Re: [fonc] 90% glue code [universal language]
On 4/20/13, John Carlson yottz...@gmail.com wrote: How do these handle infinite sets? :D You have to handle infinity the same way a computer does: make up a special symbol and let it use different rules. You make up a name and describe the behaviour of the thing named by logical statements that can be encoded in the notation. Several people have experimented with number notation systems inspired by or layered on top of the boundary/name-based notation, but the basic system is strictly binary logical, not numerical. I'm playing with expressions that denote circuits that compute mathematical functions, which is the obvious natural way to express numbers and do math with the notation, and of course anything a computer can be made to do (floating point, NaN, Infinity, etc) can be expressed in the notation. I'm hardly a sophisticated source for this stuff- I'm in way over my head -but there is a lot of rich and detailed information at the websites mentioned. Warm regards, ~Simon C. S. Pierce, Existential Graphs, circa 1890 Spencer-Brown, Laws of Form Bricken, http://iconicmath.com/ Shroup, http://www.lawsofform.org/ Burnett-Stuart, http://www.markability.net/ The history of mankind for the last four centuries is rather like that of an imprisoned sleeper, stirring clumsily and uneasily while the prison that restrains and shelters him catches fire, not waking but incorporating the crackling and warmth of the fire with ancient and incongruous dreams, than like that of a man consciously awake to danger and opportunity. --H. P. Wells, A Short History of the World ___ fonc mailing list fonc@vpri.org http://vpri.org/mailman/listinfo/fonc
Re: [fonc] 90% glue code [universal language]
You have to handle infinity the same way a computer does: make up a special symbol and let it use different rules. This is pretty much correct. For any concept of infinity, it should behave consistently with what it represents in terms of the operators of a given system. For example, in Euclidean space, if you multiple infinity by a number, you get infinity back. If you invert infinity in a circle, you get the center of the circle as a result and so forth. ___ fonc mailing list fonc@vpri.org http://vpri.org/mailman/listinfo/fonc
Re: [fonc] 90% glue code [universal language]
On 4/20/13, John Carlson yottz...@gmail.com wrote: Do you need one symbol for the number infinity and another for denoting that a set is inifinite? Or do you just reason about the size of the set? Is there a difference between a set that is countably infinite and one that isn't countable? I barely know Russell's paradox... you're ahead of me. Well, for what it's worth, quoting from Meguire's 2007 Boundary Algebra: A Simple Notation for Boolean Algebra and the Truth Functors: Let U be the universal set, a,b∈U, and ∅ be the null set. Then the columns headed by “Sets” show how the algebra of sets and the pa are equivalent. Table 4-2. The 10 Nontrivial Binary Connectives (Functors). NameLogic Sets BA Alternation a∨b a∪b ab Conditional a→b a⊆b (a)b Converse a←b a⊇b a(b) Conjunction a∧b a∩b ((a)(b)) ___ NOR a↓b a∪b (ab) ___ Sheffer stroke a|b a∩b (a)(b) Biconditionala↔b a⊆b⊆a (((a)b)(a(b))) -or- ((a)(b))(ab) (Apologies if the Unicode characters got mangled!) Check out http://www.markability.net/sets.htm also. I don't know much about set theory but I think the Universal set stands for the set of everything, no? Cheers, ~Simon The history of mankind for the last four centuries is rather like that of an imprisoned sleeper, stirring clumsily and uneasily while the prison that restrains and shelters him catches fire, not waking but incorporating the crackling and warmth of the fire with ancient and incongruous dreams, than like that of a man consciously awake to danger and opportunity. --H. P. Wells, A Short History of the World ___ fonc mailing list fonc@vpri.org http://vpri.org/mailman/listinfo/fonc
Re: [fonc] 90% glue code [universal language]
I think that concepts in some sense transcend the universe. Are there more digits in pi than there are atoms in the universe? I guess we are asking if there are transcendental volumes which are bigger or more complex than the universe. If the universe contains the transcendental as symbols then how many transcendental symbols are there? I think you still run into Russell's Paradox. On Apr 20, 2013 9:15 PM, Simon Forman forman.si...@gmail.com wrote: On 4/20/13, John Carlson yottz...@gmail.com wrote: Do you need one symbol for the number infinity and another for denoting that a set is inifinite? Or do you just reason about the size of the set? Is there a difference between a set that is countably infinite and one that isn't countable? I barely know Russell's paradox... you're ahead of me. Well, for what it's worth, quoting from Meguire's 2007 Boundary Algebra: A Simple Notation for Boolean Algebra and the Truth Functors: Let U be the universal set, a,b∈U, and ∅ be the null set. Then the columns headed by “Sets” show how the algebra of sets and the pa are equivalent. Table 4-2. The 10 Nontrivial Binary Connectives (Functors). NameLogic Sets BA Alternation a∨b a∪b ab Conditional a→b a⊆b (a)b Converse a←b a⊇b a(b) Conjunction a∧b a∩b ((a)(b)) ___ NOR a↓b a∪b (ab) ___ Sheffer stroke a|b a∩b (a)(b) Biconditionala↔b a⊆b⊆a (((a)b)(a(b))) -or- ((a)(b))(ab) (Apologies if the Unicode characters got mangled!) Check out http://www.markability.net/sets.htm also. I don't know much about set theory but I think the Universal set stands for the set of everything, no? Cheers, ~Simon The history of mankind for the last four centuries is rather like that of an imprisoned sleeper, stirring clumsily and uneasily while the prison that restrains and shelters him catches fire, not waking but incorporating the crackling and warmth of the fire with ancient and incongruous dreams, than like that of a man consciously awake to danger and opportunity. --H. P. Wells, A Short History of the World ___ fonc mailing list fonc@vpri.org http://vpri.org/mailman/listinfo/fonc ___ fonc mailing list fonc@vpri.org http://vpri.org/mailman/listinfo/fonc
Re: [fonc] 90% glue code [universal language]
Take my word for it, theory comes down to Monday Night Football on ESPN. On Apr 20, 2013 10:13 PM, John Carlson yottz...@gmail.com wrote: I think that concepts in some sense transcend the universe. Are there more digits in pi than there are atoms in the universe? I guess we are asking if there are transcendental volumes which are bigger or more complex than the universe. If the universe contains the transcendental as symbols then how many transcendental symbols are there? I think you still run into Russell's Paradox. On Apr 20, 2013 9:15 PM, Simon Forman forman.si...@gmail.com wrote: On 4/20/13, John Carlson yottz...@gmail.com wrote: Do you need one symbol for the number infinity and another for denoting that a set is inifinite? Or do you just reason about the size of the set? Is there a difference between a set that is countably infinite and one that isn't countable? I barely know Russell's paradox... you're ahead of me. Well, for what it's worth, quoting from Meguire's 2007 Boundary Algebra: A Simple Notation for Boolean Algebra and the Truth Functors: Let U be the universal set, a,b∈U, and ∅ be the null set. Then the columns headed by “Sets” show how the algebra of sets and the pa are equivalent. Table 4-2. The 10 Nontrivial Binary Connectives (Functors). NameLogic Sets BA Alternation a∨b a∪b ab Conditional a→b a⊆b (a)b Converse a←b a⊇b a(b) Conjunction a∧b a∩b ((a)(b)) ___ NOR a↓b a∪b (ab) ___ Sheffer stroke a|b a∩b (a)(b) Biconditionala↔b a⊆b⊆a (((a)b)(a(b))) -or- ((a)(b))(ab) (Apologies if the Unicode characters got mangled!) Check out http://www.markability.net/sets.htm also. I don't know much about set theory but I think the Universal set stands for the set of everything, no? Cheers, ~Simon The history of mankind for the last four centuries is rather like that of an imprisoned sleeper, stirring clumsily and uneasily while the prison that restrains and shelters him catches fire, not waking but incorporating the crackling and warmth of the fire with ancient and incongruous dreams, than like that of a man consciously awake to danger and opportunity. --H. P. Wells, A Short History of the World ___ fonc mailing list fonc@vpri.org http://vpri.org/mailman/listinfo/fonc ___ fonc mailing list fonc@vpri.org http://vpri.org/mailman/listinfo/fonc
