Quantitative Mathematics and Qualitative Life and Soul : The letter killeth, but the spirit giveth life

Rudolf Steiner:

Knowledge attained in those regions where the crutches of sense perception are lacking can be most readily understood where the freeing from such a perception is most easily gained. This is the case with mathematics. Mathematics is therefore the most easily acquired preparatory training for the occultist who seeks to rise to bright and radiant clarity in the higher worlds, and not to a dim sentient form of ecstasy or to dreamy premonitions. The occultist and mystic live in the same light-filled clarity, within the supersensible world, as the elementary geometer does in working with the laws of triangles and circles. True mysticism lives in light, not in darkness. 

It can also be easily misunderstood when the occultist who is speaking out of aconviction that can be called Platonic demands that research be carried out in the manner of mathematics. One could assume that mathematics is being overrated. This is not the case. However, they are guilty of such an overestimation who only allow something to count as exact knowledge to the extent that it falls within the realm of mathematics itself. There are natural scientific researchers of the present time who reject every statement in the fullest sense as unscientific which cannot be expressed in numbers or figures. For them, where mathematics ends, vague belief begins; and therefore every claim to objective knowledge must cease. It is precisely those who object to the overestimation of mathematics who are able to become the true judges of that genuine crystal-clear type of research that also proceeds in the spirit of mathematics, even in those regions where mathematics itself ends. In its most immediate sense mathematics is only concerned with the quantitative. Its realm ends where the qualitative begins. 

Thus it is also a question of researching in the strictest sense within the field of the qualitative. . . .

                                                       

Thus it all depends on the human being rising, through the type of self-discipline indicated above, to sense-free perception. The doors to mysticism and occultism are only unlocked in this manner. One of the paths leading to a purification from life in the sense world is through a schooling carried out in the spirit of mathematics. And just as the mathematician first stands firmly in life, when because of his training he is able to build bridges and tunnels, that is say, he is able to quantitatively master reality, so they too are only able to master and understand the qualitative realm who have first understood it in the ethereal heights of sense-free perception. This is what the occultist does. And just as the mathematician uses mathematical laws to fashion iron structures into machines, so the occultist shapes the life and soul in the world using the laws of these realms that he has grasped in a mathematical way. The mathematician returns to the world with his mathematical laws; the occultist no less with his laws. And just as little as the non-mathematician can understand how a mathematician works on a machine, so just as little can the non-occultist understand the plans by which the occultist works upon the qualitative forms of life and soul. 

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Source: June 21, 1904. GA 35 pp. 6-7