It's possible that hospitals were claiming something like a car crash victim with COVID as a COVID death for extra funding, making actual total deaths less due to COVID than reported, meaning what he said was true, even while the hospital is full of people with COVID, possibly including that very car crash victim.
Other official facts of the time period included 1. standing in a restaurant without a mask on is almost terrorism and 2. sitting at a restaurant without a mask on is fine.
Numbers of cases, deaths, and how those numbers are tabulated are factual data. We can argue over the data quality, but at this point we have data from many independent countries' health services. Our view of these facts has gotten better with time, and we now have more certainty than we did in the early days of the pandemic.
Recommendations, regulations, and responses to the pandemic as it happened are factual in the sense that they happened, but are not "facts" in the same way. It is not a fact that standing in a restaurant without a mask was terrorism and sitting was fine. Instead, given the information available at the time, and the practical requirement to have your mask off to eat, this policy was chosen for a time as a risk mitigation balanced with practical requirements. The appropriateness of this policy is a matter of opinion.
You forced me to not actually read the dissent but to CTRL+F "immune,", because I couldn't believe a person/demigod serving in such an incredibly honorable and powerful position would ever write a rant with the same word 4 times in a row.
All knowledge/predictions are encoded as a chain of probabilities that something is true, otherwise, what else is it? My brain calculates 0.8 * 0.3 * 0.5 * 0.6 in order to make a 3-pointer, but Michael Jordan's brain ... well his mitochondria does a triple back flip and inverts the voltage into a tachyon particle.
According to billionaire-owned media, the owner of which is owned by a trillionaire investor, you are a conspiracy theorist: both parties work for their constituents.
If you wanted to have state with pure functions, you would, according to DRY, be compelled to write the bind operator. You wouldn't have known to call it a monad or why some basement theoretician likens it to a burrtiofunctor, but you nevertheless would have made the obvious coding solution.
Is this possible for rotation without a PhD in geometry or algebra?
Well! I don't have a PhD at all, but I think the exponential map is a surprisingly intuitive operation once you get used to it. It works on all kinds of operators. I'd argue for teaching it much earlier, in intro calculus, to introduce the idea that e^(a d_x) f(x) = f(x + a). But it still feels like there is some magic in the fact that works that I don't have a really satisfying explanation for (although it is easy to see by expanding the Taylor series).
The magic comes from the fact that you can decompose a translation (as in your example) into a bunch of little ones. So you want an operator that has the property that F(a)g(x) = g(x+a) = F(a/N)^N g(x). Equating F(a) to F(a/N)^N (for any N) reveals the exponential structure. I’m sure there are other ways but this is the first that comes to mind. You can also try using a very small translation F(da) and that will give you some insight too.
Yeah, I know how to derive it, but it still feels very unsatisfying to say: voila, you can put derivatives inside functions. It would be a hard sell to an intro calculus student, even though the concept would be very useful at that level.
You certainly do not need to have a phd in geometry and algebra for this. For example, the exp map is used all the time in robotics particularly in rigid body dynamics and kinematics.
IMHO, geometric algebra makes certain things clear, but it's also oversold as something new or novel. It can be recast in the language of differential forms (covariant multivectors) which is very often used in physics.
For what it's worth, differential forms have plenty of their own pedagogical problems. IMO most of the value in them comes from the concept of multivectors, and very little from the fact that they're 'dual' to regular vectors (which is a finicky detail necessary to do covariant geometry correctly, but not useful for general intuition).
