Recent content by PAllen

Unfortunately, while I have been hoping for Hau for many years (I met her once at a talk), I have developed the opinion that the Nobel committee has some blind spot. There have been so many years when she would have be an obvious choice over those chosen, IMO. So I have given up hope.

One thing that, to me shows a missing element of actual understanding, is the completely unique mistakes the top bots still make (as of March 2026, using the premiere paid version of each) playing chess. Most humans will miscalculate or miss simple tactics. They will never decide “it would be...

Here is another one for comparison between free Claude.ai and the paid version. The free version analyzes the following incorrectly: “Consider a baseball at rest, and another rapidly moving one aimed to miss it by 6 inches. Consider that the gamma factor of the approaching baseball is 10^54...

On the other hand, here is a financial example free Claude gets wrong, and the prompt needed to correct it: “I want to use an SBLOC to fund part of a down payment for a conventional mortgage application. How will this be treated?” It will spout incorrect information about interest on the LOC...

Note, 3 test problems I gave Claude 6 months ago that it got wrong, it now gets right. These had to do with local, smooth, isometric embeddings.

Here is one. Note, I get varying answers at different times, but all neglect to correctly describe the extreme anisotropy of what happens to the solar system. By not conceptually understanding that most of the solar system would see the collision highly attenuated (though still very extreme) the...

How different are the paid versions from the free versions? I have used the free versions of chat gpt, claude, and gemini. All leave me unimpressed whether trying a technical discussion or an economic simulation. I find a glaring error every other page or so of conversation. I actually do find...

I agree there is something to this point of view.

I am a strong believer in absolute grading. In effect, there is a contract between teacher and student: this is the material to be mastered; each grade is a degree of mastery. In principle, that may mean almost no As one year, or 35% the next, depending on actual achievement.

Recursion: see recursion

I ask again what has been asked before. I don’t believe it is a violation of PF to state: here is a set of formal assumptions I tried to derive consequences from. With that spirit, you can post your starting assumptions. Note also, someone in this thread referred to the notion of test theories...

My understanding is that it would take a much stronger shell than that to keep the water liquid; so it would beak or stretch.

I freeze glass jars with water filled to 2/3 all the time, with no breakage. They are covered, but not securely airtight. So, after freezing, the ice in the jar has gone up higher than the water was, but no breakage if I leave enough space for the expansion. Even if the cover was truly airtight...

Frequently Doppler is used to define mutual rest, by absence of shift. Of course this is just one definition, but it is ONE. It generalizes uniquely and invariantly to any GR situation. Using this definition, then all aspect of SR Doppler carry over quantitatively to GR. You may say that it is...

The issue with this comparison is the at some point we agree there is no baldness. In the case of spectral shifts in GR, all the essential features of Doppler remain: for a given detector at a reception event, every different state of motion at the source event produces a different result, in...