Saturday, September 12, 2009

For the Greeks, number is magnitude, the essence of all things perceptible to the senses

[A century earlier Goethe had, with firm conviction and care insisted on the insight and synthetic judgment required to detect the idea of observation. Both Goethe and Jaegar took considerable pains to uphold the highest standards of epistemic virtue, even if both these standards entailed entirely different. (Datson/Galison)"
The clash of these difference of epistemic virtues between the metaphysical associations of "truth to nature" and quantitative sensible reality of "mechanical objectivity" is no where as apparent as in the controversy involving Ernest Haeckel -who I argue in other places is the figure to whom Western Integral theory can be traced back
Science, Culture and Integral Yoga Re: Objectivity by Lorraine Datson & Peter Galison (Book Review by Norberto Serpente) by Tony Clifton on Sat 05 Sep 2009 03:07 PM PDT Profile Permanent Link 10:30 AM]

[Mediation and memory in the theory of money via The Memory Bank by keith on 9/10/09 According to Spengler, the West had exhausted the historical impulse given by its modern version of economic life (featuring money and machines) and a new phase, based on politics, national religion and war, was about to take over. This was not a bad prediction, but Spengler’s interest for us lies in how he conceived of the relationship between money and other universals.
Following Goethe, Spengler made a contrast between history (becoming) and nature (what has become). The counterpart of longing, of the desire to move forward that is becoming, is the dread of having become, of finality or death; and this pair together drive cultural creativity.
‘Life, perpetually fulfilling itself as an element of becoming, is what we call ‘the present’, and it possesses that mysterious property of ‘direction’, which men have tried to rationalize by means of the enigmatic word ‘time’.’
On the one hand, there is measurement of time as duration; but the idea of history as becoming, as irreversible direction, is particular to the West. Number belongs to nature as the chief sign of completed demarcation, of all things that have become themselves.
‘Mathematical number contains in its very essence the notion of a mechanical demarcation, number being in that respect akin to word, which…fences off world-impressions.’
Spengler identifies a break between classical antiquity and the modern West. For the Greeks, number is magnitude, the essence of all things perceptible to the senses. Mathematics for them was thus concerned with measurement in the here and now, visible and tangible. ‘Numbers are symbols of the mortal’. All this changed with Descartes whose new number-idea was function – a world of relations between points in abstract space. Whereas the Greeks sought perfection within the concrete limits of nature and society as they experienced them, now a passionate Faustian tendency towards the infinite took hold, married to abstract mathematical forms that increasingly freed themselves from concrete reality in order better to control that reality. The new mathematics was thus immaterial, resting on abstract analysis, dissociated from magnitude and transferred to a transcendental relational world, a process culminating in ‘victory over the popular and sensuous number-feeling in us all’.
2:21 PM 2:48 PM]

Although it is difficult to agree fully that transitions in society follow shifts in theory, the latter, no doubt, are helpful pointers but no determinants. [TNM]

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