I mean antecedent of the Newton and Leibniz.tano-urayoan wrote:Are you sure about your references that indicate that Pascal almost invented calculus? Which by the way is different from your previous remark: "Newton, Leibniz and Pascal all simultaneously invented calculus"(which is already false as Pascal precedes the other 2) If that is the case We should include Archimedes, Fermat and others also.User923005 wrote:It is well known that Pascal "almost" invented calculus. See, for instance:
Authorship eternal
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tano-urayoan
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Re: Authorship eternal
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User923005
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Re: Authorship eternal
The intention of my posting was not made clear at all, which is of course entirely my fault and due to poor communication skills.
The point which I was badly trying to make is that technical achievements arrive at a particular point in time because all of the necessary precursors are completed.
If you examine Pascal's work on sums of powers, you will find that he is doing calculus for the special case of polynomials only. He did something similar for the sine function. Of course that is not at all like the general case composed by Newton and Leibniz but those came a bit later after even more information had built up.
If Newton and Leibniz had not invented the calculus during that time frame, someone else would have done so within 100 years. (The only reason I gave such a large span is that both Leibniz and Newton were prodigal genius figures and so it might take someone else a lot longer to put 2 and 2 together).
In a similar way, during WWII, the US, Japan, and Germany were all working on the atomic bomb. It is not a coincidence that all 3 were making an effort because the necessary information was present. Jet propulsion was also developed independently in several places.
All technical or scientific disciplines move forward by sharing and compounding of information. Since information is now expanding exponentially, I expect all scientific and technical areas to also move ahead exponentially.
I hope that the point I was attempting to make is clear now.
The point which I was badly trying to make is that technical achievements arrive at a particular point in time because all of the necessary precursors are completed.
If you examine Pascal's work on sums of powers, you will find that he is doing calculus for the special case of polynomials only. He did something similar for the sine function. Of course that is not at all like the general case composed by Newton and Leibniz but those came a bit later after even more information had built up.
If Newton and Leibniz had not invented the calculus during that time frame, someone else would have done so within 100 years. (The only reason I gave such a large span is that both Leibniz and Newton were prodigal genius figures and so it might take someone else a lot longer to put 2 and 2 together).
In a similar way, during WWII, the US, Japan, and Germany were all working on the atomic bomb. It is not a coincidence that all 3 were making an effort because the necessary information was present. Jet propulsion was also developed independently in several places.
All technical or scientific disciplines move forward by sharing and compounding of information. Since information is now expanding exponentially, I expect all scientific and technical areas to also move ahead exponentially.
I hope that the point I was attempting to make is clear now.
Re: Authorship eternal
Yes, other examples: The telephone was invented simultaneously by Elisha Gray and Alexander Graham Bell. The modular synthesizer was invented simultaneously by Don Buchla and Robert Moog.
These are "same year simultaneous" so the 100 years span for independent invention by someone else seems very plausible.
These are "same year simultaneous" so the 100 years span for independent invention by someone else seems very plausible.