In this recent post arguing for the converse of cogito ergo sum, two comments were elicited for which the response I felt was better promoted to a new post. Plus, of course, the ever present problem for the regular blogger is solved … that is on what to write? Two responses, not entirely unrelated by frequent commenter, the Jewish Atheist who first remarks:

Intelligent space aliens would discover i2=j2=k2=ijk=-1 but would likely have a completely different theology. Math equations are universal. Theological angel-pin-dancing calculations?

There are two problematic features of this response. The first is the (especially the first) Star Trek alien problem, that is all too often aliens are portrayed as humans in rubber suits. Their concerns, appearance, and their communications are all to often human with a small twist. JA elaborates:

People from different cultures on Earth come to the same conclusions about math. They differ on theology. This is because math is a formal system learned by humans and theology is just made up.Are you really denying that given an intelligent civilization elsewhere that they would almost certainly discover i2=j2=k2=ijk=-1? And that they would almost certainly have created thousands of their own theologies that bear only superficial resemblances to Earth’s theologies? If they had theologies at all?

This follows much the same vein. So there are really two questions at hand here. The first is how fundamentally immutable are mathematical truths and how much of our mathematical construction is human, or to coin it more poetically what parts of math are divine and what parts mortal? The second issue offered here is on the theological side. To put it bluntly, our interlocutor insists that theological ideas are “just made up” and specifically made up in a way that math (such as the Brougham bridge example noted earlier) is not.

In early formulations of quantum mechanics Erwin Schrodinger and Werner Heisenberg developed two early formulations of an underlying theory of the hydrogen atom. In appearance they were very different, Herr Schrodinger’s formulation was analytical with complex wave functions who’s norm represented a probability distribution for the electron. Herr Heisenberg’s formulation, not widely taught so much today, involved infinite hermitian matrices. It turns out that it was demonstrated, by Herr Schrodinger that they were the same. Why bring this up? Well, mathematics and mathematical developments underly much if not all of the scientific advances of the modern era. If our “alien” species was indeed as or more advanced than we then one should expect that for them as well, mathematical developments might be expect to as with the two gentlemen aforementioned have different but equivalent formulations.

JA remarks that “People from different cultures on Earth come to the same conclusions about math.” But by and large this is not actually the case. Most of the body of mathematical knowledge is not independently discovered. In various cultures, we learn and borrow what works and what is beautiful from others. The Roman West and the Indian East did not independently discover the notion of “0”, but the Indian did … and its utility was shared and eventually found its way to the West. In fact, remarkably little of mathematics was independently discovered by different peoples. Similarly for comples numbers like i and (and j and k for the quaternions noted above).

Following Stephen Hawking’s little bookGod Created the Integers, integers or starting with counting numbers form a fundamental building block for human mathematical constructions. But, imagine for a moment an alien species for which integrality and counting items are not natural. If the natural elements of an alien’s natural environment, its self, and surroundings are motile and boundaries of self fluid … it might be that integers are a fundamentally unnatural concept. Mathematics as developed by such a species might be very different than ours. Imagine again, another species, perhaps dolphin/sonor equipped in which communications develops along by passing or “shaping” 3 dimensional spatial images (in sound or light). For such a species geometrical ideas and intuitions might overshadow analytical ones. Again, their mathematics might be very different.

Ultimately however, we expect following the Wigner paper noted earlier on the “unreasonable success of mathematics” in describing physical phenomena that our shared universe and its physical laws might force mathematical developments if not in identical forumulations instead in ones like Heisenbergs Hermitian matrices vs Schrodingers wave functions into equivalent ones. That fundamentally is why we expect that aliens in a lot of ways will arrive at mathematical constructions that parallel ours.

Which leads us to theology. JA claims that theologians are “just making it all up.” However it may be that some religious fakirs are fakers, pardon my pun, but by and large that is the exception. Theologians and religious thinkers are specfically not “making it up.” They are honestly engaged in the process. They follow methods. One example of this one might take the Jaroslav Pelikan book I recently discussed ( Interpreting the Bible and the Constitution). The legal community surrounding the Word of our nation, i.e., Constitution is surprisingly like the theological community in very many ways. The legal process of developing Constitution as well as the common law and other legal processes are not the same as mathematical proof, but it is also definitely not “just making it up.” If it was all “just made up”, then one couldn’t have arguments on legal matters. You can’t argue about the rules of Calvin ball. You can argue theology and law (and mathematics). Why? That is specifically because it is not “just made up.”

If ethics are the basis for laws, Alasdair MacIntyre (Whose Justice? Which Rationality?) among others have noted the difficulties that different ethical frameworks and people who base their ethical rational have in communicating between each other. This is a problem which legal and ethical people have to confront. Theologically speaking the religious communities face the same problem. The demonstration of “equivalences” (and isolating differences) is more difficult than the mathematical community. Broad questions like “Who are we? Why are we here? Who made this world? Why?” are those which religions answer. Observation of the world and our experiences in it have been distilled into answers, which we call religion. To answer the question about aliens and their religious beliefs, I do think that the religious beliefs of aliens would have amost as much connection with ours as our mathematical ideas might have as well.

This is an incomplete answer to the questions posed, but … it is a start I hope.

Filed under: ChristianityEthics & MoralityMark O.ReligionScience

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