The More I Find Out About Imaginary Numbers, The Stranger It Gets

On page 191 of the book "Einstein Gravity in a Nutshell," author Anthony Zee quotes Hermann Minkowski's stance on special relativity by saying, "The essence of this postulate may be clothed mathematically in a very pregnant manner in the mystic formula 3*10^5 km = square root of -1 seconds."  Very, very interesting stuff relating time and space by a connection to imaginary numbers.

And in Tristan Needham's book Visual Complex Analysis, page 241 relates the complex plane to celestial mechanics.  It gives the equation for an ellipse centered at the origin of the complex plane to be z=p*e^(it)+q*e^(it).  Okay, that's fine.  But what's REALLY surprising is if you square that whole equation on both sides.  Translating z to z^2 you get (p*e^(it)+q*e^(it))^2 = (p^2)*e^(i2t)+(q^2)*e^(i2t)+2pq.  The first two terms give you another origin centered ellipse, but the third term, 2pq, shifts the ellipse so that the origin point is now at the focus.  So we have an ellipse in the complex plane with the focus at the origin point.  Very much like Kepler's 1st law of planetary motion.  But why should anything in the complex plane bear any resemblance to planetary motion?  It's absolutely bizarre.

I believe there's a lot more underlying the structure of imaginary numbers that we have not yet found out.  That's why they possess such a mystic property for me for the time being.  When you first see that square root of negative one, you dismiss it as nonsense, but when you look deeper and see great and beautiful things coming out of them, it doesn't seem so much like nonsense anymore, even though you can't fully explain what's going on.  It reminds me of God, who is easy to dismiss at first, until you look a bit more deeply and see beautiful and mysterious things that are difficult to explain.

Wrong in Name Only

I believe very few people in this world are true moral relativists.  Most people are not okay with the idea that what they believe to be right and wrong carries no more weight than a psychopath's ideas regarding morality.  A few people are.  Someone who does is a very interesting person and is a true nihilist in every sense of the word.

But there are quite a few atheists out there that claim to be moral relativists and are not using that self-description accurately.  They would cry foul over and over if a state or world religion was imposed on them by popular demand, and would probably go to the grave defending how right they are.  Someone who truly believes in relativism would not behave in such a dedicated manner.  A person who believes that their opinion carries THAT much weight, particularly more weight than an entire population, must believe that the entire universe agrees with them.  This can only be the case if morality is objective.  Moral objectivists believe certain actions on this earth are inherently wrong, not just wrong in name only.

I am unsure why more atheists don't describe themselves as moral objectivists even though that term would be more accurate to all but the most blatant nihilists.  I think many atheists are worried that categorizing an intangible thing that can't be measured like morality as an actual real thing is too unscientific and makes them worried that such an action would begin to resemble a religious practice.  Sam Harris has been trying to resolve this and has been actively trying to promote moral objectivity in the atheist community.  He sees the logical fallacy in trying to claim some moral beliefs are more accurate than others while holding on to the relativist title, and that's why he rejects moral relativism.

I'm a moral objectivist and a believer in a supernatural entity that dictates morality.  So I don't have to wrestle with the moral relativism stuff.  Instead I have to wrestle with issues like why did God pick the things he picked as wrong, and where does God come from and things like that.  Some of those things I don't worry too much about, because I know no matter what I believe I'll have to reach an irreducible axiom at some point that can't be further justified and just has to be accepted.  Atheists have the easiest time of this because they have the fewest axioms to justify.

Truth Is Not Mighty When It Is Meaningless

There are a few mathematical truths out there that seem to have no real meaning.  You cannot properly construct a regular polygon with 65,538 sides using a compass and straightedge alone, but you CAN properly construct a regular polygon with 65,537 sides using a compass and straightedge alone .  It's true.  But not too many people would find any meaning in that statement.  This would imply that certain truths exist that are, well.... unimportant truths.  I suppose you could also call these weak truths, or truths that are not mighty, because they lack any real significance it seems.

I often run into a lot of ideas on the internet that imply that everything in the world has no real inherent significance and the only significance that exists is in the eye of the beholder.  I imagine if you suggest that nothing has any significance, that would imply that truth itself has no significance.  Why would it?  Why would you make an exception for just that one thing?  Why should I have to assign meaning to that value just because you do?  If you say significance is relative, you can't say my holding truth as insignificant is wrong and your holding truth as significant is right.  Truth is weakened beyond repair when there is no inherent significance behind it.

So the only way to say that truth is important in ALL frames of reference is to hold that there's at least one thing in this world that has inherent significance.  If that's the case, how in the world did truth become the sole attainer of the lofty status of having inherent and not assigned value?  Very difficult to explain.  I turn to God for that.

Why My Desire To Go To Church Is Stronger

I grew up in a household where it seemed my dad practiced religion regularly but my mom did not.  Both were very good people, so I knew church wasn't really necessary to make you a good person.  Plenty of people are good without going to church.  So why go?

Initially I went because I was scared of Hell, and I wanted to know what I could do to avoid that place.  But over time, as I read the Bible more and as I found out more about life, I realized that in the past there were quite a few people who went to church regularly who were NOT good people, people like the Pharisees that Jesus always complained about.  Those posers were just pretending to be good, and God wasn't going to be fooled by that.

For a good while, I thought reading the Bible and trying to be a good person was good enough, and I knew God didn't like lukewarm people in his church.  He wants people to have genuine feeling for him.

But then as I became a father, I realized how important it is to try to give a child a moral center of some sort so that they know that right and wrong are just not arbitrary.  Finding out what is arbitrary and what is not is tough for a field like ethics where you don't have quantitative measures of things like you have in chemistry or physics.  

I read part of the Quran out of curiosity but I never finished my copy.  I think I only read 100 pages or so.  It never really offended me but I just wasn't into it.  However, I read quite a few books of the New Testament over and over because I was so impressed with the Apostle Paul's eloquence.  His words gave so much hope to a world where it's easy to see a lot of uncomfortable ugliness, like many of those gruesome nature scenes from the film Buffalo Rider.  Paul was sure that this world was not all there was.  And as I re-read his words, I became sure as well.  Just from trusting in God alone.  

But I didn't know what God wanted me to do other than just provide for my family, because I felt there was something more I could do that I had a real passion for.  And as much as I admire so many churches for their outreach programs of feeding the homeless or handing out Bibles, I did not feel best suited for that kind of work.  What I did notice was that the only times Christianity and science are mentioned in the same breath is when Christians are trying to refute evolution or justify Noah's ark.  And I thought, heck, Christians can do a lot more science than that!  Michael Faraday was a devout Christian and he pioneered the field of electricity like no one else had before him.  Bernhard Riemann and Carl Gauss pushed geometry to new heights that even more than 150 years later are just barely within the grasp of the human mind.  Even today Christian apologist John Lennox made his mark as a professor of mathematics at the University of Oxford.  Not an easy thing to do even for scientifically adept minds.  Yet, I see over and over the idea pushed that religious people are somehow incapable of understanding and appreciating scientific ideas, or that their religion hinders their mental progression.  This was not the case for Friar Gregor Mendel, devout Hindu Srinivasa Ramanujan, or Reverend Thomas Bayes.  They made great strides in thinking, and I think all would credit a large part of those strides to the fire within them that they had for pursuing the beauty of God and better understanding the world he created.

We will never understand beauty scientifically but it is a real non-arbitrary thing.  It reminds me of Godel's incompleteness theorem that says there are certain things out there that are mathematically true, yet are mathematically unprovable.  

So, as someone who has a background in the natural sciences (B.S. Mathematics, UT Austin, 2004), and an interest in scientific topics like geodesics, I wanted to make it VERY clear that I DO believe in God, and that my belief in him does not hinder my scientific abilities or curiosity.  If anything, that belief makes them stronger.  Granted I am never going to win a Nobel Prize or a Fields Medal or anything, but that lack of talent is not due to my religious affiliation I assure you.  I also have a background in accounting as well, but I'm not sure that matters as much.

So now my primary desire in going to church is to demonstrate that somebody who does have a mathematical background and some definite experience in the logic of Boolean algebra is still on God's side.  I want them to say, "That guy may not be a super-genius, but he is no dummy either.  He has a scientific mind and he wants to make it clear that he believes."  I'm just one man, but that's all the difference I can make.

What do physics and economics have in common?

 The other day I noticed the equation for escape velocity in physics (Escape velocity - Wikipedia) is pretty much exactly the same as the equation for economic order quantity in accounting (Economic order quantity - Wikipedia).

It made me wonder, what in the heck does the equation for computing how to escape earth's gravity have to do with how much stuff you should order when you're ordering more inventory?  Strange.  Especially since the derivations of the formulas are totally different.

But I wasn't able to come up with anything terribly exciting to explain the similarities.  In one case you're trying to find the lowest amount of energy to escape the earth without wasting extra energy, and in another case you're trying to find the lowest amount of cost to order what you need without wasting extra cost.  So cost is like energy which makes sense.  Other variables aren't quite as clear.  Quantity ordered is like velocity, demand is like the gravitational constant, and holding costs are like the distance from the center of the gravitational body.