Why Has None of Computer Science been Formalized?
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From: Chris Menzel on 19 Sep 2006 13:33 On 19 Sep 2006 09:23:35 -0700, Steven Zenith <stevenzenith(a)gmail.com> said: >> > The root of 2 is not a real number, >> >> Yes it is. What do you think it is? > > The square root of 2 is an irrational number. Among mathematics, the real numbers include the irrationals (indeed, it is exactly those that distinguish the reals from the rationals).
From: Charlie-Boo on 19 Sep 2006 13:41 Steven Zenith wrote: > Charlie-Boo wrote: > > > You have the time to write about 10 pages of claims, but not enough > > time to write 1/2 page giving the formalization of some results to > > prove your claims? I see. > > I am working from memory and referring you to the references. If CSP > (the basis of the Roscoe reference) is not a formalization of > concurrency and communication (a branch of computer science) then > please explain to me why you consider it inadequate. I'd be genuinely > interested to hear your account. What are some of the theorems from that branch of CS? Which of these theorems does CSP formally generate? > Your references to problems in CS - such as the halting problem - are > straight forward enough. Any good formalism should be able to represent > them, should they not? Yes. And who has given a formal derivation of that and the other theorems? > Please provide a reference to CBL, I'll take a look at it. http://www.arxiv.org/html/cs.lo/0003071 This also answers the previous question. Thanks for the interest. C-B > With respect, > Steven
From: Charlie-Boo on 19 Sep 2006 15:05 Steven Zenith wrote: > Charlie-Boo wrote: > > Functions don't terminate. Programs terminate (or not.) Functions are > > defined (or not.) > > This is semantics only. A defined function that has no instance is > meaningless. What do you mean by a "defined function" - a function plus input on which it is defined? What do you mean by not having an instance? > > > The root of 2 is not a real number, > > > > Yes it is. What do you think it is? > > The square root of 2 is an irrational number. Aren't irrational numbers real numbers? > > > so in most languages direct use of the number would formally > > > produce a type error, > > > > How can you "use the number in most languages"? How would that work, > > exactly? > > Well, since the type of root 2 is irrational type and the expression is > likely a floating point type then in strictly typed languages you would > get a typing error, while in non-strict languages you would not. How do I "use the square root of 2 in a language"? Any numeric expression in a language is either a rational number or a symbolic representation of an irrational number. Each is appropriate for its language. > > > I did then observe that even if we picked a number of decimal points, > > > either implicitly or explicitly, there was no guarantee that the value > > > could be computed on any computer > > > > No, all computers have the same computing power. > > Not in practice. Also, architectures vary giving vector machines, for > example, different characteristics from non-vector machines. You are not talking about Computer Science. (Funny you should say that about me!) Sorry, this is all too much for me. If you'd like to look at my ARXIV paper, then I'd appreciate it. Otherwise, this jumbled discussion of mathematics, computer science, and electrical engineering (replete with errors) is hopeless. C-B > With respect, > Steven > -- > Dr. Steven Ericsson-Zenith > IASE, Sunnyvale, California
From: Steven Zenith on 19 Sep 2006 21:02 Chris Menzel wrote: > On 19 Sep 2006 09:23:35 -0700, Steven Zenith <stevenzenith(a)gmail.com> said: > >> > The root of 2 is not a real number, > >> > >> Yes it is. What do you think it is? > > > > The square root of 2 is an irrational number. > > Among mathematics, the real numbers include the irrationals (indeed, it > is exactly those that distinguish the reals from the rationals). Of course, I stand corrected. I spend so much time with the irrationals that I forgot they are classifiable as infinite reals. So I guess my type error claim fails, and that would indeed account for the classification. With respect, Steven
From: Steven Zenith on 19 Sep 2006 21:23
Charlie-Boo wrote: > Steven Zenith wrote: > > Charlie-Boo wrote: > > > > Functions don't terminate. Programs terminate (or not.) Functions are > > > defined (or not.) > > > > This is semantics only. A defined function that has no instance is > > meaningless. > > What do you mean by a "defined function" - a function plus input on > which it is defined? What do you mean by not having an instance? There is a distinction, is there not, between the definition of a function and its use? > > > > > The root of 2 is not a real number, > > > > > > Yes it is. What do you think it is? > > > > The square root of 2 is an irrational number. > > Aren't irrational numbers real numbers? My mistake. I forgot that irrationals are in fact classified as infinite reals - hence my typing error - that's what come from working in isolation :-). I am sure that the typing issue is exactly the reason for the classification - which is really unsatisfactory, but that is an issue for another day. > > > > so in most languages direct use of the number would formally > > > > produce a type error, > > > > > > How can you "use the number in most languages"? How would that work, > > > exactly? > > > > Well, since the type of root 2 is irrational type and the expression is > > likely a floating point type then in strictly typed languages you would > > get a typing error, while in non-strict languages you would not. > > How do I "use the square root of 2 in a language"? Any numeric > expression in a language is either a rational number or a symbolic > representation of an irrational number. Each is appropriate for its > language. That symbolic representation has to be converted to an approximate value at some point if it is to be used in a calculation. My claim of a typing error is bogus in any case. With respect, Steven |