The Voice of Allan Zade
Human knowledge developed over time for many centuries. Mathematics originated in the Middle East and replaced the traditional Roman method of calculation. Gradually, other branches of knowledge began to utilize mathematics to meet their needs. However, the primary distinction between all other branches of knowledge and mathematics remains ever the same.
Any branch of knowledge (branch of science) answers the central question ‘How?’. Mathematics answers the secondary question ‘How much?’ In other words, mathematics needs other branches of knowledge as its “hosts.”
- Allan Zade
The best example of such a relationship is Newton’s work, ‘Mathematical Principles of Natural Philosophy’, which brought mathematics to physics.
Sir Isaac Newton (4 January [O.S. 25 December] 1643 – 31 March [O.S. 20 March] 1727) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Enlightenment that followed. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, achieved the first great unification in physics and established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, though he developed calculus years before Leibniz. Newton contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science.
- Ref. # 1
Allan draws your attention to the sequence of fields where Newton’s activity was mentioned: 1- mathematics, 2- physics, 3- astronomy, 4- alchemy, 5- theology, and 6- authorship. That implicitly gives you the idea that mathematics is the most outstanding achievement of Newton. However, that idea is wrong because mathematics relies on data from other branches of knowledge, as mentioned above. In other words,
Mathematics means nothing without numerical data
- Allan Zade
In Newton’s case, he utilized data that was already known before his work in celestial mechanics and physics. For example,
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, which was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary velocities vary.
- Ref. # 2
In other words, Johannes Kepler published his research and findings in that area 34 years before Newton was even born (1609 against 1643). In other words, the laws of planetary motion were known long before Newton.
Moreover, Newton was not an independent researcher like others. He was hired to make something that we call today ‘some mathematical model of a physical process.’ People who hired him needed a “mathematical model” or way of thinking that not only explains celestial mechanics through qualitative descriptions but also provides a quantitative explanation. It was a specific task for a mathematician.
Newton’s achievement was highlighted because of his perspective on physical interaction, which can be formulated as follows.
All laws of physical interaction are the same for any entity involved in a given interaction.
- Allan Zade | statement A
As a result, he came to the point of view that an apple that "falls and hits his head" follows the same law of interaction as all other planets “falling to the Sun.” It was a critical moment for him because it transformed his mind to an understanding of some general force that affects all things in the universe, “from an apple to a star.”
Later, the point of view formulated as the statement A mentioned above served as the basis for the scientific method. The primary reason for that method was a requirement for physical support for any point of view that can be treated as a scientific one.
At the same time, it requires Reproducibility for experimental support of every scientific point of view.
Reproducibility measures the degree of agreement of an experiment or study performed by different individuals in different locations and with different instruments. An experiment that is reproducible if it can replicate the results anywhere and by anyone who properly follows the procedure.
- Ref. # 3
Therefore, reproducibility is the physical output of statement A.
Further development of science was relatively straightforward until physics encountered a highly challenging question dating back to Newton’s works. Newton has some papers related to light. According to his mechanical point of view, light appears as a vast number of corpuscles traveling at finite velocity. Variation in the physical aspects of those corpuscles seems to a human being as colors.