War, Mathematics and God | Herb Silverman

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I've been actively engaged in two wars in my life, but I don't receive or deserve veterans' benefits. My most recent service occurred during the manufactured war by Fox News, the "War on Christmas." Yes, I plead guilty to wishing people "Happy Holidays" around winter solstice time, and I have even been known to provide a pagan history lesson to those who insist on telling me that Jesus is the reason for the season.

My earlier war arrived as a card game I learned at five, a game called "War." Two players are dealt 26 cards face down. Each then simultaneously shows the top card, and the player with the higher card takes both exposed cards and places them at the bottom of the player's stack. If both cards are of equal value, there is a "war." Each combatant places the next three cards face down, and the fourth face up. The card of higher value captures all the cards played and puts them at the bottom of his or her stack. The war ends when one person has all 52 cards.

I was very good at "War," or so I thought. I hadn't yet heard about "confirmation bias," which can cause us to remember more victories than defeats.

When I finally realized that the game was skill-free, I lost interest. Knowing that the outcome is completely determined once the deck is shuffled and dealt, I began to invent variations. For instance, I'd put all four aces (the highest value) in one stack and the remaining 48 cards in the other stack. After playing five times, the stack with four aces won all, but once. I concluded that it was better to start with the four-ace stack.

I hadn't realized that I was applying a naïve version of a Monte Carlo method, where a large number of repeated trials produce reasonably accurate probabilities for the outcome of an event. In fact, the simplistic childhood card game of "War" has much in common with my subsequent career as a research mathematician. Mathematics is also a completely determined game that starts with a set of assumptions called axioms (the axioms for "War" are shuffle and deal) and follows rules from which the truth of mathematical statements (conjectures) can be discovered. What makes mathematics more interesting than "War" is the ingenuity required to prove or disprove conjectures based on the axioms.

Mathematicians usually begin with axioms that seem "self-evident" because they are more likely to guide us to real-world truths, including scientific discoveries and accurate predictions of physical phenomena. Most ancient religions are also loosely based on an axiom or a set of axioms. The most common axiom is "God exists," which is not as self-evident as it appeared to be in a pre-scientific world.

I ask you: Which abstraction is more practical for better understanding and solving real world problems: mathematics and its scientific implications, or God? Even religious believers no longer attribute an eclipse to God's wrath. We know that the next total lunar eclipse will be on April 15. And most believers accept that earthquakes have more to do with plate tectonics than with God's anger over specific human behaviors. A "God axiom" might give comfort to some, but it lacks predictive value.

The assumptions (axioms) in monotheistic religions usually include these attributes for their God: omniscient, omnipotent, omnibenevolent, and infinite. However, religious apologists who want to avoid contradictory axioms have difficulty trying to justify an all-powerful, all-knowing, and all-loving God who allows so much needless suffering.

Written By: Herb Silverman
continue to source article at huffingtonpost.com

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1. This is almost exactly the same argument I made in my book Dot, Dot, Dot: Infinity Plus God Equals Folly published just last fall. Good stuff!

2. Sounds like Herb has read James A. Lindsay’s excellent book “Dot, Dot, Dot: Infinity Plus God Equals Folly”.

3. This is kind of interesting.

But I still struggle to take seriously anybody who is so small-minded, petty, and frankly deliberately inflammatory to go around saying “Happy Holidays” just to wind people up.

I live in a pretty broadly multicultural society and have no problem wishing people a happy Diwali or Hannukah or Chinese New Year or Eid. These festivals mean something to them and it is frankly just bad manners to try to bowdlerise them into something they are not.

The US atheists’ “war on Christmas” in infantile, counterproductive and will ultimately be self-defeating.

It also makes me look stupid in Britain. I now feel obliged to describe myself as “atheist but not of the idiot American variety” to avoid confusion. Much more of this and I’m going to start avoiding the A-word, and go for humanist or secularist or, heaven forfend, cultural Christian.

We have a responsibility to each other to pick our battles with some care.

4. I don’t think it is a good idea to call religious dogmas axioms. They are really different. Math doesn’t postulate “the circle exists”. Mathematical axioms are more like definitions, where religious dogmas pretend to provide us with real knowledge about reality.

5. *Mathematicians usually begin with axioms that seem “self-evident” *

I am interested in your definition of “self evident”. My understanding of axioms is that they are established principles or statements accepted without proof for the sake of studying their consequences. The axiom “God exists” is certainly not self-evident and arguably not even evident. As I understand the term, a self-evident statement is one that cannot possibly be untrue. An example might be “The sun is not visible at night”. If we accept that “night” is defined as a part of that time when the sun is below the horizon, the statement is self-evident. Self-evident statements are invariably vacuous and devoid of useful information (much like everything that usually follows “The reality is…”).

In mathematics, is “self-evident” different from “evident”? Perhaps a mathematical example would illuminate me.

6. @Stevehill, as I understand it the “War on Christmas” was not manufactured by atheists but by Fox News. I don’t doubt that there were atheists using the occasion to make a point. Yes we need to pick our battles and some of the things I saw seemed extreme but then in the US it seems the God squad are much more extreme and politically entrenched than in our countries.

As an Australian, I am sorry for inflicting Rupert Murdoch and Ken Ham on the world.

7. “I ask you: Which abstraction is more practical for better understanding and solving real world problems: mathematics and its scientific implications, or God?”

Depends on how you define “practical”. The God answer (a monosyllable to counter and explain absolutely everything) is more practical in that it doesn’t need to show its workings. There are no workings, in fact. The other path, involving examination, understanding, reason, mathematics etc., just looks like hassle. It’s only positive point is the niggling one that it offers a way to answer things correctly but, as the theist might answer, even a broken watch gets the time right twice a day.

8. Over on the other thread about why Bill Nye shouldn’t debate Ken Ham, PastorRileyF made the claim that God is infinite and that we are finite. How convenient for him ! How he knows this is beyond me since a sentence or two before he had told us that God is “unknowable” ! A typically dishonest religious claim.Whilst the Bible numbers those destined for heaven as 144,000, it must already be full up with good souls. But there again, with an “infinite” God, surely there must be room for more ? I am reminded of Hilbert’s Grand Hotel with an infinite number of rooms each with a guest. Even if an infinite number of new guests turns up there is always room for more. Hilbert famously claimed that actual infinities cannot exist, but surely if I raise my arm to shoulder level, it has gone through an infinite number of positions ?

Yes some infinities are bigger than others ! I if wheel my arm round and round, it surely goes through a larger number of infinite positions than it would just raising it to shoulder height ?

As for an “infinite” God, why did He feel the need to rest on the 7th day ?

9. In reply to #8 by Mr DArcy:

Yes some infinities are bigger than others ! I if wheel my arm round and round, it surely goes through a larger number of infinite positions than it would just raising it to shoulder height ?

Those infinities are the same I think. I assume you mean that if you move your arm in a circle there are an infinite number of positions contained in that arc using a real number measuring system. I.e., take 360 degrees and there are an infinite number of decimals — to pick a few at random 280.1,280.11,280.111, like that? And if you describe the line your arm makes raising to shoulder length you could do the same thing.

But those are both the same in terms of infinity at least from what I remember of basic set theory which was a long time ago. The different kinds of infinities are denumerable and non-denumerable. The natural numbers are denumerable the reals aren’t. You can map an infinite number of dunemerable sets onto a non-denumerable one but if I’m understanding your example both of them are non denumerable.

This is an example of why I find it annoying when people talk about how it’s impossible to comprehend the mystery of infinity, blah, blah, blah. There are actually a lot of interesting things that are quite comprehensible, although not intuitive, I still find it hard to intuit the concept that some infinities are bigger than others, but it’s a lot more interesting to actually talk about infinity as a mathematical concept than to indulge in pseudoscience rhetoric about how mysterious it is.

10. Red Dog:

You can map an infinite number of dunemerable sets onto a non-denumerable one but if I’m understanding your example both of them are non denumerable.

And in between each denumerable position (an infinite number) there is a an even larger infinity of irrational (can’t be written) numbers of positions for the arm !

11. This exactly is discussed in Dr. J.A.L.’s book, Dot Dot Dot, Infinity Plus God Equals Folly, right down to the card analogy. His book was published last year.

Someone’s been doing their homework reading assignments!

12. In reply to #3 by Stevehill:

This is kind of interesting.

But I still struggle to take seriously anybody who is so small-minded, petty, and frankly deliberately inflammatory to go around saying “Happy Holidays” just to wind people up.

I live in a pretty broadly multicultural society and have no problem wishing people a happy…

If you found this interesting, you should read Dr. James A. Lindsay’s book, Infinity Plus God Equals Folly! He published it last year. The similarity between that book and this article is so similar it’s palpable.

13. My most recent service occurred during the manufactured war by Fox News, the “War on Christmas.”

People have to understand that there are matters of principle at stake.

There is serious advertising revenue to made from advertising junk Xmas presents and junk decorations, – and serious profits for Fox’s advertisers from selling them!

14. I am not American but isn’t happy holidays something that predates all this socalled new atheism v creationist stuff we have today. I seem to remember seeing imported tv programs some thirty years ago where happy holidays was said with no more of a controversial intent than someone saying have a nice day. And was always said in the same insincere manner.

15. In reply to #14 by jjbircham:

I am not American but isn’t happy holidays something that predates all this socalled new atheism v creationist stuff we have today.

My comments were really directed to the rather provocative adverts American Atheists ran in Times Square around Xmas, and the rather silly “Hail Mary” Superbowl advert.

I accept that perhaps in America more than anywhere else in the “free world” atheists need to stand up and make clear that they are not pariahs, are fit to hold political office etc. But these tactics will come across to a lot of sincere people of faith as being offensive, and that will rebound.

As Winston Churchill said, jaw-jaw is better than war-war.

16. To cope with the lack of predictability you just make your god an infinite variable. “God is mysterious” works just fine for religios

17. The concept of infinity to me as a child was something that was never ending… a long line stretching from the past into the future…..always stretching ahead of us beyond our knowing…

But as an adult I’ve a new understanding that nothing is infinite on its own….everything has a prescribed life span even stars and galaxies etc. So the thing that is infinite is the continuous chain of energy being passed on through constant newly evolving living systems and beings in the universe …..the energy transfer will continue far into the future but none of us will know about it or what form it may take…..the only constant is the universe itself….but being constant doesn’t mean it is infinite either…it may have a life span of 15 billion years but I’m sure it would be recycled into other stuff after its end anyway as everything else has been since the big bang,
so maybe that’s Infinity and I’m not mathematical at all….