Actually, they have for a large majority of the population. And fun fact: that debate is still going on, and the Mathematical Association of America (MAA) enacted a rule prohibiting calculator use in AMC.
Math fosters critical thinking, and we've been in a critical thinking deficit for decades and decades. I don't think we can afford to sink even deeper...
My question would be if "math" is the right tool for that. It can achieve that as a side-effect, but how we express it and talk about it is full of legacy cruft, cargo-culting and general bullshit that makes it not exactly snap into place for all kinds of brain wirings.
Math I believe is not an end in itself. Maybe with that perspective, solutions that satisfy our needs there can be found
Because the 1890s and 1930s were famous for their population wide critical thinking, of course. Good heavens, what do they teach in the schools these days.
I mean you may be trying to make a point but the counterpoint is Einstein, Bohrs, Planck, Shannon, Turing, Von Nuemann, Feynman, Bohr and most of the other big names all came out during that time.
In contrast since then we've had almost not noteable physicists or Computer Scientists that I'm aware, we've got a couple, Hawking and Knuth. But apart from that I don't know if there is a single scientist I could point out today that has revolutionized our understanding or even done any real breakthrough work in the field of Physics since Einsteins era.
A more apt analogy is the diminishing understanding of assembly language and machine instruction sets. I love programming and something got lost in both transitions, first to high level languages and now to coding agents. I am quite sure some contexts will require programming by hand for a long while as there are still people who are writing amd64/avx512/sass by hand. I hope in time we will find new ways to enjoy solving problems with this new programming modality. By now, I am pretty sure it is here to stay and evolve from its current crude form.
> the diminishing understanding of assembly language and machine instruction sets
This is true and nobody complains that GCC or LLVM is making programmers dumber. They are code-generation tools from higher-level source code. Much like LLMs are code-generation tools for higher-level language/prompting.
Man, Usenet had the best online discourse - hardly any angry personal flaming because people dared to disagree. And Twitter, wow that was just pure rationality. slashdot - practically a masters program.
Now, they all did have gems of interaction that would could find by sifting thru the dumb stuff, but I find that property of discourse to be pretty steady. I've even found some interesting comments on YouTube videos and newpaper websites.
Not really the same, since your average calculator doesn't take over executive function. The user thought and decided what needs to happen, down to one extremely well-specified task, which is so unambiguous that it can be completed by rote and without context.
This is more like paying someone else to read your math homework, generate answers, and maybe even submit them on your behalf. If that had been the (average) student experience, math skills really would have collapsed.
I think we'll find that the people doing that, like the people spending all their time and energy reading slasher pulp fiction in the 1950s, won't be doing as well as the people learning to enhance the power of their education and their expertise via LLMs and strategic alternating between GenAI and thinking about problems. And eventually, if society ever steadies up a bit, people will learn the useful ways of using technology in school and youth; and we'll be glad to be alive to see such marvels.
Assuming we can re-establish the will for democracy and taking care of the whole group.
I don't think it's quite as bad, but I'm imagining someone in the 1950s going: "People just have to use methamphetamines responsibly in their work, and then we'll see the massive benefits as widespread adoption unlocks the potential of the human mind."
In other words, a positive outcome with thing X is possible but there are also big behavioral and cybernetic pitfalls, ones which are suspiciously persistent.
Those are some big ifs and assumptions unfortunately, and the use of AI unfortunately has an isolating effect that is only likely to move the needle in the wrong direction.
I also can't make butter by churning or soap from lye and animal fat or what ever.
However, I can use mathematica to demonstrate the criteria for various forms topological stability of solutions to many types of differential equations. I'd rather live now.
That's a very good point. People don't pull out their calculator in the grocery store to do analysis of unit costs or whatever, it's too much of a hassle for that small kind of analysis. But calculators have robbed us of the need to be good at doing that math in our heads. So the math doesn't get done.
Many grocery stores will already give you a per oz or per unit price so you can compare pricing for different brands that have different sizes. It's a very handy feature.
This is exactly the right analogy. Granted LLMs are a more sophisticated calculator and engineering is still adapting to this wonky/evolving technology. But to pretend it's a coming catastrophe is to ignore every past parallel development - where this has not happened.
Math skills are at their lowest point ever in modern society, and many are still advocating for the reduction in reliance on calculators for this reason.
"Mental math skills" literally did collapse tho??? "Math skills" to write proofs (which a calculator cannot do) is a fundamentally different skill set than that "math skills" of mechanically doing arithmetic (which a calculator does do).
Seems like critical reading skills have already collapsed.
With a calculator you still need to understand the fundamentals of mathematics. You also need to understand how to operate a calculator and know its functions.
Even when removing numbers and manual calculation, being a function or formula oriented mathematician still requires you to know the theory and functionality.
With an LLM, you don't even need to know anything other than asking the robot to perform. You don't understand the output, nor can an unskilled person explain it.
This is the same kind of analogy people make when they "poo-pooh" any sort of technological advance, especially with AI.
"Oh, that old simple device didn't displace anything, so this one which is now quickly taking over every job will be just like that simple one". So I guess people today know how to sew and knit and bake bread?
"Oh, humans were always needed, so it'll be the same this time." Is that true of horses and oxen after cars and tractors were invented?
Actually, they have for a large majority of the population. And fun fact: that debate is still going on, and the Mathematical Association of America (MAA) enacted a rule prohibiting calculator use in AMC.
https://ivyleaguecenter.org/2024/03/12/over-reliance-on-calc...
Math fosters critical thinking, and we've been in a critical thinking deficit for decades and decades. I don't think we can afford to sink even deeper...
> Math fosters critical thinking
I kinda agree, but I also kinda disagree.
My question would be if "math" is the right tool for that. It can achieve that as a side-effect, but how we express it and talk about it is full of legacy cruft, cargo-culting and general bullshit that makes it not exactly snap into place for all kinds of brain wirings.
Math I believe is not an end in itself. Maybe with that perspective, solutions that satisfy our needs there can be found
Because the 1890s and 1930s were famous for their population wide critical thinking, of course. Good heavens, what do they teach in the schools these days.
I mean you may be trying to make a point but the counterpoint is Einstein, Bohrs, Planck, Shannon, Turing, Von Nuemann, Feynman, Bohr and most of the other big names all came out during that time.
In contrast since then we've had almost not noteable physicists or Computer Scientists that I'm aware, we've got a couple, Hawking and Knuth. But apart from that I don't know if there is a single scientist I could point out today that has revolutionized our understanding or even done any real breakthrough work in the field of Physics since Einsteins era.
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> we've been in a critical thinking deficit for decades and decades.
Compared to when?
I have heard stories of cashiers being incapable of giving correct change. So yes it has happened.
I guarantee you that it's always been the case.
A more apt analogy is the diminishing understanding of assembly language and machine instruction sets. I love programming and something got lost in both transitions, first to high level languages and now to coding agents. I am quite sure some contexts will require programming by hand for a long while as there are still people who are writing amd64/avx512/sass by hand. I hope in time we will find new ways to enjoy solving problems with this new programming modality. By now, I am pretty sure it is here to stay and evolve from its current crude form.
> the diminishing understanding of assembly language and machine instruction sets
This is true and nobody complains that GCC or LLVM is making programmers dumber. They are code-generation tools from higher-level source code. Much like LLMs are code-generation tools for higher-level language/prompting.
Math skills had never anything to do with arithmetic. Maybe Ramanujan discovered a couple of theorems by dealing with numbers themselves. That is it.
Online discourse though is collapsing under dumb AI talking points.
Man, Usenet had the best online discourse - hardly any angry personal flaming because people dared to disagree. And Twitter, wow that was just pure rationality. slashdot - practically a masters program.
Now, they all did have gems of interaction that would could find by sifting thru the dumb stuff, but I find that property of discourse to be pretty steady. I've even found some interesting comments on YouTube videos and newpaper websites.
Arithmetic skills. And they probably have?
Not really the same, since your average calculator doesn't take over executive function. The user thought and decided what needs to happen, down to one extremely well-specified task, which is so unambiguous that it can be completed by rote and without context.
This is more like paying someone else to read your math homework, generate answers, and maybe even submit them on your behalf. If that had been the (average) student experience, math skills really would have collapsed.
I think we'll find that the people doing that, like the people spending all their time and energy reading slasher pulp fiction in the 1950s, won't be doing as well as the people learning to enhance the power of their education and their expertise via LLMs and strategic alternating between GenAI and thinking about problems. And eventually, if society ever steadies up a bit, people will learn the useful ways of using technology in school and youth; and we'll be glad to be alive to see such marvels.
Assuming we can re-establish the will for democracy and taking care of the whole group.
I don't think it's quite as bad, but I'm imagining someone in the 1950s going: "People just have to use methamphetamines responsibly in their work, and then we'll see the massive benefits as widespread adoption unlocks the potential of the human mind."
In other words, a positive outcome with thing X is possible but there are also big behavioral and cybernetic pitfalls, ones which are suspiciously persistent.
2 replies →
Those are some big ifs and assumptions unfortunately, and the use of AI unfortunately has an isolating effect that is only likely to move the needle in the wrong direction.
> And math skills are going to collapse from calculator reliance.
People can no longer drive a stick-shift car, whereas it used to be that a valet would always be able to drive one to park it.
I also can't make butter by churning or soap from lye and animal fat or what ever.
However, I can use mathematica to demonstrate the criteria for various forms topological stability of solutions to many types of differential equations. I'd rather live now.
That's a very good point. People don't pull out their calculator in the grocery store to do analysis of unit costs or whatever, it's too much of a hassle for that small kind of analysis. But calculators have robbed us of the need to be good at doing that math in our heads. So the math doesn't get done.
Many grocery stores will already give you a per oz or per unit price so you can compare pricing for different brands that have different sizes. It's a very handy feature.
And it's so often wrong that you better be doing sanity checks if you use it for anything.
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That's mandated by law, not because the grocery story wants to.
This is exactly the right analogy. Granted LLMs are a more sophisticated calculator and engineering is still adapting to this wonky/evolving technology. But to pretend it's a coming catastrophe is to ignore every past parallel development - where this has not happened.
Math skills are at their lowest point ever in modern society, and many are still advocating for the reduction in reliance on calculators for this reason.
https://ivyleaguecenter.org/2024/03/12/over-reliance-on-calc...
While on my high school math team, we weren't allowed to use calculators at school. Being able to work quickly without one was too important.
"Mental math skills" literally did collapse tho??? "Math skills" to write proofs (which a calculator cannot do) is a fundamentally different skill set than that "math skills" of mechanically doing arithmetic (which a calculator does do).
Seems like critical reading skills have already collapsed.
No.
With a calculator you still need to understand the fundamentals of mathematics. You also need to understand how to operate a calculator and know its functions.
Even when removing numbers and manual calculation, being a function or formula oriented mathematician still requires you to know the theory and functionality.
With an LLM, you don't even need to know anything other than asking the robot to perform. You don't understand the output, nor can an unskilled person explain it.
They probably have though.
Seems like we're doing fine though, yeah?
Could be a doing a whole lot better. Do you think there's an abundance of critical thinking in society? Because math skills aid in that.
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When I look at the state of software engineering, "fine" is not the word that comes to mind https://xkcd.com/2030/.
If we're going to be the last generation that understands code at this level, we need leave it in a much better state before we die.
Not really, no. It's embarrassing how many people lack the ability to do basic arithmetic.
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This is the same kind of analogy people make when they "poo-pooh" any sort of technological advance, especially with AI.
"Oh, that old simple device didn't displace anything, so this one which is now quickly taking over every job will be just like that simple one". So I guess people today know how to sew and knit and bake bread?
"Oh, humans were always needed, so it'll be the same this time." Is that true of horses and oxen after cars and tractors were invented?
Your calculator isn’t designed to keep you addicted to it and doesn’t have baked in orders like “be humorous and irreverent when appropriate.”
Also, yes I am dependent on a calculator.
1) have they not? 2) not a level comparison