Have you ever wondered how a mirror works? It flips things around from left to right, but why not from top to bottom? And if you lay on your side it flips your image from top to bottom, but not left to right. What's going on?
Kids love to play with mirror reversed letter and numbers almost as soon as they learn how to read, but most of us don't go much further. There are three levels of understanding what's going on. For the mirror imaging the first level is enough. I'm going to ask you to make your own simple demonstration to get to that aha moment.
You'll need an arrow. Something like this:
Cut one out of stiff paper or cardboard. I won't tell anyone if you want to be artistic.
You'll also need a very flexible reusable glove, the kind that you have to peel rather than slip off. Thin rubber, latex or something else. Again artsy is fine by me.
You'll also need a mirror to stand in front of. I'll wait...
OK.. hold the arrow to your right. Point it up towards the ceiling, down towards the floor, left and right taking note of what happens. Now try it with your other hand. The mirror is doing what experience tells you it would, but you have a nice label on the direction of the arrow.
Point it at the mirror and move it towards the mirror to where it touches. Then pull it back. Interesting, eh?
Glove up and point a finger towards the mirror. Pull off the glove and carefully watch what happens.
The mirror is flipping the image along the axis going into it. It pulls your image through itself.
That's it. The axis of symmetry for a mirror - its special direction - is your line of sight.
Going deeper and understanding how a mirror reflects light takes an understanding of electromagnetism .. Maxwell's equations. Deeper still, what's going on between light and matter, requires quantum electrodynamics. But they're overkill to understand why mirror images work like they do.
William Rowan Hamilton had become obsessed with the idea of a three dimensional number system - sort of analogous to complex numbers being a two dimensional system. The story he later told was every morning his son would say 'papa, can you multiply triples?' to which Hamilton would sadly shake his head and say 'no, I can only add and take away'. Then, on a walk on the 16th of October, 1843, he crossed the Broom Bridge in Dublin and suddenly knew how to do it. Rather than adding a single dimension to the complex plane, he'd add two giving three imaginary dimensions and one real dimension perpendicular to them. In his excitement he carved it into the bridge with his knife: i2 = j2 = k2 = ijk = -1
He called them quaternions. They had some use in the day, but when people invented linear algebra, the technique fell by the wayside ... that is until quantum mechanics came along about eighty years later. And then computer graphics further down the road.
It turns out they're a lovely way to think about quantum mechanics and perform real calculations. Erwin Schrödinger knew enough about forgotten math to realize it was a beautiful gem. Decades later, trying to improve the speed of computer graphics, a physicist realized they could be a key to quickly calculating rotations in space -- and Tomb Raider became the first computer game with smooth graphics on using relatively primitive personal computers.
Hamilton had other accomplishments that deeply impacted physics and math, but the quaternion story has a certain romantic element. To this day physicists gather at the Broom Bridge on the 16th of October to celebrate.
The story of physics is that it's extremely important to think broadly and to keep expanding your learning. It is also is relevant to education and work across many fields today. That's what I want to get to, but first this wonderful parody of a certain song.. perhaps the best math song ever.
What prompted all of this was an email with a link describing the most contrarian college in America. It's laser focused on a vision of an education seemingly without much a nod to vocation ... seemingly.. I'd argue that it's too focused on a narrow piece of education, but have no doubt its graduates have learned how to learn.. they have the beginnings of a real education. Mark Roosevelt, its President, sums it up:
Education should prepare you for all of your life. It should make you a more thoughtful, reflective, self-possessed and authentic citizen, lover, partner, parent and member of the global economy.
It takes a special kind of student to thrive in a school like that. I wouldn't have survived - my interests, those that I was motivated to dive into, lay elsewhere. I'm happy it exists and that there is spectrum of schools for those who look.
My belief is a deep education with at least a few focuses creates the second type of person Claude Shannon describes:
“There are some people if you shoot one idea into the brain, you will get a half an idea out. There are other people who are beyond this point at which they produce two ideas for each idea sent in.”
The ability to get multiple ideas is core to serious play and creativity. I'd claim focusing on education rather than finding the minimally easy path helps create the neural connections that make this possible.
A worry is that many, if not most, schools and students tend more towards vocation. Focus on what is important to get a degree that will get you employed to pay off that mountain of debt. Many (not all) businesses, on the other hand, would do well to have broader employees who are still learning and growing - those who can think creatively. There is a disconnect.
I hope this focus on vocation changes. The rate of real change is great and people will keep up better if they are broader and more adaptable. When recommending colleges I tend to focus on education .. often to the consternation of those asking. Of course I may be a poor example. My education was far too narrow, but I've been lucky and curious enough to have been able to expand it a bit. The other note is you can get a wickedly broad experience at many more places than you might imagine.
Finally there's this odd emphasis on over-scheduling many pre-college kids, but I've probably written on how it kills creativity enough.
At a birthday party the other day conversation turned to privacy. When someone complained about the erosion of our right to privacy I saw an opening to ask a question:
"When was the golden age of privacy in America?"
Among a dozen people there was nearly universal agreement around the time of the Bill of Rights. After all those founding fathers .. I just listened. It turns out they were wrong.
The idea of privacy was almost foreign in Revolutionary America. While the founders were arguing various rights for landed white males, the only nods to privacy were associated with the ownership of property - notably intellectual property. People were encouraged by the Revolutionary government and later the Federal government to spy on each other to ferret out who might be breaking a boycott or somehow not supporting the cause. Punishment came through social pressure like public shamming and sometimes worse.
You might think living in relative physical isolation as a farmer without telephones, cameras and Internet would give you serious privacy. The rub was you had to deal with others in your community. You had to buy and sell goods and services, most people went to church and so on. Chances were you'd never travel far from where you were born so you were surrounded by people who knew quite a bit about you. You were defined by your reputation and position. It probably seemed very normal to most people.
Change first emerged not on farms, but in the cities among the wealthy. With property came the idea of ownership and protection. This extended inside the house where there might be servants By the mid 1700s doors began to appear inside homes along with this radical new privy. Dealing with one's personal matters became a private affair. Jump ahead to the 1820s and even homes of the emerging middle class had private rooms and privies.
The South followed suit, but it took time and was more isolated. Travelers noted, with some shock, that as late as 1850 many houses were doorless inside and multiple families sleeping in the same room. Like New England change first came to the wealthy, but slaves and indentured whites were not allowed these luxuries. The right to this kind of privacy was reserved for certain social classes and skin colors.
I've written about the role of technology and will write more in the future, but privacy stakes me as something of a paradox. Many of us point to the erosion we think is caused by technology, but at the same time there have been great strides in other forms of privacy - keeping the government out of the bedroom and reproductive rights in general come to mind.
I've had conversations with legal scholars and historians. All told me they can't think of a simple robust definition even though all of us think we now what it is. At a high level I think it is at the boundary of the relationships among yourself, the state, religion, your work, your family and community and technology. We're each members of several larger wholes as well as being an individual. Change any of these in some major way and there is a need to be societal renegotions . Technology has been something of a cauldron of change over the past hundred and twenty years or so. .
We've always had problems with the judgement of others ..particularly when it's capricious, mindless or evil. With work some of these practices can be discovered although rectifying them can be difficult. Now we have massive data collection schemes often using data and data processing of questionable and untraceable provenance sitting in judgement. People point to China and its citizen scores, but Google, Facebook, Amazon and others are doing similar things here. As Cambridge Analytica taught us sometimes all a potential user of this information needs is a relatively simple toolkit.
Laws will always trail - except perhaps in authoritarian countries. Europe is taking some small steps with GDPR at this point. China and other countries (and companies!) are moving in the opposite direction. And many in the Western world believe privacy (whatever that means) is a human right. We are seeing regionalization and balkanization of the Internet and that may be just the beginning. And remember those algorithmic reputation and judgement engines.. So many difficult questions are raised.