5 ms·

When I use a computer to do work I want the computer to be right. I want to be able to trust the computer. With the inherit non-determinism and probabilistic na

by gortok 4mo ago

When I use a computer to do work I want the computer to be right. I want to be able to trust the computer. With the inherit non-determinism and probabilistic nature of generative-AI, that fundamental reason why I engage a computer is lost. If the spreadsheet is wrong, it’s because the math is wrong, it’s because I made a mistake. It’s not because all of a sudden the computer decided the nature of algebra should be different than it is. Part of the reason why humans are rejecting AI is that we are putting it in places where it makes no sense, or places where humans prefer a human in the loop, there are plenty of places where machine learning algorithms make sense, but customer service is not one of them.

jstummbillig 4mo ago
Reality is non-deterministic (not actually, but in practice). We do strange things to balance this out all the time. Thinking that computer software must be exempt from that mess as a goal is just strange, and concerns itself too much with the ideal of a tool and not enough with the more important question: What if our lives get much, much better? Roughly everyone wants more out of life including the top one percent (and I don't mean the top 0.0001%, just your ordinary industrial nation doctors). How could we possibly morally justify denying everyone the best shot to get at least to that level, and I mean living people RIGHT NOW, ASAP not in a few hundred years? Who would be okay to say "yeah but you know, artists, copyright" and deny those who benefit most from this the opportunity? How could we not take this shot? I understand perfectly well that a lot of things will need reconfiguration and that it's going to be painful, but dear lord, let's focus on making it go well instead of ending it.
- pesus 4mo ago
  > How could we possibly morally justify denying everyone the best shot to get at least to that level, and I mean living people RIGHT NOW, ASAP not in a few hundred years? How exactly do you think this is going to happen?
  - jstummbillig 4mo ago
    By trying! How else is it going to happen? Are we going to deny the immense potential? Nobody needs to draw up a specific plan for that to hold true, we are good at figuring shit out and using tools. I am not saying it's going to work but we are not getting much smarter right now, and we really need all the help we can get to accelerate more complicated stuff. And it is accelerating! Will it be as useful as I hope it will be? That is entirely beside the point. This post was not at all about me assigning any chance of the good outcome. Just that there is no other ethical option.
    - pesus 4mo ago
      > By trying! How else is it going to happen? Are we going to deny the immense potential? Trying what, though? What is it? Immense potential for what? So far this entire comment doesn't actually say what you think we should do in any capacity. It doesn't really say anything at all.
- bheadmaster 4mo ago
  > Reality is non-deterministic (not actually, but in practice). At a quantum level, it is also actually non-deterministic.
  - RadHazard 4mo ago
    That's a common misconception.
    - bheadmaster 4mo ago
      Care to elaborate?
      - RadHazard 4mo ago
        The probabilities in quantum mechanics don't mean there is no determinism. The "answer" to determinism is dependent on your interpretation of quantum mechanics. Even then, take the popular many worlds interpretation. Some see it as supporting determinism and some see it as not supporting it. I wish I could find the pbs spacetime video that talks about it much more eloquently than I can. Somewhat tangential but if you're interested take a look at the relational interpretation: https://en.wikipedia.org/wiki/Relational_quantum_mechanics https://en.wikipedia.org/wiki/Relational_quantum_mechanics . It doesn't get discussed much and it made me think differently about the topic.
        bheadmaster 4mo ago
        Any interpretation that asserts a deterministic universe must invent a "hidden" mechanism which causes the apparent non-determinism, and which we cannot measure nor predict. By Occam's razor, it is more probable that the universe is simply non-deterministic.
        RadHazard 4mo ago
        The flaw is the assertion that the probabilities make non-determinism apparent.
- deleted 4mo ago
  [deleted]
- stackghost 4mo ago
  >What if our lives get much, much better? Roughly everyone wants more out of life including the top one percent (and I don't mean the top 0.0001%, just your ordinary industrial nation doctors). How could we possibly morally justify denying everyone the best shot to get at least to that level, and I mean living people RIGHT NOW, ASAP not in a few hundred years? This is satire, right? If you seriously think that AI is going to improve the lives of anyone except the robber barons who own the AI you are absolutely delusional.
- breezybottom 4mo ago
  This is completely incoherent. Of course we need deterministic computer programs; much of society depends on it.
  - jstummbillig 4mo ago
    All software written will not disappear. There is nothing keeping us from using partly undeterministic software (see: humans) to write deterministic programs.
  - michaelrpeskin 4mo ago
    What does the N in NP stand for? I'm a bit joking, but we've been working in deterministic computation for so long, we don't even think of there being another way. But seriously, I do view AI as the input to a deterministic machine. Junior engineers (well all engineers) aren't deterministic, and we've made processes to direct their behavior towards making better software. AI agents do a better job of following my processes than engineers. We move up the stack towards testing and verification rather than writing. That doesn't make me sad, after 40 years of coding, I'm kind of tired of it. I have more ideas than I can code, so I'm happy to give AI my ideas and have it code for me. I had a former manager tell me that all technology problems are really people problems, now maybe all technology problems are all agent problems and we just have to get comfortable with managing agents like we got comfortable with managing people.
- awkwardpotato 4mo ago
  > Thinking that computer software must be exempt from that mess as a goal is just strange Software is deterministic, it has been since its inception[0]. Why go from something objective/provable to something that does "strange things", when we already have former? It's like making bricks out of paper and declaring "actually, this is logical next step for bricks because stuff waves in the wind". > What if our lives get much, much better? What if not? [0] (Yes not really/actually if we're being pedantic)
  - win311fwg 4mo ago
    > Why go from something objective/provable to something that does "strange things", when we already have former? Because we like computers to feel like they are fast, mainly. Most compilers, for example, are non-deterministic because they can be made to run faster if they ignore things like thread execution order. Same goes for LLMs. Technically they are as deterministic as any other software, but we allow GPUs to play fast and loose with floating point numbers to speed things up, which gives the impression of "strange things".
  - deleted 4mo ago
    [deleted]
  - jstummbillig 4mo ago
    Here is a simple and possibly clarifying thought experiment: Would you be willing to switch your standard of living with the standard of the median person living on this planet? (And I would urge you to look up what that looks like, in case you are unsure). As long as you are not (and I sympathize) I have zero clue how to justify any delay in getting everyone at least to our current level. I understand that there are risks and we should work hard to guard against them. But no society has seriously considered giving up driving while we figure out global warming. People want a good life, that's just the selfish fucks we are, and it's upon those with clout to will it for everyone. > Why go from something objective/provable to something that does "strange things", when we already have former? Because it does something different. It's not from/to. LLMs are subbing in for humans, not for deterministic computing. Replacing deterministic computing with LLMs for tasks that have be perfectly solved without LLMs would be wasteful and silly.
lwhi 4mo ago
I'm not sure I fully agree with this. We can use the computer to build a deterministic system. People aren't fully deterministic either.
- nrightnour 4mo ago
  Correct. Also, the better one gets at using AI, the better they can predict where AI might fail. This allows you to both work 10x faster and prevent many mistakes, which puts you far ahead of not-using-AI.
- cryo32 4mo ago
  Yep. Exactly why we use machines. They do the deterministic bit quickly. We do the other bits.
- nonethewiser 4mo ago
  Correctness can also be guaranteed by non-deterministic systems [0]. You do trade time predictability though. It will eventually give the correct answer, we just dont know when. I keep thinking about the implications of this. So in some sense it's less about being inaccurate and more about prematurely stopping (or not having a well defined target, but that's a whole other mess). In theory, if the target is well defined and it never prematurely stops, the question changes from "will the output be correct" to "when will it be done?" [0] https://en.wikipedia.org/wiki/Las_Vegas_algorithm https://en.wikipedia.org/wiki/Las_Vegas_algorithm
  - SpaceNoodled 4mo ago
    > we just dont know when Ah, so it's merely functionally useless, if not theoretically.
    - nonethewiser 4mo ago
      Guaranteed correctness on an unknown timeline is a pretty interesting tradeoff and not novel. It's just how probabilistic systems work. I dont really understand your position. Do you think AI is useless?
ericmcer 4mo ago
Heavily agree. The computer should be a force for order, because being a living creature is chaos. That said LLMs can be used in ways that promote order. People just got excited and wanted to believe they could be trusted in chaos mode. For reference chaos mode would be prompting something like: "Look at my journal entries and tell me what I should do to fix my life". Versus using one to build a table of common themes and analyzing the resulting spreadsheet yourself.
- Zigurd 4mo ago
  Part of the reason coding agents are widely accepted and used is that human coders are chaos, and human coders have spent a lot of time building tooling to ameliorate chaos. Everything from git to language design, to lint, to profilers, etc. was built to keep the human chaos out. It's pretty good at keeping the LLM chaos out, and when it blows up anyway you can roll it back to the previous commit.
- btbuildem 4mo ago
  I think we got excited / wanted to believe that we won't have to expend any effort whatsoever, and the AI could "do it all". The reality (as far as I can comprehend it) seems to be that AI expanded the scope of what we can shove into one mouthful, and now it takes much more effort to chew. Metaphorically speaking.
kypro 4mo ago
> there are plenty of places where machine learning algorithms make sense, but customer service is not one of them. You're optimising for quality, where as companies optimise for some balance of quality and cost. AI might not be quite as good as a skilled human, but it's often good enough and a lot cheaper, so companies use it. I actually think customer service is one of the few places it makes sense to use AI – at least to some degree. AI can provide immediate support to customer queries, and can usually handle the majority of basic issues customers have. You might need to escalate to a human in edge cases, but that's how you balance quality and cost.
- gortok 4mo ago
  > You're optimising for quality, where as companies optimise for some balance of quality and cost. To be clear; in our current stage of capitalism, companies are largely optimizing for how much quality they can sacrifice before they lose too many customers to justify the sacrifice in quality. Companies are optimizing for cost, and part of the backlash against AI is the backlash against the overt quality sacrifices made by companies. This trend will hopefully continue.
nonethewiser 4mo ago
This is an interesting way of thinking about it. I generally agree. I especially agree that anti-AI sentiment partially comes from miss-using it. However: Determinism isn't a requirement for 100% correctness. A Las Vegas algorithm is randomized, non-deterministic and guarantees 100% correctness [0]. The execution can be different every time but the result will always be correct. determinism does not lose accuracy. It does lose time predictability. So if your problem with AI is accuracy, then in theory your problem is just premature stopping. [0] https://en.wikipedia.org/wiki/Las_Vegas_algorithm https://en.wikipedia.org/wiki/Las_Vegas_algorithm
- layer8 4mo ago
  The economics of it (token cost) means, however, that what will be chosen most often is the barely sustainable minimum level of quality, aka race to the bottom. AI is more cost-sensitive in that way than humans caring or not caring about making things robust and correct used to be.
  - nonethewiser 4mo ago
    For sure, that's why I say in theory. Also models aren't perfect. You can't plug in an explicit target and ensure it doesnt stop prematurely and expect 100 accuracy. But that's not because it's non-deterministic, since clearly non-deterministic systems can be 100% accurate.
- fluoridation 4mo ago
  A Las Vegas algorithm requires that you have a deterministic test that can definitively determine the correctness of an intermediate result. So what you're saying is that what it takes to make LLMs give 100% correct results is having a human between the LLM and the user, who's capable of re-prompting on incorrect answers from the LLM. Well, if the human is there, why not just ask the human? What value is the random number generator adding? Like the GP said, the point of determinism is that you can trust the correctness of the results, without doing any checking. Solved problems stay solved.
  - 4mo ago
simianwords 4mo ago
working with a non deterministic tool requires taste and judgement. if you want full determinism AI is not for you but it has a market for other people?
monitron 4mo ago
Precisely! I don't think this is the whole problem but it's a part of it I keep coming back to. We took the one thing that computers were good at (getting the same answer every time, quickly and efficiently) and tossed it out the window. Good AI system design can help somewhat, but even if you give the LLM a calculator tool, it's not guaranteed to use it every time, or to write the tool use correctly, or to copy out the answer correctly.
mgfist 4mo ago
> there are plenty of places where machine learning algorithms make sense, but customer service is not one of them. I don't care about human vs AI, I just want my issue resolved. Whatever does that the best and fastest. Or even better, for there to not be an issue in the first place.
- webdood90 4mo ago
  The root of all our evils, right here. We only want the fastest cheapest thing possible, without thinking about how it impacts literally everything else about our world.
  - satvikpendem 4mo ago
    They never said fastest or cheapest, they said it should resolve the issue. A fast cheap human who can't is not better than an AI that can.
DamnInteresting 4mo ago
One recalls the Pentium FDIV bug, where an estimated 1 in 9 billion floating point divides with random parameters would produce inaccurate results[1]. A small subset of Pentium users would ever encounter the problem, yet it was considered a major controversy, and Intel ultimately replaced $475 million worth of CPUs (in 1994 dollars)[2]. [1] https://en.wikipedia.org/wiki/Pentium_FDIV_bug https://en.wikipedia.org/wiki/Pentium_FDIV_bug [2] https://www.tomshardware.com/pc-components/cpus/its-been-30-years-since-intels-infamous-pentium-fdiv-bug-reared-its-ugly-head-a-math-bug-caused-intels-first-cpu-recall https://www.tomshardware.com/pc-components/cpus/its-been-30-...

by gortok 4mo ago

jstummbillig 4mo ago

Reality is non-deterministic (not actually, but in practice). We do strange things to balance this out all the time. Thinking that computer software must be exempt from that mess as a goal is just strange, and concerns itself too much with the ideal of a tool and not enough with the more important question: What if our lives get much, much better? Roughly everyone wants more out of life including the top one percent (and I don't mean the top 0.0001%, just your ordinary industrial nation doctors). How could we possibly morally justify denying everyone the best shot to get at least to that level, and I mean living people RIGHT NOW, ASAP not in a few hundred years? Who would be okay to say "yeah but you know, artists, copyright" and deny those who benefit most from this the opportunity? How could we not take this shot? I understand perfectly well that a lot of things will need reconfiguration and that it's going to be painful, but dear lord, let's focus on making it go well instead of ending it.

pesus 4mo ago
> How could we possibly morally justify denying everyone the best shot to get at least to that level, and I mean living people RIGHT NOW, ASAP not in a few hundred years? How exactly do you think this is going to happen?
- jstummbillig 4mo ago
  By trying! How else is it going to happen? Are we going to deny the immense potential? Nobody needs to draw up a specific plan for that to hold true, we are good at figuring shit out and using tools. I am not saying it's going to work but we are not getting much smarter right now, and we really need all the help we can get to accelerate more complicated stuff. And it is accelerating! Will it be as useful as I hope it will be? That is entirely beside the point. This post was not at all about me assigning any chance of the good outcome. Just that there is no other ethical option.
  - pesus 4mo ago
    > By trying! How else is it going to happen? Are we going to deny the immense potential? Trying what, though? What is it? Immense potential for what? So far this entire comment doesn't actually say what you think we should do in any capacity. It doesn't really say anything at all.
bheadmaster 4mo ago
> Reality is non-deterministic (not actually, but in practice). At a quantum level, it is also actually non-deterministic.
- RadHazard 4mo ago
  That's a common misconception.
  - bheadmaster 4mo ago
    Care to elaborate?
    - RadHazard 4mo ago
      The probabilities in quantum mechanics don't mean there is no determinism. The "answer" to determinism is dependent on your interpretation of quantum mechanics. Even then, take the popular many worlds interpretation. Some see it as supporting determinism and some see it as not supporting it. I wish I could find the pbs spacetime video that talks about it much more eloquently than I can. Somewhat tangential but if you're interested take a look at the relational interpretation: https://en.wikipedia.org/wiki/Relational_quantum_mechanics https://en.wikipedia.org/wiki/Relational_quantum_mechanics . It doesn't get discussed much and it made me think differently about the topic.
      - bheadmaster 4mo ago
        Any interpretation that asserts a deterministic universe must invent a "hidden" mechanism which causes the apparent non-determinism, and which we cannot measure nor predict. By Occam's razor, it is more probable that the universe is simply non-deterministic.
        RadHazard 4mo ago
        The flaw is the assertion that the probabilities make non-determinism apparent.
deleted 4mo ago
[deleted]
stackghost 4mo ago
>What if our lives get much, much better? Roughly everyone wants more out of life including the top one percent (and I don't mean the top 0.0001%, just your ordinary industrial nation doctors). How could we possibly morally justify denying everyone the best shot to get at least to that level, and I mean living people RIGHT NOW, ASAP not in a few hundred years? This is satire, right? If you seriously think that AI is going to improve the lives of anyone except the robber barons who own the AI you are absolutely delusional.
breezybottom 4mo ago
This is completely incoherent. Of course we need deterministic computer programs; much of society depends on it.
- jstummbillig 4mo ago
  All software written will not disappear. There is nothing keeping us from using partly undeterministic software (see: humans) to write deterministic programs.
- michaelrpeskin 4mo ago
  What does the N in NP stand for? I'm a bit joking, but we've been working in deterministic computation for so long, we don't even think of there being another way. But seriously, I do view AI as the input to a deterministic machine. Junior engineers (well all engineers) aren't deterministic, and we've made processes to direct their behavior towards making better software. AI agents do a better job of following my processes than engineers. We move up the stack towards testing and verification rather than writing. That doesn't make me sad, after 40 years of coding, I'm kind of tired of it. I have more ideas than I can code, so I'm happy to give AI my ideas and have it code for me. I had a former manager tell me that all technology problems are really people problems, now maybe all technology problems are all agent problems and we just have to get comfortable with managing agents like we got comfortable with managing people.
awkwardpotato 4mo ago
> Thinking that computer software must be exempt from that mess as a goal is just strange Software is deterministic, it has been since its inception[0]. Why go from something objective/provable to something that does "strange things", when we already have former? It's like making bricks out of paper and declaring "actually, this is logical next step for bricks because stuff waves in the wind". > What if our lives get much, much better? What if not? [0] (Yes not really/actually if we're being pedantic)
- win311fwg 4mo ago
  > Why go from something objective/provable to something that does "strange things", when we already have former? Because we like computers to feel like they are fast, mainly. Most compilers, for example, are non-deterministic because they can be made to run faster if they ignore things like thread execution order. Same goes for LLMs. Technically they are as deterministic as any other software, but we allow GPUs to play fast and loose with floating point numbers to speed things up, which gives the impression of "strange things".
- deleted 4mo ago
  [deleted]
- jstummbillig 4mo ago
  Here is a simple and possibly clarifying thought experiment: Would you be willing to switch your standard of living with the standard of the median person living on this planet? (And I would urge you to look up what that looks like, in case you are unsure). As long as you are not (and I sympathize) I have zero clue how to justify any delay in getting everyone at least to our current level. I understand that there are risks and we should work hard to guard against them. But no society has seriously considered giving up driving while we figure out global warming. People want a good life, that's just the selfish fucks we are, and it's upon those with clout to will it for everyone. > Why go from something objective/provable to something that does "strange things", when we already have former? Because it does something different. It's not from/to. LLMs are subbing in for humans, not for deterministic computing. Replacing deterministic computing with LLMs for tasks that have be perfectly solved without LLMs would be wasteful and silly.

lwhi 4mo ago

I'm not sure I fully agree with this. We can use the computer to build a deterministic system. People aren't fully deterministic either.

nrightnour 4mo ago
Correct. Also, the better one gets at using AI, the better they can predict where AI might fail. This allows you to both work 10x faster and prevent many mistakes, which puts you far ahead of not-using-AI.
cryo32 4mo ago
Yep. Exactly why we use machines. They do the deterministic bit quickly. We do the other bits.
nonethewiser 4mo ago
Correctness can also be guaranteed by non-deterministic systems [0]. You do trade time predictability though. It will eventually give the correct answer, we just dont know when. I keep thinking about the implications of this. So in some sense it's less about being inaccurate and more about prematurely stopping (or not having a well defined target, but that's a whole other mess). In theory, if the target is well defined and it never prematurely stops, the question changes from "will the output be correct" to "when will it be done?" [0] https://en.wikipedia.org/wiki/Las_Vegas_algorithm https://en.wikipedia.org/wiki/Las_Vegas_algorithm
- SpaceNoodled 4mo ago
  > we just dont know when Ah, so it's merely functionally useless, if not theoretically.
  - nonethewiser 4mo ago
    Guaranteed correctness on an unknown timeline is a pretty interesting tradeoff and not novel. It's just how probabilistic systems work. I dont really understand your position. Do you think AI is useless?

ericmcer 4mo ago

Heavily agree. The computer should be a force for order, because being a living creature is chaos. That said LLMs can be used in ways that promote order. People just got excited and wanted to believe they could be trusted in chaos mode. For reference chaos mode would be prompting something like: "Look at my journal entries and tell me what I should do to fix my life". Versus using one to build a table of common themes and analyzing the resulting spreadsheet yourself.

Zigurd 4mo ago
Part of the reason coding agents are widely accepted and used is that human coders are chaos, and human coders have spent a lot of time building tooling to ameliorate chaos. Everything from git to language design, to lint, to profilers, etc. was built to keep the human chaos out. It's pretty good at keeping the LLM chaos out, and when it blows up anyway you can roll it back to the previous commit.
btbuildem 4mo ago
I think we got excited / wanted to believe that we won't have to expend any effort whatsoever, and the AI could "do it all". The reality (as far as I can comprehend it) seems to be that AI expanded the scope of what we can shove into one mouthful, and now it takes much more effort to chew. Metaphorically speaking.

kypro 4mo ago

> there are plenty of places where machine learning algorithms make sense, but customer service is not one of them. You're optimising for quality, where as companies optimise for some balance of quality and cost. AI might not be quite as good as a skilled human, but it's often good enough and a lot cheaper, so companies use it. I actually think customer service is one of the few places it makes sense to use AI – at least to some degree. AI can provide immediate support to customer queries, and can usually handle the majority of basic issues customers have. You might need to escalate to a human in edge cases, but that's how you balance quality and cost.

gortok 4mo ago
> You're optimising for quality, where as companies optimise for some balance of quality and cost. To be clear; in our current stage of capitalism, companies are largely optimizing for how much quality they can sacrifice before they lose too many customers to justify the sacrifice in quality. Companies are optimizing for cost, and part of the backlash against AI is the backlash against the overt quality sacrifices made by companies. This trend will hopefully continue.

nonethewiser 4mo ago

This is an interesting way of thinking about it. I generally agree. I especially agree that anti-AI sentiment partially comes from miss-using it. However: Determinism isn't a requirement for 100% correctness. A Las Vegas algorithm is randomized, non-deterministic and guarantees 100% correctness [0]. The execution can be different every time but the result will always be correct. determinism does not lose accuracy. It does lose time predictability. So if your problem with AI is accuracy, then in theory your problem is just premature stopping. [0] https://en.wikipedia.org/wiki/Las_Vegas_algorithm https://en.wikipedia.org/wiki/Las_Vegas_algorithm

layer8 4mo ago
The economics of it (token cost) means, however, that what will be chosen most often is the barely sustainable minimum level of quality, aka race to the bottom. AI is more cost-sensitive in that way than humans caring or not caring about making things robust and correct used to be.
- nonethewiser 4mo ago
  For sure, that's why I say in theory. Also models aren't perfect. You can't plug in an explicit target and ensure it doesnt stop prematurely and expect 100 accuracy. But that's not because it's non-deterministic, since clearly non-deterministic systems can be 100% accurate.
fluoridation 4mo ago
A Las Vegas algorithm requires that you have a deterministic test that can definitively determine the correctness of an intermediate result. So what you're saying is that what it takes to make LLMs give 100% correct results is having a human between the LLM and the user, who's capable of re-prompting on incorrect answers from the LLM. Well, if the human is there, why not just ask the human? What value is the random number generator adding? Like the GP said, the point of determinism is that you can trust the correctness of the results, without doing any checking. Solved problems stay solved.
- 4mo ago

simianwords 4mo ago

working with a non deterministic tool requires taste and judgement. if you want full determinism AI is not for you but it has a market for other people?

monitron 4mo ago

Precisely! I don't think this is the whole problem but it's a part of it I keep coming back to. We took the one thing that computers were good at (getting the same answer every time, quickly and efficiently) and tossed it out the window. Good AI system design can help somewhat, but even if you give the LLM a calculator tool, it's not guaranteed to use it every time, or to write the tool use correctly, or to copy out the answer correctly.

mgfist 4mo ago

> there are plenty of places where machine learning algorithms make sense, but customer service is not one of them. I don't care about human vs AI, I just want my issue resolved. Whatever does that the best and fastest. Or even better, for there to not be an issue in the first place.

webdood90 4mo ago
The root of all our evils, right here. We only want the fastest cheapest thing possible, without thinking about how it impacts literally everything else about our world.
- satvikpendem 4mo ago
  They never said fastest or cheapest, they said it should resolve the issue. A fast cheap human who can't is not better than an AI that can.

DamnInteresting 4mo ago

One recalls the Pentium FDIV bug, where an estimated 1 in 9 billion floating point divides with random parameters would produce inaccurate results[1]. A small subset of Pentium users would ever encounter the problem, yet it was considered a major controversy, and Intel ultimately replaced $475 million worth of CPUs (in 1994 dollars)[2]. [1] https://en.wikipedia.org/wiki/Pentium_FDIV_bug https://en.wikipedia.org/wiki/Pentium_FDIV_bug [2] https://www.tomshardware.com/pc-components/cpus/its-been-30-years-since-intels-infamous-pentium-fdiv-bug-reared-its-ugly-head-a-math-bug-caused-intels-first-cpu-recall https://www.tomshardware.com/pc-components/cpus/its-been-30-...