On Genius in the Fields of Science and Art

Dr Heiner Eckert
Lecture given at the Ugi Conference on »Multi-Component Reactions« at the Technical University of Munich (TUM) on 22nd September 1995 on the occasion of the 65th birthday of Professor Dr Ivar Ugi (5th September 1930 – 29th September 2005).


The lecture uses selected figures from the fields of science and art to demonstrate the factors that characterise »geniuses« in general. It then develops a short theory on »genius« that explores both the shared characteristics of and significant differences between artists and scientists. The speed at which events are processed in the human brain plays an essential role in this investigation.

Johann Sebastian Bach (1685-1750)


Four notes, one topic: the notes B-A-C-H and the order in which they are placed represent the tone sequence of a melody. In fact, this melody was composed by no other than Johann Sebastian Bach, whose succession of notes reflected his very own name. The B-A-C-H melody can be found towards the end of his »The Art of Fugue« [1] and in Fugue no. 4 of his »The Well-Tempered Clavier«. With the latter piece, Bach shone the spotlight on what is now the commonly heard temperament of keyboard instruments at an early stage. Given that the leading instrument makers at the time were determined to remain with the old (meantone) temperament, Bach decided to take an offensive approach. He used an organ made by the famous instrument builder Gottfried Silbermann to play a piece in B major (with five sharps), which sounded terrible in meantone temperament due to the so-called »wolf interval«, so much so that Silbermann ripped Bach’s wig off his head in a fit of rage [2].
02-500px-B-a-c-h.svg1Bach had a particular preference for the fugue as a strict compositional technique that stands out due to its extremely high degree of structural logic. Bach used this technique to celebrate true musical orgies in which he shines the spotlight on charming melodies in a fireworks display of mathematical operations that clearly demonstrates the genius of perfection.

Leonardo da Vinci (1452-1519)


Leonardo da Vinci is the ingenious counterpoint to the perfectionist Bach. He is a painter, architect, engineer, scientist and inventor all rolled into one and his famous paintings demonstrate an extremely high level of sophistication, with the »Annunciation« making it clear that Leonardo was a master of central perspective.



Alongside his artwork, da Vinci’s inventions were also well ahead of their time. His cannon with shrapnel bombs, for example, is an outstandingly good invention. Leonardo himself describes it as »the most deathly machine around […] with a ball at its heart that explodes, causing the other balls to scatter immediately, just as fast as a Hail Mary« [3a]. Leonardo also produced an astoundingly precise theoretical plan for another invention in the form of the worm drive, an extremely special mechanical drive arrangement that was finally manufactured long after his time, namely not until the 18th century [3b]. On top of all this, he also allegedly produced plans for yet another invention, the details of which are virtually identical to those of today’s contemporary chain-driven bicycle [4].

05-Leonardo_Folio_133v_Bicycle.1With his ingenious work in his role as an artist right through to his brilliant creations as an engineer, Leonardo da Vinci boasted an immense spectrum of talent that nobody on Earth has since been able to match. He truly is the ultimate universal genius.

Gottfried Wilhelm Leibniz (1646-1716)


The multi-genius Gottfried Wilhelm Leibniz is a similar type of genius to Leonardo da Vinci but comes from a scientific and academic background. He studied Law, Science and Philosophy in his place of birth and home city, Leipzig, before moving to the German city of Jena to study Mathematics. At the age of twenty, he completed his Doctorate in Law and immediately declined the offer of a position as a professor. Shortly after making this decision, Leibniz was appointed as a councillor at the appellate court in the German city of Mainz [5a]. At this early stage of his life, it was already clear that Leibniz did not plan to follow a systematic career path. Instead, his mind bursting with ideas constantly leapt from one field of activity to another, always with full intensity, representing a genius of versatility and energy.
As a child of the late Thirty Years’ War, Leibniz made a huge attempt to reconcile the two Christian confessions but neither he nor anyone else was able to successfully do so [6a]. Leibniz is the protagonist of the modern world of science. He developed infinitesimal calculus in the field of mathematics [7a], introduced the integral symbol that is still used today [7b] and also created the number system that now forms the basis of modern electronic computers. When talking about his work, Leibniz stated that: »binary characteristics are more complete than decimal characteristics or any other approach« [6b, 8a]. He went on to construct a mechanical calculator [7c, 8b] and was able to sell a small quantity of these tools to the tax authorities.
09-Leibnitz-Integral-large-a.2As a philosopher, Leibniz wrote a text known as the Monadology [5b, 9a, 10, 11]. The intellectual approach taken in this piece went on to be explored in the modern physics of Einstein a good 200 years later, namely the notion that units of being (»monads«) harmonise (in pre-established harmony) without influencing each other and that every single monad therefore reflects the entire universe.


Leibniz knew no boundaries and always thought big, so much so that he strived to create a universal academy featuring the world’s most distinguished and prominent scientists from locations as far away as China [6c]. Although the time was not yet ripe for such an idea, he did succeed in establishing the Academy of Sciences in Berlin, which was later renamed the Prussian Academy of Sciences. Leibniz also actively inspired the creation of further academies in Saint Petersburg and Vienna. The first German scientific journal, »Acta Eruditorum«, was published in 1682 and was, of course, another development instigated by Leibniz [5c]. In the last few years of his life, Leibniz was showered with praise in the form of an abundance of distinctions and awards and was even given the noble title of »Reichsfreiherr« (baron). Nevertheless, after Leibniz’ death, his employer, the Elector of Hanover, chose to stay away from his funeral [9b], representing a logical parallel to the death and burial of another genius, Mozart.

Johann Wolfgang von Goethe (1749-1832)


Why is it always Goethe who is quoted at every opportunity when there are plenty of other literary figures to choose from? It can’t simply be due to the expressiveness of his language alone because his counterparts were equally expressive. Nevertheless, it is clear that he was particularly successful at personally appealing to every individual. It can therefore be assumed that he had an excellent understanding of human nature and this was indeed true: Goethe was the master of understanding people and no aspects of human nature were unknown to the old charmer. This ability was the product of Goethe’s high degree of realism, which is precisely what defines his specific genius as an ardent realistic artist with strong inclinations towards the field of science. Goethe was a precise observer, which enabled him to already identify and describe evolution in the plant and animal kingdom at an early stage [12]. Despite his work in the field of science, he viewed things with the eyes of an artist. This was also the approach taken in his criticism of scientific methods, which even provided food for thought for scientists and was expressed in Goethe’s Theory of Colours [13]:

»In research into nature, we consider the error of placing more importance on a derived phenomenon and less importance on an archetypal phenomenon to be extremely severe.«

Of course, we cannot leave the topic of Goethe without at least presenting a very short poem that actually provides a more comprehensible insight into the academic artist than any attempts to explain his work:

»Ihr glücklichen Augen,
Was je ihr geseh’n
Es sei, wie es wolle,
Es war doch so schön«
»You happy eyes,
whatever you have seen,
be it what it may,
it was certainly beautiful.«

It is now time to explore the ingenious inventions that have had the most momentous influence on the world as we know it: engines. Engines form the basis of all industrial drive systems and transport and traffic solutions and therefore play an essential role in facilitating people’s modern-day mobility.

Nicolaus August Otto [14],
12-Nikolaus August Ottoampnet_photo_20160125_111674.2

a travelling salesman in the German city of Cologne, used compression and a magneto ignition system to develop the gas engine into a reliable four-stroke machine and founded the engine manufacturing company Deutz AG near Cologne. As business started to go well, Otto was immediately hit by a legal setback when his rights were challenged and virtually completely destroyed in a multitude of patent proceedings.


Rudolf Diesel [15]

13-Rudolf-Diesel-DBP_1958_284_Rudolf_Diesel.2Rudolf Diesel came up with his inventive objective while attending a lecture given by Carl von Linde on the topic of thermodynamics, at which he decided to use a higher heat gradient to achieve a higher degree of efficiency, with the simultaneous increase in pressure in the fuel and air mixture resulting in self-ignition.
This marked the start of the success story of the diesel engine. Nevertheless, Diesel also fell victim to a multitude of merciless patent proceedings and saw only one way to escape from the vigorous attacks: to take his own life. He drowned in the English Channel while sailing to England.
Two other revolutionary inventions that shape our modern-day lives were rapid data transmission and the generation of high-voltage currents, which opened the door to the entire world of electrical engineering.

Werner von Siemens (1816-1892)


After completing thorough training in technical and scientific subjects during his time at a military academy, where he was also trained as an officer, rising up through the ranks to the role of Artillery Lieutenant, Siemens [16] identified telegraphy, the rapid transmission of data, as a lucrative future market. He went on to build the Prussian and Russian telegraph lines together with his brothers and the Indo-European Telegraph Line from London to Calcutta via Tehran with his English company. Siemens also installed the first transatlantic line between Ireland and America after the American Civil War, as well as inventing the needle telegraph.
His most prominent and momentous invention, however, was the dynamo based on the principle of electrodynamics, which first facilitated the use of efficient power engineering, namely the use of an electric current as a source of energy. He additionally presented the first electric trolley bus in Berlin.
When it came to dealing with patents, Siemens proved to be more skilful than Otto and Diesel, so much so that the first German Patent Act was created on the basis of his suggestions. Siemens was the first engineer to become a member of the Prussian Academy of Sciences founded by Leibniz.


Tesla three-phase asynchronous motor, 3 kw, 1888
Jacobi-motor, 300W, 1834

Albert Einstein (1879-1955)


In the middle of the First World War, during the period of strong attrition warfare, Einstein [17] discovered cosmic harmony hidden deep below the surface with the basic equations of his theory of general relativity, stating that: »I believe in a God who reveals Himself in the harmony of what exists«. With this statement, he provided a precise description of the pre-established harmony of the monads in the philosophy proposed by Leibniz and went on to further develop this school of thought 200 years after it was first established.
The Prussian cultural scene was flexible enough to approve suitable vocations for Einstein as an unconventional individualist. Alongside his role as a university professor, he was also appointed Director of the Kaiser Wilhelm Institute for Physics, where he was additionally freed from all teaching obligations.
When referring to Heisenberg’s theory of quantum mechanics, Einstein claimed that: »Heisenberg has laid a big quantum egg. In Göttingen, they believe in it (I don’t!)«. Einstein then reached for the stars by attempting to tackle the unified field theory, which aims to bring together the physical sub-areas of gravitation, electromagnetism and, more recently, strong and weak interactions. This aim still remains unachieved in the present day and Stephen Hawking is currently working intensively on solving the mystery.
Einstein’s activities in the world of politics actually strongly contradicted each other: he spent many years advocating pacifism before going on to suggest that President Roosevelt build an atomic bomb and then, before the weapon was actually used, demonstrating against nuclear war. It may, however, be the case that he wasn’t as contradictory as it may seem at first glance. In fact, Einstein can also be considered to be the mastermind behind the strategy of nuclear fear. Nevertheless, his political activities made his life increasingly difficult: plans were made to murder him and proof of incitement of this crime resulted in punishment by justice in the form of a $6 fine [18], which apparently reflected the societal value of a genius at the time. When talking about his political activities in his later years, Einstein himself stated that: »equations are more important to me because politics is for the present, but an equation is something for eternity«.
17-Lise_Meitner12.2 The fundamental possibility of generating huge amounts of energy based on Einstein’s concept of mass-energy equivalence had now been identified and further explorations into the topic used the process of nuclear fission. Significantly, the first successful nuclear fission experiment was not carried out by physicians but by the chemist Otto Hahn. Chemists like to experiment and even if they are sometimes not precisely sure what they are doing, they normally do it right by intuition. The task of interpreting the theory was then also completed by Hahn’s long-standing colleague, the nuclear physicist Lise Meitner [19].

Justus von Liebig (1803-1873)


Justus von Liebig is an extremely strong representative of the guild of geniuses. He invested his earnings from his literary works into his chemical research activities without hesitation, despite not yet having completed the work for which he was paid [20, 21].
Liebig was rather successful when it came to preventing people from gaining an insight into himself as a person, but we want to give it a try anyway. After extremely successfully resisting all efforts made by his parents, school or apprenticeship to provide him with a decent qualification, Liebig whinged and whined until at the age of 17, he was finally able to study Chemistry in Bonn (which was possible without completing school education at the time). The young Liebig was a very active and outspoken student and was frequently involved in demonstrations and riots until, after the police searched his house, he decided to flee. His professor Kastner, the most well-known German chemist of the period, obtained a grant for him to study in Paris. During his absence, Liebig was granted his doctorate in Erlangen »in absentia«. The topic of his thesis, »On the Relationship between Mineral and Plant Chemistry«, was well ahead of its time.
After being recommended by Alexander von Humboldt, Liebig was appointed as an associate professor at the University of Giessen by the government, against the will of the university itself. He attracted students away from the existing main professor, Mr Zimmermann, without even trying, which eventually led Zimmermann to commit suicide in the Lahn river. Liebig’s most momentous acts were:

1) Reforming university teaching by introducing practical sessions with educational objectives that were predefined in a curriculum.

2) Elementary analysis: Liebig transformed what was previously known as an art into a routine.

3) Fertiliser theory: Liebig’s elementary analyses of dried plants and their ashes revealed that the elements of the ashes needed to be replaced and based on these findings, the idea of fertiliser was born. According to Liebig, »stall manure can be replaced with mineral elements«. The extent to which this statement was correct is proven by the 100,000,000 tons of nitrogen that are now converted every year using the Haber-Bosch process. With this discovery, Liebig made an economic breakthrough in the field of global food security und nutrition and therefore sparked the agrarian revolution!

19-Liebig-Bilder-figuritas-liebig-11-12-14-15-cubo4) Enabling a social breakthrough thanks to his work on meat extract, baby food, baking powder, coffee substitute, etc. One of his main achievements was making life easier for working mothers by significantly reducing the time and effort involved in making meals, which marked the dawn of the instant meal era. Liebig brought all of these activities together under one roof in the form of his Liebig Company.

Liebig was not only a genius in terms of chemistry, but also a brilliant scientist when it came to both teaching and research, an ingenious business man with a scientific focus, similar to Siemens and, last but not least, the game-changer who solved the main global problem of his time, feeding the population.
As these achievements show, Liebig became a extremely level-headed individual, despite, or maybe even precisely because of, his eventful youth. He was able to clearly identify the feedback that achievements in the field of applied science provided for pure science, stating that:

»The inventions made by people in the fields of trade, industry, medicine, mechanics and astronomy provide the facts that are absolutely essential for the future development of the world of science.« [22a]

Liebig also saw no mystery whatsoever in the science of alchemy, claiming that

»Alchemy has never been anything other than chemistry.« [22b]

When consulted as an expert in a criminal case, Liebig’s objective considerations enabled him to improve the way in which the truth was established, thus resulting in the revision of what was common legal practice at the time [21b]. A countess of Görlitz had been discovered lying dead under her davenport desk in her boudoir one morning. Both her corpse and her desk were burnt and partially charred. The countess’ servant was accused of murder and his defence plea claimed that Mrs von Görlitz had been drinking heavily, thus causing her alcohol-soaked body to self-ignite and also set her desk on fire. This was based on a standard claim that had successfully established itself as a reason for exoneration in such cases at the time. Liebig, however, argued that water makes up three quarters of the human body and that as a result, the body cannot get any hotter than the boiling point of water, which is several hundreds of degrees below the temperature required to ignite alcohol. He also stated that the body cannot burn until all of this water has evaporated, which in turn cannot occur unless heat is supplied from an external source. He therefore concluded that the death of the countess was without a doubt a case of murder and that she had fallen asleep at her desk and then been set on fire while she slept.
One of the witnesses to the case was the architecture student August Kekulé, who was so fascinated by Liebig that he decided to study chemistry instead.


A brief theory of genius

So what is the ultimate definition of a genius?
When answering this question, it is easier to approach it from an art-related perspective:

True artists express thoughts and ideas.

This statement summarises not one, but two main characteristics that define geniuses: they first need to have a top-quality idea, but other people have such ideas too. Geniuses therefore also need to be able to articulate and establish this idea and if they are unable to do so, at least need to present it in such a manner that it can be resurrected at some point in the future. (A good example of this is Leonardo’s inventions, some of which were not actually created until centuries later. Leibniz’ Monadology and Bach’s music were also developed and established on a similar time-scale). This point leads us to the third and most important characteristic of geniuses: being ahead of their time. A highly gifted and talented individual can only become a genius if they have a far-sighted idea or create something new. The difference between talent and genius is achieving a perfect balance.

The fact that geniuses are future-oriented automatically differentiates them from other talents, so to speak, because all future-oriented ideas and developments are initially incomprehensible and uncomfortable. They are therefore dismissed by non-geniuses as unimportant or nonsensical, and definitely as superfluous, because they are unwilling or even unable to explore them due to their incapability to understand the future-oriented concept. In this case, feelings of aggression also arise: non-geniuses accuse geniuses of being incompetent, meaning that life as a genius is extremely uncomfortable.

It is, of course, logical that an idea that is not inherent also cannot be expressed in an inherent manner. Geniuses therefore often face the challenge of having to force their ideas against the beliefs and wills of experts, which requires the use of unconventional methods. As a result, the non-conformity that makes geniuses so easy to identify is not a quirk, but actually a necessary strategy that they need in order to make a mark. Another main characteristic of geniuses evolves almost naturally from the properties already identified: geniuses are extremely versatile and set themselves many targets before working to achieve them all at the same time. This applies to both artists and scientists alike. So how do they differ? We can differentiate between artists and scientists with regard to the method and way in which they understand and express things:

While artists see things as a whole, scientists view the individual parts.

In the case of Goethe, we already discovered how an artist criticised the scientific method of failing to focus on the whole picture [13]. The scientist Liebig, on the other hand, claims that the ability of an observer depends precisely on being able to see the individual elements that make up the whole [21a].

»To this effect, when researching nature, we consider it to be an extremely severe error when more importance is placed on a derived phenomenon and less importance is placed on a archetypal phenomenon, or even when the derived phenomenon is turned upside down and its composite is considered to be a simple element while a simple element is considered to be a composite, which has led to extremely fantastical complexities and confusions throughout the field of the study of nature, from which it is still suffering.«

J.W. v. Goethe

»There is no art as difficult as the art of observation, which requires an educated level-headed spirit and well-trained experience that can only be obtained though practice; for observers are not those who see what is in front of their eyes, but those who see the elements that comprise it and how these elements are connected to the entity as a whole.«

J. v. Liebig

The presentation of scientific findings occurs in logical steps, namely in comprehensible parts of the entire phenomenon. Art, on the other hand, aims to present the entire phenomenon in one fell swoop, so to speak. People’s capacity to understand such presentations is, however, hopelessly overburdened in terms of intellect alone. Nevertheless, people do have perceptive abilities in all of their senses that enable them to effortlessly process highly compressed sets of information. The world of art makes use of these abilities when communicating its messages.


[1] Hans Heinrich Eggebrecht, Johann Sebastian Bach, in: Die Großen der Weltgeschichte (»Great Figures in World History«), volume VI/1; ed. Kurt Faßmann, Kindler Verlag publishing house, Zurich, Switzerland, 1977, p. 394
[2] Gertrud Loos, Temperierte Stimmung, – ein musikalischer Kompromiß, Beilage zur Schallplatte »Das Wohltemperierte Klavier Erster Teil« (»Tempered Scale – a Musical Compromise«, as an insert with the record »The Well-Tempered Clavier – Part 1«), Odeon, order no. O80605S
[3] Ludwig H. Heydenreich, Bern Dibner, Ladislao Reti, Leonardo der Erfinder (»Leonardo the Inventor«), Belser Verlag publishing house, Stuttgart, Germany / Zurich, Switzerland, 1987; a) p. 122; b) p. 162
[4] Carlo Zammattio, Augusto Marinoni, Anna Maria Brizio, Leonardo der Forscher (»Leonardo the Researcher«), Belser Verlag publishing house, Stuttgart, Germany / Zurich, Switzerland, 1987, p. 154
[5] Gerhard Kropp, Philosophie (»Philosophy«), Verlag Lebendigen Wissens (Humboldt Taschenbücher) publishing house, Munich, Germany, 2nd edition; a) p. 69; b) . 72; c) p.70
[6] E. Hugo Fischer, Gottfried Wilhelm Leibniz, in: Die Großen der Weltgeschichte (»Great Figures in World History«), volume VII/1; ed. Kurt Faßmann, Kindler Verlag publishing house, Zurich, Switzerland, a) p.223; b) p. 221; c) p. 225
[7] Großes Handbuch der Mathematik (»The Big Guide to Mathematics«), ed. W. Gellert, H. Küstner, M. Hellwich, H. Küstner, Buch und Zeit Verlagsgesellschaft publishing house, Cologne, Germany, 1970; a) p. 414; b) p. 456; c) p. 678, 778
[8] Knaurs großes Buch der Mathematik (»Knaur’s Big Book of Mathematics«), ed. Richard Knerr, Lexikographisches Institut publishing house, Munich, Germany, 1989; a) p. 130; b) p. 576
[9] Friedrich Heer, Gottfried Wilhelm Leibniz, Fischer Bücherei publishing house, Frankfurt / Hamburg, Germany, 1958; a) p. 130; b) p. 7


[10] Hans Heinz Holz, Leibniz, Verlag W. Kohlhammer (Urban Bücher) publishing house, Stuttgart, Germany, 1958, p. 29
[11] Karl Vorländer, Philosophie der Neuzeit (»Philosophy in the Modern Age«), in rowohlts deutscher enzyklopädie (»Rowohlt’s German Encyclopaedia«), Rowohlt, Hamburg, Germany, 1966, p. 76
[12] Leo Krell, Leonhard Fiedler, Deutsche Literaturgeschichte (»German Literary History«), Buchners Verlag publishing house, Bamberg, Germany, 1962, p. 182
[13] Johann Wolfgang von Goethe, Zur Farbenlehre, Didaktischer Teil, Zweite Abteilung, Physische Farben (»Theory of Colours, Educational Section, Part Two, Physical Colours«), chapter 176
[14] Gustav Goldbeck, Nikolaus August Otto, in: Die Großen der Weltgeschichte (»Great Figures in World History«), volume VIII/2; ed. Kurt Faßmann, Kindler Verlag publishing house, Zurich, Switzerland, 1977, p. 582-595
[15] Kurt Schnauffer, Rudolf Diesel, ibid., volume IX/1, p. 344-363
[16] Sigfrid von Weiher, Werner von Siemens, ibid., volume VIII/1, p. 174-185
[17] Armin Hermann, Albert Einstein, ibid., volume XI/1, p. 14-33
[18] Stephen W. Hawking, A Brief History of Time, Rowohlt Verlag publishing house, Hamburg, Germany, 1988, p. 220
[19] Exhibition: »Lise Meitner, the Life and Work of Nuclear Physiscist« at the Lise-Meitner-Gymnasium advanced secondary school in Böblingen, Germany, 23.3.-3.4.1987
[20] Otto Krätz, Justus Liebig, in: Die Großen der Weltgeschichte (»Great Figures in World History«), volume VII/2; ed. Kurt Faßmann, Kindler Verlag publishing house, Zurich, Switzerland, 1977, p. 692-707
[21] Jacob Volhard, Justus von Liebig, volume I, Verlag Johann Ambrosius Barth publishing house, Leipzig, Germany, 1909; a) p. 382; b) p. 177-179
[22] Wilhelm Strube, Der historische Weg der Chemie (»The Historic Journey of Chemistry«), VEB Deutscher Verlag für Grundstoffindustrie publishing house, Leipzig, Germany, 1976; a) p. 109; b) p. 82