There is no reason to believe that we would have a common point of discussion about science or mathematics with intelligent extra-terrestrial life-forms. Or so says André Kukla in his now not-so-recent (I started writing this a while back) BJPS article, worth reading in full if you’ve access through your institution or someone else’s, & if not then this post offers a poor man’s précis anyway. Myself, I do not agree with Kukla, & raising as he does a slew of innovative arguments against a position I recently held on the grounds of intuition alone, I am moved to sustain it by reasoning instead.
Broadly, Kukla’s article is about the uniqueness of science, the description of natural laws that we construct and agree upon at any one point in time, as opposed to the uniqueness of said laws. The crux of his argument is that it is reasonable to expect our body of science to be disjoint from that of the non-terrestrials, though he is clear that this is a position of agnosticism rather than contradiction. After all, Kukla argues, there is a lot of volume in ’science-space’ (not his term) that was once unexplored by us, and there is very probably at least as much again that is unknown. The non-terrestrials could easily have sampled this space rather differently, so perhaps we don’t have a common science after all.
The argument advanced in his article, which is very nicely written, is somewhat more nuanced than I have made it above, though not too much more so. It is framed as a response to the viewpoint famously advanced by Carl Sagan through the winsome organ of Jodie Foster: that mathematics (and perhaps physics) transcend psychical distance. There is no way, Sagan would have it, that beings could be intelligent enough to communicate with us and not possess some common body of scientific knowledge. Kukla immediately points out that the reasoning informing this conclusion is never articulated by its advocates.
The article contains a number of potential rebuttals to the main argument, followed by suggested counter-arguments to the rebuttals. Though this is done briefly (the complete article is just nine pages), and there is likely to be ground to tread there, I will focus on what I believe is a strong objection that is not dealt with in the article.
Mathematics, even more so than physics, is a hierarchical discipline. This is apparent in the progress of civilization at large—we think of today’s technology as more advanced than that of a century ago, rather than merely as a separate, but equal, sampling of the space of ideas. Could this be illusory? I would think that it is not, for, just as with modern mathematics, we rely on extending previous work rather than beginning completely anew.
I don’t know what structure best represents fields of knowledge, and I welcome suggestions from the audience; but a dependency tree certainly seems like the way to go, inasmuch as undergraduate university courses have pre-requisites and the GIMP software package in Linux has several less specialised, more fundamental, software requirements, and so on. I picture the advancement of knowledge as the exploration of ever-higher limbs of such a tree. The important thing is that the stuff at the bottom tends to be very, very general, so that it is necessary for the understanding of nearly everything, but sufficient for virtually nothing. And this is the stuff we are most likely to have in common with an alien life-form.
There are two questions standing in the way of my conclusion, then: i) is it possible to arrive at a high branch of the knowledge tree via a different trunk?; ii) could there be completely seperates tree of knowledge? If (i) is the case, a more general structure than a ‘tree’ is needed to represent the dependencies of knowlege. However, I am skeptical of this in light of the structure of the fundamental fields of human understanding. They are uniformly connected, so that even if one doesn’t start with Euclidean geometry before getting to general relativity (Christoph Schiller-style; see chapter 6 especially), you’ll be getting around to it at some point. [JBJ: Rereading this, I think this paragraph could do with further thought, but I leave it for now.]
Completely separate trains of knowledge seem more plausible, if only because I wouldn’t know if they weren’t. But this seems to be strongly dependent on environment, and the statement that an alien species has no in-common knowledge to humans then boils down to claiming that there is absolutely nothing about their physical environment that could be a suitable point of departure. And this is the nub of what I want to say: even though we’re talking about crazy alien species, we are still implicitly restricting ourselves to alien species within our Universe.
Don’t forget the possibility that we could meet an alien species and they’d be, like, OMG, those n00bs still think that light travels at constant velocity!!1! LOLOLOL!!!11!1
I like this internet meme where exclamation marks are replaced with ones to emulate the typography of idiots. I can see someone producing a work of high fiction in the next few years written entirely in that style.
In a similar vein, there was a Paul Krugman post about the financial crisis where he described the original Paulson plan as “all your bailout are belong to me.” And then he won the Nobel Prize.