April 26, 2006

One Logic

Mixolydian Don posts a brief discussion of mathematics by Benedict XVI:

It seems an almost incredible thing to me that an invention of the human intellect and the structure of the universe coincide: the mathematics we invented really gives us access to the nature of the universe and permits us to use it. [...] I think that this intersection between what we have thought up and how nature unfolds and behaves is an enigma and a great challenge, because we see that, in the end, there is one logic that links these two: our reason could not discover the other if there were not an identical logic at the source of both.

Read the rest. This is the sort of thing that always gives me chills. (The good kind, I mean, like the kind that comes on hearing a particularly beautiful piece of music. Mom always said it was the Holy Ghost brushing by.)

Douglas Adams (of Hitchhiker's Guide to the Galaxy fame) wrote about this intersection of mathematics and nature, too. It was a central theme of Dirk Gently's Holistic Detective Agency and also appeared in several of Adams' essays in The Salmon of Doubt. But Adams was a confirmed atheist. It used to infuriate me that he could, as it were, so clearly see God's thumbprints yet at the same time deny their existence.

As mathematics is intimately related to all the hard sciences, I think that what B-16 has to say about it is also generally applicable to them as well. I also think that his understanding of the interplay of faith and reason at this interesection he describes, is a far more sophisticated and beneficial approach than the usual useless debates about creationism and intelligent design on which some people squander so much energy.

Posted by Robert at April 26, 2006 09:01 AM | TrackBack
Comments

I've always enjoyed seeing math in nature as well - and been annoyed by Adams' inability to grasp what he came so close to but missed because he would not acknowledge the possibility of God. Dirk Gently's was one of my favorite books of his, because of how well he wrote about it.

If we stopped squabbling about creationism etc and switched to things more likely to be persuasive, both sides would lose out on their ability to call people pig-headed and ridiculous, and that would just be no fun. (:

Posted by: beth at April 26, 2006 09:41 AM

I think that this intersection between what we have thought up and how nature unfolds and behaves is an enigma and a great challenge, because we see that, in the end, there is one logic that links these two: our reason could not discover the other if there were not an identical logic at the source of both.

Mathematical reason is, at heart, an intellectual, logical, scientific process. Math has basic roots in the eminently testable and observable, and builds from those premises to the more theoretical disciplines and sciences, which are still iterative processes for defining the universe around us.

So it doesn't seem at all a mystery to me that our intellectual, iterative methodology in figuring out the universe leads us to ... "intersect" or "cooincide" with the logic that apparently governs the universe. Because, er, that's what we're trying to figure out in the first place, all the while making up our own language to do just that.

For the developed human logic to mirror nature isn't an amazing collision; it's a necessary component of a successful effort. Sort of like going into a wood to look for bark and bear shit and .. finding it.

How this indicates God is a mystery to me.

Posted by: Bill from INDC at April 26, 2006 09:51 AM

Well, you have to read the rest of B-16's thoughts to see what he's talking about. He goes on to say that there is a logical structure to the Universe and that all of our science and technology are dependent upon its absolute trustworthiness. He concludes by saying, frankly, that either you believe God is behind it or not:

To come to the definitive question, I would say: either God exists or he doesn’t. There are only two options. Either one recognizes the priority of reason, of the creative Reason that stands at the beginning of everything and is the origin of everything – the priority of reason is also the priority of freedom – or one upholds the priority of the irrational, according to which everything in our world and in our lives is only an accident, marginal, an irrational product, and even reason would be a product of irrationality. In the end, one cannot “prove” either of these views, but Christianity’s great choice is the choice of reason and the priority of reason. This seems like an excellent choice to me, demonstrating how a great Intelligence, to which we can entrust ourselves, stands behind everything.

This is where one crosses over from observation to faith and is, at least as I understand it, the heart of the enigma about which he's talking.

Posted by: Robbo the LB at April 26, 2006 10:07 AM

Making up a language to describe logic is not the same thing as creating logic. Our powers of reasoning have led us to discover that 1+1=2 and we are able to use our mathematical language to describe that. However, we did not create the logic that made that mathematical statement true.

I think that is what B16 is getting at- why is it true? What makes it true?

Posted by: dillene at April 26, 2006 10:23 AM

There are only two options. Either one recognizes the priority of reason, of the creative Reason that stands at the beginning of everything and is the origin of everything – the priority of reason is also the priority of freedom – or one upholds the priority of the irrational, according to which everything in our world and in our lives is only an accident, marginal, an irrational product, and even reason would be a product of irrationality.

Meh. He sets up a false choice - reason (in the form of deciding that there must be a Creator) vs. random irrationality. Here's why it's a false choice:

1. He conflates immutable physical laws with the concept of non-randomness, and hence a guiding hand. Not a self-evident link.

2. He conflates Christianity with the choice of reason. If you accept the premise that "reason" is a priority, and that "reason" leads one to the conclusion that a sentient creator is responsible for the immutable laws that govern the universe (and I don't, necessarily), then the rational individual must also accept that the concept is only one small sliver of Christianity itself.

Accepting a Creator is a fundamental basis of the religion, to be sure, but mixed in with a great deal of extraneous irrationality. So the idea that Christianity is "choice of reason" seems like a rather, um, selective conclusion. Based on his criteria in the piece (that the rationally determined existence of a creator is prime, and that we should prioritize the rational over irrational judgment), we should all opt to be Deists.

And the fundamental, cliched trump card:

3. If rationality leads one to the conclusion that immutable law and complexity must have a Creator - who is necessarily complex and omnipotent - then who created the Creator? And who created him? And him? And him?

Whoa dude. Like, my head is spinning.

Posted by: Bill from INDC at April 26, 2006 10:30 AM

The intersection of literature and reality can be at times quite coincidental but no less jarring for being so. I have in my lifetime looked up from reading two separate books, specifically a Jack Aubrey novel by Patrick O'Brian and A Sentimental Journey by Lawrence Sterne, during passages denoting (respectively)wariangles and mating sparrows, to see a wariangle and mating sparrows. Both were exceptional events, as I had never before seen a wariangle (known here in Texas as a butcher bird), and the mating sparrows were on a fence at eye level directly outside my bus window, in a bus station at which my transportation had just arrived.

However, I have numerous times read about birds when none were seen upon my looking up. So the improbability of the two unlikely events has likely balanced out over my lifetime with the much more common, or likely, events. I think this may have been a theme in Adams' work.

Posted by: Austin Mike at April 26, 2006 10:38 AM

Making up a language to describe logic is not the same thing as creating logic.

I didn't suggest that it was, only that it's a component of how humans engage the process, and hence what the Pope looks at when he's amazed at the confluence fo the two. The laws of the universe necessitate an action, we devise a language to describe or successfully infer that action (math), and we're shocked that what we figured out naturally mirrors what we're looking for?

The creation of logic itself is not by necessity rationally assigned to a design or sentient Creator, though it does follow from some master plan - that master plan very well might be an endless series of random interactions within immutable boundaries, that give rise to amazing complexities (like humans, and the logic itself).

If one chooses to believe that God set this plan in motion, that's fine, but it's not THE evidently rational choice. The strictly rational choice is "I don't know."

Posted by: Bill from INDC at April 26, 2006 10:49 AM

Despite my fondness for Benedict XVI, I think I end up closer to Bill's position in this debate -- the fact that mathematics can describe the universe is not that remarkable to me.

Anbd the so-called "laws" of nature are not immutable and mathematically perfect. The are only observable and repeatable. They are "good enough". Let me explain what I mean.

Newton's "laws" are a good description of the universe, when looked at at a certain scale. But even a mathematically elegant (and reasonably accurate and precise) model such as Newton created cannot explain phenomena at the edges of his system, such as the behavior of subatomic particles. You end up coming up with new mathematical models to address these -- Einstein's relativity and Heisenberg's uncertainty principles have to be invented and they, too, describe the situation with a reasonable degree of accuracy, but probably aren't perfect. They also require you to reject Newton's system in certain respects, even though you know that system is accurate enough for almost any purpose an ordinary person might have (up to and including the moon landing). Subatomic particles scoff at Newton's laws -- they are jaywalkers who defy his authority.

This even horrified Einstein -- remember the "god does not play with dice" quote when he was confronted with Heisenberg's model.

The universe may have fundamental laws and may have a creator. But it is a mistake to think of mathematics or science as being fundamentally dsifferent from language. They merely describe things more accurately than language does.

Posted by: The Colossus at April 26, 2006 10:50 AM

And btw, the conclusion that there definitively IS NO CREATOR, no way, no how, is also an irrational choice, IMO. One can infer it as a subjective philosophy, or as an implied reality, but seriously stating it as hubristic fact is as irrational as stating the converse, to me.

Posted by: Bill from INDC at April 26, 2006 10:53 AM

And, as Pascal noted, probably not the best wager, in case he does exist . . .

Posted by: The Colossus at April 26, 2006 10:58 AM

Yeah, but Pascal's Wager is a fraud, as you can't have true faith simply as a rational decision to cover your bases.

You might follow the tenets of a religion if you think that rules are what buys you a pass into heaven (as when the church actually sold those - literal passes into heaven - what were they called?), and then the wager would work - but something tells me that such cold calculation is missing the whole point.

And inversely, there is an atheist's wager, in that if you behave with a moral conscience, and there is a God, he isn't going to burn you just for failing to give him mad props, yo, but reward (or not punish) you based on the value of your soul.

Posted by: Bill from INDC at April 26, 2006 11:08 AM

Excellent discussion, class.

Posted by: Robbo the LB at April 26, 2006 11:30 AM

Another way to look at this: do you believe that logical principles exist independently of our ability to discover and describe them? If you do, then the question becomes: where did those principles come from? To say "I don't know" is a cop-out. Everything created has a creator. There must be a primary cause.

Posted by: dillene at April 26, 2006 11:44 AM

Another way to look at this: do you believe that logical principles exist independently of our ability to discover and describe them?

Yes. But I believe that "logical principles" are our ability to describe what we'll more accurately term "natural law;" they are humanity's best language and process for interpreting the world around us. To the extent that they are successful in terms of naming consistent, observable (directly or inferentially) and reproducible phenomena, they do not exist independently; they are a consequence. Still, all "logic" is a limited human construct.

As to your main question, whether "natural laws" exist independently from our ability to categorize, discover and describe them, sure, of course they do. But our logic is the child of the iterative process of natural law too.

To claim either as some sort of objective evidence of God is odd.


To say "I don't know" is a cop-out.

No it's not, it's the only strictly logical conclusion. Asserting absolute or fundamental knowledge based on incomplete evidence is a "cop out," or more accurately, an intellectual and emotional vanity.

Your statement that "Everything created has a creator" is not testable, and hinges completely on what you define as "a creator." If a lightning bolt striking a shallow pond of water counts as a "creator," than yes, everything that we've observed thus far has a "first cause." If you mean an omnipotent spiritual being in the sky must have consciously created everything, then your statement is purely subjective romance, as the only things in nature observed to have sentient creators are fauna.

And in the case of humanity, all that's required for creation is a sixer of wine coolers and the backseat of a Chevy wagon, a standard far lesser than omnipotence, far greater than impotence.

As for everything having first causes, this harkens back to my point three, above:

3. If rationality leads one to the conclusion that immutable law and complexity must have a Creator - who is necessarily complex and omnipotent - then who created the Creator? And who created him? And him? And him?

This conundrum applies not only to the religious concept of God, but all first causes, random, biological, the Alien Lord Xenu, whatever. Frustrating if you think about it too long.

Posted by: Bill from INDC at April 26, 2006 12:18 PM

I was going to ask you, Bill, whether you believed the Big Bang was a one-off event or whether it was (or is) part of an infinite chain of Big Bangs and Gnabs Gibs.

Simply put, God can't be proved. Some people use this to dismiss his possibility completely, while others (including some folks here) are good enough to say "I don't know".

I don't think B-16 is trying to prove God's existence by mathematics - in his last paragraph, it seems to me that he is consciously taking the next step of relying on faith to get there. You may disagree with that, but remember who you're dealing with - there's not much room for advancement in the Vatican for agnostics. (In my own Episcopal Church, of course, it is a different story....)

Posted by: Robbo the LB at April 26, 2006 12:38 PM

One of the things I dislike about the "seeing God in math" concept is the way it tends to be used. For example in that Kirk Cameron video they use it to make a circular argument. They basically try and argue that you look at the order in the universe it means that there must be a Creator. But you could say that order doesn't have to be the result of a Creator because you can find order in nature, as a result of natural laws. Then Kirk Cameron will just say that those laws had to be a result of a Creator because human intelligence can create order. Which makes no sense.

Essentially seeing God in math is like seeing God in a sunset, it's subjective.

Posted by: dorkafork at April 26, 2006 12:45 PM

I was really crushed to read Salmon of Doubt, and find that an author I've admired and respected for years terms himself a "militant atheist."

Posted by: Sobek at April 26, 2006 12:50 PM

3. If rationality leads one to the conclusion that immutable law and complexity must have a Creator - who is necessarily complex and omnipotent - then who created the Creator? And who created him? And him? And him?

If there is one "thing" that is timeless and has always existed, why couldn't it just be the Universe? Or more specifically, a Universe that expands and contracts infinitely?


Posted by: dorkafork at April 26, 2006 12:51 PM

Essentially seeing God in math is like seeing God in a sunset, it's subjective.

Personally, I see God in a baby's smile.
Also, those Fanta ads with the singing women.

Posted by: Bill from INDC at April 26, 2006 01:02 PM

Everything created has a creator. There must be a primary cause.

That's an argument by induction, and induction only works within the framework of a space-time manifold where the Principle of Uniformity applies. [Or in an equivalent symbolic space - i.e. mathematics.] You cannot take that and claim that the Universe as an entity is subject to the same laws. The Universe is, by definition, causally closed. There is no possible logical connection between the laws that apply within the Universe and the creation of the Universe. (Because if there were such a connection, the definition of "universe" would change.)

This claim is, in a word, specious.

Posted by: Pixy Misa at April 26, 2006 01:32 PM

He goes on to say that there is a logical structure to the Universe

This is the key.

The Universe is self-consistent. That's why we can describe it in mathematical terms; mathematics is built up from the foundation of Logic and can be used to describe any self-consistent system. It's not so much magical as unavoidable.

And if the Universe is not self-consistent, well, purple peas in catfruit gravy.

and that all of our science and technology are dependent upon its absolute trustworthiness.

That's not right.

Science is founded on the assumption of this logical consistency, but science and technology are only dependent on its empirical trustworthiness. It's only required to actually work, not to be proven to work.

Posted by: Pixy Misa at April 26, 2006 02:30 PM

Moving back to Douglas Adams, recall his tale of the puddle that awoke one morning and marveled that its container fit so precisely. Clearly, reasoned the puddle, that container must have been intelligently created just to hold itself and no other possible puddle.

Math, logic, our rules of inference, are analogous to that puddle - they have arisen from the nature of their container and not vice versa. We can conclude nothing about the container's intentions or origins simply because our tools, created to fit exactly that container, successfully do do. Nothing mystical here, folks. Adams had a special ability - he didn't miss what wasn't there.

Posted by: Flint at April 26, 2006 03:52 PM

I follow you till the last sentence, Flint. But just because the puddle was incapable of divining the purpose or meaning of its container doesn't mean there wasn't any purpose or meaning. That's where I think Adams falls down.

Posted by: Robbo the LB at April 26, 2006 04:43 PM

(as when the church actually sold those - literal passes into heaven - what were they called?)

Plenary indulgences.

I was really crushed to read Salmon of Doubt, and find that an author I've admired and respected for years terms himself a "militant atheist."

Why? I'm an atheist and I have always been a big fan of C.S. Lewis. Why the hell would it bother you that an author you liked had different beliefs than yours?

Posted by: mantis at April 26, 2006 05:02 PM

I enjoyed the Pensees, but the wager struck me more as a roulette wheel. All these arguments aside, belief in a 'creator' doesn't get you anywhere as far as identifying that creator and the standards that this powerful being will presumably use to judge you at the same time that he keeps all the electrons spinning and all the nuclei together. Why doesn't the creator have a blog? That would be really helpful.

Posted by: slickdpdx at April 26, 2006 05:43 PM

[A]
Everything created has a creator. dillene at April 26, 2006 11:44 AM

Translated means: "I [you] believe in cause and effect, everything happens for a reason."

response:
I agree. Although man has a bad habit of making stuff up when he can not, or has not yet, found the reason/cause for.


[B]
There must be a primary cause dillene at April 26, 2006 11:44 AM
Translated means: "I [you] believe that to trace back causes would lead us to a first or 'primary' cause"

response:
This assumes 'Time' is linear only, which is not the case, as I believe Einstein long ago proved and which Pixy Misa mentioned in the comment of 1:32 PM. Non-linear cause and effect would be when the effects of a cause happened prior in “Time” to the cause.

[C]
“I would say: either God exists or he doesn’t. There are only two options. Either one recognizes the priority of reason, of the creative Reason that stands at the beginning of everything and is the origin of everything …or one upholds the priority of the irrational, according to which everything in our world and in our lives is only an accident… In the end, one cannot “prove” either of these views”.Beneidict quote Posted by: Robbo the LB at 10:07 AM

-“either God exists or he doesn’t. There are only two options”-
Response: Well it depends how one defines the word “God”. Benedict assumes his chosen definition, but there are endless definitions, not just two. Myself I see the three letters which make up the word ‘god’ as representing a very very simple prehistoric and broad concept: i.e. “everything” or “life and death”. It’s an all-purpose concept which requires a lot of qualification yet, ironically, is often wielded without qualification as if it means some one thing. To use it without qualification is like pointing to a room full of people and asking your friend “do you see him?”, akin to saying “either Everything exists or it doesn’t” or “do you believe in Everything?”. The big controversy is not whether someone “believes” in Everything or Life and Death
but rather - What their definition of Everything is, what their definition of Life and Death are..

- “the priority of the irrational, according to which everything in our world and in our lives is only an accident”-
Response: An "accident" is not necessarily irrational, it is simply an occurance we personally didnt forsee, or perhaps desire.

“either God exists or he doesn’t …In the end, one cannot “prove” either of these views”
Response: Translation: ‘One cannot prove whether life exists.’ The poor man is lost.
If there is one absolute fact humanity has to work with and build upon it is that Life exists---we are living beings. It follows that life has value. All healthy morals of civilization are built upon those two understandings.

Posted by: Civilization at April 26, 2006 05:50 PM

EDIT:

-“either God exists or he doesn’t. There are only two options”-
Response: Well it depends how one defines the word “God”. Benedict assumes his chosen definition, but there are endless definitions, not just two. Myself I see the three letters which make up the word ‘god’ as representing a very very simple prehistoric and broad concept: i.e. “The reason for everything” or “The reason for life and death”. It’s an all-purpose concept which requires a lot of qualification yet, ironically, is often wielded without qualification as if it means some one thing. To use it without qualification is like pointing to a room full of people and asking your friend “do you see him?”, akin to saying “either there is a reason Everything exists or there isn’t” or “do you believe there is a reason for Anything?”. The big controversy is not whether someone “believes” in a reason for Everything or a reason for Life and Death but rather - What is their definition of Reason, what their definition of Everything is, what their definitions of Life and Death are.
...

“either God exists or he doesn’t …In the end, one cannot “prove” either of these views”
Translation: ‘One cannot prove whether life exists.’
Response: If there is one absolute fact humanity has to work with and build upon it is that Life exists---we are living beings. It follows that we have a Reason to value Life. All healthy morals of civilization are built upon The fact of life and our Reasonable placement of Value upon our life.

Posted by: Civilization at April 26, 2006 06:38 PM

EDIT II:

“either God exists or he doesn’t …In the end, one cannot “prove” either of these views”
Translation: ‘One cannot prove whether a reason for life exists.’

Posted by: Civilization at April 26, 2006 06:42 PM

In Closing:

As to the reason for life, well he is right , I doubt man has the ability to comprehensively know the largest reasons, the largest causes, Yet we need not know all the reasons for us to recognize and value what we have.

Posted by: Civilization at April 26, 2006 06:47 PM

We exist for the sole purpose of proving ourselves to a God whom you cannot prove does not exist.

You can't handle the truth.

Heh.

Posted by: Woody at April 27, 2006 06:19 PM

There is no mystery that math (and other forms of logic) fit nature so well. They were created (by us) to describe nature. Calculus was invented to describe a phenomenon that Newton measured. As we looked closer and closer, that math fell apart (because the micro world is so f**ked up). A new math came from the old math and newer math from that, and so on and so on until it becomes a better and better approximation of the thing it is trying to describe. It is, as dorkafork mentions above, circular reasoning to say that there is something supernatural involved in this. It is amazing that our brains have created so much wonder in so short a time (a function of the invention of the book more than anything else), but that any expectation of a creator can lie behind that has no grounding in logic. Saying there might be is a function of faith, and sure it makes people feel nice, but there is no way to establish which story is the best one, Jesus, Buddah, Mohammud, Flying Spaghetti Moster are all equivalent. One is not better than another in terms of validity (although a stripper factory and a beer volcano in heaven certainly has my vote).

For this comment:
the usual useless debates about creationism and intelligent design on which some people squander so much energy.

To a scientist, this argument is not a useless debate, but a matter of life and death. If we "teach" the controversy" as our deep thinking leader so casually mentioned recently, we undermine the very essence of scientific inquiry. If you want to get into it, I would be more than happy to, but realize this, it IS a big deal and it can destroy science education in this country if the ID/Creationists get their way in the public schools.

Posted by: LB Buddy at April 29, 2006 06:27 PM

...it IS a big deal and it can destroy science education in this country if the ID/Creationists get their way in the public schools.

Yup

Simply put, God can't be proved.

Nope.

The existence of God can't be proved by humans. But an omnipotent God certainly would be able to prove to humans that he exists. Maybe he's got reasons not to do so, or maybe he reveals himself directly only to his chosen few, but it doesn't make much sense to me.

If I created the universe, things would be different.

Posted by: owlish at April 29, 2006 10:29 PM

i believe in infinitesimally less than one god.

on the other hand any formal system sufficiently powerful to do arithmetic is going to have undecidable propositions.

the world is here, we can agree on that. it either got here by magic or else it took a really long time. neither view is an excuse for irrational or uncivil action.


while you're at it print and read the "modern translation" of godel's incompleteness theorem here http://www.miskatonic.org/godel.html. really read it and understand it.

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