charles babbage, ada lovelace, and the bernoulli numbers

CHARLES BABBAGE, ADA LOVELACE,

AND THE BERNOULLI NUMBERSThomas J. Misa

Charles Babbage InstituteUniversity of Minnesota

www.cbi.umn.edu | FB/BabbageInstitute

Stevens Institute of Technology: Ada Lovelace Conference 18 Oct. 2013

CHARLES BABBAGE, ADA LOVELACE, AND THE BERNOULLI NUMBERS

✤“Was Ada LoveLace first computer programmer?”

• Popular acclaim = yes !

• Scholar’s evidence ~ no

• examine: Lovelace’s ‘note G’ to 1842 Menabrea Sketch

• and: AL–CB letters

Ada Lovelace days 3/24 + 10/15

ADA LOVELACE: FIRST COMPUTER PROGRAMMER ?

•“founder of scientific computing” <www.sdsc.edu/ScienceWomen>

•“In 1842, Ada Lovelace ... wrote the first computer program” <NYT 10.15.2013>

•“the first algorithm intended to be processed by a machine ... world’s first computer programmer” <Wikipedia>

ADA LOVELACE: FIRST COMPUTER PROGRAMMER ?

• “extent of [her] intellectual contribution to Sketch ... much exaggerated” CKA (2013): 44

• “most of technical content and all of the programs” were Babbage’s CKA (2013): 44

• “[her] achievements ... not [sic] to deserve the recognition accorded” D.Stein, Ada–Life [MIT 1985] xii (CKA’s source? 1st ed. Computer = 1996)

• Cf. Fuegi and Francis, “Lovelace & Babbage . . . 1843 notes.” IEEE Annals 25#4 [2003]: 16-26.

ADA LOVELACE: FIRST COMPUTER PROGRAMMER ?

Babbage, Passages [1864]:

• “various illustrations [Sketch] ... selection entirely her own. So was the algebraic ... problems, except ...”

• ... Bernoulli numbers that CB “offered to do to save Lady Lovelace the trouble.”

• “This she sent back to me ... having detected a grave mistake which I had made....”

ADA LOVELACE: FIRST COMPUTER PROGRAMMER ?

Charles Babbage:•born 1791•Cambridge 1810-4•1822-: Difference Engine•1834-: Analytical Engine•1842: lecture in Italy ➥ Menabrea Sketch•1846-8: Difference #2•1871 died ‘irascible’

Ada Byron Lovelace:•born 1815; ‘Lady King’ 1835-; ‘Countess...’ 1838-•Mary Somerville (CB)•private math studies de Morgan: “drowning in Calculus” [11/1841]

•1843: translation of Menabrea + A-G ‘notes’•1852 died (£600 to CB)

ADA LOVELACE: FIRST COMPUTER PROGRAMMER ?

AL to CB [summer 1843] N=23:

• “I want to put in ... Bernoulli’s numbers ... how an implicit function ... worked out by the engine ... [without] human head & hands first. Give me the necessary ... formulae.” [n.d.]

• “I am doggedly attacking ... all the ways of deducing the Bernoulli Numbers.” [5 July]

• “Table & Diagram ... infinite patience & pains ... are seriously wrong.... I have done them [over] in a beautiful manner, much improved....” [Sat. 6:oo]

Toole: 198 + Stein: 107

ADA LOVELACE: STEAMPUNK MOMENT

Lovelace talks to paleontologist Mallory FRS

• “Fundamental relations in science of harmony ... are susceptible to mechanical expression....”

• “... my marshaled regiments shall ably serve the rulers of the earth. And of what materials...? Vast numbers.”

•Numbers of Bernoulli ➳

Gibson & Sterling’s Difference Engine [1991]: 94

ADA LOVELACE: FIRST COMPUTER PROGRAMMER ?

“Numbers of Bernoulli”

• sequence of ‘rational’ numbers

• Swiss mathematician Jakob Bernoulli [1713] + Japanese mathematician Seki Kowa [1712]

• Taylor series for (hyperbolic) tangentEuler-Maclaurin formula [integrals~series]

• number theory (Riemann zeta function)

ADA LOVELACE: FIRST COMPUTER PROGRAMMER ?

Lovelace’s note G to Menabrea Sketch: <www.fourmilab.ch/babbage/sketch.html>

• “steps ... engine could compute the Numbers of Bernoulli ... a rather complicated example”

• “in which B1, B3 ... are the Numbers of Bernoulli”

• expand . . . divide, derive, multiply, multiply, write general form . . . .

(8.)

ADA LOVELACE: FIRST COMPUTER PROGRAMMER ?

Lovelace’s note G to Menabrea Sketch: <www.fourmilab.ch/babbage/sketch.html>

• (8.) “enables us to find ... any nth Number of Bernoulli B2n-1, in terms of all the preceding ones, if we but know the values of B1, B3…B2n-3. ‣Let n=1, and calculate (8.). The result is B1.‣Let n=2. Calculate (8.) for this value of n, substituting the value of B1. The result is B3.‣Let n=3. Calculate (8.), substituting the values of B1, B3. The result is B5. And so on, to any extent.

• We append to this Note a Diagram and Table”

ADA LOVELACE: FIRST COMPUTER PROGRAMMER ?

Lovelace’s note D to Menabrea Sketch:

Lovelace’s note G to Menabrea Sketch:<www.fourmilab.ch/babbage/figures/menat6_1-5k.png> [high-res]