MikkW

Worth noting explicitly, the Danish government is in general much more hands-on in the economy than in most other countries. I don't know specifically how that manifests itself here, but I expect that's an important part of it

I didn't miss that. That doesn't change what the rest of your post objectively is saying. (Well, I did overlook the bit about same-sided exploration. But idk, the way this post was worded kinda kills my desire to do that)

Edit: as far as the interlude, it only makes sense given the flawed thesis that is the precise thing I'm reacting negatively to.

Uh, no.

Maybe I just genuinely care about not having terrible things happen to me and everyone else in the world? There's no game there, no broken addiction mechanisms inside.

I strong-downvoted this. [edit: I removed a statement about my feelings in reaction to this, that I feel was a little too much]

I just want to do what I can to keep the people I love from dying.

I'm confused about how this is funded. I notice "this sounds like a scam" alarm bells going off in my head (to be clear, I don't assign high probability to this actually being a scam, I'm just noting that that alarm bell is sounding)

When I was reading the omelette example, I was not thinking at all what the rest of this post is about

There was a recent article on Vox's Future Perfect [1] about the advantages and drawbacks of billionaire philanthropy.

This made me think of Public Goods Markets such as quadratic funding. These mechanisms provide advantages that neither billionaire philanthropy nor the traditional approach to government spending provide, since the distribution of money is decided according to the daily judgements of individuals, rather than by beauraucrats and political considerations as in governmental spending, but is more responsive to the multitude than traditional philanthropy.

[1] Note: I do not endorse the anti-muskism contained in the article (To be clear, I am roughly aligned with their take re: OpenAI)

This comment had negative karma when I looked at it. I don't think we as a community should be punishing asking honest questions, so I strong-upvoted this comment.

A- Look around you. You can see things above and below you; to the left and to the right; and in front of and behind you. These 3 dimensions seem to be the space that we live in, and it makes sense to use 3 numbers to specify different positions within that space- for example how many meters in front of me, to the right, and below me some object is.

B- But there is also time. Some things have already happened in the past, and some things I anticipate to happen in the future. This means that those 3 numbers do not suffice to describe every position in the entirety of the thing we exist in- a fourth number is needed to describe when things happen (in physics it is popular to say that the speed limit of the universe, the same speed light travels at, is equal to 1. Under this convention, these 4 numbers are all of the same nature, though the difference between time-coordinate and a difference between space-coordinate have, as far as I can tell, different importance)

C- Consider the surface of our planet. Just as 3 numbers can identify a position in the space of our universe, two numbers suffice to pinpoint some position on the space of our planet. The crust of the earth, the outermost rocky layer of our planet, has varying heights at different longitudes and latitudes. It makes sense to talk of what we might call a *field*, something that for any given latitude and longitude, tells us what height the crust of the earth terminates at- a function from a pair of real numbers, R^2, to another real number. This field has type signature R^2 -> R.

D- Consider the air above the surface of our planet. At every different altitude (as well as position on the surface of the earth), there is a different pressure of the air, and a temperature of the air. Whereas the height field maps R^2 to R, the pressure and temperature fields each map R^2 (the surface of the earth) times R (altitude) to R (temperature / pressure). These fields therefore are of type R^3 -> R (Note that R^2 * R is R^3). (This actually isn't quite right, because there we are only concerned with the pressure above the surface of the earth, but low enough that air is reasonably plentiful)

E- Indeed, neither the temperature and pressure of the air (on the scale of seconds, minutes, and days), nor the height of the earth's crust (on the scale of millions of years) are constant over time. So really, the temperature and pressure fields do not map R^3 to R, but rather R^4, and the height field maps R^3, not R^2 to R, once we include the time coordinate to capture the varying values across time.

F- The most prominent physical theories about the nature of our universe suggest that fields are not just a useful tool to capture data about arrangements of atoms on a human scale, but are a fundamental thing about the nature of our universe, even at tiny, tiny scales. There are some ways these fields differ from the fields I have named so far. Whereas the temperature field gives a real number - that is, a number on the number line, for every position, these fields often return complex numbers - numbers who can give negative numbers, or even other complex numbers, when they are multiplied by themselves (in contrast with real numbers, which always give a non-negative number when squared). In addition, these fields often don't have a single scalar value, but are collections of different numbers called vectors and tensors (or even something called a spinor)

G- Another, quite interesting, difference between the fields physicists use to describe our universe at tiny scales, and the fields I have named so far, are that these fields are "quantized". To explain this, I'll tell you that I have memories of sometimes eating Nutella on toast at a hotel, and the Nutella would come in these little packets, where you take off the lid, and then spread the Nutella on the toast. Maybe if I was feeling like conserving food, I'd only take one packet of Nutella - but I'd never do that. I'd always need to take at least a second packet of Nutella, maybe a third or a fourth, if I have a big sweet tooth (I do). But I'd certainly never use half a packet of Nutella. If I open the packet, I'm going to put all the Nutella on the toast.

Generally, I'd try to spread the Nutella as evenly across the toast as I could, but it's inevitable that a little more Nutella will get clumped in one area, making another area be spread a little thinner.

It's almost like there's a "Nutella" field, which would tell me how thick the spreading is at different points on my toast. And this field, if I were to add up the Nutella across the entire toast, would have either 1 (yeah right), 2, 3, or 4 packet's worth of Nutella (technically, if I just had plain toast, there would be 0 Nutella on the toast), but certainly not 2 1/2 packets - I don't want to waste what I've opened! Just as there is always an integer number of packets of Nutella on my toast, the fundamental fields of our universe have an integer number of packets of whatever it is they measure- but at any given point, it could be 0.483 or 0.314, or whatever inches of Nutella.

H- Here's some of the fundamental fields of our universe. There's the electromagnetic field, which as its name suggests, gives rise to electricity and magnetism, as well as light. There's the weak fields W-, Z, and W+, which play a role in some atomic phenomena. The electromagnetic and weak fields are actually alter-egos of the "electroweak" fields, which have the names weak hyper-charge and weak isospin, which give rise to electromagnetism and the weak force by interacting with the "Higgs field".

There's an interesting difference between the electroweak fields and the Higgs field. The electromagnetic (EM) field has 4 components, one for the time dimension, and 3 for the 3 spatial dimensions. The time-component of this "four-vector" gives the electric potential, while the spatial components give the magnetic potential. Since the field returns a vector, which is like a little arrow pointing in space, at each position, when we imagine rotating the universe, the arrow rotates along with the universe. But the Higgs field, while it does consist of more than one scalar, does not have components that rotate with the universe, so whereas the EM field (as well as the weak fields) are called "vector fields", the Higgs field is called a "scalar field". Vectors are also called order-1 tensors, and scalars are called order-0 tensors, so the Higgs field might be thought of as an "order 0" field, while the EM and weak fields are "order 1" fields. This reminds me of the strong field, which is the other "order 1" field in the Standard Model. Whereas the EM field returns a single four-vector, and the weak fields are 3 different four-vector fields, there are 8 four-vector fields comprising the strong field, representing the 8 different ways the 3 strong-charge colours can be combined to carry the strong force. (I'll spare you the details of that)

Are there "order-2" fields? Well, yes, but it's not typically treated on a scale where we expect quantization, and so it's not part of the standard model. But in General Relativity, Einstein has his important Einstein Field Equation. The essence of this equation is simple, he says that two different 4x4 matrices (that is, order-2 tensors) are proportional to eachother: The Einstein tensor, which tells us about how the very fabric of our universe's space and time are curved, and the Stress-Energy tensor, which tells us about the energy (which is equivalent with mass) and momentum contained at a certain point in our universe. So the Einstein tensor field, while not treated alongside the fields of the Standard Model, is just as much a fundamental field, and is an order-2 field.

I) If you multiply two vectors in the right way, you can get an order-2 matrix. So in some sense, a matrix (an order-2 tensor) can be thought of as the square of a vector. But surely there's nothing like a square root of a vector, right? I mean, what would that be? An order 1/2 tensor? Well, actually, yeah, there's such a thing, and we need it to understand fermion fields like the electron field or the quark fields. These order-1/2 tensors are called "spinors", and consist of two complex numbers, and rotate when we rotate the universe, just like vectors do. But the weird thing is, we would think that if we rotate the universe by 360 degrees, the universe should be exactly the same as it was before the rotation. And while vectors behave that way, spinors actually end up getting negated as a result of rotating the universe 360 degrees, and it's not until we have rotated the universe 720 degrees, that everything ends up as it was before.

The fermion fields make up what we usually think of as matter, as stuff. These fields include the electron field, the neutrino field (which is like the electron field, but has no electric charge), the up-quark field, and the down-quark field. Those are the "first generation of matter", and there's actually 2 other generations of matter, which each have corresponding fields to those 4 fields. The quark fields are different from the electron and neutrino fields, because there's actually 3 spinor fields per quark field, one for each of the 3 "colours" a quark can have (these are the charges that interact with the strong force), whereas leptons like the electron and neutrino don't interact with the strong force, and don't have colour.

Sometimes, I like to imagine the fermion fields slightly differently. Just as an excitation in the photon field is actually a combination of excitations at the same time in both the weak hyper-charge and weak isospin fields (the electroweak fields) at the same time, and not a fundamental thing in itself, I imagine something similar for the fermion fields (I'll ignore the different generations of matter for now). So, let's stick with the neutrino field as one of the fundamental things - a fermion with no electric charge, no strong ("colour") charge, basically close to non-existent (but nonetheless existent). I'll just rename it the "neution" field in my imagined framework, to avoid getting too confusing. But instead of treating the electron and quark fields as a different thing, let's posit a "negaton" field and some "coloron" fields. In my imagination, an electron is simultaneously an excitation in both the neution and "negaton" field, with the negaton providing this composite particle with an electric charge of minus 1 (or minus three-thirds, if you prefer). The coloron fields (one for each of the 3 strong charges) would provide the composite particle with a colour charge and positive two-thirds electric charge, so quarks would be a lepton plus a coloron.

Now that I'm writing out this idea, I do find myself questioning it, because the Pauli exclusion principle says that there cannot be two excitations of the same fermion field in the same state (this is, however fine, and even "encouraged", for the boson fields like the electromagnetic field). This does not preclude excitations of the up and down fields, or electron field, from being in similar states, if they are indeed completely distinct fundamental fields (as traditionally assumed), and this matches as far as I know with observation, but it would, I would expect, preclude the neutions corresponding to an up and down quark, from being in the same state. So unless something about the composition of these fields I imagine prevented the excitations in the neution field from being in the same state when the corresponding excitations in the composite up and down quark fields were in similar states, this would undermine that framework.

I think that is all I have to say on the subject of the fundamental fields of our universe, for now.

I agree that "Factorization" is a good, erm, framing for Cartesian Frames

Interesting. I note that I would be weary of introducing a fungus that can spread within my house, without doing due diligence.