Lichtso

What an awful paper title, saying "Symbolic Graphics Programs" when they just mean "vector graphics". I don't understand why they can not just use the established term instead. Also, there is no "program" here, in the same way that coding HTML is not programming, as vector graphics are not supposed to be Turing complete. And where they pulled the "symbolic" from is completely beyond me.

Well, the Schrödinger equation only describes the evolution of the wavefunction over time (which is indeed a similarity with classical mechanics). But how the wavefunction then further relates to the actual "state of system" is up to the interpretations of quantum mechanics. And there in lies my point: That because of the superposition the way time works in quantum mechanics (properties are simultaneously in a combination of states) is very different from classical mechanics (properties are in exactly one state at a time), even if both have a "t" in their equations.

> For example, in classical mechanics you cannot rotate in a way that makes the time coordinate fall in a space coordinate, while you can do that in relativity

That is a good point. Maybe it is fair to say that in classical mechanics we start out with an additional separate geometric dimension (which only translation / shifting is allowed in). And in special relativity it gets promoted to a full spacial dimension, allowing all sorts of transformations.

> Both describe the evolution of a system using differential equations in time

All areas of physics use differential equations, and so does relativity which you are contrasting these two against next.

> both treat the world as having a single shared time (like "frames in a movie"),

I think you misunderstand what the "frames in a movie" meant. It was about the distinction of time being modeled as discrete or continuous.

What you are talking about ("single shared time") is indeed a shared property of all other areas, which are not relativity, by the virtue of not being relativity (which introduces the distortions that make a single shared time impossible). But that is a tautology.

> I think the main differences are what evolves in time

All four areas are somehow describing the evolution of matter and energy. Again, not a difference.

> and also quantum mechanics possibly needing different rules for what happens to the system when a "measurement" happens.

Measurement, collapse and conscious observers are unnecessary additions which are not needed for a complete description of quantum mechanics. I would instead argue that the main difference to classical mechanics and relativity is the superposition principle (which has nothing to do with measurement): The idea that the properties of things are not in one state at a time but in a combination of states simultaneously. And that in turn means you can not model time as a simple 1D axis anymore.

> because e.g. the standard model doesn't have time symmetry.

My point was about flipping the direction of the flow or the role of past and future. The standard model has time reversal symmetry if you also flip matter and anti-matter, which for the sake of the argument makes no difference because you can't tell which one you are made of. From the POV of anti-matter people we are the ones made from anti-matter or matter which moves backward in time. Which strengthens the point that only thermodynamics assigns a clear direction to the flow of time.

> SR says that the symmetries we expect of spacetime are wrong, and that a very different group of symmetries applies.

Can you elaborate on that? Are you referring to the free fall equivalence principle?

Yes exactly, continuous collision detection (CCD) is what I am referring to.

https://scholar.google.com/scholar?q=continuous+collision+de...

- Classical mechanics: Basically views time as another spacial axis. In classical mechanics bodies can be viewed as being a 4D extrusion of their 3D shape along a 1D time path. High precision simulation of classical mechanics does not model time as steps / frames in a movie, but as a continuous 4D geometry.

- Relativity: Builds on classical mechanics idea that time is a geometric axis and using a 4D coordinate system. What is further added is the possible distortion of that 4D spacetime.

- Quantum mechanics: Strictly speaking quantum mechanics does not model time at all. It is more like algebra. It only describes equivalences / transformations which can occur. When we reformulate some algebraic expressions we don't think of the steps we take as time steps. It wouldn't work anyway because there are many possible paths not one. It is not a 1D sequence but a graph, which can even contain cycles.

- Thermodynamics: None of the other areas of physics make time "pass", because to them time is symmetric and past and future might as well be swapped. Only thermodynamics introduces an asymmetry by coupling it to information theory: On the macroscopic average, entropy can not decrease, only increase. Thus, we get a global gradient form low to high entropy, which is what makes time irreversible on a large scale.

> Regulating the tech Market is great for local tech

Except, it is not. At least not in the situation that the EU is in. Because all regulations are a constant burden on business, small relative to big corporations, huge for medium companies and insurmountable for startups.

The EU has no big players, not a single one! We have a few medium players like SAP and that is it. So, we are already far behind and every weight we load on to drag us down is another nail in the coffin.

The "can be arranged" is the tricky part. E.g. you might know from context that some states are impossible (where the probability distribution is zero), even though they combinatorially exist. That changes the entropy to you.

That is why information and entropy are different things. Entropy is what you know you do not know. That knowledge of the magnitude of the unknown is what is being quantified.

Also, the point where I think the article is wrong (or not concise enough) as it would include the unknown unknowns, which are not entropy IMO:

> I claim it’s the amount of information we don’t know about a situation

Both parties contributed to and maintained the status quo, because they both profit from it. Game theory works out and both try to balance their power roughly 50/50 and keep everybody else out of the game.

All topics are polarized to the extreme to fit into the 2 party divide. If a third party would emerge it would be slightly closer to one of the poles. Then it would immediately make that side lose even if more people voted for that position. That is because there is no percentage voting but a cascaded threshold voting. Thus, suppressing underdogs is in the interest of both.

Abstract example:

44% vote party A for X

10% vote party B for X

46% vote party C against X

44% + 10% = 54% for X, but 46% is the biggest party so they win

Question is why the Grand Old Party suddenly quit that century old cartel.

If you mean people hired to hire other people, then yes, strongly agree. The entire thing is built on the assumption that your company will have a high turnover rate.

That is something that should be avoided by employers as it for one increases the average compensation niveau faster than employee retention would and also constantly restarts opportunity costs as new employees take time to settle into their new roles. Yet, here we are and it is not only acceptable, but also standard procedure.

I generally agree, in the long term there will be far less need for teachers, as there will be less need for human jobs to be taught.

However, creating many individual systems which are better than a human in a specific area each is very different from one unified and integrated system which combines all of them. The latter will take a lot longer to achieve. Until then there is value in teaching humans.

If the technology is truly as capable as humans in many domains (and that might still take a while), it will not matter anymore whether it is a good teacher or not. The need for (and thus value of) human labor will depreciate and so will its "supply chain" the education sector.

> hope they get some education, but the reality is that we use schools for free childcare

Exactly, teachers will be less and less pedagogs and more and more wardens.

> empirical evidence

That is going to be a though one, at least direct measurements are pretty much ruled out if you consider that the plank length is about a quadrillion (yes, really 10^15) times smaller than the classical electron radius.

So, we will have to settle for indirect evidence and theoretical results.

Discrete spacetime does not necessitate a regular and nicely ordered tesselation, it could be pure chaos or be non-geometric.

Before we thought that energy, mass and matter were completely continuous and that turned out to be wrong.

> The Planck length has no physical significance > There is no evidence to suggest that space is discrete at that scale

Bekenstein bound and "planckian discreteness".

Reality is most likely not composed of a regular tesselation of simple geometric shapes such as a cartesian voxel grid as that would introduce massive anisotropy. But, there is still theoretic evidence suggesting that spacetime is indeed discrete at the lowest level.

> why seven is such an important number cross-culturally

I think it is more likely Miller's law [0], that is the average number of "registers" a human mind has [1].

[0]: https://en.wikipedia.org/wiki/Miller%27s_law#In_psychology [1]: https://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus...

It is true that Vulkan usually is behind DirectX by two to three years, but it gets there eventually. Keep in mind that Vulkan tries to cover a wider range of devices and platforms. Also, in my experience as a contributor to GPU HALs, Vulkan is far more thought-out while DirectX is usually a ship-quickly mess. Vulkan obviously benefits from hindsight here.

I have found that procedural generation tools such as Blender are a good substitute for (single-player) Factorio. Especially the node DAGs such as shaders and now geo-nodes feel a lot like belts, inserters and assemblers.

Plus in the end you are not just increasing some game item count, but get beautiful scenes to marvel at: https://www.youtube.com/watch?v=vW9pCT5ouZ8

When working with meshes what you generally want is is quads, not triangles. The reason is that quads form nice closed loops.

Further more you would only allow quads to meet in 3, 4, or 5 edges per vertex. The 4 edges per vertex is the "normal" case that most of your mesh should have, it causes a regular grid of parabolic (euclidian) geometry with neutral curvature. Then patches of these meet in vertices with 3 edges to make it elliptic geometry with positive curvature or 5 edges to make it hyperbolic geometry with negative curvature.

You can ignore all of these and just randomly connect nearest neighbors to form triangles. But, then you still have only geometry, no useful topology, so not any better than a point cloud. A good topology is necessary for texturing, skinning, animation etc.

Already was somewhat degraded by the EU parliament:

https://proton.me/blog/eu-parliament-chat-control

> They wind up creating simulations that just enforce their bias (because they write code that assumes their biases).

Agreed, such simulations can not be used to answer specific questions. Same thing also goes for weather / climate models, not just human economy.

> try to predict the stock market -- this is essentially what you are asking

No, it is not what they are asking. Mistake here is confusing what is called microstate and macrostate [0] in statistical mechanics.

E.g. yes you can not predict the path an individual gas molecule will take around a driving vehicle because it is a highly chaotic system [1]. And the same goes for individual stocks at a specific time. However, that does not mean that air flow simulations are not possible or useless, quite the opposite.

[0]: https://en.wikipedia.org/wiki/Microstate_(statistical_mechan... [1]: https://en.wikipedia.org/wiki/Chaos_theory

While I don't think we live inside a simulation or that there is an outside, you might enjoy the book Simulacron-3 [0] or its movie adaptation Welt am Draht [1]. It is about the protagonist realizing that they are an agent in an economic computer simulation.

[0]: https://en.wikipedia.org/wiki/Simulacron-3 [1]: https://en.wikipedia.org/wiki/World_on_a_Wire

I sometimes play with this thought as well, and I think we will see more of it as AI technologies allow for more realistic behavior of virtual agents.

The reason why I think having virtual agents instead of real players is important is because real players are not invested enough. They can always switch to a different reality whereas virtual agents are stuck and have to live with the consequences of their actions. That does change the dynamics a lot.

> Systemic changes need to originate somewhere, right?

Yes, but that does not need to be morals, values, ethics or ideology.

Instead I prefer Kant´s idea of the categorical imperative whereby the question only is if a society following specific rules would satisfy its members long term. It is more pragmatic as it shifts the question from should/shouldn't to does it work out.

The alternative to the current model is not to have no services at all, as that makes no sense, agreed.

> The libertarian notion that taxes are extortion is frankly childish in how overly simplistic it is.

The argument is weak because you constructed a straw man. The libertarian notion is not to live without any of the services provided by a state, but to have different providers which are in competition. The issue is that the state / gov has a monopoly but is exempt from antitrust laws.

The implementation is tricky though because in reality, when functions of the state are privatized there is often a huge amount of lobbying and corruption involved and these functions are given to a small group of big companies which effectively form a cartel once again. Then they extract all the economic value left in the infrastructure, the privatization is declared failed and undone, effectively another channel of syphoning tax money into the hands of big companies.

Everybody is giving advice on how to imagine and intuit about integer dimensions beyond 3.

But what about fractional dimensions (not to be confused with fractal dimensions)? Any advice about reasoning about the geometry of lets say something 0.6309297535... dimensional? It seems so easy, I mean it is somewhere between 0 and 1 dimensions, both of which have trivial geometric interpretations.

Closest I could think of is doing augmentations into the next highest integer dimension. That would be similar to how we often use projections to lower integer dimensions to think about higher integer dimensions, but in reverse.

And yes, fractional dimensions do exist, just like fractional derivatives or fractional Fourier transform, etc.

Many 3D content creation tools such as Blender [0] have SDF [1] (e.g. metaballs in Blender) and CSG [2] (e.g. boolean modifier in Blender) features. But these are rarely used as they can only define volumes, not surfaces. And we are usually interested in surfaces for assigning textures and materials. Thus, polygons / meshes and curves / splines dominate the industry.

[0]: https://www.blender.org/ [1]: https://en.wikipedia.org/wiki/Signed_distance_function [2]: https://en.wikipedia.org/wiki/Constructive_solid_geometry

> Biases are just weights on an always on input.

Granted, however this approach does not require that constant-one input either.

> There isn't much difference between weights of a linear sum and coefficients of a function.

Yes, the trained function coefficients of this approach are the equivalent to the trained weights of MLP. Still this approach does not require the globally uniform activation function of MLP.

1. Interestingly the foundations of this approach and MLP were invented / discovered around the same time about 66 years ago:

1957: https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Arnold_repr...

1958: https://en.wikipedia.org/wiki/Multilayer_perceptron

2. Another advantage of this approach is that it has only one class of parameters (the coefficients of the local activation functions) as opposed to MLP which has three classes of parameters (weights, biases, and the globally uniform activation function).

3. Everybody is talking transformers. I want to see diffusion models with this approach.

That would be true for a single node / single layer. But once the output of one layer is fed into the input of the next it is not just a linear combination of splines anymore.

The first question is why is there a divide between CPUs and GPUs in the first place. Yes, the gap is closing and both categories are adding features of one another but there still is a significant divide. IMO it has to do with Amdahl's law [0]. In that sense CPUs should be called Latency-Optimizing-Processors (LOPs) and GPUs should be called Throughput-Optimizing-Processors (TOPs).

More specifically [1] we could also call CPUs long / deep data dependency processors (LDDPs) and GPUs wide / flat data dependency processors (WDDPs).

[0]: https://en.wikipedia.org/wiki/Amdahl%27s_law [1]: https://en.wikipedia.org/wiki/Data_dependency