3 ms·

> In graph theory, a tree is a cycle-free graph and a triangle is a cycle of length 3. Ergo, a triangle is not a tree. Mathematics is not a rigorous language,

by breck 7y ago

> In graph theory, a tree is a cycle-free graph and a triangle is a cycle of length 3. Ergo, a triangle is not a tree. Mathematics is not a rigorous language, so I'll put the crux of my argument in Tree Notation, which is a rigorous language: betterGraphTheoryLanguage nodeCell cycleNode triangleNode extends cycleNode cells nodeCell nodeCell nodeCell There you go, a triangle is a cycle with length 3. Ergo, a triangle is a tree. typo fix: changed Trees to Tree Notation.

klyrs 7y ago
> Mathematics is not a rigorous language Uh huh. Great start... > I'll put the crux of my argument in Trees, which is a rigorous language Interesting how you're overloading the word "tree" in this context. You're presenting a definition in the format of a tree. And concluding that the resulting object is itself a tree. It's like saying that swords are made of wood, and proving it by carving the definition of a sword into a piece of wood. This is quackery. Graphs, and trees, have perfectly rigorous definitions. They've been defined in a plurality of rigorous languages. Your "definition" doesn't even mention edges, unless they're implied by "cycleNode" somehow; in either case it appears that your "better" graph theory only contains a single graph of any given order. Graph theorists expect a few more than that.
- breck 7y ago
  Just because Mathematics is one of the most rigorous languages we have, does mean it is rigorous. It would be like saying Roman Numerals are not a great language for math. If I say that today no one blinks an eye. But if I said that 2k years ago people would say "Uh huh. Great start...". Let me define a "rigorous" language. A rigorous langauge is one which can be defined completely in a single document starting with 0 and 1 and working it's way all the way up to whatever it is you want to prove. > Graphs, and trees, have perfectly rigorous definitions. They've been defined in a plurality of rigorous languages. If you can provide a link to a single page that starts with 0 and 1 and builds all the way up to defining "graphs and trees" and how a "triangle is not a tree", then I will agree with you. > Interesting how you're overloading the word "tree" in this context. Sorry, that was a typo, I meant to write Tree Notation. I'll fix.
  - panic 7y ago
    > A rigorous langauge is one which can be defined completely in a single document starting with 0 and 1 and working it's way all the way up to whatever it is you want to prove. Is there a document like this for your tree notation? Not trying to criticize; I'm legitimately interested to see how this would be done.
    - breck 7y ago
      > Is there a document like this for your tree notation? I wish. We have a lot of ongoing threads about it. Someone has one somewhere for logic gates, IIRC. Here's a snippet from 1 from a conversation the other day on how to build up to an if statement. 0 1 2 10 ... i 01101001 ... f 01100110 ... if 1 2 Obviously that's not ideal but hopefully some more data on what we are talking about with that. The idea is we'd like to be able to compare 2 systems objectively and decide which is the simpler one. Here's a rough paper from 2017 (before I had any experience in academia): https://github.com/treenotation/jtree/blob/master/papers/paper3/countingComplexity.pdf https://github.com/treenotation/jtree/blob/master/papers/pap...

by breck 7y ago

klyrs 7y ago

> Mathematics is not a rigorous language Uh huh. Great start... > I'll put the crux of my argument in Trees, which is a rigorous language Interesting how you're overloading the word "tree" in this context. You're presenting a definition in the format of a tree. And concluding that the resulting object is itself a tree. It's like saying that swords are made of wood, and proving it by carving the definition of a sword into a piece of wood. This is quackery. Graphs, and trees, have perfectly rigorous definitions. They've been defined in a plurality of rigorous languages. Your "definition" doesn't even mention edges, unless they're implied by "cycleNode" somehow; in either case it appears that your "better" graph theory only contains a single graph of any given order. Graph theorists expect a few more than that.

breck 7y ago
Just because Mathematics is one of the most rigorous languages we have, does mean it is rigorous. It would be like saying Roman Numerals are not a great language for math. If I say that today no one blinks an eye. But if I said that 2k years ago people would say "Uh huh. Great start...". Let me define a "rigorous" language. A rigorous langauge is one which can be defined completely in a single document starting with 0 and 1 and working it's way all the way up to whatever it is you want to prove. > Graphs, and trees, have perfectly rigorous definitions. They've been defined in a plurality of rigorous languages. If you can provide a link to a single page that starts with 0 and 1 and builds all the way up to defining "graphs and trees" and how a "triangle is not a tree", then I will agree with you. > Interesting how you're overloading the word "tree" in this context. Sorry, that was a typo, I meant to write Tree Notation. I'll fix.
- panic 7y ago
  > A rigorous langauge is one which can be defined completely in a single document starting with 0 and 1 and working it's way all the way up to whatever it is you want to prove. Is there a document like this for your tree notation? Not trying to criticize; I'm legitimately interested to see how this would be done.
  - breck 7y ago
    > Is there a document like this for your tree notation? I wish. We have a lot of ongoing threads about it. Someone has one somewhere for logic gates, IIRC. Here's a snippet from 1 from a conversation the other day on how to build up to an if statement. 0 1 2 10 ... i 01101001 ... f 01100110 ... if 1 2 Obviously that's not ideal but hopefully some more data on what we are talking about with that. The idea is we'd like to be able to compare 2 systems objectively and decide which is the simpler one. Here's a rough paper from 2017 (before I had any experience in academia): https://github.com/treenotation/jtree/blob/master/papers/paper3/countingComplexity.pdf https://github.com/treenotation/jtree/blob/master/papers/pap...