Created???

[Gadianton]

I think MG in referring to valuing Mormon theology he means the body of teaching,

No doubt, and normally I wouldn't be pedantic about it. Most people probably would use "theology" "teachings" and "beliefs" interchangeably, I'll bet I have done so myself, and really, who cares. Except, MG boasts that no other religion could be more advanced than what he learned as a toddler and he also drones on about how he constantly has to clarify misinformation and so if he's going to use words he doesn't understand in his boastings, perhaps he should taken to task to use them properly. I mean, as far as a representative on the forum who doesn't appear adequately informed, MG ranks pretty high up there.

[huckelberry]

Physics Guy, I enjoyed your use of math as a comparison but find myself with reservation. I feel like saying my brother is a mathematician but I am not. Pardon if I am using my ignorance to be simplistic.

To my understanding math is a language to describe relationships. It has developed to be able to describe complicated, perhaps subtle relationships as well as simple arithmetic but is it not like other languages whose truth is in the application. Inaccurate or incomplete measurement yields false result no matter the quality of math involved. Garbled math could harm good data. I see one can trust good math not to distort results or relationships.

That might be quite different than religious proposals.

Maybe not absolutely different. People understand uncertain life process through large general ideas which have a sort of process function. The quality of that function, clarification, or distortion is important a trying to rely on the function is a choice of belief. I am seeing religious beliefs as a possible example. There is some experiential feedback but perhaps not enough to force a conclusion about reliability of guiding idea. But people choose the way guiding ideas are used.

[Physics Guy]

I'm sure that many agnostics, for example, are quite able to suspend disbelief in gods, or a particular god, and use this state to examine hypothetical questions such as those concerning what you might expect to see in the real world if god beings existed with specific properties and attributes.

But, in my opinion, that is not the same as believing in such, or choosing to believe in such.

I'm sure there are degrees, of how long you spend thinking as though something were true, and of how much effort you invest, or risk you run, that will only pay off if the something is true. I don't think, though, that there is really any qualitative line between this kind of provisional thinking as though something were true and any kind of belief. When I think about why I believe the sun will rise again tomorrow, or that an object will fall if I drop it, I don't find any convincing proof that demonstrates that I totally know those things. I just find a cost/benefit/risk/reward analysis telling me that it's not worth spending any time or effort at all in thinking about the alternatives. Oh, maybe it could be worth it to spend a few minutes once in a decade or so, like to ballpark the odds of a really big gravitational wave coming through; but not much more than that.

There are things like that, where one alternative merits no significant amount of attention, and there are things where both alternatives are about equally worth considering, and there are all the other stages in between. Over time things can move around on the scale, either because I gather more evidence about how things actually seem to be in the world, or because the cost or risk of assuming the thing is true goes up or down. With imaginary numbers, the cost falls as you get used to the rules of complex arithmetic and it stops being a mental effort. I reckon most initially strange ideas become easier to entertain with practice, to the point where one can cease to think at all about alternatives just out of habit.

Imaginary numbers, as you point out, have the huge advantage that they can be made (and have been made) subject to a consistent set of rules and formal operations that give reproducible results that are useful in the real world.

Right, and this is why we like them. Most religions also involve consistent rituals and doctrines, shared by adherents all over the world, and often supporting various good works. There's a difference of degree in just how consistent things are. I don't know any bodies of religious doctrine that are as clear-cut as arithmetic. On the other hand, though, I think it's a naïve fallacy to hold everything to the standards that are attainable in the simplest cases. I think that's like refusing to eat anything except mush because mush doesn't need chewing and so chewing should never be necessary.

By the way, can you believe that Euler's Identity is - I want to say "real"! - true? Can you choose to disbelieve it? How on earth, or in heaven, can e, i, and π be related in this way? Yet, as with plain imaginary numbers, if you apply the "rules" it's impossible to deny the reality.

I don't really remember, but I'm pretty sure that I myself didn't fully believe the identity at first. I was probably told that it was an amazing result that had to be true because mathematical authorities said so, and I probably accepted that mathematical authorities really endorsed it, but I expect that I entertained a strong suspicion that it might be just an arbitrary mathematical game rule with no relevance to the real world—a bait-and-switch trick, in fact, in which one invented some weird new kinds of mathematical operation and just called them by misleadingly familiar names, like multiplication and exponentiation, even though the names didn't really fit.

(That sort of thing happens a lot. So-called "quantum teleportation", for example, actually involves only communication, not transportation. It's a real thing, but it's not what it sounds like.)

It takes quite a bit of practice with complex numbers before you appreciate that in this case the familiar names of multiplication and exponentiation and so on actually do fit, and are not misleading, because they really do stay exactly the same except for the one added rule that there is a number whose square is negative one. It's not so much bait-and-switch as finding the last piece of the puzzle and putting it into place. There was a hole in arithmetic that was just waiting for i; we never noticed before, because we didn't know what we were missing, but once you see how it fits, you can never go back.

For the god(s) question, do we simply lack a consistent set of rules and formal operations that give universally reproduceable results that are useful in the real world? Might this then allow us to choose to believe in god(s). Or might it be the case that application of such rules and operations would cause the belief to emerge, to creep up on us, without our having to, or being able to, make the choice? We would simply believe/accept/whatever?

Yeah, as I noted above, there's a tendency to get used to anything. At some point it can just become part of one's identity.

In physics we still love complex numbers, but there were several decades in the late 19th century, maybe extending into the early 20th, when people really loved a more complicated version of complex numbers, called "quaternions". Besides i, you added j and k, so that together with ordinary real numbers, there were now four kinds of numbers. Quaternions were a big deal, in their day. In a way, we still have them, but just as a set of two-by-two matrices that crop up now and then, and don't need any new rules beyond the usual matrix rules. Nobody thinks about quaternions any more. With historical hindsight, quaternions are an example just like my complex numbers example of how "choosing to believe" can be good, except on the other side. Sometimes "choosing to believe" leads to believing all of the time, but it's just a habit or fad.

[Physics Guy]

This is the first argument I've read that makes the concept of 'choosing to believe' an idea that's worth considering. Fortunately, I have just enough of a background in math for it to make sense to me. However, now that you've brought it up, I can think of parallels where choosing to accept what seems to be an abstraction is necessary in the fields of art, music, and economics. I'm sure there are dozens (hundreds? thousands?) more.

Thanks for phrasing the question, of whether choosing to believe could ever make sense, in a more neutral way than I've heard before, so that it made me try to think about the possibility seriously. I'm also sure that there are lots of examples analogous to complex numbers. I think we may have learned something, just from this example, about the grammar of belief, so to speak.

Believing in i does not mean believing that among the ordinary real numbers there is one that somehow squares to minus one. What this means to me, by way of analogy, is that if there is a proposition which is supposed to refer to things one already knows, and mean exactly what it would normally mean in that context, then no, one cannot simply choose to believe that proposition.

Instead, believing in i means considering a whole new kind of number. How can there even be a new kind of number? That doesn't make sense at all, if one is used to thinking of "number" as exactly the kind of thing that's involved in counting one's fingers or maybe cutting up pies. So, okay, maybe even calling i a number at all isn't the right way to introduce it. We could call it a new kind of thing that is in some ways like a number, except. It has its own kind of rules that are like arithmetic for numbers, and furthermore these new arithmetic-like rules for these new number-like things fit together quite easily with actual numbers and actual arithmetic. If we put it like that, it would probably be easier to get people to think about complex arithmetic. The greatest fans of ordinary arithmetic, who are most unwilling to believe that any number could ever square to a negative, might be eager to learn of a new thing that resembles arithmetic and offers additional insights.

So for it to make any sense to choose to believe something, I'm thinking, the something has to be some new kind of thing that isn't already known, but that can't be excluded, based on what we already know.

"Can't be excluded" isn't the same as "isn't excluded". A hypothetical medieval peasant, at least according to trope, thinks the world is flat. The peasant's world view excludes the idea of a round Earth, but their experience only extends a few miles. They know that those few miles are pretty darn flat, but they can't really exclude the possibility that the world is a sphere with a diameter of eight thousand miles. They can easily imagine their few known flat miles extending much farther, whether to an edge at some point, or forever. They should recognize, though, that they can't really rule out a round Earth, because the round Earth is really an idea about something that they don't currently know at all, namely the world far beyond the few miles that they know. This subtlety in what is or isn't excluded seems pretty clear for peasant Flat Earthism, but it may not be easy to recognize in other cases.

[malkie]

I'm sure that many agnostics, for example, are quite able to suspend disbelief in gods, or a particular god, and use this state to examine hypothetical questions such as those concerning what you might expect to see in the real world if god beings existed with specific properties and attributes.

But, in my opinion, that is not the same as believing in such, or choosing to believe in such.

I'm sure there are degrees, of how long you spend thinking as though something were true, and of how much effort you invest, or risk you run, that will only pay off if the something is true. I don't think, though, that there is really any qualitative line between this kind of provisional thinking as though something were true and any kind of belief. When I think about why I believe the sun will rise again tomorrow, or that an object will fall if I drop it, I don't find any convincing proof that demonstrates that I totally know those things. I just find a cost/benefit/risk/reward analysis telling me that it's not worth spending any time or effort at all in thinking about the alternatives. Oh, maybe it could be worth it to spend a few minutes once in a decade or so, like to ballpark the odds of a really big gravitational wave coming through; but not much more than that.

There are things like that, where one alternative merits no significant amount of attention, and there are things where both alternatives are about equally worth considering, and there are all the other stages in between. Over time things can move around on the scale, either because I gather more evidence about how things actually seem to be in the world, or because the cost or risk of assuming the thing is true goes up or down. With imaginary numbers, the cost falls as you get used to the rules of complex arithmetic and it stops being a mental effort. I reckon most initially strange ideas become easier to entertain with practice, to the point where one can cease to think at all about alternatives just out of habit.

Imaginary numbers, as you point out, have the huge advantage that they can be made (and have been made) subject to a consistent set of rules and formal operations that give reproducible results that are useful in the real world.

Right, and this is why we like them. Most religions also involve consistent rituals and doctrines, shared by adherents all over the world, and often supporting various good works. There's a difference of degree in just how consistent things are. I don't know any bodies of religious doctrine that are as clear-cut as arithmetic. On the other hand, though, I think it's a naïve fallacy to hold everything to the standards that are attainable in the simplest cases. I think that's like refusing to eat anything except mush because mush doesn't need chewing and so chewing should never be necessary.

By the way, can you believe that Euler's Identity is - I want to say "real"! - true? Can you choose to disbelieve it? How on earth, or in heaven, can e, i, and π be related in this way? Yet, as with plain imaginary numbers, if you apply the "rules" it's impossible to deny the reality.

I don't really remember, but I'm pretty sure that I myself didn't fully believe the identity at first. I was probably told that it was an amazing result that had to be true because mathematical authorities said so, and I probably accepted that mathematical authorities really endorsed it, but I expect that I entertained a strong suspicion that it might be just an arbitrary mathematical game rule with no relevance to the real world—a bait-and-switch trick, in fact, in which one invented some weird new kinds of mathematical operation and just called them by misleadingly familiar names, like multiplication and exponentiation, even though the names didn't really fit.

(That sort of thing happens a lot. So-called "quantum teleportation", for example, actually involves only communication, not transportation. It's a real thing, but it's not what it sounds like.)

It takes quite a bit of practice with complex numbers before you appreciate that in this case the familiar names of multiplication and exponentiation and so on actually do fit, and are not misleading, because they really do stay exactly the same except for the one added rule that there is a number whose square is negative one. It's not so much bait-and-switch as finding the last piece of the puzzle and putting it into place. There was a hole in arithmetic that was just waiting for i; we never noticed before, because we didn't know what we were missing, but once you see how it fits, you can never go back.

For the god(s) question, do we simply lack a consistent set of rules and formal operations that give universally reproduceable results that are useful in the real world? Might this then allow us to choose to believe in god(s). Or might it be the case that application of such rules and operations would cause the belief to emerge, to creep up on us, without our having to, or being able to, make the choice? We would simply believe/accept/whatever?

Yeah, as I noted above, there's a tendency to get used to anything. At some point it can just become part of one's identity.

In physics we still love complex numbers, but there were several decades in the late 19th century, maybe extending into the early 20th, when people really loved a more complicated version of complex numbers, called "quaternions". Besides i, you added j and k, so that together with ordinary real numbers, there were now four kinds of numbers. Quaternions were a big deal, in their day. In a way, we still have them, but just as a set of two-by-two matrices that crop up now and then, and don't need any new rules beyond the usual matrix rules. Nobody thinks about quaternions any more. With historical hindsight, quaternions are an example just like my complex numbers example of how "choosing to believe" can be good, except on the other side. Sometimes "choosing to believe" leads to believing all of the time, but it's just a habit or fad.

You've given me a lot to think about, both from your above reply, and from your other recent replies on this thread. I hope I can find the time and mental wherewithall to respond to the points you've made.

I remember quaternions - vaguely