Joys and virtues of obsolete technologies
Transcript of Joys and virtues of obsolete technologies
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Joys and virtues of obsolete technologies
Steven F. Bellenot
Department of MathematicsFlorida State University
Math Tech, Valdosta State University, Valdosta, GA, Feb 23,2007
Steven F. Bellenot Joys and virtues of obsolete technologies
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Obsolete
Definition:1 No longer produced; out of date.2 Biology Less developed (formly or related species);
rudimentary; vestigial.
I just bought a computer and now it is obsolete.The dinosaurs disappeared from the historical record.This antique is valuable because they stopped makingthem.Vestigial organs like the appendix.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 3: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/3.jpg)
Obsolete
Definition:1 No longer produced; out of date.2 Biology Less developed (formly or related species);
rudimentary; vestigial.
I just bought a computer and now it is obsolete.The dinosaurs disappeared from the historical record.This antique is valuable because they stopped makingthem.Vestigial organs like the appendix.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 4: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/4.jpg)
Obsolete
Definition:1 No longer produced; out of date.2 Biology Less developed (formly or related species);
rudimentary; vestigial.
I just bought a computer and now it is obsolete.The dinosaurs disappeared from the historical record.This antique is valuable because they stopped makingthem.Vestigial organs like the appendix.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 5: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/5.jpg)
Obsolete
Definition:1 No longer produced; out of date.2 Biology Less developed (formly or related species);
rudimentary; vestigial.
I just bought a computer and now it is obsolete.The dinosaurs disappeared from the historical record.This antique is valuable because they stopped makingthem.Vestigial organs like the appendix.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 6: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/6.jpg)
Obsolete
Definition:1 No longer produced; out of date.2 Biology Less developed (formly or related species);
rudimentary; vestigial.
I just bought a computer and now it is obsolete.The dinosaurs disappeared from the historical record.This antique is valuable because they stopped makingthem.Vestigial organs like the appendix.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 7: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/7.jpg)
Which is larger?
Which of eπ or πe is larger?
Found as the problem of math riddles book in the 1960’sPerhaps a Math Puzzle book by Martin GardnerPerhaps The Unexpected Hanging and Other MathematicalDiversions 1969.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 8: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/8.jpg)
Which is larger?
Which of eπ or πe is larger?
Found as the problem of math riddles book in the 1960’sPerhaps a Math Puzzle book by Martin GardnerPerhaps The Unexpected Hanging and Other MathematicalDiversions 1969.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 9: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/9.jpg)
Which is larger?
Which of eπ or πe is larger?
Found as the problem of math riddles book in the 1960’sPerhaps a Math Puzzle book by Martin GardnerPerhaps The Unexpected Hanging and Other MathematicalDiversions 1969.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 10: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/10.jpg)
Which is larger?
Which of eπ or πe is larger?
Found as the problem of math riddles book in the 1960’sPerhaps a Math Puzzle book by Martin GardnerPerhaps The Unexpected Hanging and Other MathematicalDiversions 1969.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 11: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/11.jpg)
Log-Log Duplex Deci-Trig
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 12: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/12.jpg)
Slide Rule
invented by Oughtred in 1622 just a few years afterlogarithms.Mannheim (1851) Modern slide rule with A, B, C and Dscales.Made the trip to the moon with Apollo.essentually disappeared in 1970’s when all the slide rulemanufactors silently quit, perhaps in response to the HP35.now a collectors item.variations in size, circular, with microscope.Over 40 million produced.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 13: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/13.jpg)
Slide Rule
invented by Oughtred in 1622 just a few years afterlogarithms.Mannheim (1851) Modern slide rule with A, B, C and Dscales.Made the trip to the moon with Apollo.essentually disappeared in 1970’s when all the slide rulemanufactors silently quit, perhaps in response to the HP35.now a collectors item.variations in size, circular, with microscope.Over 40 million produced.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 14: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/14.jpg)
Slide Rule
invented by Oughtred in 1622 just a few years afterlogarithms.Mannheim (1851) Modern slide rule with A, B, C and Dscales.Made the trip to the moon with Apollo.essentually disappeared in 1970’s when all the slide rulemanufactors silently quit, perhaps in response to the HP35.now a collectors item.variations in size, circular, with microscope.Over 40 million produced.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 15: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/15.jpg)
Slide Rule
invented by Oughtred in 1622 just a few years afterlogarithms.Mannheim (1851) Modern slide rule with A, B, C and Dscales.Made the trip to the moon with Apollo.essentually disappeared in 1970’s when all the slide rulemanufactors silently quit, perhaps in response to the HP35.now a collectors item.variations in size, circular, with microscope.Over 40 million produced.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 16: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/16.jpg)
Slide Rule
invented by Oughtred in 1622 just a few years afterlogarithms.Mannheim (1851) Modern slide rule with A, B, C and Dscales.Made the trip to the moon with Apollo.essentually disappeared in 1970’s when all the slide rulemanufactors silently quit, perhaps in response to the HP35.now a collectors item.variations in size, circular, with microscope.Over 40 million produced.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 17: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/17.jpg)
Slide Rule
invented by Oughtred in 1622 just a few years afterlogarithms.Mannheim (1851) Modern slide rule with A, B, C and Dscales.Made the trip to the moon with Apollo.essentually disappeared in 1970’s when all the slide rulemanufactors silently quit, perhaps in response to the HP35.now a collectors item.variations in size, circular, with microscope.Over 40 million produced.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 18: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/18.jpg)
Slide Rule
invented by Oughtred in 1622 just a few years afterlogarithms.Mannheim (1851) Modern slide rule with A, B, C and Dscales.Made the trip to the moon with Apollo.essentually disappeared in 1970’s when all the slide rulemanufactors silently quit, perhaps in response to the HP35.now a collectors item.variations in size, circular, with microscope.Over 40 million produced.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 19: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/19.jpg)
Virtues of the Slide Rule
Scientific notation, estimation, no batteries required.Develops analog reading abilities. (Gauges, dials)Parallel computing.Wonderfull applicaton of Logs. Intermediate valuetheorem.Intermediate results were stored.Stable design:
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 20: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/20.jpg)
Virtues of the Slide Rule
Scientific notation, estimation, no batteries required.Develops analog reading abilities. (Gauges, dials)Parallel computing.Wonderfull applicaton of Logs. Intermediate valuetheorem.Intermediate results were stored.Stable design:
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 21: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/21.jpg)
Virtues of the Slide Rule
Scientific notation, estimation, no batteries required.Develops analog reading abilities. (Gauges, dials)Parallel computing.Wonderfull applicaton of Logs. Intermediate valuetheorem.Intermediate results were stored.Stable design:
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 22: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/22.jpg)
Virtues of the Slide Rule
Scientific notation, estimation, no batteries required.Develops analog reading abilities. (Gauges, dials)Parallel computing.Wonderfull applicaton of Logs. Intermediate valuetheorem.Intermediate results were stored.Stable design:
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 23: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/23.jpg)
Virtues of the Slide Rule
Scientific notation, estimation, no batteries required.Develops analog reading abilities. (Gauges, dials)Parallel computing.Wonderfull applicaton of Logs. Intermediate valuetheorem.Intermediate results were stored.Stable design:
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 24: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/24.jpg)
Virtues of the Slide Rule
Scientific notation, estimation, no batteries required.Develops analog reading abilities. (Gauges, dials)Parallel computing.Wonderfull applicaton of Logs. Intermediate valuetheorem.Intermediate results were stored.Stable design:
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 25: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/25.jpg)
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 26: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/26.jpg)
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 27: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/27.jpg)
Slide Rule Scales
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 28: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/28.jpg)
Logarithm Tables
Napier’s Bones 1617Doubled the life of astronomers.Great application of the laws of exponents.Linear interpolationTable lookup also used for trig, factors, integrals, Laplacetransforms . . .Which is larger log log π + log e or log log e + log π?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 29: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/29.jpg)
Logarithm Tables
Napier’s Bones 1617Doubled the life of astronomers.Great application of the laws of exponents.Linear interpolationTable lookup also used for trig, factors, integrals, Laplacetransforms . . .Which is larger log log π + log e or log log e + log π?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 30: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/30.jpg)
Logarithm Tables
Napier’s Bones 1617Doubled the life of astronomers.Great application of the laws of exponents.Linear interpolationTable lookup also used for trig, factors, integrals, Laplacetransforms . . .Which is larger log log π + log e or log log e + log π?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 31: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/31.jpg)
Logarithm Tables
Napier’s Bones 1617Doubled the life of astronomers.Great application of the laws of exponents.Linear interpolationTable lookup also used for trig, factors, integrals, Laplacetransforms . . .Which is larger log log π + log e or log log e + log π?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 32: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/32.jpg)
Logarithm Tables
Napier’s Bones 1617Doubled the life of astronomers.Great application of the laws of exponents.Linear interpolationTable lookup also used for trig, factors, integrals, Laplacetransforms . . .Which is larger log log π + log e or log log e + log π?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 33: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/33.jpg)
Logarithm Tables
Napier’s Bones 1617Doubled the life of astronomers.Great application of the laws of exponents.Linear interpolationTable lookup also used for trig, factors, integrals, Laplacetransforms . . .Which is larger log log π + log e or log log e + log π?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 34: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/34.jpg)
Math Wars
Math wars was roughly speaking a term used over the battleover pencil and paper calculation vs calculators.
Which was the correct way to introduce elementary agechildren to arithmetic. (US education 1990’s)Which is the correct way to do arithmetic. (Algorists vsAbacists, the 400 years war)
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 35: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/35.jpg)
Math Wars
Math wars was roughly speaking a term used over the battleover pencil and paper calculation vs calculators.
Which was the correct way to introduce elementary agechildren to arithmetic. (US education 1990’s)Which is the correct way to do arithmetic. (Algorists vsAbacists, the 400 years war)
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 36: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/36.jpg)
Math Wars
Math wars was roughly speaking a term used over the battleover pencil and paper calculation vs calculators.
Which was the correct way to introduce elementary agechildren to arithmetic. (US education 1990’s)Which is the correct way to do arithmetic. (Algorists vsAbacists, the 400 years war)
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 37: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/37.jpg)
400 Years War
From roughly 1100 to 1500 there was a battle between:
Abacists Use Roman numerals along with the abacus.Algorists Use Hindu-Arabic numerals along with the appropiatealgorithms for calculation.
Highlight: Florence 1299 forbid the use of the new numbers infinancial procedures.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 38: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/38.jpg)
400 Years War
From roughly 1100 to 1500 there was a battle between:
Abacists Use Roman numerals along with the abacus.Algorists Use Hindu-Arabic numerals along with the appropiatealgorithms for calculation.
Highlight: Florence 1299 forbid the use of the new numbers infinancial procedures.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 39: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/39.jpg)
400 Years War
From roughly 1100 to 1500 there was a battle between:
Abacists Use Roman numerals along with the abacus.Algorists Use Hindu-Arabic numerals along with the appropiatealgorithms for calculation.
Highlight: Florence 1299 forbid the use of the new numbers infinancial procedures.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 40: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/40.jpg)
400 Years War
From roughly 1100 to 1500 there was a battle between:
Abacists Use Roman numerals along with the abacus.Algorists Use Hindu-Arabic numerals along with the appropiatealgorithms for calculation.
Highlight: Florence 1299 forbid the use of the new numbers infinancial procedures.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 41: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/41.jpg)
Roman Numerals
Letter stand for values: I for 1, V for 5, X for 10, L for 50, Cfor 100, D for 500, M for 1000.Arranged in decreasing size. (MCV and not CVM)Letters are repeated for missing values: III for 3, XX for 20,etcSometimes shorthands: IV for 4, CM for 900.Other extensions.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 42: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/42.jpg)
Roman Numerals
Letter stand for values: I for 1, V for 5, X for 10, L for 50, Cfor 100, D for 500, M for 1000.Arranged in decreasing size. (MCV and not CVM)Letters are repeated for missing values: III for 3, XX for 20,etcSometimes shorthands: IV for 4, CM for 900.Other extensions.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 43: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/43.jpg)
Roman Numerals
Letter stand for values: I for 1, V for 5, X for 10, L for 50, Cfor 100, D for 500, M for 1000.Arranged in decreasing size. (MCV and not CVM)Letters are repeated for missing values: III for 3, XX for 20,etcSometimes shorthands: IV for 4, CM for 900.Other extensions.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 44: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/44.jpg)
Roman Numerals
Letter stand for values: I for 1, V for 5, X for 10, L for 50, Cfor 100, D for 500, M for 1000.Arranged in decreasing size. (MCV and not CVM)Letters are repeated for missing values: III for 3, XX for 20,etcSometimes shorthands: IV for 4, CM for 900.Other extensions.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 45: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/45.jpg)
Roman Numerals
Letter stand for values: I for 1, V for 5, X for 10, L for 50, Cfor 100, D for 500, M for 1000.Arranged in decreasing size. (MCV and not CVM)Letters are repeated for missing values: III for 3, XX for 20,etcSometimes shorthands: IV for 4, CM for 900.Other extensions.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 46: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/46.jpg)
Virtues of Roman Numerals
Forced one to use an abacus (matched too)Much harder to alter entries (try changing an id’s XVIII toXXI)numeral vs numberLook important? Use on clocks and movie copyright dates.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 47: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/47.jpg)
Virtues of Roman Numerals
Forced one to use an abacus (matched too)Much harder to alter entries (try changing an id’s XVIII toXXI)numeral vs numberLook important? Use on clocks and movie copyright dates.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 48: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/48.jpg)
Virtues of Roman Numerals
Forced one to use an abacus (matched too)Much harder to alter entries (try changing an id’s XVIII toXXI)numeral vs numberLook important? Use on clocks and movie copyright dates.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 49: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/49.jpg)
Virtues of Roman Numerals
Forced one to use an abacus (matched too)Much harder to alter entries (try changing an id’s XVIII toXXI)numeral vs numberLook important? Use on clocks and movie copyright dates.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 50: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/50.jpg)
Virtues of Roman Numerals
Forced one to use an abacus (matched too)Much harder to alter entries (try changing an id’s XVIII toXXI)numeral vs numberLook important? Use on clocks and movie copyright dates.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 51: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/51.jpg)
Virtues of Abacus
Counting table ancestor: some lines in the sand and somestones to count with. Indeed calculate comes from calculuswhich is latin for stone. Abacus comes from the greekabax, table covered with sand or fine dustpositional representation. (1950’s netherlands used themin education)paperless office (paper wasn’t cheap in dark ages)add, subtract, multiply, divide
There is a on-line book on how to use the abacushttp://www.tux.org/ bagleyd/takashikojima1.pdf
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 52: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/52.jpg)
Virtues of Abacus
Counting table ancestor: some lines in the sand and somestones to count with. Indeed calculate comes from calculuswhich is latin for stone. Abacus comes from the greekabax, table covered with sand or fine dustpositional representation. (1950’s netherlands used themin education)paperless office (paper wasn’t cheap in dark ages)add, subtract, multiply, divide
There is a on-line book on how to use the abacushttp://www.tux.org/ bagleyd/takashikojima1.pdf
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 53: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/53.jpg)
Virtues of Abacus
Counting table ancestor: some lines in the sand and somestones to count with. Indeed calculate comes from calculuswhich is latin for stone. Abacus comes from the greekabax, table covered with sand or fine dustpositional representation. (1950’s netherlands used themin education)paperless office (paper wasn’t cheap in dark ages)add, subtract, multiply, divide
There is a on-line book on how to use the abacushttp://www.tux.org/ bagleyd/takashikojima1.pdf
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 54: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/54.jpg)
Virtues of Abacus
Counting table ancestor: some lines in the sand and somestones to count with. Indeed calculate comes from calculuswhich is latin for stone. Abacus comes from the greekabax, table covered with sand or fine dustpositional representation. (1950’s netherlands used themin education)paperless office (paper wasn’t cheap in dark ages)add, subtract, multiply, divide
There is a on-line book on how to use the abacushttp://www.tux.org/ bagleyd/takashikojima1.pdf
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 55: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/55.jpg)
Virtues of Abacus
Counting table ancestor: some lines in the sand and somestones to count with. Indeed calculate comes from calculuswhich is latin for stone. Abacus comes from the greekabax, table covered with sand or fine dustpositional representation. (1950’s netherlands used themin education)paperless office (paper wasn’t cheap in dark ages)add, subtract, multiply, divide
There is a on-line book on how to use the abacushttp://www.tux.org/ bagleyd/takashikojima1.pdf
Steven F. Bellenot Joys and virtues of obsolete technologies
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Steven F. Bellenot Joys and virtues of obsolete technologies
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Euler turns 300
Euler didn’t have the technology to prove his analytical resultswith the same rigor required by today’s standards. Or he livedbefore Cauchy invented ε-δ technology.
The Basel problem S =∑
n−2 =? was first donenumerically.Euler knew π = 3.141592653589793238 . . .
Euler computed S = 1.6449340668482264364 . . .
Euler came up with an agruement that S = π2/6 and thenumbers above proved it. (It is better than the currentexperiments of quantum mechanics)Euler eventually answered all the weaknesses of hisagruement, — some many years later.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 58: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/58.jpg)
Euler turns 300
Euler didn’t have the technology to prove his analytical resultswith the same rigor required by today’s standards. Or he livedbefore Cauchy invented ε-δ technology.
The Basel problem S =∑
n−2 =? was first donenumerically.Euler knew π = 3.141592653589793238 . . .
Euler computed S = 1.6449340668482264364 . . .
Euler came up with an agruement that S = π2/6 and thenumbers above proved it. (It is better than the currentexperiments of quantum mechanics)Euler eventually answered all the weaknesses of hisagruement, — some many years later.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 59: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/59.jpg)
Euler turns 300
Euler didn’t have the technology to prove his analytical resultswith the same rigor required by today’s standards. Or he livedbefore Cauchy invented ε-δ technology.
The Basel problem S =∑
n−2 =? was first donenumerically.Euler knew π = 3.141592653589793238 . . .
Euler computed S = 1.6449340668482264364 . . .
Euler came up with an agruement that S = π2/6 and thenumbers above proved it. (It is better than the currentexperiments of quantum mechanics)Euler eventually answered all the weaknesses of hisagruement, — some many years later.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 60: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/60.jpg)
Euler turns 300
Euler didn’t have the technology to prove his analytical resultswith the same rigor required by today’s standards. Or he livedbefore Cauchy invented ε-δ technology.
The Basel problem S =∑
n−2 =? was first donenumerically.Euler knew π = 3.141592653589793238 . . .
Euler computed S = 1.6449340668482264364 . . .
Euler came up with an agruement that S = π2/6 and thenumbers above proved it. (It is better than the currentexperiments of quantum mechanics)Euler eventually answered all the weaknesses of hisagruement, — some many years later.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 61: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/61.jpg)
Euler turns 300
Euler didn’t have the technology to prove his analytical resultswith the same rigor required by today’s standards. Or he livedbefore Cauchy invented ε-δ technology.
The Basel problem S =∑
n−2 =? was first donenumerically.Euler knew π = 3.141592653589793238 . . .
Euler computed S = 1.6449340668482264364 . . .
Euler came up with an agruement that S = π2/6 and thenumbers above proved it. (It is better than the currentexperiments of quantum mechanics)Euler eventually answered all the weaknesses of hisagruement, — some many years later.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 62: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/62.jpg)
Euler turns 300
Euler didn’t have the technology to prove his analytical resultswith the same rigor required by today’s standards. Or he livedbefore Cauchy invented ε-δ technology.
The Basel problem S =∑
n−2 =? was first donenumerically.Euler knew π = 3.141592653589793238 . . .
Euler computed S = 1.6449340668482264364 . . .
Euler came up with an agruement that S = π2/6 and thenumbers above proved it. (It is better than the currentexperiments of quantum mechanics)Euler eventually answered all the weaknesses of hisagruement, — some many years later.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 63: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/63.jpg)
Summing ζ(2)
Integral test∑∞
N+1 n−2 ≤∫∞
N x−2 dx = 1N , Euler needed to
sum 1019 terms.The Euler-MacClaurin formula.Accelerating series convergence, Euler transformationx = y/(1− y) maps y = 1/2 to x = 1.Is this like turing completeness? Namely the fastestcomputer can’t do anything a turing machine can do, norany faster mod polynomial time.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 64: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/64.jpg)
Summing ζ(2)
Integral test∑∞
N+1 n−2 ≤∫∞
N x−2 dx = 1N , Euler needed to
sum 1019 terms.The Euler-MacClaurin formula.Accelerating series convergence, Euler transformationx = y/(1− y) maps y = 1/2 to x = 1.Is this like turing completeness? Namely the fastestcomputer can’t do anything a turing machine can do, norany faster mod polynomial time.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 65: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/65.jpg)
Summing ζ(2)
Integral test∑∞
N+1 n−2 ≤∫∞
N x−2 dx = 1N , Euler needed to
sum 1019 terms.The Euler-MacClaurin formula.Accelerating series convergence, Euler transformationx = y/(1− y) maps y = 1/2 to x = 1.Is this like turing completeness? Namely the fastestcomputer can’t do anything a turing machine can do, norany faster mod polynomial time.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 66: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/66.jpg)
Summing ζ(2)
Integral test∑∞
N+1 n−2 ≤∫∞
N x−2 dx = 1N , Euler needed to
sum 1019 terms.The Euler-MacClaurin formula.Accelerating series convergence, Euler transformationx = y/(1− y) maps y = 1/2 to x = 1.Is this like turing completeness? Namely the fastestcomputer can’t do anything a turing machine can do, norany faster mod polynomial time.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 67: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/67.jpg)
Divergent Series
Abel on divergent series (1828):. . . Divergent series are in general the work of the devil and it isshameful to base any demonstration whatever on them . . . Forthe most part the results are valid, it is true, but it is a curiousthing. I am looking for a reason and it is a very interestingproblem.Modern theory starts with Frobenius(1880).A good source isHardy’s book (1948) [Now printed by AMS (1992).]
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 68: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/68.jpg)
Divergent Series
Abel on divergent series (1828):. . . Divergent series are in general the work of the devil and it isshameful to base any demonstration whatever on them . . . Forthe most part the results are valid, it is true, but it is a curiousthing. I am looking for a reason and it is a very interestingproblem.Modern theory starts with Frobenius(1880).A good source isHardy’s book (1948) [Now printed by AMS (1992).]
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 69: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/69.jpg)
Divergent Series
Abel on divergent series (1828):. . . Divergent series are in general the work of the devil and it isshameful to base any demonstration whatever on them . . . Forthe most part the results are valid, it is true, but it is a curiousthing. I am looking for a reason and it is a very interestingproblem.Modern theory starts with Frobenius(1880).A good source isHardy’s book (1948) [Now printed by AMS (1992).]
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 70: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/70.jpg)
Divergent Series
Abel on divergent series (1828):. . . Divergent series are in general the work of the devil and it isshameful to base any demonstration whatever on them . . . Forthe most part the results are valid, it is true, but it is a curiousthing. I am looking for a reason and it is a very interestingproblem.Modern theory starts with Frobenius(1880).A good source isHardy’s book (1948) [Now printed by AMS (1992).]
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 71: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/71.jpg)
Human Calculators – Idiot Savant Dase
A person who is mentally handicapped (or otherwise isordinary) but displays brilliance in one area, especially oneinvolving memory.
Computed π to 200 digitsHired by Gauss (first person to buy computer time?) tofactor the intergers from X to Y.
Steven F. Bellenot Joys and virtues of obsolete technologies
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Human Calculators – Idiot Savant Dase
A person who is mentally handicapped (or otherwise isordinary) but displays brilliance in one area, especially oneinvolving memory.
Computed π to 200 digitsHired by Gauss (first person to buy computer time?) tofactor the intergers from X to Y.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 73: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/73.jpg)
Human Calculators – Idiot Savant Dase
A person who is mentally handicapped (or otherwise isordinary) but displays brilliance in one area, especially oneinvolving memory.
Computed π to 200 digitsHired by Gauss (first person to buy computer time?) tofactor the intergers from X to Y.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 74: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/74.jpg)
Human Calculators – WW2
Calculator was a job title during World War II. Often female, shewould do calculations for the military.
Steven F. Bellenot Joys and virtues of obsolete technologies
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Slide Rule in High School Education circa 1964
Taught in Chemistry class. Along with scientific notation,the ideal gas laws and molarity calculations.Getting the decimal point correct. (Estimation.)Percentage error, significant digits.Low cost items, roughly $3 ($15-$20 in current money)No S or T scales, so the technology wasn’t used inTrigonometry class. (Most Trig students had already takenChemistry.) Trigonometry classes used tables of trig andlog functions.Drawing and reading graphs.
Steven F. Bellenot Joys and virtues of obsolete technologies
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Slide Rule in High School Education circa 1964
Taught in Chemistry class. Along with scientific notation,the ideal gas laws and molarity calculations.Getting the decimal point correct. (Estimation.)Percentage error, significant digits.Low cost items, roughly $3 ($15-$20 in current money)No S or T scales, so the technology wasn’t used inTrigonometry class. (Most Trig students had already takenChemistry.) Trigonometry classes used tables of trig andlog functions.Drawing and reading graphs.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 77: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/77.jpg)
Slide Rule in High School Education circa 1964
Taught in Chemistry class. Along with scientific notation,the ideal gas laws and molarity calculations.Getting the decimal point correct. (Estimation.)Percentage error, significant digits.Low cost items, roughly $3 ($15-$20 in current money)No S or T scales, so the technology wasn’t used inTrigonometry class. (Most Trig students had already takenChemistry.) Trigonometry classes used tables of trig andlog functions.Drawing and reading graphs.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 78: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/78.jpg)
Slide Rule in High School Education circa 1964
Taught in Chemistry class. Along with scientific notation,the ideal gas laws and molarity calculations.Getting the decimal point correct. (Estimation.)Percentage error, significant digits.Low cost items, roughly $3 ($15-$20 in current money)No S or T scales, so the technology wasn’t used inTrigonometry class. (Most Trig students had already takenChemistry.) Trigonometry classes used tables of trig andlog functions.Drawing and reading graphs.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 79: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/79.jpg)
Slide Rule in High School Education circa 1964
Taught in Chemistry class. Along with scientific notation,the ideal gas laws and molarity calculations.Getting the decimal point correct. (Estimation.)Percentage error, significant digits.Low cost items, roughly $3 ($15-$20 in current money)No S or T scales, so the technology wasn’t used inTrigonometry class. (Most Trig students had already takenChemistry.) Trigonometry classes used tables of trig andlog functions.Drawing and reading graphs.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 80: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/80.jpg)
Slide Rule in High School Education circa 1964
Taught in Chemistry class. Along with scientific notation,the ideal gas laws and molarity calculations.Getting the decimal point correct. (Estimation.)Percentage error, significant digits.Low cost items, roughly $3 ($15-$20 in current money)No S or T scales, so the technology wasn’t used inTrigonometry class. (Most Trig students had already takenChemistry.) Trigonometry classes used tables of trig andlog functions.Drawing and reading graphs.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 81: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/81.jpg)
Slide Rule in High School Education circa 1964
Taught in Chemistry class. Along with scientific notation,the ideal gas laws and molarity calculations.Getting the decimal point correct. (Estimation.)Percentage error, significant digits.Low cost items, roughly $3 ($15-$20 in current money)No S or T scales, so the technology wasn’t used inTrigonometry class. (Most Trig students had already takenChemistry.) Trigonometry classes used tables of trig andlog functions.Drawing and reading graphs.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 82: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/82.jpg)
Success of the Calculus Reform
The rule of four:
Graphs to replace reading scales (gauges)(Numerically) Tables to replace using log/trig tablesVerbally to replace what?Formulas to replace what?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 83: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/83.jpg)
Success of the Calculus Reform
The rule of four:
Graphs to replace reading scales (gauges)(Numerically) Tables to replace using log/trig tablesVerbally to replace what?Formulas to replace what?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 84: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/84.jpg)
Success of the Calculus Reform
The rule of four:
Graphs to replace reading scales (gauges)(Numerically) Tables to replace using log/trig tablesVerbally to replace what?Formulas to replace what?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 85: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/85.jpg)
Success of the Calculus Reform
The rule of four:
Graphs to replace reading scales (gauges)(Numerically) Tables to replace using log/trig tablesVerbally to replace what?Formulas to replace what?
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 86: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/86.jpg)
Programing Assignment #7
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 87: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/87.jpg)
Wag the dog
Graphics Processors double in speed every 12 months (vs18 for CPUs).But they are for games, hence only single percision.Slide rules disappeared because they were a small and notvery profitable part of scientific instruments.HP quit making graphing calculators briefly. The TI-89hasn’t improved mathematically since 1999 and the priceas gone up.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 88: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/88.jpg)
Wag the dog
Graphics Processors double in speed every 12 months (vs18 for CPUs).But they are for games, hence only single percision.Slide rules disappeared because they were a small and notvery profitable part of scientific instruments.HP quit making graphing calculators briefly. The TI-89hasn’t improved mathematically since 1999 and the priceas gone up.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 89: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/89.jpg)
Wag the dog
Graphics Processors double in speed every 12 months (vs18 for CPUs).But they are for games, hence only single percision.Slide rules disappeared because they were a small and notvery profitable part of scientific instruments.HP quit making graphing calculators briefly. The TI-89hasn’t improved mathematically since 1999 and the priceas gone up.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 90: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/90.jpg)
Wag the dog
Graphics Processors double in speed every 12 months (vs18 for CPUs).But they are for games, hence only single percision.Slide rules disappeared because they were a small and notvery profitable part of scientific instruments.HP quit making graphing calculators briefly. The TI-89hasn’t improved mathematically since 1999 and the priceas gone up.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 91: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/91.jpg)
Victorian Internet
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 92: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/92.jpg)
Larger – revisited
αβ < βα ⇐⇒ β ln α < α ln β ⇐⇒ ln α
α<
ln β
β
Need to maximize f (x) = ln xx which by calculus happens when
f ′(x) = 1−ln xx2 = 0 or ln x = 1 or x = e So αe < eα for all α 6= e
including π.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 93: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/93.jpg)
Larger – revisited
αβ < βα ⇐⇒ β ln α < α ln β ⇐⇒ ln α
α<
ln β
β
Need to maximize f (x) = ln xx which by calculus happens when
f ′(x) = 1−ln xx2 = 0 or ln x = 1 or x = e So αe < eα for all α 6= e
including π.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 94: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/94.jpg)
Larger – revisited
αβ < βα ⇐⇒ β ln α < α ln β ⇐⇒ ln α
α<
ln β
β
Need to maximize f (x) = ln xx which by calculus happens when
f ′(x) = 1−ln xx2 = 0 or ln x = 1 or x = e So αe < eα for all α 6= e
including π.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 95: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/95.jpg)
eπ Wins
ln(x)/x0.368
2.71828 xSteven F. Bellenot Joys and virtues of obsolete technologies
![Page 96: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/96.jpg)
Summary
Does the history of obsolete technology give insight intothe rapid change of today’s techonology?The analog world had virtues.
Steven F. Bellenot Joys and virtues of obsolete technologies
![Page 97: Joys and virtues of obsolete technologies](https://reader031.fdocuments.in/reader031/viewer/2022020704/61fb5afa2e268c58cd5d3191/html5/thumbnails/97.jpg)
Summary
Does the history of obsolete technology give insight intothe rapid change of today’s techonology?The analog world had virtues.
Steven F. Bellenot Joys and virtues of obsolete technologies