Tuesday, July 4, 2017

What is the 4th of July all about, anyways?

Earlier this evening, Eric and I left our apartment with a bowl full of firework popcorn.  We were met by a man who saw us in our red white and blue t-shirts and said, "I did graduate high school, but what is it all about, anyways?" We were confused for a bit, and then realized that he was asking what the Fourth of July is all about. We told him that it was about independence from England, and went our way thinking it was all a bit strange, especially the preamble.
Firework Popcorn -
drizzle melted white and milk chocolate over plain popcorn,
then sprinkle Pop Rocks for a festive treat.

But I was thinking about it. The Fourth of July is one of my favorite holidays. It always means fun. Many of my favorite Fourth of July memories include hamburgers, hot dogs, family and fireworks. I have spent 4th of Julys in Canada, in Georgia, at a religious camp, at space camp, and in Texas.  I even spent a 4th of July in Bilbao, Spain.  

However, the 4th of July has to be more than just food and fun.  It is more than a fun time to celebrate in the middle of the summer.  It is more than fireworks and a day off of work.  It is our country's birthday.

But why?  Why do we make a big deal about it?  Why is it such a big deal anyways?

Wikipedia says: "Independence Day, also referred to as the Fourth of July or July Fourth, is a federal holiday in the United States commemorating the adoption of the Declaration of Independence on July 4, 1776. The Continental Congress declared that the thirteen American colonies regarded themselves as a new nation, the United States of America, and were no longer part of the British Empire."

Image result for declaration of independence
We hold these truths to be self-evident,
that all men are created equal,
that they are endowed by their Creator
with certain unalienable Rights,
 that among these are Life, Liberty
 and the pursuit of Happiness.
America is a great place.  Sometimes as a native, I take it for granted, but let us think together about all that America represents.

America is baseball and apple pie.  America is football. America is George Washington, Abraham Lincoln and Martin Luther King.  America is a land settled by pilgrims in search of religious freedom.  It is the pursuit of happiness and the American Dream.  It is "We the People," "I have a dream" and "We choose to go to the moon." It is John Glenn and Taylor Swift.  It is Chinese food and Italian food and Greek food and taco trucks.  It is the great melting pot of cultures. 

It is capitalism and faith and community.  America is a place where I am free to pursue my dreams and be whoever I want to be.  America is a land of opportunity, blessed by the hand of the Almighty.  God bless the USA.

What is the big deal about the 4th?  It is a day when we can remember and celebrate the wonderful land we live in together.

Tuesday, September 13, 2016

My mathematical thoughts on Institute today

I always try to read my scriptures in both English and Spanish, because it gives me two different perspectives on the same idea.

However, today, being fluent in math, gave me some additional insights into my institute class today.  Today we were reading Moses 1: 24-42, which is basically God's response to Moses's 2 questions: "[W]hy are these things so[?]"  and "[B]y what thou madest them?" (See Moses 1:24)  These are some pretty deep questions, and something that I think we should all spend some time pondering.  (God often provides deep meaningful insight we when ask the right questions.)

God responds by telling Moses that he has made "worlds without number" and that "innumerable are they unto man; but all things are numbered unto me, for they are mine and I know them."  (See Moses 1:33,35)  This is probably because we just had the lecture on countability in Analysis, but I started asking myself what is the order of the set of all worlds.  (Here is the Wikipedia page on Countability)

Mathematicians deal with the infinite all the time.  It is a concept that we are very comfortable with.  Dr. David Brown said recently that an engineer's or a computer programmer's task is to solve one problem at a time, but a mathematician's task is to solve every similar problem at the same time.  In order to do this we work with infinite sets every day.  Because we touch infinity, some mathematicians realized that some infinities are different than others.  The following is some definitions and explanations of mathematics to the lay reader.

When we talk about the cardinality or order of a set, we mean that we want to describe how many objects are in a set.  A set is finite if there are a finite number of things in them (that is there is a N in the positive integers, such that the number of things in the set is N).   A set is infinite, or not finite, if there are not a finite number of things in them (that is there is no N is the positive integers, such that the number of things in the set is N).  A set is countable, if there are the same numbers of things in it as the positive integers (that is that there exists a surjective* function from the positive integers onto the set.  That means that you can line up every element in some order and associate each one with a positive integer somehow.)  A set is uncountable, if there are more things in it than the positive integers (that is there is no surjective function from the positive integers onto the set.)   
These definitions lead to surprising results (at least they were surprising to me).  For example there are the same number of even positive integers as there are positive integers, because you could just use the function f which maps from the positive integers to the even positive integers given by the f(n) = 2n.  Clearly**, this function meets the requirements for countability, and therefore the even positive integers are countable.
Another result from these definitions is that there are more  real numbers than there are natural numbers, and that the real numbers are uncountable.  The proof to this statement was made by Georg Cantor and is called Cantor's diagonal argument.  It is a really cool proof, but quite involved.
So I was sitting in my institute class thinking about the order of the set of all worlds.  I know from my physics classes that the visible universe extends in every direction  for about 14 billion lightyears (this is a measurement of distance, not time), I also know that we have every reason to believe that the universe continues farther than we can see for ever.  I also look at the images taken by the Hubble telescope taken of a single point of darkness in the night sky and they get something like this: 

Hubble Deep Field
Nearly every spec of light in this image is a galaxy.  This leads me to believe that galaxies are dense in the universe (and therefore that worlds are also dense in the universe.)

However this doesn't help with determining if the number of worlds is countable or uncountable (as the rational numbers are dense in the real number line and the real numbers are also dense.  However the rational numbers are countable***, but the reals are not.)   So I am pretty sure that as far as science is concerned we can only guess if the set of all worlds is countable or uncountable.

However God told Moses that they are "innumerable," and since Moses hadn't studied modern Analysis, and wasn't concerned with their countability, maybe God just meant that they are infinite.  But the word "innumerable" sounds a lot like "uncountable" to me.  So maybe God was letting us know that not only is the set of all worlds not finite, but it is also not countable.

So if the set of all worlds is indeed uncountable, then the verse "and innumerable are they unto man; but all things are numbered unto me, for they are mine and I know them." takes on deep significance.
If God can somehow know an uncountable set, and know every member of an uncountable set, then God really is omnipresent.  This deep insight helps me to understand how God can know and answer every single prayer, because somehow he understands every member of an uncountable set, of which I am a part.

Sunday, September 11, 2016

My level of sacrifice

My second mission president made sure that we all knew that we should attend the temple when we returned home.  He even coined a phrase "your level of sacrifice," to describe how often we should attend the temple.  He explained that early in his marriage when he lived far from the temple, he only went to the temple a few times a year, and it was a sacrifice for him.  But later when they built a temple closer to his house, he found that attending the temple once a month had become casual, and then he increased his temple attendance to a weekly activity.  He said that for each individual and at different times of life, the level of sacrifice will be different, but that it is important to attend the temple often enough that it becomes a sacrifice.

Although I regularly attend/work in the temple, I haven't truly understood what "level of sacrifice" really means.  I have lived extremely close to a temple my whole life, and I have regularly attended the temple at least once a month, sometimes even multiple times in a week.  I love the temple and I love the spirit I feel in the temple.

I have always felt that what I was doing was enough, temple attendance once a week is surely sufficient for a busy college student.  And I have always felt blessings from my regular temple attendance.

For the last several months I have had the opportunity to serve as a temple worker in the Logan Temple, which means that I sacrifice every Saturday afternoon/evening to serve in the temple.  And I love it.  This amount of time is a sacrifice, but it hasn't ever been a hard sacrifice to make.  I love being in the temple, and I couldn't imagine anywhere else I would rather be.  It wasn't really a sacrifice but a privilege.

But this semester has been hard.  I am taking 2 senior level, 1 graduate level, and 1 (I don't know where to put it, but extremely advanced) math classes.  On top of that I have committed to spend at least 16 hours a week doing research for my favorite professor.  (Which is super awesome, bytheway.  And we hope to get a publishable paper out of the experience. :D)  On top of that I am TAing my favorite class, also for my favorite professor, which means hours spent helping students with their homework and even more hours spent grading their papers.  But I love it.  However, it all adds up to I am spending 10 to 12 hours a day doing math.  I have a lot to do, regular homeworks to turn in, and extremely advanced concepts to learn.  (In my graph theory/combinatorics/optimization/whatever it is class we are pushing the frontiers of mathematics and it is super exciting.)

I love my life, and I love doing math and I wouldn't change anything about how much time I have to spend to keep up with all of my responsibilities.

But Friday afternoon, while I was in a study group doing some Modern Algebra, I looked ahead at the weekend, and realized that I needed to complete my Modern Algebra homework, start on my Analysis homework, finish my Linear Algebra homework, and start in on my first mock paper for my Graph Theory class before Monday.  I also had just received a large stack of papers to grade. On top of that I needed to spend 3 more hours doing research, and I also had a new graph theory book I wanted to break into.  Friday afternoon, I looked at everything that needed to be done, and the amount of time required to do it in, and thought it was impossible.

For the first time in my life, going to the temple on Saturday evening was really going to be a sacrifice.  (Not just of play time and free time, but of actual real projects and responsibilities).  I love the temple, but it seemed on Friday afternoon, that there was no way that I could attend the temple and still finish everything that was necessary.

I went home and spent all of Friday evening grading papers.  Then I woke up (early, without setting an alarm, God must have blessed me), finished grading and doing my research.  On top of my busy schedule, I have made a personal commitment to myself not to do work work on Sunday (For me that means grading and research, since I am getting paid for it, but I still allow myself to do homework on Sunday.  It is a personal choice between me and the Lord, and I am comfortable with it.), so that means that I had to finish all of my work work before I went to the temple on Saturday, and hope that somehow all of the homework would find a way to get done.

Then I went to the temple, and it was good.  The peace I felt there was real, and although I didn't really do much besides smile at patrons and point them in the right direction, it was where I needed to be.  I felt immediate results from my sacrifice.  While I was in the temple, I knew that even if I didn't get everything done, even if I don't get high grades in my classes because of the sacrifice I had made, it would be alright.  The temple is good, and being there is what I need to do, and a sacrifice that I need to make.

Now, looking back on the weekend, Sunday Evening, I see that God has multiplied my time.  Not only did I finish all of my homework goals, and my work stuff, but I also had time to listen to the CES devotional.  I even got started on next week's homework for my Linear Algebra class.

For me the biggest miracle was my Modern Algebra homework.  We are learning category theory (if that means anything to anyone reading this blog post), and it is super abstract.  I am having problems understanding the definitions, let alone understanding any method to prove the results that we are expected to prove.  I have had two study groups on the same homework assignment, and I still had no idea (not really) what I was doing.  I came home from Ward Prayer, and started on my Modern Algebra homework, and with relative ease found myself understanding the definitions and the notation.  What once was a fuzzy cloud of intangible ideas has now been penetrated.

(And after I finished my homework, I still had time to socialize for an hour or so with two different social groups.)

I am a math major, and I have been carefully planning and counting my time, and I can't explain it.  I was able to accomplish more in one weekend, learn more, and master more, then should be possible.  And I spent a very large portion of it serving the Lord or worshiping Him at church.  Sacrifice works.

Monday, May 4, 2015


President Packer has shared an experience of his about a conversation with an atheist.  The man told him that no one could know if there was a God, Elder Packer told him that he knew, and proceeded to illustrate his point by asking the man to describe the taste of salt.  And although the man knew what salt tasted like, he couldn't describe its taste in words.  The same can be said of the Holy Ghost.
I sat in an airplane next to a man who so strongly expressed his disbelief in God that I bore my testimony to him. “You are wrong, I said, “there is a God. I know He lives!” 
He protested, “You don’t know. Nobody knows that! You can’t know it!” When I would not agree with him, the man, who was an attorney, asked perhaps the ultimate question on the subject of testimony. “All right,” he said in a sneering, condescending way, “you say you know. Tell me how you know.” 
I felt perhaps, that I had borne my testimony to him unwisely and was at a loss as to what to do. Then something came into my mind. I said to the man, “Let me ask if you know what salt tastes like.” 
“Of course I do,” was his reply. 
“When did you taste salt last?” 
“When I just had dinner here on the airplane.” 
“You just think you know what salt tastes like,” I said. 
He insisted, “I know what salt tastes like as well as I know anything.” 
“If I gave you a cup of salt and a cup of sugar and let you taste them both, could you tell the salt from the sugar?” 
“Now you are getting silly,” was his reply. “Of course I could tell the difference. I know what salt tastes like. It is an everyday experience.” 
“Then,” I said, “assuming that I have never tasted salt, explain to me just what it tastes like.”
After some thought, he said, “Well, I suppose you could say that it is not sweet and it is not sour.” 
“You’ve told me what it isn’t, not what it is.” After several attempts, of course, he could not do it. He could not explain, in words alone, so ordinary an experience as tasting salt. 
I bore testimony to him once again and said, “I know there is a God. You ridiculed that testimony and said that if I did know, I would be able to tell you exactly how I know. My friend, spiritually speaking, I have tasted salt. I am no more able to tell you in words how this knowledge has come to me than you are able to tell me what salt tastes like. But I say to you again, there is a God! He does live! And just because you don’t know, don’t try to tell me that I don’t know, for I do!” (The Candle of the Lord, Elder Boyd K Packer)
I know what salt tastes like.  I eat salt with almost every meal.  It brings out the flavor of the food, and makes meals more delicious.  Without salt, many food become bland and boring.  Could you imagine eating potatoes without salt?  But even though I know what salt tastes like, I can not describe the taste of salt.  It is salty.  It isn't sweet and it isn't bitter.  But more than that, words just don't exist to describe the taste.

Similiarly, I know what the Holy Ghost feels like.  I am not making up emotions, nor am I confusing the experience with something else.  I have felt the Holy Ghost, and I know what it feels like.  I know the difference between the Holy Ghost and emotions.

But more than that, when I was baptized, I received the gift of the Holy Ghost.  This means that I have the right to have the Holy Ghost as my constant companion.  Just like eating salt is an everyday experience, feeling the Holy Ghost is an every day experience.  It brings out the flavor of life, and makes experiences more delicious to me.  Just like I wouldn't want to eat French Fries without salt, I wouldn't want to live one day without the Holy Ghost.

Friday, May 1, 2015

Multiple Versions of the First Vision

A week ago I had a conversation with an agnostic, an atheist, and a Buddhist about religion.  One of them brought up the fact that there are multiple versions of the first vision as evidence that Mormonism has changed over time.  I didn't know that there were multiple versions of the first vision, and even if there were I would have assumed that they said essentially the same thing.  They don't.  But regardless of that, I didn't answer as well as I could have, and now I wish I had the chance to talk to them again.  Maybe they will read this blog.  Maybe not.  But this is how I wish I would have responded now that I have done my research, read the different accounts, and prayed, and prayed, and prayed.  

First I consulted Google about the different accounts and I found: https://www.lds.org/topics/first-vision-accounts?lang=eng.  The main differences between the two different accounts is that in the first, which Joseph wrote in a private place never intending it to be published, Joseph only mentions seeing the Lord.  Notice the use of the singular.  In the second, Joseph records that he saw two personages.  

The article gives various possibilities for the differences inbetween the two accounts.  Joseph could have merely been emphasizing the part of his vision when Jesus, the Lord, talked to him.  Or he could have also referred to both individuals as the Lord.  
There are other, more consistent ways of seeing the evidence. A basic harmony in the narrative across time must be acknowledged at the outset: three of the four accounts clearly state that two personages appeared to Joseph Smith in the First Vision. The outlier is Joseph Smith’s 1832 account, which can be read to refer to one or two personages. If read to refer to one heavenly being, it would likely be to the personage who forgave his sins. According to later accounts, the first divine personage told Joseph Smith to “hear” the second, Jesus Christ, who then delivered the main message, which included the message of forgiveness.10 Joseph Smith’s 1832 account, then, may have concentrated on Jesus Christ, the bearer of forgiveness. 
Another way of reading the 1832 account is that Joseph Smith referred to two beings, both of whom he called “Lord.” The embellishment argument hinges on the assumption that the 1832 account describes the appearance of only one divine being. But the 1832 account does not say that only one being appeared. Note that the two references to “Lord” are separated in time: first “the Lord” opens the heavens; then Joseph Smith sees “the Lord.” This reading of the account is consistent with Joseph’s 1835 account, which has one personage appearing first, followed by another soon afterwards. The 1832 account, then, can reasonably be read to mean that Joseph Smith saw one being who then revealed another and that he referred to both of them as “the Lord”: “the Lord opened the heavens upon me and I saw the Lord.”11
In order to read the different accounts and explain the differences between them, you must first choose one of two axioms.  Either Joseph Smith told the truth in all the accounts, in which case he was a prophet of God, or Joseph Smith lied in one or more accounts, and then it is reasonable to assume that he wasn't a prophet of God.

Using just the various accounts of the first vision, it is impossible to tell which axiom is true.  Both can be explained using simple logic and it comes down to an interpretation of what Joseph Smith meant when he wrote it.  Anyone who know me, and knows how much I struggle with literature classes, will understand that this is a question I try to avoid as much as possible.  I don't know what the author meant when he/she wrote something.  It is impossible to say.  All you have is the words on the paper, and they can mean whatever you would like them to mean.  You can not say for certain what the author meant when he/she wrote something.  The only way to know for certain what the author meant is to ask him/her and be reasonably assured that the author is telling the truth when he/she responds.  Unfortunately Joseph Smith is dead, so we can't ask him what he meant.  (Imagine how great that would be, if when reading a particular difficult text, like Isaiah or Shakespeare, instead of just grasping at straws trying to understand the meaning, you could just call the author up on the phone and ask them.  I think that would solve every student's problems in literature classes instantly.)

So just looking at the accounts of the first vision, there is no way to know what is true.  Either Joseph Smith lied or he told the truth.  Either he was a prophet or he wasn't.  Choose your axiom, and you can defend it either way.  This corresponds with an agnostic view towards the world.  You can't know, so stop trying to know because you will just keep getting into circular arguments.

Fortunately, we have more resources available then just the original sources of the first vision and the various commentaries on it.  Joseph Smith translated (or made up, depending on the axiom you choose) a work of ancient scripture, the Book of Mormon.  This is the only book on the face of the earth with a promise of its kind in it.  The book promises that if you will read the book, ponder its message, and ask God, then you will come to know the truth of it.
We invite all men everywhere to read the Book of Mormon, to ponder in their hearts the message it contains, and then to ask God, the Eternal Father, in the name of Christ if the book is true. Those who pursue this course and ask in faith will gain a testimony of its truth and divinity by the power of the Holy Ghost.
Suppose that Joseph Smith told the truth. (As anyone who has taken mathematical analysis has practiced, it is possible to consider that something is true, without actually accepting it as truth, and then seeing where it leads.)   Then there is a reasonable explanation between the differences of the accounts.  Then Joseph Smith was a prophet of God, and the promise made in the Book of Mormon is a promise from God.  Then you can pray to know the truth, and God will answer you.

This is as far as my proof can go.  Unlike mathematical proofs, I can not demonstrate it for you, and stop my argument with a QED.  Only God can prove it to you.  You have to read the book yourself, and then ponder in your heart it's message.  Then you must ask God, in faith, and you will come to know for yourself that it is true.

If Joseph told the truth, then he wasn't the only witness to the events surrounding the first vision, and although we can't ask Joseph what he meant by the differences in the accounts, we can ask God if they are true.  This is a much better practice of obtaining truth then by trying to understand what the author meant when he wrote it.

I have asked God if it is true, and He has answered me.  But before I get to my witness, I want to share the testimony of Elder Holland, a special witness of Christ.

Later in this same talk, Elder Holland says, "In this I stand with my own great-grandfather, who said simply enough, “No wicked man could write such a book as this; and no good man would write it, unless it were true and he were commanded of God to do so."

I know that the Book of Mormon is true.  I know because I have prayed and asked God if it is true.  And every time I get the same results.  In a way, more powerful than words, I know that it is true.  The Holy Ghost testifies to me of its truthfulness.  In fact, as I am writing these words, again I am receiving a witness from God that it is true.  

I don't know how to reconcile the differences between the different accounts of the first vision, but I know that the Book of Mormon is true, thus I know that Joseph Smith was a prophet, and he didn't lie.  He did see God the Father and his Son Jesus Christ.  And the church that he established is the Kingdom of God on Earth once more. 

If you want to know of it the truthfulness of the Book of Mormon, if you want to know if Joseph Smith told the truth, or if you want to know if the Church of Jesus Christ of Latter-day Saints is the Kingdom of God, then all you have to do is ask.  Start by supposing that it is true (remember that you can suppose something is true, before you have established it as fact -- mathematicians do it all the time), then read the book, and in faith, ask God.  You will get a witness from the Holy Ghost.

(Note that it is super important to start by supposing the Book of Mormon is true, because then the promise in the Book of Mormon is from God, and it is a real promise.  If you start by supposing the Book of Mormon is false, then the promise in the book was made up by a liar, and you can't do anything about it, and it won't lead you to any more conclusions.)

Monday, October 13, 2014

To Know God (Para conocer a Dios)

So a major theme of this semester for me is knowledge, and how some types of knowledge are different from others (specifically, science and religion).

I was catching up on the Bible Videos, when 1 Corinthians 13:12 really struck me.  Paul says "now I know in part; but then shall I know even as I am known." In Spanish there are two different words for knowing: saber and conocer.  

Saber is to know a fact, to know how to do something, to know something thoroughly, whereas conocer is to know a person or to be familiar with something (see this online spanish lesson for further grammatical instruction).

As I have been thinking about knowledge this semester, I have mainly been thinking about saber, or factual knowledge.  But when Paul is talking about it as he is known, the "I am known" part seems to imply conocer.  Just to check I looked it up in Spanish, and every time Paul uses a form of the verb "to know," Paul uses the word conocer

And then I remembered John 17:3, "And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent," and I wondered what type of knowledge eternal life, or knowing God, is, and so I looked that up in Spanish as well, and it is also conocer.  

For me saber is the cold, hard facts, while conocer is more intimate and personal.  Saber is the experiments and data; saber is what can be taught in a classroom.  But conocer is personal experiences, and more importantly personal relations.  Learning about God, and the gospel isn't enough.  The facts aren't good enough for eternal life.  Eternal life will come by personally knowing and developing a close relation with God.

It appears that I have been looking at knowledge incompletely.  I would now say that for the most part Scientific Knowledge is the things that can be known (saber) and that religion is the things that can be known (conocer).

What do y'all think?

Una tema mayor de este semestre para me es el conocimiento, y como son algunos tipos de conocimiento diferente de otros (especificamente, la ciencia y la religión).

Estaba mirando los Videos Biblias, cuando dí cuenta de 1 Corintios 13:12 (lo siento, solamente está en Inglés).  Pablo dice, “Ahora conozco en parte; pero entonces conoceré como fui conocido.”

En Inglés, solamente hay una palabra para saber y conocer, y estaba pensando del conocimiento (y tal vez la sabiduría) en inglés, que son el mismo.  Pero con está escritura, pensaba que la diferencia entre saber y conocer es muy importante.

Y despues, pensaba de Juan 17:3, “Y ésta es la vida eterna: que te conozcan a ti, el único Dios verdadero, y a Jesucristo, a quien has enviado.”

De acuerdo con estás dos escrituras, parece que lo más importante para la vida eterna es conocer o sea desarollar una relación personal con Dios.

Entonces, parece que estaba pensando de sabiduría incompletemente.  Creo que el Conocimiento de la Ciencia es lo que uno puede saber y religión es lo que uno puede conocer.

¿Qué piensen ústedes?

Wednesday, October 1, 2014

Christmas Wish List

Here is my wish list for my Christmas.  I will add to it as I think of things.