The Sign of The Cross - Latin Lesson #1

Because Latin is the official language of the Roman Catholic Church (thus helping all who use it to remain obedient to the Church), and because it is not our native tongue (thus making present the mystery of God and prayer in the very words we use), the Red Cardigan Society has a wholly positive view of the moderate use of Latin in prayer and liturgy. For that reason, we will be posting Latin lessons from time to time, designed for the person who has no inclination to learn the proper grammatical procedures of Latin. Thus the mystery of Latin will not remain also inaccessible.

To begin with, the sign which begins all things:

In nomine Patris, et Filii, et Spiritus Sancti. Amen

In is rather obvious. Nomine means name, like our word "nominal", which means "in name only", like "he is only nominally a Catholic". Patris is "of the father", coming from the word pater, where we get "paternity" and "patron". The "of the" part comes from the declension of the noun [the genitive case]. [It comes from pater, -is, which is betrayed as a third declension noun by the genitive -is]. "et" means and, as in "et cetera", meaning and the rest. "Filii" is son, from filius, where we get "filial". Spiritus Sancti means [literally "the breath/air/soul/life of the sacred/divine/holy", spiritus being in the nominative case, sancti in the genative, a la Whitaker's Words]. Sancti here is the same word used in the "Sanctus" or Holy sung at Mass. And "Amen" is exactly the same!


Perhaps a discourse on the great mystery of the Sign of The Cross is due on this blog, but for now, revel in the mystery of the Trinity which you can now invoke in this mysterious, but now access able, language.

Update

I appologize dear dedicated readers for being so negligent in my regular updates. I imagine you have been dying for a post.

I don't know how anyone can properly call Calculus work ... it's simply too fun (note the cool graph with all the arrows):

My literature class is done. I wrote a paper about God's paradoxical existence to finish it off... it really wasn't very good, so I won't post it. Well, I should clarify that: I could have never gotten away with such unsatisfactory logic and rhetoric in high school, where my teachers had Ph.Ds in philosophy and used them, but alas, since I arrived at college teachers are well-read hippies.

We are learning about options in interest theory. So, for instance, I am a corn farmer, and I make an agreement with you, a cereal maker, that if corn prices plumet, you pay me some money, and if corn prices skyrocket, I'll pay you some money. That way we both make off well. This is also the sort of stuff that causes people to lose billions of dollars speculating... the terminology of the buisness ought to warn you from the get go: "long naked call", "short covered put", "strangle", "straddle", "collar"... somehow "butterfly" got in there too.

Economics is sssslllloooowwww.

And accounting is unadaulterated boredom. I was hoping it'd pick up a bit, because we were going to be doing the same things we do in interest theory, but the book dumned it down to such a deplorable state that it was painful. I had to muster every ounce of self-control not to write a snarky comment about the improper use of the word "discount rate".

As Spring Nears

It seems like summer outside, and spring hasn't even started. In that spirit, here is a graph.

y=x^5-sin(y^2) with y=25*x^4

Incidentilly, if you look from the top down at all the places where the leg meets the seat, they are all circles. Observe:

No doubt there are easier ways to make chairs, but I was in the mood to use Sine tonight.

Unsolvable Problem

I'd bet money I was given an unsolvable problem. Now, there are plenty of problems in mathematics that aren't solved yet. For instance, nobody knows how to find a, b and c such that a^n + b^n = c^n for any n greater than 2. A guy named Fermat claimed he knew how, but its pretty sketchy: just before his death he wrote in the margin of a book that he found a "a truly marvelous proof that it is impossible", but "this margin is too narrow to contain it." Not exactly the way to mathematical progress, Pierre...

I'll save you the gory details and show you my Excel worksheet which I constructed after all else failed:

I apologize for the poor quality. At any rate, this is a bond amortization schedule. I was given the two numbers in bold, from which I calculated the i=9.53% you see in the side using a cool Excel function called "Goal Seek". The problem asked for me to return the book value at time=0, which I worked backwords to find $1528.62.

All was good, or so I thought. The problem also mentions that the bond is redeemable at $1,000 at the end of n years. That means that at some point the book value should equal $1,000. And this is precisely why my pencil and paper failed me: the book value never gets to 1,000. I cut out the middle stuff to show you the book value at 100, 500 and 1,000 years. As you can see, it isn't going to go any lower than 1258.89 (see the boxed cell)!

So on the one hand I got a seemingly legitimate answer by ignoring that sentence, but it has never seemed a very wise strategy to go about solving math problems by proving they contradict themselves. Class is in half an hour... hopefully that will shed some light on the subject.

Interest Schemes

So a few weeks ago I gave you this offer:

The effective annual interest rate is 4%. You pay me $300 today and I will pay you $0.50 a day forever - you'll make your money back in two years!

I told you I wouldn't do it, but I was wrong. Way wrong in fact - were talking trillions in 20 years...


So... I've got a new scheme for you and I'm pretty sure I'm not wrong on this one. I'll leave this one open ended and you can leave your opinion in the form of a comment.

Yes or No? - You pay me $2,000 today, and I'll pay you $50 three times a year until you die. The interest rate is 2.45%. You expect to live at least 30 more years.

Hint: find the atomic number of nickle. At this number of years the two plans are equal (the interest rate was choosen for such an outcome).

Week 4

Week 4 was a week of 4 exams. Hopefully that phoneomenon doesn't occur in the comming weeks (7 exams in week 7?!?). What with all those exams, the amount of new material covered was pretty limited (though that seems to be a reoccuring trend in these little entries)...

Calc III: we drew more pretty pictures... and still no real Calculus! My soul panneth for a double integral!

English: we are doing a research project for the rest of the semester, and are currently selecting our topics. I'm leaning twords Vatican II.

Interest Theory: nothing new. The class got murdered by a difficult test: my 83% was the 3rd highest score in the class. Our professor appologized profusely, saying that he lost a fair amount of sleep after he saw how poorly we did (he was scared we'd all drop out of the class. Nobody did). After steping away from the monster test I got a bit of a better grip on it. Here was one problem:

[insert politically correct name here] takes out a $100 loan from PayDay Loans and pays $115 in 2 weeks. If the $15 is understood to be interest convertible daily, how long would it take for a $100 loan to grow to $500,000 at that interest rate.

The answer: 853 days (about 2 years and 3 months)
The moral: stay away from PayDay Loans

Economics: *yawn*... *snooze*... -- those are the typical sounds heard in class. It's not that the material is boring (it's really intersting!), but it's being govered ssssoooo sssslllllooooowwwwwlllllyyyyy!

Accounting: were getting into managerial accounting, which deals with helping big wigs in buisness make decisions. To that end, we learned how to classify production costs...

What I Learned - Week 3

You didn't miss much last week: it was boring! But this week is particularily interesting!

It seems that Calculus III is Calc I and II in 3d, which makes for some cool pictures, and even more so makes me extremely thankful for computers! Imagine doing this by hand (you can see by the angled edges that the computer even had some troubles!):

This is the graph of the vector-valued function r(x)={cos(5x),sin(x),sin(6x)}.

In literature I wrote an essay about Nietzsche (famous for saying "God is dead", among other witty aphorisms), Aristotle (famous for saying "By nature, all men desire to know"), and the Catholic Church (popular culture doesn't seem to care what they say...) and the agreement between the three. You can see the difficulty: you got an atheist, a pagan who was philosopically very Christian, and the Church. You can read it here!

Interest theory is by far the coolest. We have been working with annuities, which is a fancy word for repeated payments. Would you take this deal (I would'nt!):

The effective annual interest rate is 4%. You pay me $300 today
and I will pay you $0.50 a day forever - you'll make your money back in two years!

And economics is boring. The subject is wildly interest, but the monotonous pace that it is taught at is as obnoxious as the immature freshman who occupy the class' seats... we have been talking about supply and demand for a week and a half now. I figured that was common sense.

And accounting really is boring, the subject that is. I'll spare you the gorey details, but this week we learned about various ratios to analyze a company's position in the short and long-term.

An Email from my RA

Our floor kinda stinks...

Hey Guys,
I don't know if you noticed, but our floor hasn't smelled the greatest lately. So...with that being said, I have a few suggestions that could help remedy that problem:

-Shower on a regular basis.-Don't let your dirty laundry sit around too long. If you still don't know how to use the washing machines downstairs, I would be happy to teach you.
-Throw away old food, especially if it's moldy or rotting. It doesn't hurt to clean out your fridge once in a while. You never know what you might find.
-Keep your door open. Our wing is pretty good about keeping the doors open, but let's make sure we keep that up.
-Open your windows once in a while. I know it's cold, but opening your window wide for ten minutes helps. Or opening your window slightly for an extended period of time helps, too.
-Don't keep garbage in your room that smells bad. Put it in the garbage chute by the drinking fountain.
-Flush the toilets after each assault on porcelain bay.

Now, I'm not saying you guys aren't doing these things. And I'm not even saying that it's our wing that's the problem. BUT, in all fairness, I just think it's best to send these reminders out to everyone. I hope your week is off to a good start. Any questions, comments, or concerns let me know.
David

Roommates

Nick was eating shredded squid that he brought back from China today. He offered me some an I politely declined...

We also moved his desk today. He decided to bunk his bed earlier this week, but his desk covered up the ladder, so he was climbing on furniture to get into bed, almost always kicking something off as he did. I asked him why he didn't move his desk several times, and eventually (he's far too nice) he said that he didn't want to move it because then his light would be right next to me and he'd keep me up. I assured him that I don't think it will be a problem, and that if it is I will simply turn the other direction.

The other night I came back from a friends room and he asked if I was talking about God (he's noticed that I really like to do that), and I said I did. And he said "why don't you talk about girls sometime", and I said that we did, on account of it being the feast day of St. Agatha. Today I was singing a hymn because I was in one of those moods where you have absolutely no reason to be frustrated but you are, and acting on your foolish feelings only leads you into them being actualized. And Nick asked me if I was happy about a girl. I told him I didn't care about girls and he repeated my styalized "girls" at least 5 times.

Exam Number 2

In the future a common theme for this blog will be the 9 exams one must take to become a certified actuary. I am currently preparing for number 2 (I haven't taken 1 yet - that's for next year). The second exam is about interest and introductory financial math (i.e. really weird schemes to try to make money... like derivities, and swaps, and who knows what else!).

My professor has supplied my class with 5 past exams. Now, in 2003 they changed the exam so many of the questions are unaplicable, but it is all still quite helpful. Like a true student actuary I made an excel table which has a box for me to check when I successfully answer each question, and also a little formula which calculates how many I've done. Right now I'm 2% way through, after answering 4 questions correctly. I don't know how to do the other 98% yet, but I still have 11.5 weeks of class left... My favorite one so far:


Mike receives cash flows of 100 today, 200 in one year, and 100 in two years. The
present value of these cash flows is 364.46 at an annual effective rate of interest i.
Calculate i.

The answer is about 13%.


A short side comment: it's interesting to note the names the exam uses: Mike, Bruce, Robbie. Not these PC names I'm used to seeing in text books. The world became a considerably weirder place when text books decided it was neccessary to have a Jamal and Carlos in every problem. I digress...

Leisure

Last night (Saturday) I was sitting on my bed doing my Interest Theory homework and Nick (my roommate) walked in and said "you do too much homework". I laughed a bit, because I didn't really think I was doing homework: it was fun! Homework should be drudgery. Boring, unbearable and taxing. But not mathmatics homework... oh no. On Friday I did 2 hours of Calculus homework (even though, to my extreme dismay, we have yet to do any Calculus yet!), and it was by far the highlight of my day.

Some might say that I'm weird, but I have Aristotle on my side:

Hence, ... those arts were discovered which had to do neither with pleasure nor with necessities, and this happened first in those places where men had leisure. That is why it was in Egypt that the mathematical sciences were first developed, for there leisure was available to the priestly caste.

Back at School

I think it might be a fun weekly post to tell you one problem I have encountered throught the week in each of my classes.

Calc III (bold letters are vectors): find the norm of a+b if a=<1,5> and b=<3,7>. Answer: 4*sqrt(10)

English 112: Write about something you did to illustarte your current understanding of what it means to be ethical. Describe what happened, what you did, the reasoning of your decision to act (or not act) at that time. Then go on to explain to your reader why it was thical or unethical. Answer

Interest Theory: Your great-great grandpa left you $100 on July 26, 1876. Assuming an effective annual rate of interest 5%, what is his gift worth on January 26, 2010. Answer: $67417.31

MicroEconomics: What is economics? (It is truely a principles course...) Answer:
Economics is a study of how society chooses to manage its scarce human and material resources which have alternative uses, to produce goods and services for present and future consumption.

Accounting: Prepare the StockHolders' Equity section of the balance sheet. Answer: I'll spare you the agony. I got to make a pretty Excel picture at least...

Bridge

WARNING: MATHEMATICAL CONTENT!

As I approach my 'toughest' final of the week (a bridge tournament), I thought I'd share some numbers with you.

A bridge hand consists of 13 cards from a standard 52 card deck. There are 635,013,559,600 hands you can be dealt while playing bridge. You would have to play 24,836,748 hands per day to play every bridge hand over the course of 70 years - that's 287 hands per second.

There are 53,644,737,765,488,792,839,237,440,000 possible hands to be played by the whole table. That amounts to 82,472,935,650,000,000,000 hands a second, played since the earth was created around 4.54 billion years ago.

You have a 566,976 times better chance of being struck by lightning than getting a hand with all of one suit. Surprisingly, you are just slightly more likely to be struck by lightning twice than to get this hand.

You have a .2% chance of having all of the aces, a .00017% chance you'll have all the kings to go along with it, and a .00000000006% chance the queens will join the party. If it is any consolation, you have a 98.7% chance of having at least one of those cards.

Figure this one out:

A large sign in the library says:


Looking for a computer?
Go to: http://labs.uwec.edu/OpenSeats/index.asp


You don't have to be a math major to scratch your head at that one...

A Long Overdue Post

I'll tell ya, not much happens around here. I had two hours to kill before a meeting, so I decided I'd write a blog post, but I got side tracked trying to figure out the location of a point inside a square which maximizes the length of the four lines connecting that point to the squares corners. I didn't really need the fancy computer software I was using: of course it occurs in the four corners. Though a 3-d graph of the values would be kind of nifty. I digress.

I got my first fungal infection, and I suppose that's news to write home about! Everybody tells you that if you don't wear shoes in the showers you'll get all sorts of funk on ya feet, but I acquired my massive fungal infestation on my thigh! It has now spread in little splotches all over my body, after my home remedy fungal ointment proved ineffective, and I spent another five precious days treating a non-existent bacterial infection, per doctors orders. But now my guns are effectively loaded, and the enemy stands no chance.

Final are coming up. Finals week is referred to as "the dead hours", or "dead week" and, in fact, there was even a lengthy article about attempted suicide in the school newspaper. I am happy to report that the prospect of finals week has not brought me to suicide. In fact, it seems to me that a week in which you only have to go to class 2 hours a day is a most desirable week. Granted, 30% of your grade rides on that class, but you have plenty of time to study, and that is an understatement. I have already eyed up a good selection of books in the library (mostly children's books, a genre that I have been delving in to more and more as the "academic" books I am required to read leave me sorely disappointed in "sophisticated" thinking).

And other than that, I am quite out of things to write about, though I should mention that I'm quite glad we are in Year C now, and Luke (my second favorite Gospel, next to John) is the Gospel for the next 50 Sundays!

UPDATE: HERE'S TODAY'S WAY COOL MATH PICTURE!

The square measured here has a side length of 10. the two lower axes measure the distance of the point from one of the vertical sides one of the horizontal sides. The vertical axis shows the measure of the segments connecting the point to the corners of the square. Maximum occurs at (10,10, 53.77), though (10,0,38.10) gives a surprising run for it's money! Oh! Maybe this is the next one: find the point at which z/(a+b) is greatest. But of course! (0,0,EXPLOSION!) I'll stop the math humor while I'm not too far behind.

What Gives!

Now, you don't need to be a math major to conjecture that as we enter the winter, and it gets quite a bit colder, skirts should get longer, and as we move back into the spring and summer months, well then, at least there is a half-ways reasonable excuse for wearing short skirts (though modest is, at all points of the year, hottest, and I'm not refering to temperature). Yet, I am finding that skirts are actually shorter now than 2 months ago! The style goes something like this: wear black leggings that cover your whole leg, and then put the shortest possible skirt on which will, in theory, cover your behind, though it's all really quite optional in reality. This can be represented visually below:

An example of reasonable winter attire:

An example of unreasonable winter attire:

Would it be too cynical to point out that my classes are far easier to understand than my peers?

The Hailstone Sequence

So, here is the pretty picture I made today. An explentation is below, if so desired (but count yourself warned).

WARNING!!! MATHEMATICAL CONTENT!!!



The Hailstone sequence is the sequence defined as

If a(n-1) is odd, a(n)=3*a(n-1)+1, and
if a(n-1) is positive, a(n) = a(n-1)/2

Unfortunately I don't have subscripts at my disposal, so the function/sequence bleedover will have to suffice.

While it has yet to be proved, it is thought that the hailstone sequence converges to 1 for any starting number a(n). I was interested in the number of steps it took to reach one. For instance, starting number 2 obviously takes 1 step, and 4 takes 2. 3 takes 8 steps, while a starting number of 5 only takes 6. The graph then displays on the X-axis the starting number, and on the Y-axis the number of steps (for lack of a better word... perhaps "iterations"?) it takes to arive at one. I'll admit I stole the idea for such a graph from Wikipedia, but they only went up to 9,999, so I consider myself the victor, even more so if Excel could have more than 16384 columns, which my buddy pointed out is 2^14! He's a computer science major, so a more sophisticated graph may be forth coming.


On another note, a Saturday morning impromptu math class (a full 6 days of quality education for a 5 day price!) to learn about mathematical induction was scheduled. I am most excited!

Random Prejudices

I find it very helpful to identify which of your prejudices are "random" and which have some basis behind them. For instance, a random prejudice of mine is a dislike of umbrellas. There is nothing wrong with the umbrella, in fact it is a generally good thing, I think all would conclude. I couldn't explain my reasoning behind my prejudice because I have absolutely none. Even still, every time the smallest amount of precipitation falls on campus I am utterly discouraged by the sight of so many umbrellas.

A non-random prejudice, a very just prejudice, is my dislike of same-sex bathrooms. Of course, I have been using a "same-sex" bathroom my whole life: few homes have facilities designated for women and men. But this is different. On every floor of the library, right next to the elevators there is a woman's restroom and a men's restroom, where the sexes can be with only their same kind, except on the second floor. For some reason the second floor is well-advertised as have two same-sex bathrooms. What's the point? The whole character of the bathroom is lost. There might have been a girl in my men's bathroom! The men's room should be a place where you can be away from the other sex! So, while I normally I abide on the third floor, reading St. Theresa's "Life", or on the fourth floor, studying Wheelock's Latin, yesterday I was on the second floor doing Calculus (learning why e^(Pi*i)=-1, in fact!) and I had to use the restroom. It was quite a dilemma for me, because I refused to support the misguided same-sex bathroom. Fortunately I had enough time to run up to the third floor, and entered the small, most perfect, men's restroom. I even had to wait for another fellow man (so much better than waiting for a girl) before I could relieve myself.

Excel

I found myself with nothing to do this afternoon, which is always an unsettling feeling, so I decided that I was going to make a liturgical calender using Excel in these stretches of time. Actuaries use Excel alot, and it's a pretty nifty program to boot (which is probobly why they use it), so I figured I ought to know how to use it.

Well, as you know, Easter falls on a different day each year (anywhere from March 22 to April 25 in fact). The calculation actually has to do with the lunar cycle: "Easter day is the first Sunday after the 14th day of the lunar month (the nominal full moon) that falls on or after 21 March (nominally the day of the vernal equinox)." Needless to say it gets quite difficult. The other liturgical dates aren't nearly as difficult: the First Sunday in Advent, which is comming upon us quickly, is 4 Sundays before Christmas.

So I figured that it'd be best to tackle Easter first. I used dateofeaster.net (conveniant...) to figure out how it was actually done. I used a different column to calculate the letters for each year and when I got the finished column (the date of Easter) I opened up another handy Microsoft product, Word, and used the "Replace" function to consolidate my formula. Unfortunately Excel cut me off at 9000 characters for my formula, so I needed to use two columns and hide one (oh, but I will have victory one day). My formula was so long because of the steps where you need to determine the day of the week and then do different things for each day; I did this by determining the day of the week, and then having a different "if" statement for each day, which takes 7 times the charachters I think it really ought to. I also found a more simple algorithm by a certain Carl Friedrich Gauss. But after quickly figuring out the First Sunday in Advent (which took a measly 350 characters in comparison!) I'm calling it quits for today.

The Early Bird Yet Again Gets The Worm!

This weekend is homecoming weekend. I first realized this was the case because the Most Honorable Emmet Horan All-Male Sanctuary is on ultra-super-secret lock down. Residences of this Most Honorable Hall must enter through the front door only, and show their school I.D. to go to their rooms. I'm quite amazed that I wasn't woken up by drunkards last night, as usually happens on Friday nights, and would especially happen on such a riotous Friday night. No, I slept like a baby and arose at 5:35 this morning, just in time to pray Lauds, take a shower, throw on some clothes, and arrive at mass with enough time to collect my mind. Though collecting my mind was quite difficult this morning; as I was putting on my last articles of clothing (red socks for St. Ignatius!) I heard the unmistakable sound of several sousaphones (the tubas you see in marching bands the wraps around the player). As I exited the building I saw no less than 15 sousaphones in the middle of the basketball courts which are in the middle of the residence halls, playing the UW Platteville fight song (our opponents in the football game later today), and after than simply making a ton of noise. It was a glorious sight. As they continued playing shouts rang from all around them: "no wonder nobody likes band geeks"... "you suck!". To fully appreciate the situation you must understand that the dorms make a square, so everything echos quite well. An exuberant conversation 100 yards away is easily picked up. The flatulant sounds these guys were making echoed quite well. I could still hear them when I was 400 yards away.

The joys of getting up early...