208
10 Statistics and Other Concerns
compared to the change in the position of the Moon. For Scheveningen, the
tide comes an hour or two earlier (and also more than ten hours later) than
the passage of the Moon through the meridian, but that high tide is in fact a
tidal wave that originated about two days earlier. Along the Dutch coast, this
difference is also not the same everywhere as in Scheveningen. In Vlissingen
it is less than an hour, in Den Helder it is six hours, and it is almost ten and
a half hours in Eemshaven, Germany. It is not as easy as it seems to choose
between the accepted and Kapteyn’s explanation based on such a comparison.
Nevertheless it remains incomprehensible to me how Kapteyn could have been
so wrong.
Kapteyn, in his lecture, further treated cases where the Moon is not above
the equator, and differences in the tides with geographical latitudes. Today a
lecturer would have mentioned the fact that the Moon always keeps the same
side facing the Earth due to tidal action, but Kapteyn did not. That the tidal
wave slows down the rotation of the Earth with an increase in the duration of
the day by 1 s per about 50,000 years, and that the Moon as a result moves
away from us by 3–4 cm per year, was not known.
10.2 Statistics
Kapteyn has also been extensively involved in the field of statistics. There were
in Groningen two demonstration models, which he had designed and were
built, probably in the workshops of the biology department. Fig. 10.3 (left)
shows the classical ‘normal distribution’, also called Gauss distribution. This is
the probability distribution that occurs frequently in nature. From the funnel
above, small bullets are dropped down through a system of small horizontal
plates. Between every two plates the hole is large enough so that the balls can
easily pass and in the row underneath the plates are arranged in such a way
that each little plate is exactly straight underneath a hole. Chances are the same
each time that a small bullet that falls on a pin will pass it on the left or on the
right. The bullets are collected at the bottom and that results the well-known
‘normal’ probability distribution. Many things (such as the height of persons)
follow such a distribution quite accurately.
The ‘machine’ was not Kapteyn’s original idea. Sir Francis Galton (1822–
1911) was the first to design such an instrument and had called it a ‘quincunx’.
The version in Fig. 10.3 still exists in Groningen.
Kapteyn was interested in the ‘skew’ distribution. For illustration he used
the example of the distribution of the size of berries. It is quite possible that the
diameters of the berries are distributed as the normal distribution, symmetrical
10 Statistics and Other Concerns
compared to the change in the position of the Moon. For Scheveningen, the
tide comes an hour or two earlier (and also more than ten hours later) than
the passage of the Moon through the meridian, but that high tide is in fact a
tidal wave that originated about two days earlier. Along the Dutch coast, this
difference is also not the same everywhere as in Scheveningen. In Vlissingen
it is less than an hour, in Den Helder it is six hours, and it is almost ten and
a half hours in Eemshaven, Germany. It is not as easy as it seems to choose
between the accepted and Kapteyn’s explanation based on such a comparison.
Nevertheless it remains incomprehensible to me how Kapteyn could have been
so wrong.
Kapteyn, in his lecture, further treated cases where the Moon is not above
the equator, and differences in the tides with geographical latitudes. Today a
lecturer would have mentioned the fact that the Moon always keeps the same
side facing the Earth due to tidal action, but Kapteyn did not. That the tidal
wave slows down the rotation of the Earth with an increase in the duration of
the day by 1 s per about 50,000 years, and that the Moon as a result moves
away from us by 3–4 cm per year, was not known.
10.2 Statistics
Kapteyn has also been extensively involved in the field of statistics. There were
in Groningen two demonstration models, which he had designed and were
built, probably in the workshops of the biology department. Fig. 10.3 (left)
shows the classical ‘normal distribution’, also called Gauss distribution. This is
the probability distribution that occurs frequently in nature. From the funnel
above, small bullets are dropped down through a system of small horizontal
plates. Between every two plates the hole is large enough so that the balls can
easily pass and in the row underneath the plates are arranged in such a way
that each little plate is exactly straight underneath a hole. Chances are the same
each time that a small bullet that falls on a pin will pass it on the left or on the
right. The bullets are collected at the bottom and that results the well-known
‘normal’ probability distribution. Many things (such as the height of persons)
follow such a distribution quite accurately.
The ‘machine’ was not Kapteyn’s original idea. Sir Francis Galton (1822–
1911) was the first to design such an instrument and had called it a ‘quincunx’.
The version in Fig. 10.3 still exists in Groningen.
Kapteyn was interested in the ‘skew’ distribution. For illustration he used
the example of the distribution of the size of berries. It is quite possible that the
diameters of the berries are distributed as the normal distribution, symmetrical