I have defended Kant’s view that mathematics largely consists of synthetics a priori propositions. What sorts of ramifications does this claim have on the natural sciences of our day? Even well before Kant’s time, mathematics was known to be useful in navigating the great sea of Nature; it has been more than a mere raft or lifeboat on which we keep ourselves afloat – with the aid of mathematics we have deployed a full Navy of tools for unraveling secrets and probing her depths. For hundreds of years, by means of the scientific method, we have been able to capture physical phenomena in representation of quantities such as space and time, mass and volume, et cetera, and we have always judged these results beautiful. How many forces have we conquered and brought under our domain? How many mysteries have been solved, how many technologies have been produced, how many wonders have we worked which would make even the great Kant’s head spin? (And how proud have we become as a result? How arrogant?)

Mathematics cannot, however, get us very far without a guiding physical principle or some empirical referent. Perhaps it will surprise us that today physics has run up against an experimental wall. Our largest particle accelerators still cannot produce the ever-elusive Higgs boson, and still less are we able to confirm the outlandish conjectures of string theory, with its bizarre compactified micro-dimensions and vibrating loops of energy, or the completely mysterious dark matter/energy which seems to pervade the stars: existing everywhere yet being seen nowhere. Without the aid of experiment or any physical principle, we have the safe embrace of our H.M.S. Empiricist and readopted 17th Century metaphysics! In fact there are quite a few giants in the field today who remain outspoken devotees and disciples of those great Rationalists, particularly G.W. Leibniz and Baruch Spinoza. With a zealous return to pre-Kantien metaphysics, mathematics has become elevated as never before – its necessity assuming a divine role – being nothing short of the very Mind of God ( I urge you to check out Paul Davies’ book by this same title, which investigates whether the universe itself could be called rational, and what that would mean). Instead of a superficial set of formulae which is merely helpful or useful in parameterizing natural laws, the new theoretical physics says that math has, in a real sense, become the universe – its no longer seen for what it is: representation. In this arena, the mathematical object must somehow assume the role of a physical principle itself, either through appeal to its alleged beauty or through some other metaphysical claim: perhaps by referring to a common transcendent origin, shared by math and the world. Mathematics and scientists alike have long assumed that the necessary quality of mathematical propositions ensures that universality of the subject matter, and this has led them to embrace a Platonic view of mathematics (that the objects or propositions of pure math enjoy an existence independent of our thought). Many theoretical physicists and mathematicians even today hold this romantic notion very dear to their hearts.

However, cognitive science, in recent years, has produced research which resonates more closely with Kant’s conviction: that mathematics has no other origin that our own intuitions. These are not necessarily vague, however. They arise from a very specific embodied experience. According to this theory, we map through metaphor ( a fundamental cognitive operation), a concrete bodily experience onto our conceptual networks. A fascinating book on these developments is Where Does Mathematics Come From? By Gerge Lakeoff and Rafeal Nunez. Case studies cited in this book have shown that while we do come into the world with some spatial and arithmetical capabilities (such as subitizing: being able to recognize the difference between small quantities of up to three or four), almost the entire body of mathematics beyond is extended through the same cognitive mechanisms found in the rest of our conceptual system: image schemas, conceptual metaphors, blending and so on. From geometry to arithmetic, from sets to calculus – every bit of mathematics takes form in our minds through metaphors based on our experience of embodiment: containers, extended spaces and lines, continuous paths of motion, collections of objects, and many others.

Of course, even without the consideration of an embodied mathematics, I still think it rash to believe that purely theoretical enterprises such as superstring theory might actually succeed. Galileo, who famously remarked that the universe was written in the very language of the mathematics, could never accept pure apriorism as a valid approach to nature, “After all, our disputes are about the sensible world, and not one of paper”. According to cognitive science, mathematical intuition and our embodied experience of the world are conceptualized together in the same way, through identical metaphors; it is therefore obvious that mathematics truly is our “language” for describing nature in any sufficiently technical detail (through it is certainly not the universe’s language). It is also not the only language. Remember: there is also the poet of any language. Perhaps these, you will say, are not as useful. But, are they thereby less valuable? My first lesson in the history of metaphysics and natural science: the mathematical overestimates itself.

Still, it is exceptionally amazing claim that the intuitions arising from our own embodiment could be extended successfully to all cast reaches of the cosmos, even into unseen dimensions and down to the most miniscule particle. And it would be nothing short of fantastic if it were true, but nonetheless it remains a metaphysical conjecture, and cannot be used to support any such physical theory. If accepted, this assumption would make possible such theories, but it would not prove them.

Yet I would recommend extra caution when inquiring into wholly unfamiliar entities: black holes, the big bang, compactified micro-dimensions and so on. Such bizarre environments may be severe odds with our own embodied experience. To argue on the grounds of mathematical consistency or elegance alone is to commit a logical fallacy. We cannot say that a theory demands such and such symmetries, and therefore it must be so; this is to argue circularly, because such “demands” arise only from the fact that our mathematical intuitions are grounded in a specific embodied understanding – we simply cannot cognize it by any other conceptual metaphors. If cognitive science is on the right track, then essentially they will have resurrected Kant’s position, which means only that appearances will always and everywhere be brought under the laws of our intuition ( which, as it turns out, is determined by our embodied experience) – not the other way around.

Thus embodiment presents a challenge to theoretical sciences, because to affirm a theory about unobserved entities on purely mathematical grounds is to assume that they possess symmetry with our own experience. Is mathematics really capable of describing the birth of the universe? Careful: allegedly the entire space-time continuum as it is extended today was crunched into one singularity! The density and temperatures within such an object (if it can even be called an object – I don’t think it can be) is unfathomable. Our intuitions are almost useless in this scenario; time itself can hardly even be said to exist at this point (space an time were born with the expansion of the cosmos) and causality therefore breaks down. It is difficult to say whether the laws of physics, as they stand today, would be the same under such extreme conditions. I will certainly grant that humans may be capable of mathematically describing the big bang – if and only if they could have an experience of it!

I believe we are creative enough creatures to observe even the most bizarre phenomena and yet find a way to adapt our conceptual metaphors to fit the data (quantum mechanics is good evidence of this). But the birth of the cosmos is not a phenomenon anywhere to be seen or experienced and cannot become representation as such. Hume. The staunch empiricist, warned against speculations regarding the origin of our universe, humorously remarking that creation is one experiment which cannot be reproduced!

Cosmology has high hopes, however, of one day being able to look so deep into space that we might witness the creation event as it actually unfolded! After all, looking out is in fact a looking back, through time. As it stands, we can already capture images of the forming cosmos just 300,000 years or so after its birth. There is a small chance that cosmologist may produce the first concrete evidence in favor of (or against) the new particle theories, such as superstrings. Still, I choose to remain skeptical, if only for some silly philosophical reasons. Although I suppose we could hold out hope that the Platonists are correct- then perhaps it will be only a matter of time before someone clever enough gets a sufficient glimpse of the right mathematical object or Form to solve the theory of everything. Sound silly to you?

Well, go look it up for yourselves: within the last decade or two, a small library of popular literature on the subject has suggested that leading physicists believe this very same proposition. It is the hope of discovering a unique theory of everything. I recommend Brian Greene, Michio Kaku, or Paul Davies for further reading. Others, who have come to recognize the futility of signaling our one solution among the hundreds which string theory suggests, have instead adopted the (no less bizarre) view that our universe is but one in a series of infinitely many – that each solution to the string equations represent a valid and actually existing universe among a vast sea of them. This is the multiverse theory. For this account, I wholeheartedly recommend Leonard Susskind’s The Cosmic Landscape, which also contains food commentary criticism of the “anthropic principle”-a controversial idea in science today: the claim that this particular universe must have been selected from among the vast number of possibilities (or developed in such a way) so as to support intelligent beings. If you read up on what “scientists” are doing today, you will undoubtedly find yourself exclaiming, “Wait… How is that any less speculative than pure metaphysics?” The only answer I have been able to extract seems to be: because, unlike metaphysics, it is an exercise in pure mathematics! Great, if you happen to be a Platonist. But should cognitive science pronounce the last word on the ontological status of these objects… physicists may have to reevaluate their newfound method, or even abandon it altogether!