tl;dr "Polysemantics" are just a unisemantics you don't understand.
If you want to learn more about this, this is what depth psychology is about (Carl Jung, et al).
This is also essentially the idea behind monotheism vs polytheism. It's about engaging with and trying to understand the profound underlying unity of the myriad phenomena.
Ironically, that has been that way for most people since forever.
Comparing with the situation in programming, where code evaluation (obviously analogous to "understanding") is that bottleneck now, should get people the idea of being in the same boat.
I’d say it’s understanding in general. We currently have zero evidence the AI models can understand mathematical breakthroughs in a productive way. (When they intuit a new technology or theory from a mathematical construct, we’ll be along that way.)
What is that the bottleneck for, though? Certainly, it's tautologically the bottleneck for "humans understanding math"; but what about things like using math to drive discoveries in other fields, or for practical work in CS, or applications elsewhere? I fear that practically those aren't bottlenecked on human understanding.
It is my understand that there isnt a lot of innovation here. Rather the (broad) field of mathematics got mined for solutions that already existed within the corpus.
It implies "We didn't know we already knew how to solve these problems". How is that a good look for mathematics as a field?
Did you read any of the explanations from mathematicians over the last month? What part of them do you disagree with?
For example [1]:
> In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align.
Or [2]:
> Use of AI tools, when done responsibly, can support not just the initial generation of a solution, but all of the valuable followup activities that traditionally flow out of that solution. But at the current time, the opposite is often occurring: problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is "solved", and do not understand the AI output well enough to answer questions on the result, give talks, or otherwise interact with the rest of the field.
> ...
> solutions to open problems are now being harvested at large scale in an unsustainable fashion, leaving entire fields of mathematics much less fertile than when such problems were solved in the traditional "Math 1.0" fashion.
> prompters who have no interest in the broader field itself once their initial target is "solved"
This applies to all fields and pursuits where AI is effective. Yes I think about this with regards to various things I’m working on.
This is just the nature of things, you need to adapt and not throw a tantrum like a child. You need to not behave like Terrance Tao who is essentially like a child in an adult’s body in terms of his behavior and lack of wisdom, and keep in mind he was a child prodigy so this isn’t a knock at all or statement about his intelligence, only his development as a man.
You can mourn, as I have for the field of programming as I knew it which I have loved since I was a child, but you need to move on.
If AI can actually replicate mathematicians, sure. We don’t have evidence it can. We have evidence it can do useful stuff once promoted by human mathematicians. But if all the Terence Taos “move on,” we won’t have those in America anymore.
(The irony of ironies would be the mathematicians prematurely moving on causing American AI progress to stall in the future.)
I have no doubt it can’t actually replicate the type of thinking that makes great mathematicians great. That’s why I said the field has changed, not that it’s not a thing anymore. They will be doing different things and what we consider mathematical research will look different.
I completely reject the idea that releasing proofs is bad for the field of mathematics. Yes, it holistically changes the role for mathematicians, and they might not like where the change leaves them, but I do not think it harms the field overall.
Best I can tell the biggest complaints are really just that the future of their career is largely combing through lean and they don’t want to do that. Too bad. Adapt or get off the pot.
Mathematicians need to completely rethink the prestige paradigm. Counting proofs no longer works. That doesn’t mean there’s nowhere for them to go. Now it’s about gleaning human understanding from the lean. Maybe in the future LLMs can do that too and it’ll be all about formulating new conjectures.
One of the things the Bible does particularly well is express ideas succinctly. Yes I know you can pull out exceptions but classically this was interpreted as itself having significance.
Are we reading the same bible? The bible is a super meandering document that repeats itself a bunch and also contradicts itself. (which is to be expected if you assume its some sort attempt at writing down and standardizing an oral myth tradition that came before it)
The Bible is fundamentally a collection of different works. Within those works, I generally agree that the ideas are fairly succinct. But because there are multiple documents in the Bible which cover roughly the same events, it kind of necessarily isn’t succinct as a single cohesive document.
In other words, if you rewrote the Bible as a single document, yeah, it’d be like 10% as long. But that isn’t how it was made.
I’m guessing you haven’t read it in Hebrew because the Hebrew is pretty succinct.
As for meandering, the narrative follows people who travel around to different places so I don’t know what you mean. The canon of the Bible doesn’t arrange all the books chronologically. You can read them in chronological order if you want.
This is precisely because you are a foreigner of minority ethnicity (the minority ethnicity points towards hailing from a more traditional culture compared to if you were white and therefore you would be from Europe which does not have a traditional culture, it has a modern culture).
To clarify the idea: you have a healthy social matrix but if you marry and settle in the US, your grandchildren won't.
The term "Senate" comes from the Latin word "senex" meaning "old man", and obviously the US inherited the term "Senate" from ancient Rome. This is a basic structure of society.
The issue is that this particular group of people older than 65 at this particular time in world history (which you happen to be living in) are Boomers who are probably the most child-like, foolish, and ignorant generation of people in world history, due to the circumstances of their upbringing (post-WW2, high technology, opulence, drug use, sexual revolution, peace in the developed world).
This isn't ageism, since normally old people do tend to have more wisdom and knowledge than young people.
There is something that really went wrong with the Boomer generation. The goal of every society is basically to survive their Boomer generation which many are not really seeming to manage.
Notice that Senate wasn't the only governing party in ancient Rome. Also "old" is relative. It meant "too old to serve in military", with Sulla's reforms the minimum age was 31 and even before that most influential senators were 40-50.
For emperors: out of 80 only 14 were over 65. 2 resigned/died at 66, 1 at 67, 2 ruled only few months, so really 9 out of 80. Rome is not the place to look for old rulers
Right you have to distinguish between the executive and legislative/judicial.
The executive being young and legislative/judicial being old was pretty typical across the ancient world.
Also people tended to not live as long in old age as they do now, we have lots of advanced medical interventions we can do to keep our old people alive and accumulating power and wealth.
Also Rome had a much healthier triangle-shaped demographic/population pyramid so they had more youngish people to draw on for elite qualities. They also had an active military culture so young people could actually prove themselves in leadership positions and make a name for themself. In the developed world in the current period that is not the case.
In general, insightful social commentary have this sort of quality i.e. "I'm with you on this but where you've taken this idea seems out there", like by definition, but it does require a level of humility.
I'm not necessarily declaring what I'm saying to be insightful but what you're describing is what a typical reaction to insightful social commentary looks like.
I'm glad your cancer was taken care of and you're healthy now.
Note to everyone reading your comment:
This is a typical psychological response, a deep need to trust the given system you're in, especially when it comes to serious medical issues.
This will lead to suboptimal outcomes and/or severely harm you in most circumstances. The people in these systems are just people, they make mistakes, they have their own personal issues, they have their own interests. The people who designed these systems are just people as well, they make mistakes, the systems are flawed, the system itself has its own interests and logic.
You need to be your own advocate, do your own research, not take what people say or do as gospel.
And yes genetic testing is extremely valuable in modern cancer care, a good oncologist will do this immediately.
Wel, here is the cycle. Tech and food, opulence gives you free time, free of struggle. The idle people indulge in more science and produce more opulence and more idle people. Tye climate and bio ecosystem turns against the excessiive idle population. Struggle is again reinstated. The new generations give control back to nature.
Right the goal is to have opulence, free time, and also not to become decadent. There is a process by which this gets better over time (generations, cycles), each successive cycle has the potential for retaining memory/historical consciousnesses/psycho-social development. Just intentionally doing nothing/halting progress is not the answer and also it just trivially leads you to being wiped out (like via military means) by people who actually do things/progress. This is the basic flaw in Kaczynskian thinking, it requires all of humanity/nations to 'collude', it's a basic game theoretic issue.
>> There is a process by which this gets better over time.
It's a zero sum game. It appears to get better only because you are only looking at the corner that was wiped clean, but not the other corners where the garbage went to. And for some reason the "wiped clean" state is considered a good thing. Other misconcieved "good" things are straight edges, flat surfaces, smooth curves, uniform colors and shapes, artificial uniformity in general, thinking hard, smartness, precision, excessive hardness or strength, extreme skills, any characteristics that reflects a lot of human/macine effort etc.
Human progress doesn't require too much of human agency to the extent of causing irreversible effects or a great risks. Right now the agency is completely out of pace with the nature, arrogantly driving things and crumbling down when nature stares back at.
It's simply the case that material conditions are better than they were 50,000 years ago and also better than they were 2,000 years ago. It's also the case that overall the general level of refinement of the average person is higher, you can just read the things people used to do to each other and how they lived.
Again this recourse to nature is just druidism. You have a particular metaphysics and morality, it's just wrong.
You are literally posting on the internet, likely from an air conditioned room. You can and should stop using these things.
If you want to learn more about this, this is what depth psychology is about (Carl Jung, et al).
This is also essentially the idea behind monotheism vs polytheism. It's about engaging with and trying to understand the profound underlying unity of the myriad phenomena.
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