We sometimes use our emotions, what we value, to make decisions. What are the decisions picked? They are premises in well defined axiomatic systems of the real world.
Intensity of emotions can be quantified. Intensity exists. It's a different story why we can't show exact biochemistry process taking place.
Our emotions come from our values. Also, our values come from our emotions. The two neural systems provide continous feedback to each other.
It is beyond me why the concept of a function, in math, has to be introduced so late in education. It's just pairing of numbers....
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Premises in math are theorems in fields in which math is applied. That's why, even math is built from axioms, it can link with real world.
I like when a physicist postulates! Using fancy word "postulate" to say "I have no idea where this formula comes from, but it might work!"
Axioms in one system are theorems in the other.
Axiom: your home light switch can be ON or OFF. Theorem 1: You switched to ON. Theorem 2: You switched to OFF. Proof: directly from Axiom.
From "About..." section of book "Mathematical Physiology": Of interest both to applied mathematicians and quantitative physiologists :-)
As long as you explain students that math deals with counts only and logic applied to it can be applied eslwehere freely, it's a good start.
Math should help you to think more freely, not to prohibit your all other thoughts and thinking in order to correctly add two numbers.
I've watched a movie, I've read a book, I've listened to a song. How about I've written a book, I've made a movie, I've composed a song?
Precise logical processing in thinking is necessary but not sufficent to succeed. Assumptions must be correct and valuable.
Your brain logical unit will process anything with same accuracy, be it input from an emotional response or from strict scientific thinking.
It's hard not to be emotionally attached to your scientific thinking :)
Emotions continuously make axiomatic systems and your logical brain process it, because it only deals with raw truth values.
Sometimes emotions create an axiomatic system and then present it to your brain logical center for processing. Bad input gives bad output :)
Your brain has amazing logical mechanism that can process any axiomatic system presented to it. That's why car salesman can sell you a car!
Again they made a movie from all the things you already know and you are aware of. but again you failed to link them in that particular way.
Stand-up comedian may not make more logical connections than a good mathematician, but, impact of result is much greater. Chose right links.
While repeatedly asking "Why?" can eventually bring you to quantum physics, asking "How I can link things " will lead you to new inventions.
One postulate in logic can be interpreted in billion ways.
I have a strong feeling about that axiomatic system.....
Statement ''you might have a chance'' is better than ''you never know''.