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Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @05:37PM (#41814017)
The notion is AFAIS that a deterministic algorithm is obviously not reasoning, and a deterministic algorithm interspersed with dice rolls is obviously not reasoning either.

Of course, some would beg to differ. It's quite common nowadays to believe that we are something like the latter.

Re:Understanding the Limitations of Mathematical Reasoning i... by pishpash on Friday October 11, 2024 @05:55PM (#41814207)
Why is a deterministic algorithm not reasoning? Reasoning is very deterministic.
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @06:16PM (#41814388)
It's not about (in-)determinism really, it's about the algorithm part.

An algorithm that does something can in principle be ran by someone who doesn't know what the algorithm does. You could have a kid calculate an integral by giving it a sequence of directions whose purpose it doesn't understand (e.g. cut out some cardboard that matches the shape, put it on one side of the scale, place enough unit cardboard pieces on the other side until they are even, then tell me how many pieces you put).

Reasoning has more to do with how the problem came about. A person had to come against a certain problem, figure out a way in which they can solve it, then apply the (perhaps algorithmic) solution. The algorithmic part is only an artifact.

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @07:04PM (#41814757)
But isn't figuring out a way to solve also algorithmic? In a lot of cases it is simply bruteforce trying out different things based on the concepts you know about and mixing them.
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @07:44PM (#41815048)
You are right that relevant memories and analogous experiences come up and are used as building blocks in our evaluation/exploration of a problem, but it doesn't seem to me an algorithmic procedure at all.

You can trace out your journey in solving a problem, in retrospect, but could you encode it into a "solving-a-problem" algorithm?

I think you could extract some kind of generic template for problem solving: you come up with an idea, you evaluate whether it is the solution, you adjust the idea if not.

But this is a template, not an algorithm. Coming up with an idea has to do with filtering the old and new memories/perceptions that come to mind: does this one seem right? or this one? Evaluating whether it is right is also an active process of asking questions. It involves memory (of the problem to be solved), attention (to the potential solution), judgement (do they fit together?), etc.

None of these are a predetermined sequence of steps you apply mechanically, such as the child "solving an integral" above.*

*Of course, the child is problem-solving in the sense that it's trying its best to follow your instructions. "Did I cut it right?" "Are the scales even?" But this is not the problem of "solving an integral" to which it is completely oblivious to.

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @08:00PM (#41815142)
I think it can be an algorithm, it just that the algorithm will be a very complex one compromised of many different algorithms. It's not an algorithm anyone could practically follow in their lifetime. But there's plenty of algorithms people can't follow in real life.
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @09:06PM (#41815477)
If all one has is hammers, one can start seeing nails everywhere.

A screw? That's just a nail which will damage the wood.

A tomato? That's just a soft screw which splatters. Etc.

What purpose does seeing everything through the lens of an algorithm serve? Is the movement of an electron an algorithm? Is a polar planimeter an algorithm? [0]

We design algorithms to solve certain problems. It's part of our problem solving activity. But for what purpose would we go around, assuming things that don't look like algorithms are actually algorithms that are just outside of our reach? This doesn't solve a practical problem, so of what use is that, and where does it lead?

My long-winded answer is: We derive satisfaction from being in principle powerful. Our mechanistic/computational knowledge of nature allows us to bend certain parts of it to our will. If there are parts we cannot control, it's at least consoling that we in principle could know/control them. So we stretch computational/algorithmic terms as far as we possibly can. In the end, it envelops us as subjects. We end up in a rather cliche epiphenomenalism + causal determinism worldview:

- "Yeah, we have experiences, but they're just inefficacious artifacts of underlying chemistry."

- "You - the person who is reasoning - don't actually know what reasoning is like, it's really a very complex algorithm which we could never know or follow."

The only way such an uninspiring outlook can subsist is because it jives well with some modern dreams:

- "We only need X more compute and Y more years to bend Z part of nature to our will and bring utopia." (cue all the AI hype, see relevant frontpage entry [1])

- "If we're just a machine then maybe we can hack-reward-centers/optimize-drug-concoction/upload-to-mainframe-for-immortality" (cue quasi-immortality pitches and externally-enforced-happines pipe-dreams)

- "If I'm just a machine then I'm not responsible for my shortcomings - they're just the outcome of my wiring I cannot influence." (a nice supplement for absolving oneself from responsibility - to oneself)

- "If all is mechanical, then I'm just a temporarily embarrassed sovereign over everything. After all, if I just knew the mechanism behind things, then I could bend it to my will."

- "I have to believe this because it is obviously true." (maybe the saddest of them all, since it promises nothing except the joy of being right and having others be wrong. it also seeds the others)

[0] http://psychsciencenotes.blogspot.com/2015/07/brains-dont-ha...

[1] https://news.ycombinator.com/item?id=41813268

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @09:43PM (#41815643)
> What purpose does seeing everything through the lens of an algorithm serve?

To me at least it helps me understand how things work. What is an alternative? Because alternative seems like some sort of magic I wouldn't understand.

> Is the movement of an electron an algorithm?

I think there's a lot of argument and complexity to what an electron exactly is or does, and what its properties actually mean, but I would imagine in general from particle and other levels whole universe can be just a deterministic algorithm, and so anything can be an algorithm. Universe has certain laws and rules which could in theory be simulated, but the simulation must have more capacity than the universe itself has so we inside the universe likely can not do it unless we find a mechanism to somehow bypass this.

> But for what purpose would we go around, assuming things that don't look like algorithms are actually algorithms that are just outside of our reach? This doesn't solve a practical problem, so of what use is that, and where does it lead?

If I try to think of what is the algorithm behind something, it helps me understand it better. Intuitively I think there's a complex algorithm behind everything, and it's just a matter of spending time and effort to figure out what it exactly is. It's unrealistic to get close to the real detail and nuance of the algorithm, but already trying to figure out the algorithm brings me closer to understanding.

> We end up in a rather cliche epiphenomenalism + causal determinism worldview

Wait -- what is wrong with that? And also I don't think it's cliche, I think it is likely to be the case?

> - "You - the person who is reasoning - don't actually know what reasoning is like, it's really a very complex algorithm which we could never know or follow."

I mean writing it down on the algorithmic level is not something we can consciously follow easily. However our brain within us is following those algorithms in the level of efficiency that we cannot consciously follow at that speed step by step, just following the instructions.

> The only way such an uninspiring outlook can subsist is because it jives well with some modern dreams:

I think my outlook is at least inspiring to me.

> - "If we're just a machine then maybe we can hack-reward-centers/optimize-drug-concoction/upload-to-mainframe-for-immortality" (cue quasi-immortality pitches and externally-enforced-happines pipe-dreams)

I do think theoretically it would be possible to hack humans to have constant "heroin like euphoria". I'm not sure I exactly care for it, but I do think these things could be done, I just don't know when, is it 50 years, 100 years or 1000 years. Of course while I say right now that I don't exactly care for it, if I tried it for once I would be hooked on it forever, assuming it has no tolerance build up or other negative effects making me consider to quit it. But even real heroin is terribly hard to quit while it has tolerance build up and side effects.

> - "If I'm just a machine then I'm not responsible for my shortcomings - they're just the outcome of my wiring I cannot influence." (a nice supplement for absolving oneself from responsibility - to oneself)

I'm inclined to think that the World is deterministic, yet I happen to also think that I have reward mechanisms that make me ambitious in a sense that I want to achieve certain goals to feel rewarded and in order to achieve those goals I have to overcome many challenges and improve certain shortcomings because it's needed to achieve those goals. If someone is using those as an excuse they would likely be the type of person to find an excuse in anything anyway. And if they do have goals they want to reach they will be affected by that, because there's certain behaviour that will get you to your desired goals and certain behaviour that is not. Taking responsibility and ownership is rewarded and if you do that, you will reach your goals with higher probability. I don't buy into the sort of thing where "something is bad because some people might use it as an excuse". Because finding an excuse is usually about the mindset, not about what kind of excuses are possible to select from. An AI bot with good goals and reward system, despite it being very obvious that they are programmed and deterministic wouldn't go about to make those excuses. But an AI bot trained to make excuses and be rewarded for it, would keep making excuses no matter what.

Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @11:23PM (#41816142)
Thanks for your thoughtful response.

The view you are elaborating has a logic to it. You could argue it's the zeitgeist, at least among educated and STEM-adjacent circles. Hence my comment of it being cliche: you see variants of it all the time, and it gets a bit jading by virtue of being wholly unconvincing (to me).

In general, I think the utility of seeing everything through a mechanistic/algorithmic lens is overblown. When I'm doing technical work, I put my STEM hat on, and sometimes write algorithms. For the most part, I let it rest though. And I don't feel I understand the world any worse for dropping such mechanistic world-images I may have held years ago (I'm more at peace with it, if anything). In hindsight, the ROI on the skill of mechanistically dissecting anything you look at is rather low and hardly transferable ime. The ensuing "understanding" a passing regurgitative satisfaction.

If there's anything I really want to push back on, however, it's the notion that the views you hold do not influence the range of ways in which you develop yourself in an important way. If one truly holds the view that one is responsible for one's actions, and not the whims of determination of chance, where is the space for the excuse "it's not up to me"? Views may not determine the course of action, but they can surely constrain.

Disentangling one's views from one's behavior can go a long way in measured, written discussions like this, but I don't see it being the case in real life. It is the case however, that we can be a hodge-podge of contradictory views and standards, and that we commit to one for a moment, then to another. This is a matter of strength and cohesiveness of character. And we are good at "saving face" in front of us and others. For example, if you've met people who partake in a vice yet will say stuff like "This is bad for me." - the actual underlying view is "This has obvious drawbacks but I still think the enjoyment is worth it." It's only when they can maintain the view that the drawbacks are not worth it, that they can break out.

Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Saturday October 12, 2024 @12:56PM (#41820540)
> The view you are elaborating has a logic to it. You could argue it's the zeitgeist, at least among educated and STEM-adjacent circles.

You could argue that most opinions or beliefs about how the World operates are cliche or similar if that's the case, there's only so many different beliefs that make any sense at all to hold and it's likely there's a group of people holding those beliefs as well and that they are not original at all. And you could also argue that a belief that 2 + 2 = 4 is cliche, because so many people believe that to be the case.

> In general, I think the utility of seeing everything through a mechanistic/algorithmic lens is overblown.

That requires some sort of measurement on how many people see it through that lens and what they evaluate it as, but I'm seeing the opposite since most of the time I find it the other way around.

> And I don't feel I understand the world any worse for dropping such mechanistic world-images I may have held years ago (I'm more at peace with it, if anything).

I can't tell how other people understand the World, since one of the learnings throughout my life have been that different people ingest information in so many different ways. Some think in images, some are not able to picture things in their mind, some don't have inner monologue. So naturally there would be a different methods of understanding things. But if I think of myself, I understand things best when I think of them as algorithms or mechanical steps that I think through. I have trouble understanding or remembering facts on their own, without internalizing the mechanisms, the cause and effect after if I have done that, it feels to me like I actually understand it. I don't even know what other way there is to understand that. It's perfectly possible that there's some other innate ways of understanding things or having a feeling that there's understanding, that I can't get just because I'm wired in a way that makes me understand things only if I can think of it as an algorithm. E.g. what I've found fantastic for learning subjects myself is actually coding through them or trying to simulate them using code. It actively engages my mind to try and simulate whatever happens in the real world. And subjects I had trouble engaging with in school, if I go through coding them, I feel like I'm actually learning them and becoming smarter. E.g. if I want to truly learn biology I should build a simulation tool that will simulate how cells behave, whatever different things in cells do, how organs work, etc.

> If one truly holds the view that one is responsible for one's actions, and not the whims of determination of chance, where is the space for the excuse "it's not up to me"?

I still don't see it in that way. Everything being deterministic and algorithmic doesn't make me have those excuses. I happen to have a reward mechanism, that rewards me for e.g. eating. It's been shaped by the process of evolution. I have many other reward mechanisms. I didn't choose those reward mechanisms myself, but I strategize on how to achieve those rewards, and I know that playing a victim is not a way to achieve your goals. Certainly there are people who mistakenly might believe that, but it happens to both, whoever believes in determinism and whoever believes in some sort of free will. I know that if I do good work, I get good rewards. So I do good work.

> Disentangling one's views from one's behavior can go a long way in measured, written discussions like this, but I don't see it being the case in real life. It is the case however, that we can be a hodge-podge of contradictory views and standards, and that we commit to one for a moment, then to another. This is a matter of strength and cohesiveness of character. And we are good at "saving face" in front of us and others. For example, if you've met people who partake in a vice yet will say stuff like "This is bad for me." - the actual underlying view is "This has obvious drawbacks but I still think the enjoyment is worth it." It's only when they can maintain the view that the drawbacks are not worth it, that they can break out.

Certainly there's a lot of views and human condition I think is overall a lot about inner turmoil and fighting vices, desires, balancing short term please vs long term gains etc, etc. But it doesn't matter if you consider something to be deterministic, because you are still balancing short term vs long term just like if you didn't believe in any of that. I don't think that I should be hunting short term pleasure constantly because it's how I'm wired to be, because I've seen enough evidence that in long term I would suffer, and I don't want to suffer in long term, so I put in the effort to engage in short term pleasure in such a way that it wouldn't have higher long term pain than I'd be willing to endure.

I can even visualize these aspects algorithmically and mechanically. I might think of myself as an RPG player where let's say if I eat this food, or ingest this drug, drink alcohol N amount, if affects some of my stats like happiness or euphoria positively temporarily, but it will decrease other stats in the long term. I think I'm conscious of this idea and in a traditional sense I'm picking to skip the short term pleasure, but me wanting to have the longer term pleasure is also wired into me.

Re:Understanding the Limitations of Mathematical Reasoning i... by pishpash on Friday October 11, 2024 @06:22PM (#41814425)
I think you overlook how algorithms come about. How does GPT write novel code, which are algorithms?
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @06:28PM (#41814475)
Not sure I track. It would help to know where you're coming from.

Given a long enough life-span, a lot of pencil and paper, and some dice, I could do the forward passes of GPT and "write novel code", without there having been any reasoning about the code I'm writing down - I wouldn't even need to know what the code is about.

Re:Understanding the Limitations of Mathematical Reasoning i... by XenophileJKO on Friday October 11, 2024 @11:03PM (#41816051)
I mean in theory I could sit and calculate electrical and chemical potentials and interactions and figure out what your next comment will be.
Re:Understanding the Limitations of Mathematical Reasoning i... by tananan on Friday October 11, 2024 @11:24PM (#41816146)
Hard disagree ;)
Re:Understanding the Limitations of Mathematical Reasoning i... by anonzzzies on Saturday October 12, 2024 @02:12AM (#41816854)
if we knew you were religious, which we would do if we had a mapping of your brain, we would have known you were going to make this comment
Re:Understanding the Limitations of Mathematical Reasoning i... by mewpmewp2 on Friday October 11, 2024 @07:02PM (#41814742)
And couldn't the whole World be deterministic in the first place, or is there an idea that some RNG is generating all the "reasoning" that is happening everywhere in the World?

And if it's RNG, how could RNG be possibly creating all this reasoning (like some people want to believe quantum mechanics possibly enables consciousness on some odd levels).

Re:Understanding the Limitations of Mathematical Reasoning i... by ActorNightly on Friday October 11, 2024 @08:38PM (#41815365)
There is a difference between determinism in the sense of given a certain input, you allways get a certain output, and determinism in the sense of given a certain input, and knowledge of the sub universe in which the problem applies, get a certain output.

I.e an agent that can reason can deterministically figure out that the most probable way of getting information to complete the answer would be to go out on google and do searches, but we don't deterministically know what the information that exists at that point and time on google, so the answer could be different.

Re:Understanding the Limitations of Mathematical Reasoning i... by amelius on Saturday October 12, 2024 @06:22AM (#41818056)
> a deterministic algorithm interspersed with dice rolls is obviously not reasoning either.

There are multiple ways to explain to you that you are wrong. If I roll some dice to choose which way I will use to explain it to you, then why is this not reasoning?