BMJ No 7072 Volume 313

Seven Deadly Sins Saturday 21-28 December 1996

Circaseptennial rhythm in ear growth

Jos Verhulst, Patrick Onghena

Recently, Heathcote reported enduring growth in the ears of male patients (on average 0.22 mm a year in patients aged 30 or over).(1) Our previous work had made us aware of the existence of a circaseptennial (about seven years) rhythm in certain developmental aspects of the human skull.(2) We therefore decided to examine the data of Heathcote for a possible seven year periodicity in ear growth.

Methods and results

For every age we calculated the mean ear length from Heathcote's raw data. We produced an uninterrupted sequence of yearly ear length values from the age of 30 to 83 (data were missing at certain ages above the age of 83). A total of 201 measurements were available for this span of 54 years. For each age, n, we then calculated a smoothed ear length as the mean of the mean lengths for ages (n 1), n, and (n + 1). This procedure resulted in mean smoothed ear lengths for ages 31 to 82. We calculated ear growth at age n in two steps. Firstly, we calculated the change in ear length at age n as the mean smoothed ear length at age n minus the mean smoothed ear length at age (n 1). Secondly, we calculated a smoothed ear growth at age n as the mean of the mean growth rates at ages (n 1), n, and (n + 1). These smoothing procedures reduced the large impact of scatter resulting from the small sample. We thus obtained smoothed growth rates for ages 33 to 81 (table 1).

Table 1 - Smoothed ear growth rates for ages 33 to 81 (calculated from raw data of Heathcote(1)). To show circaseptennial periodicity, data are arranged in seven phases
Phase	Age (years)	Rate (mm/year)	Age (years)	Rate (mm/year)	Age (years)	Rate (mm/year)	Age (years)	Rate (mm/year)	Age (years)	Rate (mm/year)	Age (years)	Rate (mm/year)	Age (years)	Rate (mm/year)	Mean rate for phase (mm/year)
I	33	0.73	40	0.63	47	-0.91	54	0.8	61	0.64	68	0.69	75	0.48	0.44
II	34	0.65	41	0.46	48	0.82	55	1.45	62	0.62	69	0.32	76	1.19	0.79
III	35	1.54	42	1.85	49	1.64	56	0.63	63	0.87	70	-1.45	77	1.96	1.01
IV	36	1.06	43	0.99	50	1.45	57	-0.53	64	1.3	71	-0.83	78	0.62	0.58
V	37	0.23	44	0.01	51	-0.09	58	-1.36	65	0.82	72	-0.11	79	-1.18	-0.24
VI	38	-0.17	45	-2.02	52	-0.67	59	-0.88	66	-0.26	73	0.7	80	-1.51	-0.69
VII	39	-0.62	46	-2.1	53	-0.12	60	0.62	67	0.72	74	-0.13	81	-1.66	-0.47

We performed a spectral analysis of these data using the sas spectra procedure.(3)(4) This analysis showed the presence of a sinusoidal component in the time series, with a period of seven years (Fisher's k = 8.59, P = 0.0009). Growth velocities peaked around multiples of seven years (phase III). Surprisingly, negative growth rates tended to be seen at the minima. Around the age of 70 a maximum was lacking, which may be an artefact due to the paucity of data around this age (for ages 69, 70, 71, and 72 there were only six measurements).

Comment

The idea of a seven year rhythm in human development is old, dating back at least to ancient Greece. Reports on circaseptennial phenomena are, however, scarce in recent published work.(5)

Seven year periodicity remains comparatively unknown, perhaps because it is not looked for by many researchers. This may be because no major seven year rhythms seem to be present in the natural environment. In this respect, the circaseptennial rhythm differs fromthe better documented circadian and circaseptadian rhythms, which can be linked to the day-night cycle and to tidal periodicities, respectively.

The presence of a circaseptennial pattern of human ear growth raises a number of further questions. Firstly, are the period and phase observed in this sample universal in humans? Secondly, do other structures such as the nose show lifelong rhythmic growth? Finally, are there corresponding patterns in other species?

We thank Dr J A Heathcote for kindly providing us with his raw data.

Funding: None.

Conflict of interest: None.

Correspondence to: Dr J Verhulst,

Karel Oomsstraat 57,
B-2018 Antwerp, Belgium.
Email: jozef.verhulst@ping.be

Louis Bolk Institute,
Drierbergen,
Netherlands

Joe Verhulst,
associated researcher

Faculty of Psychology and Education Sciences,
Katholieke Universiteit Leuven,
Leuven Belguim

Patrick Onghena,
associate professor in educational statistics

References:

1 Heathcote J A. Why do old men have big ears? BMJ 1995;311:1668.

2 Verhulst J, Onghena P. Cranial suture closing in Homo sapiens: evidence for circaseptennian periodicity. Ann Hum Biol (in press).

3 Fuller WA. Introduction to statistical time series. 2nd ed. New York: Wiley, 1996.

4 SAS Institute. Statistical analysis system. Version 6.08. Cary, NC: SAS Institute, 1989.

5 Verhulst J, Onghena P. Periodic birth-year pattern of the founders of quantum mechanics. Psychological Reports 1996;78:19-25.