Math

[keithpenrod]

I'm a math grad student, so that's why I think about math all the time.  But, anyway, I see all the time the scientific method contrasted with the "religious" method.  Of course, this is very valid.  The one accepts new evidence, whether it is supportive or destructive of current beliefs, while the other rejects any that is contradictory to one's pre-conceived notions. 

However, I wonder if perhaps the analogy to math is more closely in line than science in general (I hope you don't mind me including math as one of the sciences).  This is my reasoning.

In my own opinion (and it appears Plato would agree with me), mathematics is the pursuit of truth--not the physical, measurable truth we observe in the universe, but abstract truth based solely on logic and reasoning.  Religion also claims to be the pursuit of truth and is also very abstract.

In mathematics, certain things are assumed to be true.  These are called axioms.  Everything in math is either something that is assumed to be true (for example, a definition is assumed to be true simply because it's an explanation of what something is or what a certain term means) or is proved to be true beyond any reasonable doubt through logic.  Anything that does not fit into one of these two categories is either false or is called a conjecture (being believed to be true, but having no proof and not "self-evident" enough to be considered an axiom). 

In religion, certain things are assumed to be true.  Logic is also used, and quite often the logic is sound (considering, of course, that the assumptions made to begin with were true).  For example, assume that god exists and that he feels love toward us.  Then, it would follow (from our definition of love) that he would be motivated to help when we are in trouble.  It would also follow that communicating to him what our needs are would make it more likely for him to notice and fill those needs (assuming that communication with him is possible). 

So, I suppose what I'm saying is that perhaps one reason why religion is so appealing to many is the reason that mathematics is so appealing to mathematicians.  Certain things simply can't be proven without assuming something.  (I'd argue that absolutely nothing can be proven without first assuming something.)  So, it seems reasonable to mathematicians to assume that, for example, the Zermelo-Fraenkel axioms of set theory are true (sorry for getting technical).  Then these axioms are used to prove many results about sets and things that can be done with sets.  Similarly, it seems reasonable to believers to assume that god exists.  Some believers may cite certain things that they think are evidence for this claim, some may admit that they have no evidence to support it.  But, at the same time, there really isn't any evidence to support any particular axioms in mathematics either. 

But, to get back to the original thought, this is where math and religion are different--it's the same argument as always used in comparing science with religion.  In math, if someone doesn't like an axioms or a set of axioms, they're entirely welcome to develop their own axioms and develop a universe of mathematics based on those axioms.  In fact, this kind of thing is encouraged.  Euclid gave five postulates (which we would now call axioms) dictating geometry.  The fifth axiom, which stated one way means that rectangles exist, is often dropped and replaced with a different axiom, yielding elliptical geometry or hyperbolic geometry or some other such thing.  The beauty is that these are all different possibilities and they each have their own benefits.  Perhaps such theory can coincide with or support something in reality, and perhaps it cannot.  But, as a simple abstract chain of logic, these imaginary universes can exist and many things can be said about them.

Religion does not welcome this.  Like math, in religion there are many people who set their own axioms (one god, two gods, thousands of gods; whether prayer is effective in changing god's will or just in learning it; what behavior is considered moral by god; etc), but unlike math, when people do this they are not welcomed, they are not applauded for their exploration of truth.  They are called heretics and apostates.  This type of thing divides believers.  They're not able to accept someone else's axioms because they insist that their own are correct.  Perhaps part of the reason is that they think that their own beliefs about god are in fact reality, whereas mathematicians view a certain set of axioms not necessarily as reality but merely as an abstraction possibly attempting to explain reality. 

Oh boy.  Sorry if that's way too long and confusing.  I have these ideas in my head and sometimes they're hard to express, and sometimes I just ramble.

[xSilverPhinx]

Yes but...math works.

[keithpenrod]

Yes but...math works.

That's the point I meant to make.  If I think all odd numbers are prime, but then someone comes along and factors 9 as 3*3, then I drop my conjecture and go with the obvious result that not all odd numbers are prime.  Mathematicians reach a consensus.  Religionists just disagree with each other.

[Pharaoh Cat]

Yes but...math works.

Perhaps we could start a religion named Placebo whose creed would be one sentence:
"We believe in God and God's love because it makes us feel good." 

[Crow]

Very nice comparison and would agree with you, the reasons you mention about math being open to challenge is why its such a good tool for science, if the tools aren't able to advance the science will eventually stagnate and theories wont be able to be further refined beyond a certain point. It is also the reason why religion does stagnate and becomes out dated as society advances and social thought evolves.

As you mentioned Euclid you should check out this edition of 'The Elements of Euclid' its fantastic. The elements of Euclid in living color.

[Jose AR]

This forum is great! I hoped there were people out there obsessing over IDEAS. I think I need new friends because it seems people are not interested in ideas. My friends want to talk about media experiences, activities, and possesions, which are all great, but ideas rock. I am not a scientist or mathematician and therefore give my opinion (ramble) about your idea based on what I imagine those disciplines are like.

I always thought of math as another kind of language. Languages are arbitrary and they are internally coherent and consistent. There is no empirical evidence to prove the form of a past tense verb. But language can also describe material objects or non material concepts. Language can also take the form of arguments, debates, evidence, and proof in a very real way.

When I read about science, I read books written for me, the non scientist. But when I try to read something "heavy", say in biology, the ideas are expressed using the language of math. Math seems to be another language that we have invented that describes material objects and their properties and relationships better that written language. When I look at a research paper on any topic, it seems to talk to the reader in math (so I need some one to "popularize" the science for me)

Math is also a study (or science) of its own. And I think this "branch" of math is what you, a mathematician call "math". And its this kind of math (pure math?) that you liken to religion. So there are two kinds of math. One is a set of tools for describing material reality, the other a theoretical (and infinite?) quest for something (truth?).

Both math and religion can be arcane, indecipherable, therotetical and even removed from reality. But I can't accept that science or math are like religion, except that they are both complex cultural linguistic memes. Theoretical math is an ever expanding awesome grand palace. Hallways and rooms expand in every direction, in every dimension. I can imagine that the time it takes to educate a mathematician will always be increases as this edifice becomes larger, stranger, and just plain harder to understand.

Religion is no grand edifice! It is more like a shiny gem, all you can really do with it is polish it and make it shinier. Theologians are not scientists. there is no "theological method". Religion is more like a circus tent, and all the work of the clerics is bent on reworking the "truths" to make the same tired three ring circus seem new and exciting. There's a sucker born every minute and a huckster ready to take them for all they're worth!

Religion pretends to be seeking the holy grail, but there is no grail, there is no single perfect ideal form. Instead there is just messy, quirky, sometimes elegant, sometimes incomplete science. Science is always on shaky ground, becuase there's the possibility of a new "force" or theory that changes everything. I think thats an uncomfortable idea for many people. But god is always there for us. Hush little human, it'll hurt less if you don't think.   

[keithpenrod]

I always thought of math as another kind of language. Languages are arbitrary and they are internally coherent and consistent. There is no empirical evidence to prove the form of a past tense verb. But language can also describe material objects or non material concepts. Language can also take the form of arguments, debates, evidence, and proof in a very real way.

It is a foreign language.  And it does take several years to master, just like any language does.  Every field has its own jargon, but I think for most fields it's only just jargon--with math, it really is a whole new language.  There're rules for syntax and everything.

Math is also a study (or science) of its own. And I think this "branch" of math is what you, a mathematician call "math". And its this kind of math (pure math?) that you liken to religion. So there are two kinds of math. One is a set of tools for describing material reality, the other a theoretical (and infinite?) quest for something (truth?).

Yes, actually the two are called applied math and pure math.  It's not uncommon for a pure mathematician to look down condescendingly on an applied mathematician and for applied people to think pure people are snobbish.  Personally, I don't enjoy applied math very much at all.  It's riddled with calculation and mind-numbing algorithms.  Pure math is rich with ideas, logic, and theory.  It's like an adventure--a new adventure every day.

Both math and religion can be arcane, indecipherable, therotetical and even removed from reality. But I can't accept that science or math are like religion, except that they are both complex cultural linguistic memes. Theoretical math is an ever expanding awesome grand palace. Hallways and rooms expand in every direction, in every dimension. I can imagine that the time it takes to educate a mathematician will always be increases as this edifice becomes larger, stranger, and just plain harder to understand.

Religion is no grand edifice! It is more like a shiny gem, all you can really do with it is polish it and make it shinier. Theologians are not scientists. there is no "theological method". Religion is more like a circus tent, and all the work of the clerics is bent on reworking the "truths" to make the same tired three ring circus seem new and exciting. There's a sucker born every minute and a huckster ready to take them for all they're worth!

Religion pretends to be seeking the holy grail, but there is no grail, there is no single perfect ideal form. Instead there is just messy, quirky, sometimes elegant, sometimes incomplete science. Science is always on shaky ground, becuase there's the possibility of a new "force" or theory that changes everything. I think thats an uncomfortable idea for many people. But god is always there for us. Hush little human, it'll hurt less if you don't think.   

Now, that's not entirely true.  While religion probably isn't seeking truth, as it claims to be, it does evolve and change over time.  Arguments that would convince intelligent but non-questioning people a few centuries ago, that were typically employed by religions, would not work today.  The logic (which all too often is double-think) that persuades the intellectuals to be believers has been refined to accomodate more intelligent thinking.  I think of it kind of like evolution--that it adapts in order to survive.  If, for example, churches were still claiming that the world was flat, I guarantee they'd have very few followers.  So, it's not necessarily the same arguments going on.  The same acts, yes--the acts of denying empirical evidence, making science an enemy, and stubbornly refusing to change one's doctrine.  But, I think it has evolved. 

But, yes, I think you did get one of my main points in that (pure) math and religion are both abstractions.  Applied math attempts to describe the world around us, and religion does (to an extent) as well.  But, they're both just sort of abstract ideas that people have come up with and sit and reason about.  Theologians do argue the logic of religion, much the same way mathematicians argue the logic of math.  Perhaps one main difference is that math has progression as its purpose, its goal.  Mathematicians are constantly seeking new truths to declare using previous results.  Religion only progresses because it is forced to in order to stay alive.  It lives to perpetuate itself, and does what it must in order to do so. 

[Pharaoh Cat]

It (Math - PC's insertion) is a foreign language. 

It sure is.  Any chance you could drop in on the Ancestor Paradox thread, here on this same forum, and resolve the dillemma for us?