### It's good to know things; if we didn't know how to read or write, our little meeting here wouldn't have been able at all, dear reader. It's important to know things, to know the alphabet and some basic math, as these are the tools we have, the only tools we have to try and understand, to make sense of the world we occupy.

_{source: Wikimedia Commons}

A linguist might be able to assert that he or she has an understanding of the Roman - and other alphabets, but for the rest of us it suffices to just know the letters that make up the alphabet. Similarly, when it comes to "the language of the universe," mathematics, it's enough to know certain rules and equations, whereas a mathematician or theoretical physicist needs to understand them in order to be able to grow their knowledge about the subject matter. We live in the fortunate circumstance, here in the rich west at least, almost all of us know how to read and write, as well as some basic math; I 'm sure we all know the Pythagoras Theorem in which the sum of the squares of the lengths of the two rectangular sides of a rectangular triangle equals the square of the length of it's diagonal side. That last sentence also illustrates mathematics' particularly efficient style of notation; a^{2} + b^{2} = c^{2}.

To know this equation is enough for practical application; you might be interested in the distance you have to travel when traversing a square lot of land on it's diagonal. It takes something else all-together to really understand why the Pythagoras Theorem works, why it is true. Like anything else in any other science worth it's salt, these mathematical rules and equations need proof, because therein lies understanding. The most well known proof for the Pythagoras Theorem deals with the area of the squares you can draw along each of the triangle's sides; the fact that the equation contains three squares might have hinted at the usability of squares...

The proof I found easiest to understand was the one dealing with similar triangles; you can divide any rectangular triangle into two smaller rectangular triangles with the exact same angles that are proportional to each other. It is believed that Einstein came up with this proof by himself in his teenage years, unknowing of the fact that the same proof had been done several times before. This proof is summarized in the image right after this post's intro, and it's immediately clear that the area of the full triangle is equal to the sum of the area's of the two smaller triangles. If you want a full explanation as well as the interesting story about Einstein's teenage mathematical adventures, you can read "Einstein’s First Proof" in The New Yorker.

_{source: Picpedia}

This is not displaying any understanding on my part of course, I didn't come up with this on my own; for me, I have to file this under the category of knowledge. But I think it's a good illustration of the difference between knowing and understanding for all of us. It should also illustrate how knowledge is good, but can also be dangerous, it can also arrest us in the road to further understanding of nature, of reality, if there is such a thing. If science is an accumulative process of building understanding from previous knowledge that came from earlier understanding, it's not hard to imagine we might be heading in a completely wrong direction in further understanding reality. We might fail to look for, or keep an open mind regarding "unknown unknowns," in our hunt for the "known unknowns" so to speak.

Einstein's generation of astronomers "knew" that we lived in a static, eternal and static universe, known as Hoyle's Steady-state model of the universe. This resulted in him adding the cosmological constant to his equations of general relativity. As it turns out he needed this constant to constrain the expanding universe he found in his equations, to the "reality" of Hoyle's model. Although he regarded this "fudging" of the equations as his biggest mistake, Einstein was later vindicated of course, when Hubble saw the universe expanding through his telescope...

What I wish for, is that our educational system, as well as we our-self in daily life, give more focus to understanding and less to just blindly repeating "knowledge" presented to us. We're unfortunate in the sense that our political as well as our economical systems (they're actually the same), don't promote critical thinking, or out of the box thinking. We're boxed in primarily by religion, politics and above all the economy in our daily thought-processes. Just close your eyes when you're at work, at a restaurant, or at a party, and listen for the words "money," "price," "(good / bad) deal," "income," "taxes," "rent," "mortgage," and so on, and you'll quickly see (or hear) that so much of our conversation and interaction is ruled by the economy; it's the hardest box to break out of, because whereas there are several religions to choose from, two or several political party's and politicians to choose from, there's only one world economy.

Anyhow, that's all I wanted to say today. I'll give the final word to... Well... You of course have the final word, dear reader, I'm just sharing mine. But here I'll give the last word to Neil deGrasse Tyson once again. He's not my favorite scientist, as I think he's just a touch too much infatuated with the "glamorous" side of science, but he's a great communicator nonetheless and often has very useful things to say, like on this occasion about the difference between knowing and understanding, and why understanding their difference is so important and useful, in just five minutes. He frames it as the difference between looking at "knowledge" as an answer, instead of looking at it as a process of understanding.

_{Neil deGrasse Tyson on Knowledge vs. Thinking}

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