Sunday, August 31, 2008


Okay, Girls.

Now that school is starting I'm not sure how much I will be contributing to this group for the time being. If we read really slowly I might be able to keep up, but other than that I'm just going to be fully immersed in what we're learning here at home and doing some of my own pleasure reading (including Andrea & Kaylie's book!). I will do my best, but that's where I stand as of today. Just FYI.


Thursday, August 28, 2008

Moving on

Andrea's not reading Young Fu so let's move on to The Screwtape Letters. Really I'm just excited to get to the book about Colombia and since I've already read the Screwtape Letters, I'm not so motivated to read it again. Maybe if you guys posted brilliant thoughts I will be more motivated. We'll see.

Wednesday, August 20, 2008

Guess What!

Hey guys....
I wanted to join your ranks (well, not you, Ju). I hate being left out of things!!!
So.....I'm expecting my fifth baby! Pretty sweet. Pretty un-planned. Just thought I'd let you know. I'm due in March. I will have three children with birthdays in a 30 day time period. Pretty wild.

Ju's Young Fu

Okay, so I read this a long time ago but totally remember loving it. I think what I loved about it mostly were the wise sayings from his teacher friend and the Chinese proverbs written throughout the text. I do agree that there was no real climax in the story. However, I think Young Fu's "luck factor" was also symbolic of those the Chinese deem to be worthy or of value. I think even in our culture we can look at the lives of some great leaders and say they were "lucky" when in reality they were being preserved and saved for a greater mission. We don't know the extent of Young Fu's life after the book ends, but we know that he will continue to do great things (in the fictional world at least). I also thought this book would be a great introduction to Chinese history for when my children are older. It may not have the full content of the history, but it does give a great prelude to further studies and inspired me in such a way to want to learn more about that particular culture.

Monday, August 18, 2008

Young Fu

I have to agree with Kami's comments. There was no climax and Fu was too lucky. I think the most interesting part of the book was the section after the story that talked about China then and now - the changes that have occurred. My book had an introduction and a foreword by two very well-known authors. One of them promised that if you like Tolkien (and someone else who's name escapes me), then you will love this book. I did not think this novel was on par with Tolkien at ALL! In reading more about the two authors who wrote the intro and foreword, they both have a history in China during that time period, so I think their comments were based more on nostalgia than true scholarship. Which is disappointing!

Wednesday, August 13, 2008

American Revolution/Colonial Times

You might try Paul Revere's Ride
Also the d'Aulaire books on George Washington and Benjamin Franklin.
There's a magic tree house book on the subject.
Felicity, from the American Girl series grows up in Colonial Times. :-)
There's a Diane Stanley book (she's so awesome) called Joining the Boston Tea Party

"The Courage of Sarah Noble" is a good one for younger kids.

I have a bunch of ideas from the Sonlight Curriculum. I usually just use what I can pull from the library and I haven't checked on that yet. But here's what Sonlight uses for American History:

American Adventures 1 - Greenberg SL3 (many topics 1770-1870)
The Story of the USA: A Young Nation Solves Its Problems - Escher SL3

Pocahontas and the Strangers - Bulla SL3
Squanto, Friend of Pilgrims - Bulla SL3

What's the Big Idea, Ben Franklin? - Fritz SL3
Ben Franklin of Old Philadelphia - Cousins SL3
Mr. Revere and I - Lawson SL3
And then What Happened, Paul Revere? - Fritz SL3
Can't You Make Them Behave, King George - Fritz SL3
Johnny Tremain - Forbes SL3 (American Revolution)
Toliver's Secret - Brady SL3 (American Revolution)
Phoebe the Spy - Griffin SL3 (American Revolution)
Martha Washington (Childhood of Famous Americans) SL3
Meet George Washington - Heilbroner SL3
George Washington (Childhood of Famous Americans) SL3
Winter at Valley Forge - Knight SL3 (1777)
If You Were There When They Signed the Constitution - Levy SL3

Meet Thomas Jefferson - Barrett SL3

Diary of an Early American Boy - Sloane SL4 (1805 pioneer life)
Johnny Appleseed - Kellogg SLK

Ben and Me - Lawson SL2 (Ben Franklin)

I'm sorry if those aren't helpful for a five year old. These are mainly for my eight year old daughter. The SL3 means it's Sonlight's level 3.

A long time ago I read a fabulous book called "The Signers: the 56 Stories behind the Declaration of Independence". It's not a read aloud for young kids but it was FABULOUS and I told the kids the stories in my own words. Many of the stories moved me to tears as I told my children about the courage of the men who signed the Declaration of Independence.

Tuesday, August 12, 2008

Sign of the Beaver

I just skimmed Sign of the Beaver to see if I could read it to Miriam this year as it pertains to pioneer/pilgrimy people. Such a great book, but it might be a little slow for a five year old.

For all of my vast knowledge of literature, I'm having a hard time coming up with many fiction titles that deal directly with colonial America. Pre-revolution and during the revolution specifically. Johnny Tremain is the classic. Witch of Blackbird Pond another classic--too old for Miriam though. Why aren't there more books about puritan girls? About Jamestown lasses?

If you can think of any, let me know. Of course, I'm not reading just colonial books to her (boring for a whole year) but I am surprised at how shallow the lit is for this time period. Obviously, I'm missing something.
I requested the book from the library and I think I didn't get in there to pick it up soon enough. So now I either re-request it or skip it altogether. But based on Kami's less-than-enthusiastic review, I might just skip it. Anyone care? :-)

Young Fu of the Upper Yangtze

I'm completely wimping out on this. But if Andrea can get by on that pathetic post about Fermat, then I don't feel so bad. I did read Young Fu. It was interesting but nothing spectacular I thought. The most interesting part to me was the clash of the old traditions in China with the new influences coming in (ie the priests healing vs. the foreigners healing). Also, seeing the seeds of communism in China start growing even as the National Government was consolidating. All in all, it was an interesting to read about the culture but I wish it had more information and more history of the major events of the time. Granted, this is aimed at a young audience, so really for it's audience, it's quite good. His master, Tang, was my favorite character. His short adages and proverbs were always good. Young Fu seemed too much a golden child to be realistic to me. I think the main thing lacking in this book was a climax though. It didn't really have one at all, hence I was never really drawn into the story very much. Those are my thoughts, sorry it's so short--I'm trying to finish a major sewing project so I don't have time for much else.

Sunday, August 10, 2008


First, isn't it cheating to hold an impromptu discussion on a book that I haven't read in awhile? JULIA????? You could have warned me!!! :-)

So this is one of my all-time favorite books. It's inspiring, it's informational, and it's hopeful.
That's all I have to say. It's one the those books I plan to re-read, at least partially, on a regular basis to keep me motivated and focused.

And that's all I have to say because it's been far too long since I've read it and I don't want to get it confused with "There Are No Shortcuts" - also by Rafe.

Friday, August 8, 2008

Ju--practicing multiple choice tests

Julia, I loved that Rafe went into detail about how to teach your students to be excellent test-takers--mostly because homeschoolers are shooting their kids in the foot if they neglect test-taking skills. Besides, it made me feel good because that is exactly what I did with my students. I was no Rafe--but I did a few things right!

Standardized tests

Education used to be based around a personal understanding of each student and each student's progress, and students used to not pass grades if they couldn't do the work. We don't hold students back anymore because that might mess with their self-esteem (whatever), and we don't have enough teachers anymore to really get a personal understanding of each student (who could with over 30 students in a classroom), so instead of figuring out ways to really help our students in a less-than-ideal situation (too many kids per class from less than ideal homes with bitter, overworked teachers), the FEDERAL government stepped in (that's where things went really wrong), and started mandating testing before they would give out funds to school districts.

First, education is a state level issue so whenever the federal government gets involved things go downhill fast--because what backwoods Alabama kids need is not the same as what inner-city ESL kids need. Education is best handled at a local level.

Second, taking funding away from struggling schools has got to be the number one stupidest thing anyone has ever thought of. It was supposed to "encourage" teachers to improve test scores, which resulted in the things Rafe was talking about--panicked teachers who help the kids cheat, or yell/scream/pull their hair out, over the tests. The teachers care about getting the funding because they care about their kids and their jobs. When funding gets cut, teachers get fired, class sizes get bigger, and students suffer.

If you've ever heard of teachers talking with great bitterness about No Child Left Behind--that's why. More high-stakes testing with threats of funding loss and worse, your district getting taken over by businessmen. Nothing worse than that really, because education cannot be run like a business no matter how good it sounds when a politician is talking about it.

So--we have an incredible number of tests that take up and incredible amount of a teacher's time, and because there are so many of the lame things, our kids have stopped worrying about them. I thought it was interesting that his kids thought they meant something. In Utah, there are so many tests that the kids often fill in blanks to make pretty pictures, or fall asleep, or most often--skip school that day. It is impossible to convince students that the school's funding is worth them showing up to take a test that doesn't affect their grade because we don't get the results in time to even tell the kids how they did. The whole thing is LAME.

I'm not against testing--but the system is seriously sick in the testing area. And what makes it worse is that parents who have no idea what the tests are even designed to demonstrate, read about test scores and get all up in arms about the teachers not doing their job. Give me a break.

Thursday, August 7, 2008

Firey Teaching

Okay, I should NOT be responding because I really need to pack for our trip, BUT I'm so tired of cleaning, packing, and organizing I really just want to respond to this email. I may give stuff away from the 2nd half of the book, Ans, but I must. AND, I have to say Kelly is the first to recommend it to me, so she gets to comment as well!

Using Trust rather than Fear
"Never use fear as a shortcut for education." p 6
I thought the same thing as you with my own children and how they have learned to "fear" me more than to "trust" me (in some areas of their lives - - i.e. cleaning their bedrooms - - okay, so, maybe fear doesn't work there either! hee-hee)

Quote from Measure for Measure, Shakespeare:
"Our doubts are traitors,
And make us lose the good we oft might win
By fearing to attempt."

Moral Levels of Development
LOVED this as well. And if you read Ron Clark's 55 Rules, it adds upon this whole concept of raising strong, intelligent, independent and confident children.

Why do we settle? I would agree that there aren't necessarily "bad" teachers out there, but there are many who settle for mediocrity. Who want to make it easier for themselves and their students. BUT can you blame them? After seeing the HOURS Esquith put into his teaching I realized why more teachers are not like him.

You mentioned, also how the teachers would step in to fix the problems of their students. Parents do this ALL THE TIME!! The kids come to them with any problem, big or small, and the parents give an answer: "You should...." "Go do...." Instead, we need to help our kids become problem solvers, thinkers! When my kids have come to me with problems (sometimes in hysterics), I've started to ask them a question, "What are our solutions." I remember Brooklynn freaking out about a lost something and I asked the question. She said, "There are no solutions!" (enter: the tears!) I just stayed calm (one trait I constantly need to work on when my girls go into needless hysterics) and said, "Well, go think about it and come back with a list of solutions." Well, she stomped out of the room (still crying) only to come back a few more minutes with the "something" found. I just think it's so easy to tell our kids how to behave, how to feel, how to think - - and then we get frsutrated as they get older and don't know how to make wise decisions. Duh! (read pp 147-148: How to solve a problem)

p. 141 "To help young people become remarkable, we need to challenge them with lessons theywill use for the rest of their lives."

This is so key, I agree. And it's something I've not been so strong at teaching. Writing came so easily for me, I don't even remember learning how, I just alwasy seemed to KNOW. Therefore, I just assumed my kids would know how to write. Ha! We've worked on it and come a long way, but this year we are mostly focussing on writing. EVERYTHING will involve writing (especially for John). I am so excited about it!

Esquith also made me realize that TV/Movies are actually good learning tools if used properly! (maybe you haven't gotten there yet, Ans). . . Before reading his book I would use "educational movies" as babysitters for my kids. They were still learning, right?! Well, let me just tell you how my whole perspective has changed and we are watching some really sweet movies! I've never seen a Shirley Temple movie until last night. It was great and the kids loved it. Anyway, I put Esquith's idea to a challenge. John wanted to watch Fetch with Ruff Ruffman (PBS kids show). Well, I told him he could only watch it if he wrote 5 sentences afterwards telling me what he had learned. He watched it and then couldn't come up wiht 5 sentences. I told him he still needed to do it. Well, he let it rest. Then, the next morning he woke up and said, "Mom, can I watch Fw/RR again and finish my sentences?' Well, he did and he wrote some great sentences. We sat down with the sentences and did all the correcting then and there - - grammar, spelling, penmanship! Then, he had to rewrite it with the corrections and in his best handwriting. John LOVED it! He didn't fight me on it one bit because I had taken one of his passions and turned it into a learning experience. LOVE writing!!

Standardized Testing
"Despite the fact taht standardized testing was conceived to help our children, in practice it has only contributed to their failure." p 75

"We adults must work hard to help the kids navigate the ridiculous hoops through which they are asked to jump." p 80

"In an era wehn 'You are your test score' has become accepted . . . we adults must work hard to make sure kids know that their test scores are actually a very small part of who they are." p 83

p. 174 "I believe that many of today's . . . schools are making a . . . significant mistake in how thye think about college. They place so much emphasis on getting into college that they lose sight of the larger issue of finishing college."

Andrea - explain this more to me (because I'm a critic) -- what is up with these tests? Washington's is HORRIBLE. AND, why are the teachers so limited on their cirriculum choices. I know, its' better to have a guideline, but does it need to be so set in stone and according to what administrators think? How do parents change this, or can they? I know there's a cirriculum board & all. Anyway, this is just one part of the book that frustrated me about the public school system (though I'm generally NOT anti-public school nor am I critical of the teachers themselves - - just to clarify!).

Final Note
p. 108 "Teachers and parents must remember that our children should be the performers, even if they are not perfect. That's the beauty of art - - we strive for perfection but never reach it. The journey is everything."

Enough Said!


P.S. I won't comment on Young Fu until I get back from Utah. I read it awhile back, but may need to refresh. LOL

First Installment of Teach Like Your Hair's On Fire

Okay, okay, I know this isn't the assigned book, but since I picked it up I can't put it down so Young Fu is just going to have to wait a few days.  Kami finished it, by the by, so I expect some comments on it will be posted by early next week.  I plan on finishing it Sunday at the latest.  Too bad I wasn't reading it when I stayed up until 4:30 am the other morning, but that is another story.

So, Julia told me to read this book and I am halfway through and thoroughly enjoying it.  A few comments.

First of all, I don't know how I missed Lawrence Kohlberg's 6 levels of moral development, but I am looking the man up to read more.  What a lovely way to teach your kids about the ultimate goal--and there are so MANY excellent examples to use to demonstrate the highest level (I have a personal code  of behavior and I follow it).  Loved that he uses Atticus Finch as the ultimate example--it is a great one, even if I was surprised that he was reading To Kill a Mockingbird with his fifth graders.  I guess preserving innocence isn't a factor when you teach in inner-city LA.  

I really loved this idea of the moral levels.  I plan on making Timothy make a really great, permanent, display of some sort of all the levels and for the rest of their lives my children will be thinking about what level different people are at as we evaluate behavior in every setting.  Louis L'Amour books would be excellent for this.  As would people like Emmeline B. Wells.  (Kammers--call me, I decided what I was going to do with that and it is BRILLIANT.  So . .  . call me.)  

So that was great right off the bat, although I want to read what Mr. Kohlberg has to say on the subject as he's the man who developed the idea.

--Next, I really liked what Esquith (the author) had to say about discipline shouldn't be based on fear, but trust.  I believe whole-heartedly that it is true.  I hate it when Miriam looks scared of me (of all the kids, she's the one most justified in looking that way), but man it is harder to control your temper than anything else in the world.  At least, for me.  

pg 31 had a great quote:  "Powerful forces of mediocrity have combined to prevent perfectly competent children from learning to love reading.  These forces include television, video games, poor teaching, poverty, the breakup of the family, and a general lack of adult guidance."  He missed a few, but great summary of all that's wrong with education that has almost nothing to do with teachers.  He mentioned some really horrible teachers in his book--which is strange, because overall, I only had two teachers that I thought were really despicable.  Most were totally okay with mediocrity, however, and that is a problem.

pg. 41: "Most parents and teachers agree that when a skill is being taught, there needs to be an assessment to see if proficiency has been achieved.  Discussion is never enough."  Esquith is referring to teaching reading here, and I wholeheartedly disagree.  Comprehension questions never help students comprehend what they have read better.  Comp questions determine whether or not kids know how to take tests.  If the students know the answers for the test, they knew them before the test or they were able to eliminate the worst answers.  

Discussing what you have read is the second best way to increase comprehension and "test" comprehension.  Writing about what you have read is the best way to fine-tune what you think about what you read.  As he mentions later--writing requires a precision that discussion does not.  However, I cannot agree that students need anything besides discussion and writing for learning to comprehend reading.  We need to give our students multiple choice comprehension tests so they can practice their test-taking skills, not their comprehension.

pgs.  45-48 about how the teaching of grammar and writing has gone downhill over the years was brilliant and hilarious--my fav part so far.  Example: 2000 (as in the year): Our school adopts a new basal reading series.  We are assigned two literacy coaches to help the teachers.  One of the many jobs of the literacy coaches is to remove the grammar books from classrooms.  Teachers are told they may teach grammar only from the new materials.  Instructors complain that while the new series does indeed address parts of speech and sentence structure, the older grammar books do a far better job.  Teachers are told they must surrender the grammar books anyway.  We ask if we can compromise and use the grammar books as a supplement to the official school texts.  This is not allowed.  Frightened younger teachers turn in their books.  Some clever older instructors hide the books or share one series among themselves and teach their children good grammar secretly.

AHAHHAHAHHHA.  Okay, maybe I laughed so hard because that happened at my school.  All the English teachers, except the ones on the adoption committee for the new texts, hid at least three of the old books before giving up the rest reluctantly.  All of our meetings for the rest of the year were about whether or not we were ONLY USING THE NEW BOOKS.  Whatever--I thought the new books had a few cool things, but my kids wrote.  They didn't do lame-o questions in a textbook.  I was frequently in trouble.  In fact, one of the teachers was annoyed with me because she was a special literacy coach for those who needed extra help in reading and she got tired of my students saying, "Mrs. Young already taught me that."  Apparently, I was stepping on her toes by teaching comprehension skills.  Love that Esquith describes staff meetings as worse than chemotherapy--too true.

pg. 50: "In room 56, rather than receive poor grades, my students are told they must get at least 90% or better on grammar assignments or do them again.   The Dreaded Rewrite makes kids understand that Room 56 is a serious place and they might as well listen, try hard, ask questions, and get things right the first time."  Very similar to my teaching philosophy of quality over quantity, and TJEd's only accept quality.  A VERY important teaching principle.

pg. 74: "It is ironic that the people most obsessed with testing children do such a poor job of creating conditions in which the kids will perform well."  Amen and amen.

The whole section on science and letting kids make mistakes and figuring out what they did wrong and fixing the mistakes themselves is pretty critical.  I remember way too many times I feigned complete inability in order to get a teacher to do my work for me.  As a teacher, it is always easier to do the work than listen to a student whine.  I want my kids to be better academic problem solvers than me.

That's all for now.  I'm about halfway through and enjoying it.  One thing I've noticed, it's pretty obvious, is that exceptional teachers don't have lives.  I would never be willing to be the kind of teacher he is as a wife and mother because there isn't enough balance.  Our education system combined with our dismal expectations combine to make it almost impossible for teachers to achieve exceptional levels with their students in a normal school day because the kids are going home to imperfect situations.  

Kammers-you would like this book.  I just realized how choppy, disorganized, and poorly written this whole post is.  Forgive me--as I am just a product of a broken-down education system, the technological age of informal writing such as text messaging and email, and I am lazy to boot.  :)

Sunday, August 3, 2008


“If Fermat did not have Wiles' proof, then what did he have?” (284). Wouldn't it be fascinating to find out if Fermat really did have the proof or not? The great thing about this theorem is that even after being “solved”, it's still an enigma because we know that if Fermat solved it, he must have used a different method. When I got to this part of the book, right at the end, I heard dramatic music playing in my head. The problem is still there – how did Fermat reach his conclusion?

I completely forgot I wanted to comment on that too. Doesn't that just drive you a little crazy?? I want to know how Fermat solved it. Errrrr....

Saturday, August 2, 2008


Loved this book. I don't have much to say about it because there wasn't anything to really agree or disagree but I will say that I loved how hilarious some parts of it were, and I loved the parts about the women mathematicians. Amazing. Overall, it was very well-written, engaging history and even the math parts didn't bore me! Excellent writing.

The Proof is in the Pudding

I love math books! Real math books, anyway. Books about mathematicians and the math that they discover. I've read books about Descartes, Blaine Pascal, and other mathematicians. I've also read books about code-makers and -breakers from WWII. They all fascinate me. Which I find odd, really, because I don't understand math very easily.

I was hooked on this one right from the start.

There was so much information packed into this one book. I can hardly wrap my mind around it. I don't even know what to focus my essay on!

I read several sections of Fermat's Enigma to Josh, always finishing with: “if that's not a testimony of God, then I don't know what is!” I think one of the reasons I like math is that it's so orderly. My favorite “testimony” parts include the mathematics found in music, the pi ratio of rivers, the perfect number 6, and the friendly numbers. People have drawn such interesting comparisons between math and God. I thought the argument that St. Augustine made in “The City of God” about 6 being a perfect number and the earth being created in six days just fascinating.

One of the things that was new to me was the camaraderie within the mathematic community. I didn't realize that they tend to work so closely together, bouncing ideas off each other.

As much as this book is about a math problem, it's also definitely about the passion that envelops people and the tightness to which they can hold to an idea or a dream. It seems true that those who rise to the top of a field (any field) are the ones who are most passionate about it; who pursue their dream unceasingly. This book was chalk full of stories about people who followed their passion. What great examples they set for us.

Regarding mathematics: the intense concentration involved; the difficulty behind it all, astounds me. At one point, describing Wiles' lecture course on a portion of his proof, Nick Katz says, “There was no way in the world that anyone could have guessed what it was really about. It was done in such a way that unless you knew what this was for, then the calculations would just seem incredibly technical and tedious. And when you don't know what the mathematics is for, it's impossible to follow it. It's pretty hard to follow it even when you do know what it's for” (242-243). This quote, coupled with Nick Katz's explanation of the work required to check the proof (256) shows the huge amount of difficulty behind the math involved. It's just crazy to me that the best minds in the world found it difficult to check his proof!

“If Fermat did not have Wiles' proof, then what did he have?” (284). Wouldn't it be fascinating to find out if Fermat really did have the proof or not? The great thing about this theorem is that even after being “solved”, it's still an enigma because we know that if Fermat solved it, he must have used a different method. When I got to this part of the book, right at the end, I heard dramatic music playing in my head. The problem is still there – how did Fermat reach his conclusion?

I think the concept of hard work and perseverance is demonstrated repeatedly by the many mathematicians who devote whole segments of their lives to one problem. Hard work won't necessarily always be rewarded with success, but when it comes, success is all the more sweet because of the effort taken to get it. Sacrifice and discipline make good work partners. It's a lesson worth learning well.

I want to finish by quoting what I thought was probably the funniest moment in the entire book (and I liked Euler's proof of God, also): “When asked for his reaction to the proof, Shimura gently smiled and in a restrained and dignified manner simply said, 'I told you so.'”(280). I just loved that answer. Finally, to be justified after so many years! It must have felt good.

Fermat's Enigma

My copy is overdue at the library, and since I plan on making a trip there this afternoon, I figured I'd better write this. Anyway, I really enjoyed this book too! I thought it was fascinating, although it completely lost me towards the end when it started talking about modular equations.

One of the main reasons I liked it so much, is that it made me appreciate how amazingly intelligent humans can be and the potential we have. Does anyone remember in Anne of Green Gables when Anne is talking to Diana about whether she would be infinitely good, stunningly beautiful, or astoundingly intelligent? (I paraphrased that.) Well, I always--even as a kid--would have chosen the intelligent one, although I felt rather guilty because I thought I should chose the good one. Anyway, this book made me wish that again. The genius of the people involved is really humbling to me. It kind of puts me in awe of the human race again, since generally speaking I don't have a high opinion of the average joe.

I had no idea of the complexities of mathematics in the theoretical realm and how many applications that has. For instance, how all the rivers can be calculated to have a ratio of pi between the actual length and direct distance. Also, to me, the author is right that mathematics has an appeal because "Mathematical theorems rely on this logical process and once proven true are true until the end of time." vs. "...the hypothesis becomes accepted as a scientific theory. However, the scientific theory can never be proven to the same absolute level of a mathematical theorem: It is merely considered highly likely based on the evidence available." pg. 21

The development in mathematics and the logic involved is incredible to me too. I loved how the author explained parts of this, "The solution for Bombelli was to create a new number, i, called an imaginary number... This might seem like a cowardly solution to the problem, but it was no different to the way in which negative numbers were introduced." pg. 84 To me, imaginary numbers are so completely odd and hard to comprehend (yes, I'm not that great in math). It makes i seem more normal to read "It should be noted that mathematicians consider imaginary numbers to be no more abstract than a negative number or any counting number. Furthermore, physicists discovered that imaginary numbers provide the best language for describing some real-world phenomena." pg 86

I also loved, "I am a liar!" pg. 141 and "This statement does not have a proof." pg 142, it's so fun to try to wrap your mental abilities around those. Hee. Hee. Also another fun logical "proof," was Pascal's "religion was a game of infinite excitement and one worth playing, because multiplying an infinite prize by a finite probability results in infinity."pg. 21 Although not logical at all, and certainly no proof, was Euler's "Sir, a+b nth power/n=x, hence God exists; reply!" pg. 76--I was laughing out loud when I read that anecdote.

I'll end with that since I have to go get me crying baby. Chau.