Mathematical Beauty and Creativity

http://vimeo.com/77330591 - Beauty of Mathematics

http://www.firstpost.com/topic/organization/pixar-pixar-and-math-disney-pixars-brave-wonder-moss-video-EnaA9ZRPXiE-35299-1.html - Wonder moss

http://fineartamerica.com/featured/4-flow-of-life-flow-of-pi-cristian-ilies-vasile.htmll - Flow of life / flow of pi

I got thinking about this topic when a friend on Facebook liked this quote. I fully agree with this quote in all aspects and I want to draw attention to point II. Music is mathematical - pitch, frequency, rhythm and meter - really all of music can be described by mathematics.  Destin from Smarter Every Day did a great video of a beatboxer (Flula) in slow motion In it he shows how overtones produce a unique sound signature. It also goes over the different mathematical components that make up sound. I'm not saying that music can be replaced by mathematics, only described by it. We can do the same with art. In fact, in the special features of the Disney-Pixar move Brave they describe how math is used to create the amazing world shown in the film. Really, mathematics is a language that can be used to describe just about everything within our world. Not just the sciences but also the arts. I am not saying that it can be used to predict things. Nassim Nicholas Taleb would tell us that anytime we have a human element involved, predictions go out the window. But mathematics can be used to describe it in its present state.

Many think of mathematics as cold and unfeeling. Statistics and probability are guidelines not rules. The mathematical analysis of a painting will never look the same as the painting itself. Algorithms can't put their heart and soul into producing a piece of music like a composer might. To call someone "calculating" is usually considered, if not an outright insult, a derogatory remark used for villains and along the lines of "heartless." I think that this view of mathematics is one of the big reasons that many see the arts and mathematics as mutually exclusive. It is not uncommon for me to hear, "I'm one of those English people / art people / music people and so can't do math." I think my previous examples demonstrate that mathematics is not separate from the arts, but rather is something that can help us understand it even more.

So rather than continue my reasons why people don't like math, I want to demonstrate some of the beauty of mathematics. It is my hope that the following examples may be appreciated regardless of mathematical ability. Just like art or music you don't have to know how to create it in order to enjoy it.

First, fractals.

[picture citation]
Simply Googling "fractals" and looking at the images will give you lots of cool pictures, both from nature and artificial. Fractals are produced you have a design replicate itself so that ever successive generation or iteration looks like the initial one. The picture above shows how every new iteration branches the same way that the first do. If you were to zoom in (or out on a fractal you would find yourself looking at the same image, they are infinite in their presentation. One of the most famous fractals is the Dragon Curve. Numberphile did a great video on the Dragon curve and how it works.

The second example I want to look at is an artist by the name of Cristian Ilies Vasile. Numberphile introduced me to his art in one of their videos - Pi is Beautiful. Looking like a web of colored lines Cristian plotted the digits 0-9 in a circle and then starting with 3 he drew a line to 1 then to 4, back to 1 and continued along the digits of pi. He's done the same with e and the golden ratio. Like the Dr. James Grime points out, this is math for art's sake. There is no real mathematical use for these pictures, but they are quite striking. Check out the link on Cristian's name above. I would love to pick up one of his pictures myself and am hoping to in the near future.

A year of blogging

Three hundred and sixty-four (and a quarter) days ago I started this blog. I did it for personal reasons - a way to express myself and a place to share the things that I thought were cool in this world. Since then I have learned about a lot of things, found new sources of information for my interests, and even picked up a couple of followers. The blog has seen over 3600 hits (an average of about 10 a day) and this will be my seventy-fourth post.

I have enjoyed the last year and am looking forward to future blogging. I've learned that having a public blog encourages me to write. Whether it's to express the things that I find magical about this world or the experiences that I have because I have made a public statement that desirous readers can find a new post on Thursdays (or Mondays) I feel obligated to produce it. This is different from when I've kept a journal written by hand. While I do not have the privacy that a bound journal gives me, I find that the blog provides me with a similar forum to express myself.

In thinking about my bound journals with the evolution of my handwriting evident between the pages, some may feel that a blog is not the same. Randy Pausch, a professor at Carnegie Mellon University, pointed out in a lecture on time management that many also disparage over the lack of letter writing in today's society. He countered that E-mail is still communication and is recorded and searchable, something that handwritten letters are not. I feel the same way about a blog. I don't mean to say that blogging or E-mail is better than keeping a handwritten journal or posting a letter but simply that the activity of recording our lives happens in many ways. Blogs and E-mail are not the same as their handwritten counterparts and that is okay. My only hope is that both mediums fulfill the purpose that I use them for - self-reflection, insight, meditation, and a record of myself for others.

However they happen, the mental processes that go into blogging and keeping a journal (those mentioned above) are healthy for people to engage in. Our brains are complex and never turn off voluntarily. Ever moment of every day and night it is doing something. introspection, self-reflection, meditation, and other such activities are useful as we sort through the stuff that our brain has collected and begin to make sense of it all. It allows us to see how we fit in with and interact with the world. I used to think that meditation was the processes of thinking of nothing, but I don't see it that way anymore. For me, meditation is a chance to focus my thoughts and identify what is important in life. There are enough things vying for our attention that we often need to simply slow down and focus on one thing at a time.

Here's to the first year of delving into a mixed mind. I'm curious what the next one will bring.

Dumb Customers

Today has been trying. I won't go into all of the details but at the end of the day I told my sister to apologize to her husband because I acted like many who caused him to leave his previous career. He mentioned once that he never minded the work he had to do, he just hated the customers. I also seem to remember him saying that "customers were dumb." I won't disagree with him. There are many people who don't know what they want / need and when problems arise because of it they tend to blame the person trying to help them. I just didn't think I was one of them. Today I was a dumb customer. If it hadn't been for a service provider that was mindful and skilled I would have ended up spending over three times what I did in the end. They were patient with me, explained things, and made sure that I was taken care of in the best way, not the way that I thought. My experience reminded me of a page I read from Ctrl+Alt+Del, a web comic enjoying, making fun of, and exploiting ideas from all things video games. The page in question is here, and really is true in many cases. While I do enjoy reading Crtl+Alt+Del I do have to give a content warning for strong language. It is not omnipresent but can appear in excess in different strips.

As I thought back on my lapse into "Dumb Customer" mode I tried to look at what my problem was. I think that the biggest thing was my knowledge level. I knew enough to be dangerous. I figured that the problem I was facing was one that I could overcome because I knew how to do X. The problem was that I was discounting Y and Z because I didn't know how to do them. The problem couldn't possibly be something that I didn't know how to fix. I think the other thing was that I was stressed out. It had been a long day and I had already spent a lot of money that I hadn't intended to. This interfered with my reasoning - blinding me even more. I just wanted something done and wanted it done in a timely manner. Now, before you think too badly of me, I was not disruptive or belligerent, I was just being dumb. I may have been a bit tiresome, but my wife, family, and most of the people that know me will say that I tend to talk to much and think I'm funnier than I am. My sin was one of thinking that I knew what I was talking about and not thinking all the way through the situation. I am grateful the professionals did and approached me about it.

I'll have to remember this experience and that we all are "dumb customers" at some point or another. We all are the reason that service providers, retailers, and just about everybody else has training in customer service. When you think about it, customer service is helping the person in the best way possible. Because you have more experience in your field you often understand why the customer may not benefit from what they want. The situation is kind of like my five year old daughter. I don't really think I'm much smarter than her, I've just had more practice at it. Remember, as you utilize services and products that the personnel that you're dealing with have more practice than you do. If they don't, make sure you find somebody who does.

A new you for the New Year

Many people for New Years make resolutions on what they want to achieve within the next year. I didn't. Not that I don't desire improvement, but rather I know that I'm horrible at keeping them. Like many people though, my new year has already involved trips to the gym.

I have never been much interested in working out. I enjoy active recreation: sports, hiking, backpacking, rock climbing, airsoft, and other outdoor activities, but I have never been much for going to the gym for the sake of health, purposeful exercise. The closest I ever got to a regular routine was when I took an aerobic kickboxing class my freshman year of college. I remember waking up one morning after class so sore that I couldn't feel my body and when I did all I could feel was how sore it was. I enjoyed myself and did feel pretty good. I also remember receiving my first ever candid compliment. At the end of the semester I went into my own work and a former colleague said that I was "looking great." So, you'd think that I would have kept it up, but I didn't. I took a physical education class ever semester after that, but they were activity based, not exercised based.

The last four months or so I have been taking advantage of a program at work that enables me to make use of the gym while I'm here. As I don't have anybody to play racquetball with (the activity I've done elsewhere to exercise) I found myself developing my own routine. I have to confess that A big part of it has been focused around my involvement in airsoft - an activity similar to paintball where people shoot each other with 6mm plastic BBs. The first couple of times I went I would find myself out of breath and the next day would be so sore I could barely walk. Those early workouts involved a mix of walking, running, and sprinting interspersed with sit ups and push ups. I would often motivate myself with thoughts of airsoft and how I wouldn't be totally flagged after the games.

Exercise is a pretty hot topic in society. The first lady, Michele Obama, initiated the Let's Move program to encourage kids and adults to have more physical activity. The Mayo Clinic, US News and World Report, and the Center of Disease Control, with a bunch of others, have reasons why exercise is beneficial including: natural stress relief, improved mental and physical health, to combat depression and dementia, and to improve self image. I can agree with all of the reasons give on that, as I have seen it in my own life. I do have to say that there are side effects to regular physical exercise - the biggest is that when you start you might feel like you are just going to have to live with being sore for the rest of your life. I am happy to say that that may pass in time, or at least lesson. Technically, if you're exercising right you will have something that is sore, but that is only because as your body grows you need to push it further to continue to receive benefits from exercise. If you only stay with the same level of intensity you will plateau and will not improve.

There are lots of exercises you can do. Aerobic activities include getting your heart rate up and is often used to lose or maintain weight. Flexibility training, such as yoga, is exactly what it sounds like and may be combined with meditation, but not always. Strength training uses resistance in the forms of everything from springs to weights to build muscle mass and increase muscle definition. There are lots of ways to combine the different forms into a single workout and everybody has a different preference. If you don't have access to a gym, there are still many ways to exercise. The trick, I've learned, is to find out the exercises that you enjoy doing. As you get more comfortable with exercising and come to enjoy different parts, you'll find yourself trying new things. Today I started into a lifting routine, something that I didn't think I would do four months ago.

So whether is for a New Years resolution or just because, get out and get active because it really is a great way to stay healthy and enjoy life. 

The 2nd situation: Dealing with our own problems

In the 1st part of this discussion I explained how people sometimes feel frustrated when they "get the run around," and how this is often because they do not know what kind of help they need. This week I'm looking at situations that we all hate. Where we are in an unfortunate place and we were the ones that put ourselves there. As an advisor I see this a fair amount. The most common situation is when a student fails a class or an semester (or several) and is then faced with the consequences. In some cases all the student needs is a little "GPA damage control," something that is easier than many think. Other times, the student may be facing a three year suspension from classes, denial of financial aid, being unqualified to apply (or unsuccessful in applying) to their program of choice. Whatever the situation is it's not uncommon that the person who has put themselves there chooses to reject responsibility and pin it on something or someone else. A common expression used by guilt avoiding students is, "The professor failed me." My thoughts make me want to say, "Are you sure it wasn't your assignments, papers, and test scores that didn't fail you?"

To be fair, there are circumstances beyond our control. Insurmountable obstacles that cannot be overcome by sheer determination and will power. Relatives die, people get sick, jobs experiences layoffs or go out of business. This post is not to claim that any failure is a result of our own lack of desire or ability. I am not claiming that all misfortune is the fault of the person experiencing it. The purpose of my post here is to address when people to not acknowledge where the responsibility lies and instead choose to affix it to something else. Again, this tends to be off of themselves and onto somebody else.

It can often be challenging working with these students (I'll stick with academic situations as I am most familiar with them). They may rant and complain about their professor, the university, the services provided, and everything else under the sun. Any mention of what they may have done (or may not have) is met with counter accusations about what others did (or didn't) do. For example, my office handles compliance with the developmental placement and completion policy for the university. The consequences of not taking or not passing the mandated classes vary between minimal to restrictive. Students that don't pass the class do so for a number of reason most of them circumstances beyond the students' control. However, a small group of students simply refuses to take the mandated classes. Perhaps they don't agree with the policy. Perhaps they don't like required coursework. Perhaps they simply don't like to bow to authority. For whatever reason, they don't follow the policy. A small group of them will then take issue with the university for blocking their registration, as they were told would happen. I hate to confess that I have often wanted to inform these students, "We told you so!" or "Why did this happen? Oh, it's because YOU didn't follow the policy." Needless to say, these statements would never make the situation better.

So what do you say when someone is upset or frustrated? First, they may just be venting. Just remember that they are not angry at YOU, they are just being angry TO you. While never a pleasant experience, understanding that it's nothing personal can help you listen without defending or retaliating. Once they've got it out of their system, often these people are more than willing to listen to what you need them to do to solve the situation. The trick is not to take it personally.

Regardless of whether or not the person is venting, the best way to help them is pretty simple. The first step is to apologize. This does not mean that you agree with them or their frustration, just that you are sorry that they are frustrated. This is also a good time to acknowledge their emotions. It does no good to tell someone, "You shouldn't be frustrated about that." It is similar to telling someone, "That doesn't hurt" when they are injured. Apologizing helps them understand that you wish they weren't frustrated and expresses empathy.

Second, you want to make sure you listen to them. Like I mentioned last week, often people don't know exactly what kind of help they need. Make sure you listen so you can identify the concerns and separate the facts from the emotions. Remember that listening also means asking appropriate questions, but don't rush them. Let the person talk uninterrupted.

Third, you want to actually remedy the situation. You do everything you can to get them the help they need. If what they need done isn't in your department, you get them specific information and help them contact those that can. Never let a student leave your service without knowing what needs to be done, by who, and when in order to get their solution. This includes things that they need to do. Make sure that you are attentive, informative, and helpful. Using the Arbringer Institutes' ideas from Leadership and Self-Deception or The Anatomy of Peace are very useful in all steps of the process, but are of particular note while you are helping the person. It's important not just to provide assistance, but to make sure that you are doing it for the right reason. Wrong reasons include: to get them out of your office, because it's your job, because you want to earn a service award. The only right reason to help someone is because you want to make their experiences better as a human being. Anybody who has been served can tell when some is doing something for the right reason and when they are looking to get something out of it. Do everything you can for the person and be as accommodating as possible. This does not mean to let them walk over you, but simply to make sure that you have done everything that you are able to do to help them.

Lastly, you will want to thank them for bringing the situation to your attention. This is a great final step as it closes the interaction with an interest in the future. You are telling them that now that you know about this you will be better able to help them and others in the future. If you had to refer them elsewhere, you can also ask them to report back to you when and how their situation is resolved.

When I did sales training for one of my jobs (it turns out I'm a horrible salesmen) they talked about how there is a percentage of people who will never buy the product and a percentage of people who will always buy. As a salesperson, your focus is the percentage in the middle who might. The same applies to resolving problems. There is a portion of the people you deal with who will never be satisfied with your service. The trick is to not let it get to you and make sure that you give everyone the same level of service because you won't know who wouldn't be pleased until you've done everything you can.