Multiple relationships: looking at the numbers

I did this exercise a couple of months ago, but I thought I would discuss it here in light of another math moment. Above is a standard 10 X 10 multiplication table. Most of us were required to memorize this at one point or another in grade school. The line on the diagonal shows the squares of each number. You probably noticed in grade school that the table is identical when mirrored across that line, i.e. 3*4 is the same as 4*3.

But now look at the group of boxes. If we look at the number in the middle we can refer to the numbers around it by location: so the red number is North, Green - East, Purple - South, Blue - West. What I want to point out is the relationship between these for numbers. So when I say NW that means 24 and 21.

Now that I've set this up, take a look at the NW and SE numbers. The difference between them is the same, i.e. 3. Now look at NE and SW. Again, the difference is the same, i.e. 11. It doesn't matter what number you pick, the differences between NE:SW and NW:SE will be the same. Perhaps I missed the boat on this back in grade school, but I think that is kind of cool. Also consider this, if you shift the center number down and over (say to 40), the relationship stays the same for the NW:SE numbers, and if you moved it down and over the other way (to 24) the NE:SW relationship is the same.

Now what happens if you just shift the number down (to 32). The difference for NE:SW becomes increases to 12 and NW:SE increases to 4. But if you shift it right (to 35) the NW:SE difference drops to 2 while the NE:SW difference stays at 12. How does this work, you ask?

LIKE THIS!

This was the original excel sheet I set up when I looked into this. This is the way you read it.

1 - Locate a blue line (e.g. in the upper left corner), look at the numbers that are on either side of that line (2 and 6). The difference between those numbers is equal to the axis number the line passes through (3) plus one.

2 - For the red lines, it is the axis number minus one. The easiest example is the longest that runs through the squares. all of the numbers mirrored across it are the same.

So, go back to our original example - 28. The blue line (the NE:SW difference) crosses the axis at 10, giving us a difference between numbers of 11. the red (NW:SE) line crosses at 4 resulting in a difference of 3.

Any movement along any single line will result in the same relationship between the numbers. Now, what happens if you don't know where the line will cross the axis? For instances, we can see where the blue line would cross on the number 336 and we will pretend we don't see the red line either. The key is to find the factors with the least difference. In this case it's 16 and 21. To figure out what the blue (NE:SW) difference will be take the absolute value of the difference of the two factors (i.e. 16-21 = 5) for the red, you take the sum of the factors (i.w. 16+21=37).

Now this is probably way more than you wanted to know about the multiplication table (or what I do in my free time), but there is an even simpler way to do this. It's called finding the slope! Finding the slope of a line has been done for centuries. And I just discovered it!

Not really. the multiplication table is basically one quadrant of the coordinate plane. When viewed like this (with the factors on the top and left) we are looking at the lower right quadrant (+X, -Y). If you remember from those grafting equations classes the slope is rise (the difference in Y) over run (the difference of X). Technically all of these lines have a slope of 1 because they are straight and at a 45 degree angle, but this is how it works.

As we treat this as a coordinate plane all of the factors at the top (the X axis) will be positive while the numbers at the left (the Y axis) will be negative. So we take our original box:



The differences (or slopes) between our coordinates are:
S and E =  -4 (rise) plus +7 (run) = +3
S and W = -4 (rise) plus -7 (run) = -11
N and W = 4 (rise) plus -7 (run) = -3
N and E = 4 (rise) plus +7 (run) = +11

Since we only care about the distance (not the direction) we can eventually just use the absolute values which give us 3 and 11.

There you have it. I have proven that slope exists within the multiplication table. What does this mean for the world of mathematics? Probably very little. But It was a fun adventure to figure this out. As I work in education, I have been asked by many students, "When will I use math?" My 10th pre-calculus teacher, Mrs. Mead, use to answer many of those questions with, "You won't. This is to get you to think."

As this post has gone on long enough, I will simply close by agreeing with Mead. The math you see in a textbook is not the math you are doing in your head when you look at a clock, try to figure out a sale price, or even the advanced equations of speed and distance when you drive. However, the basic nature of algebra is such that it forces your brain to think on higher levels and puzzle out solutions. That is the nature of math. And that is why it is needed.

Muse on that.

What can you see?

I can see you! Granted I was looking at the back of my iPod or rather my mirror when I took this. You can actually see the bathroom lamps and my iPod (the black box below the lights) in the reflection from my eye.

That is not the reason I took this picture, nor the item of interest I thought of. As you can see, my eye is red. If you pulled up "causes for bloodshot eyes" in Google you would get a lot of sources that all say pretty much the same thing. That red eyes are caused by a number of reasons that you may or may not want to be worried about.

However, out of all the reasons you can find, this site was the first to mention the particular reason my eyes are red in this picture - tiredness. If I am up too late, my eyes go red. Sometimes it's bad enough that my vision becomes very blurry and my eyes hurt. Most of the time they just go red. If I'm doing things with family or friends, I'll sometimes ask how my eyes look as an indicator of when I should turn in. If they start to look bad, it's time for bed.

I've worn glasses since I was in 6th grade. My younger sister is the only other sibling that wears them (that is out of 4 siblings), but that is just for driving and computer use. I've always found my family's vision interesting. My father wore glasses from the time he was 8 or so, but neither one of his brothers did until they were older. Now my father is the oldest of 3 boys and I'm the 2nd oldest (but oldest boy) of 5. So from what I can see, it is likely that my son will need glasses, but not my daughter. While nearsightedness (or Myopia) has been shown to be hereditary, I don't know if it will effect my family as I've predicted here.

We'll have to see what happens.

I'm not going to tell you how late I was up last night, but I will say that it is really hard to put down a good book. As I have been plugging authors, I'll mention Megan Whalen Turner, author of The Thief, The Queen of Attolia, the King of Attolia, and A Conspiracy of Kings. She was the guest of honor at this years LTUE symposium. We bought her books and my family (who was able to stay later than we were) got them signed for us. I've read the first three before and am rereading them so I can enjoy the 4th. They are wonderful on many levels and are prone to keep you up reading when you probably should call it a night.

Remember: when your eyes turn red, it's time for bed.

The Serial Story

I will gladly say that I do not have television. Not that I don't have A television set, but I do not have an antenna or cable signal. And I really don't care. This is because of a number of factors: my family's love of reading, habit - I grew up with little to no television viewing, and also because of technology - the internet provides a lot of substitutes to television. I'm really don't have anything against television itself as a medium or even against many of the programs. Although there are some that portray things I think are better left alone.

The reason I bring this up is to accent that I enjoy stories in long form, like a lot of what television is doing, but I do not have that source for myself. Consequently I read a lot of books with sequels and series. Just thinking off the top of my head, there are at least 5 series that I have started that I'm currently waiting on books. This is also visible in my selection of web comics.

For this post, I wanted to return to some musing about serials and their origins. A serial of course is when a story is published / produced in segments or parts. This is the definition of television dramas. Often once the story is complete they are complied into one volume for future consumers (think DVD box set). The same is true of books. I understand that Charles Dickens wrote many of his stories in serial format, and the original Hitchhiker's Guide to the Galaxy was produced as a weekly radio drama. Even Larry Correia, one of my favorite authors, wrote a serial story online before selling his first bound novel. So even going beyond a series of books, many books were produced a little at a time.

There are many reasons to do a serial. It might be the form of your medium. Television and radio have always had to work with limited time. If you notice, production requires lots of time and money. So if a TV studio is going to poor millions of dollars into a story, they like to release it a bit at a time so if it's going to go south they can stop it before they become too invested. Serial also supports how we consume media. I don't know anybody who has the time to sit and read a book over a 45 hour and 37 min period in one go. Even if you are like me who will dedicate a couple of hours to reading a book (usually between 10:00 pm and 2:00 am) there are few books I have read in one sitting. (I can only think of three, and they were all less then 300 pages).

I think one result of writing (or at least releasing) material in a serial is that it builds suspense. It leaves the audience thinking and dwelling on it. I understand the show Lost had a huge online following while it was on. I know that when I watched the first season of 24 back in college I would talk about and research it between episodes. The same is true with books. Lemony Snicket used online games and puzzles to allow readers of his Series of Unfortunate Events to see extra content and as precursors to the books coming out. Granted, many of the things done "between installments" is for the purpose of reminding consumers to keep with the story. But when the story is good, consumers need very little encouraging to keep consuming.

I wanted to blog about this for two reasons. First, the serial format is nothing new to television as it started long before broadcast media and second, my sister, EA Younker, is currently releasing one of her unpublished works on Wattpad a couple of chapters at a time. This is not the first time she has done this with alpha and beta readers. My older sister got one of EA's books chapter by chapter as she edited it and I got another. Bragging point - EA's first published novel is coming out this year by TM publishing. I got to read one draft and I liked it. I'm looking forward to getting it to see the finished product. To return to Game Over, She is doing this so people can see how she writes as well as to get feedback from potential readers of her other stories. Check it out and the next time you sit down to watch (or read) your latest favorite drama, think about how long we as a society have been consuming stories that we have to wait for.

Writing is the answer not 42.

Douglas Adams asked in his book The Hitchhiker's Guide to the Galaxy, "What is the meaning to life, the universe, and everything?" The great computer Deep Thought gave the answer, "42." There are many that think this is still fundamental correct, but when it comes to Life, the Universe, and Everything in Provo, UT the answer is "writing" (and by extension reading).

This year my wife and I were finally able to attend one of the greatest writing symposiums in the inter-mountain west: Life, the Universe, and Everything. My mother wrote in her weekly E-mail that this was the fifth year they have attended. The biggest draw for us this year was that my younger sister and father were presenting a research paper they had written entitled, "Reactors built in the 20th  century blow up in the 21st." It was a discussion of the shift in science fiction from space opera to dystopian and apocalyptic. It was fascinating to hear both the origins and the progress of sci-fi, particularly as I tend to be picky about what sci-fi I read.

We enjoyed the few other panels we were able to attend. Although, I was reminded that just because people are on a panel doesn't mean that they are the most knowledgeable on the topic. It reminded me of this Schlock Mercenary comic. There was some good discussion, but it was also entertaining to watch one of the panelists do everything possible not to roll her eyes on a number of occasions as people said things she disagreed with. I was also able to attend a discussion on how to write action done by one of my favorite authors, Larry Correia. Larry is one of the authors I wanted to go all "fanboy" on. He is very good at writing action that keeps you engaged and I don't think there has been a book he's written that I didn't stay up late (or early i.e. past 2:00 am) to finish. Several of his 400+ page books I've read in less than a 48 hour period.

As we drove home, my wife commented that I should consider taking up writing again. That is, I have considered taking up writing and my wife was recommending that I consider it again. I have not written anything of particular note, but I have some ideas bouncing around my head that have been marinating for a while. I do enjoy learning about the writing process and how to improve writing, but I've come to see myself as an informed consumer. With that said, I do enjoy putting ideas on a page and I think that was one the the catalysts of keeping a blog. Writing gives me a way to think or should I say muse.

No singing at the dinner table

While I was still at my parents (and even now when I visit) we would discuss the family rule: no singing at the dinner table. The discussion inevitably was about why we had that rule. In almost all instances, whenever that discussion was had, that rule would be enforced by the end of the meal. It's not that my family is against music, but rather that we are loud enough already that singing just takes the volume through the roof. While I've never considered music a huge part of my life, I've realized how much of an impact it's had on me.

I was musing on this as I drove home yesterday with my kids. I often sign to them in the car to keep them occupied and yesterday was no exception. However, yesterday was different for two reasons. First, we sang along to the radio (normally I sing a cappella) and second I had a bad cold. I normally don't sing when I have a cold as it throws my voice waaaaaayyyy off. My normal range is a nice comfortable baritone, but when I have a cold all I can do is sing deep bass or falsetto, and my falsetto is bad. So, there I was belting out popular songs to the radio in my falsetto voice and just not caring what I sounded like. As I sorted through the radio stations for songs I wanted to sing it really got me thinking how music effects us.

Just a simple search of the "effect of music" will turn up lots of search results. I took the low hanging fruit and just looked through the first one. I won't get into all of the stuff mentioned there (although it's pretty cool), but will give some of my reflections on music.

One day in elementary school my mother, a fan of classical music, gave me a CD of Handel's Water Music. Having grown up enjoying the NPR program "Shickele's Mix" on Saturday mornings I too enjoy classical music, but I am much more a Beethoven and Saint-Saens kind of person. Why was Mom giving me Handel? It turns out Water Music has been shown to help people spell better. It didn't help me, but I think i was supposed to play it. Like I said, I prefer Beethoven. Moonlight Sonate can relax me every time I hear it. It plays to the deep parts of my being and strums the strings of enchantment. It brings images of warm fires, bright stars, and dark rooms with large windows. The Piano Guys, one of my favorite music groups, did an adaptation called Moonlight, and while their version doesn't give quite the same feelings it still resonates with me. My wife and I are proud to be members of the Founders Club of The Piano Guys. Seriously, check them out.

I could post a lot more on music, but I think that is enough for now. Muse on your music and check back later.

Not that kind of post

I received this wonderful magnet in the mail this weekend. It was enclosed in a letter from my mother. She only lives about 50 minutes away, but felt that was still far enough away to receive a letter.

What is this all about? The Month of Letters was started by Mary Robinette Kowal (note, Robinette is her middle name, not maiden) back in 2010. I became aware of it last year when I started following her on Twitter (@maryrobinette) and heard about her preparations. The challenge: write a letter everyday that the mail goes out, and then make sure that it is posted. You can read the full challenge by clicking on the Month of Letters link above. This year I was glad to be a recipient, even if it was from my own mother.

I received this letter the same weekend that I heard about the USPS cutting Saturday deliveries because of budget reasons. Just about everyone I know will acknowledge that I love technology and the things it can accomplish. With that said, I love receiving stuff in the mail. I love the convenience of being able to download content directly to my computer, but I got absolutely batty when I am expecting something in the mail. It drives my wife nuts. I was disappointed to hear about the cut in service. There is something nice about going to the mail box and not just finding the usual stack of bills and credit care / insurance offers, but something from a friend or family member.

I am not participating in Month of Letters this year, but I am planning on doing it next year. Hopefully that will be before the US government decide to cut the USPS and simply privatize the who shebang. But before that happens, think about what it feels like to get that letter (handwritten or otherwise) and take advantage of what the Postal Service can do over posting on the internet. I'll just mention this one: E-mails have "attach," letters can "enclose."

(Just to put a plug in for Mary Robinette Kowal (not that she needs it) - she is a fantastic author of short and long fiction, a member of the Writing Excuses podcast panel, a professional puppeteer, a voice actress, and a collector of typewriters. She wrote two of my favorite books, Shades of Milk and Honey and Glamour in Glass. I'm going to start keeping track of authors in my "Mentioned in my Blog" and I'm glad to list her as the first.)

Scones and Biscuits. Water and Hell.

I was listening to Grammar Girl's "Quick and Dirty Tips" podcast this morning (episode 355) and she was talking about subject-object usage. The subject being the person/object that is the instigator of the action (verb) upon whatever the object is. So, "I threw the ball" involves "I", the subject, "throwing", verb, "the ball", object. While you can tell that spelling is not always my best skill and I have a tendency to think faster than I type (i.e. I occasionally drop words on accident) I enjoy language and how it works and flows. However, English grammar for me did not start to make sense until I studied Russian. I started in 10th grade and eventually minored in it. My teachers talked about subject, verb, object, indirect object, gerunds, imperatives, post predicates, etc. and unless I learned what the blazes those were in English I did not know how to use them in Russian. I'll be honest, I like Russian grammar than English grammar. It is a lot more structured yet maintains some great freedoms of expression.

It's curious how American English has formed over the years. I had a linguistics class my fresman year, "Latin and Greek Elements in English" taught by the wonderful Dr. Mark Damen. I describe his lectures as going to a stand up comedy about Greek tragedy. I almost fell out of my desk one day from laughing so hard in his class. In addition to being a very humorous professor, he is also very thought provoking and I consider him one of the best instructors I ever had. He had a lecture on "American English" in this class and the biggest thing I took away from the class was in language, just like biology, separation breeds new species. If you take two microbes that are initially identical, and separate them in different environments you will eventually end up with two differ species of microbe. We are not taking about trans-species evolution, but simple adaptation. The same is true of languages.

English is a wonderful example of this because the British Empire spread the language everywhere. You have British English, Australian English, Indian English, American English, African English, and even Engrish (although that is due to bad translations more than long time development). Not only do these groups speak with different articulation, and use words differently but also some have words that others don't. Several years ago my wife and I were at a restaurant for dinner. Behind me, in the next booth over, there was a couple from the British Isles as we could tell from their speech. Not being able to help it we heard their exchange with the waitress when she came to take their order...

Guest: "Excuse us, but what is a Navajo Taco?"
Waitress: "It's got beans, and lettuce, and hamburger on a scone."
Guest: "Oh, you mean a biscuit. We know that what we call scones, you call biscuits."
Waitress: "No, it's not on a biscuit. It's on a scone."
Guest: (pause) "So, what's a scone?"

I can't remember the reply, but I do remember smiling at the confusion of both parties. The waitress probably didn't think anything else in the world could be called a scone and the guests were amazed that even with their preparation, the language barrier had still managed to rear it's ugly head.

So, remember, as you travel and learn new languages, or different versions of your native one, Just expect to put your foot in your mouth at least once. For my part, I managed to change, "Would you like me to boil (some) water?" into "Would you like me to burn in Hell?" As soon as I said it, I realized what I had said. To his credit, my friend replied, "Would you like me to answer that questions?"

Holding hands

When it comes an image of "being in a relationship", holding hands is one of the most basic and often seen. When two people are seen holding hands it is culturally understood that they are involved in each others' lives on a higher level simple friends. I remember holding hands for the first time with my wife (she was my friend then, of course) and the comforting feelings of closeness it gave. It felt like we were coming together as something more than friends. Maslow, in his hierarchy of needs, lists "Love & belonging" directly above those of basic safety. This implies that after our own physical needs and safeties are secure we begin to reach out to others and seek companionship.

I began thinking about this yesterday when I was in one of the student lounges and overheard a conversation between two young women discussing their current relationships. The first had just broken up with her boyfriend after receiving a call from "his baby's mother." The second was unsure of her relationship. She liked the guy but felt like it was hard to bring up bad news because he was "too sensitive." That part of the conversation was far more interesting as the two expressed their expectations for a partner and from themselves in a relationship.

I came across this article on Kansas State's homepage. It states that in many ways it is healthy for tweens and teens to have celebrity crushes. I particularly liked this quote from it:

"If you and your best friend swoon over a celebrity together, then it's helping you figure out where you fit with your friends and with your peers," Myers-Bowman said. "But, for example, if all your friends like Ryan Gosling and you like Sean Connery, you get to feel what it's like to be different from everyone else, and you get to process those feelings."

I'm not sure if any of the women I know didn't swoon over Sean Connery when they were teenagers. My sisters were rather partial to him in "Darby O'Gill and the Little People."

My wife and I are approaching our 7th wedding anniversary this year. If we were living in Germany and Gabriele Pauli had succeed in passing her legislature then we would be looking at "renewing our vows" in order to stay married. While we've been married we've often wondered where we would be if we hadn't made that decision. I for one feel that deciding to marry my wife was the single greatest decision I have ever made. I remember people telling us that it would be hard and I don't remember a many people telling us how good it could be. But I can say that for better or worse, poor or poorer (I work in education, there is no rich), sickness and health, and every other dichotomy imaginable I am a better and happier person because of my marriage.

My invitation: Muse on your relationships and see where your thoughts lead you.

Poetry and why I memorize it

This is a picture of my mother and my daughter headed back to the car after a couple hours of sledding. I was thinking about how lucky I am to have such a wonderful family. It was the first time that my kids have been sledding and while my daughter was running my mother and myself ragged, my son was more than content to sit and watch. And eat snow. He had a little difficulty as his thumbs were crammed in with his finger in his mittens. When I told my mother she immediately replied:

Thumbs in the thumb place,

Fingers all together.

This is the song we sing in mitten weather

When it's cold it doesn't matter whether

Mittens are wool, or made of finest leather.

Thumbs in the thumb place,

Fingers all together.

This is the song we sing in mitten weather.

I had to look this up. According to this website it is a song written by Rachel Buchman. I had never hear it before and knowing my mother she probably learned it from her childhood or just for the heck of it. Yes, this is my same mother that got me to appreciate math. Her professional training was in engineering, but she has always been an avid reader of literature, fiction, non-fiction, and poetry. She could of completed an English lit minor with all the classes she took. She passed that love of reading down to us kids and I hope to pass it along to my children as well.

Returning to the topic I proposed, I was not always an advocate of memorizing poetry. When I was in 8th grade I told my English teacher that we should "Never memorize anything you can look up." She was not impressed. Not even when I mentioned that it was Albert Einstein that said that first. I can remember having to memorize two different poems between 8th and 9th grade. There may have been more but I can't remember them. I only succeed at doing one of them - "Old Ironsides" by Oliver Wendell Holms. The other one I was didn't memorize was "Invictus" by William Ernest Henley.

While I have always appreciated poetry, I didn't always see a need to memorize it. I grew up on Shel Silverstein, and Jack Prelutsky, as well as the large binder of poems that my mother had put together for a poetry class she had in college. My father enjoyed poetry as well, reading to us from Robert Service and Rudyard Kipling when we were camping. I enjoy the flow of language and the way poets will engage in "word smiting" to create images. I even wrote poetry while in high school and little in college. However, I never set out to actively memorize a poem.

I think the turning point for me in actually wanting to memorize poetry came with my children. My daughter used to suffer from acid re-flux and I would sing to her as she would try to fall asleep. I looked up the complete lyrics to "Scarborough Fair," I pulled out children and church song books, and even sang her songs that I had learned in Russian. I like to think that my singing helped her fall asleep, but I think it just helped me bond with her. What are songs but poems to music. The flame was lit.

Then my daughter came to the age of questions and wonder. She is still very much in this stage, but a couple of years ago, I remembered my mother reciting poems to us as we learned about the world around us. Whenever my wife made meatloaf I cursed that I didn't know the words to "My mother made a Meatloaf." or "The Turkey shot out of the Oven" when we had one in the oven ourselves. I wasn't completely hopeless when it came to poetry. Often, when she helped me with the dishes (I was the dishwasher for the most part), I would recite "If you have to Dry the Dishes" by Shel Silverstein. But I wanted more.

The last reason for wanting to memorize poems was my own personal enjoyment. I wanted to have words close to me. There is a rhyme and reason (pun very intended) to poetry that tends to resonate with me. When I see the sunrise I think of "The Morning Song in the Jungle" by Kipling. When I walk outside into the cold winter air I hear "The Ballad of Blasphemous Bill McKie" by Service. When my daughter is filled with insatiable curiosities I remember "I Keep Six Honest Serving Men" (Kipling again). When I watch my son grow and learn new things I ponder upon "If" (Kipling once more). And when I find myself in trial and tribulation, "Invictus" bears me up. Yes, I went back and did what I couldn't do in 8th grade.

And I am very glad I did.

Death and Taxes

Yesterday I was doing taxes. I still have to some more things associated with it. I'm not sure if there has been a year when doing taxes was not a major,multi-day project. I could pay someone to do it for me, but it isn't that much of a hassle for me to feel justified in it. Regardless, there is a reason that people say that the only two things that are certain are death and taxes.

Think on this though. Most Christian sects and many other religions believe in some form of life after death. So, really, according to most people that means there is really only one certainty - taxes.

Isn't that a happy thought?

Binary, Trinary, and Troll. Oh my!

I watched the latest Numberfile video, going over what viewers' favorite numbers are. That got me thinking about my favorite number. My thoughts mulled it over for a couple of minutes, but then I thought of different number and how they looked in different number systems. The fact that I know different number systems is due to my mother, but also a clock.

Growing up we had a clock whose face looked like this. Good old Roman Numerals. I = 1 V = 5, X=10, etc. In order to tell time we had to know how to count to 12. My mother taught us not only how to read the clock but count to what ever number we wanted to in Roman Numerals. Interesting fact. Did you know that most movie production dates are still given in Roman Numerals at the end of the film? Check it out. They got a little shorter when we passed the year 2000 (MM). Before the were something like MCMXCVIII (1998). Granted, this year would be MMXIII, so still a mouthful.

I think that clock just opened up the flood gate because we learned binary and a basic understanding of any of the non-10 bases. The year, 2013, would be 11111011101 in binary, 2202120 in trinary (which is used in this card trick),  many and 3 lots, 3 many and 1 lots; 3 many; and 1 in troll counting from Terry Pratchett books, and 7DD in hexadecimal. I'm still working on dozenal/duodecimal system, but it would be 11E9 (had to look up the equivalent of 10 and 11: X and E respectively). To finish up, I had a friend that was doing a masters in theoretical numbers systems. To explain it he used the example of a clock. So 2013 on a clock could very well be 8:13 pm, which is about the time I'll finally get to relax tonight.

So, the next time you see a number or you wish math wasn't so hard, think about how many different ways there are to count, or how we could have ended up counting and then be relieved that we are not trolls.

Doesn't that make you feel better.

I'm already teaching my daughter Roman Numerals. They are used as the chapter numbers in the book we're reading. She's turning five this month. Oh, and what's my favorite number? 11. But I'm not going to tell you in what system.

(All calculations were done without the use of a calculator or internet conversion device. Why, because I like math. Blame my mother... and the clock. You can check my math below.)