John the Baptist

Today is the feast day of John the Baptist. The homily given by my pastor was simple short and effective: "In the words of John the Baptist 'I must decrease so He can increase.'"

This statement is a focal point in the Gospels. Even more so it is from the person who Jesus calls the greatest man to live. It is completely counter to everything we are ever taught in our culture. So even deeper it is one of the essentials to the Christian lifestyle.

Just like living the Sermon on the Mount is something that is only attainable by the Saints, this idea of doing all things for not you own glory but for that of Jesus is also Saintly. For even in writing this blog I hope I have better opportunities in life for doing so. This idea of decreasing your own self in order to lift up something else is not only in the Gospel message but is the core of the Kantian Good Will.

Kant wants to say the only way one can determine if they have a good will is if they are willing to do something that will hurt themselves but they know it is the right thing to do. This seems to be the idea of John here as well. He must decrease his ministry so that people do not miss the Messiah. How difficult it must be to stop what you love to teach just so you don't guide someone the wrong way.

Keys of Heaven

So this Sunday's Gospel reading was about Jesus giving the keys of the kingdom to Peter, Mt 16:13-20. The first reading is the preimage of this scene where the Lord tells the master of the palace Sheba that Eliakim will replace him, Is 22:19-23. From this story we derive many things but mostly the role and founding of the Church.

So one might ask why is this mathematical, but I want to contend that this story eludes to the very philosophical structure of mathematics and then relate it to the Church. First, what I ask what does a key that opens doors and locks doors do? For one it allows people to see into the room, it also allows for people to enter the room, it sometimes even allows someone to change the decorations of the room or use the room for storage. One thing it does not do is allow the shape of the room to be changed, nor does it change the view from the windows. My point is that keys will allow us to do minor things to rooms but the structure and fundamental elements of the room is already in place.

This is largely how I view mathematical research. Academics is the pursuit of knowledge by opening doors and seeing if we find an answer there. Sometimes we take problems to different rooms to discover potential solutions and other times we just curse the room we are in since it isn't helping us at all. The structure of the palace is the foundations of mathematics that has been set up through the centuries of studying. These things are unlikely to be changed, there will always be an infinite number of prime numbers, there will always the be same number of integers as rationals, etc. Of course the rooms that researchers open do more than just light their own path. By opening new ideas and areas mathematicians are able to drive the field into new directions allowing others make use of the newly opened rooms. This is why we have so many theorems that are discovered at the same time (not to mention that the Communists didn't let people publish freely). So in many ways the mathematician is just a keeper of the keys to mathematics.

This observation gives me new insight (to my very limited sight) into the Church's role with Her keys. In the same way, Jesus has set the foundations of the Church for us to discover by viewing, using, and closing rooms. Thus we are able to discover what seem to be new truths but are actually new use of the same truths. Furthermore, this gives the mandate for the leaders of the Church to open doors that will bring new fruits to the people of our time. The leaders are able to set the sight of all the Church in a direction that will allow our Church to proceed together towards God's Kingdom.

Now there are other things to get from these passages but I just wanted to take a moment to look at the beauty of our Scriptures in relation to mathematics.

Intelligent Design Bad Arguments

Okay so I am a bit annoyed at the bad arguments surrounding Intelligent Design, both for and against it. This blog is inspired by Charles M. Madigan's article "God's Imperfect World".

From the article I want to discuss two flawed arguments.

First, people often make is that if God is perfect and all powerful then how can he create such an imperfect world.

Second, if evolution hasn't affected any of our creation why do we have useless body parts such as the appendix or what seems to be messed up body parts like our shoulders that seem better suited for creatures that walk on all fours.

Okay the first point is a common flaw with argumentation that either God doesn't exist or God is not perfect and all powerful. Not usually an argument that is used in the intellectual design debate. So why did God create those creepy crawling things that just annoy the heck out of everything that they ever come into contact with, e.g. look at pictures of things that live deep in the ocean. Or another example cited by Madigan is the preying mantis where the female dines on the male after copulation.

So Madigan seems to think that the set of living things on this world is a bad set since not every thing in the set seems to have a purpose or operate by some set of civilized rules. To complete the argument one needs to also include all those things that are not living that also seem strange and not necessary, like Death Valley or Antarctica or broccoli. Thus we come to the point that the set of things in this world are not really perfect but one can always show that they are imperfect through the right lenses. I contend this is an flawed way of looking at this set.

First problem is how to define perfection. One cannot contend that something is perfect or imperfect without giving some sort of qualifications for being perfect or imperfect. For example, if I said the world is imperfect because it contains things with cause pain to other living creatures, then I have defined perfection to be that which does not cause pain to living creatures. This is a bit of a silly definition because how many times do living things want pain, for example humans want the pain of being on fire so that our skin does not burn off leaving us for dead. So without a definition of perfection a perfect world does not exist period.

But what if we had an appropriate definition of the perfect, not that I believe we could ever find one. Then we could ask why is our world not that world, if in fact it isn't that perfect world already. Well to attack God's perfection one would first need to decide if the perfect world is even attainable. For example, if I have a set of numbers such that all the numbers are greater than 1 and also negative I would have an empty set of numbers. There are no candidates for that perfect set of numbers. Then if the perfection is attainable is it unique, otherwise how would we choose the true perfection. For example. what if I changed it to be a set of numbers such that all the numbers are greater than one and almost negative. Well here I can define almost negative in a number of ways, e.g. within 5 of being negative. What makes me choose 5 versus 6 or 10. In fact any number would suffice for my definition so what does picking one number over the other really matter when I am picking this new perfect set. Thus we have a case where there are an infinite number of perfect sets such that they are all good enough in that they still have that quality of perfection. There are for sure sets that are not perfect such as those actually containing negative numbers since all numbers in the set should be greater than 1. So before one can attack the imperfection of the world we must have a definition of perfection and a unique possible world that is a perfect world and not this world, or at least a characteristic of this world that excludes it from the set of possible perfect worlds. Otherwise, there is now way of claiming that this world is better or worse than any other world. In math terms, the set of possible worlds is not well ordered.

The second point is a gentler point that is flawed on both sides. First people who claim that God did not use evolution at all in the creation of the world we reside in are no longer arguing Intellectual Design but rather good old fashion Creationism. Second people who argue that science rules the roost and not accepting science's creation story all the way to the Big Bang or beyond is all the same as Creationism are also flawed in their inability to see the arguments clearly. So before one can argue that Intellectual Design is flawed because there is a design flaw in humans and other animals, the debate needs to include what has been evolved and what has been specifically designed.

This task of specifying what is actually design goes back to the question about perfection. Since Intellectual Design wants to hold that humans are the greatest creation, one must ask what makes them the greatest design. For example, I could have a computer program that has a very crappy human interface but be the greatest design for computations. Does this mean that the program is not the greatest design available? Furthermore the program will itself gain new programmers working on it and it will evolve with a better human interface but if it is the greatest design for computation then that part has nowhere to go and thus only other parts of the program evolves. Thus in the same way the Intellectual Design argument can hold that the design of the human is the greatest while allowing for other parts of the design to have evolved. At the heart of the matter I believe that is what Intellectual Design wants to do, to allow for evolution within the specific design of the human but for the human parts, what some will call a soul, to be that of divine creation.

Now whether Intellectual Design or Creationism or Evolutionary Theory is the right way to look at creation, I don't know. I go with the motto: "All models are wrong, but some models are useful." Who is right really doesn't matter too much to me, but getting the argument correct is just good manners.

I hope I have clearly explained why these are bad arguments, if not just comment and I will explain further.

The Sunday Sermon

So it has come to my attention that the vast majority of Catholic homilies really only speak to the choir. Often they are just the same old lessons taught over and over again, and seeing as I have been through 7 complete liturgical cycles, I have gotten a bit tired of the usual drab.

My call is for priests to become preachers that call out to those who do not know Christ. How many stories do we hear of people being converted by hearing an excellent preacher? But take anyone to a Catholic Mass today and usually you have trouble keeping them awake, and the 14 minute homily is only believeable if you already know Christ. I am proposing that the homily be changed from a rambling on things that Catholics like to hear to a challenge to know Christ. This challenge should ring out for both Catholics and non-Catholics, and most especially for those who know Christ not at all.

That is just a bit of my rant for the day. I am just tired of hearing homilies that just challenge me to stay awake or not look at my watch.