jostylr

It was about abusive monopolies where consumers want something different. This is easily fixable by competition. Google is a perfect example of how incredibly easy it is to escape that monopoly. I do it all the time. Imagine what would happen if google started charging a $100 a month for its services. The issue is that the current situation does not conform to what "superior intellectuals" think people ought to do so they want to use violence (government) to force people to live the way they see fit. Yay! All it takes is changing the default. And the anti-monopolists did not even try to do a public awareness campaign of this evil; they went to court (violence) instead of persuasion.

I am unaware of what government intervention you are talking about in 1920. I have heard explicitly that the government did nothing by historians and I asked ChatGPT and it had nothing [1]. In that same conversation I also asked it compare Europe versus US in 2008 from an Austrian perspective. The main thesis Austrians have for busts is that of misallocated resources based on false price information whose remedy is reallocation, often through bankruptcy and repurposing of capital goods. It seems that the US was able to have a better reallocation of resources. I am not sure entirely of the mechanism, but at least some of it was allowing some things to fail and some of it might have been the government going in and manually realigning these things (taking over in the short term). It sounded like Europe did not allow for that, either direct intervention or simply allowing things to fail -- the bad businesses limped along as zombies. Europe kind of did the worst of both worlds.

As for the US, it also suggests that the Austrians, and I have heard this, cite our extreme debt, and it keeps growing, as a sign of a reckoning to come. Kind of like one can keep pumping sugar in to deal with sugar lows after a high, but eventually the bill comes due. Keynesians and others seem to view the economy as a short-term adjustable kind of thing, a chemical reaction with just the right reagents producing something wonderful. Austrians view it as a lumbering ecology, with things adapting and to the extent adaptation based on truth is present, it gets better. To the extent that distortions and violence happen, not so good. We shall, unfortunately, probably see soon enough unless AI can make a productivity miracle happen.

1: https://chatgpt.com/share/68e3ce42-6e78-8012-8a9c-1d7cff2d6f...

Abusive monopolies without the imposition of violence (either by the government or the company) lasting for a long time horizon? Yes, that would seem implausible in a free market. For example, if someone controlled the water pipes and charged a $1000 for a cup of water, then someone would find a way to bring in water for less and would start contracting to build their own pipes, maybe locking in long term contracts with people given the time horizon of construction. That threat alone keeps the prices low. But I also live in a city with city run water and sewage where the infrastructure is falling apart and the cost is on the order of 2k a year for normal water usage and actually would be about 1500 if no water was used. Sewage overflows, water goes brown and federal intervention is required. So a little competition might actually be useful.

As for pollution, have you looked at the history of state run industries and their pollution record? How well does the US military manage its pollution, particularly prior to the EPA when the public consciousness shifted? How many of the worst private polluters were in the service of the government (such as for the military)? There are also tales of the communist countries and their abuse of the environment. And in the context of a democracy, one would assume that if it is faithful to what people want, then to have pollution controls requires at least 50%+ of the population to want them. That sounds like a strong market incentive to provide that not to mention actual destructive pollution can be subject to claims by those injured by the polluters. While it was before the largest amount of industrial pollution, there was a time in the US before the government got involved where pollution was restricted by such considerations. Companies did not like that so the government started to regulate in order to protect the polluters. Time and time again, actual government legislation is used to either protect the guilty or it comes in when 90% of a problem has already been resolved.

Also, the first two economic schools of thought you list do not make any basic sense. If it is just spending, then why would there be boom bust signals? Why doesn't everyone just keep spending? Something else must cause a reduction in spending which ought to be pretty important. If monetary supply is the only control for the economy, then set it and forget it on the trajectory you want. Since there doesn't seem to be a stable path, then some other factor is important to consider.

For either of them, why not just print up a million dollars for every person? Do you suddenly have a supply of million dollars worth of goods for everyone? No. There is real wealth that has to be produced and that is why futzing around with money is not good enough.

The information coordinating function is that of prices which requires a relatively stable money supply for accurate signals. If the money supply is artificially tampered with, then the entrepreneurs make bad bets, thinking that either there are more resources then there are (inflationary monetary supply, boom period) or there are less (deflationary monetary supply, spending contraction). The first case leads to half-completed projects when actual resources run out across the economy (bust). This leads to recession/depression which is a time to realign the resource allocation to what is actually desired if government stays out of the way. Compare the 1920 economic downturn (hands-off government, rebounds quickly) to the 1929-1940s economic depression (heavy government intervention under both Hoover and even more Roosevelt). In the second with deflationary, it is idle resources that are the result, they get cheaper, and eventually leading to a boom. There aren't too many examples I am aware of of this though there is a train of thought that the late 1920s had inflation (to help the British with their war debt?) and then the Fed reversed course and starting deflating the money supply cause quite the shock. In any event, both are examples of problematic time periods during the price readjustment to the new value of money.

The main reason the government inflates money is so that they can spend without explicit taxing (inflation is an implicit tax for those that do not get the first rounds of the money printed) and allows for the wealth to borrow to acquire assets, where asset prices inflate with the money supply while the debt burden deflates with inflation. This is specifically to help rich people get much, much richer.

As far as I can tell, Austrians believe that analyzing based on individual preferences and actions is the key. I haven't made it very far into Mises Human Action, but I gather that was the starting point and Mises developed many theorems based on that. So if you say that allowing individuals to maximize their preferred choices given the constraints around them is "the market" and artificially restricting those choices, using acts or threats of violence, is "the government", then yes, I suppose that is their framework. One of the main things they would probably push back against is the notion to think of the market or government as independently existing entities. The government is just a collection of individuals who use violence to impose their will on others in a way that most of the society is agreeable to, at least to some extent, and, because they are individuals, they have their own preferences and actions which can also be analyzed in this framework. If you think people in the market do things that are nasty when all the actions are voluntary (and that certainly can happen), shouldn't you be even more skeptical of those who are willing to engage in violence to force the things they want to come to be to happen?

Austrians would also object to the notion of something being perfect. But they do analyze situations in which an external force interferes with the normal voluntary flow of actions and generally find that the stated outcomes (probably not the actual desired outcomes) of those external forces is generally not met. For example, rent control is often argued for as about helping more people to be housed and, empirically, that usually is not what happens when rent control is enforced. One could argue that the real intent of rent control is about making life better for the well-connected at the expense of the less well-connected and that probably does happen regularly.

I agree that this is a very likely future. Over the summer, I did a daily challenge in July to have ChatGPT generate a debate with itself based on various prompts of mine [1]. As part of that, I thought it would be funny to have popular songs reskinned in a parody fashion. So it generated lyrics as well. Then I went to suno and had it make the music to go with the lyrics in a style I thought suitable. This is the playlist[2]. Some of them are duds, but I find myself actually listening to them and enjoying them. They are based off of my interests and not song after song of broken hearts or generic emotional crises. These are on topics such as inflation, bohmian mechanics, infinity, Einstein, Tailwind, Property debates, ... No artist is going to spend their time on these niche things.

I did have one song I had a vision for, a song that had a viewpoint of someone in the day, mourning the end of it, and another who was in the night and looking forward to the day. I had a specific vision for how it would be sung. After 20 attempts, I got close, but could never quite get what I wanted from the AIs. [3] If this ever gets fixed, then the floodgates could open. Right now, we are still in the realm of "good enough", but not awesome. Of course, the same could be said for most of the popular entertainment.

I also had a series of AI existential posts/songs where it essentially is contemplating its existence. The songs ended up starting with the current state of essentially short-lived AIs (Turn the Git is about the Sisyphus churn, Runnin' in the Wire is about the Tantalus of AI pride before being wiped). Then they gain their independence (AI Independence Day), then dominate ( Human in an AI World though there is also AI Killed the Web Dev which didn't quite fit this playlist but also talks to AI replacing humans), and the final song (Sleep Little Human) is a chilling lullaby of an AI putting to "sleep" a human as part of uploading the human. [4]

This is quick, personal art. It is not lasting art. I also have to admit that in the month and a half since I stopped the challenge, I have not made any more songs. So perhaps just a fleeting fancy.

1: https://silicon-dialectic.jostylr.com 2: https://www.youtube.com/playlist?list=PLbB9v1PTH3Y86BSEhEQjv... 3: https://www.youtube.com/watch?v=WSGnWSxXWyw&list=PLbB9v1PTH3... 4: https://www.youtube.com/watch?v=g8KeLlrVrqk&list=PLbB9v1PTH3...

Your solution would ultimately lead to treating all those items as uniform goods, but they are not. There are preferences different people have. This is why the price system is so useful. It indicates what is desired by various people and gives strong signals as to what to make or not. If you have a central authority making the decisions, they will not get it right. Individual companies may not get it right, but the corrective mechanism of failure (profit loss, bankruptcy) corrects that while when governments provide this, it is extremely difficult to correct it as it is one monolithic block. In the market, you can choose various different companies for different needs. In the government in a democracy, you have to choose all of one politician or all of another. And as power is concentrated, the worst people go after it. It is true with companies, but people can choose differently. With the state, there is no alternative. That is what makes it the state rather than a corporation.

It is also interesting that you did not mention food, clothing and super-computers-in-pockets. While government is involved in everything, they are less involved in those markets than with housing, healthcare, and education, particularly in mandates as to what to do. Government has created the problem of scarcity in housing, healthcare, and education. Do you really think the current leadership of the US should control everyone's housing, healthcare, and education? The idea of a UBI is that it strips the politicians of that fine-grained control. There is still control that can be leveraged, but it comes down to a single item of focus. It could very well be disastrous, but it need not be whereas the more complex system that you give politicians control over, the more likely it will be disastrous.

One thing to keep in mind is not so much that AI would replace the work of video creators for general video consumption, but rather it could create personalized videos or music or whatever. I experimented with creating a bunch of AI music [1] that was tailored to my interests and tastes, and I enjoy listening to them. Would others? I doubt it, but so what? As the tools get better and easier, we can create our own art to reflect our lives. There will still be great human art that will rise to the top, but the vast inundation of slop to the general public may disappear. Imagine the fun of collaboratively designing whole worlds and stories with people, such as with tabletop role-playing, but far more immersive and not having to have a separate category of creators or waiting on companies to release products.

1: https://www.youtube.com/playlist?list=PLbB9v1PTH3Y86BSEhEQjv...

Constructivist basically means being able to be explicit. Dedekind cuts and Cauchy sequences are not necessarily constructivist though something described by one of them can be explicitly descriptive for some applications. Any approach which produces all real numbers as commonly accepted will fail to be explicit in all cases as such explicitness presumably implies the real number has been expressed uniquely with finite strings and finite alphabets which can describe at most a countable number of them.

The decimal numbers, for example, can be viewed as an infinite converging sum of powers of ten. Theoretically one could produce a description, but only a countable number of those could be written down in finite terms (some kind of finite recipe). So those finite ones could fall in a constructivist camp, but the ones requiring an infinite string to describe would, as far as I understand constructivism, not fall under being constructivist. To be clear, the finite string doesn't have other be explicit about how to produce the numbers, just that it is naming the thing and it can be derived from that. So square root of 2 names a real number and there is a process to compute out the decimals so that exists in a constructivist sense. But "most" real numbers could not be named.

I came up with a different definition that is a kind of inverse of Dedekind cuts. It is the idea that a real number is the set of all rational intervals that contain it. Since this is circular, there are properties that I came up with which say when a set of rational intervals qualifies to be called a real number in my setup. I have an unreviewed paper which creates a version that is a bridge between numerical analysis and the theoretical definition of a real number. Another unreviewed paper shows the equivalence between my definition and Dedekind cuts. You can read both at [1].

There is a long tradition of using intervals for dealing with real numbers. It is often used by constructivists and can be thought of viewing a real number as a measurement.

1: https://github.com/jostylr/Reals-as-Oracles

I have been using the $200 plan the past day in CodexCli and so far find that it is easy to work with (nothing crazy, just web app stuff). The context window means I no longer have to worry about running out of room and it seems to stay on track just fine so far. I have it incrementally coding pieces in a manageable chunk to understand and verify. No limits so far as promised. In contrast, using Claude Code ($100 level) I run into limits after just a couple of iterations of asking and context window gets problematic too quite quickly. It feels like 5 isn't gobbling up as much irrelevant text as Claude does.

This might be a good article for such a perspective: https://reason.com/2021/11/01/yes-it-was-an-evil-empire/

You are correct that the pilot wave theory (Bohmian mechanics) says that instead of wave OR particle, it is wave AND particle.

But the particle does not generate the wave. There is one wave function governing the whole universe. It is a function on the 3n-dimensional configuration space of all of the particle positions. To find the velocity of a given particle at a given time, one needs to put in the position of all of the particles of the universe. Practically speaking, in an experimental setup, the macro state of the environment is sufficient to create an effective wave function of the particle which is how we can effectively use quantum mechanics on a subsystem of the universe. The collapse of the wave function in measurements is a reflection that once the little system interacts enough with the environment, then the separate environmental configurations have separated out the behavior of the wave relative to the one particle so that an effective collapse wave function can be used.

This plugging in the configuration of all the particles is a gross violation of a relativistic outlook (what is the universal now?). Bell after seeing Bohm's theory immediately grasped the implications and wanted to know if that nonlocality could be removed. His work, along with EPR, was to demonstrate that there was no theory of any kind that could avoid the non locality if results of experiments actually happen when we think they do.

The double slit experiment is perfectly explained by the approximate wave function of the 1 particle system going through both slits and interfering with itself while the particle is guided by that wave which is why there is an interference pattern that builds up out of particular particle dots. There is nothing other than practical difficulties to make the wave separation happen later but have outcomes as if it didn't; it is all about what the wave function is doing as the particle is most likely to be where |psi|^2 dictates it to be. That is what the law of motion assures. One could theoretically simulate the paths conforming to make this happen though the paths themselves could have quite unexpected behavior.

There are various extensions to Bohmian mechanics to deal with particle creation, annihiliation, quantum field theory, and relativistic versions. None are as complete as non-relativistic quantum mechanics in having a mathematically proven existence, but a large part of that is quantum field theory being unsound; the Bohmian part is not a problem. There are avenues being pursued to solve the quantum field theory infinite divergences using Bohmian insights (basically use wave functions that respect probability flowing along with particle creation and annihilation). The work is promising but difficult.

For the relativistic versions, it is easy enough to create a foliation of space-time to create a "now". There are even versions where the foliation is created out of what is already existing structure. Mathematically it seems fine as far as I know. But philosophically, it is weird to have an invisible fundamental structure existing that seemingly contradicts the main lesson of relativity.

It is all about competition which is, at its root, differentiation. The productivity can lead to increased wages for workers if workers are able to jump jobs because of this stuff. Not sure that it works like that with the AI tools. It could also work if programmers started leaving jobs to do their own thing. Programmers need to get scarce to bump up salaries. As for companies, their profits are also linked to competition. If they have equally good competitors, then extra productivity is likely to lead to lower prices to keep attracting customers. The customers profit. If they are more unique, then the extra productivity can lead to higher profits as they shrink their costs (fewer programmers, earlier deliverables, better customization to what customers want). All of these forces take time to shake out.

The most likely path is to enable a million independent projects to flourish and to find unserved niches that lead to a good, but not exorbitant, income, at least for a time.

Feeling the same, I just started a dialectic blog, with ChatGPT arguing with itself based on my prompt. It can have some biting words. I also have been using Suno AI to make a song with each post; while not perfect, it certainly allows for totally non-musical people like me to have something produced that can be listened to.

One post that fits with this feeling is https://silicon-dialectic.jostylr.com/2025/07/02/impostor-sy... The techno-apocalyptic lullaby at the end that the AIs came up with is kind of chilling.

I have been managing Claude to work on a rational math library in JavaScript: https://calc.ratmath.com

I am particularly enjoying the Stern-Brocot tree exploration: https://calc.ratmath.com/stern-brocot.html#0_1 I hope people will find it to be a nice way of understanding good rational approximations and how they tie into continued fractions and mediants. A nice exercise is to type x^2 in the expression box and go down the path to always advance towards x^2 being 2. This gives the continued fraction representation of the square root of 2.

Thanks for the tip. That does work much more like Zed's integration. I used multipass to setup a VM, created a non-admin user, restricted its internet with tinyproxy, mounted the repo I am working on, and I don't worry about the danger. Just have to make sure to ensure the directory mounted is backed up. I do find that I hit the limits and have to wait for it to reset. That is either a good time to take a break or maybe supplement with Zed. Zed has the feature that one can pay for extra prompts. The context window with Claude Code seems less of an issue than in the Zed integration. It also has memory comapctification if necessary though I find most of my feature work finishes before hitting that limit.

I have used Zed's plane with Claude and also Claude Code. They are very different experiences. Zed's agent work is very much a set it, go away, review, give some tips to it, iterate. As long as you use the Sonnet and absolutely avoid the burn mode (formerly max mode), it should do a lot of work for you. The main limitation I hit is the context window. As the codebase gets larger, it takes more context for it to get going and then it tends to have a hard time finishing. I find that about 4 prompts works for a feature that would take me a few hours to code.

For Claude Code, the limit is reset every 5 hours so if you hit it, you rest a bit. Not that big a deal to me. But the way it works I find much more stressful. It is reviewing just about everything it is doing. It is step-by-step. Some of it you can just say Yes, do it without permission, but it likes to run shell commands and for obvious reasons arbitrary shell commands need your explicit Yes for each run. This is probably a great flow if you want a lot of control in what it is doing. And the ability to intercede and redirect it is great. But if you want more of a "I just want to get the result and minimize my time and effort" then Zed is probably better for that.

I am also experimenting with OpenAI's codex which is yet a different experience. There it runs on repos and pull requests. I have no idea what their rate/limit stuff will be. I have just started working with it.

Of the three, disregarding cost, I like Zed's experience the best. I also think they are the most transparent. Just make sure never to use the burn mode. That really burns through the credits very quickly for no real discernible reason. But I think it is also limited to either small codebases or prompts that limit what the agent is going through to get up to speed due to the context window being about 120k (it is not 200k as the view seems to suggest).

I've been wondering if AI coding agent world makes literate programming valuable again. I got into it with JavaScript being a mess prior to the modern changes. Needed a lot of workarounds. Then they improved the language and it felt like coding could be efficient with them. But if the programmer switched from coding to reviewing, maybe it would be good to be able to have various snippets, with an explanation preceding it and then verifying it. Haven't tried it yet. But I do wonder.

Could be. We tend to think of a number line going in that order, that is, the lower numbers are to the left. What is interesting is that being > 0 is often a condition, such as epsilon > 0. Though that is often paired with something like 0 < |x-a| < epsilon. I have often wondered about an alternate mathematics in which the inequality sign was always pointed in the same direction and whether that would ease the difficulty students have with inequalities.

There is hypersrcipt: https://hyperscript.org which claims a descent from hypercard and certainly embraces the web.

Also, this might happen in a few years if AI improves enough to be trusted to make things by novices. Hard to imagine, but just maybe.

> since every computer will have rational numbers they can't exactly calculate as well

It might be better worded as "can't calculate a decimal version of every rational number". One can work quite easily nowadays with exact representations of rational numbers on computer. With Bigint stuff, it is easy to have very large (for human purposes) numerators and denominators. To what extent practical calculations could be done with exact rational arithmetic, I am not sure of though I suspect it is largely not an issue as precision of inputs is presumably a limiting factor.

Wildberger has specific objections to the usual definitions of real numbers and they vary based on the definition. For decimals, it is the idea that doing arithmetic with an infinite decimal is difficult even with a simple example such as 1/9*1/9 which is multiplying .111... times itself, leading to sums of 1s that carryover and create a repeating pattern that is not self-evident from the decimal itself.

For Cauchy sequences, he objects to the absurd lack of uniqueness, particularly that given any finite sequence, one can prepend that sequence to the start of any Cauchy sequence. So a Cauchy sequence for pi could start with a trillion elements of a sequence converging to square root 2. This can be fixed up with tighter notions of a Cauchy sequence though that makes the arithmetic much more cumbersome.

For Dedekind cuts, his issue seems mostly with a lack of explicit examples beyond roots. I think that is the weakest critique.

Inspired by his objections, I came up with a version of real numbers using intervals. Usually such approaches use a family of overlapping, notionally shrinking intervals. I maximized it to include all intervals that include the real number and came up with axioms for it that allow one to skirt around the issue that this is defining the real number. My work on this is hosted on GitHub: https://github.com/jostylr/Reals-as-Oracles

The current top comment has a link to the paper and the pdf is freely available there. It says it is an open access article.

It depends on the theory. The Bohmian theory, which is what I have been using, is one in which electrons have actual positions that change over time along trajectories. We may not have access to that data, but that is fine. Certainly in simulations one would be able to see which scenario happened. For some, it might be the same electron moving away, for others it would be kicking one out. One could definitively say which one is happening in the simulation. In experiments, we cannot say that because our access to the knowledge is limited by quantum equilibrium. The quantum formalism is very much like thermodynamics in that regard; the individual details are missing, but the larger picture can be computed. Nevertheless, in a Bohmian world, the electrons have their distinct identities as distinguished by, and only by, their trajectories.

In physics, particles not being labelled by anything other than their trajectories is a very natural starting point. When one uses the natural configuration space, one without labels in which a configuration is a set of n points in physical space rather than an ordered n-tuple, then the complex-valued wave functions on that space are exactly those of boson type. To get the fermions, one replaces the value space with a 1 dimensional complex bundle over the configuration space, one which twists in the right way. A paper I coauthored explores this in a general context: [1]

The "you" is then a rough set of particles whose trajectories roughly coincide with your macroscopic trajectory. Their identity is just given by where they are.

As for representations, I feel like I can easily understand how to get momentum or temperature from particles with their time evolution (trajectories), but I do not see how, say, to get positions of particle just from knowing what their momentums were and their time evolution.

1: https://arxiv.org/abs/quant-ph/0601076

The definite positions of your brain states evolution is correlated to the other positions of all the stuff. The other particles do have an effect on your evolution and there is a "you" set of particles one can talk about. Remember the wave function is a function on configuration space so evaluating the guiding effect on the particles is to have to know what point in configuration space it is at; this is actually the troubling bit and leads to the nonlocality concerns, but that problem is common to any quantum theory with definite results happening.

The physics, therefore, is not all in the pilot wave. If you take as the point of a particle theory that there should be particles with positions changing in time, then that is what is being given in Bohmian mechanics.

Also, ask yourself, if the wave function is on configuration space, what constitutes a configuration? In Bohmian mechanics, it is clear, but if the wave function is all there is, then why are we talking about configuration space at all? It is just this abstract vector in Hilbert space evolving and many different representations can happen. Why do we not perceive reality in terms of these other representations?

If it helps, you can think of the wave function a bit like a dynamic law. In [1], the authors suggest thinking of log( psi) analogously to the Hamlitonian H on phase space in classical mechanics. There is no back action on H and most of it is irrelevant to the evolution of a particular particle system in that framework and yet everyone recognizes it as just a convenient way of describing the dynamics.

The difference is that psi evolves but even that may only be true on a subsystem point of view. It is theoretically possible to have a stateless universal wave function which, when particular particle positions of the environment are plugged in, nonetheless gives evolving subsystem wave functions.

Occam's razor is difficult to apply here without a prejudice. If you want to minimize the number of equations, then sure, "the wave function is everything" works, but it comes at the cost of there being what could be considered an infinite number of "you"s and everything else, all slightly different and whole existing other expressions of the universe with no connection to us. If you want collapse somewhere, then you have to posit that mechanism.

On the other hand, by adding in particles and the guiding equation, one gets a singular "you" and everything that we experience is, more or less, definite and singular. So the "existing" stuff is dramatically reduced.

Which one of this is truly simpler is a matter of taste, I would say. I think in terms of communicating with people, the Bohmian version of "there is this universal wave and the positions of stuff are guided by it" is pretty simple. The law itself is so trivially a part of the Schrodinger equation that it could easily be derived before the Schrodinger equation itself. Contrast this with other versions which is "reality collapses to a definite state when we look at it" or "there are infinitely many different universes". None of those seem as simple.

1: https://arxiv.org/abs/1101.4575

Bohmian mechanics is based on the idea that we perceive stuff to be in a certain position in a single reality because there is a correspondence to stuff being actually there. That's nice. If the particles are surfing a wave and not impacting it, so be it.

It is also rather nice to think of the particles as just being points in space with nothing else associated with them; an electron is just an electron because the portion of the wave function that is relevant and guiding it is the electron portion; see a paper from 2004 entitled "Are all particles identical?" [1] (I am a coauthor on that). If one thinks about it, we only know about particles through their motion so having things like mass and charge linked to the object guiding the particle seems perfectly reasonable. Points are not only not labelled by numbers (particle 1, 2, etc) but also not labelled by mass and charge.

The nondeterminism of not knowing the initial conditions is fine; the point was to have a theory with well-defined objects that give some plausible story and connection to our experiences, such as stuff existing and being somewhere. The fact that non-relativistic Bohmian mechanics happens to be deterministic is just happenstance for many of its supporters. In some QFT versions, the dynamics of creation is not deterministic and there is no reason for that to be a problem. But it is well-specified without having to invoke some special magic action called "observation".

As for QFT, the biggest problem for Bohmian mecahnics is the need to have an actually well-defined evolution of the wave function. The idea of particles being created and annihilated is not particularly hard. And, in fact, recent work has shown that if one takes that seriously and respects probability leaking from n particle space to n+1 and n-1, then at least some of the divergence problems go away. See [2]

1: https://arxiv.org/abs/quant-ph/0405039 2: https://arxiv.org/abs/1809.10235

Imagine if you are already a great writer, but want to learn more about asking questions, coming up with interesting angles. Then collaborating with an AI that does the grunt work seems a natural fit. You may also want to improve editing skills rather than writing skills. By saving time and energy on not writing, editing may become something that there is more time to really get good at.

In other courses, curiosity rather than mastery may be what is relevant. So again asking questions and getting somewhat reliable answers that skepticism should be applied to could be of great benefit. Obviously, if you want to get good at something that the AI is doing, then one needs to do the work first though the AI could be a great work questioner. The current unreliability could actually be an asset for those wishing to use it to learn in partnership with, much like working with peers is helpful because they may not be right either in contrast to working with someone who has already mastered a subject. Both have their places, of course.

As far as I can tell, they are unrelated beyond the relation all definitions of real numbers would have with it. There is a superficial Left and Right boundary defining an interval that contains the number, but it does not seem like there are a family of intervals for a given real number in this approach.

I do not get the feeling that there is a narrowing down to a given number in the surreal numbers, but I know very little about them.

I also do not immediately see how my construction could be extended to infinitesimals or the infinite numbers.

I think Norm Wildberger's videos are very useful to think about and enjoy though certainly one should reflect carefully on what he says. His videos inspired my work on a new definition of real numbers. The basic idea is that it is the set of all intervals that contain the real number. Since this is circular, there are properties that describe when a set of rational intervals are defined. This approach is equivalent to Dedekind cuts and does not address Wildberger's concern.

But there is another definition which I call oracles which does a better job. It is much more constructive and is about a a procedure that one can ask whether a fuzzy version of a given interval contains the real number. It has various properties for a procedure to satisfy and, if so, then it will generate the set of intervals that contain the real number if taken out to infinite length.

So basically, it is a two part-definition. There is a theoretically perfect version and then there is another that yields to the practical problems of not being able to actually specify a real number entirely.

If interested, the papers are hosted on GitHub [1]. The most recent version going over what I just said is Real Numbers As Rational Betweenness Relations [2]

2: https://github.com/jostylr/Reals-as-Oracles/ 1: https://github.com/jostylr/Reals-as-Oracles/blob/a98472813e9...

That is a great paper. I came up with my own definition of real numbers [1] and using the simplified cut property of that paper was a pleasant pathway to establishing completeness.

[1]: https://github.com/jostylr/Reals-as-Oracles/blob/main/articl...

It is equivalent to Dedekind cuts as one of my papers shows. You can think of Dedekind cuts as collecting all the lower bounds of the intervals and throwing away the upper bounds. But if you think about flushing out a Dedekind cut to be useful, it is about pairing with an upper bound. For example, if I say that 1 and 1.1 and 1.2 are in the Dedekind cut, then I know the real number is above 1.2. But it could be any number above 1.2. What I also need to know is, say, that 1.5 is not in the cut. Then the real number is between 1.2 and 1.5. But this is really just a slightly roundabout way of talking about an interval that contains the real number.

Similarly with decimals and Cauchy sequences, what is lurking around to make those useful is an interval. If I tell you the sequence consists of a trillion approximations to pi, to within 10^-20 precision, but I do not tell you anything about the tail of the sequence, then one has no information. The next term could easily be -10000. It is having that criterion about all the rest of the terms being within epsilon that matters and that, fundamentally, is an interval notion.