Corrections to the Pleasures of Counting For First Reprint

PLEASE NOTE: Since html does not deal easily with formula those who have browsers which can deal with such things will be better off using DVI PS or LATEX

Here is a list of corrections and additions for the first reprinting. I should like to thank Robin Chapman of Exeter (first mistake spotted), Professor Cassels, Dr Garling, Dr Osborne, Professor Barenblatt, and Prof J. Taylor (all of Cambridge), Harold N. Ward (University of Virginia), Adam Atkinson, Paul Shallhorn and Pat Henry for spotting various problems and for telling me about them. I would particularly like to thank Douglas Quadling and Dr Francis Clarke (Swansea) for long lists of useful comments.

Side note on page 54

Some bats have a mechanism for making themselves temporarily deaf when emitting sound bursts. (See [260], a book evidently written by a man who has never seen a bat he did not love.) They use high frequency sound because their prey is small.

Side note on page 190

According to Arnol'd in [264], Kolmogorov started as a student of history. His first paper, written when he was seventeen, concerned the mediaeval tax records in Novgorod. After he had presented his conclusions to a seminar he asked the historian in charge whether he agreed with them. `Young man,' the professor said, `in history we need at least five proofs for any conclusion.' Next day, Kolmogorov switched to mathematics.

Side note on page 221

When we talked about oxygen absorption we assumed that the area for absorption A was related to the volume V of an animal in the same way as the surface area of a sphere is related to its volume so that A is proprtional to V to the power 2/3. But we noted on page 218 that lungs look very `fractal'. If the surface of the lung has `Richardson number' different from the surface of a sphere then we would have A is proportional to V to the power beta with beta not equal to 2/3 and the slope of the mouse-elephant curve becomes easier to explain. (See pages 342-5 of [261].)

Side note on page 392

However, most of those whose opinions I respect reject Penrose's views on the nature of human thought `not because they are crazy, but because they are not crazy enough'.

Side note on page 501

(Added in second printing.) If you wish to write complex formulae, I strongly recommend Grätzer's Math Into LaTeX [263].

Side note on page 505

Hacker lore says that two heads are faster than one and three heads slightly faster than two. Thereafter, adding manpower to a software project actually makes it slower. The only way to speed up a project is to use cleverer people. Hence the three Knuth rule. If three Knuths working together cannot do it, it cannot be done.

Page 53, line before (i) add

(The restrictions on theta-subscript1 are rather arbitrary, but some restrictions are needed.)

Page 53, near middle of written matter.

Replace angle BCX by angle ACX.

Page 53, 4 lines up.

Replace a=AX cos theta_{1} by AX=a sin theta_{1}.

Page 53, last displayed formula should read.

a sin theta_{1}=2r sin theta_{1}-theta_{2} over 2

Page 59 middle. Replace

for 1 leq i leq n$ and guess that that a_{m+1} will be close to

T_{n}(a_{m-n+1},a_{m-n+2},dots ,a_{m})=P(n)

by for 0 leq i leq n-1 and guess that that a_{m+1} will be close to}

T_{n-1}(a_{m-n},a_{m-n+1},dots ,a_{m})=P(n)

Page 79, line 2

replace k=b=1 by k=c=1

replace b(t)=1-r(t) by b(t)=1+r(t)

Page 79, first displayed formula

replace r'(t)=-(1-r(t))r(t) by


Page 79, second displayed formula replace r(t) over 1-r(t)=r(0) over 1-r(0) e^{-t} by

r(t) over 1+r(t)=r(0) over 1+r(0) e^{-t}

Page 79, end of first para replace

r(t) tends to 0 for all t>0.


r(t) tends to 0 as t tends to infinity.

Page 120

In the 2nd displayed formula replace tau=gl^{-1}t^{-2} by tau=gl^{-1}t^{2}. As a consequence, in the 4th, 5th and 6th formula g/l should be replaced by l/g. Finally in line -7 replace `varies inversely with' by `is proportional to".

Page 121, REPLACE side note as follows

According to materials scientists, when molten glass cools it remains a liquid but one whose coefficient of viscosity increases as the temperature decreases. Thus we can blow glass at high temperatures, mold it at lower temperatures and so on. However, the demonstration of liquid properties for glass at room temperature lies at the very edge of modern experimental technique.

Page 126, add at end of first side note

The treatment of dimension I have given follows the traditional pattern in glossing over certain points. In [261] Barenblatt takes a more modern approach and shows that, if we think a little harder, we can understand a lot more.

Page 133, bottom line

Replace `wave front' by `shock front'.

Page 143, Page 143, first equation after 7.1

should not read (x,y,z,t)=(ct',0,0,t) but should read (x,y,z,t) =(ct,0,0,t).

Page 166. In BOTH Figure 8.2(a) and Figure 8.2(b)

Replace squareroot2 on x-axis by 1/squareroot2.

Pages 167 to 171.

A factor of 1/2 is missing in many of the formulae. The correct factor may, of course, be found by setting f=1. Alternatively: wherever ))b/N appears replace with ))b/(2N); on page 168 lines 7, 8 and 9 replace f(rb/N)b/N by f(rb/N))b/(2N); page 171, second displayed formula, replace h by h/2.

Pages 175 and 176

Replace l/g by g/l wherever it occurs.

Page 177, 3/4 down

Replace `collected paper with' by `collected papers) with' and `velocity?)' by `velocity?'.

Page 186, top third TWICE

Replace K(t) by Kt.

Page 187, one third down

Replace `not much bigger than l' by `not much bigger than l^{2}'.

Page 264, Figure (e)

Replace 3 on top path by 2. Replace 1 on almost vertical path by 0.

Page 264, Figure 11.5

Label on edge XY replace 10p+10 by p+10

Page 274, last line but one of Exercise 11.2.6

Replace 10p+10 by p+10.

Page 278 line 19

Extra space between ) [and] are

Page 290 line -5 replace

for all integer r with R geq 1.


for all integers r with r geq 1.

Page 291, last displayed formula

Replace pi by its square root.

Pages 331, 391, 392

The correct possesive form is Hodges'.

Page 331, 3/4 way down. Replace

A is encoded by SA, B by SB and so on.


A is encoded by S(A), B by S(B) and so on.

Page 364, 1/4 way down

Replace `Feynmann' by `Feynman'.

Page 403 First part of proof

There are three places where the power 1-uN should be replaced by (1-u)N. It is not made clear where the condition 0 leq u leq 1 comes in (observe that u/(1-u) leq 1). I have rewritten the proof slightly to make this clearer.

Page 419, First line Exercise 17.4 (ii)

Replace chi(0)<0 by chi(0)>0.

Page 419, Second line Exercise 17.4 (ii)

Replace chi(t)<0 by chi(t)>0.

Page 420, line 19

Replace `nth generation' by `n+1st generation'.

Page 428, last line of (i)

Replace `K=L-1/4' by `K=1/4-L'.

Page 428, first line of (ii)

Replace `K=-1/4' by `K=1/4'.

Page 428, displayed formula in (iii)

Remove the factor of 1/2.

Page 428, last displayed formula

Replace `L-1/4, by `1/4-L'.

Page 440.Replace first displayed formula in (ii) by

dI/dS=dI/dt dt/dS= (beta SI-gamma I)/-beta SI=-1+gamma/beta S}

Page 442, third displayed formula up should read


Page 442, second displayed formula up should read


Page 443, line 10

Replace `Claude' by `Claud'.

Page Page 490, line 10

Replace Adam's [by] Adams'.

Page 517, line 5 ending with 37-8

Add `Batchelor's paper was [262].'

Page 528

Additional Bibliography

[260] J. D. Altringham. Bats, Biology and Behaviour. OUP, Oxford, 1996

[261] G. I. Barenblatt. Scaling, Self-similarity and Intermediate Asymptotics. CUP, Cambridge, 1996

[262] G. K. Batchelor. Kolmogoroff's theory of locally isotropic turbulence. Proceedings of the Cambridge Philosophical Society, 43:533-59, 1947.

[263] G. A. Grätzer. Math into LaTeX. Birkhäuser, Boston, 1996.

[264] S. H. Lui. An interview with Vladimir Arnol'd. Notices of the AMS, 44(3):432-8, April 1997.

Page 531, add page reference

historians, killjoy, routed, 104, 153, 190

Page 531, under Knuth K. E., add item

three Knuth rule, 505

Page 531, replace

lungs, as surfaces of nearly infinite area, 218


lungs, as fractals, 218, 221

Page 531, under menagerie, mathematical, add item

bats, 54

Now go onto corrections not in first reprint

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