This particular professor has been teaching for 30 years. I'm not sure I find your explanation all that convincing in light of that, especially since this isn't an isolated opinion.
I'm much more interested in how much the average student has had a phone to distract them during their lifetime. For the incoming 2025 class of 18 year olds, the iPhone came out the year they were born. So potentially 100%. I expect that plus the availability of LLMs is a deadly combo on an engaged student body.
Based on the intro of the article, the university where this professor works is likely below median. Each year the typical student at his/her university is worse because the best students go to better schools
That rabbit hole will make you angry, then sad, then hopeless. I live in Chicago, on the South Side. The number of foolish fads in education have been forced on poor children for decades. It is shameful. Children should not be experimented on because their parents could not afford Catholic school or a house in the suburbs. Rich white people enjoy warping the minds of black children far too much. They never experiment with their own children, only ours. It is sickening.
As someone working in a niche area, I can confirm. It's shocking how little tech adoption there is in my industry. Plenty of low hanging fruit.
However I still sympathize with the parent comment. The niche-industry-exception state of affairs will become less true over time. And then you're left with the same set of incentives (minus dedicated hobbyists).
I haven't read this yet but I see one of the two authors is George R. R. Martin? That's cool! Does he normally contribute to this kind of thing? I had no idea.
I appreciate write-ups of failed experiments like this. They're sorta like null results in science, but for engineering. And they can help others from needlessly walking down the same path.
If everyone only wrote about their successes, we'd all have to independently rediscover failures behind closed doors.
I think because a full proof covering existence and uniqueness will either be really long or require tools from outside the scope of the text. E.g. there's a somewhat concise proof using linear algebra which I'll partially reproduce below. (I like this proof because the equation is derived from first principles rather than starting with an ansatz.)
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Let x_n be a sequence defined by the recurrence relation:
x_{n+1} = a * x_{n-1} + b * x_n
Observe that if we define a sequence of two-element vectors of successive elements:
[x_0] [x_1] [x_2]
[x_1], [x_2], [x_3], ...
then we can form the relation in terms of matrix/vector multiplication:
[x_1] = [[0 1]] [x_0]
[x_2] [[a b]] [x_1]
Let's name the sequence of vectors as y_n and call the matrix M:
y_1 = M * y_0
We can get the next term in the sequence with another multiplication:
y_2 = M * y_1
= M * (M * y_0)
= M^2 * y_0
By induction we have:
y_n = M^n * y_0
M has characteristic polynomial:
r^2 - br - a = 0
with roots:
r_1 = (b - c)/2
r_2 = (b + c)/2
c = √(b^2 + 4a)
Therefore we have by diagonalization:
y_n = S * [[r_1^n 0 ]] * S^(-1) * y_0
[[0 r_2^n]]
where S is the matrix of eigenvectors. From here, we can finish our existence and uniqueness proofs from the existence and uniqueness of the eigenvalues of M.
I'm much more interested in how much the average student has had a phone to distract them during their lifetime. For the incoming 2025 class of 18 year olds, the iPhone came out the year they were born. So potentially 100%. I expect that plus the availability of LLMs is a deadly combo on an engaged student body.