Optical Absorption

For one of the classes that I teach the students use a device called a spectrophotometer. Basically this device works by shining a light through a sample and measuring the amount of light that gets through the material. This device is more than a fancy light meter which simply measures intensity. This device can break down the transmitted light into specific wavelengths and thus measure the amount of light transmitted for each wavelength. By measuring the amount of light transmitted we can figure out the the absorption which can tell us something about the specific properties of the material.

In this case my students are trying to determine the band gap energy for different semiconductors and also whether or not the band gaps are direct or indirect. I plan on posting about this lab at some point, but for now I just wanted to mention one thing that I measured. While I was in the lab one day I put my glasses in the detector and measured the absorption of the plastic lenses. The results I got are shown in the graph below (click on it to view it bigger).
The wavelengths that I measured extended from 800 nm (infrared) to 200 nm (ultraviolet). In the graph I only show down to 400 nm because below that my glasses absorbed too much light and the detector could not get accurate readings. Still you can see a sharp increase in the the absorption as you approach 400 nm. Other than the region below 400 nm my glasses did not absorb much light. This can be seen by the low measurements that are all below 0.05. To give you an idea of what this means, all throughout the visible spectrum ( ~400-720 nm, except for the tiny bit close to 400 nm) my glasses absorbed less than 10% of the light. An absorption rating of 1 would mean that an object absorbs 90% of the light, a rating of 2 would mean it absorbs 99%, 3 99.9% and so on. Typically an absorption rating of 7 (99.99999% absorbed, yes that can be measured) or higher is considered fully opaque.

As you might notice the absorption of the plastic in my glasses is not constant. There are small bumps or waves in the graph. These bumps are a result of the the thickness of my glasses and some slight internal reflections inside the material. These bumps are useful because from the size and shape of the bumps we can figure out the index of refraction for the material that my glasses are made from. That would be useful information to know if I were the one designing the glasses since the index of refraction determines the corrective ability of the lenses, and the curvature needed to make them work. Unfortunately I did not put my glasses in straight in the detector which meant that the path of the beam was not normal (perpendicular) to the surface of the lens. This makes the measurement more difficult (i.e. it would take more work than I'm willing to put into it) so I was not able to figure out the index of refraction for my glasses.

My Favorite Christmas Song

There are many Christmas songs and carols out there and while I like many of them that I like there are a few that I really enjoy. But there is one Christmas song that I would have to say is my favorite. It is called "Mary's Lullaby" written by Bertha Kleinman with music by Wanda West Palmer [Update 12/25/13: You can purchase the sheet music here]. Most people who read this blog may recognize the song from the Mesa Easter Pageant but it was written long before it was used in the pageant. Below are two videos of performances of the song.



The accompanying text for this video reads: "This recording was made in 1980 at a church Christmas program. Mary was holding her nine-day-old son, Kristopher. She was first privileged to perform this song in the early 1970s before it was even published and has been invited to sing it many times since, so she almost feels like it is her song. The music was written by Wanda West Palmer and the words by Bertha Kleinman."



The accompanying text for this video reads: "This recording was made in 2003 at a church Christmas program. Mary was holding her 2 month old grandson Kevin. 23 years earlier, she sang this song to Kevins father, Kristopher, who was nine-days-old at the time. (See [The first video]). Mary considers this is her songs as she was first privileged to perform it in the early 1970s before it was even published. The song was written by Wanda West Palmer and the words were written by Bertha Kleinman. It has been a part of the Easter Pagent at the Mesa Arizona Temple for many years."

For those who are interested the lyrics read:
All mine in your loveliness, Baby, all mine;
All mine in your holiness, Baby Divine.
Sing on, herald angels, in chorus sublime;
Sing on and adore, For tonight you are mine.
The wise men are coming to worship their king.
The shepherds are kneeling, their homage to bring.
Out yonder, the star over Judah will keep;
No harm can befall thee, then sleep, Baby, sleep.
Oh, let me enfold thee, my baby, tonight;
While legions are singing in joyous delight.
A new star has risen to hail thee divine,
For you are a king, But tonight you are mine.
Away spectered future of sorrow and plight.
Away to the years that must follow tonight.
The pangs of Gethsemane, let them be dim;
The red drops on Calvary, not, Lord, for him!
Oh, let me enfold thee, my baby, tonight;
While legions are singing in joyous delight.
A new star has risen to hail thee divine,
For you are a king, But tonight you are mine.
All mine in your loveliness, Baby, all mine;
All mine in your holiness, Baby Divine.
Sing on, herald angels, in chorus sublime;
Sing on and adore, For tonight you are mine.

Moral Discipline

A few months ago I wrote a post about research done by a Dr. Dan Ariely. Part of the work done by Dr. Ariely showed that people tended to be more honest when they were reminded of their moral code (even if it was a nonexistent moral code). In my previous post I concluded that "In the absence of a moral code, or a consistent moral code, it would seem that the only way to keep most people honest would be through active regulation of their actions."

About a month after writing that post I watched a talk given by Elder D. Todd Christofferson of the Quorum of the Twelve Apostles. The talk was entitled Moral Discipline and I found it very interesting because he spoke on almost the exact same topic that I had covered, but with more insight and more advice as to what to do about the problem. Here are some excerpts from the talk that I found very interesting.

"The societies in which many of us live have for more than a generation failed to foster moral discipline. They have taught that truth is relative and that everyone decides for himself or herself what is right. Concepts such as sin and wrong have been condemned as “value judgments.” As the Lord describes it, “Every man walketh in his own way, and after the image of his own god” (D&C 1:16).

As a consequence, self-discipline has eroded and societies are left to try to maintain order and civility by compulsion. The lack of internal control by individuals breeds external control by governments. One columnist observed that “gentlemanly behavior [for example, once] protected women from coarse behavior. Today, we expect sexual harassment laws to restrain coarse behavior. …

“Policemen and laws can never replace customs, traditions and moral values as a means for regulating human behavior. At best, the police and criminal justice system are the last desperate line of defense for a civilized society. Our increased reliance on laws to regulate behavior is a measure of how uncivilized we’ve become.”2

In most of the world, we have been experiencing an extended and devastating economic recession. It was brought on by multiple causes, but one of the major causes was widespread dishonest and unethical conduct, particularly in the U.S. housing and financial markets. Reactions have focused on enacting more and stronger regulation. Perhaps that may dissuade some from unprincipled conduct, but others will simply get more creative in their circumvention.3 There could never be enough rules so finely crafted as to anticipate and cover every situation, and even if there were, enforcement would be impossibly expensive and burdensome. This approach leads to diminished freedom for everyone. In the memorable phrase of Bishop Fulton J. Sheen, “We would not accept the yoke of Christ; so now we must tremble at the yoke of Caesar.”4

In the end, it is only an internal moral compass in each individual that can effectively deal with the root causes as well as the symptoms of societal decay. Societies will struggle in vain to establish the common good until sin is denounced as sin and moral discipline takes its place in the pantheon of civic virtues.5"

Essentially the argument is that as societies fail to maintain and encourage moral codes the only other alternative to maintain a civil society is to increase the number and enforcement of laws, or as Elder Christofferson put it, "The lack of internal control by individuals breeds external control by governments." It is with these ideas in mind that I look at societies like those in France or Greece and find it odd that they accept or (as in the case of Greece) actively encourage protest and violent protest as a legitimate means of expressing political frustrations, and then they complain about living in a "police state". In my own experience with places where I have lived, the places where protest was not the first resort of political expression have tended to be more peaceful and less prone to be characterized as having a "police state" mentality. But in places (such as Argentina) were protest and violent protest was a societal tradition the people tended to complain more of government oppression and viewed police and other government forces as adversaries rather than protectors.

What I have learned from observing these different societies is that if people want peace then there needs to be more moral discipline and less unbounded personal freedom. More responsibility and less entitlement. More reminding and less enforcement. Only then can we be free.

SLC Non-Discrimination Ordinance

Recently there have been a number of news stories (Deseret News, AZCentral) relating to the recent passing of a set of non-discrimination ordinances (pdf) regarding discrimination against people in Salt Lake City because of sexual orientation or gender identity (SLC City Code 10.04 and 10.05). What was also notable about the incident was that The Church of Jesus Christ of Latter-day Saints also expressed their support for the city ordinances because, "they are fair and reasonable and do not do violence to the institution of marriage."

So what is it about how these city ordinances are written that would bring official recognition and acceptance from the Church? Also after reading several comments posted after the news stories there were a number of concerns raised by people concerned with the implications of the new city ordinance. So what were the main concerns and how do these city ordinance address them?

Effectively these ordinances make it illegal to discriminate against someone in terms of employment and housing based on sexual orientation or gender identity. It establishes a procedure for filing complaints and resolving disputes that may arise due to allegations of discrimination. These city ordinances are in addition to the previous ordinances regarding discrimination based on race, gender, religion or country of origin.

In relation to these ordinances some of the main concerns that people voiced in the online forums were:

1. If I have a small basement apartment that I am renting out, will this force me to rent it out to a homosexual couple?

2. Will this force religious book stores, such as Deseret Book, to hire cross dressers?

3. If I fail to hire someone and it then turns out that they were homosexual, can they sue me for discrimination?

4. If I am single and living in an apartment with other single people, does this mean that a gay couple can move in to my apartment and I (and my landlord) can't do anything about it? As in, we can't object?

So how do these two city ordinances address these concerns, if at all?

First let us look at the exceptions provided. Both religious organizations and "expressive organizations" (such as the Boy Scouts of America) are expressly exempt from these city ordinances. While that solves some of the potential problems it does not address any of the above concerns. It turns out that the first three objections are addressed and the fourth may be addressed depending on how certain language is interpreted.

1. In this objection the concern is that under this ordinance a family living in their own home will be forced to rent out a basement apartment to a homosexual couple. This is expressly addressed in the exceptions. Effectively the ordinance exempts small privately owned apartments such as basement apartments because in order for the ordinance to apply you must,

"own an interest in or title to four or more single-family dwellings held for lease or sale at one time, and are located inside the City....[sell] two or more single-family dwellings inside the City, and in which the owner did not reside in the dwelling within the 24-month period preceding the sale or rental of the dwelling....use the service or facilities of any real estate broker, agent, or salesperson, or of any person in the business of selling or renting dwellings."

It also further specifies that owners are exempt if, "The rental of a dwelling that is occupied or intended to be occupied by no more than four families living independently of each other, when the owner actually maintains and occupies part of the dwelling as a residence."

That takes care of the first objection.

2. Will this force religious book stores, such as Deseret Book, to hire cross dressers? In terms of hiring practices the ordinance stipulates that employees must adhere to "reasonable rules and regulations and other job related qualifications required by an employer." This would include a dress code (no pun intended). There are also other provisions to accommodate for positions where "sexual orientation or gender identity are bona fide occupational qualifications for employment."

3. If I fail to hire someone and it then turns out that they were homosexual, can they sue me for discrimination? The concern here is that this city ordinance will create a special protected class of citizens that will be able and willing to sue at the drop of a hat, and that the major employers and landlords of the city will be open to all kinds of lawsuits for discrimination. This concern is addressed in its own section.

"This chapter does not create a private cause of action, nor does it create any right or remedy that is the same or substantially equivalent to the remedies provided under federal or state law. This chapter does not create any special rights or privileges which would not be available to all of the City’s citizens because every person has a sexual orientation and a gender identity."

This section is particularly interesting in that it prohibits a "private cause of action". This phrase is a technical legal phrase with a specific meaning, and with interpretations related to several supreme court cases. From Wikipedia, "Implied cause of action is a term used in United States statutory and constitutional law for circumstances when a court will determine that a law that creates rights also allows private parties to bring a lawsuit, even though no such remedy is explicitly provided for in the law. Implied causes of action arising under the Constitution of the United States are treated differently than those based on statutes."

In other words, if there were a private or implied cause of action then someone could bring a lawsuit against someone else even if there is no law expressly allowing it, i.e. there is no law expressly prohibiting the actions of the person being sued. What this means for the SLC ordinance is that someone cannot bring a lawsuit against someone else under violations of this city ordinance. The only way legal action can be brought under this city ordinance is through the complaint and arbitration provisions provided under the ordinance.

So in answer to the question, If I fail to hire someone and it then turns out that they were homosexual, can they sue me for discrimination? No. They can file a complaint which will then be investigated, but they cannot sue. Also this section in the city ordinance makes another interesting point. Even though it does not explicitly say it it implies that sexual orientation and gender identity is not a civil right, nor is it open to the same protections guaranteed to any other civil right protected by the Constitution or by law.

4. The last objection is not expressly covered in the city ordinance but depending on how a certain sentence is interpreted it may be. That sentence (in context) says,

"This chapter does not apply to a temporary or permanent residence facility operated by a nonprofit organization; a charitable organization; or a person in conjunction with a religious organization, association, or society, including any dormitory operated by a public or private educational institution, if the discrimination is based on sexual orientation or gender identity for reasons of personal modesty or privacy or in the furtherance of a religious organization’s sincerely held religious beliefs."

The key phrase here is "for reasons of personal modesty or privacy". While in context this may be a rather qualified statement, it may apply in most situations of concern where someone, or even a group of people, feel that they have a reasonable expectation of modesty and privacy. Thus in cases of college dorms and other comparable housing units, under this ordinance the tenants may insist on a having a reasonable expectation of modesty and privacy. In other words, in an apartment that can allow six single students, four of the residents can object to a homosexual couple moving in and the landlord can agree and not allow the gay couple to keep their contracts. As I said, this particular situation may not be covered by the city ordinance depending on how the language is interpreted. Still any major concerns may be covered under the section that explicitly prohibits the creation of a special protected class of citizens. As the code states, "This chapter does not create any special rights or privileges which would not be available to all of the City’s citizens". In other words, they will be treated like everyone else.

So while the non-discrimination ordinance allows for the basic, "common sense" rights associated with human dignity, it does not create a special, privileged class of people that have access to more rights, protections or remedies than others. It guarantees that homosexuals will be treated with fairness and equality, just like everyone else, while at the same time preserving the rights to religion and expression that all other people have. In other words, this city ordinance does not establish the rights and freedoms of one group of people by infringing on the rights and freedoms of another group of people.

On How We Know: The Sixth Sense

This is a continuation of my series On How We Know. The introduction can be found here, and a full listing of articles can be found here.

In considering the knowledge we gain from sense experience the question arises, where do feelings of the Spirit or Holy Ghost fit into this. As we learn from one passage in the Doctrine and Covenants the feelings or knowledge imparted by the Spirit can be described as a "burning in our bosom". Feeling the Spirit can also be described as enlightening our understanding, or simply enlightening. So the question that we might consider is how feeling the Spirit or the influence of the Spirit relates to our other senses.

Some people choose to define it as a sixth sense that we have. In other words, when we feel the Spirit we feel it through our "spiritual sense organ" much in the same way we sense anything else through our other five senses. Without elaborating I will say that this always seemed a little ridiculous to me. While it may be useful to talk about the Spirit in this way so that those who do not understand can begin to understand, I think that it is not ultimately useful or even instructive to talk about feeling the Spirit in terms of having a sixth sense. So what is it then?

Better yet is the approach expressed by Joseph Smith as explained by Truman G. Madsen,

"On the senses, a colleague at an eastern university said to me one day, "Yes, I've heard you Mormons have a sixth sense. You do. It is the sense that enables you to swallow this nonsense called Mormonism." Even if you conclude with certain scientific naturalists that anything that is nonsensory is nonsense, that is an endorsement, in a measure, of your heritage. Said Erastus Snow, referring to the Prophet,

"Joseph taught that the Spirit of the Lord underlies all our natural senses, that is seeing, hearing, smelling, tasting, touching. The Spirit communicates with the spirit of man and enlivens all the other senses. [BYU Special Collections, MSS. 44, Folder 5]"

Thus the sensations of the spirit and the feeling we have from the Spirit are the same things that connect all our normal senses to our spirit. It is the stuff of spirit, and when the Holy Ghost speaks to us it is directly to our own spirit, that which is the repository of knowledge and awareness. Thus the sensations of the Spirit are the sensations of sense itself.

On How We Know: "Why do you doubt your senses?"

This is a continuation of my series On How We Know. The introduction can be found here, and a full listing of articles can be found here.

In the book A Christmas Carol by Charles Dickens, the ghost of Jacob Marley confronts the character Ebenezer Scrooge, and after introducing himself the ghost and Scrooge have a rather interesting conversation. I will include the first few lines here:

"You don't believe in me," observed the Ghost.
"I don't," said Scrooge.
"What evidence would you have of my reality beyond that of your own senses?"
"I don't know," said Scrooge.
"Why do you doubt your senses?"
"Because," said Scrooge, "a little thing affects them. A slight disorder of the stomach makes them cheats. You may be an undigested bit of beef, a blot of mustard, a crumb of cheese, a fragment of an underdone potato. There's more of gravy than of grave about you, whatever you are!"

In this exchange the ghost of Jacob Marley asks a rather interesting question, "What evidence would you have of my reality beyond that of your own senses?" Essentially Jacob Marley is asking, "Is there any other possible way for you, or anyone else, to gain knowledge of reality than through your senses?" and the natural conclusion to this thought is that if there is no other way to gain knowledge of reality then, "Why do you doubt your senses?"

Scrooge's response is anything but unique. It is the response of sceptics and philosophers from many ages of Western Philosophy. Perhaps the one who expressed it better than anyone else, and is best known for it, is Rene Descartes. His particular approach even has its own name, the method of doubt. In applying the method of doubt, Descartes had a specific goal in mind, to find the foundations of reality, but unintentionally his method of doubt started a tradition that has continued and influenced us to this day. It introduced into not just Western Philosophy, but all of Western Culture a fundamental distrust of our senses. I have heard Descartes', and Scrooge's, arguments repeated over and over by college professors, by high school teachers and even by elementary school children. Even though most people live and act as if their senses are a good indication of what is real, the same people will immediate express doubt in their own senses, and especially those of others, when what they sense does not agree with what they already "know". There is always some other explanation that explains what someone saw or otherwise sensed. These doubts are given particular force because of the tradition we have of doubting or senses.

So let us consider this doubt, do we have any reason at all to doubt our senses? Essentially the argument of Descartes, and Scrooge, is that there exist well known instances where our senses cannot be relied upon. The classic example is dreams. We can "sense" things in our dreams that are not really there. This is not confined to our dreams but occasionally, as Scrooge points out, our senses can be cheated by other things, such as indigestion or other substances. So the question is, "Where do we draw the line?" How do we determine which sensations are real and which are false? The answer of Descartes was essentially, "Because I don't know where the line is I am going to assume that there is no line and that I can't trust any of the sensations I have." While Descartes ultimately acknowledges that this approach is insane, the damage was done and he had introduced the idea that because there is some doubt as to where the dividing line is between two things, in this case sensations corresponding to reality and those that do not, then we cannot assume that any of our sensations correspond to reality and we must doubt everything.

Effectively what Descartes has done is to confuse the ocean for a continent because he was standing on the beach and did not know where "dry land" ended and the water began. The method used by Descartes and the argument of Scrooge is like someone standing on a beach and wondering where the land ends and where the water begins. After puzzling over it for a while this person concludes that there is no such thing as land because they cannot clearly discern the boundary between a continent and an ocean. They then head inland away from the ocean and begin to talk to people and tell them that they are not standing on dry land but that they are actually in the middle of the ocean. In their defence they point to the presence of lakes, rivers and even glasses of water to prove that we do not live on a continent but that we live in the ocean. If someone actually attempted this and spoke like this then they would quickly be picked up by the authorities and taken to a "safe place" with padded walls. But in the case of philosophers instead of being ignored as insane they are called great and have their works and ideas spread around like manure.

Just because the boundary between an ocean and a continent is not well defined to someone standing on the beach does not mean that there is not a distinct, well definable and immediately recognizable difference between the two. Doubting the existence of a continent because the waves are washing your feet is an act of severe intellectual dishonesty. In the same way, doubting all our senses because a few of them may not actually correspond to anything in reality is also an act of severe intellectual dishonesty.

Continuing with this analogy we note that on continents there are lake and rivers which some will use to cast doubt on our assertion. These I will liken to physical injury, drugs and other mind altering substances. The fact that I can mention them in the context of "mind altering" indicates that there is a distinct, well definable and immediately recognizable difference between normal sensations and those arising from drugs or physical conditions. Again there is no reason to doubt the veracity of all sensations, or the existence of a continent, just because you are dabbling your feet in a river or a lake.

Related to this is the misguided approach of trying to "discover" something about reality by deliberately partaking in mind altering drugs. This would be akin to stating a desire to understand the rocks and dirt of a continent and then promptly going for a swim and spending your time staring at a fish.

So how do know to distinguish between between sensations that give us knowledge of reality and those that do not? The answer to that question is inextricably bound up with the answer to the question "How do we gain knowledge?" which is the purpose of these essays. So we know the limit or boundary by applying the selfsame modes of knowing that lead us into all knowledge. As for giving a more exact answer I would ask, "How do we recognize the boundary between land and water?" Understand that and you can learn to recognize the boundaries between sensations that give us knowledge of reality and those that do not.

On How We Know: The Prerequisite of Reason

This is the second in my series of On How We Know. The introduction can be found here, and a full listing of articles can be found here.

It might be said that the role or use of reason is a doubled edged sword which can greatly help or hinder those who use it. On the one hand, reason is something that is necessary for our existence as it is an integral part of our identity and allows us to understand, solve and overcome many of the problems of life. It give us our quality of life and allows us to understand and comprehend things beyond our own experience. In this respect it is one of the most powerful tools at our disposal. It is a tool to make all tools. But this powerful tool can be mislead and misguided. If we use it at the exclusion of all of the other modes of knowing, then our own reasonings can lead us into erroneous conclusions from which it can be difficult to extract ourselves. Now not all false reasonings will lead us into such a dismal mire of intellectual quicksand, but very rarely will you find quicksand on dry, solid ground.

To begin the process of understanding the proper role of reason let us consider two examples. The first is an experience that I had a few weeks ago while teaching some of my students about Newton's Laws. My students were performing an experiment to prove Newton's first law. The experiment consisted of balancing different forces in order to achieve equilibrium. In discussing the lab with some of my students I asked them about the uncertainty associated with the lab, as in, how much certain variables could change and they would still get the same result. At this point I asked my students which of the two important variables they were measuring had a greater effect on the overall uncertainty of the experiment (to get an idea of what I am talking about, imagine flying in an airplane from New York to Los Angeles. To get there I need a bearing (direction) and a distance. If I am off by one mile in the distance it is not as critical, but if I am off by one degree I could end up missing my target by more than 50 miles. In this case the uncertainty in the bearing is more important than the uncertainty in the distance.). So I asked my students to tell me which of the variables they were dealing with was more important to the uncertainty, and after I got some answers with an explanation of their reasoning I asked the question, "How do you know that?" At that point I got blank and dumbfounded stares from my students, as if to say, "What do you mean, "How do we know that"?" This group of students had just given me their answer, they had thought it through, given me their reasons as for why they thought they were correct and then when I asked them to back up their reasoning with "proof" (i.e. another mode of knowing) they were floored. It was as if it had never occurred to them that thinking about something and coming up with a good "reason" was not sufficient "proof".

The attitude of my students is hardly an isolated incident, but is indicative of a more general attitude found among those who commonly use reason to understand the world. A more striking example of this type of attitude can be found in the early works of Ludwig Wittgenstein. In the famous introduction to his book Tractatus Logico-Philosophicus he states, "the truth of the thoughts communicated here seems to me unassailable and definitive. I am, therefore, of the opinion that the problems have in essentials been finally solved." So firm was his conviction that in his short book he had managed to solve all of the problems of philosophy and logic that he thereafter left his studies at Cambridge and did not return for eight years.

In both of these examples the common element is a firm belief that what has been reasoned out is correct and there is no more need to continue with an investigation or even to reason further. Certainly there is the temptation that when we have thought about something to a sufficient degree and come to a resolution, we think that there is no further need to reason it out and understand it more, let alone use any of the other modes of knowing to confirm our reasoning. Like Wittgenstein there is the tendency to think that when we have come to the logical conclusion of our thoughts then there is no more and nothing further to be understood or considered about the topic.

So what is the remedy for this way of thinking? How do we escape this way of approaching learning, which if unchecked will result in our misunderstanding the nature of things? The answer, though simple, is almost unheard of, or even entirely unheard of, in the realm of epistemology. Quite simply, the remedy for these ailments is humility. In a brief search of The Standford Encyclopedia of Philosophy, not a single article about humility is given, and most references to humility are under the category of religion, and not knowledge. There is a reference to humility in a article on wisdom but humility is ultimately written off as "not promising". This is unfortunate because if humility was taken as the necessary prerequisite to reason then that would solve most, if not all, philosophical problems.

So why humility? Why would I call it a prerequisite for reason? In explaining this I will give my reasons for thinking this, but without considering the full implications, the rest is left as an exercise to interested reader.

Humility is a necessary prerequisite to reason because it is what allows us to use reason and to learn from it. Using reason without humility is an ineffectual exercise of the mind, yielding no useful results. To give a personal example, I once was considering a philosophical problem well known for its difficulty, it had to do with the issue of Divine knowledge and free will. In my mind there was an irreconcilable conflict between the two. It was something that I could not, for all the time and effort I put into thinking about it, reconcile what I considered to be an impenetrable barrier separating me from the answer. I even discussed the idea with others but to no avail. Some simply resorted to calling it a mystery and refused to discuss it further. But I was not content.

Many years later I had the opportunity to take a class on general relativity. After wading through six months of a rather difficult class, the teacher paused to point out a minor result that came from a rather complex set of equations. It was in that instant that my troubles with the issue of Divine knowledge and free will were dispelled. Now, what my professor pointed out did not give the answer or the solution to the problem, but at least in my mind, I now understood that it was possible for there to be a solution. It was as if I were standing on the top of a very tall mountain and I suddenly understood the extent of the intellectual journey I would have to take to finally reach the answer, but at least I knew that there was a resolution.

To give you the scope of the understanding that I came to, from the time that I had first seriously considered the problem, to when I had my "Aha!" moment, five years had passed. I was most of the way through an undergraduate degree in physics. I had embarked on a course of study that required me to learn general relativity, arguably one of the most difficult concepts in all of physics, and only after all that could I come to the point where I could say, "Aha! There is an answer." Even though I did not know what the answer was I could know that there was an answer.

Now you may be wondering how a class on general relativity resolved one of the most difficult problems in all of Western Philosophy. To answer that you would need a degree in physics, and to take a good course in general relativity, not to mention years of considering the problem and personally considering all the options. But for those who don't have the time or the desire to receive a degree in physics, the only other option available to resolve issues similar to the conflict between Divine knowledge and free will, is humility.

There were several things I learned from this experience and I will mention a few of them here. First I learned that humility was a necessary prerequisite to learning anything through reason. Without humility we cannot begin to understand things beyond our own experience, which is the whole purpose and end of our reason. Second I learned that the answers to specific questions may come from unexpected sources, and this recognition is intrinsically related to humility. When I first considered the issue of Divine knowledge and free will I had no idea that I would have to learn a lot of math and a lot of general relativity before I could resolve that issue in my mind. But as I had asked for the answer from Someone who knew how to give it, it was in effect the perfect method to answer my question. This taught me that, I as the student, the one who did not know the answer, could not dictate the answer to the Teacher, the One who knew the answer. Again this proved to me that humility is the prerequisite to learning by reason.

So what do we do when we have humility? With humility we acknowledge our weakness and ignorance, and begin the process of being taught by One who knows. Then, as Joseph Smith put it, ". . . Having a knowledge of God, we begin to know how to approach Him, and how to ask so as to receive an answer. When we understand the character of God, and know how to come to Him, He begins to unfold the heavens to us, and to tell us all about it. When we are ready to come to Him, He is ready to come to us.”9 (From Teachings of Presidents of the Church: Joseph Smith, Ch. 2)