You can do that using differential forms as well - using the co-differential δ, we can write a single equation (δ + d)F = J. However, from the perspective of Yang-Mills theory, that's a rather questionable approach as we're stitching together the Bianchi identity and the Yang-Mills equation for no particular reason...
Cool, I didn't know that. Still, the main point of the geometric algebra version is that it's not a "stitching" exercise, but a natural operation in the algebra -- and even better, an invertible one.
Microsoft is not your friend. Like most large companies, it tries to game the system to the detriment of the general public: Monopolistic practices (embrace-extend-extinguish, discounts for hardware vendors that only bundle Windows, ...), lobbying for software patents, tax avoidance, all that jazz.
There are also concerns with regard to civil liberties such as spying on their customers out of self-interest and on behalf of the US government, cooperating with authoritarian regimes such as China or their participation in Trusted Computing. Also note that while nowadays, just like many other tech companies, Microsoft might get criticized as being 'woke' by people with a certain political outlook, in the late 2000s, they were throwing people off xbox live for mentioning being gay in their profiles (or just having the surname 'Gaywood', for that matter).
This sounds like "Microsoft has done some bad things, ergo it must be a villain that makes the world worse". That doesn't seem like a sensible evaluation strategy.
In 2014, Springer and IEEE had to retract 120 comp-sci papers that were gibberish generated with SCIgen. The problem persists as of May 2021[1], and given the advancements in LLMs, I wouldn't be surprised if things are getting worse...
The Sokal article wasn't retracted and the editors still claim that they didn't make any mistake allowing his nonsense to be published. Can you see the difference?
Shrugs. It's an issue, but not necessarily as extreme as some people make it sound, and not entirely limited to the social sciences (see e.g. the justification of the physicist who approved Igor Bogdanov's thesis back in the day: All these were ideas that could possibly make sense. It showed some originality and some familiarity with the jargon. That's all I ask.).
I agree, in the grand scheme of things it's really nothing. It doesn't really bother me that someone somewhere published some nonsense. It only irks me the persistent defense of these obviously wrong decisions. Just admit you fucked up and move on. If the publishers did just that it would long have been forgotten.
The Hubble sphere (the place where recession velocities hit the speed of light) is not the same as the particle horizon (our past lightcone at current cosmological time, the boundary of the observable universe) or the cosmic event horizon (our past lightcone at infinite cosmological time, the boundary of the asymptotically observable universe).
Observations indicate that the expansion of the universe is accelerating, and the Hubble constant is thought to be decreasing. Thus, sources of light outside the Hubble horizon but inside the cosmological event horizon can eventually reach us. A fairly counter-intuitive result is that photons we observe from the first ~5 billion years of the universe come from regions that are, and always have been, receding from us at superluminal speeds.
This is correct: For example, at time of emission of the light we receive today, GN-z11 had a recession velocity above 4c. A redshift of 1090 (which is the approximate redshift of the cosmic microwave background) corresponds to a recession velocity on the oder of 60c.
The party line is that energy is not conserved at cosmological scales. However, it's more of a semantic question: We can tell you exactly by how much it gets violated (that's basically the first Friedmann equation), and if you prefer, you can attribute the missing energy to the gravitational field. A lot of physicists don't like that approach as it isn't possible to write down a corresponding stress-energy tensor, ie gravitational energy cannot be properly localized.
Not sure that's convincing: Why would I multiply a unit of time (Yug) with unit of distance (Yojan) to arrive at the distance to the sun? Also note that per Wikipedia, the historical value of the Yogan can range from 3.5km (~2.2 miles) to 15km (~9.3 miles). How was the value of 8 miles chosen?
You can do that using differential forms as well - using the co-differential δ, we can write a single equation (δ + d)F = J. However, from the perspective of Yang-Mills theory, that's a rather questionable approach as we're stitching together the Bianchi identity and the Yang-Mills equation for no particular reason...