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Jul 25 2006
Eureeka! Mathematical Proof Of God's Existence!

Hi, everyone!

Sorry it's been so long since I posted anything. I've been without internet access for a while.

I recently had a discussion with a very bright and courteous Christian (he labels himself an agnostic Christian). It was exciting and I learned quite a bit. However, he brought up the issue of a mathematical proof of God's existence, and I had little to say as a response, since I'm almost as good with math as I am at brain surgery! I asked for more information on this supposed proof and he supplied the following link.

Well, there you go! I suppose we can all stop arguing against God's existence now! Here's mathematical proof!!! Haha!!!

I know we've got quite a few mathematicians in the group and I'd like to hear your thoughts on this article. (It's not a primary source, but rather a short article written for general Christian readers. However, it incluedes the names of some of the mathematicians who've been developing these "proofs" and you may be able to find their original work on-line.) I know some general rebuttals to the "Fine Tuning" argument, but I'd like something a little more concrete. Any thoughts anyone has on this article and the math involved, I'd appreciate it! (Oh, and I realize it's difficult to explain this kind of math on my, very simple, level, but if you could make it as easy to follow as possible, I'd appreciate it!!!)

Thanks everyone!

--Billy Kelly

Jul 26 2006

There are three arguments offered in this article. Two of them are completely ridiculous and the third is an argument that has been losing ground for centuries.


First, the most mathematical of the three is the formula e^(pi i)+1=0. This is a pretty formula because it contains several of our most important constants. It is also true.

But, does it have anything to do with a proof of god? It comes down to the SAME dumb question we've been talking about forever, but now put in a context of advanced mathematics to "wow" people. The question is this: can something beautiful and complicated exist without it having an intelligent creator?

This formula is an indication of the beauty and complexity of math. As I'll explain below, it does link together algebra, geometry and calculus as the article explains. But, quite to the contrary of their conclusion, I would say that what it proves is that beauty and complexity CAN exist without a creator.

Math definitely has many beautiful and interesting things in it. What about the Pythagorean theorem, is that a proof of the existence of a deity? Why go that far, what about 2+2=4? What about the fact that 3 is prime but 6 is not? These are all truths within mathematics. But, most people -- even devout theists -- do not seem to think that god had the choice of making a universe where 2+2=7, where 6 could not be factored as 2*3 or where right triangles in a plane do not satisfy the Pythagorean theorem. The relationship between e, pi, i, 1 and 0 is pretty and interesting -- especially because e, pi and i arise in very different areas of mathematics. However, as one learns more mathematics it becomes less mysterious. Although e comes from calculus and pi from geometry, these are really NOT unrelated areas: the Fundamental Theorem of Calculus in its multi-variable format makes it clear that calculus really IS about geometry after all. And the role of i (from algebra) is not so amazing either. That algebra and geometry are just two different ways of looking at/talking about the same mathematics was a discovery of Descartes way back when, and in terms of complex numbers this manifests itself as the statement that multiplying by imaginary numbers can always be interpreted as rotations in the plane. When you look at it this way, e^{x i} for any real number x is just a rotation by x radians and then it becomes completely obvious that when x=pi you end up with a -1.

In conclusion (of the part about e, pi, i, 1 and zero) once you understand math you see that it HAS to be that way. It wasn't a choice god made to select this beautiful formula over some alternative. Once you have circles, calculus and complex numbers, this is a formula that they DO satisfy. Amazingly, this beauty and complexity exists without any plan. There are lots of other such beautiful things in mathematics, some of which quite clearly demonstrate the fact that complexity arises even in very simple systems.


The part about probability and mutations reveals the ignorance of the author of the article. The things they say here are so far from true, I'm even having trouble understanding what they THINK they are saying. I mean, they talk about "particles mutating"...particles don't mutate! But, really the heart of the problem with their "argument" is this statement:

Even if we limit the number of necessary mutations to 1,000 and argue that half of these mutations are beneficial, the odds against getting 1,000 beneficial mutations in the proper order is 2^1000.

It makes no sense and I cannot figure out how to even figure out what they mean. They seem to be claiming that the odds of getting a PARTICULAR sequence of 1000 mutations is (one in?) 2^1000. That's the odds of flipping a coin 1000 times and getting heads each time...but I don't know WHAT it has to do with the question they claim to be looking at. It is as if they are saying that with each generation the off-spring either gets the right mutation OR another mutation which rules them out, and what is the odds that they end up with the right mutation every time for 1000 generations.

There are 2 serious problems with this argument:

BIG ONE: The probability of some event occuring (like getting these 1000 mutations) must somehow be dependent on the amount of time. They are claiming that it is 1/2^1000 per what? per year? per decade? per millennium? It seems to me (using the coin analogy) that they are seeking these 1000 mutations in 1000 successive generations. Or, to consider the coin analogy, even though the odds of flipping a coin 1000 times and never getting tails is small, if you flip a coin repeatedly until you get 1000 heads it will NOT take that long (we expect this to occur in about 2000 flips!) In the same way, you will EVENTUALLY get those 1000 mutations, and though it is unlikely to occur in 1000 generations it won't take all that long for it to happen!

NUMBER TWO: This past July 4th, Maria S. Valencia of Upper Darby, Delaware County, won the Pennsylvania Lottery’s July 4, Millionaire Raffle game. The odds against her winning were 1 in 625,000 (unlikely but much easier to think about). The argument used in the article is this: since she only bought one ticket, it is not possible that she won.


Yes, that seems to be their argument. Her odds of winning were 1 in 625,000 and since she would have had to have bought many thousands of tickets to get the odds up high, it is not possible that she won.

Look, SOMEONE was going to win the Penn Lottery, and even though the odds of Maria Valencia winning were quite small, we cannot use this improbability after the fact to claim that she did not really win.

In the same way, the authors of the article are figuring out the odds that exactly the right mutations will occur to produce US (humans), rather than just asking, if mutations occur with each generation what is the probability that after billions of years some complicated creature will have evolved. This latter probability will be MUCH higher, just like the probability of SOMEONE winning the drawing were not small, but 100%!


The only actually interesting point the article makes is the so-called "finely tuned universe" argument. At least this one deserves some discussion!

The idea that "there must be a god because our world is so perfectly suited for life" has a long history.

First, people claimed "since each animal is in just the right place (fish in the water and not in the sky, giraffes where they can eat leaves from trees, etc), God must have PLACED them there". Of course, once one has even the most basic notion of natural selection, this argument collapses. If one RANDOMLY placed fish and giraffes in places around the world, it would not take long before there were only fish in water and giraffes near trees. So, despite the fact that such order SEEMS to require thought, it turns out that it establishes itself pretty quickly without any need for intelligent guidance. In other words: it turns out that there really is no other choice, such order is just the way life happens.

The next such argument was the idea that the earth was perfect for life.

Just the right temperature, presence of water, presence of air, etc. Again, it seems that SOMEONE must have planned it this way for us. But, another non-supernatural argument explains this apparent mystery. Once we realized how MANY planets there were, it was no longer a surprise that SOME of them would happen to have the right conditions for life. In other words: it is not a surprise that of the billions of planets out there, we find ourselves on one of the ones whose conditions are right for supporting life. (Plus, I'd like to add that life is a lot more versatile than we expected when we first made these claims. We now find life on Earth in inhospitable places where we would not previously have imagined it COULD live -- deep sea lava vents, under the polar ice cap, deep in desert sands, etc. -- and so maybe conditions suitable for life are not as rare as we thought.)

Nobody claims that the distribution of life on earth or the suitability of the earth's environment are proof of god's existence anymore. So, I would say that this argument is "retreating". But, it isn't completely gone. The remaining argument is that the very constants of nature (especially the relative strengths of the fundamental forces: gravity, strong, weak and electro-magnetic) are "finely tuned" for life. So, whoever MADE the universe must want there to be life here.

I do not have an easy answer for this one like I did for the others, but that is only because we are really IGNORANT about the universe today as we were about the planets 400 years ago.

So, I cannot say that this argument is completely ridiculous. But, I can say that it is very weak, because I can see several possible alternatives...and they look just like the ones from the past.

* There are several different versions of physics (e.g. a variant of string theory and a popular interpretation of quantum mechanics) that posit the existence of many universes. At this point, this is certainly a speculative idea. BUT, if it turns out to be true that there are billions and billions of universes, each a little different than the others, then it would not be so strange for SOME of them to have just the right "choice of parameters" to support life.

* We don't really understand physics, don't let physicists fool you. (I've published quite a few papers in physics journals, so I feel qualified to say this.) Yes, we've got great formulas that predict things quite well, but we are really lacking in our understanding of it. Just as there have been breakthroughs in the past that changed our understanding of physics, there will be more in the future. The next big theory may well explain that things HAVE to be this way. I mean, even though we talk about the odds that gravity is this strong and the weak force is that strong, how do we know that they COULD be different? Maybe they are both manifestations of the same thing and one cannot be changed without the other. When this happens in mathematical physics we say that these two parameters are COUPLED. (Interestingly, in my own area of "soliton waves" there were arguments that certain phenomena were not possible because the odds of the forces being balanced just right were very small that turned out to be wrong because they failed to take coupling into account.) What I'm saying is this: we don't really know what the odds of the universe being like this ARE because we don't know what the other possibilities are. It is like the argument that somebody must have put the animals where they belong because otherwise we'd see fish in trees...perhaps when we understand it we'll see that there IS no other way it could be.

* Finally, I'm very skeptical about the idea that we even KNOW what sorts of universes could support life. It may well be that if the mass of the electron was twice as big, then life AS WE KNOW IT would not exist, but as has been proved so often in the past, we might not be able to imagine how life could exist in those conditions until we find it. Then we say, "Oh yeah! I guess life COULD exist like that after all!"


Hoping I did not say anything stupid or waste your time,


Jul 27 2006

Alex shows the flaw in their PART II argument, but it's always nice to have a concrete counterexample as well: Domestic dogs are a good one.

No domestic dog breeds existed before humans. Their origin is not a mystery. We know from genetic studies that all domestic dogs are descended from gray wolves, and they did so over the last 10,000-15,000 years. Observation suggests that there must be at least 1000 mutations that differentiate a chihuahua from a wolf. Yet these mutations obviously did occur since we have chihuahuas. People did not cause the mutations since chihuahuas in their present form existed at least 100 years before people had any understanding of the mechanism of inheritance, much less DNA mutagenesis - concept unknown before the second half of the 20th century.

And keeping with Alex's point, if chihuahuas went extinct and we had to start over from wolves, it is unlikely that we could get exactly the same type of dog again. We could probably get a small short haired dog, but it is unlikely that we could get a breed that we could call a chihuahua.

Aug 4 2006

Hi, Laura and Alex!

Thank you both for your contributions! Everything you said made perfect sense! And no, Alex, you didn't waste my time or say anything stupid! I'm not sure you could do such a thing if you tried!

In fact, I thought your responses were so good I've invited my Christian friend to read them and to comment on them if he feels so inclined.

It is interesting that Christians seem to have this notion that contemporary math, science, and philosophy all come together to "prove" God's existence. Based solely on my own discussions with many of them (admittedly not the best way to go about forming such an opinion and making such a generalization) I think they are only studying the issue from one side; the theistic side. Most of the Christians I speak to haven't even heard of many of the atheists and skeptics who debunk these ideas, (and fewer still have actually read any of the atheists and skeptics I have in mind). They seem to have insulated themselves against any possible criticism of their views. Wrapped in a bubble of theistic thought, they only read those who support their views and they consistently have their views justified. They read Strobel, McDowell, Dembski, and Behe and think there's no way they're wrong. But they never (or seldom) expose themselves to the other side. And they end up with the impression that there's plenty of proof for God's existence, and atheists must be willfully ignorant of it all.

So, how do we get Christians to read the opposing side? How do we get them to see that reason is a better tool for understanding truth than faith?

Sorry. I know there are no easy answers to these questions. It's just frustrating to talk to theists sometimes. It feels like we're speaking two different languages because there is such a huge rift between reason-based thought and faith-based thought. Yet if we could find a way of bridging this rift...

Any suggestions? Thanks again, Laura and Alex! And thanks to anyone who responds to this meandering rant! I apologize if I'm not making any sense!


Sep 24 2006
nice discussion!

I really enjoyed reading both Alex and Laura's responses to the initial question. Such an interesting topic with very well-written responses!


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