All the text books I've ever seen had practical examples in them.
Like determining the height of a tree or a house simply based on trigonometry.
Your suggestion is interesting but I am not convinced that a student would be helped by aligning the examples with their interests.
I could see a student asking how trig relates to computer games and the example the LLM generates becoming much more involved.
I see no problem with the examples being boring. The people that developed these techniques had such fundamental problems to solve and the wonder to me is the human mind that came up with these
methods.
All this to say, maybe we lack appreciation for the fundamental sciences that underpin every aspect of our modern lives.
> All the text books I've ever seen had practical examples in them. Like determining the height of a tree or a house simply based on trigonometry.
The trouble is a lot of those practical examples fall into the, "why would I care category". I had a high school physics teacher who described his university antics, one of which included a funny story of a bunch of his friends climbing on top of each other to measure the height of a flag pole. I guess the profs got tired of dealing with students scaling flag poles because I was measuring the height of mountains on the moon at the same university a couple of years later. The thing is nobody really cares about the height of a flag pole, while only a few would care about the height of the mountains on the moon.
The reality is the interesting applications are much more involved. They either require a depth of thought of process or a depth of knowledge that isn't appropriate for a textbook question. Take that trigonometry in games example. The math to do it was in my middle school curriculum, but it becomes obvious that computer graphics is more than trigonometry the moment you try to frame it as an example. I had linear algebra in high school. That will take you pretty far with the mathematics, but it will also be clear that a knowledge of computer programming is involved. Even knowing how to program isn't going to take you all of the way because few are interested in rendering verticies and edges ...
And that is just the obvious progression of knowledge in a simple application. Physics itself involves buckets full of trigonometry in extremely non-obvious ways, non-geometric ways.
I agree with your point in general, but I do find myself actually using trigonometry for fairly basic real-world purposes more often than one might expect. For example: how big of a piece of material fits in a particular position if it’s not parallel or perpendicular to the stuff around it? If a rope supports a load in the middle, how much tension does the rope need? How much of an angle should be cut into a door to comfortably clear the jamb? (If you’ve never contemplated this before: a door with a rectangular cross-section will have less clearance to the jamb when almost closed than when fully closed.)
Rambling off-topic, but I remember being very impressed at how a uniform hanging rope makes a catenary [0] shape which is related to making strong structural arches.
So maybe if the students were somewhere where the class could design and make an igloo... :p
Fun exercise for the reader: if you have that uniform hanging rope support a uniform flat suspension bridge (via a bunch of closely spaced vertical ropes), and the bridge is much, much heavier than the ropes, then you get a parabola instead of a catenary. Wikipedia gives a derivation involving differential equations, but it glosses over the actual fundamental difference between these situations. But you can explain what’s going on with just trigonometry and no calculus, let alone differential equations: consider how much weight a small section of chain that isn’t right in the middle is supporting. You’ll end up with a drawing involving a right triangle and some numbers associated with the sides, and those numbers will line up differently with the opposite, adjacent and hypotenuses in the two cases.
So your off-topic rambling isn’t off-topic at all :)
I think for me personally although I don’t use maths often enough in any practical sense, the one thing I think has stopped me progressing in life how I feel I want to has been my lack of maths knowledge. I don’t mean in a career sense but in an enjoyment sense. I watched a video about proving that the square root of two is irrational and that made me irrationally happy, and I’d love to keep going but a lot of the maths in other proofs or concepts gets absolutely insane. I don’t know how to express that to kids learning maths for the first time, though. It also almost feels like the world of math is so vast there’s something for everyone to enjoy casually. That feels like a video game analogy to me with all the different genres built around basic fundamental concepts.
> I see no problem with the examples being boring.
I'm in agreement with this point; the examples are boring, but that's not really relevant. After all, we're mostly talking about Maths ITT, not history or social sciences.
1. Some foundational study is needed before you get to the really interesting problems at a higher grade/level/school/university.
2. Who cares if they are boring? A spectacular facility to learn Maths which is demonstrated by high marks indicates better abstract reasoning skills, making it easier for specific trades to decide who is more suitable.
3. How will the kids know whether they like Maths or not if they skip trig in high school?
(Sidenote: Am I the only one who finds trig easy and everything else in Maths hard?)
Survival of the fittest should apply to businesses above anything.
If a business can't handle the regulations to not pollute water then it's a clear cut case.
This is all the symptom of laziness of the mind.
There is resistance to change, adapt and make the world a better place not just for this, but future generations.
There is no leadership in the US, no vision, no drive. The excessive wealth has created a leading class that happily rests on the laurels of prior generations while squandering the future.
This problem extends to all citizens, beyond the weak and needy, and permeates all levels of government from small to big.
I live in one of the best school districts in the US, and when I see the food the children are served I am surprised this is acceptable.
But this is what the US is, extract as much money from people while providing sub standard service. All in-the name of the free market and shareholder value.
> Survival of the fittest should apply to businesses above anything. If a business can't handle the regulations to not pollute water then it's a clear cut case.
See, there you go again, over regulating free enterprise out of existence. /s
To the main point—I guess we agree. Also: the right wing political movement in the US is an amalgam of conservative religiosity and (MFing) libertarianism. It’s frantic and fear-driven.
No! Ignoring a stop sign is such a basic driving standard that it's an automatic disqualification.
A driver that misses a stop sign would not have my kids in their car.
They could be the safest driver on the racetrack it does not matter at that point.
I actually didn't say that and am not arguing it formally - I said what I said because I think that the version difference is something that should be acknowledged when doing a test like this.
I do privately assume the new version will be better in some ways, but have no idea if this problem would be solved in it - so I agree with your last sentence.
I don't think there's an official divergence in terminology other than the version numbers (which have mostly stopped incrementing for FSD vehicle owners, meanwhile there is a lot of work going into new iterations for the version running on tesla's robotaxi fleet)
Then I struggle to understand what they should have acknowledged here concerning the software used? That they do not have access to a version of FSD which currently isn’t accessible to the public? I’d think that’s self-evident for any Organisation not affiliated with Tesla.
Ignoring a stop sign, not even slowing down, thats a major safety flaw.
I am wondering if there is a safety certification body for self driving technology.
If not, one is needed because consumers can't be expected
to be aware of all the limitations of the latest update they have installed.
There must be basic safety standards these systems need to meet, a disclaimer can't be the solution here.
Management has different layers with different goals.
A middle manager and a director certainly care a lot about accomplishing short term goals and are ok with tech debt to meet the goals.
A lot of it is perception. Writing software was long considered somewhat difficult and that it required smart people to do so.
AI changes this perception and coding starts to be perceived as a low level task that anyone can do easily with augmentation from AI tools.
I certainly agree that writing software is turning more into a factory job and is less intellectually rewarding now.
When I started working in the field (1996), I was told that I would receive detailed specs from an analyst that I would then "translate" into code. At that time this idea was already out of fashion, things worked this way for the core business team (COBOL on the AS/400) but in my group (internal tools, Delphi mostly) I would get only the most vague requirements.
Eventually everyone was expected to understand a good deal of the code they were working on. The analyst and the coder became the same person.
I'm deeply skeptical that the kind of people that enjoy software development are the same kind of people that enjoy steering and proofing LLM generated code. Unlike the analyst and the coder, this strike me as a very different skill set.
> I'm deeply skeptical that the kind of people that enjoy software development are the same kind of people that enjoy steering and proofing LLM generated code. Unlike the analyst and the coder, this strike me as a very different skill set.
indeed. people generally hate foreign/alien code, or rather - love their style too much. it is not hard to recognize this pattern - ive seen it with colleagues, with my students, with some topnotch 10x-coders back in the day. so proofing is a skill one perhaps develops by teaching others do things right, but is not something most people entertain about.
on the other hand, people who lack time and patience to implement complex stuff may benefit from this process. particularly if they are good code-readers, and some seasoned devs become such people. i can see little chance they wont be using llms to spit code out.
but the two groups largely don't overlap and are different as astronomers and astronauts.
For me it dependa on scale. Asking AI for something small and specific is a joy. Asking it to make a big change is a nightmare I so far only try every time a new model comes out.
Not everyone gets to code the next ground breaking algorithm at some R&D department.
Most programming tasks are rather repetitive, and in many countries there is hardly anything to look up to software developers, it is another blue collar job.
And in many cultures if you don't go into management after about five years, usually it is seen as a failure to grow up on their career.
Of course it is true. The thing was 90% of Amazon engineers made far more money at their job while essentially doing typical enterprise software work. This money led them believe it is some creative work. And now those task management and time monitoring tools are catching up to Amazon IT workers so they are realizing it is similar to another low end IT job/ factory work.
The pay and benefits at Amazon always seemed to offset the shit work/life balance and on-call rotation. What a gauntlet that was. The only engineers that got recognition were those that fixed high profile bugs, preferably after hours. Shipping a feature was always just "business as usual"
> if you don't go into management after about five years, usually it is seen as a failure to grow up on their career
I don't see how that's possible. Wouldn't such a norm result in something like a 7:1 ration of managers to engineers (i.e., assuming a 40ish year career, the first 5 years are spent as an engineer, and the remaining 35 as a manager)? For team managers, I've generally seen around a 1:10 ratio of engineers to managers. So a 7:1 ratio of managers to engineers just doesn't seem plausible, even including non-people leaders in management.
Have you wondered why japan, which is a powerhouse of electronics and manufacturing does not have any large software companies ?
Software is different from manufacturing.
The mindset, mentality, and culture required to do new software for an ambiguous problem is different from the mentality to produce boilerplate code or maintain an existing codebase. The later is pure execution and the former is more like R&D.
It means that the company is more likely to fire that person on the logic that they "failed" to be promoted to management, that they're "treading water" as a developer.
It's been like this for awhile now. Aside from companies like Google and Facebook, most companies are using some CRUD web app where the development consists of gluing code together for multiple third-party services and libraries.
It's these sorts of jobs that will be replaced by AI and a vibe coder, which will cost much less because you don't need as much experience or expertise.
Even before AI I've always had the perception that writing software felt more intellectually on the level of plumbing. AI just feels like a having one of those fancy new tools that tradespersons may use.
Yeah that’s what really worries me, many people have been clinging to this ability as something that’s really special and AI is really going to disillusion them.
AI needs to be trained, it cannot create knowledge in a vacuum.
I think that's why there will always be some augmentation by humans to provide the context and the knowledge
Your suggestion is interesting but I am not convinced that a student would be helped by aligning the examples with their interests. I could see a student asking how trig relates to computer games and the example the LLM generates becoming much more involved.
I see no problem with the examples being boring. The people that developed these techniques had such fundamental problems to solve and the wonder to me is the human mind that came up with these methods.
All this to say, maybe we lack appreciation for the fundamental sciences that underpin every aspect of our modern lives.