Ok, I did that philosophically bad thing again and headed to Buffalo Wild Wings with my friend. Bad in that it always turns into several hours worth of rather exhausting philosophical/rhetorical discussions. Good, though, in that I always seem to get a blog post out of it.
The other night we ended up spending a lot of time on his subject of choice – mathematics as a metaphor. And it struck me that this could be a solution to an idea I’ve been grappling with for a little while. That is, the overlap that often exists between science and literature (or, more exactly, between scientists and literary authors). You see, I’ve always been intrigued (and routinely perplexed) by how often you’ll read of prominent scientists with a strong affinity for poetry or classic literature.
And my friend’s comments on the means by which math (and, indeed, science) is a metaphor for understanding the natural world seems to me to be a possible solution to that. So, while he can do far more justice to this argument than I can, I’d like to give the math-metaphor thing a shot. The argument is that math exists as a bridge between the purely abstract and the physical world. There is the abstract, that is the ability to propose a number of possible mathematical systems that all operate within their various ground rules. And we then apply those ground rules to the world that we see. Each mathematical system operates with its own accuracy – they are able to accurately represent the world in varying degrees. Think pre/post-relativity as a great example here. Both Newtonian physics (pre-Einstein) and relativistic physics (Einstein) are simply sets of abstract mathematical equations. They gain their weight from their ability to accurately model the world we see around us. If you’ve followed some of the recent theorizing about the multiverse, you’ll have noticed that there’s a number of mathematical sets out there that represent a number of possible multiverses, from 11 dimensions to 12, cyclical views of time, and “bubbles” of universes emanating from a multiverse big bang.
Now, what all these have to do with metaphors come from the way we apply these abstract mathematical ideas. My friend’s contention is that we are using these math ideas as metaphors when we apply them to explain the world we see. a2=b2+c2 and E=mc2 are all just a bunch of mathematical proofs that bear a correlation for what we see around us. They’re metaphors.
So, what struck me is the connection between what scientists do and what literary scholars do. Both use metaphors to explain the world around us. Sure, scientists try to explain the natural world and literary scholars try to explain the human condition, but the general mindset is largely the same. (If you’re wondering how literary scholars use metaphors, just ask yourself – did Huck Finn accurately represent the tear between white and black cultures, or did Dante actually mean to describe the makeup of Hell?) And this recognition that both scientists and literary scholars use metaphors answered a much less fundamental question of why so many scientists were amateur literary scholars.
I was always fascinated when reading biographies of historical scientists, how often they would read and study literature feverishly. Aristotle is an obvious place to start. True, he was a Greek, so he dabbled in everything. But Aristotle laid the foundation for much of the scientific process. And he’s still a major player in literary circles. Newton was an extremely well read theologian. Einstein could most definitely hold his own at a cocktail party for the English Department at the Prussian Academy of Sciences. Darwin, he was highly schooled in Christian literature and philosophy. More recently, Brian Cox (personally, my favorite modern Physicist) got his start in a rock band, a variant of literature. The number of scientists who read and/or write poetry is really quite massive.
So, my reasoning is that scientists so often develop a fascination with the literary world because of an implicit connection they see between its use of metaphors and their use in the sciences. Now, I don’t think that many scientists think in quite that manner, but there’s perhaps a Freudian connection going on there.
Religion & Philosophy
And this got me thinking about the overlaps between science, literature, religion, and philosophy. Placing major thinkers into these categories is a really tricky business, as they bounce so quickly from one to the other. Even religion and science, despite the modern divide that exists between them, have a deeply intimate past historically. Gregor Mendel, if you recall, developed the concept of genes that is a cornerstone of modern evolutionary theory.
So, the line of reasoning goes that if science and literature are connected through metaphors, can the connections between science, literature, religion, and philosophy be explained in the same way? I think maybe so. Religion often operates in metaphors. David slaying Goliath is not meant to be taken literally. Neither are the ubiquitous quotes from Confucius, the dances of American Indians, or the infighting amongst Ancient Greek gods. Philosophy, I think it can be argued, operates much like Mathematics when it comes to metaphors. The various philosophical traditions that dominate Western thinking (I can’t speak with much expertise for Eastern) act much like mathematical sets. Empiricism, rationalism, and existentialism are all just philosophical “sets of equations” that help to explain the world around us – in this case usually human to human interaction.
Big Picture Thinking
So, going really big picture here, maybe the human mind has developed in a way in that it understands the outside world purely through metaphors? I know we like to think that we directly observe and interpret the world we see, but do we? Maybe that’s why we so easily slip into the “virtual reality” of the Internet. We’re simply swapping one particular metaphor of reality for another? Same with getting lost in a good book – it’s a metaphor for an existence that we can easily apply.
I’m not sure about all this. It’s based on a loose association between a scientist’s profession and leisure activities. But it is an interesting train of thought – er, metaphor – for explaining human inquiry into the surrounding world. I guess I need to go hit the psychology journals to see what’s been done on metaphors recently.
This post is the best, to date, in what is becoming my favorite blog post. Intellectually rivetting, critically engaging, and anarchically pragmatic: No holy cows spared-rationalism, empiricism, extensialism. Great job Doc.
The very mention of Metaphors conjure images of embellishing prose, ornamental writing or sheer style. That may be right, with some credence. But a somber examination point to Metaphors as a cognitive mechanism. The world out there is made sense through metaphors, ie., a mechanism that relates the abstract to the concrete, enabling a point of reference, thereby comprehension.
Coming to understanding Mathematics as metaphor is concept hard to accept. The dominating view of metaphors as a linguistic frill, a province of poets, is hegemonic. Russian Mathematician IA Manin, however, holds that the future research of Mathematics lies in the direction of undiscovered metaphors of nature.
But nature speaks the language of Mathematics, an existence outside subjective minds. The co-centric circles of a shell fish, the elliptical orbits of planets, and the motion of bodies on Earth, all speak the mathematical language. Those who can understand it, can logically master nature, so did Newton argue. Newton’s metaphors, the famous F=ma, aided by the recurring reality of gravity, granted it the status of universal truth, for the next three centuries. The postmodern critiques called it the romatic view of mathematics. Randall says science exists on its faith in mathematics.
The challenge to the Newtonian view comes from UC Berkley. Nunez and Lakoff, a mathematician and a cognitive linguist, respectively, answer where Mathematics comes from? It’s our minds, they conclude. Where else do ideas originate. Truth is embodied. There is no external, absolute existence of truth. An anti-Platonic argument, although, this time, being more than an opposing view, it’s supported by empirical evidence from neurosciences, cognitive linguistics and psychology.
Back to more serious matters: Buffalo Wild Wings and Beers on tap. Intellectual ideas and intoxication appear to be inseparable, like Egg yolk and whites, scrambled.
A less known story about Martin Luther, the 16th Protestant reformer, is that all his works, besides his 95 thesis, were recorded by his students, who stayed at his place, till dusk, waiting for the great German to sink in a few pints of beer and inspire a religious rebellion.
So, I beg to disagree with the Doc. Beers from long necks, served by long legs are places for good philosophy, not otherwise.
You know, I wonder if we can challenge that “math is the language of nature” claim. Yeah, it’s got a lot of weight from its seeming accuracy, but do recent developments in physics challenge that? Relativity is a great complication to straightforward math. Yes, relativity is still a form of math that describes the natural world – is its language. But it’s a much messier language. Then, there’s quantum mechanics. When you factor truly random behavior into our understanding of nature, does math lose its control? How do you create a mathematical set of equations that accurately factors in random behavior?
Maybe we’re starting to see cracks in the armor of that “math *is* nature” claim? Rather, math was an effective metaphor to explain the natural world for centuries/millenia, but it’s now starting to lose its effectiveness?
Dunno…
Reuben Hersh says Mathematics per se is not the problem, but complete dependence on Math is where it becomes problematic.
During the turn of the 20 century, as RH pointed out, the emergence of quantum mechanics, thanks to Einstein, Mathematics became qualitative, says Weintraub. The result was emergence of a new branch called Differential Equations, extensively used in Economics forecasting.
I should add here, its nothing but Economists in the garb of classical Mathematicians pushing their opinions through equations. Just as scientific writing warrants passive voice, devoid of personal pronouns, Economics and Finance use Differential Equations as their passive voice vehicle and hauling their agenda.
The argument of Mathematics as Metaphor extends to representing chemical equations in Chemistry. Mary Morgan in her book Models as Mediators points out how the same dynamics of representation through observation (Empiricism)is not limited to mathematics. The propblem is when the representation is taken as the truth. Financial modelling or theories (folks here don’t differentiate between theories and models) that have come to dominate operations in Wall Street is another example.
Harry Markowitz, the proponent of Portfolio Theory, which fetched him the Nobel Prize, laments why do people take his model as the universal truth, when students and professors know that people at best are only 80 per cent right. His lament, however, came 41 years after he proposed his theory as part of his Dissertaton. By that time it had become an intricate part of Wall Street’s assessment of risk. Listen CNBC any day for a few minutes, the term portfolio will pop up invariably. Markowitz’s theory became a window pane (as Miller would say about language) of looking at Finance, read our pension plans.
Now to the Rhetorician’s question, why do Mathematicians carry so much Rhetoric or persuasion or credibility. The answer goes back all the way to the Greeks, as RH would say, a nice place to start.
Ever since Plato Mathematicians have been perceived as seekers of truth. Euclid’s geometry ruled the roost, and why not, this science helped in putting up the giant Roman edifices that stand to this day. Euclid, a mathematician of the Hellinestic era, 300 BC who compiled the work of Classic Greeks, is one of the earliest Mathematicians along with Pythogoras. The credibility of geometry was in the infrastructure it enabled all around the empire. Not anymore. Most mathematics research may not enjoy empirical backing as they did in the past.
The post-modern approach to mathematics, is not one of undermining its credibility but honing a critical eye on its claims. All Mathematicians know about the Foundational Crisis that confronted them following the developments in Physics and Geometry. The outcome following the crisis points to communal dimension of Mathematics.
Mathematics and it methods of arriving at proofs is intuitive, says Morris Klien a historian and Mathematician himself. The community decides the axioms, the criteria for which remain unclear, and then rest of the folks outside the authoritative body follow it up.
It’s a common feeling among Mathematics PhD students that their work is not the Mathematics they know in their earlier student works. The reason is at the higher level it beomes an enterprise of positioning and marshalling ideas around equations and distinct departments within the field. It’s precisely for this reason that students with problems within higher level of mathematics, till recently, at Cambridge University, were directed to the Philosophy department, say Donald MacKenzie, a British Financial Sociologist.
Mathematics as language is an interesting area of research.