Some people—people who probably distrust mathematics—are quick to claim that they knew all along that some truths are beyond mathematics. But they just didn’t. They didn’t KNOW it. They didn’t prove it.
Janna Levin, A Madman Dreams of Turing Machines
Continued / context:
"… Gödel didn’t believe that truth would elude us. He proved that it would. He didn’t invent a myth to conform to his prejudice of the world—at least not when it came to mathematics. He discovered his theorem as surely as if it was a rock he had dug up from the ground. He could pass it around the table and it would be as real as that rock. If anyone cared to, they could dig it up where he buried it and find it just the same.”
I’ve just begun reading Lehrer’s Proust Was a Neuroscientist, and all I keep thinking of is that quote above.
There’s no denying the occasional prescience in art and fortune cookies, but intuition (chance) is not the same as knowing (certainty).
It’s too easy to look back on an event and create a convenient story — to ascribe cause to effect. That’s what our brains do; we make sense of the world via pattern-creation. It’s an easy trap to get caught in, but it’s not necessarily the truth.
Minimally related; I definitely thought I’d already posted that quote. Was going flipping crazy trying to remember who said it, googling the shit out of terms like [ site:olena.tumblr.com “prove” janna levin ], etc. To no avail. Hate when this happens. Secondary brain disparity?
Technically you should use CSS to center (like so), and use <em> instead of <i> / also use CSS to italicize. The older terms mostly work fine, but are not supported in HTML5.
My site is not a good example of best coding practices; I didn’t really give a damn since it was a personal work and I had to get it done fast. :/
BF: You have OVER 5000 LIKES?! What’s the point of liking anything?
I… don’t know. Guess I like selling my internet soul to Yahoo, or whatever.
There is a tremendous difference between ‘thinking’ in verbal terms and ‘contemplating,’ inwardly silent, on nonverbal levels and then searching for the proper structure of language to fit the supposedly discovered structure of the silent processes that modern science tries to find. If we ‘think’ verbally, we act as biased observers and project onto the silent levels the structure of the language we use and so remain in our rut of old orientations, making keen, unbiased observations and creative work well-nigh impossible. In contrast, when we ‘think’ without words, or in pictures (which involve structure and therefore relations), we may discover new aspects and relations on silent levels and so may produce important theoretical results in the general search for a similarity of structure between the two levels, silent and verbal. Practically all important advances are made that way.
When you have zero evidence, every assumption is basically equal. You prefer to see causes rather than effects, signals in the noise, patterns in the randomness. You prefer easy-to-understand stories, and thus turn everything in life into a narrative so that complicated problems become easy. Scientists work to remove the narrative, to boil it away, leaving behind only the raw facts. Those data sit there naked and exposed so they can be reflected upon and rearranged by each new visitor. Scientists will speculate, and they will argue, but the data they extract from observation will not budge. They may not even make sense for a hundred years or more, but thanks to the scientific method, the stories, full of biases and fallacies, will crash against the facts and recede into history.
Curious if, with all the discussion of Fact, he mentions the connection between Fact & Law (in court) and Reason & the Scientific Method.
EDIT: IGNORE THE BELOW. Unless you have the same question.
Was just a bit slow to see the arrangement in this one.
If anyone’s curious, I sort of proved it to myself, here.
"Stupid Question" time!
This is one of those things that really bothers me about math. I can easily remember how to use this process, but I don’t understand why it’s OK to do this, or how anybody figured it out in the first place. I wouldn’t think to do it of my own accord, because it doesn’t align with my idea of the “rules of math”. Thus, I feel my foundation is insecure. How can you play a strict game, requiring precise results, if you’re not sure what’s allowed or why?
So, in “completing the square”, a constant is added to both sides of an equation. Everything about the process makes sense, except that bit.
E.g., if I have A+1=B-3, I understand that I can “take 1” from the B-3 side and move it over to the A+1 side, to get A+2=B-2. Fine. The total “stuff” in the “system” remains the same.
But how the Hell is it OK to, for example, +6 to both sides? (Similar to what we do when CtS. Pretend that +6 would make my example more convenient to figure out. And note, 6 isn’t totally random, as 3 and 1 are factors of 6.)
But 6 is a quantity that didn’t belong to the equation, prior. To me, it seems like conjuration. For example, it’s ok to borrow matter (in physics) but you can’t create or destroy it. So why can I just “create” a 6 to make things more convenient for myself, if it changes the original quantity I’m working with?
Can some mathematician please explain, in plain English?
Thank you <3
Sorry I haven’t been posting much.