posted
I was talking religion with my girlfriend last night. She's a utilitarian, atheist-leaning agnostic and wondered what I get out of letting someone else influence my will.
The discussion went on a while and I made a neat analogy that I thought I'd share here to see if anyone else got a kick out of it.
As many, if not most, of you know, there is a set of numbers called "imaginary numbers". The imaginary number "i" was defined as the square root of -1. The thing is, we don't know what the square root of -1 is... it's unsolvable... it's a mystery. But by giving the unsolveable, the unknowable, a definition, we can then apply logic to it and learn from it... and, it turns out, we learn some very useful things, none of which come to mind at this instant, but complex mathematics is, I know, essential to understanding oscillating systems in ways I used to know and should know as an engineer. It seems I've lost those particular brain cells.
But the point is, Complex Math, the study of imaginary numbers, is an attempt to explain the unknowable by formulas that then have a direct impact on how we live... and religion, in my opinion, does the same thing.
There's a startling homogeneity in myth and, while this is often used to discredit religion by implying that all religion is as contrived, quaint, and disprovable as the idea that the gods live on Mt. Olympus, I submit that there's an undercurrent of wisdom that man has...a sort of knowledge of the unknowable... that is consistent and handed down through a variety of myths. Theology is the systematic study of that wisdom... Christian theology merely adds the perspective that the chief one of these myths was also a historical event.
Just some deep thoughts for a Friday... enjoy (or ignore) in whatever manner you choose.
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posted
See, but I think of religion more as ether. Remember ether? It was invented by Einstein as a placeholder in some of his relativity equations; an unknown constant that made everything pretty. It was widely believed to exist, both because Einstein believed it and because equations like to be balanced. But eventually it was outed and sent to live amongst the other discredited scientific theories. Einstein later called it his "biggest mistake".
Imaginary numbers are a little more solid than that. We know they're there, if only obliquely, because of their effect on systems like the ones you mentioned.
Religion, I think, is more of a placeholder. Although I think belief is an infinitely valuable attribute, I sometimes wonder about the focus of it.
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Hmm, I haven't grasped all you've said in the "religion" part of the analogy yet, but I see a problem with your math part: the square root of -1 isn't a mystery. It either does not exist if you work with real numbers - no real number multiplied by itself will ever give you -1 - or it exists and it is "i" if you think in two dimensions (complex numbers). Yeah, you found a new concept, but you haven't replaced any mystery by it. Provided that you build a working theory around complex numbers there's nothing strange about them. You can test its theorems, you can demonstrate stuff. On the other hand, religion might try to explain things, but I've yet to be convinced it really does as none of the "evidence" supporting those explanations is really evidence to me.
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Actually, it was the cosmological constant that Einstein regretted. His 2 papers on relativity pretty much disproved ether as thought of in his time.
You could, I suppose, make an argument that spacetime became the new ether...
I don't know what your girlfriend meant. Who is influencing your will, and how strongly? Are we talking about predestination, or listening to sermons?
I didn't get what the i analogy was either, but this may just be that my perspetive is different. I'd agree with Corwin that i is not a mystery; and for me, God's mysteriousness isn't what I love about him. It's just that everything is mysterious to some degree, because we don't know everything; so we get mystery whether we want it or not.
I don't see religion as a placeholder, but then I don't think about religion much, but rather God.
Speaking of "religion" is like speaking of "ideas": there's so much variety that we can't say much that's true about all of them. On a tangent---people often speak of "things that all religions teach" and hope to distill the wisdom of all of them and throw out all the fluff, by which they mean the things that the adherents of the religion value the most! But do all religions teach the same thing?
The Maya religion was big on cruelty, not mercy.
Daoism is (was? I'm just going by the Dao de Cheng) big on wisdom -- but only for the sages. Let the people be ignorant.
Forgiveness? We only have to go as far as Christianity and Judaism to find a big difference there.
posted
my point is, until the "invention" of "i", the square root of -1 was unknowable... and, really, it still is. We just arbitrarily said "we can't know this, but we'll call it 'i' and work from there..."
But it's an analogy... a comparison of two like things... not meant to define or fit perfectly, but to explain a more nebulous concept by a more concrete one. so, it makes perfect sense that you would find complex math more concrete and provable than theology.
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posted
You could just as easily say that we don't know what "2" is, we just gave it a label and worked from there. We do know what "i" is, not because we've given it a label, but because we understand it's properties, just like we know what "2" is because we understand it's properties.
I sort of agree with your point about the homogeneity of religious myths, but I think that there are at least two sources for the commonalities. First, as you suggest, there is a fund of wisdom available. Opposing that, however, is a weakness that runs through humans. Determining the wisdom from the codified weaknesses (and picking up the distinct wisdoms that come from the unique myths that spring from different perspectives) is a very difficult task.
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posted
Also, we don't know what an electron is. Or a sound. Or a star. Or a baby. Or . . . we know things about all these, but we don't know everything.
So it sounds like the statement is something like "God is like everything else" or "some aspects of God are unknowable," which is true enough I suppose.
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quote:Originally posted by Will B: I'm rather confused here.
Sorry
quote: I don't know what your girlfriend meant. Who is influencing your will, and how strongly? Are we talking about predestination, or listening to sermons?
She was puzzled why I needed someone else's approval of my worldview. I'm Catholic (mostly) and the authority and wisdom of the Church is important to me, even though there are aspects of it I disagree with. Last night's conversation was a snippet of my attempts to sort these issues out over time. she was wondering why I don't just believe my own modified Catholicism and be happy with it.
quote: I didn't get what the i analogy was either, but this may just be that my perspetive is different. I'd agree with Corwin that i is not a mystery; and for me, God's mysteriousness isn't what I love about him. It's just that everything is mysterious to some degree, because we don't know everything; so we get mystery whether we want it or not.
I'm more talking about religious study than religious experience here. God should not be loved for being a mystery, but He is one (assuming, as I do, that He exists)... perhaps a better way of saying it is that He is the ultimate answer to mystery. Attempts to know Him are necessarily attempts to know what we cannot.
quote: I don't see religion as a placeholder, but then I don't think about religion much, but rather God.
which is a very pragmatic way... Not that I think that is bad, but I'm talking more theoretically here.
quote: Speaking of "religion" is like speaking of "ideas": there's so much variety that we can't say much that's true about all of them.
Yes, but there's still a greater concept there. "All chairs are quite different" is a nonsense statement. If they were quite different, we wouldn't call them all chairs. (GKC, Orthodoxy)
quote: On a tangent---people often speak of "things that all religions teach" and hope to distill the wisdom of all of them and throw out all the fluff, by which they mean the things that the adherents of the religion value the most! But do all religions teach the same thing?
I am not here concerned to create a brotherhood of all religions. If they weren't different there would be no point in having different religions. I am merely saying that there is great congruency among them and that I disagree with the idea that this makes them all inventions that borrow from each other. I think it means that human experience is fairly universal and that we all have the same mysteries to solve, which we do in different ways, up to and including, like my girlfriend, busying ourselves with more pressing matters.
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posted
The problem I have with your analogy is that "i" isn't a name given to the unknowable. It is a name given to a specific concept. We know what "i" is. It is the square root of negative one. The fact that we can't express it without resorting to language outside the basic numerals doesn't mean we don't know what it is. We know what "i" is just as much as we know what -1 is.
To the degree that "God" is like "i" (your concept of what "i" is at least), sure, I'll accept you analogy as long as you are clear that you're saying "God" is also only a name we give to the "unknowable" stuff out there.
The problem is no one really uses "God" to mean the "unknowable" (except angostics, I guess). The biggest point of contention between the religious and non-religious, and indeed between these religious and those religious, is that the religious think they can know God. They're "God" isn't a label fixed to a set of "things we don't know". It is a name given to a specific being they claim to know very much about.
Or are you arguing that God, like "i", is just a name for something you can't know but which you find useful?
[edit: I type too slowly. Mr. Squicky already said the gist of the first part of this post.]
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quote:Originally posted by KarlEd: Or are you arguing that God, like "i", is just a name for something you can't know but which you find useful?
I wouldn't say I'm arguing it so much as suggesting it as a way of viewing "religion" as a human concept.
As has been pointed out amply above, one place the analogy breaks down is that there is far more consensus about "i" than about "God". Again, this is the result of using something more concrete to get a picture of something more ethereal (to wrap around back to "ether" ) which, to me, is the whole point of making an analogy.
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quote:Originally posted by MrSquicky: You could just as easily say that we don't know what "2" is, we just gave it a label and worked from there. We do know what "i" is, not because we've given it a label, but because we understand it's properties, just like we know what "2" is because we understand it's properties.
I don't really see it that way (obviously). We can hold "two". We can see "two". We can conceptulaize and concretize our knowledge of "two" in wasy that we cannot do for "i". And the only property we really understand about "i" is that i^2 = -1.
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posted
Aside: Complex numbers have physical manifestations in the real world. For example, the complex component of power, IIRC, has a measurable effect on the transmission medium.
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No we can't. We can hold two of something and see two of something, but we can't hold or see the abstract concept of "two" itself. Two isn't concrete, and even if it were, your argument would expand to saying we don't know what anything that is not concrete is. For example, we wouldn't know what "math" was, as after all we can't hold it or see it.
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posted
Well, the problem I was trying to point out is not where the analogy breaks down, but that I think where the analogy "works" you would find few religious people who agree with you.
You've basically said that "religion" is an attempt to explain the "unknowable". That sounds like an agnostic's description of religion far more than a theist's.
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You can hold or see what we call two things, but that is not two. And I'd like to see you see or hold negative two . Even moreso I'd like to see you see or hold an irrational number, though I can prove they exist purely from the existence of two, the existence of square root (another thing with a sound physical approximation), and the existence of multiplication and division.
And really, we can find real world examples of i, too, though they take a slight bit more. For instance, certain circuits we know work can be explained if you run your calculations with imaginary current (I think its current). Or we can do certain physics calculations far more easily if we make one of the axes imaginary -- that's pretty darn real, at least as real as assigning the axis integral values.
i isn't a thing. Thinking of it as something to be explored and new properties discovered is fallacious, as fallacious as thinking we're going to discover new properties of two.
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quote:Originally posted by twinky: Aside: Complex numbers have physical manifestations in the real world. For example, the complex component of power, IIRC, has a measurable effect on the transmission medium.
That's an important part of my point, Twinky It something that by definition is not real, but has a real effect.
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You are using real in two senses. "Real number" is just a title. By that definition, birds, bees, flowers, and pumpkins are not real, since they aren't real numbers.
By the non-mathematics, more generic definition of real, it could be argued that all numbers are real, or that no numbers are real. But whichever way you argue, i is just as much a number as two, or pi, or negative five.
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quote:Originally posted by fugu13: Even moreso I'd like to see you see or hold an irrational number
*pi's fugu*
Seriously... if I've a circle in my hand, I'm holding an irrational number somewhere... either the diameter or the circumference of that circle is an irrational number of (insert unit here).
as for the whole "all numbers are merely concepts" idea-- I'm not nearly so platonic... and I don't think that the names "real numbers" and "imaginary numbers" were chosen accidentally. I'll certainly concede, again, that "i" is amuch more knowable concept than God... my point is that both the study of complex math and the study of God came about from trying to understand and develop real applications of things that were unknowable.
Fugu, you are cueing me to where it sounds like I have been a little confusing. I am not saying that "i" is like "God" by direct analogy. I am saying that like complex mathematics, religion-- the attempt to know God, arose from an attempt to explain something that we couldn't conceive of but could sense in operation around us, as twinky points out. This paragraph's language is imprecise but I think you can get a sense of it here.
Karl... I think it sounds more like an agnostic viewppoint because I'm trying to look at religion from a neutral, almost anthropological view point, rather than an adherent of a particular one.... an attempt at a worldview outside my own.
Edit: I should also add that I'm not trying to prove or push anything here... just trying to think out of my own box... and I'm not even sure why or what my point is... just exploring ideas...
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No, no physical circle is actually a circle. You are never holding pi because no physical circle actually has pi embedded in it. For all we know, its useful to do calculations with irrational numbers, but all exact physical measurements we encounter (not that we could ever make one) are rational.
What it really seems, though, is that there's no such thing as an exact physical measurement (how many things am I holding isn't taking a measurement, really, its making a metaphor between a number and the things you are holding; I'm speaking of things such as length and duration, those measurements that can be done continuously and aren't chunked and arbitrary -- for instance, what happens if I brush a bit of lint off one of the two hats I'm holding. Am I now holding less than two hats? Was I holding more than two hats before?).
The names real numbers and imaginary numbers are almost entirely arbitrary. The latter one got picked because it was new and confusing (similarly to how new and confusing negative numbers were for a while), and the former got coined by Descarte because it related nicely to the latter.
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quote:Originally posted by twinky: Aside: Complex numbers have physical manifestations in the real world. For example, the complex component of power, IIRC, has a measurable effect on the transmission medium.
That's an important part of my point, Twinky It something that by definition is not real, but has a real effect.
Sure. And insofar as any analogy is good, it's fine. I mean, pretty much all analogies are rough around the edges, right?
However, I think the problem with this particular analogy is that it doesn't work as well for someone who doesn't already believe in god. If you believe in god, well, yeah, of course god is an unknowable entity that still has a real effect on the world! Those effects are described in some detail in various scriptures and experienced more directly by many believers. If you believe that god does not exist, however, the analogy isn't as compelling. You can still say that the idea of god has real effects on the world, but you can say that of any ideology.
So I think the analogy is apt from your perspective, but from my perspective I don't quite... well, it doesn't resonate. It doesn't make me go "Oh! That's what you mean!" So I'm not sure how much it can help your girlfriend to understand your perspective. I understand that kind of situation, to an extent, since in that particular aspect my relationship is sort of the reverse of yours. Posts: 10886 | Registered: Feb 2000
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Look, all numbers have a set-theoretic definition. This is no less true for imaginary numbers than for the reals. There's no more mystery about where i comes from than there is about where 1 comes from.
(That's not to say that there isn't a very significant mystery about what numbers might be.)
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Yes, you were holding more than two hats, before. You were holding two hats and a piece of lint... which seems to be residing in my navel at the moment .
So what happens when something goes faster than the speed of light and the Lorentz contraction constant becomes wholly imaginary? we aren't sure... but we would know if the constant was "two" or "pi". That right there shows a pretty solid differential between our knowledge of even irrational real numbers and imaginary ones.
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posted
If you hold a circle, you are likewise holding an e and an i, because e^{2 i pi) = 1. That lets you hold a 1 and a 2 as well. Except, of course, that it's a really stupid analogy, because you aren't holding a circle, you're holding something vaguely roundish.
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quote:Originally posted by King of Men: If you hold a circle, you are likewise holding an e and an i, because e^{2 i pi) = 1. That lets you hold a 1 and a 2 as well. Except, of course, that it's a really stupid analogy, because you aren't holding a circle, you're holding something vaguely roundish.
Yes.
Twinky... I think your comments indicate that, out of the people I missed with this, you came closest to what I was driving at. Disappointing to hear that I wasn't able to really get outside my own head as far as I had hoped on this.... but you can't blame me for trying (or fault me for being unwilling to) Posts: 3846 | Registered: Apr 2004
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We don't know anything can go greater than the speed of light .
What happens when an equation says we need the square root of two buses to carry kids to school? We round up, we don't know what the square root of two buses would mean in that context.
Say I cut a bit off the hat that doesn't stop the hat from functioning as a hat -- its still a hat, even though I've removed a bit.
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quote:Disappointing to hear that I wasn't able to really get outside my own head as far as I had hoped on this.... but you can't blame me for trying (or fault me for being unwilling to)
Well, the mere fact that your analogy with numbers breaks down doesn't mean you don't ultimately have a good point. There are plenty of mysteries in the foundations of math and science that God could be compared with.
By the way, it sounds like you and your gf have a strong connection on an intellectual level, which is awesome.
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I think Jim-Me's point about the underlying universal pattern beneath certain sorts of narratives and almost all religions bears repeating. I invite everyone to read at least summaries of the work done by Frazer (Golden Bough) and Campbell (Hero with a Thousand Faces). I have been thinking a lot over the last few days about the monomyth, sympathetic magic and the scientific method, how they intersect, and the possible implications of their overlapping...
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I've always found myself very skeptical of Campbell. Who needs a mystical explanation of why god/hero myths were always popular, when we have a good sociological explanation on hand: they served to justify the divine rule of kings who in turn supported the artists.
Brin has made this point in writing a few times, I think.
By the way, David, good to see you posting again.
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Here's one thing you might think on: contrast the Campbell-style "hero's journey" of one great being's struggle with another form of narrative that's become popular in the last couple centuries: the evolutionary narrative of constructive competition (and cooperation!) between many interconnected creatures.
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posted
First of all, I'm not looking for a mystical explanation, but a psychological one. When you (especially if you read the exhaustive Golden Bough) begin to realize that specific details in the story are universal, even in cultures with wildly different structures and mores. And I'm not just talking about any god/hero myth, but specifically the one in which a hero undergoes a life-transforming series of trials to bring a gift (usually life) into the world. It's obviously a reflection of the seasonal cycle, and arguably has roots in the matriarchal sacrifice of sacred kings in later winter to ensure crop renewal. But when we examine how deeply this story has insinuated itself into our very psyches (see Jung), we are not remiss in asking whether there might be an underlying (innate? genetic) predisposition to see ourselves and the world in these terms. I then see a connection between this and the self-concept of the scientist and her method. I may be making too much of the metaphor, but I find it interesting and perhaps worthy of further thought.
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May I reccomend Chesterton's The Everlasting Man(e-text at the link) as a Christian viewpoint on Frazer and the like?
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quote:Karl... I think it sounds more like an agnostic viewppoint because I'm trying to look at religion from a neutral, almost anthropological view point, rather than an adherent of a particular one.... an attempt at a worldview outside my own.
Just wanted to poke in and say that I understand where you are coming from, Jim-Me, now that you have explained further. Sorry if I sounded confrontational. (Maybe some carry-over from the ID thread, I dunno )
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Jim-Me, I liked your analogy, it was appropriate for the time. Of course all analogies fail when trying to analyze them deeply, that's why they're analogies. Yeesh. Posts: 1412 | Registered: Oct 2005
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quote:She was puzzled why I needed someone else's approval of my worldview. I'm Catholic (mostly) and the authority and wisdom of the Church is important to me, even though there are aspects of it I disagree with. Last night's conversation was a snippet of my attempts to sort these issues out over time. she was wondering why I don't just believe my own modified Catholicism and be happy with it.
That interests me. On the one hand, I *do* just believe my modified Catholicism, and dont' mind much if I have a disagreement with the Catechism. OTOH, I like points of congruence. Maybe it's just fun to have like-minded people. Maybe there's more to it. We do speak of a "community of faith," rather than having communities, and having faith, as though they have nothing to do with each other.
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I don't think I know enough about "i" to understand the analogy. "i" seems like a concept I can get through my day without. Though I think I know enough to know that it is involved in electronics, and the smooth operation of my day absolutely depends on it. But I don't have to know about it for it to work in my life.
Though, for a long time my appreciation of God was about on that level.
Oh wait, we are talking about Religion or God?
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We are talking about the study of and attempt to get to know God without commenting on which, if any of them, He or She may be...
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Jim-Me, I was already aware of Chesterton's thesis, but thanks for the link. Obviously it's much easier for a non-Christian to see Christianity as just another iteration of a deeper, simply story than as having been prefigured in that story, but I respect the rationale as consistent with your faith.
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