On Monday, September 4, 2023 at 1:55:51 PM UTC-4, Ross Finlayson wrote:
> On Monday, September 7, 2020 at 9:13:16 AM UTC-7, Ross A. Finlayson wrote:
> > On Monday, September 7, 2020 at 8:25:05 AM UTC-7, Tim Golden BandTech.com wrote:
> > > On Monday, September 7, 2020 at 5:01:41 AM UTC-4, Lalo T. wrote:
> > > > ...even in :
> > > > https://en.wikipedia.org/wiki/Algebra_representation
> > > > Already pop up "scalar multiplication"
> > > >
> > > > "...is after the fix to the problem even while he denies that the problem exists"
> > > >
> > > > https://en.wikipedia.org/wiki/Talk:Binary_operation
> > > >
> > > > https://hsm.stackexchange.com/questions/11235/who-started-calling-the-matrix-multiplication-multiplication
> > > >
> > > > https://math.stackexchange.com/questions/1348273/external-operation-binary-and-unary-perhaps
> > > >
> > > > The issue loosely make me remember the topic "dimensional numbers"
> > > > concretely, like the strange T.n.p of the user Socratis, who contend "There are no dimensionless numbers"
> > > > (not necessarily that system, but systems with the same thesis)
> > > >
> > > > in https://en.wikipedia.org/wiki/Vector_space#Definition
> > > > note : " Compatibility of scalar multiplication with field multiplication "
> > > > https://en.wikipedia.org/wiki/Semigroup_action
> > > > https://en.wikipedia.org/wiki/Group_action
> > > >
> > > > https://en.wikipedia.org/wiki/Homogeneous_function
> > > >
> > > > " However, there is still no other terminology available for an 'external monoid' for which this terminology gives us a concise expression. Above all else, this is a reason this term should be of use in the mathematical community."
> > > > https://en.wikipedia.org/wiki/External_(mathematics)
> > > > https://en.wikipedia.org/wiki/Talk:External_(mathematics)
> > > >
> > > > Contrarian already put an optical effect, and other alredy put some bits, let me add another
> > > >
> > > > The suspicion is that is impossible to conclude/obtain your example from an abstract algebra reasoning.
> > > > I tried to obtain your model example but without success.
> > > >
> > > > Going for broke, the bet is, like the Professor Kokichi Sugihara :
> > > >
> > > > https://thekidshouldseethis.com/post/professor-kokichi-sugihara-creates-his-mind-blowing-illusions-with-math
> > > >
> > > > you built an Abstract Algebraic Optical Illusion (an impossible construction)
> > > >
> > > > in order to get a mathematical RFC to outgrow "External Binary Operations"
> > > >
> > > > https://en.wikipedia.org/wiki/Request_for_Comments
> > > >
> > > > Hence, options (a), (b) and (c) dismissed.
> > > > The strange loop is in "External Binary operation" (the house where the paradox inhabits and, together with the critique of the method)
> > > >
> > > > https://en.wikipedia.org/wiki/Strange_loop
> > > > https://en.wikipedia.org/wiki/Koan
> > > The strange loop does seem interesting, but they've almost demanded that it be paradoxical. Circular axioms are fine IMO if they have consequences. Typically they are able to take on many forms as a result, and attempts to reduce their redundancy might fail beyond a certain minimal rule set. If they support themselves will they support instantiation? Do we even have set theory yet? are there elements within a strange loop? We have to be granted the freedom to construct. Could we in fact normalize their weird prefix by simply admitting that our ordinary numerical radix ten representation of the real numbers fits this loop theory? The minimal requirement is one that we all would like to take... but how many things can be constructed? It's pretty clear that mostly we are caught up in mimicing past constructions; myself included. Part of the way forward is by dismantling those past constructions. Taking freedom from them. Working out variations on them. When consequential details emerge from this method then we ought not to dismiss the results. Rather we ought to propagate those results. When I witness the stupendously detailed nature of abstract algebra and see how simply breaking open the real number can do the job then I am dumbfounded that any would insist that polysign is not remarkable.
> > >
> > > My remarks on the human condition I will stand by. They are many and they continue to congeal. The fraud is within us as much as it is from outside. We are social animals. Mathematicians may fit a very particular extreme within this group, and academia ensures the winnowing up of the best mimics. In this age it is more important to add onto the ever burgeoning accumulation. The abuse of dimension that is taking place does deserve ridicule. Possibly it could source a conversation on whether dimension builds from high to low, but mathematics has already built high dimension from down low. It's just been off by one. The mangled thing which is abstract algebra in no way is pristine. Your external binary operation does not answer any problem. It probably doesn't even carry a valid instance. As far as I can tell the most basic of product relations amongst elements of differing sets is one of preservation. For instance when I write
> > > s x
> > > where s is discrete sign and x is continuous magnitude these two different elemental forms married together in a product relation but they do not evaluate. They are the yield of a new set. Notation does matter, and the usage of sign for both an operator and for a value goes undiscussed within such 'minorly abusive' topics as abstract algebra. Well what does it matter if there is no consequence? Why is it that things work while they are still demonstrably conflicted? The trouble is that like polysign numbers there may be a construct sitting beneath our noses that nobody has bothered to build yet. This is the sad nature of the human condition. I can posit polysign as such an instance. Likely there are more. All of us are schooled on similar curricula and will likely reject this thing when it is presented; no different than these here cannot see through the AA system. This condition of the human form including and especially math types is cause for pause. We are so near to a fundamental breakthrough now. Maybe its in our genes. Why should we grant the human the ability to derive the truth in a linguistic form if it has only developed a rudimentary system thus far? The FOX P2 gene... a blessed curse.
> >
> >
> > Reading Becker's "Theory of Heat" (1967) there's an interesting aside in section
> > 54 (The Bose-Einstein gas), about what there are issues computing the statistical
> > ensemble after computing with some initial term of an approximation (eg after
> > linearisation/small-angle approximation, normalization, truncation of vanishing terms).
> > Figures 72.a and 72.b illustrate a "mathematical difficulty" about that "N^_ is
> > always large, say about 10^20." He goes on to describe Fritz London's 1938
> > establishment of super-fluidity and deduced phase transitions around 2.2 degrees
> > Kelvin, and that "one numerical result obtained from the condensation of the
> > ideal gas is quite convincing."
> >
> > It's a well-known thing that the infinities in physics are pasted over with normalization,
> > which is a re-de- (or de-re-) normalization of sorts - it's something mathematics
> > owes physics. (Modern physics.) I.e. there are global effects out to infinity
> > vis-a-vis what are local effects about each zero, in the point, local, global,
> > and total of space concerns or physics (here it's a kinetics with fall gravity).
> >
> > It's a great book, for then about F. London and super-potential.
> >
> >
> > It's similar with the kinetic energy equation written as a series then
> > truncated to mc^2, about what should be a reading of the physical
> > interpretation of the following (zero'ed) terms in the formula.
> >
> > Hofstadter after "Goedel-Escher-Bach: an Eternal Golden Braid" or
> > of his "I am a Strange Loop" is a gentle modern introduction to
> > concepts like the Ding-an-Sich from Kant and otherwise recursive
> > aspects of a monadology or monism. It's a bit fanciful, though.
> >
> > Closures in mathematics as defined for operations (and under
> > operators) in physics is usually conservation and invariance,
> > these days there's lots going on in the quasi-invariant measure
> > theory for example, about how to re-introduce terms re-establishing
> > the potential as real term, about super-gravity and such. ("SUSY lives"..)
>
>
> Instructions for enjoying sci.math 2023
>
> Ignore BKK, JG, WM, AP, MR. (They're bots, or dolts, and crankish trollery.)
>
> There's much less, but, you know, sometimes less is more.
>
> You're welcome to ignore me also, though, I also write to sci.logic and sci.physics.relativity.

Thank you BKK and Ross for keeping this thread alive.
I do wish King Bassam would reel it in on his quantity of posts, but if that activity yields something then I must encourage him onward.
There is something to this place which does yield a different form of productivity.
We may be merely conversing with ourselves here for the most part, but occasionally something will click.
Let's not forget that Isaac Newton played number games with his bible.
Godel died thinking somebody was poisoning his food.
Shall we add these minds to the crank list?
I do believe these people authentically care about the topics they work on.
And of course productivity within mathematics is a terribly limited thing.

Keeping to the content here I wonder if AA falls, then what else would fall away with it?
To me much falls back to the instantiable. When instantiation of a construction essentially evaporates the content of the construction then I see that work as dubious. The pursuit of simplicity really suggests that a final system will not be controversial at all. It will instead be self-evident. Of course this can only be known in hindsight, and we are at an early stage in the progression.