THE FOURTHWAY MANHO EJOURNAL Volume 150 August 15, 2021 

MATHEMATICAL THOUGHTS; RESEARCH FINDINGS AND USAGE OF KNOWLEDGE By Professor Dr. Tan ManHo (An excerpt from the original work, Real World Views, Book 2, by Professor Dr. Tan ManHo entitled "Biocosmic NervoReflectant, The Theory of Material Reflection in Man; Inner Development and Social Upheavals" July 1973 ~ September 1974 Discourses, Chapter 1, Section C & D: "Mathematical Thoughts; Research Findings and Usage of Knowledge", pp. 9 ~ 19)
C. MATHEMATICAL THOUGHTS
1 Does it require deep intuition to comprehend that the mathematics of man is an algebraic symbolic representation and quantification of the material phenomena of the external world, that external process when men become aware of can lead to formation of new forms of mathematics and that material phenomena determines the nature of the essence of mathematics? What else does the history of mathematics shows is none other than its evolving characteristics? From the formal type to the dialectal type; from Euclidean mathematics to the calculus of Newton and Leibnitz? The more the consciousness of men in a historical period the more profound and peculiar is their mathematical thoughts.
2 When philosophizing science from their standpoints as the center of gravity or launchpad, the positive scientists ended themselves into narrowedmindedness uncalled for, weak and strayed general generalization improper to their scientific thought discipline. When so “drunk” in mathematics, they begin to see mathematics as a great mystery, and that all beings – God, the cosmos, the biological beings and many more beings – must be mathematical in essence and quality in personality or appearance. Everything sits on mathematics in the way of the Indian philosophy that the Universe sits on the tortoise back which in turns sits on the Elephant. So with the religious man, everything is created by God! And finally with the naturalist, everything is Nature. However, every thoughts comes from your head including mathematical thoughts! Mathematics is part of the head in the reasoning process of the intellectual center and even in the narrower specifics of induction, deduction, generalization, etc. in the logical part of the mind over quantities pure and applied. By pure is meant abstraction of the objective outer world phenomena into the subjective quantities and proceeding quantitative evolution from there within itself and by applied is meant materialization or realization of these mathematical outcomes within itself back to the objective outer world and changing the world outside. The linkpin is MEASURE which link and bind quality and quantity through a MEASUREMENT process.
3 The way I examined mathematics previously (before 591972) is incorrect. I was halfconfused with formal logic and dialectical logic. After this date, I have understood; I supposed, the essence of dialectical mathematical logic is a form of mathematical thoughts and formal mathematical logic is its incomplete static part. The bursting asunder of the formal deductive mathematical logic within my inside into the new dimension of dialectical logic for mathematics is the source of my “confusion” experience. I was seeking in mathematical processes those evidences of dialectical logic but found myself thinking in favor of the Hegelian logic to match pure mathematics that directs to itself and also the inversion of this Hegelian logic or Marxian dialectical logic that directs to the phenomenal or outer world. This pure mathematics functions in the dimension of the inner world of man without Hegelian notion of measure and without application (Applied Mathematics).
4 The essence of mathematics is deductive reasoning from explicitly stated assumptions called postulates. Mathematics is not the essence of all knowledge or the God or the dominating gravitycenter in the thought world peculiarly much indulged in and much drummed in imbalance by most western education of my time. So biological science, psychological science, social science, cosmic science and others are gradually forced to wear only the spectacle of mathematics – gravitating on quantities or at most measures and disfavored the qualitative aspects of the real world – thus lopsidedly gravitated at the expense of other types of valuable knowledge and may cause their omission in history and the gradual fall of a nation world wide because of this unbalanced gravitation.
5 Physics is a logical system of thought is a state of evolutions. The basis cannot be obtained merely by experiment and experience. Its progress depends on free invention ……. I haven’t the faintest doubt that I am right. (Albert Einstein) A logical system of thoughts is in the inner world and experiments and experiences are due to our interactions or exchanges with the outer world. Our inner world has a great degree of freedom and free will but our outer world has material beings with insides which can be as free as our own inner world and the outer world has their own inner worlds too! 6 The logical is historical, historical sequence of description is the fundamental basis. To speak logically is to be able to explain and describe in a historical manner – one phenomenon leading to the other but unidirectionally. By historical is meant the actual processes nature undergoes and by logical is meant the formal logically correct interpretation of these processes of nature. The postulations which have no real world object reference but purely mind inner world reference subjects especially in pure mathematics shall end in the “pure” abstract thoughts. It does not end in the objective reality but does not mean it will never end into objective reality. Because it is pure mathematics its objective reality is the thought objects but the thought objects can also be the real objects in the objective reality. The more the referencing to objects in the objective reality the more will the pure mathematical thoughts be enriched, modified or changed to accommodate the facts in the objective reality. An object in the objective reality or real world object reference is the specific quality observed and posited in a logical reasoning mind for which mathematical quantification is the next stage of its development. The outcome would still be still be in the real world object reference unless on its path of reasoning an inner world reference subject(s) has been introduced in error.
9 A sphere can be considered to be made up of many right circular cones having apexes meeting at one point purportedly at the center of the sphere and having infinitesimal planar circular base areas on the surface of the sphere. The smaller the base areas and the greater the number of such cones, the greater is the proximity to a perfect sphere. However, to become a sphere the vertical height and the slant height must be the same. Geometrical shapes are nonlonger called by the same name because qualitative transformation has occurred. The qualitative transformation has occurred because the controlling conditions or nodes have changed. But changes have occurred only quantitatively within the controlling limits beyond which qualitative change to the existing geometrical shapes must occurred and a new name must come in place for call and with new definitions for the controlling limits. So in the world of planes there are the triangle, the square, the rectangle, the parallelogram, the circle, the ellipse and the countless polygons which are all qualitative planar geometrical beings (creatures) contained and held in qualitative position by the controlling limits of specific quantitative units of the points and lines. So are the other geometrical shapes in the solid world such as the cone, the sphere, the pyramid, the square, the rectangular, the triangular blocks and the polygonal blocks or the nonEuclidian threedimensional spherical sphere of Riemann. So also are the spatialtemporal world such as movies and videoframes and our real living world where time is introduced as one such controlling condition to both quantitative and qualitative transformation. Much more unimaginable is the spatialtemporaleternity geometrical shape of our Real Universe which is more to the one where our spaceships hop from one such spatial planet to another in time. The Euclidean Geometry is not the Real World Geometry. Professor Einstein’s SpatialTemporal “Geometry” is one that is much closer to a Real World View. The 7dimensional “Geometry” is the yet to be conceivable or feelable with our current state of being.
10 Mathematics is the most highly developed form of communication by means of signs which in themselves are meaningless. .....… that this is possible is one of the most wonderful outcomes of modern science, for which we owe mostly to Niels Bohr. However, instead of Hertz’s expression “images”, I would prefer expressions such as “visual aids” or “partial visual aids”. In the end, all sensory perceptions are images, and what really lies behind the “phenomena” (that which Kant calls “the thing itself”), remains obscure. (Max Born)
2 Research: Does it basically essential to show a PhD to be able to do preknown and prefixed research topics? What then does man do research for? And what do we mean when we do research? Is research a necessity? And should research be stopped by the license of a PhD that might be annexed in the Research Act? Institutionalized permission for research is not beneficial to mankind where consciousness and intelligence have other sources of origin as well – from forces of production and social relations of productions, from gods, from gene, from planetary influences, from good health, from good exercise, from good food, from the sun, from high level gurus, from good air, from personal hard work, from nature, etc. One of which is from buildings and administrative operations plus paper work with procedures and a mediocre “research commander” who only exercises powers of position because he is appointed there from the process of the social relations of production. The history of the development of the forces of production necessarily follows an everincreasing trend in the capitalist socialeconomic formations and also that of the socialist socialeconomic formation. It is this force of production which determines or rather compels man to achieve more accurate knowledge of the phenomena of matter in motion. The forces of production tend to grow rapidly and also that of the thoughts that follow, which tend to be lagged behind the development of the forces of production. The development of human knowledge behaves in a form similar to “Maxwell’s Distribution Law.” It is impossible to completely obtain a stage of the mind whereby all phenomena of matter is accurately understood. New phenomena will unceasingly evolve out or become perceptible to the senses and to understand them requires further studies, a necessary outcome in the process of research. An analysis that follows is a necessary outcome. Research needs not be a job of a research institute, although a research institute is socially committed to research but in most cases only launders research works of uninstitutionalized freelance researchers. The moment when a mind “fixed” onto a problem, a research process has already started and will ultimately reach somewhere. Some research pieces are welldone, some are not. The welldone are those which correctly interpret the objective reality, whilst the poor ones are those which have been subjective in approach to a problem. At this juncture, the researcher must hide his research work from being reworded and legally institutionalized by someone else. (April 24, 1973)
3 It is the falling of the apple that led Newton to the discovery of the Law of Gravitation. This is outside the man but there must be a ready psyche with the right bud to ready to grow this branch of knowledge. The main cause for the discovery of Kekwe ring was that he dreamt of a snake coiling. This is inside the man but there must be something outside which he has been working on very hard to absorb and digest what is impressed. The first approach started out from the outer world stance while the latter from the inner world. If you sit in a room, not exposed to the outer world and nurture your mathematical thoughts days and nights, the ghosts of pure mathematics will live with you!
4
The logical is historical. The historical is primary. The
logical is secondary. If the logical is not historical then that logic
is called formal logic. If it is historical it is called dialectical
logic. But historical is also chronological. It flows in one
time dimension. But time has 3dimensions and formal trialectical
logic is more holistic than dialectical logic, and dialectical logic is more
holistic then formal logic. The historical is not pure moving
historical process of thesis, antithesis and synthesis but in the history
creates discontinuities and “note” in accordance with the octave logic.
Everything is material, even knowledge is material. Spirit would be fine matter. This is the same saying: everything is spiritual, even knowledge is spiritual. Matter would be coarse spirit.
Statement 2: It does not recognize anything save that perceived by the sense organs

