Quote: To square, subtract 1 to obtain 40 and add 1 to obtain 42. Next multiply 40 x 42. Don't panic! This is simply a 2-by-1 multiplication problem (specifically, 4 x 42) in disguise. Since 4 x 42 = 168, 40 x 42 = 1680. Almost done! All you have to add is the square of 1 (the number by which you went up and down from 41), giving you 1680 + 1 = 1681.
Question: Seriously, how are you supposed to just do this in your head?
Comments: Alright, I wasn't sure when this was due because you didn't have a due date. It took me a while to read. I found this quote most interesting because I know a lot of equations involve squaring numbers. I mean, in my head, I just knew there was a way. It was multiplication, there is usually some pattern in that. Even so, I highly doubt I could remember this process well enough. It's a little complicated and I would actually rather use a calculator. That is all.

Quote: "The solution is to gradually become free of societal rewards and learn how to substitute for the rewards that are under one's own powers."
Questions: Why are people always so drawn to society? Why do people need reassurance? What decisions do people make that must weigh so heavily on others?
Comments: This one is sort of self explanatory. I find this quote to be something I personally practice. As I am a person who need compliments and reassurance now and again, I am the type to find my own rewards in things. I think this is what makes me motivate myself and be personally proud of my achievements. I feel like this is why I feel like I've never accomplished enough, which would be a good or a bad thing. A bad thing because it does feel frustrating sometimes and it's almost as if you don't care about the input of others, which I still think is important. A good thing is because it could be such a useful motivator depending on how you take it. I take personal rewards as something you can spoil yourself with but still keep yourself in check. When the good things are something you can control (the rewards) I find running life to be easier. Some may see that as wreckless, perhaps view it as no self control, but I find it keeping in control of my life and my environment.

"If you believe intelligence is a fixed quantity, then every educational and professional encounter becomes a easier of how much you have."

"With a learning goal, students don't have to fell that they're already good at something in order to hang in and keep trying. After all, their goal is to learn, not to prove they're smart."

"The experiment suggests that flow, the deep sense of engagement that Motivation 3.0 calls for, isn't a nicety. It's a necessity. We need it to survive. It is the oxygen of the soul."


I didn't really have questions but I do have a long response to this, because I found these lines particularly interesting. Alright, I'll be honest, I was just going to skim through this but I remember Rachel saying to read all you can before college so… I read it. These lines popped out to me the most because I have always been asking myself how to define "smart".

All my life, people called me smart for reasons I didn't really understand. I felt like I knew the knowledge, but knowing was all that was required of me, it wasn't so much of an improvement for me. As my life went on, I developed wonder throughout everything I did. When it came to drawing, I often said, "I wonder how this'll look," or "I want to learn how to use this technique".

Something I know that I do just to, as they say, "barely pass" is read books, by far. I honestly hate reading. I don't know why, but the tediousness and the lack of visuals don't help me very much. Either way, with books that don't catch my interest right away are sort of.. put to the side to me. I know what I need to and that's all. It's like, I remember the scenes that will be on the test and I know what it means, but it's not something that I would actively apply anywhere else.

I think that's why I struggled with history so much. It was because I didn't really see the choices or the cause and effect that happened. There were tons of things that happened, but my goal was just to learn the facts. Even that didn't work, just because I was too unmotivated to memorize the facts.

Last thing I want to add is that oxygen to the soul.. was very comical to me. Not in the, "Oh that's ridiculous way" but in the, "Wow, that is actually a really good way to compare and measure it". It made me think that suppose I am unmotivated. The symptoms are just that! I feel lethargic, agitated, can't sleep, etc. When I am motivated to do things, it does feel really good to have that drive to accomplish things. When I don't have it, which could last from hours to months, it feels terrible. I feel lazy, pretty much.

Quote: "Read “Bringers of Light” and “Conversations with God” by Neale Donald Walsch. Read “Zen and the Art of Happiness” by Chris Prentiss. "
Questions: None
Comments: Okay, I only have comments about this to be honest and I warn you, this is going to be long. I have nothing against reading these books, as people may believe since I am not religious or spiritual, but the only thing I didn't like was when it said this after, "This book will give you the knowledge and instruction to be happy at all times regardless of the circumstances. These books will help you decide what you want to do in this life and how to get to that point." Personally, I feel like they are saying that all of these things are easy to accomplish. In my opinion, they're not. But that's life. The upside to this is that all of your life is about how you look at things. I agree with the whole, "will give you a new way of looking at your existence" but they speak of it like a process that is 100% going to success, almost like a media pitch? I may be all over the place with my opinions on this one, but it seems a bit one sided as if they're giving you options but those are the only options you can choose from, meaning you aren't really deciding for yourself about different questions in your life.

Also, going on the whole "The Rubber Band Method", this idea is in my opinion, not the best solution. Negative thoughts come to you with whatever age group you are in. Without negative thoughts, you couldn't really tell the difference of the things you like and you dislike. I feel the only reason negative thoughts give forth a bad name is because some people dwell on them and use them to define their whole nature. For example, I have many negative thoughts about many things, but it doesn't limit my ability to do things. Just because I don't like someone's skirt doesn't mean I can't work with them. I feel that thinking positively all the time is almost like avoiding the negative things in life instead of confronting them. Another example. If I think negatively about someone's personality, I'm not going to snap myself with a rubber band to get rid of it. It may severely downgrade my performance level as well as theirs if they do not understand that they may be doing something negative. But here's the catch, they may think what their doing is positive. I do believe in a positive atmosphere, but what i find most interesting about people is their negative thoughts. Personally, I stay happy because I genuinely feel happy. If I am feeling negative thoughts that make me unhappy, I will voice them because: 1. It may be unintentional and 2. I will at least get some sort of outcome versus trying to avoid the thought. Again, huge paragraph here and I am all over the place. As I'm voicing these thoughts, I am also thinking about them. Crazy right? But hey, it leaves room for counter opinion.

Senior Project Proposal

I honestly have no idea what I want to do for senior project. I've been thinking and thinking and thinking and not a lot has come to mind. I came up with a lot of little ideas like using the images formulas and derivatives make and create an image. For example, learn about the rate the ripple of a dropplet expands and using that as the ripple of a drawing of a pond or something. Of course, the picture being all mathematically planned. I think that would be cool. I really don't know what I want to do, but I know I want it to have something to do with art or being able to draw. Maybe animation, I like that too. I would like to learn about the real world uses when learning about rates. Not so much in the stock market, but more like the natural beauties of the world. Perhaps the melting of ice burgs in the north pole? Something that has something to do with me. Something like how we applied fractals to how the world flourishes, I thought that was cool.

Quote: "By defining all the truths he could think of, he was able to build many proofs about numbers and shapes that we have used ever since. Once of his most wide-reaching proofs was about prime numbers. "
Questions: Could we use this method to accomplish other things? Does topics in other subject also associate themselves with this?
Comments: Okay, I'll admit, I didn't read a lot of it. It was a little lethargic sounding, but I did find a quote I thought could sort of compare to my life now. When he talked about defining all the truths, it reminded me of how I do math. It's like.. the first truth is that you sold the problem. You have defined that work. The second truth is checking your work. By checking your work, you are defining another truth. After defining all those truths, you basically have a completed building block of math. I thought that was just interesting to compare something like that to a small scale use of arithmetic.

Quote: "The speed at which a trained abacus user can calculate sums is remarkable, and proficient users are even able to visualize the movement of the beads in their heads in order to achieve astonishing feats of mental arithmetic."

Questions: Do people now day have this skill? Is mathematics a skill you can practice even when you're bad at it? What is the extent of mental math you can accomplish?

Comments: I thought the invention of this tool was interesting in general, this quote for the description was what I saw in particular. In some ways, I would like to learn to do mental math like this. I'm a very visual person, which is why I always have to draw pictures and multiply out numbers for myself. My mental math works to a good degree, but is it possible that I can improve it using this abacus tool enough? I think it's interesting that you can just visualize these numbers. Personally, I think I would confuse myself too much. Either way, it brings to light a new way of thinking, a new way of doing mathematics. How we're learning mathematics stems from that, but for kids now a day, calculators are the best thing ever. I feel like we are slipping on our mental math. It makes me wonder, if we incorporated this tool in our learning, would we subliminally learn mental math too?

Quote: "Numbers are words (and symbols) that we use to describe patterns."
Questions: Are there different contexts of numbers?
Comments: I thought this was a fun quote overall. People scour the globe looking for new ways of communication. As humans, we've created tons of new types of communications. Now we are looking to animals and learning their type of communication. I related the quote to this because I know scientists are actually using numbers (Statistics, data, readings) to decipher the communication of other living things. In a way, math communicates other communication. Weird huh?

Quote: "Because zero is a relatively new invention for humans, we normally use zero purely as a cardinal number, so we define quantities with it but don't count with it."
Questions: Why zero specifically? How did people not know when they didn't have anything?
Comments: Zero sounds like one of those things that people overlook because it's just.. there. I personally find it a little befuddling that zero was such a difficult number to work with. I mean, I understand it a little better now that we are studying calculus, but I find it funny how all the simple things are usually the hardest to understand, if that makes any sense.

Quote: "When these conceptions are generalized to more than two dimensions, they open the door to Riemannian geometry, tensor sensor analysis, and the idea of Einstein."
Questions: Was having a set number of dimensions a huge thing?
Comments: Let's be honest. This reading was insufferable, they keep getting worse. I usually find a few lines that I particularly like, but not in this one. The one I chose was one that just led to a bigger idea, completely unrelated to the article, but I chose it anyway. The thing I noticed about this line is that life has those sort of domino effects. I'm sort of relating this to Rachel's class instead, but when we read that short story "Harrison Bergeron", I thought about this quote. In that story, everything was equal, no one was smarter or faster than anyone else. But... this quote doesn't show the competition of work (Though there may have been intense competition), it shows the process of being inspired and working off the idea of another person which isn't equal, but it's progressive. I don't know, I was terribly bored by the reading and when that happens, my mind wanders off into space.

Quote: "The distinction between pure and applied mathematics did not exist in Euler's day, and for him the entire physical universe was a convenient object whose diverse phenomena offered scope for his methods of analysis."
Questions: Why isn't it? The outcome of his thinking was still applied right?
Comments: I'll be honest, this reading was a little boring. There were a lot of shapes and pattern figure-outing but it didn't really dig deep into any cool philosophy like how one infinity is bigger than another. This line, however, I found rather interesting. This sort of sums up what I think of the world. We have to admit there are millions of mysteries of phenomena that we have yet to discover. However, when we grasp it by some means of observation, of course the opportunity is going to be seized. The wording itself stood out to me just because I feel like that would be along the lines of something I'd say.

Quote: Leibniz was torn between the contradictory claims of science and philosophy as ways of knowing reality, but he leaned in the direction of science.
Questions: How do people know which one to believe? How did philosophy come to be so different from science?
Comments: I found this interesting because I know there are facts, science, and stuff like that. But there is also opinions. Everyone has their own truth, does that mean philosophy is truth too? I find this interesting just because they are so similar yet they both contain totally different aspects.