The Logical Conclusion

About sixty years ago John Nash published a paper called "Equilibrium Points in N-Person Games". This paper changed modern economic theory in a very real way. While I certainly can't claim to fully understand his theories, and definitely can not explain that theory, I'm intrigued by the interaction between his theories, and the debates raging in our governmental system right now.

Someone who understands this better may correct me on my explanation of Nash Equilibrium here, but let me try to explain it to you in terms of a two person "game". Each person has a set of "positions" which he may select from, and each combination (from the two players) of positions, entails a certain pay off for each player. (winnings or losses) The players alternate turns changing their position, each attempting to maximize his payoff. A Nash Equilibrium of pure strategies exists if there is a position from which neither player wishes to move. In other words bother players have maximized their payoff. The key point is that it is not their maximum theoretical payoff. (Player A may be able to earn a higher pay off if he could force Player B to chose a position that was less advantageous to Player B) He has maximized his realizable payoff. For instance, if you are maxing a widget, you calculate that your max profit not based on what it would be if you could control the price charged you by your material suppliers, but based on the prices which the material supplier specifies for you.

That is Nash Equilibrium in a very very simplified form that does not deal with mixed strategies and many other subtleties, but hopefully will be sufficiently clear to support the following discussion. In a nut shell, Nash's theory says that the best possible outcome is not achieved by an individual player maximizing his own output, but by maximizing his own out put, and all the other players outputs.

Now from an economic standpoint, this is hugely beneficial. It is really a statement of the simple (and in my opinion obvious) fact that things work out better for everyone else when people cooperate. When to countries sit down reasonably and establish trade agreements, both benefit from the prosperity brought on by trade. This should be a reminder to us all the next time we feel like just being a jerk about something and not cooperating just to tick someone off. (I've NEVER been guilty of that)

But that's the rub isn't it? This only works in the abstract where people do not have feelings which can be hurt, beliefs which they will not violate, and rights which they value above monetary profit. What happens if one person decides not to play the game according to the rules? Well obviously for the system to work, there must be an enforcer. For the good of the majority who are all benefiting from this game being played by the rules, and possibly even for the good of this individual who will also benefit from playing by the rules, someone must have the authority to enforce. In a family this is the parents. If the kids are working or playing together and one child is ruining the fun for everyone else, that child can be disciplined in order to maintain a good environment for all involved.

I hope you can see where I am going with this, but I am attempting to develop it all as systematically as possible.

I want to now take a look at our health care system. This may seem like a completely random quantum leap to some, but bear with me and I'll hopefully make it clearer what that has to do with the previous discussion.

Consider, if you will, our entire health care system as an N-player game. The players are individuals, doctors, hospitals, and insurance companies. (You'll see why I left the government, and lawyers out in a few moments) There exists some equilibrium point of prices and services for this system where patients pay a certain amount for insurance, hospitals charge a certain amount for services, etc. etc. This is the system in its pure state. However, the problem is that we don't live in a mathematically ideal society. Let's start with the government. The government sees itself as the "enforcer". What they have done is, rather than leaving the rules of the game the way they naturally would develop, they step in and change the rules to make them "better". For instance, hospitals are required by law (rule) to provide emergency care for anyone that shows up, regardless of their ability to pay for it/have it covered by insurance. We could debate whether this is a good or a bad thing, but it's the rules. However, what this essentially does is change the payoffs for players. Now patients have the option, rather than paying into the system and obtaining the care they need, or simply saving their money for emergencies, of simply relying on the hospital care which they are guaranteed, regardless of if they can pay for it or not. You may have heard of this referred to as the "free rider" problem. The free rider drives the price up for all those who have bought into the system. What's the solution to this? Well obviously, from the standpoint of the Enforcer, the solution is to set up a new rule which says everyone must have insurance. That way, by including everyone in the system, Nash's principles once again apply, right?

Sort of. The problem is that this approach only is acceptable in the abstract. Take a look at what we've done. By applying principles and logic, we've constructed a system in which the government has the right, for the good of the masses, to tell you how you must spend your money. This is exactly communism. It abolishes private property and instead establishes a system where your property is only yours as long as you are willing to use it the way the government wants you to use it. Obviously this is only one small aspect of the system, but analysis of many others shows the same result. It is a principle which the founders understood, but which we seem to have lost sight of. To wit, government involvement which does not have strict unbendable limits put upon it, regardless of the area, leads to more government involvement both in that and any related area. It is a self perpetuating system to which the only logical result is total control by the government.

I mentioned lawyers earlier. I think the roll of lawyers in the health care system is drastically underestimated. Essentially what lawyers do is to manipulate the legal system and drag it in between the different players (in particular the patients and the doctors) and use it for personal gain by preventing cooperation between the players which is necessary for a beneficial outcome to all. Essentially their sales pitch to the patients is, forget the payouts that everyone else goes by, I can get you a much larger payout from your doctor by using the legal system. (They never mention the payout they are actually looking for themselves.) What this does is it seperates the patient from the doctor because now the doctor must constantly be in fear the he will be sued. The result is increased cost to everyone involved in the system. Insurance companies must pay more in settlements. Patients must pay more in insurance to cover the huge settlement costs. Doctors must pay more in insurance to cover law suits. Patients must pay more to doctors to cover the doctors extra insurance. The only beneficiaries are a small number of the patients, and the trial lawyers. But what I find interesting is that it is really an example of how Nash equilibrium DOES work. If cooperation between players is prevented, the result is that everyone loses.

Now considering my previous warning about government involvement, you may think it hypocritical of me to say that the government must execute reform in this area. But notice what I said. It is not that the lawyers are players in the system who are refusing to play by the rules. The lawyers are actually inserting the government into the health care system. So once again the problem is government involvement, though indirectly this time. What the government needs to do is reform its laws to prevent itself from being dragged into the mess.

One point which I intended to cover but skipped over was the immorality of government forcing participants into playing the game the way the government wishes them to play the game. (Telling doctors what tests they must run, how much they must charge. Telling insurance companies what premiums should be, who they must cover, and similar issues. ) But again, just briefly, it quickly becomes clear that the only way this can be implemented is by total control. If the government tells the doctor he must lower his price, he is perfectly free to simply leave, if that is more beneficial to him. (this is already happening btw) When this happens, then thte whole system starts to collapse, unless the government extends its power further to not only tell doctors how they must perform their jobs, but THAT they must perform them. And anyone that thinks we are actually all that far from that situation, is, in my opinion, simply fooling themselves.

Until next time...

Let Me Clarify

I discussed in my previous post the cost of Liberty. I wish to clarify. In previous generations countless men have laid down their lives to purchase Liberty for their country and their families. This is, perhaps obviously, the ultimate sacrifice. But what will be required of us? It is possible that my life, and the lives of others may be required, but I think there is a sacrifice which, in this day and age is almost as difficult for us, that I think is likely to be required of all of us. That is the sacrifice of our time and money, most importantly time. We are so busy in our day and age. So busy, and yet we hardly do anything. We spend all our time trying to make a living, spending the money we have on cars which don't last, clothes that are out of fashion before we pull them off the shelf, entertainment that is passing, and houses that many of us will never own, and most of us will not leave to our children. Those of us who are Christians spend time worshiping on Sunday, and perhaps some time during the week doing devotions and reading an occasional book. These pursuits are more lasting, but how much of our time do we actually spend on that as compared to our transitory obsessions? And indeed, I don't intend to say that only that which is eternal is relevant. Far from it. One of the chief things which I think we all should be doing is improving our minds and ourselves by extensive study and reading. Why?

I strongly believe that knowledge is power. If we are to win the battle before us, we must be well armed. Our chief weapons are our minds. These we must sharpen by study and application. This preparation requires sacrificing time and energy which could be used to improve our financial status, enjoy a movie, or drink a beer. (Though personally I think beer is a great companion to a good book) How many of us really understand the workings of our government, its history how it has developed, and the governmental theory and philosophy from which it has been devised? How many of us really understand free market capitalism, both in its strengths and its weaknesses, and understand the alternatives as well, how they have developed, the worldviews which they are based on, and why the do not work? How many of us understand the structure of our judicial system, how it has developed, and how it was originally intended to function?

We can not all be experts in everything. But we if we as a people are to remain free, we must understand what our government is doing, and the long term import of policies and worldviews. I will go into this in more depth in my next post.

My disorganization in this post is profound.

The next area which we must sacrifice is in the training of our children. They are the next generation of leaders, and we handicap them if, after spending all this time and energy educating ourselves, we force them to do the same thing by not passing on that which we have learned. I will expand on this more another time.

The last way I will address right now which we must sacrifice, is by participating in the function of our society and government. We must actively support good candidates, even if it is only in our discussions. We must educate ourselves on the various candidates and their views on the issues at stake. We must run for office ourselves. Political offices should not be filled by lifetime politicians, they ought to be filled by true civil servants. Our governmental system was never intended to provide political careers. I strongly feel that one of the greatest plagues on our government is the career politician. It is a pest which must be eradicated. Again, I have taken on so much in this post that there is no way I can discuss all of it in any detail whatsoever, but term limits on EVERY politician must be put into place. We must be willing to step up, even if it's not what we would prefer to be doing, and run for office at the local and state level. Societies are changed from the bottom up and so are governments.

Once again my thoughts have simply flowed freely onto the keyboard rather than being organized in any cohesive form. But perhaps I paint a picture for you of the sacrifices which Liberty requires of us. We must be willing from time to time to lay down our ambitions, our energies, and our time, in order to fight for the precious Liberty which our fathers gave to us. And we must do so because if we do not, all our time, our energies, and our ambitions will ultimately be spent in vain.

The Price of Liberty

I ask you: what is the price of Liberty? Not what have others payed that you might have it. What are you willing to pay to keep it.

I have asked myself this question countless times over the past months. What would I be willing to pay to protect my Liberty, and more importantly the Liberty of my family and my nation?

Now consider what is the cost of Liberty. What may be required of you in order to protect Liberty? The answer, if we know the first thing about history, is quite clear. All.

Now I ask you a third thing. How do these two compare? If one does not meet the high standard of the other, you are now depending upon the courage and the dedication of your compatriots as well as your fathers to protect your liberty. And you may be assured that when a country judges the cost of Liberty a price too high to pay, what liberty they have will not long be theirs.

This is not fear mongering, this is not melodrama, this is simple fact. Liberty comes at a price. I submit to you that our country has long since judged Liberty to costly a gem to maintain. We rather want the security of government backed loans, "guaranteed" health care, and guaranteed schooling. (I do not say guaranteed education) And also I say with Benjamin Franklin, "They that give up essential Liberty to purchase a little temporary safety, deserve neither Liberty nor safety."

WAKE UP! We sit in our living rooms and complain and argue to one another about the politicians up in Washington, or the goons running the local school board, and then go on our daily lives like there's nothing we can do to change it.

Decide now whether Liberty is worth the price which she demands. If so then stand up and fight for her. And if not, then I don't want to hear another word about what you think of the most recent boondoggle coming out of Washington. We must be involved. You do not change the course of a battle by sitting on the sidelines and shouting ridicule at the enemy. Gear up and get out there! You win the battle by controlling the tide, and right now the enemies of Liberty have stormed the field and the few voices still out there are fighting back to back, just trying to survive.

The first thing that I need to do is educate myself. I know far to little about far too many issues. Think of this as training. If you're going to win the war, there must be intensive, rigorous, demanding training. The second thing I'm going to do (and I say this with all trepidation, cause I know my own track record) is write. More my own benefit, than anything. I don't even know if anyone has read my previous post, or if anyone will read this one. But I find that putting my thoughts into writing, clarifies them in my own mind. The third thing I must do is to pray. Pray for opportunities to be involved. I have no idea what form that will take, but if the battle is to be won, we must all be involved. There can't be any hanging back and hoping to avoid the conflict.

I'll end there, ignoring everything I have ever learned about how to write as it pertains to a sound introduction and conclusion format. think of this as a To Be Continued...

Please bear with my prolific grammatical errors. I fix them as I see them, but confess I am far too lazy to do a real proof reading of my posts.

Speaking Out

Does anyone out there listen? Probably not. Then why, you might ask, do I bother? Is it just because I enjoy hearing myself talk? Perhaps sometimes. Sometimes I think it's just to vent my own frustration and feelings of helplessness of doing anything with the situation. What can one small voice do to make a difference in sweeping floods of rhetoric (or more often lack thereof) that flood our radio waves, our television sets, and the internet. But I have decided that I will speak out. I will speak out, not because I think I'm the most qualified person to do so, not because I think I will be able to convince the masses with my oratory skills, or, heaven knows my complete lack of blogging skills. But I will speak out cause it's the right thing to do. I am a citizen of two countries, and one state. Let me list them for you in the order in which they take priority: I am a citizen of a Heavenly country. I am a citizen of the great state of Alabama. I am a citizen of these United States of America.

As I begin to write, I find that my fingers are flooded with all of the thoughts that have been flooding my mind over the past months, and I don't know how I will possibly get them all out. Even less do I know how I will make any order of them. But since I have started on this path, let me further expound upon my previous statement about who I am in terms of my citizenship.

My Heavenly Home
Anyone who reads this probably is familiar with my faith and my beliefs. By the grace of God I was raised in a Christian home, and brought up to love the Lord. He has never failed, despite my weakness and my rebellion, to be faithful to me, and thus my allegiance lies first and foremost to him. No other entity to which I have pledged allegiance may rightfully ask me to betray this most fundamental allegiance. In fact, my Heavenly Country so defines my life and relationships, that I only understand what it means to be a citizen of an earthly country in terms of who I am as a citizen of my Heavenly Country. Since I am not half as eloquent as Patrick Henry, I'll let him speak for me:

"Bad men cannot make good citizens. It is when a people forget God that tyrants forge their chains. A vitiated state of morals, a corrupted public conscience, is incompatible with freedom. No free government, or the blessings of liberty, can be preserved to any people but by a firm adherence to justice, moderation, temperance, frugality, and virtue; and by a frequent recurrence to fundamental principles."

I could expound upon this much further, perhaps I would bore you and you would never get to finishing.

My State of Citizenship
Now you may say I've got it wrong. I am a resident of my state, and a citizen of my country am I not? I am an American, and proud to be one. I believe I live in the greatest country in the world. But I also believe that the only reason we are as great as we are today is that we are still living on borrowed capital from our Founding Fathers. And the vision which they had for our country was one in which the States had Sovereignty, and the primary function of the federal government was in dealing with foreign nations or matter which concerned the nation as a whole. Thus I say, and I believe that almost all of the Founding Fathers would agree with me, that my allegiance lies first with my state, before my country. Incidentally, I think that Patrick Henry (again) said it best:

"The liberties of a people never were, nor ever will be, secure, when the transactions of their rulers may be concealed from them."

For this very reason, only specific, very limited authorities were given to the Federal Government. It is much easier for citizens to keep an eye on government which is close to home.
One of my other heroes, forced to chose between his state and his country put it this way: With all my devotion to the Union and the feeling of loyalty and duty of an American citizen, I have not been able to make up my mind to raise my hand against my relatives, my children, my home.

My Country of Citizenship
Having no particularly brilliant thoughts on my relationship to my federal govt that have not already been expressed in my previous discussion, I will simply quote Thomas Jefferson on what the relationship with the government should be:

"A wise and frugal government, which shall restrain men from injuring one another, which shall leave them otherwise free to regulate their own pursuits of industry and improvement, and shall not take from the mouth of labor the bread it has earned. This is the sum of good government, and this is necessary to close the circle of our felicity"

I feel somewhat more relieved now that I have spilled a small portion of my thoughts onto paper. Perhaps I shall make this a habit. I welcome any input from the two of you that will actually read this.

A New Perspective on Holidays

I'm just gonna say it. holidays suck when you spend them alone. They really do. Even it being the kickoff of college football this weekend doesn't redeem it. Cause ultimately, it just means you have a lot of time to sit around and think about how alone you are. :-P

I'm kinda hoping I might happen upon an invitation somewhere at church today. I know that's shameful...but what can I say?

In other news...MD disappointed me more than I expected. What the heck is up with Georgia's offense coughing up the ball and not being able to put any points on the board? And Oklahoma...I know you were playing without one of the best QB's in the country, and without an excellent receiver...but you should have been able to put BYU away. That's shameful. And finally, VT, I KNOW you've got more offense than that.

Need To Know

Here at Reason, we do our part to provide you with all the information that you need to know to live a happy, successful, and rewarding life. Here's a word for today, or rather, the number for today. This is the first number that is evenly divisible by every number from 1-10,000.

57933396702876429686922708791662400986348602979985188253931383511489793001457731823088325981761829221665744176794023407056559491402467891577328326763021299466843118474637852656831938521549472347971073068161679301705472685236926463387338495220571064420250677315000599457941340849496227227628926493771018264821842230370349640102573492881424317306189569467101495834601991270039918780924506495405797923762205360790652073159333382795670426041033566699342449050309786673681670483369155689567554239898879039744147333971988258061042090970476729293484513072443614795766878726325795854855394491290821167148355514749149683707585283381546153703014210442470318180511906691108325146494219343498899382918018246586609827667470329166012110874981104800415741527586280026737848182673635645872230905234515169611121042867043956727839314198728626274066655467846183343599194761590368608472578398169740111485924046986870714883894285841394964627408094161019230662749101230783008668676907211199488107523306410531772045452853957706873238466829988649822157557103503283563398281775464911904789159515900987401574678885942493907604740891878907698622679570965569483682456042918236444719794534411171907606336090534029349351300276141892529795448751826394399153216183270385737795748770508612096374765333578237973395907265484337502903901947799663388329849198045756207969590055686607678195206367273600632909417024224754750428711236917913663419215925830944035539848749163178489614227546656090790164108195741048033614368495827231281392190063051315248070192263400801315095608512139510731469732311313898995746040563433121427776071482655904346538281010668476731132415829844984600414136781404774213539507859790229205890271721600309169926806121871750008163738773911610009508609149665332579632767397078877996926581337419351834754370411008686136818501030862345505385357198060894463821342298717851567836562984344806469613768024764967372979655179066074398198246805104576134474823016488842818077041661676098399378809713894284994865370648616800689225595431967181072865363430005250840767890912164530705704936837915584856606960687347372391339254432119085932175541392954343684716695162629271229789289404752104218596977036941910521266321726821940533986384237994403780618301379099347975260122724194454275088825587044488208965690373706904056926509324696308810974331790119456438147168585552011926921912167450509941646104076818762060881903969616431646384985895944231218505620547093874241169759205450145478746112796898626711966320965057212219958567338851356631739947125096250452942497473309299907612330435197454392788637359253116308685007014249605492659524429134513344137517101872279428202285951652856354827230765931502805341696470148698002737700823078904634554776750169178259216255903968865588749827789888950172452455448248833712309835657561369233157977405579365293671943131412034109901944892819245001657496671822581274180596255340507054499934060282320458240722454209933569735940032859109934686878274110864394924463573852015338428881961843292083566034669814619612606638283615766521897504566616272305253931938372830446073384019299355320864342734019517633662346790422915951954822645137091494126100390104510987373366328615363056042137440808225973600809566845718073791616927784260557845021823094999326904373592319407516660896764388092262510369182153559285446074990941863516247226532653142198551840063631989428776799533286215464660644129411503287306838551341184739976807097763115368031748646043780549055143428297230678053738453010234949008253769355207208167999203353157524666017029803679612131824740794652592875662818479980117505768541194835524231818203552256426752730455115752280837099763237606348192867936457993970866446264015812819179994138642295108872381709181937092290392544335464025324661284746003660247161196698209062164637264114930766444473471083408200329662059064201896721165015687487728300854501780810155844837489798144309942999091774466406270065305461848242329380636274754660519867343112275861821293501112101434868225378041813836808745417606289159904294165941408692922250601127804971962342807927743390030395048263275616935165347620718001157478088456439083590834464409622781693790883289597024043982584220069224170235863458745344365684082114430362867446193601075569803650773018026700003812298460527976219100308016537538008597751565631582745643139434508332515569645426771080000093248326671232352303901422

my program took 52.403000 seconds to compute, which i was pretty proud of.

The original problem was to find the smallest number divisible by 1-20, but aftter realizing that my program solved that in less than .5 microseconds (0.000000 sec) I decided to test how fast it actually was. 1-100 it was still registering a flat 0 seconds. 1-1000 it came in at 0.125. The calculation for 1-100,000 I left running over the weekend at work. no idea if it's solved it yet. but if the time increase is exponential, as it appears to be, I'm guessing not. I'm also somewhat curious what python's limit is on the size number it can handle. just to give you a perspective on how big that number is, a lower limit estimate of the number of atoms in the universe is ~3x10^79. I should have just checked the string length in python, but I forgot to. However, that number is on the order of 6x10^4000.

So that's if for today, and remember, you are a really, REALLY tiny insignificant part of a BIG universe, and yet God knows every hair on your head. how about that, eh?

Code is written in python. I'm not actually positive this is correct...cause I was just trying to remember it here, but it's pretty close. I'll check it when I go to work on tuesday.

n=10000 #Establish search boundary
c1 = c2 = n #Establish dummy variables
for n range (n+1, 1, -1): #Establish range
while c1%n != 0 : #I only pretend I know what I'm doing
c1 = c1+c2 #If you actually read all my comments, you'll realize I am NOT a "real" programmer
c2=c1 #But it's fun anyway
print 'The smallest number divisible by 1-', n, 'is', c2, '.' #Booya baby

The key to this program is recognizing the following. Assume you have a number "a1" that is divisible by "b" and "c", and you want to find the next smallest number, "a2" that's also divisible by "d". By necessary consequence:

a2 = a1+x*a1

where x is a positive integer. The easiest way to convince yourself of this is to realize that since the a1 component of a2 is divisible by b and c, the a2-a1 component must also be divisible by b and c. And since we just stated that a1 is the smallest integer evenly divisible by both b and c, a2 must be some integer multiple of a1. So each iteration of the while loop simply adds another value of "a1" and checks to see if the new number is divisible by the current number in the for loop.

The only other "trick" is to start at the top rather than the bottom. This makes your convergence much faster, since you are working in much larger steps right off the bat. In fact, the program converged to the solution for 1-20 in 81 iterations!

Enjoy!

Man vs. Wild

In this special man vs. wild edition, you'll catch of the real struggle, and what it must have been like to survive in primitive times. No camera men and support crew, just me and the brutal truth that is nature.

5:30 finds me on the side of the lake with my trusty rod and real, trolling for bass. Time passes and I have no success in catching the fish that will provide vital nutrients for my survival. After an hour and a half I decide to try for panfish or bluegills instead. I catch a couple small ones, but nothing that has enough meat on its bones to feed my hungry stomach. after obvserving the movement of some smaller panfish among the rocks in the shallows, I change techniques and let the bait drag and bounce slowly along the bottom rather than zip through the water. On my second cast I meet with great success. I reel in a gorgeous 9" panfish. That should go a long way towards keeping me alive. not having a chain or a bucket to secure the fish, I simply lay him on the grass far enough away from the water that he won't flop in. With those kinds of results, I've got to see if I can get another one to make a full meal out of it. Then I spot him. about 20 yards away, a heron is obviously eyeing my fish hungrily. He slowly stalks the fish, moving when he thinks I'm not looking. Twice I chase him away as he makes a dash for my precious dinner. Then it happens: several quick tugs on my line alert me that I've caught the rest of my dinner. Within seconds the fish is out of the water and on the bank. At that moment my heart lands in my stomach like a brick as I hear a squack and turn to see the Enemy scoop up the fish and take off across the lake. About 200 yards down the bank I watch as the heron gulps down the fish without so much as a please and thank you. The sun has set as I look bleakly at the 5 inch fish on my line, and with a sinking heart, realize that I will be going hungry tonight.