Charles Babbage: Difference between revisions
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https://www.google.com/books/edition/Annual_Report_of_the_Board_of_Regents_of/bc4rAQAAIAAJ?hl=en&gbpv=1&pg=PA289&printsec=frontcover | https://www.google.com/books/edition/Annual_Report_of_the_Board_of_Regents_of/bc4rAQAAIAAJ?hl=en&gbpv=1&pg=PA289&printsec=frontcover | ||
== On the Economy of Machinery and Manufactures == | |||
Very easy to understand machinery simply by observing it (v) | |||
Machinery offers 3 advantages: addition to human power, economy of human time, conversation of common substances into valuable products (6) | |||
“At increase of knowledge, as well as on the contrivance of every new tool, human labour becomes abridged.” | |||
Tools used to replace hands; tools used to aid those with lost limbs, disabilities (14) | |||
Entire chapter on copying as important to a mechanical age | |||
Points out the difficulty of printing mathematical tables (59) | |||
== Ninth Bridgewater Treatise == | |||
Individuals attribute their own imperfect understandings to that of God | |||
Must base understanding in facts and arguments, not wild fancies of passion or of impulse | |||
Chapter 2 | |||
Uses example of Calculating Engine: imagine a wheel, showing a series of numbers; “how long you will have counted before you are firmly convinced that the engine has been so adjusted that it will continue whilst its motion is maintained, to produce the same series of natural numbers?” (35) | |||
But what if the law changes as 100 million, to go up by triangular numbers multipled by 10,000? And then law fails again after 2761? Etc | |||
Observer would have to change the law he deduced from observation; and the adjustment “might have been as fully foreknown as the commencement, as was the regular succession” (39) — but we don’t know the reason, except it is “a necessary consequence of the mechanical structure of the engine” (39) | |||
Imagine a second engine, wherein the laws could be changed at any time | |||
“Which of these two engines would, in the reader’s opinion, give the higher proof of skill in the contriver?” (40) — the one that needed no intervention but was designed from the start (even though we can’t thought present means of analysis understand its design) | |||
Analogy to changes in nature — there is a design created by ‘a degree of power and of knowledge of a far higher order” (46) — e.g. findings of geology | |||
Chapter 3 | |||
Before printing, “accidental position determined the opinions and the knowledge of the great mass of mankind” (52) — only oral information accessible — after printing, knowledge can accumulate, science can advance | |||
Chapter 4, 5 | |||
Geology suggests earth is millions of years old, contradicting Genesis in Bible; ample evidence from geology at this point | |||
Attempts to reconcile genesis with scientific understanding; offers historicist interpretation of Bible | |||
Chapter 6 | |||
On desire for immortality; many dashes set between paragraphs | |||
Chapter 7 | |||
Meditation on deep time | |||
Chapter 8 | |||
Miracles are not deviations from God’s law’s but “the exact fulfillment of much. More extensive laws than those we suppose to exist” (93) | |||
Example of the engine again — imagine a maker who can push a lever on the engine, and one instance in the series changes before going back to normal order | |||
Example of conical refraction and experimentation | |||
Chapter 9 | |||
Once we speak, we quickly hear the sound and then it becomes inaudible; but the movements of air caused continue to reverberate; a being that could see all movements of atoms could see “the circumstances of the future history of the whole of the earth’s atmosphere” (112) | |||
Could also look back and find the origins of chaos | |||
“Thus considered, what a strange chaos is this wide atmosphere we breathe! Every atom impressed with good and with ill, retains at once the motions which philosophers and sages have imparted to it, mixed and combined in ten thousand ways with all that is worthless and base. The air itself is one vast library, on whose pages are for ever written all that man has ever said or even whispered. There, in their mutable but unerring characters, mixed with the earliest, as well as the latest sighs of mortality, stand for ever recorded, vows unredeemed, promises unfulfilled, perpetuating in the united movements of each particle, the testimony of man’s changeful will.” (112-3) | |||
“No motion impressed by natural causes, or by human agency, is ever obliterated.” (114) | |||
Chapter 10 | |||
On Hume’s argument against miracles; using math to analyze it | |||
Chapter 11 | |||
Imagine calculating engine, can follow any algebraic law — while calculating, can also switch to any other law, then revert back | |||
Using thought experiment to argue against Hume | |||
Chapter 12 | |||
Pain of doing something wrong; knowledge creates virtue by enabling us to learn from mistakes | |||
Advocating for advances in science to know better | |||
Chapter 13 | |||
Imagine the calculating engine could change its laws, but “at a time not foreseen by the person employing the engine” (152) | |||
Chapter 14 | |||
Thoughts on the origin of evil — but a fragment saying he was unable to complete it | |||
Appendix, Note B, “On the calculating engine” | |||
== Bibliography == | == Bibliography == | ||
Latest revision as of 17:23, 21 January 2026
Timeline
1791, December 26: born
1814: graduates with BA from Cambridge
1814, July 2: marries Georgiana
1815: series of lectures on astronomy to the Royal institution
1816: elected member of the Royal Society
1819: travels with his friend John Herschel to France, meeting intellectuals; probably sees Le Tables du Cadastre of the French Ordnance Survey undertaken by Baron Gaspard de Prony; de Prony organizes 3 commitees to make and check calculations, result is logarithmic tables in 17 folio ms volumes, wanted to print them but proved to be difficult/costly (Essinger 2004, 60)
1821, Summer: Royal Astronomical Society asks Babbage and Herschel to check astronomical tables; tedious work, Babbage says: "How I wish these calculations could be executed by steam!" (Essinger 2004, 66); sets him off thinking about Difference Engine
1821-1833: working on automatic cogwheel-based machine to calculate and print mathematical tables, the Difference Engine
1822, Spring: had assembled small cogwheel mechanism, demonstrates it to Royal Astronomical Society on June 2, 1822 and open letter to Sir Humphrey Davy, president of Royal Society, July 3, 1822, second paper to Royal Astronomical Society on 13 December
1823, July 21: gov't grant of 1500 pounds
1827, February 27: father Benjamin dies, he inherits his wealth
1827, August/September: wife Georgiana dies
1832: finishes 1/7th of Difference Engine
1834, December: conceives of Analytical Engine, not just for mathematical calculations, using punched cards of Jacquard's loom; on December 15, Lady Byron writes about his excitement over discovery in her journal (ESsinger 2004, 81-2)
1839, December: writes letter to François Jean Dominique Arago requesting copy of Jacquard portrait woven by Jacquard loom and any memoirs about him (Essinger 2004, 46-7)
1840, August: leaves England for Paris then Lyons and Turin
1842, 3 November: letter from exchequer saying government was abandoning support for difference engine
1871: died
Tables of Constants in Nature and Art
On the Economy of Machinery and Manufactures
Very easy to understand machinery simply by observing it (v)
Machinery offers 3 advantages: addition to human power, economy of human time, conversation of common substances into valuable products (6)
“At increase of knowledge, as well as on the contrivance of every new tool, human labour becomes abridged.”
Tools used to replace hands; tools used to aid those with lost limbs, disabilities (14)
Entire chapter on copying as important to a mechanical age
Points out the difficulty of printing mathematical tables (59)
Ninth Bridgewater Treatise
Individuals attribute their own imperfect understandings to that of God
Must base understanding in facts and arguments, not wild fancies of passion or of impulse
Chapter 2
Uses example of Calculating Engine: imagine a wheel, showing a series of numbers; “how long you will have counted before you are firmly convinced that the engine has been so adjusted that it will continue whilst its motion is maintained, to produce the same series of natural numbers?” (35)
But what if the law changes as 100 million, to go up by triangular numbers multipled by 10,000? And then law fails again after 2761? Etc
Observer would have to change the law he deduced from observation; and the adjustment “might have been as fully foreknown as the commencement, as was the regular succession” (39) — but we don’t know the reason, except it is “a necessary consequence of the mechanical structure of the engine” (39)
Imagine a second engine, wherein the laws could be changed at any time
“Which of these two engines would, in the reader’s opinion, give the higher proof of skill in the contriver?” (40) — the one that needed no intervention but was designed from the start (even though we can’t thought present means of analysis understand its design)
Analogy to changes in nature — there is a design created by ‘a degree of power and of knowledge of a far higher order” (46) — e.g. findings of geology
Chapter 3
Before printing, “accidental position determined the opinions and the knowledge of the great mass of mankind” (52) — only oral information accessible — after printing, knowledge can accumulate, science can advance
Chapter 4, 5
Geology suggests earth is millions of years old, contradicting Genesis in Bible; ample evidence from geology at this point
Attempts to reconcile genesis with scientific understanding; offers historicist interpretation of Bible
Chapter 6
On desire for immortality; many dashes set between paragraphs
Chapter 7
Meditation on deep time
Chapter 8
Miracles are not deviations from God’s law’s but “the exact fulfillment of much. More extensive laws than those we suppose to exist” (93)
Example of the engine again — imagine a maker who can push a lever on the engine, and one instance in the series changes before going back to normal order
Example of conical refraction and experimentation
Chapter 9
Once we speak, we quickly hear the sound and then it becomes inaudible; but the movements of air caused continue to reverberate; a being that could see all movements of atoms could see “the circumstances of the future history of the whole of the earth’s atmosphere” (112)
Could also look back and find the origins of chaos
“Thus considered, what a strange chaos is this wide atmosphere we breathe! Every atom impressed with good and with ill, retains at once the motions which philosophers and sages have imparted to it, mixed and combined in ten thousand ways with all that is worthless and base. The air itself is one vast library, on whose pages are for ever written all that man has ever said or even whispered. There, in their mutable but unerring characters, mixed with the earliest, as well as the latest sighs of mortality, stand for ever recorded, vows unredeemed, promises unfulfilled, perpetuating in the united movements of each particle, the testimony of man’s changeful will.” (112-3)
“No motion impressed by natural causes, or by human agency, is ever obliterated.” (114)
Chapter 10
On Hume’s argument against miracles; using math to analyze it
Chapter 11
Imagine calculating engine, can follow any algebraic law — while calculating, can also switch to any other law, then revert back
Using thought experiment to argue against Hume
Chapter 12
Pain of doing something wrong; knowledge creates virtue by enabling us to learn from mistakes
Advocating for advances in science to know better
Chapter 13
Imagine the calculating engine could change its laws, but “at a time not foreseen by the person employing the engine” (152)
Chapter 14
Thoughts on the origin of evil — but a fragment saying he was unable to complete it
Appendix, Note B, “On the calculating engine”
Bibliography
Hacking 1990, chapter 7, discusses his interest in constants and developing the "Tables of Constants in Nature and Art"
Great paper on Ada Lovelace's computer program: https://twobithistory.org/2018/08/18/ada-lovelace-note-g.html#:~:text=She%2C%20too%2C%20wrote%20a%20program,the%20world's%20first%20computer%20program
Demo of Difference Engine: https://www.youtube.com/watch?v=BlbQsKpq3Ak