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2. El algoritmo Backpropagation 7

3.6. Otras decisiones de diseño

3.6.4. El entrenamiento on-line

Nigel Strudwick, JEA 71 (1985), 45–51, has already published and discussed these blocks (Pl. 5) and rightly notes that the present arrangement, with block 5 at the upper left is impossible because its height is 5.7 cm less than the block next to it (6). He might have added that it cannot belong to the uppermost course of stones, as does 6, because there is not the same amount of space above the signs.118

It does not seem impossible, however, to suggest an alternative arrangement. Although, as Strudwick says, “an unknown number of blocks is lost,” the sequence of the remaining blocks is probably correct. Block 6 belongs to the uppermost register of the scene at the right, and to the beginning of the inscription, while blocks 4 and 5 belong to the left edge. Block 5 probably goes above 4 rather than below it, since the left margin and vertical divid-

115 Fischer, Coptite Nome, no. 8.

116 Louvre C 300 (BES 9 [1987/88], 15 and figs. 1–2; pp. 21–22).

117 In Ward’s Index the owner’s title 1 = no. 1226; 3 = 1267; 4 = no. 430 (one example); for 5 cf. no. 1382 (zß

n pr ¢∂); for 7 cf. no. 45 (¡my-r ¡zwy n flkrt nswt); for 8 cf. no.

191 (¡my-r prwy nbw). The last of the titles of the subordi-

nate figures (6) is likewise found at the beginning of the Middle Kingdom, as noted carlier, but not title 2 (and 4– 5).

118 It should be noted, moreover, that the difference in height is, at the same time, too little to be explained by the presence of a drum lintel above it, or the end of a long architrave above an adjacent false door.

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ing line coincide exactly if arranged thus, but do not do so if 5 is placed below. Furthermore the second alternative would produce a gratuitous recurrence of the principal title between the mention of Cheops and Redjedef, for there is every reason to believe that the latter ruler succeeded the former. The lack of space between the hieroglyphs on these two blocks might be explained by some loss along the edge of one or both, and/or the plaster between them. In this case 5 and 4 must be placed at least one course lower than 6 for the reasons stated initially. Taking into account the minimum that is to be restored below 6, the original height of the inscription comes to at least 90 cm if block 6 is not moved still higher. This is an ex- ceptionally large proportion of text if one supposes that it belonged to a large representa- tion of the tomb owner which was placed below it, even assuming that he was seated. The small figures on the right obviously address the owner and it is therefore likely that he was, in fact, shown in this location, with his name before him.119 But the character and size of the titulary are so unusual that we cannot be sure that such a figure was present. Possibly the attendants advance towards a false door beyond the inscription.

In any case the sequence of the blocks is evidently 6–5–4, so that we may translate: (1) The Overseer of the Treasury and … of/for Sneferu; …, Scribe of Royal Decrees, … Overseer of the Chamber [of the King’s Regalia,]120 (3) …, [Overseer of the Treasury] for Cheops; …, (4) [The Overseer of the Treasury for] Redjedef; the Overseer of the Treasury for [Chephren]. If blocks 5 and 4 were spread apart, one or more titles would have to be introduced before the names of the first three kings, but it is clear that the title “overseer of the treasury,” in the last column, immediately preceded a royal name, presumably Chephren. It is also evident that Cheops’ name was preceded by more titles than in the case of any of the other rulers, a fact that would accord with the considerable length of his reign, as compared with that of his successor, and would suggest that the career of the anonymous overseer of the treasury occupied a lesser portion of Sneferu’s long reign, and did not con- tinue far into the reign of Chephren. The point of this unique presentation of the titulary is certainly to boast of a long tenure of office—35 years under Cheops and Redjedef, per- haps half a dozen years under Sneferu and a few under Chephren, representing a total of about 45 years of active duty in the same important position.

Although the repetition of a similar title is known from the considerably later monu- ment discussed in the preceding article, I am not aware of any parallel for a chronological succession of royal names in a titulary to make the point that the official in question served these kings. The closest analogy, dating to the early Fifth Dynasty, is a case where the epithet

¡m£∞ ∞r “revered with” is repeated before each of six consecutive rulers, from Redjedef to

Sahure,121 while in another case a son of Chephren repeats the same epithet before the name of that king and four successors.122 In inscriptions of the later Old Kingdom we hear of officials who exercised various offices under a succession of kings,123 but as far as titular-

119 Seated: LD II, 10, 22, 25. Standing: ibid., 19–21, 32, 46; Simpson, Kawab, Khafkhufu I and II, fig. 33.

120 Cf. p. 19 (e) and n. 39. For the title in its present form see Fischer, Egyptian Studies I, p. 30, fig. 3 (5); also: Petrie and Murray, Seven Memphite Tomb Chapels, pl. 14

(where the end of the title is to be read ). 121 Gauthier, ASAE 25 (1925), 180. 122 Hassan, Gîza IV, fig. 64.

123 E.g., Urk. I, 98 (12, 15), 142 (9–11), 254 (1–3). ES 03 FINAL Page 30 Sunday, February 25, 2001 7:52 AM

ies are concerned, those that name kings are nearly always associated with funerary cults. A rare exception is , which is evidently to be read wr-∞rp(w)-¢mwt n Wn¡s, indi- cating, as in the present case, that the high priest of Ptah held office in the reign of that king.124

The caption applied to the first of the three small figures at the upper right is also un- usual; he is called z£.f ∂t “his ‘son of the funerary estate,’”125 a term that must mean much the same thing as the more familiar sn ∂t “brother of the funerary estate.”126 With this ex- ample one may compare a Fifth Dynasty false door on which the wife of the tomb owner is identified as “his wife, the ‘daughter of the funerary estate.’”127 The same term is doubtless to be recognized in the captions of a wife who is identified as “his daughter and his funerary priest(ess);”128 although the reference to the funerary estate is missing, it is clearly implied by the second designation. In addition, two series of attendants labelled msw.f nw ∂t “his children of the funerary estate” are assigned to the tomb owner and his son, respectively, in a Fifth Dynasty tomb chapel,129 while another chapel of the same date shows an attendant who is “his ‘child of the funerary estate.’”130 Junker, in dis- cussing this, compares the caption in the chapel of W¢m-k£.¡ at Hildesheim, which he takes to mean “(seine) Stiftungskinder und -brüder,” but is, I think, more probably “his chil- dren and snw-∂t.”131

The “son of the funerary estate” is further identified as “the judicial scribe Ênt¡” and he is followed by a scribe whose name is correctly interpreted by Strudwick as N-ksmm-k£(.¡).132 It is not attested elsewhere, but the meaning “My k£ is not opposed” is almost synonymous with the well known Old Kingdom name Nn-∞ft-k£(.¡) “my k£ has no opponent.”133 The scribe

Pt¢-¢tp (or Ìtp-Pt¢) brings up the rear.

The style of the figures and hieroglyphs is decidedly mediocre, given the presumed dat- ing to the reign of Chephren. That date is borne out, however, by the wigs of the first two attendants, in which the uppermost tier of overlapping locks is larger than the rest, and dif- ferentiated by a series of striations radiating from the crown.134 Although the palaeo- graphic evidence does not provide further support for this early a date, it does not speak against it.135

124 Urk. I, 81, for which see also JARCE 3 (1964), 123, n. 1.

125 Not “his son, for whom (he) has provided,” as Strudwick translates, op. cit., p. 46. For a further example of a z£ n ∂t see Stewart, Egyptian Stelae II, pl. 37 (4).

126 Cf., among more recent discussions, Y.M. Harpur,

JEA 67 (1981), 28 f., 30–34.

127 Cairo CG 1417.

128 Mariette, Mastabas, p. 188.

129 Curto, Gli Scavi Italiani, fig. 32 and pl. 25. For msw-∂t see also Urk. I, 25 (2): “These are the priests whom I have designated as msw-∂t to do w™b-service for Hathor.” Here they are actually the children of the tomb owner.

130 Junker, Gîza II, fig. 28.

131 Ibid., p. 195. This example is shown in Kayser,

Uhemka, p. 32.

132 Strudwick, loc. cit. I have independently come to the same conclusion, which provides an Old Kingdom exam- ple of ksm “obstruct,” otherwise attested from the Middle Kingdom and later, and likewise provides the earliest evi- dence for passive s∂mm.f.

133 PN I, 168 (21).

134 JNES 18 (1959), 238–39 and fig. 4. This is particu- larly telling because it is applied to figures of such small scale; cf. Simpson, op. cit., figs. 30–32.

135 The sign is discussed by Strudwick, op. cit., pp. 48–51. The sign has already been compared with other forms in ZÄS 93 (1966), 58, fig. 3 and n. 6, where it may be seen that it resembles another Fourth Dynasty example (fig. 3 v).

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