Why would you expect this character, the one who quotes Jung at length without ever having read anything he wrote, to remember and record if and what anyone said to him about Jung?
It depends on what you want from a mathematics education and what you want from your education at St. John's. It is not a vocational school, and the mathematics we do won't strictly be aligned with any particular career path. And the other advantage/disadvantage is that almost all of the math you have learned before you start is not helpful, at least for the first two years. Neither of those things mean that the math we do is any less serious or important than the math education most undergraduates will receive. [1]
Most people that are frustrated by one of the two things I mentioned above, either experience a shift in perspective, or do not complete their studies at St. John's.
Afaik they have been trying to fudge these numbers over the past few years because admin thinks it makes the school look bad, but fewer than 50% of freshman that enroll in the college will graduate. And at least a third of those that leave don't make it past the first semester.
[1] Just to paint a few broad strokes of the highlights of our math program: Freshman study Euclid's Elements and Optics, Archimedes, and Claudius Ptolemy's Almagest, Sophomores study Ptolemy, Copernicus, Kepler's Astronomia Nova, and Apollonius' Conics. Junior's study Newton, Maxwell, Oresme, Leibniz, Pascal, Descartes, and Dedekind. And Senior's work through Einstein, Lorentz, and Minkowski's relativity papers, before rounding the whole thing off with Lobochevsky, Bertrand Russell, and Gödel.
You're totally right about mass-market entertainment, but none of that is true for art, and unfortunately, people like you going to the movie theaters to watch Fast and Furious 46 is what subsidizes an industry of people who actually care, trying to make beautiful art for people that aren't trying to OD on visual Xanax in the comfort of their blankey.
What prevents one from using this argument with everything? In a sense, I don't disagree, but what sets apart active recognition and embrace of the limitations of an endeavor, and passive resignation to the shortcomings of circumstance, which smells more of indifference from a fatal desire for sleep and forgetfulness?
The whole premise of the comment you were replying to was that we were spinning our wheels, which is not an utter refusal of progress but a characterization of progress. You responded with marveling at the things which have been achieved which you find remarkable and unappreciated. I responded by characterizing those as having some qualities of remarkability and novelty which ultimately fail to exceed wheel spinning. You are now accusing me of having set up an unreasonable standard of progress. There are two characterizations of the progress in this domain which I believe are likely but not certain accounts, maybe both are partially true, maybe just one, but both are contained by the wheelspinning metaphor. One is that progress is being made, but the progress is not forward and in fact the progress is the digging of a deeper and deeper hole that makes actual progress more difficult, and the other is that progress is being made, but that progress is that of an infinite series which logarithmically ascends from 1.0 to 1.1. There were genuine discoveries, inspiration and novelty required on the road from note identification to chord identification and deconstruction that could be reversed and reconstructed with reasonable accuracy. That does not mean that we aren't doing anything more than refining and improving the accuracy of processes which we were already performing rudimentary forms of 20+ years ago. I'm not saying there isn't progress, only that the progress is limited, and we are now reaching towards the same limits which we had begun approaching at the inception of the programmable machine and there is no escape in sight.
"The real power of a neural net is its ability to compute solutions for distributed representations. In most cases, the solutions for these complex cases are not obvious. The pitch class representation of pitch is a local rather than a distributed one. In this case a possible solution for the chord classification problem is apparent without the use of a learning algorithm. A net containing 36 hidden units, one representing each of the possible major, minor, and diminished triads, could be constructed so as to map chords to chord types. Thus our interest in using a pitch class representation was not to find this obvious solution, but to find a solution which used a minimum number of hidden units.
We hypothesized that three hidden units would be adequate and that the hidden units would form concepts of the intervals found in triads: i.e., major third, minor third, perfect fifth, and diminished fifth.
Each pitch-class net used 12 input units to represent the 12 pitches of the chromatic scale and 3 Output units to represent chord type. The number
of hidden units and the values of the learning parameters are summarized in Table 1 for each of the eight pitch class nets discussed.
Net 1 had an adjacent layer architecture as shown in Fig. 2 and three hidden units. It identified 25 percent of the chords after more than 11,000 learning epochs. When a fully connected architecture was used in conjunction with three hidden units in Net2, 72 percent of the chords were identified after 2,800 learning epochs. "
And what novel possibilities have Polyphonic Note Editing and Utterly Transparent Time Stretching brought to music? All that has been accomplished 4% YoY reduction in the cost and time of producing Mass Media, which requires a massive volume of production work. These are conveniences which are and always have been utterly conceivable consequences of sufficient engineering hours, not revolutions or fundamental changes in our relationship to the world. Even if some of those are just now coming into people's minds, all those changes were already conceived of and implemented 20+ years ago.
But the universe isn't 'composed' of subatomic particles in the way that a machine is 'composed' of parts. The laws governing subatomic particles, as far as speech is capable of representing them, are probabilistic. And, as we see in practice, we have surrendered to using aspects in the sciences. When useful, we speak of light as a wave, when useful, a particle. Really it is neither or both. The same gap in the work of the software engineer to depict the world in language. Any mode of speech can only depict one aspect of the truth at a time, even if a single language is capable of more than one mode, it can only ever express one aspect.
Your being a Neo-Darwinian and your confusion at the possibility of regression or a halt in progress are the same. Once the mollusc has "conceived" of his shell as an "adaptation" to a change in condition, he has "responded" so harshly to environmental dangers that he has closed them off almost entirely, bringing the process of speciation and adaptation to a near halt. In fact, there are countless examples of "tools" "conceived" by organisms that have been so immaculate that development has grinded to halt. Not all is progress... the world is not a machine...