[math-fun] spigot algorithm
It seems to me, wikipedia does not really define the concept. How about you propose a better definition?
="Warren D Smith" It seems to me, wikipedia does not really define the concept. How about you propose a better definition?
I should confess that I MAY have inadvertently introduced the term "spigot" back in the late 70's. At any rate I've often used it to informally describe Gosper's continued fraction arithmetic, to convey the idea of numbers embodied as infinite streams (that is, sequences, say of continued fraction terms (or, if you insist on them, digits)), where you could just "turn on the spigot" and pour out just as much or as little precision as you desired to pay for. It was part of a metaphor describing expressions as "plumbing" connecting stream operators, in contrast to the then-conventional numerical-analysis paradigm where high precision batches of bits must be computed at each stage (often only to be thrown away downstream). Infused with enthusiasm by a draft paper of Gosper's I hacked a little spigot that "spewed" the digits of e on an Apple II to show to Steve Wozniak circa 1980. I have no idea if this colorful language somehow got loose and eventually influenced Rabinowitz and Wagon, or if it's just a coincidence. Anyway, if you want to formalize this, please have at it. I will look forward to not only "spigot" but "plumbing" and "spew" as terms of art!
Please, not spew, especially anything having to do with pi. On Mon, Dec 14, 2015 at 9:38 AM, Marc LeBrun <mlb@well.com> wrote:
="Warren D Smith" It seems to me, wikipedia does not really define the concept. How about you propose a better definition?
I should confess that I MAY have inadvertently introduced the term "spigot" back in the late 70's. At any rate I've often used it to informally describe Gosper's continued fraction arithmetic, to convey the idea of numbers embodied as infinite streams (that is, sequences, say of continued fraction terms (or, if you insist on them, digits)), where you could just "turn on the spigot" and pour out just as much or as little precision as you desired to pay for. It was part of a metaphor describing expressions as "plumbing" connecting stream operators, in contrast to the then-conventional numerical-analysis paradigm where high precision batches of bits must be computed at each stage (often only to be thrown away downstream). Infused with enthusiasm by a draft paper of Gosper's I hacked a little spigot that "spewed" the digits of e on an Apple II to show to Steve Wozniak circa 1980. I have no idea if this colorful language somehow got loose and eventually influenced Rabinowitz and Wagon, or if it's just a coincidence.
Anyway, if you want to formalize this, please have at it. I will look forward to not only "spigot" but "plumbing" and "spew" as terms of art!
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MMD!! Originalnachricht Von: Tom Rokicki Gesendet: Montag, 14. Dezember 2015 18:52 An: math-fun Antwort an: math-fun Betreff: Re: [math-fun] spigot algorithm Please, not spew, especially anything having to do with pi. On Mon, Dec 14, 2015 at 9:38 AM, Marc LeBrun <mlb@well.com> wrote:
="Warren D Smith" It seems to me, wikipedia does not really define the concept. How about you propose a better definition?
I should confess that I MAY have inadvertently introduced the term "spigot" back in the late 70's. At any rate I've often used it to informally describe Gosper's continued fraction arithmetic, to convey the idea of numbers embodied as infinite streams (that is, sequences, say of continued fraction terms (or, if you insist on them, digits)), where you could just "turn on the spigot" and pour out just as much or as little precision as you desired to pay for. It was part of a metaphor describing expressions as "plumbing" connecting stream operators, in contrast to the then-conventional numerical-analysis paradigm where high precision batches of bits must be computed at each stage (often only to be thrown away downstream). Infused with enthusiasm by a draft paper of Gosper's I hacked a little spigot that "spewed" the digits of e on an Apple II to show to Steve Wozniak circa 1980. I have no idea if this colorful language somehow got loose and eventually influenced Rabinowitz and Wagon, or if it's just a coincidence.
Anyway, if you want to formalize this, please have at it. I will look forward to not only "spigot" but "plumbing" and "spew" as terms of art!
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?? WFL On 12/14/15, Pacher Christoph <Christoph.Pacher@ait.ac.at> wrote:
MMD!!
Originalnachricht Von: Tom Rokicki Gesendet: Montag, 14. Dezember 2015 18:52 An: math-fun Antwort an: math-fun Betreff: Re: [math-fun] spigot algorithm
Please, not spew, especially anything having to do with pi.
On Mon, Dec 14, 2015 at 9:38 AM, Marc LeBrun <mlb@well.com> wrote:
="Warren D Smith" It seems to me, wikipedia does not really define the concept. How about you propose a better definition?
I should confess that I MAY have inadvertently introduced the term "spigot" back in the late 70's. At any rate I've often used it to informally describe Gosper's continued fraction arithmetic, to convey the idea of numbers embodied as infinite streams (that is, sequences, say of continued fraction terms (or, if you insist on them, digits)), where you could just "turn on the spigot" and pour out just as much or as little precision as you desired to pay for. It was part of a metaphor describing expressions as "plumbing" connecting stream operators, in contrast to the then-conventional numerical-analysis paradigm where high precision batches of bits must be computed at each stage (often only to be thrown away downstream). Infused with enthusiasm by a draft paper of Gosper's I hacked a little spigot that "spewed" the digits of e on an Apple II to show to Steve Wozniak circa 1980. I have no idea if this colorful language somehow got loose and eventually influenced Rabinowitz and Wagon, or if it's just a coincidence.
Anyway, if you want to formalize this, please have at it. I will look forward to not only "spigot" but "plumbing" and "spew" as terms of art!
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (5)
-
Fred Lunnon -
Marc LeBrun -
Pacher Christoph -
Tom Rokicki -
Warren D Smith