## Sum by Hotspur

### Puzzle explanation

Corrections to misprints spelt out “I propose to consider the question, ‘Can machines think?’”, written by Alan Turing. The grid shows TURING MACHINE. The rows below that show the possible output of such a machine, with each letter in the right-hand half being the “sum” of the letter above and the corresponding letter in the left-hand half of the same row, using A = 1 or 27, B = 2 or 28 etc. Thus ACHINE + REGIME = SHORAJ and so on, down to LIBRAN + SEGOLM = ENIGMA, the name of the cipher machine cracked by Turing and others at Bletchley Park. Continuing the process, ENIGMA + XAXBGN gives COGITO (“I think”), a possible response to Turing’s question. Because of the initial error in the printed grid, COGJTO was also accepted.

The process mimics the action of a Turing machine, which is determined by (1) the current state of the machine, (2) the symbol in the cell currently being scanned by the head and (3) a table of transition rules, which serve as the “program” for the machine. The title refers to the additive process as well as Descartes’ “Cogito ergo sum”.

### Clue explanations

Conventions: * = anagram, < = reversal

 No Misprint Answer Explanation ACROSS 1 f(I)ne AMENDE (D after MEN) in AE 5 gras(P)ed ZYGOTE (do)ZY + GOT + E 10 f(R)esh MINUET UE(y) in MINT 11 disc(O)rd AJAR RAJA < 12 lea(P) AXEL AXE + (oi)L 13 l(O)w MOODY MOO + D(ut)Y 14 prote(S)t EMO (d)EMO 15 v(E)al DELI (cru)DE LI(quid) 16 o(T)ary SPEARED (P(art) + EARED) after S 18 tro(O)ps HUSSARS ASS < in RUSH * 21 (C)oat UNDE UNDER-AGE − RAGE 22 f(O)rm ARCHETYPICAL APICAL around (THE CRY) * 25 concer(N) CARICATURING (AIR CUT) * in CARING 27 Pre(S)s PROM PR + OM 30 MACHINE M + A + CHINE 31 (I)ces REGIMES EG in RIMES 32 Lo(D) HORA HO + RA 34 sho(E)s SOX S(can) O(pening) + X 35 Ar(R)an’s SAUCH S(hunned) + A + U + CH 36 coa(T)ed MUTE MALEMUTE − MALE 38 (H)eight DHOW D + H + O’ + W 39 s(E)at LIBRAN LIB + RAN 40 (Q)uit GOLEMS GO + LEMS 41 p(U)zzle ENIGMA (HARM + ENIGMA) * = A HAMMERING DOWN 1 bonn(E) AMAH MAMA − M + H 2 mu(S)s MIX FIX with M for F 3 se(T) NULLAH NULL + AH 4 w(I)ll DEMI-SEC DEMISE + C 5 cr(O)ss ZOOPHYTA ZO + OP + (t)H(e)Y (s)T(e)A(l) 6 canto(N) YODEL cryptic definition, ref. Swiss cantons 7 (C)amp GAY YAG < 8 Th(A)nks TAMED TA + MED 9 De(N)ude ERODE STEVEDORE < − VETS 15 (M)illet DURA DURA + MEN = DURAMEN 17 b(A)ne RICIN R(ickets) I(sn’t) C(ommon) I(n) N(asal) 19 (C)rab SCROG R in SCOG 20 (H)old IMMATURE IMMURE around (A + T) 23 t(I)e CHAIN UP CHIN UP around A 24 coi(N) ANNA (band)ANNA 26 plan(E) RHOMBI RH + M(an) in OBI 27 pre(S)ent PRODS PR + ODS 28 s(T)ark SHEER homophone of SHEAR 29 S(H)anks GLAMS L(evity) in GAMS 33 v(I)ctor JENA JANE * 35 u(N)der COW 2 meanings 37 pea(K) TAM MAT <