Degree of A Field Extension
Given a field extension K/F, the field K can be considered as a vector space over the field F. The dimension of this vector space is the degree of the extension and is denoted by .
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“Nothing in life possesses value except the degree of power—assuming that life itself is the will to power.”
—Friedrich Nietzsche (1844–1900)
“Take but degree away, untune that string,
And hark what discord follows!
...
Force should be right, or, rather, right and wrong—
Between whose endless jar justice resides—
Should lose their names, and so should justice too.
Then everything includes itself in power,
Power into will, will into appetite;
And appetite, an universal wolf,
So doubly seconded with will and power,
Must make perforce an universal prey,
And last eat up himself.”
—William Shakespeare (1564–1616)
“Is not the tremendous strength in men of the impulse to creative work in every field precisely due to their feeling of playing a relatively small part in the creation of living beings, which constantly impels them to an overcompensation in achievement?”
—Karen Horney (1885–1952)
“A dense undergrowth of extension cords sustains my upper world of lights, music, and machines of comfort.”
—Mason Cooley (b. 1927)