Who first invented calculus - Newton or Leibniz?
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From: John Stafford on 5 Jan 2010 13:13 In article <80022c43-5c39-46ea-ab95-6ed4e668e906(a)q4g2000yqm.googlegroups.com>, M Purcell <sacscale1(a)aol.com> wrote: > On Jan 4, 7:36�pm, John Stafford <n...(a)droffats.ten> wrote: > > It matters not. The Calculus was not philosophically rationalized until > > quite recently. Regardless, it was perfectly useful until then, and > > remains useful today. > > How was calculus recently philosophically rationalized? By recent, I mean after most philosophers were over dithering on the meaning of infinitesimals. The philosophers could not 'rationalize' the process, it seemed unnatural (another problem for the philosophers), but somehow calculus all worked very well regardless of objections. The first rationalization was when the Calculus turned to limits instead. I think it was the late 1800's. More recently, the 1960s's, Abraham Robinson returned to the interpretation of infinitesimal numbers apart from the philosophical, to mathematical theory - a stunning bit of reasoning, IMHO. I'm at a bit of a loss for precise description of the history - I no longer work at the university library (real bummer, but better pay here.) > > For the obsessive of the 'Inductive Reasoning' thread - eat your hearts > > out. > > I hope you realize mathematical induction is deductive. We may be hung on a technicality here. I agree that the vast majority of mathematics is inductive, but during the formulation of a thesis the mathematician might use induction to create a case to test for a proof, or as I hope I once wrote, once induction is complete then one moves to deductive reasoning. > > > Back to the subnect, it was found that Leibniz's approach was more > > useful, fewer hacks, more direct. Leibniz wins. > > Leibniz also published first, Newton's delay is suspect. I'm not as familiar with that history as I should be. Thanks for the nudge. Oh! I saw the new Sherlock Holmes movie. No deductions that I could find! I can explain but it might split the subject.
From: John Stafford on 5 Jan 2010 13:15 In article <EJI0n.9000$KM6.5993(a)newsfe02.ams2>, "Androcles" <Headmaster(a)Hogwarts.physics_r> wrote: > "Peter Webb" <webbfamily(a)DIESPAMDIEoptusnet.com.au> wrote in message > news:4b434c27$0$31487$afc38c87(a)news.optusnet.com.au... > > Liebniz basically invented the dy/dx notation, right? > > > > What was Newton's - the f '(x) notation, or something else? > > > > > "Atque ita summae motuum conspirantium 15 +1 vel 16 +0, et differentiae > contrariorum 17-1 et 18-2 semper erunt paartium sexdecim..." -- Principia. > > "And so the sums of the conspiring motions 15+1, or 16+0, and the > differences of the contrary motions 17-1 and 18-2, will always be equal to > 16 parts..." > > Notice that 16 is written as sexdecim. > > You wanna work in Latin? ego operor non disco latin Gawd, that's probably pathetic but I really wanted to get ego and disco into the same expression.
From: M Purcell on 5 Jan 2010 13:43 On Jan 5, 10:13 am, John Stafford <n...(a)droffats.net> wrote: > In article > <80022c43-5c39-46ea-ab95-6ed4e668e...(a)q4g2000yqm.googlegroups.com>, > M Purcell <sacsca...(a)aol.com> wrote: > > > On Jan 4, 7:36 pm, John Stafford <n...(a)droffats.ten> wrote: > > > It matters not. The Calculus was not philosophically rationalized until > > > quite recently. Regardless, it was perfectly useful until then, and > > > remains useful today. > > > How was calculus recently philosophically rationalized? > > By recent, I mean after most philosophers were over dithering on the > meaning of infinitesimals. The philosophers could not 'rationalize' the > process, it seemed unnatural (another problem for the philosophers), but > somehow calculus all worked very well regardless of objections. The > first rationalization was when the Calculus turned to limits instead. I > think it was the late 1800's. More recently, the 1960s's, Abraham > Robinson returned to the interpretation of infinitesimal numbers apart > from the philosophical, to mathematical theory - a stunning bit of > reasoning, IMHO. The use of limits does make calculus more understandable but physics still uses infinitesimal differences. > I'm at a bit of a loss for precise description of the history - I no > longer work at the university library (real bummer, but better pay here.) > > > > For the obsessive of the 'Inductive Reasoning' thread - eat your hearts > > > out. > > > I hope you realize mathematical induction is deductive. > > We may be hung on a technicality here. I agree that the vast majority of > mathematics is inductive, but during the formulation of a thesis the > mathematician might use induction to create a case to test for a proof, > or as I hope I once wrote, once induction is complete then one moves to > deductive reasoning. The argument: Statement S(1) is true. Statement S(n) implies Statement S(n+1). Therefore, S(n) is true for all n. has the form of a deductive argument; if the premises are true then the conclusion is true. > > > Back to the subnect, it was found that Leibniz's approach was more > > > useful, fewer hacks, more direct. Leibniz wins. > > > Leibniz also published first, Newton's delay is suspect. > > I'm not as familiar with that history as I should be. Thanks for the > nudge. > > Oh! I saw the new Sherlock Holmes movie. No deductions that I could > find! I can explain but it might split the subject. Haven't seem the movie but it is my understanding that kind of deduction is more a process of elimination, trying to find premises to fit the conclusion.
From: Androcles on 5 Jan 2010 13:41 "John Stafford" <nhoj(a)droffats.net> wrote in message news:nhoj-20D3C9.12152505012010(a)news.supernews.com... > In article <EJI0n.9000$KM6.5993(a)newsfe02.ams2>, > "Androcles" <Headmaster(a)Hogwarts.physics_r> wrote: > >> "Peter Webb" <webbfamily(a)DIESPAMDIEoptusnet.com.au> wrote in message >> news:4b434c27$0$31487$afc38c87(a)news.optusnet.com.au... >> > Liebniz basically invented the dy/dx notation, right? >> > >> > What was Newton's - the f '(x) notation, or something else? >> > >> > >> "Atque ita summae motuum conspirantium 15 +1 vel 16 +0, et differentiae >> contrariorum 17-1 et 18-2 semper erunt paartium sexdecim..." -- >> Principia. >> >> "And so the sums of the conspiring motions 15+1, or 16+0, and the >> differences of the contrary motions 17-1 and 18-2, will always be equal >> to >> 16 parts..." >> >> Notice that 16 is written as sexdecim. >> >> You wanna work in Latin? > > ego operor non disco latin > > Gawd, that's probably pathetic but I really wanted to get ego and disco > into the same expression. With Gawd getting in the way it's small wonder the Xtian Romans produced no mathematicians of the earlier Greek calibre. :-)
From: Androcles on 5 Jan 2010 13:52
"John Stafford" <nhoj(a)droffats.net> wrote in message news:nhoj-A74572.12130305012010(a)news.supernews.com... > In article > <80022c43-5c39-46ea-ab95-6ed4e668e906(a)q4g2000yqm.googlegroups.com>, > M Purcell <sacscale1(a)aol.com> wrote: > >> On Jan 4, 7:36 pm, John Stafford <n...(a)droffats.ten> wrote: >> > It matters not. The Calculus was not philosophically rationalized until >> > quite recently. Regardless, it was perfectly useful until then, and >> > remains useful today. >> >> How was calculus recently philosophically rationalized? > > By recent, I mean after most philosophers were over dithering on the > meaning of infinitesimals. The philosophers could not 'rationalize' the > process, it seemed unnatural (another problem for the philosophers), but > somehow calculus all worked very well regardless of objections. The > first rationalization was when the Calculus turned to limits instead. I > think it was the late 1800's. More recently, the 1960s's, Abraham > Robinson returned to the interpretation of infinitesimal numbers apart > from the philosophical, to mathematical theory - a stunning bit of > reasoning, IMHO. > Given f'(x) = [f(x+h)-f(x)]/h, it naturally follows that h is the smallest number greater than zero and cannot be divided. This statement deeply upset Bonehead Green who insisted h was divisible by 2 simply by writing h/2. Yet at the other end of the scale he'd be perfectly happy to turn an 8 on its side and call it infinity. > I'm at a bit of a loss for precise description of the history - I no > longer work at the university library (real bummer, but better pay here.) > > >> > For the obsessive of the 'Inductive Reasoning' thread - eat your hearts >> > out. >> >> I hope you realize mathematical induction is deductive. > > We may be hung on a technicality here. I agree that the vast majority of > mathematics is inductive, but during the formulation of a thesis the > mathematician might use induction to create a case to test for a proof, > or as I hope I once wrote, once induction is complete then one moves to > deductive reasoning. > >> >> > Back to the subnect, it was found that Leibniz's approach was more >> > useful, fewer hacks, more direct. Leibniz wins. >> >> Leibniz also published first, Newton's delay is suspect. > > I'm not as familiar with that history as I should be. Thanks for the > nudge. > > Oh! I saw the new Sherlock Holmes movie. No deductions that I could > find! I can explain but it might split the subject. |