Join First Church of Mathematics

[alfredo]

http://www.kentucky.com/mld/heraldleader/news/opinion/8400320.htm

Join First Church of Mathematics

By Roger L. Guffey


I have learned in 22 years of teaching that there are always new things to learn from unexpected sources. The vitriolic tirades of local ministers against gays and foreigners coupled with the money-grubbing hypocrisy of national televangelists have taught me that people will believe anything you say if your name is preceded by the title "reverend."


Since many of these appellations are self-assumed, without benefit of education or substance, I am petitioning the Department of Education to change my professional status from certified teacher of mathematics to the Rev. Roger L. Guffey in the Church of Mathematica.


I am a little contrite that I did not think of this sooner while I was reading the Book of Numbers. Adopting the title "reverend" will simplify my pedagogy enormously as mathematical logic and proof will be supplanted by opinion and bluster.

---Read more at the above link---

[rogerashton]

1. Well,

Cantor regarded mathematics as "the study of infinity" and thus a branch of religion. And then there were the Pythagoreans.

[Gman]

2. They worship right triangles??

[grytpype]

3. At least right triangles EXIST.

[Iceburg]

5. As does nothing (exist)

Where do I sine up?

[patcox2]

8. Do they really? Do the rules of mathematics "exist?"

Where are they? Think about it. I don't think its clever or ironic to compare mathematics to God, they are very similar concepts. So, what color is 7? How much does it weigh? You say that "7" doesn't have any physical existence, yet it exists? This is starting to sound absurd, you are telling me that I cannot see or hear or weigh these rules of mathematics, I cannot observe them and measure them as required by the rules of science, I must accept their existence without empirical evidence? And you say that although they are invisible, they are everywhere and control everything? Thats absurd. Why in the end they are all based on those "logical" proofs we all had to struggle through in geometry class, yet everyone knows that "logic" is not an absolute, its just the human perception of the universe, shaped by certain attributes of our brain structure related to our language abilities. So "logic" is just a construct of our limited perception that we impose upon the world, yet we have the arrogance to beleive that what we perceive as "logical" are in fact the rules that govern the workings of the universe?

[megatherium]

10. mathematicians are notorious platonists

in that their usual working assumption is that their mathematics does exist, on some plane above reality. But mathematicians have a very clear understanding of the philosophical status of their subject; they know it's a human invention.

Eugene Wigner wrote an influential article (1960) on the "unreasonable effectiveness of mathematics". If mathematics is just some sort of social game that mathematicians play, why has it proved so tremendously powerful in humankind's efforts to understand and control nature? All of modern technology, and most of the natural sciences (physics, chemistry, and even biology), are now intensely mathematical enterprises.

[rogerashton]

12. Yes, we are.

(OK, I haven't been a mathematician for a few decades, but that ealy training doesn't go away.)

And mathematics is not an invention. Mathematical objects are discovered, not invented.

That's the Platonist position, anyway, and I believe it is correct -- on the basis of my experience.

[megatherium]

15. no humans implies no math.

Crows and other creatures can count small numbers of objects. Many creatures including humans have good instinctive understanding of mechanics and a limited understanding of geometry. Human language is extremely logical. From all of these, mathematics has been invented by us. Yes it is an invention, but it is real, just as other inventions are real, such as television or aircraft. One can build a gizmo and wonder, what happens if I do such-and-such? One can write a series and wonder, what it adds up to?

Anyway, I still am a mathematician, though my career isn't always worth writing home about.

[patcox2]

19. Thats interesting; Platonism implies a belief in an unknowable perfection

Platonism, it would seem, embodies the beleif that human perception is inherently imperfect (that idea, carried to the extreme of platonism, should be anathema to objectivists), and that therev are higher realities that humans are inherently incapable of perfectly perceiving. It is no stretch at all to conclude from this that a platonist woulod never believe that science, based as it is on inherently faulty human perceptions, is capable of fully and accurately describing the universe, and that there is always a higher reality beyond our ability to comprehend. Well, jeeze, this is sure good news for a beleiver in a non-anthropomorphic "god" as a flawed understanding of a higher and imperceptible reality, isn't it?

In other words, out with it, there is nothing incompatible, and in fact there are similarities, between mathematics and religious faith.

As someone who actually understands "logic," mathematics being based on the most rigorous logic, are you ever amused by the assertions of some of the self-professed rationalists on this board who define "logic" in terms of their personal beleifs?

[patcox2]

20. Platonism is very compatible with religious faith, no?

Platonism, it would seem, embodies the beleif that human perception is inherently imperfect (that idea, carried to the extreme of platonism, should be anathema to objectivists), and that there are higher realities that humans are inherently incapable of perfectly perceiving. It is no stretch at all to conclude from this that a platonist woulod never believe that science, based as it is on inherently faulty human perceptions, is capable of fully and accurately describing the universe, and that there is always a higher reality beyond our ability to comprehend. Well, jeeze, this is sure good news for a beleiver in a non-anthropomorphic "god" as a flawed understanding of a higher and imperceptible reality, isn't it?

In other words, out with it, there is nothing incompatible, and in fact there are similarities, between mathematics and religious faith.

As someone who actually understands "logic," mathematics being based on the most rigorous logic, are you ever amused by the assertions of some of the self-professed rationalists on this board who define "logic" in terms of their personal beleifs?

[struggle4progress]

21. Unfair stereotype. Read Brouwer. eom

[scottxyz]

23. Your motion was independentely seconded

I called for people to read Brouwer (and Heyting).

You really get a different feel for math from Brouwer and Heyting and the other Constructivists.

Constructivism is also turning out to have amazingly practical and wide-ranging applications. Look at Fotini Markopolou-Kalamara.

Platonism and the "law of the excluded middle" are interesting mental gymnastics. We are seeing now that of course they have little to say about the physical world.

[rogerashton]

13. It works.

But pragmatics is only part of it.

Logic is not human. Humans are crappy at logic. Logic is something that is imposed on us whether we like it or not. Most of us don't like it, so we tell ourselves that "logic is not an absolute." Basically the idea is, if I don't waant to believe it, then it isn't true.

And you accuse the logician of being arrogant? My, my.

[megatherium]

14. humans are extremely good at logic.

Logic is basically an offshoot of our language abilities, which are astounding. Most humans in all languages (even seemingly rough languages such as creoles) follow grammatical rules with few errors.

[northzax]

16. well, it works to a statistical endpoint.

there are exceptions to almost everything.

I would posit that mathematics, per se, are natural laws, but that we (humans) may have a completely flawed understanding of what those laws mean. Simply because everthing we currently believe to be correct has proof from our perspective, doesn't mena that there aren't completely different ways of approaching those same laws that would result in 'mathematics' that look completely different from ours, act completely different and yet fit the same sets of universal laws from a different perpective.

simply, are there two completly different and alien ways of expressing the (apparently immutable law) that 2+2=4? Yes, every human race that studied mathematics came up with the same answers (that's because the aliens taught us all the same, obvioucsly, but I kid) that can be explained that all human experience on Earth is roughly the same, and follows the same overriding phyisical laws, she identical physical abilities and has the same perspective on the universe as a whole. Would a completly different experience, from a completly different perspective and skill-set, create a completely different set of mathematical laws, equally as correct, to describe the same basic principles? and does it matter?

[BeFree]

24. What the hell

Knowing just a bit of chem and math, and having read this thread, I added up those three things and here is what it equals. H₂0. Water. 2 parts Hydrogen and 1 part Oxygen.

What the hell am I saying? Math exists. It is used to describe the Generating and Organizing of Dirt, (and other little teeny tiny things like dirt). GOD. Generation, Organization of Dirt.

Science may be thought of as the language we use to describe what happens when we discover 2 hydrogen atoms with one Oxygen atom, etc., etc..? On Mars, it's a whole 'nuther language.

[rogerashton]

6. Sort of.

And don't eat garbanzos, if my memory serves (but it doesn't always).

Followers of Pythagoras, actually, who regarded math as a form of devotion. I think.

http://scienceworld.wolfram.com/biography/Pythagoras.html

http://www.otterbein.edu/home/fac/dvdjstck/papers/MathAsWorship.pdf

edits: links

[alfredo]

4. But it took Roger L Guffey to build a church around it.

[Old and In the Way]

7. Can God make a square circle?

I always ask fundy types that, just to see their critical thinking skills implode.

[struggle4progress]

9. Too easily done: just use the taxicab metric. eom

[megatherium]

11. God knew this is a mathematical impossibility

long before Lindemann proved it in 1880. Knowing it is impossible to obtain an odd number by adding two even numbers says nothing about the existence of God -- squaring the circle is impossible in exactly the same way (albeit a great deal more complicated).

We live in a universe which appears to follow natural laws, which can be beautifully and simply expressed using mathematics. To some, this suggests a rational creator. The observation that any small perturbation in these natural laws, or in the values of physical constants (such as the gravitational constant or the mass of the electron) results in a universe incapable of supporting life, has convinced some physicists that design in the universe is no longer such an outlandish idea.

[northzax]

17. but on the flip side

there is no way to know whether or not alterations of the laws of the universe would lead to a place incapable of sustaining life, since all life is a product of this particular universe and the rules therin.

Think of it this way, if the rules of checkers were different, would it still be checkers?

[megatherium]

18. It might not be checkers

but it would be void of life. A proposed solution to this puzzle is the many universes (or evolving universes) theory -- there are many universes, most of which don't support life, but a few do, including ours. Of course, none of these other universes are observable.

[northzax]

25. not neccesarily

just not life as we comprehend it. Another, slightly different universe might have lifeforms based on something besides carbon. It might have lifeforms that don't exist in any form we would recognize as 'life' just as they might not recognize us as 'life' I find the idea that our univerise is one of the chosen few that supports life to be as anthro-centric as the old terra-centric solar system. Just because, from everything we can tell, we are the only intelligent life forms, on the only life-giving planet in this little area of our universe (and it's likely we are alone in our galaxy from what we can tell) does not mean that we are special. Perhaps the next universe over has planets teeming with life forms, perhaps ours is one of the few that is this inhospitable to life, maybe that's what makes this universe special.

but, as you say, we cannot observe any other universes, so it's all shits and giggles.

[scottxyz]

22. Look up the works of Brouwer and Heyting and Markopoulou-Kalamara

Brouwer and Heyting were the "Constructivists" in mathematics.

The only things that exist in "constructivist" mathematics (also called "intuitionism") are things that you can actually construct.

In particular, the famous "law of the excluded middle" from formal logic is not allowed in constructivist mathametics.

The "law of the excluded middle" is a trick that math used to expand the amount of things it thought it could prove. Instead of trying to positively prove a particularly difficult conjecture, you attempt to prove its NEGATION and if that leads you to a contradiction, you claim you proved the original conjecture.

This assumes that every conjecture is either true or false. As Goedel showed later, there is an area in the middle for conjectures that you haven't been able to prove true or false yet - conjectures which are still undecided.

Constructivism said that just showing something wasn't false didn't mean you had proven it was true - it could still be one of those "undecideds" as well. Until positively proven, a conjecture remains undecided: proving the conjecture's negation doesn't prove the conjecture.

There is a young physicist named Fotini Markopoulou-Kalamara who has applied Heyting's and Brouwer's constructivist mathematical ideas to cosmology and physics. Her paper "What the Universe Looks Like From the Inside" is so much simpler and more believable than all that 10-dimensional string theory the other theoretical physicists talk about these days.