Visualizing a Trillion dollars

Hey guys, so I came across this on the internet. It relates to Tuesdays class where we were talking about how people have a hard time visualizing what large numbers look like, and how people don't seem to know how proportions work. So I found this site, and it basically shows what a trillion dollars looks like. It is crazy when you put that in proportion to just how much debt we are in and what that amount of money would look like if we put it in physical form. So here is the URL for the site:
http://www.pagetutor.com/trillion/index.html

Samsung vs Apple

I don't know how applicable this is, but I know we were talking about the whole patent thing in class and right afterward I just happen to come across Samsung's response to Apple and found it interesting, so I shared.

"Necessity's Mother" Discussion

I found the Chapter, “Necessity’s Mother,” to be very insightful and thought provoking.  The author provides explanation and evidence to account for the observation that some regions of the world have a greater degree of technological development than others.  He lists multiple economic, ideological, and geographic factors which he believes contribute to these differences.  I think his reasoning is sound, and the geographic factors seem to be especially important in explaining the apparent systematic differences.  He lists such factors as war, resource abundance, and centralized government (pp.250), which influence technological development.  Resource abundance, of course, is important because it determines the raw materials industries have available, as well as the types of innovation which would benefit a given society.  Government is important because it creates the environment which determines incentives inventors have to invent.  The free market in the United States, for instance, is largely unregulated by the government.  This lack of regulation allows for competition; for companies which develop technology, this means competition for innovation with the hope of increased market share and monetary gain.

In addition, the author emphasizes that the degree of innovation in a particular region is not so much dependent on one or even several “great minds,” but rather on society’s receptiveness to and ability to use the technology.   This seems reasonable since clearly not all “great” minds are concentrated in one or several regions of the world.  Once an invention or type of technology “catches” in a particular region or country, it can be “self-catalyzing.”  Such was the case with the technology boom in the U.S. in late twentieth century as computers became more affordable and more widely used.  Technology in the computer industry (and related industries) took leaps during this time not because human intelligence increased at a similar rate (because it’s a safe assumption that it didn’t), but because a market had been created that held technology which found application in a multitude of fields.  This new industry not only created a necessity, but made society extremely receptive to and hungry for more technology.  I don’t think the author intends to discredit individual “genius” or contributions, but rather point out that although these are necessary for innovation, they are not alone sufficient.

I think it’s also important to briefly touch on the interplay between technology and mathematics, as well as the way in which each seems to continually push the other forward.  On the most fundamental level, binary code runs computers. Then, programs and systems run by computers can lead to advances in mathematics, specifically in performing calculations and computations which would have previously been too time consuming to provide for any practical application.

Discussion of Jared Diamond, "Necessity's Mother"

The central focus of this article was the differential cross-cultural development of technology.  It is interesting that today the gap between technological advancements of different cultures is as wide as it is.  Now pretty much everywhere we look, there are people talking on their smart phones.  The fact is that six months from now, the smart phones we have now will be outdated and seem undesirable.  In other parts of the world, however, there are still several cultures and communities who lack the most basic developments such as running water and electricity.  Six months from now, there will likely be little change if any within these cultural communities.  Why is it that technological development takes off exponentially in some cultures, yet remains relatively stagnant in others?  The article touched on several possible rationales for this trend.  Several factors influence innovative advancement of cultures.  The differential relative economic advantage, combined with differential social value and economic prestige between cultures can definitely have an effect on a culture’s willingness to adopt new innovations. 

That being said, this article really got me to start thinking about what remarkable progressions our society has made in the last century or so.  The Wright Brothers did not make their first flight until 1903.  The first affordable automobile did not hit the market until 1908.  Yet by 1969, we had a man walking on the moon.  The key to this continual progression is the fact that one tool can be developed and then used to further develop more advanced tools and technologies. As the tools we have available become more and more complex, the potential things that we can develop using these tools will inevitably become more and more complex themselves. The article touched on this idea.  James Watt, for example, did not wake up one morning and invent the steam engine.  He actually used Thomas Newcomen’s steam engine as a model, and further developed and expanded on the ideas Newcomen already had in place.  It is interesting to consider what will come of our future should these technological advancements continue at the exponential rate they have been progressing over the last several years.   With each technological advancement we increase our human ability to understand and experience the world around us.  Technology continues to push the limits of what we can do as humans.  Will we ever get to a point where further technological advancements will not be humanly possible?  Or will these technological advancements continue to progress, giving humanity power over the unimaginable?  Five hundred years from now, will people be laughing at the technologies we find to be innovative today?

 

Amusing illustration of our discussion Tuesday.

Post limitations-READ THIS, PEOPLE!

For those commenting on posts, please keep your comment length reasonable. I'm not going to pick an arbitrary word number, but if you have that much to say, save some of it for in-class discussion.

The Lesson of Dragon's Egg and Innate Arithmetic

       I think we can all agree that reading Dragon's Egg was a bit strange. I still can't completely picture what a cheela looks like or figure out why they call north and south the "hard directions". However, it was an interesting story, and its lesson is hard to miss: math helps us survive. As human beings, we must utililze multiple aspects of mathematical thinkings to help us overcome daily situations. While the story does a great job of illustrating just how great math can be, it fails in regards to another facet of this course: ethics. Now, I understand that the math told the leader of the tribe that they didn't have enough food for the entire tribe to make it, so she made the logical choice of leaving the elderly behind. Ethically, however, was that the right decision? When the elder made the long journey to deliver food for the infants of the tribe, did the tribal leader have to just take the food and send the starving hero back to die? I guess what I'm saying is that this story really told me two things: one, that mathematical thinking is and must be used to ensure the survival of our species, and two, that mathematical thinking devoid of anything else is a sure-fire way to make some horrible decisions.
      If, as the second reading seems to suggest, mathemetical thinking is indeed an innate process, one that we are virtually born with, then it must be tempered with the other abilities of the human species. It is all well and good that humans can subitize - but so can chimps, pidgeons, and rats. Advanced mathematical thinking should not be the only thing separating us from our animal brethren. I agree that it is amazing that the brain - not just the human one - is capable of such abilties from birth. It suggests that mathematical thinking is a key component of how beings make sense of the world around them - a tool given to the creatures of creation to help them understand existence and stabilize their lives. But, since it is not a unique abilty of the human race, we must ensure that we allow all the various virtues and vices of our species to influence the way we make choices and take actions; if we do not, we'll be acting about as human as a rat.

Posting deadlines

Hi all! A couple of students have asked about this, so I'll clarify about the blog posts. The 7 PM deadline is for the two original posters only. They must have their posts up by 7 PM the night before class in order that others can respond that evening and before class on the day. ---ETD

Dragon's Egg and The Brain's Innate Arthimatic

     When I first started to read Dragon's egg, I was a little confused on what was going on, and why we were suppose to be reading it. Then by the end I realized that it was a commentary on how math may have been first discovered. To me, it seemed like the story how in order for we, as a species, to survive we must have an understanding of math. If we didn't learn how to represent our world in some abstract way, just like the cheela, we would eventually have walked towards our own doom and destruction. This story iterates for us how important math is for the continual survival and adaptation for a species.
     In the second reading, it was interesting to see that even when we are first born, we start out with a basic  understanding of math. To me it seemed like that author was saying that,  yes we are born with an ability to do some very rudimentary math, along with our primate cousins. However, the big distinction is that we have been able to take it to the  next level, to a level that other animals can't seem to get to. That is a level where we can do complex math, we can represent objects in the world using symbols. In essence, math is a human language/invention. I think that this article just furthers the argument that humans invented field of mathematics to help us understand the world around us, and that we created it out of necessity for our survival as a species, just like The Dragon's Egg. 
 

Welcome

Well, I did these in the wrong order, but welcome to the blog! Have at it!

Sample of a post and responses

This was from a reading on game theory. The 100 word min is just to force you to say something that contains a thought or two (since this is obviously a bit longer). The comments are solid and one has a relevant Youtube video link. It's representative of what people tended to do the last time we taught this course.

Title: Game Theory

Being completely unfamiliar with game theory, I found these readings very intriguing. Looking at the multiple examples of games given for the Cuban missile crisis, it seems that a recognition of the delicacy of this process is needed before going as far as making decisions based on the results. An example of this is seen as Theodore Sorensen claimed to have used a process similar to the theory of moves to predict the Soviet's responses to American strategies, and so on. As John referred to already, there are more moves the Soviets might have besides either withdraw or maintain, so lack of information is certainly a problem, without even getting into lack of correct information. Next, the way that the game is set up is also a very important factor. In the Chicken game, where honor is not included, America has the greatest payoff if they bomb in an air strike the Soviets, who are withdrawing. Certainly more thought and complexity put into the game should eliminate this situation where an obviously wrong move is preferred, but with limited knowledge of game theory this is a question that arises for me. Setting these questions aside and assuming a little bit more trust for the methods of game theory for my point here, I thought a very good example of a positive possible product of game theory analysis was in the the paper at the bottom of the What is game theory? article. In it they attempt to show that being altruistic at times inversely effects public goods provision. Namely, that punishment sought after by those individuals "motivated by reciprocal preferences" against those not contributing in society is sometimes a more positive function than altruism in motivating individuals to participate in the society. They show in the derived equations, and it seems to make sense, that the level of a certain individual's contribution declines with increasing altruism. Interesting to think about! So even though the initial readings didn't get into the specifics, and I still had a few doubts, it was still an interesting introduction into game theory and its branches. Even in the bare-boned examples it is evident that certain reactions have a higher tendency to occur than others, and can predict on some level things like prisoner behavior, or behavior of a community on the whole, which can be useful. Posted by ********** at 10:56 AM


2 comments:

Comment March 24, 2010 12:21 AM Good post! I think the point that you made about altruism versus doing things out of duty/fear is interesting. As you discuss, we need to ask whether or not instilling fear within someone is the most effective way to get them to act. I believe this can be a very complicated answer. Since many of us have at least some knowledge about traditional religious beliefs, let me use Catholicism as an example to expand on this point. As someone who is Catholic, I have noticed that the fear tactic is sometimes used to get people to do stuff, for instance go to mass or something like this.. While this fear may be "effective" because it can get people to attend, is it REALLY effective? It is from my experience that if you feel that you HAVE to go do something (out of fear/duty), you will get less out of it.. So while some people do things (b/c they feel they have to), and this may seem effective, is it REALLY effective? I suppose it depends on your definition of "effective".. It seems that the fear/duty tactic also stints personal growth.. If you do things because you feel that you need to, what happens one day if that obligation suddenly disappears.. You see that, in the long run, it was only obligation that kept you doing something.. In my opinion, it is by doing things without reward that benefits us in the long run.. In other words, we grow so much more and excel as individuals if we do things out of desire, not obligation. ReplyDelete

Comment March 24, 2010 6:49 AM That's really good. I can definitely see what Andrew is saying where he talks about not enough information being involved in game theory. It seems that sometimes there are a multitude of options and possible outcomes and true probabilities of each outcome are unknown. This is one simple example that is interesting: http://www.youtube.com/watch?v=p3Uos2fzIJ0 I'd like to think that people are generally not greedy at heart and willing to sacrifice their image/reputation for money, but that doesn't appear to be true in the above clip.