Mathematica: A Secret World of Intuition and Curiosity
you can imagine a perfect circle. imagine a straight line that crosses the circle at three points. you will see it's not possible.
This exercise tells you in the most simple case what this book is about. you already do math
3 ways to deal with wrong intutions. the first two a defences, (1) you think you are a loser, develeop an inferiority complex and stop thinking, (2) others are idiots and you where right all along. (3) perpetual-openness like einstein did
schools make two mistakes
- they exaggerate things
- they overemphasis the limits of your intuition
your intuition is your strongest intellectual resource In some sense its your only intellectual resource
behind this is a biological truth that you have experienced many many times
what's at stake here is your ability to reclaim control of the way you construct your own vision of the world
do you know how important it is to construct strong an clear mental images? we know sleep, exercise, unproccessed food are healthy
Ancient rom was not able to picture but numbers like 1 million and much less picturing 1mil-1=999,999 but you can do that easily. it is unsurpicing that we can see a distiction between 25 and 26 in a splitsecond. we inherited that but for primodial tribes this would be a big surprice. we differenciate between without noticing the advancement it brings.
Successfull math becomes so intuitive that it no longer looks like math anymore. When examples seem stupid to you, it's precively because you understand them at the deepest level.
A Language That's Not Human
At a profound level, math is the only successful attempt by humanity to speak with precision about things that we can't pont to with our fingers.
In math books, the most important passgaes aren't the theorems or the proffs: they are the definitions.
Mathematical language works like building bloks where words are really defined: that is to say, built from other words that have themselves been previously defined.
The basic building block of math are definitions. This is also called logical formalism. For example if you define an elephant as having a trunk and you remove the trunk, the elephant ceases to be an elephant. Its important to recognize that humans don't and cannot ever think like this. We would consider this way of thinking inhuman or inmoral. That is why math is hard to read. But it is the price to pay for talking about invisible things. Things we normalize cannot point to with our fingers.
Like with ai we can get upset with them.
This may annoy us, we may find it ridiculous, but we end up getting used to their psychology and, at the end of the day, we are glad to have them work for us.
Learning to See
Learning math is learning to see the objects they point to as if they where right there in front of your eyes.
This kind of seing if a function of synesthesia
Secret math is a mental yoga whose goal is to retake control over our ability for synesthesia.
Nothing I'm saying should surpise you, since nothing about it is new to you. When you learned to "see" the number 999,999,999 rather than ink on a paper, t was thanks to your command of this mental yoga. What you could do in your childhood, you should still be able to do today.
The promise of a dictionary is to define every word using other words. They they deliver because of circular reasoning.
Mathematics also def