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.

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.

On Thursday, September 7, 2023 at 2:05:00 AM UTC+3, Ross Finlayson wrote:
> On Tuesday, September 5, 2023 at 8:35:49 AM UTC-7, Timothy Golden wrote:
> > 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.
> Making constructive relations and showing how they stand regardless others,
> is different than denying others' constructive relations, which exist regardless.
>
> So, such as"retro-finitist crankety trolls", of particularly the troll-ish variety,
> who say things like "your zero doesn't exist, your signed quantities don't exist,
> these relations of reflections and rotations under multiplicities of roots their
> products don't exist, irrational don't exist, cardinals don't exist", and so on,
> is a different matter, there really is a right and wrong what "mathematical" and
> "non-mathematical", is.
>
> For example, you build a framework of relations called polysign numbers and
> it's great, it models some what are connections that relate to the underlying lattice,
> I dug up Aristotle's continuum and gave it modern language, it's great.
>
> Then it's just a usual sort of notion that the objects in the middle, numbers, and,
> geometry's objects, of all relations, have standard intepretations, and non-standard
> interpretations, if at all. There are also "reduced" or "minimal, contextually" the
> interpretations, or what suffices, while what is overall non-contradictory, in
> not allowing pathologies of definitions, or lack thereof.
>
> So, where you're making a deconstructive account of abstract algebra, it's to keep
> in mind what it means to define not just the elements, but the worlds, not just the
> points, but the spaces, not just the pair-wise, but the closures, and all sorts what
> complementary duals make that any framework including invertibility breaks both
> ways, with the forward either way and invertibility underdefined, or for example,
> closure underdefined.
>
> That's a simple part of "multiplicity theory", the theory of objects that are multiplicities
> under what is their "surface" that is much their "edge", each alone is of a "singularity theory",
> of what otherwise are the usually "indeterminate quantities" or gaps in closures or
> exceptions like starting points or bounds of pair-wise relations in points.
>
> So, you can break arithmetic down, break algebra down, break geometry down, and so on,
> as of a deconstructive account, then to relate what you've made of a constructive account,
> here polysign numbers or for example sweep, and show how they relate, either way
> relating across the lattice, or relative as the lattice, of relations of magnitudes, wholes,
> their inverses, the closures of the spaces of the sums of their differences, and so on.
>
> This way one can address real features of the non-standard, while, not being standardly just wrong.

Thu 07 Sep 2023 12:53:04 PM EDT https://groups.google.com/g/sci.math/c/yGQpEVY7n2c
On Wednesday, September 6, 2023 at 7:05:00 PM UTC-4, Ross Finlayson wrote:
> On Tuesday, September 5, 2023 at 8:35:49 AM UTC-7, Timothy Golden wrote:
> > On Monday, September 4, 2023 at 1:55:51 PM UTC-4, Ross Finlayson wrote:
> > 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.
> Making constructive relations and showing how they stand regardless others,
> is different than denying others' constructive relations, which exist regardless.

I'm sorry, but you are denying falsification any meaningful status here. In mathematics of all places, falsification deserves ultimate respect. The idea that we exist in a contorted system of mathematics which all find perfectly acceptable is grotesque. Sadly this is a statement on the human mind, and I don't mean just yours, Ross. I need mention just one term to take the whole subject down: a1X. Poof.

>
> So, such as"retro-finitist crankety trolls", of particularly the troll-ish variety,
> who say things like "your zero doesn't exist, your signed quantities don't exist,
> these relations of reflections and rotations under multiplicities of roots their
> products don't exist, irrational don't exist, cardinals don't exist", and so on,
> is a different matter, there really is a right and wrong what "mathematical" and
> "non-mathematical", is.
>
> For example, you build a framework of relations called polysign numbers and
> it's great, it models some what are connections that relate to the underlying lattice,
> I dug up Aristotle's continuum and gave it modern language, it's great.
>
> Then it's just a usual sort of notion that the objects in the middle, numbers, and,
> geometry's objects, of all relations, have standard intepretations, and non-standard
> interpretations, if at all. There are also "reduced" or "minimal, contextually" the
> interpretations, or what suffices, while what is overall non-contradictory, in
> not allowing pathologies of definitions, or lack thereof.
>
> So, where you're making a deconstructive account of abstract algebra, it's to keep
> in mind what it means to define not just the elements, but the worlds, not just the
> points, but the spaces, not just the pair-wise, but the closures, and all sorts what
> complementary duals make that any framework including invertibility breaks both
> ways, with the forward either way and invertibility underdefined, or for example,
> closure underdefined.
>
> That's a simple part of "multiplicity theory", the theory of objects that are multiplicities
> under what is their "surface" that is much their "edge", each alone is of a "singularity theory",
> of what otherwise are the usually "indeterminate quantities" or gaps in closures or
> exceptions like starting points or bounds of pair-wise relations in points.
>
> So, you can break arithmetic down, break algebra down, break geometry down, and so on,
> as of a deconstructive account, then to relate what you've made of a constructive account,
> here polysign numbers or for example sweep, and show how they relate, either way
> relating across the lattice, or relative as the lattice, of relations of magnitudes, wholes,
> their inverses, the closures of the spaces of the sums of their differences, and so on.
>
> This way one can address real features of the non-standard, while, not being standardly just wrong.

On Thursday, September 7, 2023 at 1:16:41 PM UTC-4, Ross Finlayson wrote:
> On Thursday, September 7, 2023 at 9:58:04 AM UTC-7, Timothy Golden wrote:
> > Thu 07 Sep 2023 12:53:04 PM EDT https://groups.google.com/g/sci.math/c/yGQpEVY7n2c
> > On Wednesday, September 6, 2023 at 7:05:00 PM UTC-4, Ross Finlayson wrote:
> > > On Tuesday, September 5, 2023 at 8:35:49 AM UTC-7, Timothy Golden wrote:
> > > > On Monday, September 4, 2023 at 1:55:51 PM UTC-4, Ross Finlayson wrote:
> > > > 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.
> > > Making constructive relations and showing how they stand regardless others,
> > > is different than denying others' constructive relations, which exist regardless.
> > I'm sorry, but you are denying falsification any meaningful status here.. In mathematics of all places, falsification deserves ultimate respect. The idea that we exist in a contorted system of mathematics which all find perfectly acceptable is grotesque. Sadly this is a statement on the human mind, and I don't mean just yours, Ross. I need mention just one term to take the whole subject down: a1X. Poof.
> > >
> > > So, such as"retro-finitist crankety trolls", of particularly the troll-ish variety,
> > > who say things like "your zero doesn't exist, your signed quantities don't exist,
> > > these relations of reflections and rotations under multiplicities of roots their
> > > products don't exist, irrational don't exist, cardinals don't exist", and so on,
> > > is a different matter, there really is a right and wrong what "mathematical" and
> > > "non-mathematical", is.
> > >
> > > For example, you build a framework of relations called polysign numbers and
> > > it's great, it models some what are connections that relate to the underlying lattice,
> > > I dug up Aristotle's continuum and gave it modern language, it's great.
> > >
> > > Then it's just a usual sort of notion that the objects in the middle, numbers, and,
> > > geometry's objects, of all relations, have standard intepretations, and non-standard
> > > interpretations, if at all. There are also "reduced" or "minimal, contextually" the
> > > interpretations, or what suffices, while what is overall non-contradictory, in
> > > not allowing pathologies of definitions, or lack thereof.
> > >
> > > So, where you're making a deconstructive account of abstract algebra, it's to keep
> > > in mind what it means to define not just the elements, but the worlds, not just the
> > > points, but the spaces, not just the pair-wise, but the closures, and all sorts what
> > > complementary duals make that any framework including invertibility breaks both
> > > ways, with the forward either way and invertibility underdefined, or for example,
> > > closure underdefined.
> > >
> > > That's a simple part of "multiplicity theory", the theory of objects that are multiplicities
> > > under what is their "surface" that is much their "edge", each alone is of a "singularity theory",
> > > of what otherwise are the usually "indeterminate quantities" or gaps in closures or
> > > exceptions like starting points or bounds of pair-wise relations in points.
> > >
> > > So, you can break arithmetic down, break algebra down, break geometry down, and so on,
> > > as of a deconstructive account, then to relate what you've made of a constructive account,
> > > here polysign numbers or for example sweep, and show how they relate, either way
> > > relating across the lattice, or relative as the lattice, of relations of magnitudes, wholes,
> > > their inverses, the closures of the spaces of the sums of their differences, and so on.
> > >
> > > This way one can address real features of the non-standard, while, not being standardly just wrong.
> Falsification is key in science, I imagine in mathematics that's "counterexamples".
>
> What you do is you provide counterexamples.
>
> Would you briefly define theis "a1X" ? I read it as "an object a relates 1 object X",
> where these days the theory is build on formal languages and n-ary (infinitary) relations.

It's been discussed as the OP of this thread. The point is more that they don't define it.
It is a product of two things which does not obey their product definition.
We are in their polynomial form here.
a0 + a1X + a2XX + ...
This object is not ring behaved.
Yet they claim it is ring behaved.
We simply pick it apart; the sums being supposedly ring behaved then via closure the term a1X is ring behaved. Yet a1X is composed of two elements from different sets and refuses to resolve to any elementary form. They bothered to formalize the product then through a broad lens maintain the polynomial form, but the structure of the polynomial is of sums and products which fail their own criterion.

Abstract Algebra is broken.
What they are after can be found another way.
It is far simpler than this polynomial construction in abstract X, whose next tricks of the ideal and the quotient are not at all straight-forward.
All of that to achieve a modulo form which already existed in the sign of the real value. Go mod-3 sir, and you'll have your C and get to eat it too. They prefer R[X]/(XX+1). By the time a student has achieved all of this rather a lot of water has flowed under a very rotten bridge. It's been raining a lot lately. Do you choose to cross that bridge? What lays to the other side that is worthy? Certainly to claim that polysign numbers will be found over there in some contorted form is not acceptable.

To extend though, for me, is to ponder how seemingly broken constructs can actually hold up. One of the simplest is the confusion between operator and value. Surely here there could be no room for confusion, and yet we regularly use the '+' sign for both summation and for the value of a real number. This is tantamount to treason, for an operator is to act upon values, and the confusion of the two is a complete disservice to the mathematical profession. Could this explain why so many hate the subject? The simplest mind will have the most problem with such contradiction in a supposedly pristine subject. Those who abide such contradictory logic are clearly those who excel in handling exceptions. Thence the game is raised again to test the strength of their minds, and the best mimics who concede the gauntlet in every form become the next rulers. All the while simplicity lays in another direction entirely.

Fri 08 Sep 2023 12:18:50 PM EDT https://groups.google.com/g/sci.math/c/yGQpEVY7n2c

On Friday, September 8, 2023 at 11:48:27 AM UTC-4, Ross Finlayson wrote:
> On Friday, September 8, 2023 at 8:19:11 AM UTC-7, Timothy Golden wrote:
> > On Thursday, September 7, 2023 at 1:16:41 PM UTC-4, Ross Finlayson wrote:
> > > On Thursday, September 7, 2023 at 9:58:04 AM UTC-7, Timothy Golden wrote:
> > > Falsification is key in science, I imagine in mathematics that's "counterexamples".
> > >
> > > What you do is you provide counterexamples.
> > >
> > > Would you briefly define theis "a1X" ? I read it as "an object a relates 1 object X",
> > > where these days the theory is build on formal languages and n-ary (infinitary) relations.
> > It's been discussed as the OP of this thread. The point is more that they don't define it.
> > It is a product of two things which does not obey their product definition.
> > We are in their polynomial form here.
> > a0 + a1X + a2XX + ...
> > This object is not ring behaved.
> > Yet they claim it is ring behaved.
> > We simply pick it apart; the sums being supposedly ring behaved then via closure the term a1X is ring behaved. Yet a1X is composed of two elements from different sets and refuses to resolve to any elementary form. They bothered to formalize the product then through a broad lens maintain the polynomial form, but the structure of the polynomial is of sums and products which fail their own criterion.
> >
> > Abstract Algebra is broken.
> > What they are after can be found another way.
> > It is far simpler than this polynomial construction in abstract X, whose next tricks of the ideal and the quotient are not at all straight-forward..
> > All of that to achieve a modulo form which already existed in the sign of the real value. Go mod-3 sir, and you'll have your C and get to eat it too. They prefer R[X]/(XX+1). By the time a student has achieved all of this rather a lot of water has flowed under a very rotten bridge. It's been raining a lot lately. Do you choose to cross that bridge? What lays to the other side that is worthy? Certainly to claim that polysign numbers will be found over there in some contorted form is not acceptable.
> >
> > To extend though, for me, is to ponder how seemingly broken constructs can actually hold up. One of the simplest is the confusion between operator and value. Surely here there could be no room for confusion, and yet we regularly use the '+' sign for both summation and for the value of a real number. This is tantamount to treason, for an operator is to act upon values, and the confusion of the two is a complete disservice to the mathematical profession. Could this explain why so many hate the subject? The simplest mind will have the most problem with such contradiction in a supposedly pristine subject. Those who abide such contradictory logic are clearly those who excel in handling exceptions. Thence the game is raised again to test the strength of their minds, and the best mimics who concede the gauntlet in every form become the next rulers. All the while simplicity lays in another direction entirely.
> It's called a deconstructive account, where, you consider the thing in the middle,
> then find at least two different ways of various underlying things that add up to
> the middle thing or here "the algebras", or for example "the numbers", then figure
> out how to show that either way results the same things, but they're not interchangeable
> each other.
>
> For example you might define arithmetic as + - * /, or + ... <-> / ..., showing how
> as the numbers go to infinity they result same, but for example aren't all same all
> the finite or bounded models that "complete" to them.
>
> In this manner you show "them's the breaks" while still showing how each adds up.
>
> This sort of notion of a deconstructive account, gets into the elements, for
> example "points and lines" vis-a-vis "points and point-sets", that the elements,
> of the domains of the worlds of the objects, add up. So, you can see that analytic
> geometry is just an example of this sort of approach.
>
> Then, "deconstructive account" is a phrase from literary criticism theory, but I've
> taken it for this sort of usual elementary analysis also.
>
> (I.e., the "postmodern disfigurist" who's a "modern structuralist".)

I appreciate the deconstructive, which I might actually label 'destructive', versus constructive, approaches.
I think the point is that the thing needs to work both ways.
You seem to have a problem with falsification.
Your flexibility is perhaps your downfall, and I of course mean this in no harmful way to your own persona. Still, to what degree you care to sponge up everything in print, versus actually hold it to account: I would suggest that academia has led us all astray. It is our burden whether to accept their words no matter how 'royal' their pedigree. In the accumulation the burden is beyond any to take on, and so you land just as you do.

My own approach is of a fundamental nature. Rather than mimic the accumulation I care to cut through to the simplistic; yet the term 'destructive' can only apply to things which will come apart, you see?
That we care to get to an elemental form; that an elemental form exists at all: this is a crux. This crux is indeed offended by abstract algebra.

That this approach in the physical world would hopefully lead us to the atom as fundamental; well, and in their multiple identities and spectroscopic behaviors, and removable components known as electrons, all of which are apparently identical; yes: tremendous complexity lays here which a clean theory should dissolve by deriving these details.

That the mathematical world obeys a rather different form; a very strict form; one that does not contradict itself; this criterion of mathematics is regularly offended by all. -5+(-2) will do for this proof. Simple as that.
AA is far worse. That every number system is radix-10, well what then does it mean to have a convention wherby all values communicated shall be radix-10? Is the needle labelled 'N' on your compass indeed the south pole of the compass needle? Why not label it 'S', then? Or did you want to label the north pole of the Earth the south pole to fix things up?

That humans are capable of handling such exceptions does not mean that these exceptions should be incorporated into our mathematics. It is exactly wrong to do so. That these grievances exist somewhat casts the subject as open.. Quite open, really. This of course is a very positive statement which holds up even as going foul-mouthed would hold up here equally well.