Terry Bollinger

"[In] this paper ... MOND arises from n = 0 modes of a [+1 dimension] Kaluza-Klein theory [while] dark matter ... arises from n = 1 modes, which are the lightest Kaluza-Klein particles"

"the [MOND] μ function ... emerges from ... slicing condition[s] chosen based on practical requirements such as avoiding singularities and removing [degrees of freedom] interdependencies ... Slicing conditions in 3+1-D GR define the set of spacelike hypersurfaces, Σ3(t), with spatial metric γij from one moment in time to the next, where time, t, is a global coordinate parameter. We refer to this condition as spacetime synchronization. The slicing condition enforces ... a standard interval of time at each point in a spatial manifold"

"Ironically, I'm not a big fan of E=mc2, since I immensely prefer the energy-complete, Pythagorean-triangle-compatible form:"

"[math](E)^2=(\overrightarrow{p}c)^2(mc^2)^2[/math] E=mc2 addresses only the very special case of mass at rest, and so is not very useful in any actual physics problem. I also find it deeply amusing that Einstein's original paper in which he announced his mass-equals-energy insight, "Does the Inertia of a Body Depend on Its Energy Content?", uses L in place of E, and for some odd reason never actually gives the equation! Instead, Einstein uses a sentence only to describe an equivalent equation with c on the other side:"

"If a body gives of the energy L in the form of radiation, its mass decreases by L/c2."

"-- Your points about the subtleties of the gigabyte example are correct, very apt, and interesting! In some of my unpublished work I am strong on distinguishing very carefully between "potentiality" (yor word) versus "actuality", and not just in physics, but especially in mathematics. The very ease with which our brains take potentials to their limits and then treat them as existing realities is both an interesting efficiency aspect of how capacity-limited biological cognition works, and a warning of the dangers of being sloppy about the difference. Computer science flatly forces one to face some of these realities in ways that bio-brain mathematical abstractions do not. This is why I think it is very healthy for mathematicians to contemplate what happens if they convert their abstract equations into software."

"In any case, issues such as the ones you mention are where the real fun begins! While a short essay is great for introducing a new landscape to a broader audience, there is a lot more going on underneath the hood, as you have just pointed out with your comments on both Einstein's mass equation and my gigabyte file example. An essay is at its best more like a billboard enticing viewers to visit new land, including at most a broad, glossy, overly simplified view of what that new land looks like. The real fun does not begin until you start chugging your vehicle of choice over all the &%$^# potholes and crevices that didn't show up in that enticing broad overview!"

"-- I would note that while in principle it may be possible to find any random sequence of numbers somewhere in pi (wow, that would be an interesting proof or disproof...), there is a representation cost for the indices themselves that must be also be taken into account. A full analysis of the potential of pi or other irrational numbers as data compression mechanisms would be mathematically fun, and who knows, might even end up pointing to some subset of methods with actual compression value. The latter to me seems unlikely, though, since the computation cost is likely to get huge pretty quickly."

"-- As an everyday passionate Hume in being, I Kant speak all that knowledgeably about the biological structures behind how our minds perceive reality. But I try hard to avoid the subconscious assumptions of truth that Popper up so often in physics and even math, when all one can really do is prove that at least some of these assumptions are false. Thus when writing for a broad audience, I try hard to make it easier for the reader to follow an argument and stay focused on it by simply explaining any necessary philosophical point "in line" and as succinctly as possible. The less satisfying alternative would be to give them a hyperlink to some huge remote body of literature that would then require a lot of reading on their part before they could even get back to the original argument... which by that point they have likely forgotten... :)"

"-- I am also surprised that I did not mention your baryon mass idea in my comment, since I certainly was thinking about them when I wrote the comment! I guess I was just more focused on the experimental constraints on the idea?"

"-- On the Standard Model being "relatively compact", that is, say, in comparison to string theory. But oi indeed, my emphasis was very definitely on the word "relatively"! The Standard Model as it stands is a huge, juicy, glaringly obvious target for some serious Occam outtakes and Kolmogorov compressions."

"By the way, as someone who is deeply convinced that space, a very complex entity if you think about it, is emergent from simpler principles, I found your constructive approach to it interesting."