Euler's Identity = No Creation?

Forgive me if this has been addressed before, but I could not find anything. And I am sure this idea has been addressed before, so I am also looking for some references on the topic, but does the existence of pi and e, the natural log, and especially the relationship of Euler’s Identity support the thesis that the universe exists without a divine creation?

I see it as that in any universe, Euler’s Identity must be true regardless of whether a god exists, and the universal constants are pan-universal, i.e., it is impossible to have a universe where they could not be true, and thus beyond the power of any god to make them not true - which would mean God is not omnipotent.

If I am mistaken, how? What is the relationship between mathematics and physics and metaphysics?


Also its ideas like this that make me admire Buddhism, i.e., dont worry about it, just end suffering and reach enlightenment, and the answers wont matter anyway. :wink: But suffer I still do, and enlightenment make take a few more incarnations, so I wonder about the above.

Given that we can’t even define “God” I don’t think we can draw any conclusions about “God” based on a mathematical formula.

Even after a bottle of wine (Ca’del Solo’s Big House Red, an excellent and inexpensive table wine) I have to admit being totally befuddled by your question. Euler’s Identity, as beautiful as it is, neither confirms nor denies the existance of a god or gods. It’s merely a lovely congruence of various fields of mathematics (complex analysis, trigonometry, et cetera) that gives you all of the basic constants of mathematics. Note that the standard value of pi only exists for plane geometry; against a background of non-Euclidean geometry (which is more representative of the real world), pi would have a lesser value.


For the sake of this argument, I define “God” as a being that supposedly has the power to create the universe. I do not believe in such a being. One reason I feel that way is that certain universal laws and constants are just that - constant, regardless of what universe exists and beyond the power of any being to change.

I suppose this is related to Plato’s ideal forms as well. These ideals exist whether or not the universe exists. I have heard them described as metalaws, but I cannot remember where, but essentially, even “God” cannot change these laws, which IMHO argues against the existence of such a “God” (other than as an ideal itself, but with no physical or other actual correlation to reality as we know it.)

Stranger, my point here is that pi still exists, no matter its actual value. I have not heard of a geometry where pi does not exist, and thus any universe has to have a pi to exist also, and so is a metalaw.

If we define ‘omnipotent’ as meaning “able to perform all actions, including those which are logically impossible and those which are not even actions” then yes, but isn’t this just another take on the 'can God make a burrito so big even he can’t eat it?" thing.

We don’t even need to invoke mathematics to perform this kind of trick; for example:
Can God wijikfuppet snerldy? If not, he’s not omnipotent. (the term wijikfuppet snerldy has no meaning, BTW).

Take three.

For myself, Euler’s Identity is an elegant shorthand for how mathematics has its own existence outside of any physical reality, but also that any physical reality must obey the laws of mathematics in order to exist. Essentially, that Euler’s Identity would be true in any and all universes. And so that mathematics and its underlying logic represent the highest ideals, - but it is neutral and non-sentient, and certainly not a divine creator. And though it requires sentience to ‘see’ it, like the proverbial bear in the woods, it’s still doing its business regardless of any watchers. I can easily imagine a multitude of universes that came and went without any sentient beings evolving, but those universes still followed mathematical laws.

So I believe the universe is purely a natural construct according to laws of mathematics and physics and is thus only not predicated by any creative act by any being, but it also precludes any possible ‘creative’ act. I believe that something can arise out of nothing and does not require a creator, just as mathematics does not have a creator, only discoverers of its properties.

Mangetout, using the word omnipotent was probably a mistake on my part, since that is not what I am questioning exactly. I understand the answers to the “burrito” paradox. I question that the universe not only did not require a creator, but that the universe could even have a creator.

My main problem is that this is a matter of belief, not of understanding. The underlying logic of why I believe this eludes me, but I have the strong sense that this belief is correct. I also know that this is not an original thought, but deciphering modern philosophical and ontological schools is a bit challenging to the layman, yet I am trying to figure out exactly what this school of thought is and what it entails. Two writers that influenced me greatly were Isaac Asimov and Bertrand Russell, unfortunately the latter got too esoteric for my understanding, and I am not sure if we agree on all the particulars, but they helped lead me to where I am.

Unfortunately, it is also very late, and I’ll have to let this go til tomorrow. (I really shouldnt start OPs this late either, but sadly, this is what I think about late at night.)

I am unfamiliar with Euler’s Identity. Can you point out where your link discusses it?

I don’t understand why Euler’s identity does any more (or less) to support your position than does 1 + 1 = 2.

So you’re saying that, because there are things (i.e. the laws of mathematics) that could not have been other than what they are, that leaves no room for a Creator—for someone to have decided how things should be. Is that the gist of your argument?

The problem with this argument, it seems to me, is that even though some things had to be as they are, it doesn’t follow that all things had to be as they are. There may still have been some decisions for a Creator to make, some alternatives to choose between.

And even if there weren’t—even if everything had to have been the way it is—why couldn’t the existence of God be among those things that had to be?

I agree with Thudlow. I can posit a logical mileau in which Fred+Barney=Wilma*Betty, Ed Zotti=The Queen of the Moon, and Nickelback=Good music, by the base definitions of the logical system. In any universe where logic obtains those identities will be true within that system, by definition.

So, yes, Euler’s Identity will be true in any universe in which logic applies, but perhaps in other universes it isn’t as useful.

There are stranger things in Heaven and on Earth than are dreamed of in your Geometry.

“I have not heard of…” , compelling though it may be, does not constitute evidence, and doesn’t lead to “…and thus any universe has to have a pi to exist…” Saying that ratio exists (which is all pi is – the ratio between circumference and diameter of a circle) doesn’t prove anything. And I can imagine that there might exist circumstances where pi doesn’t exist, like if there are no circles. Look up Taxicab Geometry sometime.

I’m reminded of one of those dialogues between Achilles and the Tortoise in one of Hofstadter’s Godel, Escher, Bach “Let’s see how that play would have gone if he’d caught it. Now let’s see how it would have gone if pi was a rational number.”

Euler’s identity–like all mathematical conclusions–is a consequence of logically exploring concepts and definitions we consider to be so simple that we accept them without proof. It is astonishing only because (1) it looks like other formulas which are simpler to understand, and so it is labeled “deceptively simple”, (2) it is a wholly unexpected consequence; it is not at all obvious once you understand what the basic terms mean. Nevertheless, (3) once you understand more than just the terms but the definitions/mechanisms by which these terms can be manipulated, the formula suddenly becomes simple and obvious, and is powerful enough to get you to abandon a long-held “obvious” belief.

Just to give an example, the mathematical redefinition of number to include something like i=sqrt(-1) meant we had to abandon the idea that numbers had to be well-ordered, e.g. if you allow sqrt(-1) to be a number, it is possible to prove this number is both “greater than” and “less than” 0, an apparent contradiction. That’s astonishing: (1) the statement "i<0 and i>0"is deceptively simple, but on its face patently absurd (2) it is wholly unexpected, because our basic notion of numbers says they ought to be well-ordered, i.e. a number is either >0 or <0 (or =0), but not both, (3) once you folow the proof, the result couldn’t be more obvious, and logic then gets you to abandon a believe which, until you came across this connundrum of i, could fairly be called “obvious” (to you).

I suspect this is what Agnostic Pagan means when he says Euler’s identity “support the thesis that the universe exists without a divine creation?”. Belief in God–as this board proves–is for many the most obvious and powerful truth in the universe. But mathematical statements like Euler’s identity, which so astonishingly topple ideas which are also very basic and powerful once they are understood; they represent a supreme triumph of rationality over intuition, no matter how deep-seated that intuition is.

How is this more or less true of Euler’s Identity than of any other law of mathematics?

Yes. The existence of a god or gods changes nothing. Like the existence of genii, they are mental, not physical, constructs.

I make no attempt to claim that all atheists are total relativists. Nevertheless, since Marx, atheist though has trended away from traditional realism towards social constructivism, which is the belief that there’s no outside reality and everything is made up by people. That would at least suggest that you’ve got it exactly backwards. The existence of unalterable truths such as the existence of pi points towards a God, not away.

In Orthodoxy , G. K. Chesterton between alterable an unalterable realities and points out that no traditional religion, no matter how bizarre, has attempted to dispute the unalterable realities, such as gravity or basic mathematics. It’s only the modern philosophies that have tried claiming that basic math is wrong or is changeable. Hence God has a grip on the unalterable realities. One might even argue that God is all unatlerable realities. So, for example, God could write the equation 2+2=5 on the Heavens, or inscribe it into every particle in the universe, but God couldn’t actually make two and two be five.

This approach can explain some of the FAQs about God. For instance, many complain that since God is all-good and all-powerful, therefore God must end all suffering. Thus if suffering exists, then God must not exist.

But the argument doesn’t hold water because it doesn’t grasp the difference between alterable and unalterable. Humans are sinful, and this is unalterable. You couldn’t have a non-sinful human. Sin is in the nature of humanity just like the sum of two and two is in the nature of four. Also sin leads to suffering, and this is also unalterable. Thus God can’t snap His fingers and make humans stop suffering instantaneously.

Science ficiton author Alex Popkin wrote a highly entertaining take on the absoluteness of math that’s available at Quantum Muse magazine.

That was a very poor word choice on my part. And now I have heard of a geometry that does not have pi. Thank you.

I still think my underlying thesis is valid though:

Yet looking at the geometry CalMeacham mentioned, I dont know if a physical universe could operate under those maxims - and this is where I question my thesis the most - mathematics is the greatest ideal even above the laws of physics, but which math? Is there a ‘universal’ math? Or are they purely mental constructs with a strong correlation to reality? Which comes first? Math or physics? I believe that math does, but I cannot be dogmatic about it. I am tracking down some books that discuss these issues for my winter break (so much for light reading - hah!) Any input is greatly appreciated.

I chose Euler’s Identity because of how it shows a relationship between natural numbers that seems to transcend any physical reality. That seems is what I am questioning.

If the Creator could only make choices between alternatives, that diminishes that being greatly. She would be more rightly called the Architect. If she merely shapes the materials, but does not create them, then she would be worthy perhaps of admiration and respect for her craft. I dont see how that creates (no pun intended) an imperative to worship her and devote our lives to her mysterious plans. (Not that I think a Creator has the same imperatives either.)

And yet the tradition handed down is that she was a Creator, not an Architect.

Toward your last point, I dont believe the existence of God in necessary for the existence of the universe, and I strongly suspect that the universe does preclude a God as described by Western Monotheism (i.e. the Judeo-Christian traditions, as well as the neo-pagan Goddess).

But to live up to my username, I do not rule out the existence of an Architect - an early sentient being (or race) with the power to select the amongst the alternatives and determine the shape of our current universe. But again, they were not ‘creators’, at least no more than the baker that ‘creates’ a cake out of the raw ingredients. And no imperative exists that we must follow them.

Suffice to say that I do not accept the hypotheses of social constructivism.

I never seem to get my point across when I try to say what I’m about to say (and it doesn’t help that my own views on this have changed somewhat during the years that I’ve been a member here), so if it seems confused and hard to understand rest assured that it’s probably my fault, not yours.

That said…

I think you are making an unstated assumption that needs to be brought to light. Specifically, I think you are assuming that mathematics (and in particular logic) is an accurate model of reality. But this is still an assumption. It’s a very attractive assumption, as pretty much all of us have great difficulty imagining a world where logic fails to function. It’s also an assumption supported by a great deal of evidence, in the scientific sense. But nevertheless, it’s an assumption, and like Newton’s Laws of Motion it could be wrong, or at least not the whole story.

Now, imagining “what would it be like if logic failed to function” is about as useful, practically, as imagining “what if the sun were to instantly turn into cheese tomorrow”. It’s just not something worth worrying about, except in certain metaphysical discussions.

Like this one. I think that your thesis is making the mistake of assuming that logic must hold, and that if logic dictates something then it must be true. CalMeacham has made this point already, and you’ve responded to it, but I don’t think your response really addressed this problem.

Logic and mathematics, in their modern formulations, are nothing but poetry in a fancy alphabet. They’re just games, built on air. The fact that those games correctly model everything we’ve seen reality do so far doesn’t change that fact. Now, 999 times out of a thousand “correctly modelling what we’ve seen of reality” is sufficient. But you’re trying to go a little bit further than that: you’re trying to derive a real-world conclusion out of nothing but mathematics and logic. Assuming that logic and mathematics are universal papers over this fact, but it’s still there: what you’re trying to do, in the end, is make God vanish in a puff of logic, and that’s never going to work.

And as usual it appears I’ve used a lot of words to say not a hell of a lot, but let me end with this: saying mathematics transcends reality doesn’t make it more true. In a very real sense, it makes it less true instead.

Hmm, most social constructivists are not metaphysical idealists. They believe in an external physical reality, as most of us do, but they don’t believe that it is split up into isolated chunks called ‘facts’ that exist outside of a particular paradigm. They don’t believe the world ‘speaks’ of objects or processes that our language corresponds to or represents, but view language as a tool for practical human concerns. Simply put, the world is ‘out there’ but truth is not. If anyone is at all interested in reading something by philosophers of a more constructivist bent, look into books by the later Wittgenstein, Paul Feyerabend, Thomas Kuhn, Donald Davidson, and Hilary Putnam. Oh, and Agnostic Pagan, have you heard of Roger Penrose? If not, he shares your exact viewpoint, albeit, he calls your ‘meta-laws’, “God”.