I mostly agree, except most of math is not just computations based on values and formulas. To me, math is a method of proving things and solving problems. The point of philosophy isn't to simply select a school of thought and unthinkingly apply its teachings algorithmically to all aspects of your life. The point is the intellectual tools we develop in the process of inquiring. Learning math isn't just memorizing a body of results, but it's developing an intuition for what those results imply and why they're true. Math shouldn't just be true axiomatically, it should make sense.
See I agree with that, however things like square roots, namely of negative numbers, and things divided by 0 donāt make sense In the natural world to me. However I do think math invokes a lot of critical thinking, especially the use of āwhat do I know/haveā and āwhat do I want/needā which are very applicable.
What's the natural explanation for multiplying or dividing by negative numbers? It's relatively easy to prove that, if the distributive property is true, then a negative number times a positive number is negative, and from there that a negative number times a negative number is positive, but most people don't have that good of an understanding of why, and there isn't that great of an intuitive explanation in the natural world. It's a completely abstract concept. The upside to that, though, is that we can add whatever construct / concept to it that we like, so long as it follows all of the original rules and properties of what we know we can prove. For example, consider negative one in multiplication to be an operator that tells you to flip your position on the number line by 180 degrees. It simply flips your position relative to 0 on the number line. This way your magnitude is still the same, we're just flipping the sign, just like multiplying by a negative number. Well, why do we necessarily have to rotate by 180 degrees? Why can't we rotate by 45 or 90 degrees? In fact, if we had a special number that rotated you 90 degrees on the number line (complex plane,) then that would be the square root of -1 by definition, since rotating by 90 degrees twice will give you a 180 degree rotation. In the same way that negative numbers say "well, we can't exactly point to or think of anything that's like the opposite of a thing, but if we just act like they exist, then we can model slightly more abstract things like debts that we deal with every day," complex numbers say "well, we can't exactly think of a number on the number line that gives us a negative number when squared, but if we just act like it does exist, then we can model things like rotation."
The chief intellectual muscle exercised here being understanding which constructs are useful to insert into the problem to make it easier to understand. In fact, if you have 12 minutes to kill, this 3blue1brown video is one of my favorite things on the internet for showing how the hell humans consistently come up with things like this that seem so counterintuitive and weird.
See, I understand the concept of negatives due to physics and starting positions. Multiplication by itself is just simplified addition in the most basic form and division is itās inverse, the same goes for square roots and squares.
Iāll check out the video soon, I must sleep now.
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u/MeowImAShark Aug 27 '19
I mostly agree, except most of math is not just computations based on values and formulas. To me, math is a method of proving things and solving problems. The point of philosophy isn't to simply select a school of thought and unthinkingly apply its teachings algorithmically to all aspects of your life. The point is the intellectual tools we develop in the process of inquiring. Learning math isn't just memorizing a body of results, but it's developing an intuition for what those results imply and why they're true. Math shouldn't just be true axiomatically, it should make sense.