It was her voice that made
The sky acutest at its vanishing.
She measured to the hour its solitude.
She was the single artificer of the world
In which she sang. And when she sang, the sea,
Whatever self it had, became the self
That was her song, for she was the maker.
The sea was not a mask nor she.The song and water were not medleyed soundEven if what she sang was what she heard,Since what she sang was uttered word by word. It may be that in all her phrases stirredThe grinding water and the gasping wind;But it was she and not the sea we heard
For she was the maker of the song she sang.
The ever-hooded, tragic-gestured sea
Was merely a place by which she walked to sing.
Whose spirit is this? we said, because we knew
It was the spirit that we sought and knew
That we should ask this often as she sang.
She sang beyond the genius of the sea.
The water never formed to mind or voice,
Like a body wholly body, fluttering
Its empty sleeves; and yet its mimic motion
Made constant cry, caused constantly a cry,
That was not ours although we understood,
Inhuman, of the veritable ocean.
Why do we not teach topology as a reflective subcategory with an adjoint pair?
The only principled context for Kuratowski's axioms is within the realm of adjoint pair, unit/counit, closure/interior and then from that using a grammar to build all the derived operators.
mathematics is a language about a world you cannot see with your eyes
grammar and logic are your sense of touch in this world
math world projects itself onto the world of five senses
some believe that the world of five senses must obey math world
others: the reverse
The real danger of social media is that our children will no longer get bored.
And boredom is a fundamental force in driving persistent sessions of creative discipline and exploration: a necessary precursor of any useful cultural artifact.
If logic were taught first, in place of arithmetic and numerical calculus
and the playgrounds for logical analysis being
- geometry (intuitive, visual)
- set theory (bags of objects and other bags)
then number would arise naturally in both, as
- unit sticks
- set cardinality.
The low-bar of a "Great Achievement" by AI will be for it to produce a Nobel-prize-worthy scientific artifact.
The high-bar of a "Great Achievement" by AI will be for it to produce a Nobel-prize-worthy scientific artifact *and* a short, human-comprehensible symbolic form: F = ma
it's difficult to imagine that as late as 1905/1908 it was commonplace even amongst scientists to maintain a worldview absent of atoms/molecules
the progress in a single decade, let alone century, is astounding.
as is: that of which we surely remain ignorant in 2025