If you have any different insights on these topics, please share them. Maybe some day some of these ideas will make it to the big leagues and become pro-verbs. I also have a blog for technical computery stuff - zachstechnotes.blogspot.com.

Saturday, February 1, 2014


Happiness is not found in attaining so much as it is in responding

As twenty-first century American humans, many of us live life as if it were a challenge set out by the universe to attain happiness by taking it with our own strength. We try to manipulate our lives into what we imagine will bring us joy. In the end, the thing that brings happiness is response to life, and indeed, responding is our most important function as humans.

Regardless of whether the universe was created by God, life is something that has been given to us. It is quite an agreeable situation. We didn't somehow merit life, or use our strength or cleverness to pull it out of the cosmos. And yet we live on an oasis of comfort and beauty in the midst of a universe that would seem to an outside observer knowing only the laws of physics completely inhospitable. By nature's own initiative, the liquid that we need to survive is literally suspended in the sky above us and periodically pours down all around us. Not only does this water grow plants and quench thirst, but when it is up in the sky, nature indulges its creativity by making the clouds take on titanic shapes that twice a day provide a magnificent canvas for the sun's orange and violet brushstrokes. Your only responsibility is to respond to this; you need not and cannot work to make it happen.

Clouds I've seen in Colorado, ...

... in California (the smog helps),...

... and in the pure cold air of Wyoming.

So, we've all been given this quite agreeable situation called life. Let's say that you even go and make the most of your life. You go to college and fall in love with and marry an amazing young woman. Before you know it, she's pregnant, and then you find out that you are going to have twins! Although it is a great blessing, this is certainly a lot to handle at 22. But then, a year and a half after your kids are born, it all comes down. You have a seizure that brings you to the brink of death, and you find out that your previously relatively benign brain tumor will require risky surgery, chemo, and radiation therapy. You can't drive or carry your kids down the stairs because of the risk of seizure. And, here is the supremely poignant fact: it is likely that you will not get to live long enough to see your kids grow all the way up. This is exactly what happened to my cousin, Ryan. He cannot manipulate his life into something easy; all he can do is respond.

Perhaps this lack of control means we should focus on responding better instead of achieving more. When something goes wrong, do you respond with courage and integrity? Perhaps more importantly, when something goes right, do you give it the joyous celebration it deserves, or just move on to seek more? Some of the most important things in life depend primarily on response. Consider marriage as an example. I haven't lived long enough to know this for sure, but it seems to me that a successful marriage does not depend so much on finding the perfect partner as it does on how husband and wife respond to each other once they are joined.

A Christian's life is also all about response. When the gospel is presented in the Bible (e.g. John 3:16, Ephesians 2, Colossians 1:21-22, Romans 5:15-17, 1 Peter 1:3), it is not an explanation of how a person may attain salvation for him- or herself, but rather a story of how God acted on our behalf, based on no merit or action of our own. We could not seek Him apart from his reaching out. All we are left to do is respond in faith. In my experience, this pattern of action by God and response by me continues into the sanctification phase (when He changes me, rather than only taking away my sins) of my journey with God. He causes or allows something to happen in my life that begins to change my heart, and I have the chance to respond. I can either embrace the change that he has begun, a course that is sometimes scary, unpleasant, or humbling, or I can resist and trust myself, which is often what I want to do. It is terrifying to jump off the cliff towards sanctification and place your unqualified trust in God without a full explanation. But that response is, I think, one of the deepest experiences in a Christian's life.
If you asked Ryan how he was doing before his surgery, he would respond "good". He would not mean "considering the circumstances, we are holding it together", or "I want you to think we are really strong for being able to deal with this", or even "I don't want you go keep asking me or worrying about me". Instead he actually meant that he and his wife are satisfied with what is going on. They are weary and confused, but they have joy because they believe that the very One who decreed that the clouds should be hung in the sky has promised that all things work for the good of those who love Him. Ryan told me that all of the really good things in his life, like his wife and kids, have not come from his own work, but from Providence. Because of this, he doesn't lean on his own understanding, but trusts that, as Proverbs 3 says, his path will be guided.

And that, I think, is a good response.

Wednesday, January 16, 2013

Kalman Filter Lessons (Bayes' Rule in Your Life)

The Kalman Filter is one of the most elegant and beautiful devices used in control systems engineering and is among my favorites in the list of remarkable things that I have stumbled upon in my journey to becoming an engineer. Not only is it a useful tool, but I think that we can learn something about how to think from it. So what exactly is a Kalman Filter? "Kalman" is simply the name of the guy who first put it all together, but perhaps "filter" is not the best word to describe it to someone who hasn't taken an electrical engineering class and eaten the fruit of the Tree of Knowledge of Differential Equations.

Instead, I would call it more of an "information manager". It is a set of mathematical equations that takes in pieces of information that are uncertain and combines them into a single estimate of what is really going on. If some specific conditions are satisfied (they, of course, never are quite satisfied in real life), this estimate contains all of the information that we could possibly know about the thing we are observing; it is the best estimate that we could have. The Kalman filter is built on Bayes Rule, the statistics tool that has been hyped so much in the nerd community because it helped blogger Nate Silver to correctly predict the electoral outcome in all 50 states.

So how does the Kalman filter work? I like to describe it using the metaphor of a punt returner catching a punt in a football game. When he sees the ball being kicked, he has some initial idea of how far away it is and how fast it comes off of the punter's foot. As he watches the ball, though, all he can really measure with his eyes is the angle to the ball; from so far away, he can't accurately judge the distance to the ball through vision alone. Furthermore, he cannot keep his eyes on the ball the whole time. Instead he must look down to check to see how close the coverage is. But even with these challenges, the player is able to make the catch. The key is that he also knows the physics of the system. He has practiced enough to know how the ball will behave even if his observation is limited. What is going on in his brain is very similar to what a Kalman filter does. It combines knowledge of the physics of the system with observed measurements to get the best idea of what is actually going on.

Another way to think of the Kalman filter is as a device to remove sensor noise. Let's look at an example. Say that you're trying to track the angle of a swinging pendulum. Why would you be doing this? Maybe you're trying to lower a robot to the surface of another planet; maybe you're just contriving an example that's simple enough to work out in an afternoon. Either way, the math is the same. Here is the motion of our pendulum (blue), along with the measurements that our imaginary angle sensor makes (red dots).

Our measurements are clearly very noisy (apparently the managers decided we needed to save money by buying bad sensors), and since our sensors are the only way that we can observe the system, all we have to work with is this:

This looks like a dire situation. The human eye can't even really tell that there is a sine wave in there somewhere. If we don't use any filtering, and simply string all of these sensor measurements together, we get this estimate (in red) of what the pendulum is doing.

This estimate of the pendulum's behaviour is appalling. It doesn't make any sense for the pendulum to swing like this, and we cannot trust our estimates at all. But, before we despair, we remember that we know what the physics of the pendulum should be, and thus we can write a Kalman filter. If we apply our new filter to these measurements, Voila! The new estimate matches the actual system response almost exactly:

I first learned about the Kalman Filter at the beginning of the summer of 2011 when I was working with one of my mentors, Dr. Suman Chakravorty, at the Air Force Research Lab in Albuquerque. I triumphantly presented him with a graph like the one above, immensely satisfied with my ability to vanquish sensor noise. He then proceeded to graciously explain to me that I was missing the main point.

The Kalman Filter does not just give us a single estimate of what the system is doing, but it gives us an entire probability distribution of where the system might be. With a Kalman Filter, we not only know what the pendulum angle most likely is at a given time, but we also know how far away from that estimate it plausibly could be. The graph below shows the 1σ bounds of our estimate probability distribution. If the Kalman Filter is correctly programmed, the actual pendulum angle has a 68.2% chance of being between the 1σ boundaries*. In the picture below, notice how the 1σ boundaries start far away from each other, but gradually come together, showing the Kalman Filter's accumulation of information; as more measurements are received, the filter becomes more certain about the angle. At the beginning of the simulation, the filter believes that the angle could plausibly be anywhere from -8 to 46 degrees, while at the end, it expects the angle to be between 25 and 35 degree - a very narrow range.

By understanding that the Kalman Filter's estimate is actually a probability distribution, we are getting close to the fundamental enlightenment that the filter can give us about how to weigh ideas. The key that makes the Kalman Filter work so well is that it uses the uncertainty in its current estimate to make a decision about how much it should trust new measurements that it receives.

In a sense, the Kalman Filter is constantly optimally adjusting its open-mindedness to new measurements, and I submit that this is how people should handle new ideas. The level of open-mindedness in the Kalman Filter is based on the accuracy of the physics model and the reliability of the measurements. If the observer has a very accurate model of the physics, and has received many measurements in the past, it will not be led astray by new inaccurate measurements as would be the case in the absence of a filter. If, on the other hand, the observer has few previous measurements to work with, and doesn't have a great physics model, it is open to the innovation brought by new measurements. If the physics model isn't great, and the measurements are unreliable, of course, the observer simply cannot make a good judgment about the state of the system.

I am not saying that we should use some sort of cold, hard mathematics to make decisions. On the contrary, it is usually quite impossible to make any quantitative statements about the decisions that we face in everyday life. Instead, I am saying that when we are told new things or are trying to discern what is right, we should make a conscious effort to determine the degree of reliability of the premises we hold and observations that we take in.

It seems to me that people tend to fall into one of two extreme categories: either they are tossed to and fro by every new idea that they hear (this is the side that I tend to err on) or they are almost always immovably set in the ideas that they hold. Bayes' rule and the ideas behind the Kalman Filter suggest that the "inertia" of our ideas should be dynamic and should have differing magnitudes with regard to different facets of life based on the certainty of knowledge we have in a particular area.

We are all becoming experts in certain fields. By "field" I mean any related set of activities that require specialized knowledge. A field could be anything from psychology to fishing to interacting with a specific family member. After becoming experts in a field, we can be confident that our ideas are correct and can safely reject conflicting ideas (assuming that the foundational facts haven't changed since we developed the ideas). However, before we become experts, we should be open to new ideas because our body of knowledge is still in its infancy.

People are too often too afraid to say that they don't know about something. In the extremely complex world we live in, there are a great deal of processes that are incomprehensible to our brains. Our minds are optimized for dealing with things on human scales, that is, they are adept at conceptualizing things that take place over times from 1 second to 10 years, on distances from 1 millimeter to 5 kilometers, involve groups of 1 to 500, etc., but our minds don't handle bigger or smaller processes well, and we can only begin to grasp them after years of absorbing abstract information and undergoing extensive training. Furthermore, since our brains make so many approximations and use so many heuristics, they are not very effective at understanding things based purely on reason and the testimony of others rather than direct experience. Thus, it is rare for someone to be able to fully comprehend something without having personally experienced it.

For these reasons, I think that we should admit that we simply can't be sure of the answers to most of the questions that we ask in our lives. This doesn't mean that we are unable to make decisions. Decisions don't wait until we know enough to demand being made. Sometimes if there is not more information available we have to go with our best estimate of what is right even if we are not certain about it. This is completely reasonable. However some people will make a further jump that is not reasonable. They will assume that since they have taken a course of action or made a statement, they are bound to believe that course of action or statement was right. "I acted on this idea, so it must be right; otherwise I am a fool," they say in their mind. I submit that a decision should not cause any change our level of certainty. Instead, we should be candid with ourselves about our doubtable ideas and seek real evidence to determine if our decisions were justifiable.

In a sense, a human's journey through life can be thought of as a Kalman Filter or Bayesian inference process (though it is certainly also much more than that). When we start out, we know essentially nothing about the world. As we make our way through our time on earth, we gradually accumulate information, tying ideas together and examining their consistency. This accumulation of knowledge is a collective effort by all of humanity, so we must not let pride or other forces inflate our certainty in our ideas. Instead, we should approach new fields in humility with an open mind in light of our lack of knowledge, but maintain with confidence the conclusions that we have come to based on a wealth of sturdy evidence, and treat those who have ideas that oppose ours with civility and understanding whenever possible.

* this number is actually not strictly correct for this example problem because the pendulum is slightly nonlinear and thus the Kalman Filter is not perfectly tuned, but it is close enough for illustrative purposes

Monday, October 8, 2012

The Six

The waterfall gave life to the entire valley. Its blue-green cascades ran without pause through the heat of summer, the coolness of fall, the cold silence of winter, and the brightness of spring. The river below the falls painted a broad stroke across the fields. Every year the crops would take the moisture it freely provided and use power from the generous sun to create the gift of food offered to the people. These people lived simply, giving to the land by planting and tending the fields, but accepting much more than they gave, without ever thinking too much about the providence that made their living so free from burdens. They loved and married, feasted and laughed, dug ditches, and occasionally raised a barn. There were little problems, but the people quickly found their contentment again when these passed. If the wind blowing through the valley could carry the feelings of the people, there would be no region of the country that did not have secure happiness.

One day, early in autumn, some of the farmers looked up to see dark smoke rising up from one of the adjacent valleys. They wondered together briefly about the sight, but quickly forgot about it as the wind picked up and thinned the cloud as the day passed on. The next day, though, the thin tower of smoke had grown into a thick slate-colored cloud that dimmed the sunlight every few minutes. Now fear began to creep up into the people. They did not say with words that they were scared, but as they went about their daily tasks, they would stop and spend a few moments considering what evil might be below the pillar of soot that rose over the hills. The evening meal was shared in mostly silence. The younger children did not know enough to ask what was wrong; the older children could see the uncertainty in their parent's faces, and so did not ask.

The next day, the cloud was less thick, and the sun was only dimmed occasionally. The people hoped that perhaps whatever had caused the smoke would pass without explanation or consequence. In the village at the opening of the valley, the farmers were preparing for the day's work. They were quiet with the sleepiness that lingers into the first part of the day. A few were eating, some were getting the horses and tools ready. A few eyes wandered to the southeast and could see something moving, though they could not tell what it was. They began pointing and speaking, and more of the villagers stopped what they were doing to look. There seemed to be small puffs of thin smoke drifting up from the horizon. This time, however, the smoke was not coming from the next valley. Instead, it was close enough to be coming from the very fields they meant to tend that day. There were also smaller black shapes moving in the distance. The true form of the shapes could not be discerned, but the villagers with sharper eyes could see the cadence of their movement they were bobbing up and down at the frequency of a horse's gallop.

By now, all of the morning tasks had stopped, and worried questions began to fly through the air. The minds of the village leaders worked furiously trying to decide what to do, but the time to decide was vanishing. The riders were approaching, and could now be seen clearly. There were about 40 of them charging forward, armored with blackened leather and carrying torches. There was no more time to puzzle about what to do. The words between the villagers died down until the murmur was suddenly pierced by a panicked cry of run! Those that could run took off across the fields, cutting straight lines through the crops. The impulse to flee muscled all other thoughts aside, and no things were carried, save some of the smaller children rescued by instinct of their parent. They stumbled often, but terror-charged adrenaline kept them going. However, there were some that did not escape the cluster of buildings. They hesitated at the edge of the village, feeling that they could not outrace the riders and that their settlement could somehow provide safety. Moments later, the window for action had closed. The strangers were upon them.

As the dark riders swept into and around the village, six of those that remained fled into a shed out of the way, hoping to be overlooked. But as the last of them hurried in and shut the door, it was evident that one of the men had seen them. The villagers cowered against one of the walls as the sound of hooves and boots drew near. Their breathing was replaced by gasps and shaking as they looked to the door, expecting it to swing open with the crack of a shattered latch. After a moment there was a noise, wood on wood, but the door merely shook and did not open. Something heavy, like a wagon, had been pushed up against it. Rough voices spoke outside in a strange and unsettling language. The six inside could not understand the words, but the profanity was not diminished by this barrier of syntax. A minute passed, extended by fear. Then the voices faded and there was silence, save for an almost inaudible crackling. In the darkness, the six at could not understand what was happening initially, but it soon became terribly clear. At first a thin stream, but moments later a thick flow, smoke invaded the windowless shed from under the blocked door. Soon, flames began to intermittently illuminate the group of six coughing and choking through their last moments of consciousness.


The people of the valley had now all fled to the surrounding hills. They slept in caves and tents in fear.  When they looked down on what had been fruitful fields two months ago, they saw only black, charred, desolate plains. It was winter now. Little snow had come, but the cold was present, and it was impossible to escape. The people huddled near fires and ate thin stew made from whatever was available. All of the towns and villages had been destroyed. The survivors spoke little, for they had little left to speak about. Before now, the happy security had been enjoyed without any conception that it could end.

After the first village was attacked, horsemen had been sent to find out what had happened. They found piles of smoking, charred wood instead of houses, mangled, twisted iron instead of wagons and plows. A dying horse strained to breath, collapsed near where its stable had once stood. Nothing of worth was left. The dark raiders had taken everything that could be eaten or hoarded, and destroyed the rest. The surrounding fields were void of life, burnt for no reason that the surveyors could discern. All of the houses were checked for survivors, but only a few lifeless bodies were discovered. When it seemed that there was nothing more to be seen, however, one of the horsemen saw some movement in one of the piles that had been a small building. An arm and hand was feebly reaching over one of the beams. The riders quickly converged without words on the mound of broken wood.

Six survivors were found there. Terribly burned, barely breathing, some blinded, they had broken bones from falling beams and tools. They were not dead, but they would be soon. The people of this country had never felt pain, and now they feared it. The despair among the horsemen at this sight was not bounded; their hearts fell without slowing. What was coming next? they asked themselves without consulting each other, and they found nothing solid to place any hope on. The barely living bodies were taken back to the safest place in the valley the waterfall, where the water that gave the valley life flowed from. It was clear, though, that they would only live a little longer, and that existence would be in agony. They would be dead and buried soon, but the others living in the valley now had to face an unknown enemy that they knew not how to resist.

The party of raiders that had burnt the first village was merely a scouting detachment. A few days later the main force arrived. The people of the valley had weapons, but they did not know how to fight well, and were defeated at every engagement. The only ones who survived were those that fled. Soon the leaders determined that the only response was to retreat and hope that the enemy moved on. Not many had yet been killed, and the leaders hoped to save the bulk of the population. Each family took what they could from their homes and went to the safety of the mountains. But the army of dark raiders did not leave. It became clear that they meant to stay for the winter, and that the people would have to find a way to survive with essentially nothing. The main group set up a camp and prepared a defense, hoping to outlast this calamity.

Hunger was perhaps the most sinister enemy. Men have a deep desire to be brave, but the weakness caused by a stomach that has not been adequately filled for weeks diminishes even the strongest convictions of the soul. A slow fade into helplessness is the worst end that courage can have. The men only hoped that the enemy would not attack and that some could survive into the next season. Then warmth and new growth would allow them to rebuild their former existence. As the winter supplanted the milder temperatures of fall, some began to expect that they would make it through the ordeal simply by waiting with patience. In reality, they would not be so fortunate to have the opportunity to overcome with only passive endurance.

One afternoon, when the sun had mercifully taken away the worst of the bitterness of the cold, one of the lookouts was sitting at his post on a rock near the edge of the fields. He was thinking of the life that he would have back when spring came again. Thoughts of which crops he would plant and how he would find his children playing near the stream when he returned at the end of the day filled his mind. It was respite from the stress of living in the present situation. He did not know why this disaster had happened, but he was beginning to become content with the thought that it might end. Why would they not leave us to survive?, he thought. They cannot take any more from us. He looked out over the valley. The fear that had been his companion for months was beginning to leave him. But then suddenly it returned with new strength. He saw the column of the enemy force on foot coming from their camp, armed for a fight. The people of the valley would have to defend themselves.

With haste, the men found their swords. Many of them had never used their weapon, and justified fear infected their whole bodies. They could feel it like pain. Some even fled, and with their flight weakened those that remained. They faced a most dreadful paradox. If they fought, they would be destroyed, but if they turned an ran, they would have no more reason to be. Those that had enough courage left gathered on a hillside to await their doom. The wait was longer than they wished. While they stood idle in anticipation, they did not think of the battle, but instead how their lives could have been if this evil had not come. In the approach of the evil army, they saw the final door that offered hope for the future slowly swinging shut. Finally the enemy began their final charge, and sharp fear once again filled the defenders. Their huddle began to back away from the charge. As the horde closed the last few meters, the defenders ran; no man stood his ground.

There were more invaders than defenders, and each good man found himself beaten, fighting only to survive for a few more moments. The lookout who had first sighted the enemy was desperately trying to absorb the blows of his two assailants. He and a few others had fled laterally onto one of the fields that had been burned. This had been one of the last fields to fall to the flames, and small fires still smoldered at the feet of the combatants. Clouds had dimmed the sun, and the slowly rising smoke gave an otherworldly aura to the scene. It was almost as if the defenders had already passed on to the next destination after death. Reeling backwards, the lookout tripped over a hole in the black dirt. He stumbled two more steps and fell on his back. Time dilated with the realization that this would be the end. The two attackers approached slowly, preparing to put the helpless victim's struggle to an end. But before they could, the situation changed.

It began with a warm light shining on the attacker's armor. The lookout did not know what the light was as he could not see its source, but he could tell that it was coming from several sources at ground level behind him. The evil men looked up in confusion. The lookout stared at them and they stared towards the light. The lookout felt an irrational confidence growing somehow. The light on the raiders shifted as if one of the sources had made a sudden movement, and their demeanor immediately changed. Instead of their normal arrogance, they showed confusion. In another moment the ruthless pursuers were themselves fleeing. The lookout did not know how to react to this change, so he laid still. A light source began to approach, and he looked back up towards it.

What he saw was a sight that moved him more deeply than any of the times that he had looked out over the valley before it had been ravaged. A woman stood over him. Apparently the light was emanating from her, but she did not appear to be super-human otherwise. Terrible burn scars grasped around her arms and neck, but by some unknown grace, her face and all its fairness had been spared. Her eyes looked into him, and a subtle smile crept up on the corners of her mouth. This was not a smile of amusement or folly, but the smile that comes from knowing that all tension in the world has been resolved. A blinding, piercing sense of good accompanied her approach.

The lookout had forgotten about the enemy. In this moment time no longer seemed compelled to move, so it slowed to a near stop, and hope cascaded into his heart. The woman spoke to him in a voice that was plain, but overflowing with kindness and confidence. Dear friend, fear not this enemy any longer. Take courage, for they can do us no real harm. You have resisted with valor. Now rise and use your strength to drive them from our home. She reached out to help him up. She had only her normal strength, but with his newfound hope, his rise from the ground was effortless. He looked around and saw five more of these bright beings on the field and the hills around it. Some of them were fighting and others helping the fallen. Other defenders like him were getting up and finding their new hope. One by one, they realized that these bright beings were of their own kind. Indeed they were the six that had been caught in that first savage burning. If there was something that could save these, the most helpless victims, did they need to worry at all about their own safety? It was not long before they were running across the fields pursuing the routed enemy.


That winter was harder than any other in memory, but it was also more joyful. Everything had been taken from the people, but when it was all given back as a gift, its sweetness was multiplied. The freedom of the valley was procured by the six who had suffered the most. By their suffering and regeneration, they gained an upper hand against evil. They were the instrument by which the people had been saved, but they in themselves were not the source of the salvation on which the valley's new hope had been established. There was some great but subtle power protecting that place. It was universally present in all that happened there, but in this case it had particularly manifested itself in the waterfall to heal the six. Some realized that this acute healing magic was really no more remarkable than the natural way that the power behind the waterfall and the sun and the earth provided for all of the people year after year, so they were thankful for all.

The six went on to live normally. Along with the rest of the valley's inhabitants, they married, raised crops and kids, and eventually passed away.  Seasons visited and departed, and the joyful life that the people were accustomed to returned. They remembered the invasion and were no longer so naive as to take their good lives for granted, but all who looked upon the six found hope that their happiness was secure, for they now knew the answer to this question:

What power does evil have over those who have felt its most painful sting and yet are able to do good?

Saturday, November 26, 2011

disappointment and hope

This post is not about football, but it would be a difficult task to come up with a better example of disappointment than Texas A&M's 2011 football season. At the end of August, we were ranked in the top 10, expected to compete for the Big 12 Championship, and seeking to make a name for ourselves on the national level. Today, we have nothing significant left to hold our heads high about.

Sure, there are many other teams who could say that their record is worse, that they have suffered through losing season after losing season, but none can say that their losses have been as heartbreaking as ours: Oklahoma State (now ranked 5th) - lost by 1 point at home after leading most of the game, Arkansas (now ranked 3rd) - lost by 4 points after leading most of the game, Kansas State and Missouri - lost in overtime after leading most of the game. Whatever it is that causes teams to win games, we don't have it.

And then there is the Texas game. This is more difficult to explain to people outside of A&M. It is a rivalry (at least from our side) that is on a different level from any other that I have experienced. We have played each other for 118 years, and at A&M the entire year revolved around this game. We sang about the Longhorns even when we were playing other teams and constructed 100 foot tall bonfires to prepare for the game. In Aggieland, you will find more t-shirts bashing the Longhorns than you will praising the virtues of A&M. This game was distinct from the rest of the season, and sometimes it mattered more than all of the other games combined. For us, it was like playing in a championship game every year.

But our relationship with the Big 12 was unsustainable, and the unthinkable became inevitable - the rivalry would end. The 2011 game became bigger. We needed to win it, to keep our pride, and to keep the Longhorns thirsty to revive the rivalry in the future. So on Thanksgiving night, we flooded into Kyle Field to saw Texas's horns off one last time. The first half went well for us, but, just as in all of the other important games this season, we fell apart in the third quarter. We hoped that this game would be different - that somehow the Aggie Spirit that has worked its magic in Kyle Field so many times before would overcome. And indeed this began to happen. With less than two minutes to go, we found that we had come back and were ahead by 1. All we had to do was hold off the Longhorn offense that had done little against us all night. Our hope that the season would end with something good was strong. But then Texas quarterback Case McCoy broke free at midfield and began running towards field-goal range. The heart of every Aggie in the stands collapsed like the bonfire would as it burned every year before the game. Our hope evaporated in that century-long moment as the all-white number 6 jersey sprinted down the open field towards the spot where they would kick the game-winning field goal.

And that was it. It was over. There is no next year. There are no plans for us to be able to challenge UT again. Some people will try to find bright spots in the season, or blame the UT loss on external factors like injuries or officiating, but for me, the magnitude of disappointment overshadows everything else. A rational evaluation of the situation reveals nothing to hope in.

Sadly, this kind of disappointment that cannot be circumvented by optimism is not limited to things as trivial as football. It is ubiquitous in human life on Earth. As long as humans are sinful, evil will have hold of this world. Will there ever be a complete solution to poverty and hunger? Will there ever be an end to the tyranny of the powerful over the disadvantaged? Can democracy ultimately overcome corruption and deceit? Can we avert the destruction of our natural environment? Will your life turn out to be all you hope it to be? If I rationally evaluate these situations, I find nothing to hope in.

We can try to be optimistic, but mere optimism cannot change facts. Marriages fail. Relationships crumble. Expectations are not met. Politicians deceive. Power corrupts. Reckless resource use darkens the future. Pessimism is the outlook that is consistent with reality. There is no hope in this.

So, what are we to do? We cannot find hope in humanity, but I think that there is hope in something above it. The creator of this universe is determined to reconcile and redeem His creation. This requires the ultimate defeat and destruction of evil, and the salvation of those people that God has made perfect through the death of Christ. Several things in my life that I have been putting hope in have begun to crumble this semester. But throughout my life, this hope in God's work is the only hope that I have not found disappointment in. One ancient writer put it like this:
Again I looked and saw all the oppression that was taking place under the sun: I saw the tears of the oppressed-- and they have no comforter; power was on the side of their oppressors-- and they have no comforter. And I declared that the dead, who had already died, are happier than the living, who are still alive. But better than both is he who has not yet been, who has not seen the evil that is done under the sun. And I saw that all labor and all achievement spring from man's envy of his neighbor. This too is meaningless, a chasing after the wind...
Now all has been heard; here is the conclusion of the matter: Fear God and keep his commandments, for this is the whole [duty] of man. For God will bring every deed into judgment, including every hidden thing, whether it is good or evil. 
Ecclesiastes 4:1-4 & 12:13-14

By the way*, even though I think that one day Texas A&M will cease to be hopeworthy, for now it is an institution worth being proud of. On Friday night, with the loss still weighing heavily on me, I went for a jog on campus to get some endorphins flowing. Under the big ring were two high-school or college-freshman-aged girls laughing and taking pictures with their parents. It reminded me of all of the things that I have experienced and learned here at A&M, and of what these girls, along with thousands of others in the incoming classes, are about to learn. They will learn not only about the academic fields they pursue, but more importantly about selflessness and integrity in a way that they could nowhere else. And that is what makes Aggieland special, regardless of how much the football team disappoints.

*The importance of this paragraph is insignificant compared to the preceding section.

Tuesday, August 2, 2011

absorb the bumps

Here are two very loosely related ideas:

1. Coming from the South is my favorite way to enter Colorado.

Two days ago I drove from Albuquerque, where I have been working, back home to Longmont. I can't clearly remember another time when I have come in from the South, but this time the beauty really surprised me. You cross the border from New Mexico at the top of a pass and immediately drop down into evergreen-wooded hills and mesas. The greenness of the trees alone is enough to inspire you, thanks to the unusual amount of moisture that the Centennial State has been blessed with this year. If you take your eyes off the curving, descending highway for a few moments and look west, you can see the Culebra Range of the Sangre de Cristo ("Blood of Christ") Mountains.

A mountain without a snow cap is like a lion without his mane or a ship without her flag. The snow cap is the glory of a mountain. The greatest mountains always have their snow, but most only have the privilege for a few seasons. When a mountain is bare, I imagine that it feels insecure. "What if I am really merely a hill?" it asks itself. It has little distinction from the surrounding plains and foothills. But when a mountain wears it's icy crown, it becomes a mighty sovereign over the whole region. What can challenge a mountain that reaches far enough into the frigid heights of the atmosphere to keep it's snow during all of the seasons? The satisfyingly rugged-looking Culebras wear their snow with striking regality. It's as if they are there to say "Now you're in a real mountain state."

The Culebra Range - Image Credit

For my soundtrack to entering my favorite place on Earth, I chose Colorado's own Five Iron Frenzy. I played the last three songs on the recording of their final concert - "A New Hope", "World Without End", and "Every New Day". This music is weird. If you told me that it is bad music, I don't think I would argue with you. But whatever it is, it is awesome and I love it. It seems like the people in the band experienced the gospel and then responded by playing their horns and guitars as hard as they could without worrying about much else. Maybe that's what we need to do more often: react to the gospel by doing what we are passionate about, and doing it with as much fervor as we can in a way that glorifies our Savior. This sort of brings me to my next idea.

2. Life is like skiing moguls

There is a right way and a wrong way to ski moguls. The wrong way to do it is to go slow and allow the moguls to take you across the slope and down paths that you don't want to follow. This way is miserable. In this mode, the skier is entirely focused on maintaining static stability. He wants to make sure that he can stop at any instant, and to do this, he is constantly wrestling against gravity. Every time a mogul drops off to the next, there is fear of going out of control.

The right way to ski moguls is to point your shoulders down the fall line* and go, without worrying too much about where the moguls are. You will reach a speed at which you can't stop on the next mogul. You are not stable in the sense that if you didn't have your speed, you would fall over. But you can stay in control by transferring energy each time you bounce off of a bump. Your shoulders and torso don't change direction and don't move up and down much; your legs simply absorb the bumps.

The right way - note the bent knees absorbing the bumps
In the first mode, you are letting the moguls define your path; they own you. In the second, you are picking the best route, and using the moguls to follow it. I think that this is how we should approach living our lives too. We shouldn't let the little obstacles (the moguls) define where we are heading. Instead we should focus on the big, important goals and absorb the bumps along the way.

Some people might say that this is the same as the maxim "Don't sweat the small stuff", but I think that there is something more than just that. Don't let the small problems in life control you, but DO focus on the long-term things that matter, and DO try to use the small events to guide you down the path that you ultimately want to follow. Sacrifice some immediate security to achieve what you ultimately want.

I am not yet old and wise enough to be certain of this, but this is what I think: In your career, you will be successful if you focus on long term goals and are not thrown off course by immediate circumstances. In your life, you will find happiness if you focus on relationships and love, with other people and with your Creator, and are not consumed with your own selfish petty concerns of the moment and the details of living.

*The fall line is the direction that you would roll if you were rolling down the mountain, or the negative gradient of the surface of the mountain with respect to height for all you engineers

Saturday, July 2, 2011


If the sun rises tomorrow, God will keep his word.

As I have been reading through the old testament, there have been times when I have thought to myself, "God is not being loving here", or "God is not being fair at all", but I have found this to be consistently true: God is trustworthy. He keeps his word. Even when humans screw up horribly.

A classic example of this is the story of the patriarchs. Many of you will recall how God promised Abraham a son from his wife Sarah, even though she was too old to bear children. God kept his promise despite the fulfillment seeming impossible and despite Abraham's actions that certainly did not reflect a confidence in God's promises.

A more strange and interesting example of God keeping his word comes just a bit later. A generation later, as Abraham's daughter in law, Rebekah, was pregnant with twins. God said to her
 “Two nations are in your womb,
and two peoples from within you shall be divided;
the one shall be stronger than the other,
the older shall serve the younger.” (Genesis 25:23)
"The older shall serve the younger" is a strangely arbitrary word for God to give, and it is accomplished in a strange way. First, Jacob, the younger, basically extorts his older brother, Esau, into giving him his birthright (Genesis 25:27-34). Then Rebekah and Jacob conspire together to trick Isaac (the boys' father) into blessing Jacob instead of Esau (Genesis 27). It seems to me that these actions are evil. The evil is especially poignant in Jacob's cold deception of Isaac in Genesis 27:20 and 22-24.

So, God's word is not compromised by our evil deeds. In fact it seems that in this case, he works out his word through grossly immoral humans. It's the same with the nation of Israel later on. If God wanted to choose the best people for himself, Israel should not have been chosen. All that He desires for them to do is trust in his word, a word that he has proven to them to be trustworthy over and over again. But they so often do not. If the fulfillment of God's word depended on our actions, good would have no chance.

As the Babylonian Empire's conquest of Israel and Judah was imminent, God gave the prophet Jeremiah these words (Jeremiah 33:19-26):
  The word of the LORD came to Jeremiah:
  “Thus says the L
ORD: If you can break my covenant with the day and my covenant with the night, so that day and night will not come at their appointed time,
  then also my covenant with David my servant may be broken, so that he shall not have a son to reign on his throne, and my covenant with the Levitical priests my ministers.
  As the host of heaven cannot be numbered and the sands of the sea cannot be measured, so I will multiply the offspring of David my servant, and the Levitical priests who minister to me.”

  The word of the L
ORD came to Jeremiah:
  “Have you not observed that these people are saying, ‘The L
ORD has rejected the two clans that he chose’? Thus they have despised my people so that they are no longer a nation in their sight.
  Thus says the L
ORD: If I have not established my covenant with day and night and the fixed order of heaven and earth,
  then I will reject the offspring of Jacob and David my servant and will not choose one of his offspring to rule over the offspring of Abraham, Isaac, and Jacob. For I will restore their fortunes and will have mercy on them.”

I think that the promises mentioned here have been fulfilled, at least in one sense, by Christ. He is the son of David who now reigns over the kingdom of believers and who will one day reign over the whole earth and heaven. We Christians, like an innumerable group of Levites, are all set aside for the glory of the LORD.

Just as those who heard this prophecy could not comprehend that the sunrise and sunset are accomplished by the spinning of the Earth, they could not comprehend that God's Old Testament promises would be fulfilled by Christ, who John would call "The Word" (John 1:1-14). Sometimes we cannot see how God's word will be accomplished, but it is totally rational to trust in it and act according to it. When we are at the precipice about to fall into sin, why should we ever decide that we are right and He is not? If we think that the sun will come up tomorrow, we should follow the precepts of the LORD with the same confidence.

If trustworthiness can be measured; if it can have a magnitude, then the magnitude of God's trustworthiness should be compared to the magnitude of the angular momentum of the Earth (that's what keeps the sun coming up). Like so many other things in the universe, it is so large that any conception our minds might have of it is too small.

Saturday, June 25, 2011

the resurrection

Jesus died to save people. He rose to defeat evil.

Jesus' Dominance in the Resurrection
Good Friday and Easter celebrate the central act of history - when God Himself became a man, and was brutally murdered by humans. He did this in order to take the punishment that we deserve for our sins upon himself. Because of this paradoxical sacrifice, those who give up on their own failed righteousness and rest the burden of their failure on Jesus are judged righteous by God. So, the importance of the death of Jesus is clear: He died so that we might be made clean. But what is the significance of the resurrection? If we were justified by Christ's death, then why did he need to rise again?

This is a question that my roommates and I have discussed from time to time, as in this blog post: http://kevinhubert.wordpress.com/2011/04/22/134/

Here are some quick thoughts (that aren't new or original) about why the resurrection is important:

First, it seems to me that Jesus' claims are only really be compelling if he did something like rise from the dead. Would you believe someone who came and radically challenged the culture and religious institutions, said some pretty crazy stuff, and then just died and you never heard from him again? The disciples weren't exactly doing a very good job of carrying on Jesus' words when he died. Peter had just repeatedly denied that he even knew Jesus (John 18), and the disciples were hiding behind locked doors because they were scared (John 20:19). If Jesus hadn't come back from the dead and convinced his skeptical (John 20:9)  followers that he was infinitely more than just a human leader, I think that the church would have died right there. And what would separate Jesus from all of the other radical religious reformers in history? His words would just be a collection of cryptic sayings and stories.

Thomas skeptically verifies Jesus' identity (Image Credit)

Secondly, the resurrection serves as a model for the resurrection that all those who are saved will experience someday. 1 Corinthians 15 (Thanks, Austin, for pointing this out to us) is all about this. We can be sure that there is a resurrection and that Jesus will be there because of what he did on resurrection Sunday. Both here and in Romans 5:14-17, Jesus is compared to Adam. Just as Adam was the first man of the old creation corrupted by evil, Jesus is the first of the new creation in which evil will be vanquished.

Finally - and this is the main thrust of this blog post - the resurrection is important because Jesus' work, and the story that God has laid out for the universe is not over yet. The story isn't just about God providing a ticket for us to be justified when we die. It is about Him defeating the evil that has corrupted the world.

Jesus is the the new King, the Captain that will lead the forces of good to this victory. He is also the savior who has provided a way for sinful humans to be made new and live in the perfect new creation. There is still pain and suffering in this world; the ultimate defeat of evil and judgment has not yet come. The resurrection shows us that even though we see evil now, nothing can come between Jesus and the ultimate victory.

This picture of Jesus as the King, victorious against evil, is present from the beginning to the end of the Bible. Here are just a few examples*:

In Genesis 3:15, immediately after the first sin, it is said that the offspring of Eve, Jesus, will crush the serpent's, that is, Satan's, head.

In Psalm 110, David speaks of his Lord, Jesus, who, in addition to being our eternal priest, will "shatter kings on the day of wrath", and have his enemies become his footstool.

In Isaiah 9:6-7, one of the most cited Old Testament verses about Jesus, it is said that "the government shall be upon his shoulder", and that there will be no end to this reign.

In Hebrews 2:7-8, we see that, though Jesus was made "lower than the angels for a while", everything will be put in subjection to him. This is something that we don't see yet, but we will.

Finally, in Revelation 19, we see a prophetic picture of the fulfillment of Christ's victory. John hears the multitudes declare "the Lord our God the Almighty Reigns." and this picture of Jesus is given:

Then I saw heaven opened, and behold, a white horse! The one sitting on it is called Faithful and True, and in righteousness he judges and makes war.
His eyes are like a flame of fire, and on his head are many diadems, and he has a name written that no one knows but himself.
He is clothed in a robe dipped in blood, and the name by which he is called is The Word of God.

And the armies of heaven, arrayed in fine linen, white and pure, were following him on white horses.
From his mouth comes a sharp sword with which to strike down the nations, and he will rule them with a rod of iron. He will tread the winepress of the fury of the wrath of God the Almighty.
On his robe and on his thigh he has a name written, King of kings and Lord of lords.
After this arrival, Revelation says Jesus will reign for a thousand years before a final judgment and defeat of Satan.

I think that if we think of Jesus' sacrifice to save us as the sum of all the work that God has laid out for him, we miss a great deal of the beauty and grandeur of His plan for the world. It seems to me that Jesus' task is to defeat evil, and to provide a way for some humans to experience this existence free from the evil that we brought upon ourselves. There is still abundant evil in the world. Jesus' work is not yet complete. That is why the resurrection is important.

* If you are a skeptical reader, you will notice that most of these verses clearly also reference something besides, Jesus. However, I think that the double meaning is in fact how God has chosen to reveal his plan to us in a way that is intriguing and beautiful.