A puzzle of Ernst Mach’s self portrait エルンスト・マッハの自画像の謎

Do you know who Ernst Mach is? From his last name, you may guess he was the scientist whose name bears the speed of sound. In fact, Mach was the first to systematically study super-sonic motion.


Mach (1838 – 1916, photo right) is considered by many pundits as one of the greatest 19th and 20th century physicists and philosophers. This Austrian scientist made major contributions not only to physics and philosophy, but also to physiological psychology. He also made important contributions to understanding the Doppler-effect. Another notable fact is that his critique of Newtonian ideas of absolute space and time were an inspiration to the young Einstein. He credited Mach as being the philosophical forerunner of relativity theory. Mach’s systematic skepticism of the old physics was similarly important to a generation of young German and western physicists.

He is mostly known in physics but today I am sharing this knowledge as he made some unique and interesting discoveries in the area of physiological psychology. Here are two interesting self-portrait photos (#2 and #3). They are titled as “view from the left eye,” by Mach (1870 & 1886). Have you seen them before? They certainly made me think in relation to martial arts. What are your thoughts?



Although Ernst Mach is widely recognized in psychology for his discovery of the effects of lateral inhibition in the retina (“Mach Bands”), his contributions to the theory of depth perception are not as well known. Mach proposed that steady luminance gradients triggered sensations of depth. He also expanded on Ewald Hering’s hypothesis of “monocular depth sensations,” arguing that they were subject to the same principle of lateral inhibition as light sensations were. Even after Hermann von Helmholtz’s attack on Hering in 1866, Mach continued to develop theories involving the monocular depth sensations, proposing an explanation of perspective drawings in which the mutually inhibiting depth sensations scaled to a mean depth. Mach also contemplated a theory of stereopsis in which monocular depth perception played the primary role.


The Public Domain Review


This unique self-portrait, also known as “view from the left eye”, is the creation of Austrian physicist and philosopher Ernst Mach, noted for his contributions to physics such as the Mach number (which relates an object’s speed to the speed of sound) and the study of shock waves. The sketch appears in Mach’s The Analysis of Sensations, first published in German in 1886 as Beiträge zur Analyse der Empfindungen, and is used to illustrate his ideas about self-perception.

The considerations just advanced, expressed as they have been in an abstract form, will gain in strength and vividness if we consider the concrete facts from which they flow. Thus, I lie upon my sofa. If I close my right eye, the picture represented in the accompanying cut is presented to my left eye. In a frame formed by the ridge of my eyebrow, by my nose, and by my moustache, appears a part of my body, so far as visible, with its environment. My body differs from other human bodies beyond the fact that every intense motor idea is immediately expressed by a movement of it, and that, if it is touched, more striking changes are determined than if other bodies are touched by the circumstance, that it is only seen piecemeal, and, especially, is seen without a head. If I observe an element A within my field of vision, and investigate its connection with another element B within the same field, I step out of the domain of physics into that of physiology or psychology, provided B, to use the opposite expression of a friend of mine made upon seeing this drawing, passes through my skin. Reflections like that for the field of vision may be made with regard to the province of touch and the perceptual domains of the other senses.

He gives a little more information on the origins of the image in a footnote:

It was about 1870 that the idea of this drawing was suggested to me by an amusing chance. A certain Mr L., now long dead, whose many eccentricities were redeemed by his truly amiable character, compelled me to read one of C. F. Krause’s writings, in which the following occurs:

“Problem : To carry out the self-inspection of the Ego.
Solution : It is carried out immediately.”

In order to illustrate in a humorous manner this philosophical “much ado about nothing,” and at the same time to show how the self-inspection of the Ego could be really “carried out,” I embarked on the above drawing. Mr L.’s society was most instructive and stimulating to me, owing to the naivety with which he gave utterance to philosophical notions that are apt to be carefully passed over in silence or involved in obscurity.

According to John Michael Krois the “Mr. L” in question is Mach’s colleague at Prague University, Prof. Hermann von Leonhardi, son-in-law of the Kaul Christian Friedrich Krause mentioned. Krois also tells us that this original drawing sketched in 1870 in fact differed from the woodblock of 16 years later — the right arm with pencil is absent, with a left arm instead brandishing a cigarette (which has found its way to the mouth in the 1886 image), and a steaming cup of Viennese coffee sits on a small table.


I found these self-portraits to be very interesting as the single eye Mach used was his left one. He chose not the right eye but the left one which is managed by the right side of the brain.

As of the readers know that our brain – consists of two major parts; right and left hemispheres. It is very interesting to know that these two hemispheres are not equal or redundant but rather they function differently. The left side of the brain is responsible for controlling the right side of the body. It also performs tasks that have to do with logic, such as in science and mathematics. On the other hand, the right hemisphere coordinates the left side of the body, and is the more artistic and creative side of the brain.


So, now many of the readers can guess why I picked up this subject or why I considered his drawings to be interesting. Ernst Mach is a genius of a scientist which means he must have utilized or depended much of his brain work on the left side or logic side of the brain hemisphere. But yet, he drew a self-portrait, curiously looking through his left eye which was managed or controlled by the right side of the brain or creative side.


Why did he choose the left eye vision and not the right one? It can be a mystery and as far as I know he did not write down or tell people if there was any particular reason. Was it just coincidental and had no meaning? I do not think so. I wish to share my hypothesis that there was a definite reason.



Before I present the hypothesis, I would like to bring up a couple of things from the Japanese culture. I am not 100% sure if these things have any relationship to the mystery of Mach’s portrait. However, I think it is worth the mentioning. One fact comes from Noh play that was cherished and loved by samurai especially of the senior ranks. Noh play is not too popular outside of Japan, but I assume the readers know that each Noh performer plays with a mask (photo left and bekiw right). What is interesting, at least I find, is that the holes for the eyes are made rather small. For a performer, it would be better if he could have a better vision with the larger holes. It is almost they were made on purpose to that small size. As I have not received any formal education on Noh, I can only guess that they (the Noh players) believe the narrow vision would stimulate the brain of the players and improve their performance.


The other interesting fact comes from another Japanese performing art, Kabuki which is more popular in the western world. I suspect the readers have either watched a play or at least have seen the photos or drawing of Kabuki ukiyoe (photo left). In Kabuki play, they do not wear a mask but did you know that they were trained to have one cross eye? Believe it or not, the players have to train their right eye to be crossed while the left eye to stay straight. This is indeed a strange sight if you see it closely (photo below left). They say that a player with this “strange” eyes will catch the attention of the audience. Maybe it can be true if the player is close enough to see his eyes. However, to me one cross eye seems to be too subtle for that purpose, especially to the audience who are seated far from the performing floor. I am not educated in Kabuki dance either, so I can only guess the real reason. By crossing the right eye, a player must depend on the left eye heavily for his vision. This means this player must stimulate his right side of the brain. As I had mentioned earlier, the right hemisphere is the more artistic and creative side of the brain. Therefore, my guessing is that in order to maximize or at least to stimulate the artistic side of the brain, the Kabuki players purposely train their eyes in this way.


My hypothesis:

Now back to the portraits of Mach. Why did he draw those pictures through his left eye?

This is my pure guessing but I honestly believe that there was a definite reason behind his choice. We all agree that he was a smart person and a genius scientist. It is very possible that he studied about his brain, though I am not sure if he had known that there were two hemispheres in his brain. Regardless, when he was alive in the late 19th century, I do not believe the different functionality of the two hemispheres of our brain was known even among the medical experts.


Therefore, I conclude that Mach empirically knew that he was using his left side brain when he did his mathematical thinking. He probably felt that he was over working his left side brain and not enough with the right side. Thus, he felt that he needed to train his right side brain in order to get the maximum capability of his brain. My guessing may be a wild guess but I do not think it is too far-fetched when you consider how smart and successful Mach was. Somehow he knew that right side hemisphere of his brain would stimulate his creativity that would help him in his scientific research and study.


What do you think? Whether you agree with my hypothesis here, it is still true that the world famous physicist, Ernst Mach left us a few portrait of himself with an unique technique. I think this subject deserves further study and we may be able to find a unique way to maximize our mental as well as physical performance.

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