Die Anzahl and the Relational Database

In 1827 Justus Grassmann published a paper on the theory of Zahlen in which he defines a system of accounting which catered for a whole object starting with a numeral mark. This notion of Zahlen or Anzahl was the basis of Hermann's notion of Ausdehnungs Größe and which underpinned his notion of the Mannigfähltigkeit, or Vielenfach as he called it. It is also the notion thst carries through into Levi and Ricci Tensor notation, and finally into the conception of a relational database.

One commentator remarked on the absence of matrices in Grassmann's notation. This is because the Tafel, or tabular form for the coefficients of a system of linear equations is not significant. The determinant is the key matrix idea and this Grassmann was dealing with in his algebra before many of his contemporaries.

The relational database makes a good analogy for Justus notion of die Anzahl, die Verbindungslehre von Zahlenlehre und Kombinationenlehre and thus for a different route into Grassmann's Ausdehnungs Größe.

The more I thought about Verbindungslehre the more I could not escape the congruency with the modern term Group Theory! Justus Grassmann proposed in 1827 a group theoretical approach to die Zahlen! The elements of the group were the integers, the rules of group structure was the kombinationlehre and the operations were the 4 usual ones. It is not an isolated event, as the beginnings of group and ring theory in Europe were about this time , but what it indicates is how advanced and cutting edge his mathematical explorations were, and what he intended to expose the children of Stetin to!

This was the most advanced mathematical thinking of his day, an entrance in on the ground floor to give Stetin the opportunity to play a leading role in the future of mathematics and physics!
I have just found an amazing research site which enables me to gain access to scholarship in an understandable contextualised way.
The Grassmann's are now big business in the scientific community? Hermann's work is still way in advance of today's most arcane conceptions, but his brother Robert also wrote on the Ausdehnungslehre more prolifically than Hermann!
It seems that I may have found my mysterious mathematician, and it is not Gauss or Riemann. It could be Robert his brother, who strove to promote their fathers work!

It would seem that Herrmann was overshadowed by his father and hi brother, and his genius was unrecognised against their stellar performances. Even his failure to stir interest in his thinking has to be seen in the context of proving his worth to his father and his brother.
Gauss is not let off the hook, however, as in this case influencing the father would dramatically influence the sons and Hermann in particular.

This is a family saga, not a lone lost and found mathematician!



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