There are 32 comments.

1. Member
   Mark Camp

   @MarkCamp

   8:09 AM EST ⋅ Mar 7, 2024

   Nanocelt TheContrarian (View Comment):

   Stina (View Comment):

   Nanocelt TheContrarian (View Comment):

   Stina (View Comment):

   Math is so much worse than Whiteness and Racism.

   Math posits AND demonstrates the existence of absolute truth. And it really is the only discipline that actually succeeds in that. Science, engineering, the arts all have enough relativity to demonstrate lack of clarity, or there’s more than one way to skin a cat, or that subjectivity reigns supreme.

   Math, though, always has a right answer, whether you know how to find it or not, whether you like it or not.

   Not true. See Godel’s incompleteness theorems. Any axiomatic system of second order logic will contain provable true theories that are contradictory, and the only way this can be avoided is to start with an infinite number of axioms. On the other hand, Godel’s incompleteness theorems imply that we can confirm the truth of propositions we cannot formally prove. This, Gödel affirmed, indicates that human consciousness is trans finite (or transcendent) and cannot be superseded by such thinks as AI. The scientific and mathematical worlds have never fully come to grips with Godel’s Theorems (intentionally so). They bring a type of fuzziness to math just as Heisenberg’s uncertainty principle does to physics or the Church-Turing halting hypothesis does to computer theory. Or as the Axiom of Choice does to Zermelo-Fraenkel logic.
   Your statement applies only to first order logical systems, such as Euclid’s geometry.

   Does my condition – whether you know how to find it or not – not support that?

   I understand there’s always going to be criteria or variables we cannot identify when you reach certain levels of the scientific and mathematical dimensions. That doesn’t imply non-existence. It implies an inability to identify. Chaotic Systems seek to create predictable systems where unidentifiable variables exist and account for them without having to explicitly handle them… this sounds like a similar deal.

   Yeah, I’m likely being simplistic here, because I only have a BA in math, not a Ph.D. And I’m not even particularly great with what I have.

   The statement, Whether you know how to find it or not, can imply more than one thing: That there is proof that hasn’t been found, that could be found, and some creative genius may be able to find it. Or that it is provable that a proposition cannot be formally proved. Godel’s theorems affirmed that any logical system is Incomplete, that is, will ultimately contradict itself. So we now know that, in any axiomatic system with a finite number of axioms, you will get self contradiction. It’s like trying to decide the validity of the statement of a Creatn that “All Cretans are liars”, or Russell’s paradox: Is the set of all sets that are not members of themselves a member of itself?

   It’s the difference between saying “We don’t know how to prove it” versus saying “It is not provable”. So your statement gets us almost there. But it doesn’t fit with the assertion that math always gives an answer. From a personal standpoint, I believed that math was the path to Truth when I was young, until I ran into Godel’s Incompleteness Theorems in my sanrio year of college. I made the mistake that Jon vonNeumann made when he heard Godel present his theorems: “The jig is up”. von Neumann was wrong, and I was wrong. In my case, lacking the insouciance, genius, and insight of von Neumann, I collapsed into a state of deep depression, gave up my dreams of becoming a mathematical physicist, and to the future detriment of many, went to medical school. Now, given the very sorry state of physics, including mathematical physics, I am more appreciative of my change in direction, although I was then, and remain now some 50 years later, poorly suited to the practice of medicine (which I am still practicing). You are actually more educated in math than am I. My BS is in Chemistry. Not even a minor in Math, though I did take more math courses than required for my Chemistry degree, which is how I ran into (collided with?) Godel. .

   To me, our lives now seem surprisingly and remarkably similar. I will read your posts differently and better from now on. Thanks for taking the time and effort to write it.

2. Coolidge
   CarolJoy, Not So Easy To Kill

   @CarolJoy

   5:50 PM EST ⋅ Mar 7, 2024

   Stina (View Comment):

   Math is so much worse than Whiteness and Racism.

   Math posits AND demonstrates the existence of absolute truth. And it really is the only discipline that actually succeeds in that. Science, engineering, the arts all have enough relativity to demonstrate lack of clarity, or there’s more than one way to skin a cat, or that subjectivity reigns supreme.

   Math, though, always has a right answer, whether you know how to find it or not, whether you like it or not.

   What you say is truth itself, Stina, unless you ever had to experience “New Math” – a trend in the 1980’s that abolished the addition, subtraction, multiplication and division tables and became rather touchy feelie for students here in California.

   Luckily for students, it eventually was ousted and traditional math once again was taught. (We in American society are always on one side or the other of the full swing of a  pendulum For every field but math,  the tragic  thing is that there can be good ideas right there in the middle of the pendulum’s swing that are totally ignored.)