Is there any way that I, a CLI PHP developer, could "hook into" some kind of AI blackbox?
something which would be unbearably slow to calculate in PHP but goes super fast with the ai-blackbox.exe

I think you are massively overestimating the state-of-the-art of AI.

Any AI blackbox is implemented in some programming language. PHP is not the fastest language, but its slowness is likely to be a constant factor in any computation. So the difference between you calculating it in PHP and the black-box calculating it is mostly whether you wrote the code yourself or someone else wrote it.

A general purpose question-and-answer system is actually likely to be slower than something you write yourself, because you probably have some idea of the kinds of questions you are going to be feeding the system, and could optimize based on this.

You seem to want to phrase your questions using natural language i.e. English or another human language. Natural Language Processing is a huge open area of research, and is far from solved. There are some existing techniques for this, but they are far from perfect. Anyone who has spent a day with a Siri, Google Home or Amazon Echo sees that we are a long way from being able to properly process human language.

What kinds of questions do you want to answer? Even assuming you could fully process the input to your question, you're going to have a hard time if the range of possible solutions includes &quot;all of human knowledge.&quot; Representing such knowledge, collecting the information, and searching it, are all areas of current research.
Most modern AI techniques are for specialized AI i.e. you train a Neural Network to perform a single task very well. So they don't really apply to what you're talking about.



They either agree with me that it's just nonsense and doesn't actually exist, or they link me to some massive manual which I'm utterly unable to comprehend.

This is because AI is hard. Even with specialized AI, it takes a lot of expert knowledge to train a neural network. Generalized AI is even harder.

Can I actually use this, today, for anything meaningful, in a simple way?

I think the closest you will get to this is the Wolfram Alpha API. This is a system that lets you put in a question, and sometimes returns an answer. It's best with math-style things, or with facts it can guess from i.e. Wikipedia. It is far from perfect, and far from the kind of generalized AI you're talking about. It's also proprietary software i.e. you can only run it on their servers and make requests to them. And it is not free after a certain number of requests.
You can test it out at https://www.wolframalpha.com/.

Or is this exclusively useful for a handful of scientists doing some very specific work and who need to &quot;train&quot; the AI in all kinds of ways before it can answer anything?

There is a reason there is currently a huge demand for data science and AI specialists. Currently, it takes a lot of specific work to train an AI even to perform a single task. A Neural Network is basically a graph with weighted edges, and you can automatically optimize the edge weights, but you have to figure out the graph structure yourself. There is some work into &quot;Automated Machine Learning&quot;, which tries to guess these structures automatically, but it's very much an open problem.
Essentially, it currently takes an expert to train an algorithm to perform a single task. General question and answering is mostly out of reach, even for experts.