Mr Wolff was one of those special teachers you listened to. Upon learning many of us had been assigned Fahrenheit 451 in our utopia and dystopias class, he saw an opening and got us to go to the source for later discussion. We made the pilgrimage to Val's bookstore for a copy of The Republic and read the Allegory of the Cave. I can't say much Plato stuck with me - but the Allegory led to an epiphany.
You probably know the story. If you're a bit rusty, try the video. It's just the surface, but no need to worry about that - how the prisoners see the world in 2d shadows is the point for now.
The image haunted me at first. Rather than worry about what Plato was trying to teach all I could think about was a simple case - a ruler held up to the light. All the prisoner would see is the shadow Rotate the ruler and the prisoner would see it's length change. The concept of length would mean nothing - it was far too variable.
But what if one of the prisoners was exceptionally curious and a bit mathematical? What if he imaged another dimension perpendicular to the only two he knew and worked out a three dimensional trigonometry. The ruler could rotate in this new three dimensional space producing a two dimensional projection that changed in length. It would have been a fundamental discovery for them - that the real world had three dimensions, but the they could only experience it as projections of two.
Science is about moving out of the cave.
In the early 1800s a bookbinder's apprentice named Michael Faraday started down a path that fundamentally changed the world. While Faraday had no formal education, he was insanely curious and inventive. He sat in on the lectures of Humphrey Davy and presented the great man with a beautifully bound set of the notes he took. Davy knew a good thing when he saw it and took on the young man. It was a good choice. He grew in his post and turned into the best experimentalist of the century - arguably one of the two or three best of all time.
Physicists of the day had been working with magnets and electricity. Bits and pieces were being learned but the underlying picture was elusive despite some tantalizing hints. You probably did it in grade school - run an electric current through a wire you get a magnet. There seemed to be a connection between these two forces and dozens were on the case. In one of the most important accidents in the history of science Faraday had two coils of wire near each other when he connected a battery to one and happened to notice a momentary current in the other. Disconnecting the battery produced another current. The light bulb came on before the invention of light bulbs (what was the representation for an idea back then?) In other words a changing magnetic field produces an electric field.
Unschooled in math, Faraday created visual model. He imaged lines of force connecting or repelling changes. These lines bunched up where the field was high and thinned out where it was weak. Like charges attracted (a) and unlike charges repelled (b). Lines didn't cross. While it seems simple the intuition displayed is astonishing. It turned out to be right - not only mathematically, but it hinted at a much deeper view into how Nature works .. one outside the cave.1
There's an apocryphal story that Gladstone visited Faraday's lab and asked why his work should be funded - of what use is it? Faraday was said to have replied "Why, sir, there is every probability that you will soon be able to tax it" What Faraday had discovered led to the invention of electric generators and motors. Almost as soon as that happened people started working on electric motors and lamps - and this other invention called the telegraph which led to the multiplexed telegraph which became the telephone. You get the picture... Trillions of dollars and huge changes in nearly everything we do. It also sparked James Clerk Maxwell.
Maxwell was the century's greatest theoretical physicist. Trying to come up with something comprehensive, he built on Faraday's insight and added work by Gauss and Ampère. In the process he realized electricity and magnetism weren't separate forces, but were really pieces of the same thing. Depending on your frame of reference you might see one or the other. They were manifestations of something deeper - he called the unified force electromagnetism.
Maxwell didn't stop there. Usually in the sophomore year a physics major learns what may be the first really beautiful thing she'll learn about physics. Shake an electric charge. Now you have a current starting and stopping. You do a bit of math and imagine in your mind what's going on. The shaking produces a changing electric field that, in turn, creates a changing magnetic field, but that produces a changing electric field that produces a changing magnetic field that produces a changing electric field ... you get the idea - a disturbance in electric and magnetic fields moves out from the charge you had been shaking. Now go into the lab and measure the the strength of electric forces between two changes and the strength of the magnetic force between two magnets. You plug these experimentally determined values into the simple wave equation you found by using Maxwell's equations and the simple thought experiment and you get the speed of the disturbance moving through the electromagnetic field.
The speed turns out to the the speed of light. Maxwell had shown light was an electromagnetic wave.2
These fields that Faraday imagined because he couldn't do the math turnout to be real. Maxwell had created the first great unification in physics and something unexpected and totally wonderful fell out - the connection between light and electromagnetism. Two decades later Hertz showed you could create and receive radio waves and physics departments in Europe and the US began to teach the theory of electromagnetism to physics and engineering students.
This electromagnetic field was real ... all we had to do was crawl a bit out of the cave. Real and useful .. trillions of dollars since then.
Some of us are like that dog who has to chase the tennis ball all the time. You ask the dog why and he looks at you like you just don't get it. "It's the most thrilling and glorious thing! How can you not do it?" Scientists often have difficultly communicating the beauty. If I really know the subject I should be able to describe it with words and pictures rather than the math, although that is beautiful too. I continue struggling as I work on improving. For me one on one is better - stop me and take a walk some time. Better yet is letting someone discover on their own.
I'm torn on the upcoming science marches. I'll write something addressing it directly soon, but experience with protests tells me my time is better spent communicating locally and not lecturing. Maybe if you can shake someone's imagination ... In the meantime I'll try on neat things you can observe or do - amateur science on a personal level from bats to a sport like volleyball to a number of things. stay tuned.
1 This addressed one of the fundamental problems Newton had with gravity - how did one mass manage to communicate with another? It turns out something even deeper was at work, but fields are how much of Nature works at a fundamental level. It seems a little weird, but you're made up of field disturbances.
2 From the chalkboard during one of Feynman's freshman lectures. If it isn't clear consider the conceptual model from shaking a charge. I worry that too many of us find representations like this so beautiful that we stop there and assume people have the background to appreciate what's going on. Although the special case of the shaking charge doesn't allow you to calculate anything , it does give insight to the non-physicist.
Spring is here. Asparagus! Rather than offer a recipe I suggest you go out and experiment. It is great steamed, roasted, pan fried, blanched, grilled and even raw. Roasted nuts go well and, if you can find good early blackberries....