"Contrary to what we usually believe, moments like these, the best moments in our lives, are not the passive, receptive, relaxing times---although such experiences could be enjoyable, if we worked hard to attain them. The best moments usually occur when a person's mind or body is stretched to its limits in a voluntary effort to accomplish something difficult and worthwhile."

Although that makes perfect sense, I never even thought about this. I usually just do whatever's in my comfort zone and that gives me a sense of being happy and content, but honestly it's just that: a sense. It's not true happiness or contentment.

"The foremost reason that happiness is so hard to achieve is that the universe was not designed with the comfort of human beings in mind."

This is a very interesting observation. It's also true. What kind of universe would be "designed with the comfort of human beings in mind"? Is that even possible? In an alternate dimension, are human beings and animals happy all day, every day, regardless of the circumstances?

QQC (50 Life Secrets and Tips)

Remember people’s namesso that they feel appreciated and for your own future benefit when you want something from that person. To do this, say their name back to them when they introduce themselves. Then repeat the name in your head a number of times until you are sure you have it. Continue to use their name in conversation as much as possible to remove any chance of forgetting it. If you’re still having trouble, make up a rhyme about their name: “Dan the Man” or “Natalie flatters me.”This one was huge to me. It really stood out because I make an effort to remember peoples' names, and to see it on a list like this kind of solidified my efforts.
I have a question about the whole article. What inspired this person to write this article? Did he just one day sit down and go, "You know, I'm going to try and change people's lives!"? I think it's noble and the fact that I've been thinking about this article for days since I read it really speaks to its impact. I wonder how many others feel like that.

Lecture Notes 3-3-11

Lecture notes 3-1-11

Senior Project Ideas

I would really love to do a project on how concepts that seem abstract (limits, extrema, linear approximations, etc.) are actually most common in nature and science than the easily grasped (addition, subtraction, multiplication, other basic functions). People tend to assume that calculus is some huge ethereal concept that can't possibly be connected to anything in the real world. In this project, I would apply this concept to common things like how a toilet flushes, what happens when a light fades on, or even what your couch is doing when it has a person sitting on it. These things all involve calculus, but anyone who wasn't looking probably wouldn't notice it. I want to expose the hidden numbers in these seemingly commonplace and everyday things.

QQC Chapter 1

"There are so many superstitions behind the number one, and some even have a little sense behind them." How do people assign superstition to numbers? That seems like a useless endeavor.

"'Perfect numbers, like perfect men, are very rare'". Even though this quote comes from another person, I feel like it's very true. Numbers are often fragmented and tough to understand because of their properties.

"While perfect numbers were considered to be like mystical columns that held up the universe, amicable numbers were treated like perfect partners, indicating two things meant to be together". Why are people so fascinated with viewing numbers in this way? I don't think I'll ever understand, but maybe because I come from a world where we take numbers for granted and don't celebrate them as much.

QQC Chapter 0.000000001

"While we got used to the idea that numbers might not always define a whole thing--a number might be a fraction of a whole--the idea of a decimal point took longer to enlarge. This was despite the widespread use of the abacus, which nearly expressed fractions in the way we know today."
Just putting a period in between wholes and decimals took that long to come up with? It's amazing to think that people who invented such complex things such as mathematics and numbers overlooked things we think of today as simple and commonplace.

"So fractional numbers have transformed our ability to think small and understand the dimensions of things like atoms." Fractions may seem like littlwe jerks, but it looks like without them we'd be stuck in the stone age. I wonder why they're so difficult to work with. Maybe they're just too abstract to0 grasp easily.

QQC Chapter 0

"So without actually counting or even understanding the notion of numbers, it was possible for very precise trades and transactions to take place." It's pretty cool that people were able to use numbers without even really understanding them. Wish I could do that now...

"Nothing was invented around 1,800 years ago in India. lt was a very important nothing." Nothing being important kind of strikes me as funny for some reason. Why did it take so long for humans to grasp the concept? It doesn't seem so difficult, but that's probably because we have so much experience with it, and our thinking is definitely higher level.

Gauss QQC

"...Gauss corrected an error in his father's payroll accounts at the age of 3"

Wow. Genius from a very early age. How could a child so long catch an error in something so mundane? I don't know many 3 year olds that would be going through their father's payroll accounts, let alone correcting them.

"At the age of 18, he made a wonderful geometric discovery that caused him to decide in favor of mathematics and gave him great pleasure until the end of his life."

This is funny because he was interested in something that required a lot of math courses, yet decided against it. Math must have really fascinated Gauss after this discovery for him to make a turnaround so quickly. Why wouldn't he just dive into the math courses he needed in university so he could pursue his desired major? Would mathematics today be even half as far as we are now without Gauss in the field? What would the field of philology be like today if Gauss had stayed in it?

Leibniz QQC

"Leibniz is probably better known to most people as a philosopher than a mathematician."

"No other thinker except Aristotle has rivaled him in the range and variety of his abilities and achievements."

"What manner of man was he, and how did he live, and what did he think?"

"As with most men of really great intellect, Leibniz's formal education was only a minor eddy in the torrent of thought and study and learning that was the essence of his life."

How is it possible to absorb "all the knowledge of his time"? Was there really not that much knowledge going around back in the 17th century?

Was this not the time of being accused of heresy over even the slightest tampering with religion? How did the church approve of his ideas on Christianity and Protestant views?

The fact that an 8-year-old learned Latin and German on his own makes me feel inadequate as a person. Actually, the fact that Leibniz just kept learning from birth to death makes me feel inadequate as a person.

I guess it makes sense that in that day and age a man who knew little of math would be disregarded as a thinker simply because math was such a huge thing back then. Knowing a lot about everything but math would probably only amount to 65% of the total knowledge on the planet at that time.

Leibniz really was a man of many, many, many talents. Not only that, he was good at pretty much everything he did.

I think it's funny that there's a huge "Leibniz vs. Netwon" rivalry. It's like the "band vs. band" or "overly large UFC fighter vs. overly large UFC fighter" rivalries of today. Strange how interests have changed so drastically from the 17th century.