was ambitious. To expound on what I was saying above, Leibniz was interested in an “idealized formalism” – a kind of “fundamental language of the world” if you will – that would also encompass biology and even psychology, up to the level of human thought and emotion. Again back to the computer example: Remember that even the coolest, most sophisticated things you do on your computer, like running graphics software or playing 3-D videos, ultimately arise from the manipulation and interaction of symbols in some computer program somewhere. The content and output of this program, in turn, are expressed in the binary code that actually runs the computer’s circuits. To Leibniz, there was an underlying “code” that went even further, uniting natural phenomena and human thought and cognition. Our minds and our senses perceive and filter the physical world in “macro” terms, using broad-brushed conceptual patterns like shapes and colors – what philosophers would call “Platonic universals” more-or-less – to measure and interpret what’s around us. But to Leibniz, both the world around us (the object of our perceptions, in Kantian terms) and the cognitive machinery of our brains (the subject taking in this information) are built from the same logical scaffolding, which in turn is what underlies space, time, matter, energy, and physical laws and processes themselves.

Q: Whoa! Sounds pretty heavy-duty.

Wes: But also elegant – and most importantly for Echoes of the Mystic Chords, full of storytelling potential.

Q: Why do you say that?

Wes: In turns out that if you play around with Leibniz’s ideas enough, and join them to both his philosophical successors and other treatments of metaphysics – let’s just say you get very interesting results. Leibniz himself didn’t go in this direction, but his elegant concepts and logical innovations contained the seeds of a “complete philosophy” – a broadly encompassing metaphysical system that serves as a launching pad for fruitful investigations into ancient questions. And I mean ancient – longstanding puzzles involving life, death, human thought, civilization, art, and other profound mysteries. Stated another way: Leibniz’s philosophical system, when you ponder its implications, can function on some level as the kernel for a narrative that’s fascinating and original in the context of the “big questions” we usually associate with religion or the ancient philosophies of Plato, Aristotle, or the Buddha.

Q: With all his pioneering investigations, how come we haven’t taken in more of Leibniz’s non-mathematical ideas and discoveries as part of a general education?

Wes: Because Leibniz drew a rather lousy historical lot, which makes his mind-boggling exploits all the more amazing. Unlike Leibniz’s philosophical successor Immanuel Kant (who united Leibniz’s Rationalist metaphysics with Hume’s empiricism), Leibniz never held an academic post that would have availed him of the career and financial security to concentrate on all his marvels. Thus Leibniz never published a series of self-contained volumes – like Kant’s Critiques – which would have made his findings more compact and accessible. His work was more fragmented, often appearing in the form of scattered essays and letters. Even more daunting, Leibniz had a very busy day job – and a night job, for that matter. He had to compile the genealogy for Ernest Augustus (a duke and Elector of Brunswick-Lüneburg), who provided Leibniz with some patronage, while also doing mission-critical work in law and diplomacy. (Leibniz’s academic training was in law, and to his peers and contemporaries, he was mainly known as a highly astute lawyer and diplomat.)

Q: Small miracle that Leibniz was able to do so much in math, physics, and philosophy then.

Wes: I think this if anything makes Leibniz more relatable to those of us today. Too often we’re served up bios of historical figures on a small platter, with their work and achievements seeming to emerge from a privileged perch on Mount Olympus, without the real-people-problems the rest of us have to deal with day-by-day. It’s true, many historical figures were indeed royalty, nobility, or aristocracy, with lots and lots of inherited or family wealth that freed them from the exhausting demands of a day job and allowed them to focus on what made them so well-known historically. (Byron and Montesquieu had this aristocratic background, and to be honest, it’s perhaps a good thing they did considering all the cool and interesting things they achieved.) But Leibniz never enjoyed such privilege. He had day and night jobs like the rest of us schlubs, had to earn a living and hustle for whatever he could. Again, it makes him accessible and relatable in a way many comparable historical figures are not.

Q: Was Leibniz also naïve? From what we learned in school, Voltaire based his ridiculously Pollyanna-ish character “Dr. Pangloss” in Candide on Leibniz, didn’t he?

Wes: Yes and no. I’m a major fan of Voltaire and his works, but Leibniz has been one of the most laughably misunderstood philosophers in history, especially with regard to what’s called “Leibnizian optimism.” This was lampooned (in the words of Dr. Pangloss) as “everything is for the best in this best of all possible worlds,” but this definitely was not what Leibniz was getting at, not in the slightest. Leibniz’s optimism was in fact a quite rigorous statement, comparable to what we’d today call “the weak anthropic principle” in some ways – that the presence of phenomena as we recognize them on earth must require an extremely rare and extraordinary collection of factors and initial conditions. (These and other basic Leibnizian tenets have been confirmed by modern science – remarkable considering that Leibniz was advancing them a solid 200 years before the theory of evolution.)

Q: So was Leibniz not optimistic by contrast?

Wes: No, I wouldn’t say that either. I’d say that Leibniz overall was optimistic and even idealistic (in both the philosophical and general usage senses), but he wasn’t the type of guy to wear rose-colored glasses. Remember, Leibniz was born in the midst of the Thirty Years’ War of the 1600s, which was a hell-on-earth even worse than the World Wars of the 20th century. He wasn’t naïve to suffering and misery, and he could be a hard-ass with an acid sense of humor when he needed to be. Remember, the guy had to navigate some tough lines of work, and had to be up-to-speed as an attorney and diplomat, both being functions in which he performed quite well.

Q: Last question: How did you learn about Leibniz in the first place, especially enough to be inspired to write a trilogy?

Wes: For this I owe a lot to the astrophysicist Lee Smolin, and the computer scientists (and contemporary logicians) Gregory Chaitin and Martin Davis, all of whom I referenced above. As I mentioned in the other document detailing the origins of Echoes of the Mystic Chords, I had Smolin’s and Chaitin’s books with me on that day in Taiwan, in October 2007, when I had the epiphany that eventually led to the trilogy. In their and other books and articles I read (including Davis’s), many of them chewing on pretty technical fodder, Leibniz’s name kept cropping up over and over. Naturally I was intrigued at this figure who seemed to have such a far-reaching influence on so many distinct and interesting fields, and it was from there that I realized the scope and ambitions of Leibniz’s metaphysics and general trailblazing.