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 Chapter 3 The ability to instantaneously capture the image of moving objects
(Revised 2023.05.25) 

Hokusai's The Great Wave off Kanagawa has raised various questions for the present writer. Besides the originality discussed in another article [1], one of the questions was how such high waves were generated in an inland sea such as Edo Bay, but the answer was obtained by experiments conducted by a research group at the Universities of Oxford and Edinburgh. Specifically, such a tidal wave occurred when two waves were made collided at an angle of 60°, as shown in Fig.1. [2]

(1) (2) (3)

Fig.1 (1) A Photograph of the wave, the photographing condition unknown [3] ; (2) Hokusai’s wave [4]; (3) A still of freak wave experimentally created by the team of Oxford University and Edinburgh University. [5]

Aside from the crest of the waves drawn like withered starfish by Hokusai, another question was “the ability of artists to capture the momentary image of a moving object”.

Pictures of waves drawn by artists from the 19th century onwards found on the Internet are shown in Fig. 2.

(1) (2) (3) (4) (5)

Fig.2 Paintings of waves by various artists.

(1) The Shipwreck by Joseph Mallord William Turner (1805) [6] ;

(2) La vague verte by Claude Monet (ca. 1865) [7] ;

(3) La Vague by Paul Gauguin (1888) [8] ;

(4) La Mer. études de vagues by Henri Rivière (1900s ?)[9];

(5) De Branding by W. O. J. Nieuwenkamp (1916) [10].

The present writer was first fascinated by Picture (4) by Henri Rivière and Picture (5) by W.O.J. Nieuwenkamp. In the former, water droplets were depicted as small flecks of various shapes. In the latter, the flowing water was drawn as segments with a certain width and, around the crest of the wave, they turned to an irregularly shaped mass, which was then stretched to form spherical droplets. Although Pictures (1) to (3) are distant views, the depiction of the wave by Joseph Turner in Picture (1) looks similar to that of Nieuwenkamp when enlarged.

Paintings of waterfalls were unexpectedly few, but four of them are shown in Fig.3.

(1) (2) (3) (4)

Fig.3 Paintings of waterfalls by artists.

(1) Waterfall by James Burrell Smith (1874), o/c, 50.0×69.0 cm [11]

(2) Waterfall at Terni by Camille Corot (1826), oil/paper/wood[ [12]

(3) Kizan Falls in “西遊旅譚 第５巻 (Travelogue to the West: Vol.5)” by Koukan Shiba (1803) [13]

(4) Waterfall in Mino Country in “諸国滝廻り (Waterfalls in Various Districts)” by Hokusai Katsushika. [14]

The depiction of the breaking water on the top of the waterfall in Picture (1) by James Smith looks more or less similar to that in the Turner's Shipwreck . The depictions of Terni Falls in the Apennine Mountains in the middle of the Italian Peninsula by Camille Corot, Picture (2), looks like the image of a waterfall viewed from a distance by the human eye, in which the running water becomes coarser as it falls, accelerated by gravitation. Picture (3), the sketch of Kizan Falls in Settsu Province, where Shiba Koukan stopped on his way back from Nagasaki, drew the falling water by lines and segments.

Visiting waterfalls in various districts (諸國滝廻り, Shokoku Takimeguri) was the compilation of imaginary pictures drawn without seeing the real waterfall. Although the commercial value of the pictures may be high for his seal and signature, the artistic value may not be high. The present writer had spent his childhood in the western part of Gifu Prefecture and visited the Yoro Waterfall several times in the 1950s, but it was not a wide waterfall with steps around the mouth of the waterfall, and the surrounding terrain was not suitable to build a hut, unlike the depiction by Hokusai in Picture (4).

From the above observations, I became interested to estimate in how many milliseconds the artists had captured the moving image reflected on the retina, or what the “shutter speed” would be if their eye was likened to a photographic camera.

Many photographs of moving water are found on the Internet, but in most of them, even those taken in recent years, the shooting conditions are not shown. Hence the present writer has decided to take photographs himself by changing the shutter speed stepwise. Thanks to the evolution of digital cameras, the exposure time and aperture can be automatically linked to the sensitivity of the image plate.

Since it is not necessarily easy to see the occurrence of high waves at beaches from a good angle at close distance, the present writer first went to the fountain in Ueno Imperial Park in Tokyo, but satisfactory photographs were not obtained, because the emission of water was intermittent and irregular. Next, I went to the “Nanushi Waterfalls (名主の瀧)” in the North District of Tokyo, but the place was not suitable either. Although the water falling from the mouth of the waterfall was constant as it was circulated by means of a pump, the mist from the rock surface and the basin of the waterfall covered the surroundings, hence one had to be about fifteen meters away to take photographs. In addition, the ground, wet and rocky, was bad for setting up the camera. The results are shown in Figs.4 and 5.

Fig.4 The Fountain in Ueno Imperial Park, Tokyo. By Pentax K-3ii/f=270mm (2019.02.18.).

Fig.5 Otaki (Male waterfall) in “Nanushi Waterfalls (名主の瀧)”, North District, Tokyo. By Pentax K-3ii/f=2７0mm (2019.10.02.)．

Even so, it was found that the flowing water, which looks to be a bundle of continuous parallel lines to the ordinary eye, appeared to be discontinuous in 1/20 to 1/40 seconds (50 to 25 milliseconds), and turned to be short segments and dots in 1/320 to 1/640 seconds (3.1 to 1.6 milliseconds).

In the precinct of Tsuki Shrine (調神社) in Urawa, Saitama Prefecture, where I visited for a different purpose, I found a small fountain placed in the Kamiike Pond (神池), shown in Fig.6. Although the diameter of the orifice was small and the fall to the water surface measured as short as only about sixty centimetres, the running of water was stable. In addition, the distance to the fountain from the edge of the pond was short, only four or five metres. The photographs taken are shown in Fig.7.

Fig.6 A fountain in the Kamiike Pond (神池), Tsuki Shrine (調神社) in Urawa, Saitama Prefecture.

Fig.7 The fountain in Tsuki Shrine (調神社) in Urawa. By Nikon Z6/f=200mm (2022.11.14.).

The result of the observations is summarised in Table 1.

Table 1 Observation of 16 shots.  

In these observations, it is remarkable that water, which is normally considered as a low viscosity substance[15], appears like an amorphous, elongated transparent plastic, just like the toy slime (PVA + boric acid), when photographed with a shutter speed of 1/160 to 1/250 seconds (6 - 4 milliseconds). At 1/1600 sec (0.625 millisec). the plastic-like water is broken into pieces near the surface of the pond.

Reviewing the waves drawn by the above-mentioned artists, W.O.J. Nieuwenkamp's woodcut, Picture (5) in Figure X, is close to this. The sketch was drawn in 1916, when the Kodak 1A released two years earlier [16] had a shutter speed of up to 1/100 sec. Since it should not have happened, it is impossible for him to refer to the photograph. As a draftsman, he was adept at accurately drawing the images reflected on the retina, but did he also have dynamic vision comparable to today's high-end cameras? As noted above, the paintings of Henri Rivière and Joseph Turner (1800s and 1805, respectively) also resemble Nieuwenkamp's drawings, although painted in white.

Hokusai had no doubt good kinetic vision as demonstrated in his Hokusai Comics [17], but it is difficult to judge, because his drawings, even The Great Wave Off Kanagawa, were stylised.

Recently, a toy-level apparatus, Smithsonian Wave Machine, shown in Fig.8 has been found on the Internet.

Fig.8 Smithsonian Wave Machine.

It seems a transparent, oblong pencil case-like container in which two types of immiscible liquids with different specific gravities are sealed and, when mounted on a driving device and moved like a seesaw, small crests are generated at the liquid-liquid interface. Although no reply was available from the manufacturer, the upper and lower layer liquids were supposed to be vegetable oil and coloured water, respectively. Knowing that the waves are different from those of ordinary air-liquid interfaces, the present writer obtained one unit. The container measured 310 (w) x 59 (h) x 30 (d). The driver was driven by a type c dry battery at the rate of 12.8 rpm (1 cycle/4.7 secs.).

The result was found not much useful to estimate the eye-sight of painters, as shown in Fig. 9, although anticipated.

Fig.9 Photographs of waves generated by the Smithsonian Wave Machine taken at various exposure time. By Nikon Z6/f=70mm (2022.11.28.).

Crests were not seen at the exposure time of 1 second and began to appear at 1/2 second as seen by the naked eye, but no change was observed below 1/8 second exposure time.

The conclusion obtained from Fig. 4, 5 and 7 are as follows.

When falling running water is photographed with a camera, the water which appears as a bundle of thin lines to the eyes of an ordinary person begins to be seen discontinuous at an exposure time of 1/8 second (125 milliseconds) and turns to be the assembly of broken segments at around 1/60 second ( 16.7 milliseconds). When the exposure time is shortened, it becomes almost transparent and irregularly shaped long clumps around 1/160 second (6.25 milliseconds) and elliptical water droplets are seen here and there. Below 1/250 second (4 milliseconds), the irregularly shaped long clumps become completely transparent and the rod-like water droplets become spherical.

In the light of paintings drawn after the early 19th century, before high-speed shutter cameras became common, W. O. J. Nieuwenkamp, Henri Rivière, Joseph Turner, et al. are supposed to have had the ability to memorise and reproduce the image reflected on their retina at less than 1/160 second (6 milliseconds).

The Wave Machine which generates waves at the liquid-liquid interface was of no use. If the Oxford University/Edinburgh University group, who reproduced the waves in The Great Wave off Kanagawa, will take photographs with higher shutter speeds, the true image of the crest and the rear side of the waves are expected to be clarified, rendering their work significantly more valuable. Unfortunately, the frame rate of the video posted on the Internet is insufficient to see the details.

(Below modified/added 28 May 2023)

Fig. 10 shows stills taken from the two videos of experimental wave tanks found in the Internet.

Fig. 10 Stills taken from the videos bench-scale wave tanks posted on the Internet.

Left: Wave tank (I) [18], Right: Wave tank (II) [19].

Whist the frame rate of video (I), 50 fps, is too low to show the details of high wave, in the still video (II), tough the frame rate of which is unknown but must be reasonably high, reveals as if the wave is composed of units that look like stretched transparent plastic, as observed in Fig.7.

Fig.11 shows stills taken from the video of official website of the recently opened surfing facility, “Citywave Tokyo Sakaimachi” in Ibaraki Prefecture.
   
   

   
Fig.11 Stills taken from the video of the website of “Citywave Tokyo Sakaimachi”[20].
   
The body of water crushed like a network reminds one of The Shipwreck by Joseph Mallord William Turner (Fig.2 (1)) and the Waterfall by James Burrell Smith (Fig.3 (1)), surprising me again of those painters' kinetic vision. Figure 12 shows the magnified view of crushing water in those pictures.

Fig.12 Magnified view of crushing water in The Shipwreck by Joseph Mallord William Turner (Fig.2 (1)) and the Waterfall by James Burrell Smith (Fig.3 (1)).

Acknowledgements

Thanks are due to Kanako, my granddaughter, who kindly checked and edited the English text of this article. 25/12/2022.

References