I've thought about this before. It gets harder when dealing with >2 inputs and names longer than 1 letter, so I organized it with lines to make it look more tree-like. │u│v│x│y ├─┴─├─┴─ │f │g ├───┴─ │h └─ With >2 inputs…
>it very quickly learns to work on "it's on adjacent lines therefore it's a third apart" when you read sheet music Maybe you read sheet music different than how I do, but when I play euphonium or trombone, I translate…
Wow, I wish I had this when I learned to play. Keys, clefs, and accidentals felt like a hazing ritual, completely accidental (hah!) complexity. I always hated that I couldn't read the treble instrument parts at…
Rotational symmetry or L^2 norm only matter in vector formulations. I assumed a scalar formulation. Conservation of E-field flux certainly implies additive-homomorphism (addition of charges equals addition of forces).…
Show by experiment that the force of charge0 against charge1+charge2 equals the force of charge0 against charge1 plus charge0 against charge2. Induce an additive-homomorphic property F(r,q0,q1+q2) =…
I'd like to plug the NIWA wiki network for Nintendo games. I think more independent wikis should federate in similar ways, to strategize beyond just search engine hits. https://www.niwanetwork.org/members/
My hidden assumption: I said the set of names must be countable! I assumed you would know that naming means assigning a finite string (in the Ithkuil writing system of course). and don't nitpick further or else I'll…
guess I won't respond now :( "what is a real number, anyways" is one of my favorite questions, not foolish at all
No surjective function exists from names to real numbers (diagonalization). Some like to interpret the diagonalization process to mean that unnameable real numbers exist. On the other hand, given any real number, I can…
You proved that definable implies nameable, and also unnameable implies undefinable. Obviously true. However, the idea of undefinable real numbers closely resembles a modern version of the paradox. No surjective…
Thanks for sharing! I love approval voting the most by pure simplicity and effectiveness. How does score voting work better than STAR? I thought STAR degenerates into score voting when clone candidates run? I haven't…
Ranked choice is not better. It has the center squeeze effect.
Not happy to respond to LLM talk, but you seem interested anyway. Some sleight of hand happens between "fixing a formal system" and using Cantor's theorem for the metamathematical analysis, as if we use classical set…
Exactly. For example, John Mayberry wrote "The Foundations of Mathematics in the Theory of Sets" (2000). Half of the book consists of philosophical arguments for his "Euclidean set theory" contrasted against the big bad…
For example? And does "first-order arithmetic" mean ZFC?
Not really. Math uses no physical observation, only axioms. Nothing can "prove" or "disprove" axioms. However, if observation supports the axiomatic theory, then we use the theory for physical prediction. If observation…
I recently played around with what I call "manual tail-call optimization": transform a tail call to a goto to the beginning of the function. Check it out: https://godbolt.org/z/3fY1v1oeW int factorial_loop_iterative(int…
Why yes, I want to read research confirming common sense. And more valuable, I can read the nuance of it too (quantifying how much safer compared to cigarettes).
Well, I have no clue about their relative safety and would like to read more.
Just thought of how to fix the problem I had. Since the program already highlights the inductive hypothesis blue (but doesn't underline), consider adding a clickable underline to it (Rewrite with IH) instead of…
I got stuck in a loop on 8 "Adding zero to the right", blindly following the tip below the box keeps looping induction introduction. Looping 9 times following the help tip, it eventually complains about an invalid proof…
Cool!! I really like how the overflow condition reads. "When the source and destination have the same sign, but the result a different sign, then signed addition overflows." x86 has SETC/SETNC and SETO/SETNO to pull the…
You sound like you believe in philosophical skepticism. Tell me: can a map ever properly describe the territory? When would a map properly describe the territory? (Can a theory ever properly describe reality? What does…
I included that to try to explain the symbol soup that correctly encodes the preconditions (the ∀ lines). I intended that to mean "I need to make sure that y+x doesn't overflow", even that unsigned arithmetic cannot…
Pedantically, that doesn't properly invert post-increment in the loop step. It decrements one extra time. If I need to use the loop index after the loop, then decrementing in the condition would cause problems. size_t i…
I've thought about this before. It gets harder when dealing with >2 inputs and names longer than 1 letter, so I organized it with lines to make it look more tree-like. │u│v│x│y ├─┴─├─┴─ │f │g ├───┴─ │h └─ With >2 inputs…
>it very quickly learns to work on "it's on adjacent lines therefore it's a third apart" when you read sheet music Maybe you read sheet music different than how I do, but when I play euphonium or trombone, I translate…
Wow, I wish I had this when I learned to play. Keys, clefs, and accidentals felt like a hazing ritual, completely accidental (hah!) complexity. I always hated that I couldn't read the treble instrument parts at…
Rotational symmetry or L^2 norm only matter in vector formulations. I assumed a scalar formulation. Conservation of E-field flux certainly implies additive-homomorphism (addition of charges equals addition of forces).…
Show by experiment that the force of charge0 against charge1+charge2 equals the force of charge0 against charge1 plus charge0 against charge2. Induce an additive-homomorphic property F(r,q0,q1+q2) =…
I'd like to plug the NIWA wiki network for Nintendo games. I think more independent wikis should federate in similar ways, to strategize beyond just search engine hits. https://www.niwanetwork.org/members/
My hidden assumption: I said the set of names must be countable! I assumed you would know that naming means assigning a finite string (in the Ithkuil writing system of course). and don't nitpick further or else I'll…
guess I won't respond now :( "what is a real number, anyways" is one of my favorite questions, not foolish at all
No surjective function exists from names to real numbers (diagonalization). Some like to interpret the diagonalization process to mean that unnameable real numbers exist. On the other hand, given any real number, I can…
You proved that definable implies nameable, and also unnameable implies undefinable. Obviously true. However, the idea of undefinable real numbers closely resembles a modern version of the paradox. No surjective…
Thanks for sharing! I love approval voting the most by pure simplicity and effectiveness. How does score voting work better than STAR? I thought STAR degenerates into score voting when clone candidates run? I haven't…
Ranked choice is not better. It has the center squeeze effect.
Not happy to respond to LLM talk, but you seem interested anyway. Some sleight of hand happens between "fixing a formal system" and using Cantor's theorem for the metamathematical analysis, as if we use classical set…
Exactly. For example, John Mayberry wrote "The Foundations of Mathematics in the Theory of Sets" (2000). Half of the book consists of philosophical arguments for his "Euclidean set theory" contrasted against the big bad…
For example? And does "first-order arithmetic" mean ZFC?
Not really. Math uses no physical observation, only axioms. Nothing can "prove" or "disprove" axioms. However, if observation supports the axiomatic theory, then we use the theory for physical prediction. If observation…
I recently played around with what I call "manual tail-call optimization": transform a tail call to a goto to the beginning of the function. Check it out: https://godbolt.org/z/3fY1v1oeW int factorial_loop_iterative(int…
Why yes, I want to read research confirming common sense. And more valuable, I can read the nuance of it too (quantifying how much safer compared to cigarettes).
Well, I have no clue about their relative safety and would like to read more.
Just thought of how to fix the problem I had. Since the program already highlights the inductive hypothesis blue (but doesn't underline), consider adding a clickable underline to it (Rewrite with IH) instead of…
I got stuck in a loop on 8 "Adding zero to the right", blindly following the tip below the box keeps looping induction introduction. Looping 9 times following the help tip, it eventually complains about an invalid proof…
Cool!! I really like how the overflow condition reads. "When the source and destination have the same sign, but the result a different sign, then signed addition overflows." x86 has SETC/SETNC and SETO/SETNO to pull the…
You sound like you believe in philosophical skepticism. Tell me: can a map ever properly describe the territory? When would a map properly describe the territory? (Can a theory ever properly describe reality? What does…
I included that to try to explain the symbol soup that correctly encodes the preconditions (the ∀ lines). I intended that to mean "I need to make sure that y+x doesn't overflow", even that unsigned arithmetic cannot…
Pedantically, that doesn't properly invert post-increment in the loop step. It decrements one extra time. If I need to use the loop index after the loop, then decrementing in the condition would cause problems. size_t i…