We cannot know the destination of a piece of paper falling from a tower.

Even when we can go to Mars, we will not be able to know the destination of a piece of paper falling from the top of a TV tower. This is manifestation of both the greatness and the limitation of science.
--NAKAYA Ukichirô (1958): Kagaku no Hôhô (Methods of Science), the ending sentences of Chapter 5 (my translation from Japanese).

When I was a junior high school student (12 to 15 years old), I read many books, but I did not care who wrote them. Among those books, there was a paperback. One phrase impressed me that told that there is something that science cannot achieve. Later, perhaps when I was a senior high school student (15 to 18 years old), I read the book again and identified the name of the author. Then I knew that he wrote many other popular essays about natural science as well. I thought he was certainly a scientist, and probably categorized as a physicist. But I did not realize what he achieved as a researcher until I became a university student and majored in geophysics.

NAKAYA Ukichirô was one of the founders of glaciology (science of snow and ice, not only of glaciers). His laboratory which belonged to the Department of Physics of Hokkaido University (in Sapporo) grew into the Institute of Low Temperature Science. In this case, "low temperature" does not mean temperature at which helium is liquid, but temperature at which H2O is solid. His monumental experiment was production of snow crystals in laboratory. By this way he identified the dependence of crystal types on temperature and humidity of air where the crystals were formed. Hence his best known phrase, "Snow crystals are letters from heaven." [Note 1]. He also emphasized application of science for social needs, and engaged in evaluation of snow pack as water resource. He had been a student of TERADA Torahiko both in physics and in writing scientific essays.

Though he did not explicitly mention (so I did not realize when I was young), surely the sentence quoted here is based on his experience studying the motion of snow crystals falling in the air. He explains the indeterminacy by the nature of turbulence (small-scale motion of fluids) in the atmospheric boundary layer (the part of atmosphere near the ground surface). I think his explanation is valid from the viewpoint of present science after 45 years since its publication.

But present scientists would like to explain the same concept with a new technical term: chaos. In this technical sense, chaos does not mean complete disorder. Rather it means that we find some disorderly (or complex) behavior of a system which is governed by some deterministic (not stochastic) and simple (not complex) rules. More specifically, it means that small difference in the initial condition (which may be smaller than the error range of observation) grows so large that prediction may be practically meaningless. The theory of chaos has many origins. The most familiar one to meteorologists is the work of Edward LORENZ, a theoretical meteorologist in the United States of America. Just when NAKAYA wrote this book, LORENZ was making numerical experiments with a very simplified set of equation of fluid motion, and found that roundoff of insignificant digits can sometimes yield very significant difference in subsequent time series of variables.

We know that we will not be able to have LAPLACE's demon who can predict everything given the initial condition.


[A TV (television) broadcasting tower is not essential to the story. But it was something very new when this book was written. And the TV Tower of Sapporo stands on its broadway and it is still its landmark. Surely NAKAYA viewed its construction site and wished to use it as an apparatus of his experiments. (When I was a child I was myself familiar with the TV Tower of Nagoya which stands in very similar setting as Sapporo's except that snowfall is rare in Nagoya. So, I could not imagine something like paper falling down along the tower before reading the book, but I could after.)]


  1. This is a translation of NAKAYA's original Japanese words by HIGASHI Akira (KANDA, 2005). The version which NAKAYA himself wrote in English in 1938 was "the snow crystal is a hieroglyph from the heavens." (FUJIYOSHI, 2005). KANDA (2005) shows another version written by NAKAYA in 1954.

Additional information

Part of the book of NAKAYA and other essays of his are compiled into a reader for foreign students learning the Japanese language together with scientific thoughts (DAUB & ASANO, 2003). It appears that the particular passage I introduced is not included in that book.


Conceived during the assembly of the International Union of Geodesy and Geophysics in Sapporo, 2003-June-30 to 2003-July-11. Written on 2003-July-29. Revised on 2005-Feb.-20, 2005-May-04, 2010-Feb-03.
[English home page of K. Masuda]
[Japanese edition]