"perhaps advanced ML research models will be more analogous to improvements in climbing gear, aiding the development of mountaineering as a sport, than an intrusion of corporate control into our minds". I would argue that GPS and Satellite-connected phones are already poisoning the wilderness experience.
What does the end of mathematics look like?
81–90 of 94 posts
Re: What does the end of mathematics look like?
#82Considering that mathematics is, at its core, a language for defining relationships between quantities, and then relationships between those relationships, so on and so forth, I think it's fair to assume that the possible number of such relationships are infinite. Some of these relationships will obviously be useful in the real world, but they don't always have to be. I too, suspect that we can keep on building theor…
> the possible number of such relationships are infinite I think you need to be careful taking about "infinite" in the context of math. If the number of quantities, relationships etc is finite, so are all their combinations. Even things like the infinit-ude of available numbers might have fixed patterns that render their relevant properties effecively finite, and lead to further distinctions e.g finite vs countable,…
The standard explanation of integrals as summing the areas of rectangles of decreasing width seems extremely intuitive to me without requiring the baggage of having to know some computer language. Generating functions in code are basically a rote repetition of the mathematical definitions, requiring that you also understand variables and functions and other things unrelated to the core idea.
Re: What does the end of mathematics look like?
#83Earlier quoted context omitted.
> the possible number of such relationships are infinite I think you need to be careful taking about "infinite" in the context of math. If the number of quantities, relationships etc is finite, so are all their combinations. Even things like the infinit-ude of available numbers might have fixed patterns that render their relevant properties effecively finite, and lead to further distinctions e.g finite vs countable,…
The standard explanation of integrals as summing the areas of rectangles of decreasing width seems extremely intuitive to me without requiring the baggage of having to know some computer language. Generating functions in code are basically a rote repetition of the mathematical definitions, requiring that you also understand variables and functions and other things unrelated to the core idea.
But that "standard explanation" is a process, not a definition. Riemann sums can't be used with all integrals.
In any case, if we stick with Riemann sums, there should be a strong relationship to Generating Functions (which there is).
> Generating functions in code are basically a rote repetition of the mathematical definitions
GFs with a mathematical basis may have, for example, set-theoretic definitions that are not similar to, say, Turing machines. Any non-constructivist math is automatically not like code.
Re: What does the end of mathematics look like?
#84This article is written in an unnecessarily extravagant style, IMO. Also, I appreciate anonymity, but, to my point > I live by myself in a remote mountain cave beyond the ken of civilised persons, and can only be contacted during a full moon, using certain arcane rites that are too horrible to speak of. Okay.
As always, HN has no sense of humour...
It does, but it has to be particularly funny, and the author has to tike on the risk there. Otherwise, there are too many people who think themselves humourous, but otherwise have little to contribute. The result is current-day reddit. It's beyond cringe, it's just low-effort repatative humour. some think it's just dead-internet/botted-to-hell, but I suspect even bots can make a better effort.
Re: What does the end of mathematics look like?
#85Earlier quoted context omitted.
> while the silicon closest to its capabilities needs more like tens of kW. I think looking at power consumption for the very edge of what technology is just barely capble of may be misleading, since that's inherently at one extreme of the current cost-capability trade-off curve[0] and stands to drop the most drastically from efficiency improvements. You can now run models equivalent in capability to initial version…
Well, sure, but the capabilities of the edge of tech is still not matching the human brain. And the fact the you can run older models on less power also doesn't say anything for certain. I'm not saying it won't happen, I'm saying it's not happened and it's not certain it will.
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Re: What does the end of mathematics look like?
#86Earlier quoted context omitted.
> The camera didn't kill painting But it did. Painter used to be a trade where you could sell your painting skills as, well, a skill applicable for other than purely aesthetic reasons, simply because there were no other ways to document the world around you. It just isn't anymore because of cameras. Professional oil portrait painter isn't a career in 2025.
>Painter used to be a trade where you could sell your painting skills as, well, a skill applicable for other than purely aesthetic reasons, simply because there were no other ways to document the world around you. Source? If anything I suspect there are more people making a living as painters now than at any point in history.
As a proportion of the population?
Re: What does the end of mathematics look like?
#87I think people like author are positive about us, humanity, being able to build AI or something being very close to that. I am not. From the energy efficiency perspective human brain is very, very effective computational machine. Computers are not. Thinking about scale of infrastructure of network of computers being able to achieve similar capabilities and its energy consumption... it would be enormous. With big infr…
> he energy efficiency perspective human brain is very, very effective computational machine Can you explain why you think that? Very often, mechanical efficiency outperforms biological. Humans have existed for thougsands of years, neurons even longer. Computers and AI and relatively recent, we haven't really begun to explore optimisation possibilities.
>we haven't really begun to explore optimisation possibilities.
So you're questioning the above comment's argument based on a hand-wavy claim about completely speculative future possibilities?
As it stands, there's no disagreeing with the human brain's energy efficiency for all the computing it does in so many ways that AI can't even begin to match. This to not even speak of the whole unknown territory of whatever it is that gives us consciousness.
Re: What does the end of mathematics look like?
#88Earlier quoted context omitted.
> he energy efficiency perspective human brain is very, very effective computational machine Can you explain why you think that? Very often, mechanical efficiency outperforms biological. Humans have existed for thougsands of years, neurons even longer. Computers and AI and relatively recent, we haven't really begun to explore optimisation possibilities.
The human brain runs on about 20 watts of power -- the entire body on 80 watts (at rest). Those numbers are at least good within an order of magnitude. The largest supercomputer consumes 29 megawatts of power for 1.7 exaflops. And the largest supercomputers are nowhere near the flexible generality of a human brain -- they're calculating FFTs for the test. The amount of parallelism in the human brain is enormous. Not…
Thank you, for describing with specific details about comparative capabilities vs. energy use all the main reasons why human brains are so much, much more energy efficient at all that they can do than any current computer, LLM or algorithm.
Re: What does the end of mathematics look like?
#89Earlier quoted context omitted.
> he energy efficiency perspective human brain is very, very effective computational machine Can you explain why you think that? Very often, mechanical efficiency outperforms biological. Humans have existed for thougsands of years, neurons even longer. Computers and AI and relatively recent, we haven't really begun to explore optimisation possibilities.
>we haven't really begun to explore optimisation possibilities. So you're questioning the above comment's argument based on a hand-wavy claim about completely speculative future possibilities? As it stands, there's no disagreeing with the human brain's energy efficiency for all the computing it does in so many ways that AI can't even begin to match. This to not even speak of the whole unknown territory of whatever it…
Is it speculative to suggest that technology will improve? No.
> whatever it is that gives us consciousness
talk about hand-wavy; "consciousness" might not be a real thing. You might as well ask if AI has a soul.
Re: What does the end of mathematics look like?
#90Earlier quoted context omitted.
The next logical step, perhaps ethically questionable, seems to be growing human brains for computational purposes (parallel or quantum) with high bandwidth and very efficient power consumption.
"perhaps ethically questionable"? I find it hard to think of a more ethically questionable programme!
I don't know where I got such a dark sense of humor. I find it deeply troubling that scientists are growing "organoids", little human brains, for computational purposes. Headline from 2023:
> Computer chip with built-in human brain tissue gets military funding
The project called DishBrain was spun into the startup, Cortical Labs.
> World's first 'body in a box' biological computer uses human brain cells with silicon-based computing
> Cortical Labs said the CL1 will be available from June, priced at around $35,000.
> The use of human neurons in computing raises questions about the future of AI development. Biological computers like the CL1 could provide advantages over conventional AI models, particularly in terms of learning efficiency and energy consumption.
> Ethical concerns also arise from the use of human-derived brain cells in technology. While the neurons used in the CL1 are lab-grown and lack consciousness, further advancements in the field may require guidelines to address moral and regulatory issues.