I like the concept of thinking continuously. The world would be a much better place if we could just simply connect our ideas together on all topics.
That's not exactly what I was talking about; I was speaking of the fact that energy, at its most fundamental, is nonlinear. Thus, on the macroscopic scale, quantum mechanics and classical physics converge—the classical limit. Nevertheless, it is impossible, as Planck found out, to explain some phenomena without accepting the fact that action is quantized. In many cases, such as for monochromatic light or for atoms, this quantum of action also implies that only certain energy levels are allowed, and values in-between are forbidden. In other words (and with massive oversimplification), discontinuous.Planck discovered that physical action could not take on any indiscriminate value. Instead, the action must be some multiple of a very small quantity (later to be named the "quantum of action" and now called Planck's constant). This inherent granularity is counterintuitive in the everyday world, where it is possible to "make things a little bit hotter" or "move things a little bit faster". This is because the quanta of action are very, very small in comparison to everyday macroscopic human experience.
Quanta of energy have to do with the wavelengths of light emitted from, say, an electron jumping to a lower energy level. That is what is quantized, and it comes from the boundary conditions of the energy levels themselves. I was making a comment about how many people have speculated that quantization extends to space-time itself, that we move through the universe in a quantized way; that is what a discontinuous universe would look like. This new research suggests that there aren't boundary constraints on space-time, apparently.
Ah, I see. "Smooth, not foamy" makes quite a bit more sense in this context, actually. I'm just not sure how much I want to hinge a change in our entire physical worldview on the fact that some particles acted like they were on pavement rather than gravel, as it were. This is extremely interesting, though. Planck's constant has long been thought they be-all end-all, I believe. Perhaps nuts to that."If foaminess exists at all, we think it must be at a scale far smaller than the Planck length, indicating that other physics might be involved," study leader Robert Nemiroff, of Michigan Technological University, said in a statement.
There's something about human nature that forces us to think compartmentally. We have to arrange and classify everything from taxonomy on down to our dresser drawers. One need only look to the popularity of The Container Store to see how deep our classification neurosis goes. Of course classification helps us to clarify our thinking at times, but I think it also obscures the truth in a lot of cases, as well. There are so many deep connections in life and in science that elude us, because we are so used to thinking in terms of X is X, and Y is Y.
I feel that many people that originally become interested in the maths and sciences enjoy it simply because it makes sense to them. They are able to 'compartmentalize' the information they know and use it to add on to learn more. The fact that X is X and Y is Y helps them gain insight from this information. Compartmentalizing helps us to group together information we don't know very well, organize it better to help us learn about it and then compare it with something we do know. Otherwise known as learning through analogy. I think this has a lot to do with different learning types, possibly. Left brain and right brain learning. Comparing more compartmentalized and rigid structures of math and sciences with the more flowing artistic structures of language and history. If we could connect these two learning types in the future perhaps we could begin to think continuously. In a rigid but creative structure.