When I first came to the UK, it seemed that the world worked differently. Ever so slightly, the laws of physics seemed altered. The weather seemed to be determined by different laws. Household appliances functioned through different properties. People's social understandings and interactions appeared out of phase. In ways that are hard to describe, I seemed to be in an ever-so-different parallel universe.
Of course, both the UK and US societies had developed different techniques and methods of doing things, ignoring many of the other potential options. We choose some paradigms and forget others. In some ways, this is so fundamentally obvious, it is banal to speak of it. But yet, when it is experienced first-hand, it still seems bizarre and surprising.
The same principle applies to our understanding of numbers and mathematics. Our schemas and paradigms of what numbers are, how they function, is very limited. I have already written about our common shortcoming in understanding repeating decimals, and this week, we have a video of how any multiplication problem can be solved with pencil and paper using only line drawings and no calculations:
The Technology, Entertainment, Design (TED) conference, is quite simply, fantastic. Every year they have a conference where they have talks and presentations about the coolest ideas coming up, all with the potential to alter how we perceive and interact with the rest of the world. Fortunately, they are all available online. I've only seen a few, but so far they have all been mind-blowing.
The presentation below is by Hans Rosling, and it's about statistics. And it's freakin' sweet! Not in a math-nerd way, but in an everyman way. It's 20 minutes long, and worth every minute.
The most important part of the presentation is the last five minutes. We simply must have a new paradigm of knowledge - of perceiving it and disseminating it. Rosling's presentation is one of the best illustrations I have seen of this. Governments and organizations collect massive amounts of data, and then make it inaccessible. I believe the big revolution of this century will be the liberation of data - the democratization of information. This includes statistics, but more importantly science, entertainment, culture - human knowledge in its entirety. Presently, the producers and masters of human knowledge serve as gatekeepers whose primary role is to create systems which limit access to knowledge. You have to pay dearly to buy books or go to a university. Access to an academic journal often costs $20 per article and are written as to be inaccessible to anyone who has not spent years learning unnecessary jargon. This is no way to promote and disseminate knowledge - it merely keeps knowledge within the elite who are already knowledgeable. Largely, this democratization will occur because of the Internet, but it is much larger than that as well. I believe the impact of liberated data will eventually be on the level of the creation of the printing press, or universal suffrage. It will take time (many decades), and there will be no dramatic news coverage, but the weight of the impact on society will be enormous.
For those of you wondering about the .999... (repeating) puzzle, here it is.
Take the number 1, and divide it into three equal pieces, represented as fractions. You get three 1/3s. Add them together and you get one again, right? Right.
Take the number 1, and divide it into three equal pieces, represented as decimals. You get three portions of 0.333... (repeating). Add them together and you get 0.999... (repeating) Uh Oh. That's not 1!
Except it is. 0.999... and 1 are the same number.
There are many more complex proofs for this concept, using calculus and other methods. I must admit, many of these explanations are beyond me, but I do get the take-home-point: numbers are bad-ass, and although we (non-mathematicians) all pretty much assume we understand numbers, we really do not.
That's why I think statistics are cool (shock-horror!) and I enjoy helping to teach classes about them. They can illustrate our reality in ways that elude our normal perceptions. When I say "statistics," I'm not talking about "86% of people think BrandyBrand products are GREAT!" No, I'm not even talking about Analysis of Variance or Regression, though those are the workhorses of most statistically-based research. I'm talking about multi-dimensional scaling (MDS), cluster analysis, path analysis, and similar ilk. Stuff that allows us to create physical, geometric representations of abstract mental constructs by analyzing their numerical relationships. I realize this may be sounding a bit fuzzy or ivory-tower, but I hope to explain more in future posts - it's stuff I'm still learning about, and think is absolutely fascinating - but I should be posting ocassional numbers-are-fun posts over the next few months. It's great fun, and not as scary as it sounds.
I really don't know where the time goes. It seems like I wake up in the morning, do some work, miss a lot of work I should have done, and then it is midnight. And I've had so much blogging I've wanted to do.
Ok, tell you what, how about I grade one report, and then make one blog post, one report, one post, and so on? I really can't grade too many reports in a row or they all blend together and I lose track of what is said in individual papers. So hopefully there will be a flurry of posts (and marking) today.
First off, there is a puzzle I've been thinking about, and I eventually found the answer, but I thought you might want to have a chance to puzzle it out for yourself. Here it is:
What is the mathematical difference between .999 (repeating to infinity) and 1.0?
Here is a hint: what is one third, represented as a decimal? What happens when you multiply this by 3?
The first person to get the correct answer gets a pony.
