Little facts

[Julio Di Egidio]

Little facts that make my head spin.

Shifting two numbers by 't' units.

Can you say *why* their sum is not
translation invariant while their
difference is? Namely,

a+b = a-(-b) = a-B, yet:
a+b = (a+t)+(b+t) - 2t
a-B = (a+t)-(B+t)

Julio

[Barry Schwarz]

On Mon, 28 Nov 2022 00:30:38 -0800 (PST), Julio Di Egidio
<ju...@diegidio.name> wrote:

>Little facts that make my head spin.
>
>Shifting two numbers by 't' units.
>
>Can you say *why* their sum is not
>translation invariant while their
>difference is? Namely,

If I have 3 apples and you have 2, we have 5 apples.
But if I have 6 apples and you have 5, we have 11.

On the other hand, if I have 5 and you have 2, I have 3 more than you.
Then if I have 8 and you have 5, I still have 3 more than you.

Why do you think they should be invariant? Sum is both commutative
and associative; difference is neither.

--
Remove del for email

[Julio Di Egidio]

On Monday, 28 November 2022 at 15:29:30 UTC+1, Barry Schwarz wrote:
> On Mon, 28 Nov 2022 00:30:38 -0800 (PST), Julio Di Egidio
> <ju...@diegidio.name> wrote:
>
> > Little facts that make my head spin.
> >
> > Shifting two numbers by 't' units.
> >
> > Can you say *why* their sum is not
> > translation invariant while their
> > difference is? Namely,
>
> If I have 3 apples and you have 2, we have 5 apples.
> But if I have 6 apples and you have 5, we have 11.
>
> On the other hand, if I have 5 and you have 2, I have 3 more than you.
> Then if I have 8 and you have 5, I still have 3 more than you.

Yes. More generally:

a+b = (a+t)+(b+t) - 2t // not invariant
a-b = (a+t)-(b+t) // invariant

To "explain it", one could observe:

(a+t)+(b+t) = a+t+b+t
(a+t)-(b+t) = a+t-b-t

to point out that it is a change of sign in 't'
that is making all the difference, so to speak.
But that is just one way to see the why, maybe
not even that interesting, anyway I tend to
think just geometrically and then look for ways
to express my geometric intuition/reasoning in
maths. So, maybe the problem is really trivial,
or maybe a mathematician would have something
else to say.

> Why do you think they should be invariant?
> Sum is both commutative
> and associative; difference is neither.

Because with integers we can in some sense
dispense with subtraction, i.e. by noticing
that a-b = a+(-b)... except that, apparently,
and in a sense that I still have only partly
clear, we cannot.

(And, overall, because I have been spending
too much time lately tripping over fixed points,
symmetries, conservation laws...)

Julio

[Archimedes Plutonium]

Thanks Julio and Barry, for this offers me more clarity on Schrodinger Equation of a cubic set solution versus general set. The Elements Beyond Uranium, Seaborg & Loveland, 1990, pages 72-73.

Now I take as the math equations that govern all of Physics as the calculus on New Ohm's Law Voltage = current*magnetic field*electric field, and that calculus delivers these EM laws that govern all of physics-- and governs all of mathematics also, for math is a subset of physics.

Here I use Angular Momentum L as electric field E, both are interchangeable.

0) domain law as Atomic Theory
1) Magnetic primal unit law Magnetic Field  B = kg /A*s^2
2) V = C*B*L       New Ohm's law, law of electricity
3) V' = (C*B*L)'         Capacitor law
4) (V/C*L)'  = B'        Ampere-Maxwell law
5) (V/(B*L))' = C'      Faraday law
6) (V/(C*B))' = L'      the new law of Coulomb force with EM gravity force

All the calculus permutations possible are V', B', C', and E' (same as L').

Notice that in all the calculus, only one is Addition the Voltage derivative. While the other three are derivatives of division which ends up as Subtraction. For example, the quotient rule of calculus is (V/i*L)' = B' =  (V'*i*L - V*i' *L - V*i*L') / (i*L)^2. Do you see that in every division derivative, we have two subtractions over one number.

Algebra of 3D Calculus, for remember we did the algebra of

V' = (iBL)'
i' = (V/BL)'
B' = (V/iL)'
L' = (V/iB)'

--- quoting 1st year calculus from Teaching True ---
Using the Product Rule which is (fgh)' = (f'gh + fg'h + fgh')

Capacitor Law   (i*B*L)' = i'*B*L + i*B'L + i*B*L' 

V' = (iBL)' = i'*B*L + i*B'*L + i*B*L'  here we have three terms explaining capacitors

Ampere-Maxwell Law

Using the Quotient Rule, which is (f/gh)' = (f'gh - fg'h - fgh')/(gh)^2 

(V/i*L)' = B' =  (V'*i*L - V*i' *L - V*i*L') / (i*L)^2 

Maxwell had two terms in the Ampere-Maxwell law-- the produced magnetic field and a displacement current, but above we see we have also a third new term.

Faraday Law

(V/B*L)' = i' =  (V'*B*L - V*B' *L - V*B*L') / (B*L)^2

------------
V' = (iBL)' = i'*B*L + i*B'*L + i*B*L' reduces to
    = iBL + iVL + iBL'

i' =  V'*B*L/ (B*L)^2  - V*B' *L/ (B*L)^2  - V*B*L' / (B*L)^2 reduces to
i'     = B^2*L/ (B*L)^2  - V^2 *L/ (B*L)^2  - V*B*L' / (B*L)^2 further reduces
    = 1/L - V^2/B^2*L - VL'/BL^2

B' =  V'*i*L/ (i*L)^2 - V*i' *L/ (i*L)^2  - V*i*L' / (i*L)^2 reduces to
B'    =  B*i*L/ (i*L)^2 - V*i *L/ (i*L)^2  - V*i*L' / (i*L)^2 further reduces to
  = B/iL - V/iL - VL'/iL^2


L' = (V/i*B)' = (V'*i*B - V*i' *B - V*i*B') / (i*B)^2  reduces to
L' = i*B^2 / (i*B)^2   - V*i *B / (i*B)^2  - V^2*i / (i*B)^2 further reduces to
    = 1/i - V/iB - V^2/iB^2

--------


(1) V' =  iBL + iVL + iBL'

(2) i'  = 1/L - V^2/B^2*L - VL'/BL^2

(3) B' = B/iL - V/iL - VL'/iL^2

(4) L' = 1/i - V/iB - V^2/iB^2

Alright, so I replace L' in (1) with 1/i - V/iB - V^2/iB^2

I get V' =  iBL + iVL + iB*(1/i - V/iB - V^2/iB^2 )
             =   iBL + iVL + B - V - V^2/ B


Doing the replacement in (2)

i'  = 1/L - V^2/B^2*L - VL'/BL^2
   =  1/L - V^2/B^2*L - V*(1/i - V/iB - V^2/iB^2) /BL^2
   =  1/L - V^2/B^2*L  - (V/iBL^2) - (V^2/iB^2L^2) - (V^3/(iB^3L^2))

Doing the replacement in (3)

B' = B/iL - V/iL - VL'/iL^2
    =  B/iL - V/iL - V(1/i - V/iB - V^2/iB^2)/iL^2
    =  B/iL - V/iL - (V/i^2L^2) - (V^2/i^2*B*L^2) - (V^3/( i^2B^2L^2))

Julio likes geometry, and that is my preference also, I prefer to solve problems of both science, and math, best solved by geometry, for I believe in Darwin Evolution that what evolved us from apes was the throwing of rocks and stones to garner advantage, and throwing requires the brain to advance in geometry, more than advance in quantity = algebra. To hit a target needs geometry.

So in the above, I replace Voltage = current*magnetic field*electric field (note, the * symbol is generalized multiplication and can be dot vector product or cross vector product or even scalar product).

So, well in math we can convert Voltage = i*B*E, into volume and make it easy on ourselves, as Volume = length*width*height.

Now that Volume decomposes into calculus of four differential equations of Volume', length', width', height'.

The length, width, height differential equations will end up with two subtraction terms. The Volume differential equation will be pure addition of terms.

And now, this leads me to the clarity of Cubic versus General Set in Schrodinger Equation.

If we have volume of rectangular box such as Length = 10, Width = 4, Height = 3.

But what if we have the volume of Length = 10, Width = 10, Height = 10, then we are faced with two possibilities, for our volume can be the volume of a cube in 3D or the volume of a sphere with a radius of 5.

This is why Schrodinger Equation has a General Set along with a Cubic Set.

AP

[Ross A. Finlayson]

Go on, ....

[Archimedes Plutonium]

On Monday, November 28, 2022 at 4:17:42 PM UTC-6, Archimedes Plutonium wrote:
> So, well in math we can convert Voltage = i*B*E, into volume and make it easy on ourselves, as Volume = length*width*height.
>
> Now that Volume decomposes into calculus of four differential equations of Volume', length', width', height'.
>
> The length, width, height differential equations will end up with two subtraction terms. The Volume differential equation will be pure addition of terms.
>
> And now, this leads me to the clarity of Cubic versus General Set in Schrodinger Equation.
>
> If we have volume of rectangular box such as Length = 10, Width = 4, Height = 3.
>
> But what if we have the volume of Length = 10, Width = 10, Height = 10, then we are faced with two possibilities, for our volume can be the volume of a cube in 3D or the volume of a sphere with a radius of 5.
>
> This is why Schrodinger Equation has a General Set along with a Cubic Set.

Now the above is not confined to just Cube and then a Sphere with radius 1/2 of cube side. But made more general with Rectangular Box volume replaced by ellipsoid volume. So if I have volume of rectangular box as Length= 10, Width = 4, Height= 3, I can also turn that into a volume of ellipsoid with semi-axes of 10/2, 4/2, 3/2. Keeping the curved-geometry volume less than the straightline geometry volume.

Now, has anyone asked the question what is the side view of a torus, what does that figure become in 2D geometry??

So, you hold up a torus and look at it from a side view. You cannot see the donut hole. But what does the figure become in 2D??? It cannot be an ellipse? For the bottom and top are straightlines. It reminds me of these wood tabletops that you can pull apart and add more for a larger table.

(_______)

So the ends were part of a circle from a circle torus but the bottom and top are straight lines. And what would the area of such a figure be??? A formula for the area?

AP

[Sergi o]

On 11/28/2022 2:30 AM, Julio Di Egidio wrote:
> Little facts that make my head spin.
>
> Shifting two numbers by 't' units.
>
> Can you say *why* their sum is not
> translation invariant while their
> difference is? Namely,
>

>#1 a+b = a-(-b) = a-B, yet:

so B = -b

>#2 a+b = (a+t)+(b+t) - 2t

ok

> #3 a-B = (a+t)-(B+t)

However, a-(-b) = a+b = (a+t)+(b+t) - 2t

but is not equal to (a+t)-(B+t) which is (a+t) + b - t

>
> Julio

Equation #3 does not follow from #1 or #2

[Archimedes Plutonium]

On Monday, November 28, 2022 at 8:26:15 PM UTC-6, Archimedes Plutonium wrote:

> (_______)
>
> So the ends were part of a circle from a circle torus but the bottom and top are straight lines. And what would the area of such a figure be??? A formula for the area?

Now I was looking in the math literature for a name of a 2D figure whose top and bottom were straight line segments but whose ends are parts of a circle.

It does have 2 axes of symmetry, same as ellipse. So is it a special kind of ellipse?????

AP

[Archimedes Plutonium]

Alright, it is called a stadium, and now I wonder if its area is less or greater than the area of a standard ellipse with the same axes of symmetry, I would guess the standard ellipse has more area, and whether the number quantity
of standard ellipse area subtract stadium is a significant number related to pi.

[Archimedes Plutonium]

In 3D, it is called a capsule, like a pill capsule. And I wonder if the volume of the capsule of axes A and B, is less than the volume of ellipsoid of axes A and B, I would guess so.

[Julio Di Egidio]

No: these solids also have rotational symmetries, indeed are solid of revolution (in two ways), so we can simply compare the main sections of the two solids and it should be apparent that the capsule's section (a capsule in 2D) must be strictly larger than the ellipsoid's section (an ellipse in 2D), as it "grows a rectangle" while the ellipse must stay "smoothly curved", except for the limit case where the capsule shrinks to a circle (i.e. the internal rectangle shrinks to nothing) in which case also the ellipses shrinks to the same circle.

A couple of nice links I have found:

<https://www.researchgate.net/figure/A-capsule-geometry-consisting-of-a-cylinder-with-hemispherical-ends-The-capsule-geometry_fig9_316347573>
<http://balmoralsoftware.com/equability/hemicylinder/hemicylinder.htm>

Julio

[Julio Di Egidio]

> Thanks Julio and Barry, for this offers me more clarity on Schrodinger Equation of a cubic set solution versus general set. The Elements Beyond Uranium, Seaborg & Loveland, 1990, pages 72-73.
>
> Now I take as the math equations that govern all of Physics as the calculus on New Ohm's Law Voltage = current*magnetic field*electric field, and that calculus delivers these EM laws that govern all of physics-- and governs all of mathematics also, for math is a subset of physics.
>
> Here I use Angular Momentum L as electric field E, both are interchangeable.
>
> 0) domain law as Atomic Theory
> 1) Magnetic primal unit law Magnetic Field B = kg /A*s^2
> 2) V = C*B*L New Ohm's law, law of electricity
> 3) V' = (C*B*L)' Capacitor law
> 4) (V/C*L)' = B' Ampere-Maxwell law
> 5) (V/(B*L))' = C' Faraday law
> 6) (V/(C*B))' = L' the new law of Coulomb force with EM gravity force
>
> All the calculus permutations possible are V', B', C', and E' (same as L').
>
> Notice that in all the calculus, only one is Addition the Voltage derivative. While the other three are derivatives of division which ends up as Subtraction. For example, the quotient rule of calculus is (V/i*L)' = B' = (V'*i*L - V*i' *L - V*i*L') / (i*L)^2. Do you see that in every division derivative, we have two subtractions over one number.

<snip>

Thank you, that is quite along the lines of some of my ruminations. Indeed, volume is playing a crucial role in some recent theoretical physics (look up for "amplituhedron", though it gets immediately and utterly technical), where the volume of some combinatorial structures ends up being the amplitude of the corresponding physical configuration.

The amazing effectiveness of mathematics...

Julio

[Julio Di Egidio]

For the fun of it, here is a demonstration:

<https://www.desmos.com/calculator/hgnugivzda>

Julio

[Archimedes Plutonium]

Hi, Julio, I thought I was going to have to move my talk of capsule and stadium to another thread, so as not to interrupt your thread here, but seeing that you joined in on capsule, I think I will stay here in this thread.

Julio, I want some advice from you on Wikipedia. I was stung by them in the 1990s when I did some editing of "their errors" spending quite a bit of my time in making the edit of Wikipedia errors when -- a few hours later, a Wikipedia editor reverted my input-- all a waste of time.

Wikipedia is wrong when they say a "ellipse is a oval", they are wrong in "Dandelin proof" for that is a fakery, and they are wrong when they say a "oval is ill defined or nebulous defined". And of course, their big mistake of geometry-- they claim a ellipse is a conic section yet it never was for a single right circular cone. However, if you take 2 right circular cones and join them together in <> that some cuts are indeed ellipses, but not a single right circular cone.

Julio-- I want to know what your attitude is on Wikipedia when you see they have mistakes in various entries. Has Wikipedia changed at all since 1990s when their entries are full of error, and is the best policy towards Wikipedia-- continue to ignore their many mistakes of math. For I have the feeling that many of those editors-- are just plain bullies that know little real mathematics.

What is your opinion????

[Archimedes Plutonium]

Alright, well, the Stadium figure and the Capsule figure put new life into the proof that slant cut of single right circular cone is a Oval, never the Ellipse.

And calls upon me to make another proof argument for that idea.
D
B /slant cut plane
/ \/C
_A___________/ \

Now I hope that ascii art holds up its format once I post it, for often it falls apart in ineligible.
Now I label this line from the base of the right circular cone as A. I label B as the apex of cone. I label C as the intersection point of slant cut plane D.

Now, the purpose of this diagram is to focus in on where the D, slant cut plane intersects with A and the angle formed. Hard to see from that above graphic for I had only one angle choice in ascii art. I prefer a smaller angle for the cut so it reaches out to A.

And the proofs that slant cut is Oval, never ellipse has to do with the fact that the plane passes through the center perpendicular with apex and the side nearest the right wall is closer and thus smaller than the side nearest the left wall and thus not equal, making the figure impossible to be a ellipse. And rather, instead be a oval.

Now I am going to have to elaborate on this sketch by dropping perpendiculars down from C to base A, and down from B to base A, and down from the exit intersection to base A.

I am going to have to do that for proofs of theorems about slant cut not in a cylinder, but in a barrel or torus without donut hole. I have to do these perpendiculars because I need to find out if the Circle curve maximizes area and whether the slant cut intersects a Circle Arc.

Let me define Arc as a section of a Circle. Or a section of a ellipse, or a section of a oval.

So the silhouette of Sectioning.

Sectioning a cone is /\

Sectioning a cylinder is | |

Sectioning a barrel is (__)

Sectioning a barrel is the same as sectioning a torus without the donut hole involved.

Now all of this will sound remote to people not scientists, but all of this is vital to physics especially astronomy, for gravity uses ellipses, and atomic theory uses toruses. The atomic and hydrogen bombs are details of toruses and sectioning geometry.

What I an striving for is to prove several theorems of geometry of cone, of capsule, of stadium, of a cylinder whose walls are curves --- a barrel if you please, or is a barrel a torus without the donut hole.

But first I want to review the history of the maximum rectangle or square that fits inside a circle, any given circle. Is the maximum in area going to be a rectangle or going to be a square. Let my check the literature at this moment.

Yes, apparently the Square is the largest rectangle inside a circle in terms of area. And we say a square is a subset of rectangle whose all four sides are equal.

Can we do the same with a ellipse and oval?

Now we start with a square and ask, what is the largest in terms of area of a ellipse or oval to fit inside the square? We do the same question with starting from a rectangle-- which is the larger area a ellipse or oval?? I believe the answer is a oval is the maximum area that fits inside either a rectangle or square. And if true, then I can say a Oval is a subset of a Ellipse whose 1/2 portions of the oval come from two different ellipses.

Quite the reverse of what Wikipedia editors say that a ellipse is a oval, when they should be saying that a oval is a ellipse.

AP
P.S. I need to turn this into my 220+K book of science.

[Archimedes Plutonium]

I better capture Wikipedia's muddled and error filled math of ellipse and oval, before they dispose of it and catches me complaining of their error without evidence of their muddle headed error. This is a huge problem of Wikipedia science entrees-- written by and composed by people with few Logical marbles.

--- quoting Wikipedia ---
The shape is based on a stadium, a place used for athletics and horse racing tracks.

A stadium may be constructed as the Minkowski sum of a disk and a line segment.[6] Alternatively, it is the neighborhood of points within a given distance from a line segment. A stadium is a type of oval. However, unlike some other ovals such as the ellipses, it is not an algebraic curve because different parts of its boundary are defined by different equations.

--- end quoting ---

[Archimedes Plutonium]

Alright, in this definition of Stadium figure it has to have No - Vertex.

So does that eliminate all curves except for semicircle arc, and for semiellipse arc?

I think it even allows for a what can be described as the semi-oval arc.

But it restricts the formation of a Stadium figure to no other arcs, not the semi-arc.

You cannot take a sliver of a circle curve or ellipse curve or oval curve and avoid a Vertex.

Only on a point of the circle, ellipse, oval where the curve arc is rising, then reaches its peek, then declines can I avoid forming a vertex to two parallel lines for Stadium figure.

Now, I see no way of proving that. One of those things that you can see in the mind, but cannot prove.

AP

[Archimedes Plutonium]

So, how does one prove that two semicircles fit on the ends of two parallel lines to form a smooth stadium and no vertices involved. How does one prove that such a thing can take place with semiellipse and 2 X a semioval of pick the one????

I am asking how one goes about proving no vertices and some-- with vertices if you do not have the semi-curve.

My best guess is that to avoid a vertex, you have to use a curve in which a peak point simultaneous with a lowest point is at a "moment of the end of a rise and the beginning of a fall". Perhaps calculus of 0 slope at a point and the two parallel lines are 0 slope.

Yes, so it is not that difficult.

Now a new question arises, a very important one, which will give the maximum area if we enclose the stadium in a rectangle? The semicircle stadium, the semiellipse stadium, the semioval X 2 if we enclose the figure in a rectangle. I will guess the semicircle stadium is the most dense area. What this helps to answer is in physics, are the toruses of protons are they circular or elliptical or oval toruses??

AP

[Archimedes Plutonium]

Yes, I took a look at amplituhedron-- they want to simplify, but could not understand a paragraph of what they offer. To simplify should not be to have to go through a walking on hot fiery coal to reach understanding.

[Archimedes Plutonium]

I guess physicists and mathematicians need to learn what "simplify really means". As the late Earle Jones out at Stanford remarked that "AP threw out the Rationals, then threw out the Irrationals, then threw out Reals, and not stopping there, threw out the Complex and other crazy gnarly numbers of Surreal, imaginary and you name it, keeping only the Counting Numbers, and making Decimal Grid Systems.

So the only legitimate numbers in AP's vision of mathematics are Grid Systems-- all created from Counting numbers with Mathematical Induction. And Earle was appreciative of this as well as Stanford Univ faculty allowing them more coffee and bisquit breaks.

The 10 Decimal Grid is this:

9.0, 9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0
8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9,
7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9,
6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9,
5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9,
4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9,
3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9,
2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9,
1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9,
0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,

The 100 Grid is a mathematical induction starting with 0 then 0.01, the 1000 Grid starts with 0 then 0.001.

And Earle was immensely pleased with that Simplification, a true simplification.

But as for amplituhedron, is a mockery, and only cloaked as a simplification as if the authors are trying to hide more than reveal.

The beauty of the Decimal Grid Numbers is that they are essential and required in order to do a geometry proof of the Fundamental Theorem of Calculus. You cannot do a geometry proof of FTC with the Reals because you need empty space from one number to the next. You cannot do a geometry FTC if the numbers are a continuum. You need discrete numbers to do a FTC.

So that is true, real Simplification, for I threw out every number in Old Math except for the Counting numbers. And above, if you multiply every number by 10, you get the Counting numbers 0 to 1 to 100, same goes for all the other grids. That Numbers are formed from one generator only--- Math Induction. Not were a string of kooks in math with their sack full of new types of numbers clogs up the system. Just Counting Numbers and math induction.

AP

[Julio Di Egidio]

On Tuesday, 29 November 2022 at 20:21:20 UTC+1, Archimedes Plutonium wrote:
> On Tuesday, November 29, 2022 at 4:12:58 AM UTC-6, ju...@diegidio.name wrote:

<snip>

> Hi, Julio, I thought I was going to have to move my talk of capsule and stadium
> to another thread, so as not to interrupt your thread here, but seeing that you
> joined in on capsule, I think I will stay here in this thread.

I trust your judgment on that. Besides, this thread was over anyway, and about
nothing terribly interesting...

> Julio, I want some advice from you on Wikipedia. I was stung by them in the

All relevant areas of Wikipedia have been hijacked and only offer the voice of
the worst brainwashing and global fraud. But Wikipedia is rather the example
of blind auto-organization and what we, the stupid fucking white men, do with
it. So, don't blame it, WP is in fact the thermometer of our globalized infamy
and abysmal stupidity.

> Wikipedia is wrong when they say a "ellipse is a oval",

No, they aren't, the point being, you can trust Apollonius. Maybe notice that
in the slant cut of a cone, the central axis passes by one of the foci of the
ellipse, not its center. Moreover, if you don't trust the algebra, look at the
pictures or do an experiment: go to the beach, construct a cone with sand,
then cut it with some foil or something (pardon my English), and see what
you get: it is not an oval, it is an ellipse... And here are a couple of nice
pictures, from WP's articles:
<https://en.wikipedia.org/wiki/Conic_section#/media/File:Eccentricity.svg>
<https://en.wikipedia.org/wiki/Apollonius_of_Perga#/media/File:Conic_Sections.svg>

The end of the world begins with Plato-Aristotle, but it took centuries to go
from a deranged philosophy to the total inculture and insanity that we are
down to even the most mundane aspects our lives. indeed you can trust
the Greeks for their geometry/logic, and only the Greeks...

Gottfried Wilhelm Leibniz stated "He who understands Archimedes and
Apollonius will admire less the achievements of the foremost men of
later times."

Julio

[Julio Di Egidio]

On Wednesday, 30 November 2022 at 11:14:36 UTC+1, Julio Di Egidio wrote:
> On Tuesday, 29 November 2022 at 20:21:20 UTC+1, Archimedes Plutonium wrote:
> > On Tuesday, November 29, 2022 at 4:12:58 AM UTC-6, ju...@diegidio.name wrote:
> <snip>

> > Wikipedia is wrong when they say a "ellipse is a oval",
>
> No, they aren't

Eh, I give too many things for granted. I was thinking
and I meant they are not wrong that the slant cut of a
cone is an ellipse. Of course an oval is not an ellipse,
unless one asks the ignorant, the former having only
one axis of symmetry.

Julio

[Timothy Golden]

If you think the inverse of the inverse is bad you should try out the triverse... then you'll be onto the biverse.

[Mostowski Collapse]

If you shift a by t and b by -t then the sum is invariant,
but the difference is not anymore invariant:

a+b = a+t + (b-t)
a-b =\= a+t - (b-t)

This clearly shows that the infinity borderline maybe
1.4...*10^-604 and not just 1.000... *10^-604.

[FromTheRafters]

Julio Di Egidio has brought this to us :

Of course it is easy to find contradictions.

https://www.maa.org/external_archive/joma/Volume8/Kalman/Ellipse1.html

[Mostowski Collapse]

Typical application of the (t,-t) invariant. Stretching
a circle into an ellipse. On both sides of a diameter,
the circle satisfies, taking x1 negative on the left side,

and x2 positive on the right side, diameter goes through zero:

x2 + x1 = 0

If you stretch it into an ellipse, you need t stretch,
depending on y, x1 by -t and x2 by t:

(x2+t) + (x1-t) = 0

Now multiplication has an interesting property, if
the stretching factor is r, then since multiplication
preserves sign, we get for t=r*x2-x2, and since

x2=-x1, we also have -t=r*x1+x1, and therefore:

r*x2 + r*x1 = 0

This clearly shows again that Archimedes Plutions

infinity borderline maybe 1.4...*10^-604 and not just
1.000... *10^-604.

https://www.maa.org/external_archive/joma/Volume8/Kalman/Ellipse2.html

[Julio Di Egidio]

There is no contradiction: an ellipse is an oval in the same sense
in which a circle is an ellipse, but an oval is not an ellipse any more
than an ellipse is a circle... Words mean what they mean.

Julio

[Mostowski Collapse]

Thats a quite different statement "an ellipse is an oval",
and this statement here:

AP's Proof-Ellipse was never a Conic Section

[Archimedes Plutonium]

Hi, Julio, rarely are you wrong, but in this instance you are. The axis of a cone does not shift to a focus in a slant cut.

And the Ancient Greeks were **exceptional geniuses in science** we both agree on that, however they did make some mistakes and Apollonius slant cut in cone is one such mistake.

A proof is simple-- cone and oval have 1 axis of symmetry, a ellipse requires 2, and so a slant cut in cone is oval.

But another argument is likely even easier to make, for a cone is vastly different in geometry to a cylinder. Even High School kids can see they are vastly different. So we cannot expect a slant cut in cone to deliver a ellipse when a slant cut in cylinder assuredly delivers a ellipse.

I do not know where they screwed up on the Dandelin ordeal and mega-mistake. And that Dandelin stuff shows one that if you assume a falsehood-- the cut is a ellipse-- that it can deliver any fake result you so desire.

I do not know how Apollonius never reviewed the cylinder cuts. I am told that in Ancient Greek times, the academicians rarely soiled their hands in hands on experiment. Maybe that was the case in conics, they imagined it all, and never gave hands on demonstration. No, I do not use a sand pit but better a paper cone of a magazine cover and a Kerr or Ball lid and shows me that the lower portion of the circle is augmented with a vastly larger crescent area than near the apex entry. This is a proof that the Oval is the slant cut.

[Mostowski Collapse]

You forgot to insert the word "wrong":

> A simply wrong proof is -- cone and oval have 1 axis of

> symmetry, a ellipse requires 2, and so a slant cut in cone is oval.

https://en.wikipedia.org/wiki/Ellipse#/media/File:Ellipse-conic.svg

[Julio Di Egidio]

On Thursday, 1 December 2022 at 09:58:31 UTC+1, Mostowski Collapse wrote:

> You forgot to insert the word "wrong":

While you are a retarded piece of shit converted just polluter of ponds.

Congratulations.

*Troll alert*

Julio

[Julio Di Egidio]

On Thursday, 1 December 2022 at 08:42:12 UTC+1, Archimedes Plutonium wrote:

> Hi, Julio, rarely are you wrong,

I have never shied way from mistakes, my own
and not only, since that is where we actually
learn something new. A long story in itself...

> but in this instance you are. The axis of a cone does not shift to a focus in a slant cut.

That is not what I said: it is not the axis of the
cone that shits, it is the second focus of the
ellipse that, the more we slant the cut, shifts
away from the focus that stays coincident to
the cone's central axis.

> And the Ancient Greeks were **exceptional geniuses in science** we both agree on that,

It is rather we who are exceptionally deranged:
the western civilization overall remains the
beginning of the end (of a huge cycle, if you
believe in that kind of stuff: nothing ever ends
really, not even this ridiculous tragedy).

> Apollonius slant cut in cone is one such mistake.
>
> A proof is simple-- cone and oval have 1 axis of
> symmetry, a ellipse requires 2, and so a slant cut in cone is oval.

I am sorry but your argument is wrong, rather
look at the cone right from above: then e.g. a
right cone has exactly the same symmetries
as a circle.

I remember it was counter-intuitive the first
time I have seen it, but you are simply refusing
to look at all the evidence and demonstrations,
nor will you do a sand experiment or similar:
and there I see you stuck into never admitting
even a minor mistake on your part, which
might even be understandable given the
systematic personal attacks you have endure
around here, but it is also the end of science.

My 2c. Take care.

Julio

[FromTheRafters]

To some, an ellipse is a special case of oval just like a square is a
special case of rectangle and a circle is a special case of ellipse.

Mostowski Collapse pretended :

[sobriquet]

Geogebra has some interactive visualizations..

https://www.geogebra.org/m/sQu4Zfsd

That might clarify things a bit, because it's hard to describe
such complicated and dynamic geometric 3D constructions
in words.
(It might also help to modify such visualizations so you
can see them both in 3D and in 2D side by side to verify
claims about the shape of the intersection).

[Mostowski Collapse]

I didn't object on that, the difference between the two statements is:

"an ellipse is an oval" ---> True
"Ellipse was never a Conic Section" --> False

[sobriquet]

https://www.geogebra.org/m/zHqf8Ghq

[Timothy Golden]

In some regards the cone is a ray-based device. If it were real-based you'd have a double cone. I do think it is wise to consider your cone unfolding from the raw ray. You could sort of entertain a noisy ray and you'd get a series of cones. What I find most fascinating is that the upper angle is nonexistent. It does not actually end at 2pi. This is provable by actual paper construction. simply mark the center of two pieces of paper and make a cut into this center from the edge; one cut per piece of paper. Now tape those two together and you'll have a 4pi cone; a biplane, so to speak. The concept of building spaces from naught is pertinent to cosmology which claims observable support for exactly the same.

[FredJeffries]

On Wednesday, November 30, 2022 at 2:14:36 AM UTC-8, ju...@diegidio.name wrote:

> No, they aren't, the point being, you can trust Apollonius. Maybe notice that
> in the slant cut of a cone, the central axis passes by one of the foci of the
> ellipse, not its center.

No. The central axis of the cone doesn't pass through either focus of the (non-circle) ellipse.

https://math.stackexchange.com/questions/1332189/questions-on-the-relation-of-the-axis-of-a-cone-to-its-conic-sections

https://infinityisreallybig.com/2019/02/08/why-does-slicing-a-cone-give-an-ellipse/

[FredJeffries]

Additional reference:

https://en.wikipedia.org/wiki/Dandelin_spheres

[Julio Di Egidio]

Ouch, I stand corrected: thank you.

Julio

[Julio Di Egidio]

On Thursday, 1 December 2022 at 14:47:03 UTC+1, sobriquet wrote:
> On Thursday, December 1, 2022 at 11:03:00 AM UTC+1, ju...@diegidio.name wrote:

> Geogebra has some interactive visualizations..
>
> https://www.geogebra.org/m/sQu4Zfsd
>
> That might clarify things a bit,

You need algebra to build those simulation, so
trusting those is actually trusting your algebra,
which is altogether of a different quality than
a geometric/logical argument...

Julio

[sobriquet]

It's equivalent. For instance, any straight line in geometry with slope A and y-intercept B corresponds to an equation in algebra y=Ax+B and vice versa.
How would you even come up with the concept of an ellipse in geometry without any associated algebra?
An ellipse is defined by an algebraic equation.
https://en.wikipedia.org/wiki/Ellipse
"In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant."

It involves a sum and a sum is not a geometric but an algebraic concept.

[sobriquet]

On Thursday, December 1, 2022 at 9:08:10 PM UTC+1, ju...@diegidio.name wrote:

In fact, you don't even need algebra.. you can create and manipulate the geometric
elements directly (though of course there is the associated algebra behind the
scenes).

https://imgur.com/a/gqenX8h

[Julio Di Egidio]

On Thursday, 1 December 2022 at 21:38:37 UTC+1, sobriquet wrote:
> On Thursday, December 1, 2022 at 9:08:10 PM UTC+1, ju...@diegidio.name wrote:
> > On Thursday, 1 December 2022 at 14:47:03 UTC+1, sobriquet wrote:
> > > On Thursday, December 1, 2022 at 11:03:00 AM UTC+1, ju...@diegidio.name wrote:
> >
> > > Geogebra has some interactive visualizations..
> > >
> > > https://www.geogebra.org/m/sQu4Zfsd
> > >
> > > That might clarify things a bit,
>
> > You need algebra to build those simulation, so
> > trusting those is actually trusting your algebra,
> > which is altogether of a different quality than
> > a geometric/logical argument...
>

> It's equivalent.

Which is like saying that logic is equivalent to
mathematics, after which I should say good
luck to you sir...

Of course logic is not mathematics. Unless you
ask Hilbert in spite of Goedel. Indeed "Euclidean
geometry is a mathematical system", courtesy
WP, is simply *false*, to say it is not easy to find
links on what *logic* or the geometric methods
of Euclid and postera actually are all about, and
as opposed to mathematics in particular. I was
thought that stuff in secondary school, but it
was Italy, and literally last century.

For one thing, maybe notice that we are not only
talking of the trust in the faithfulness of the
translation of the problem into a mathematical
formula, and the inverse translation of the
mathematical result to a solution to the problem,
we must also trust that algebraic manipulations
in-between preserve whatever meaning and
substance we are hoping they preserve. And,
courtesy GIT and co, we should even know that
is not a problem that mathematics can solve.

"The unreasonable effectiveness of mathematics"
indeed is so only for those who literally don't know
what they are talking about. Or prefer not to.

HTH,

Julio

[Archimedes Plutonium]

Sorry, Julio, but include Logic within your argument. Include Logic and then you are caught wrong argument for both the cylinder and cone have slant cuts of an ellipse, and that simply cannot be true. It is like saying cylinder and cone are identical geometrical objects, when obviously they are two vastly different objects.

Anyone who does not like my axes argument cone and oval = 1 axis of symmetry. Cylinder and ellipse = 2 axes of symmetry. Can simply, using logic see that the upper entry in Cone /\ on side nearest apex will have less area then the plane cut on exiting the cone. The entry near apex has less area, has a shorter distance to the center of cone while the exiting plane has a longer distance. This asymmetry of distance length is found in all Cone cuts, but never in the cylinder slant cut. Apollonius was wrong, and all who take sides with Apollonius are wrong. Why was he wrong??? I do not know, did he never play around with the cylinder?? Did he never construct a hands on cone or cylinder???

> I remember it was counter-intuitive the first
> time I have seen it, but you are simply refusing
> to look at all the evidence and demonstrations,
> nor will you do a sand experiment or similar:
> and there I see you stuck into never admitting
> even a minor mistake on your part, which
> might even be understandable given the
> systematic personal attacks you have endure
> around here, but it is also the end of science.
>
> My 2c. Take care.
>
> Julio

There is no counterintuitive in any of this. Even High School students can read this diagram and realize slant cut of cone cannot be a ellipse.

The side view of a cylinder is this

|    |
|    |
|    |

That allows cE to be the same distance as cF


But the side view of the cone is

     /\E
    /c \
F /     \


The distance c to E is shorter because the slant of the side walls of the cone are in the direction of shortening cE, whereas the slant opposite c in cF makes that distance larger than cE.

  The above is a view of a ellipse with center c and is produced by the
  Sectioning of a Cylinder as long as the cut is not perpendicular to
  the base, and as long as the cut involves two points not larger than
  the height of the cylinder walls. What we want to prove is that the
  cut is always a ellipse, which is a plane figure of two axes of
  symmetry with a Major Axis and Minor Axis and center at c.
 
  Side view of Cylinder EGFH above with entry point cut at E and exit
  point cut at F and where c denotes the central axis of the cylinder
  and where x denotes a circle at c parallel with the base-circle of
  cylinder
 
  |                              |
  |                              | E
  |                              |
  |                              |
  |x            c              |x
  |                              |
  |                              |
  |                              |
  |F                            |
  |                              |
  |                              |
  |                              |
 
 

So we can see that the distance cE = cF in cylinder for the walls are Parallel to one another, giving distance symmetry.

But in the Cone, the walls are not parallel, shortening the distance cE compared to cF. Leaving only one axis of symmetry that of EF. The oval is the conic section of a cut at a slant, while the cylinder cut at a slant is a ellipse. The Oval has just one axis of symmetry.

AP

[sobriquet]

We still don't really know what mathematics is and how it
relates to the rest of the universe.
Colloquially speaking mathematics is the most versatile and
universal conceptual framework to process information and
provides the conceptual underpinnings of science.
But in the last century science has uncovered aspects of reality
that have completely overturned any traditional philosophical
notions we had about reality and undermined even the most
fundamental concepts (like the framework of time and space and
the nature of reality or information itself).
It seem categorical approaches (rather than logical or set-theoretic)
are most promising at the moment to provide a unified conceptual
framework for mathematics.
https://www.youtube.com/watch?v=eXBwU9ieLL0

Humanity as a whole as an information processing system might
soon be augmented or even superseded by AI systems that shift
consciousness to levels way beyond what we can currently
fathom.

[Ross A. Finlayson]

https://simple.wikipedia.org/wiki/Mathematics

[Julio Di Egidio]

On Thursday, 1 December 2022 at 22:51:46 UTC+1, sobriquet wrote:
> On Thursday, December 1, 2022 at 10:20:09 PM UTC+1, ju...@diegidio.name wrote:

> > "The unreasonable effectiveness of mathematics"
> > indeed is so only for those who literally don't know
> > what they are talking about. Or prefer not to.
>

> We still don't really know what mathematics is and how it
> relates to the rest of the universe.

That is rather the unreasonable retardedness of most people...
which is also not unreasonable at all, you retarded twisted
fucks are not even good anymore to grow potato, so out of
desperation for your utter insignificance and impotence, you
shout it by flooding all channels and with just retarded
bullshit, and in so doing you are being the perfect tools of
the very abysmally retarded empire that you are...

TL;DR Go fuck yourself, you ungrateful retarded cunt.

Julio

[Timothy Golden]

Here the polysign numbers step in, for just a moment, and expose that the standing mathematics acts as a fraud that trains the mind upon orthogonality as essential and indistinguishable from independence; as if copies of the same set are not the same set. We have to admit that starting from naught we construct out of thin air, and that humans habituate even without any curriculum. With an enforced curriculum of course this phenomenon exceeds the natural effect (affect? defect.)

That time is unidirectional obviates the bidirectional real line as its representative. That one-signed numbers portray the geometry of time is beyond refutation... once you actually generalize sign. Anyone can do it. I simply happen to be one of the first to do it. There are no mistakes to be made really. I shouldn't even give it away for the joy of discovery then is not yours to have. Still, this is the way of the ages, and few to none have rediscovered Newton's law of gravitation or Maxwell's equations, or even Pythagoras's work on the right triangle. So to generalize sign let's start by pondering what a three-signed system would look like. The two-signed system obeys -1+1=0, and so the three-signed system obeys -1+1*1=0. That is the key. Spacetime support is not far away. The sum, the product; the geometry; the algebra... it's all here waiting for you. In hindsight the notion of a basis as empirical versus theoretical is worthy of discussion. Only in hindsight does the latter arrive. We understand that it has not been achieved by the modern academic system; not even through the excruciating freedoms gained in string theory has it been done. And now none will flock to polysign? What gives? Polysign numbers are very likable and can stand freely on their own without me at their helm, which I suppose is part of the problem.

[Ross A. Finlayson]

There's "ubiquitous success of mathematics in science", ....

[Julio Di Egidio]

On Friday, 2 December 2022 at 15:19:43 UTC+1, timba...@gmail.com wrote:

> In hindsight the notion of a basis as empirical versus
> theoretical is worthy of discussion.

There is not just the empirical vs the plain made up,
which is yet another plato-physicism. It's the *logical*
as the connective and justification of it all that has
been obliterated.

> And now none will flock to polysign?

Besides that I cringe at the idea of "flocking", but that
must be me: I have meanwhile totally bought into so
called Geometric Algebra. How elegant it is and how
many problems it solves(!):
<https://en.wikipedia.org/wiki/Geometric_algebra>

So, why polysign?

Julio

[Ross A. Finlayson]

Usually the same reason mountaineers give.

[Timothy Golden]

I once wrote a thread titled "give wedge products the wedgie they deserve", as I recall based on an analysis of the unit wedge vector, but I do see the new interpretations that put it all together. It appears very promising, if I could just wrap my head around it. Still, it's not as if they derive the real number and the complex number from the same ruleset, which polysign naturally yields the siblings P2 and P3 (real and complex, though the format is three-signed), and the only reason I broke in on this was the mention of space and time, and P1 clearly have time correspondence, which P2 lack, as if something bidirectional will stand in for something that is unidirectional. Treating the real value as fundamental has led math and physics down the wrong path. The progression P1P2P3|P45... has this breakpoint built into it which allows polysign to claim spacetime support... all from pure arithmetic. Lastly I think the concept of a basis and its correspondence to physics or reality is apt, and as to whether this former concept must be pure math: a sort of pure philosophy is found here which exposes what a fraud the modern viewpoint is. Pulling dimensions out of a hat is not just what string theorists have done; it is what standard physics has done as well. Yes, there is correspondence, but no; there is no theory that supported three dimensional space and time, and in this way all theory rests upon an empirical basis. This situation puts a logical foot in your mouth rather early in the process, and it is one that is lived with, without ever questioning the situation, for if one does pass through the ideal logic then the answer was that physics is still lost... only barely on its way to being found. Whether atomic theory could even enter into this situation: yes, it could, and this would be ideal philosophy, but that hope is quashed so early on in empiricism, and still a long way off from my shoes, but we've been blindsided by empirical physics. Clearly the experimentalist has the upper hand; claiming a sort of sight that operates tangentially. At some level the problem exists as a human problem: given the momentum that a potentially incorrect system has, to what degree can it self-correct? Claims that falsification is available are not proving accurate... in the human form. In other words humans are habituated and will never see the falsification; their beliefs have been enforced under threat of failure, so the curricular activities do enter into this poor situation as well. Every time I present the thermodynamic problem of slow heat conduction in a solid; a supposedly kinetic activity that completely lacks correspondence, especially in a crystalline solid; clearly there is a heat reservoir that is only loosely coupled, and the ability of physics to overlook such a simple problem is striking the pose that I've just portrayed.

[Julio Di Egidio]

On Sunday, 4 December 2022 at 16:03:12 UTC+1, timba...@gmail.com wrote:
> On Saturday, December 3, 2022 at 6:40:27 AM UTC-5, ju...@diegidio.name wrote:

<snipped>

> > I have meanwhile totally bought into so
> > called Geometric Algebra. How elegant it is and how
> > many problems it solves(!):
> > <https://en.wikipedia.org/wiki/Geometric_algebra>
> >
> > So, why polysign?
>

> I once wrote a thread titled "give wedge products the wedgie
> they deserve", as I recall based on an analysis of the unit
> wedge vector, but I do see the new interpretations that put
> it all together. It appears very promising, if I could just
> wrap my head around it.

Eh, c'mon... I just do not have the time to pursue all that
is interesting, but I remember something about Polysigned
being equivalent to Simplicial sets, which is a huge and rich
topic in itself, again up to physical models. Would be nice
to see what GA and Poly can say to/with each other.

> Still, it's not as if they derive the real number and the
> complex number from the same ruleset,

Yes, scalars and vectors are primitive, but later reabsorbed
to objects in the theory. I should ponder whether that is
purely a necessary accident of formalization, or there is
really something fundamental/substantial about it.

> Treating the real value as fundamental has led math and
> physics down the wrong path.

The idea of _continuity_ is not dispensable with: I mean,
whatever the problems are with *standard* infinities and
the *standard* real numbers, which is a separate issue.

> all from pure arithmetic.

All of the above from pure (geometric) algebra.

> This situation puts a logical foot in your mouth rather

Where, with all due respect, you are still simply
echoing the usual plato-physicism, indeed with all
its inconsistencies and/for its abuses... Not only
logic has been obliterated: as hinted at upthread,
philosophy was killed first and foremost, and any
chance of reasonable judgment with it.
<https://web.maths.unsw.edu.au/~jim/williams.html>

Julio

[Timothy Golden]

Well, and the accumulation of it all now is a thick deep stack. The idea that a noob would have to digest all that is totally unreasonable.
The cull begins... based on current behavior the American version of truth is out the window and they will continue to put science behind paywalls and continue to insert false stories into that accumulation when the need arises. I cannot believe that all who have access feel pleased about the current position. Journalists must be feeling their hearts wearing out. Scientists must be looking back at the false stories trying to make up the difference, and it adds up to no good over here. As we land in a grand reset situation it's more than a politician's problem. Especially in science we have to somehow face the problem of tolerance to new ideas, old ideas, bad ideas, and good ideas versus the culling of them. Within mathematics the sense of perfection of the standing system is overbearing. Within physics the level of regurgitant that is required to rise in the ranks may be way more than will allow for a breakthrough. I think Williams needs to allow for man at far lower stature in the universe than much of philosophy allows for. Then we admit that we are caught in a progression; one that has already taken some wrong turns and which does not readily come undone. Human habituation is largely to blame here. The human as programmable by society is operant here. This is unspeakable and worthy of censorship to those who believe that consciousness is untouchable. Getting back to the ground level however we could certainly arrive at firm footing here. That we start from naught, and that the level of progress per human is only slight; this is our actual situation. Sitting up on a bad stack and never looking back is the superior academic position; the one of entitlement. Simplicity lays elsewhere.

I do approve of the idea of getting polysign and geometric algebra together. In fact the very terminology as taken is a disappointment to polysign, whose properties are algebraic and geometric. The very geometry of the real line, which modern math builds from is in the heart of polysign, so as I reject the real number as fundamental, it is still true that the heart of the real number remains in polysign as P2; yet that heart yields P3, P4, and so on as well; and that obnoxious underling P1!

That all of these are algebraically behaved with the dictated geometry of the simplex (though this is not quite accurate, for the simplex is a frame that we do not require; it is merely the n-rays that are needed, which sum to naught.) exposes the Cartesian product as optional. Yet still some puzzle remains. In total polysign yields:
P1 P2 P3 | P4 P5 P6 ...
and this need not be a Cartesian product since each is unique and can hold its place freely amongst the others. They are siblings rather than rivals. Just as the term 'dimension' suffers a binary requirement does the term 'symmetry' too? No, yet the explanation of such problems can be exposed as embedded in the higher systems. But the logic of a simple basis; one with spacetime support; one that includes the unidirectional nature of time; one that exposes the ray as fundamental over the line; these are qualities that polysign emits.

The levels of correction that polysign expose go back through much of mathematics and subtle shifts do occur. A simple 'for instance' of the six directions of space, which in polysign can be done in four directions via P4. This is unacceptable to the mind that is trained on the Cartesian basis. The Cartesian basis will not go away, and they will insist that there were eight directions in P4, and yet we got their by generalizing sign; not by reusing it that way. This is a great instance of a human mis-step: the overlooking of an option by so many greats that it seems inexplicable; only to be found by an underling who can barely attribute his good luck.

Beyond emergent spacetime support it does look as if the polysign progression does support electromagnetism as well. I have seen the amazing coherence in geometric algebra of electromagnetism being recovered but certainly have not mastered it myself. As well there is an overlap where older 6D theories come into the picture. Whereas one might claim that P1P2P3 is a sufficient spacetime support, one may as well consider that P1P2P3P4 yields another (6D) form that has a structure which includes a pure 3D space rather than a structured 3D space. In effect the P2 and the P3 come into question since P1P4 carries enough correspondence for spacetime. Maxwell did originally claim magnetism to be a sort of space. These interdimensional forms are not at all easy to work on, but polysign does provide them with ease. All that is required is authentically generalizing sign, which is a pure mathematical concept. The possibility of a purely mathematical basis then is available but goes ignored this day.

[Julio Di Egidio]

On Tuesday, 6 December 2022 at 17:10:33 UTC+1, timba...@gmail.com wrote:
> On Monday, December 5, 2022 at 6:47:53 AM UTC-5, ju...@diegidio.name wrote:

<snipped>

> > is interesting, but I remember something about Polysigned
> > being equivalent to Simplicial sets, which is a huge and rich
> > topic in itself, again up to physical models. Would be nice
> > to see what GA and Poly can say to/with each other.

> Scientists must be looking back at the false stories trying to
> make up the difference, and it adds up to no good over here.

If "scientists", the unwilling priests of our time, learned
more than just the "natural" sciences, they would rather know,
among other things, that *all news is intrinsically false by
construction*, and how that is.

(What people generally do not realise is that the powers that
be keep for themselves the good science and are systematically
using it, in reverse...)

> Within mathematics the sense of perfection of the standing
> system is overbearing.

Eh, overbearing is only the violence that guarantees that
fraud. But let me not belabour too much on that topic,
suffice to say we are indeed in a global war, yet again.

> I think Williams needs to allow for man at far lower stature in
> the universe than much of philosophy allows for.

No, the philosopher is properly addressing the higher man
*in each and everyone of us* and, in this case, telling him
(or her): where the fuck are *you* in all this??

> The human as programmable by society is operant here. This is
> unspeakable and worthy of censorship to those who believe that
> consciousness is untouchable. Getting back to the

O. Murray, The Greek City: From Homer to Alexander, where,
among many other things political, we can learn (if we can
read) how our notion of "democracy" is the very fraud and
inversion of all true fundamental principles and practices
of democracy.

> Yet still some puzzle remains. In total polysign yields:
> P1 P2 P3 | P4 P5 P6 ...

An interesting arithmo-geometric puzzle indeed...

> one that exposes the ray as fundamental over the line

Yes, or the naturals over the integers... I too keep
finding the ray as most fundamental in most places:
e.g., after all, what is a vector if not already a ray?

> All that is required is authentically generalizing sign,
> which is a pure mathematical concept.

My possibly naive hunch is that GA happens over a field,
and that field could be Polysigned... But I won't be
speculating any more about it until I find a workable
formal system to write it in and stop just speculating.

> The possibility of
> a purely mathematical basis then is available but goes
> ignored this day.

But the very opposite is true: logic has been obliterated
and what we globally have is the triumph of the lying with
numbers. (As far as what we are talking about is concerned:
of course there is more and even worse than just that to
the global situation.)

Anyway, that much as for my science. (I start owing to
myself at least that much.) Thank you for your ideas and
feedback and let's keep in touch.

Julio

[Ross A. Finlayson]

It's encouraging you've so recently discovered these things.

[Timothy Golden]

I am not a Jordan Peterson fan, but his guest here is new to me and goes right down the alley of discussion:
https://www.youtube.com/watch?v=FEh5JyZC218&t=1h13m

Anyway, I don't think much of field theory, and it does tie back to your OP here.
Some of it arguably stems from polysign notation, but I don't mean to push that here.
The issue is logically distinct and has to do with operators versus values.
As we take the '+' sign to mean both the operator summation as well as a prefix to a value a logically conflicted notation arises which mixes the meaning of operator and value, and we can expose many such confusions in modern mathematics. Likewise, you puzzle over subtraction in the OP, yet what is subtraction but the inverse operator of summation? This fact of existence of inverse operators comes with the awareness of their lack of commutative ability, which the forward operators did have. This is true of both the sum and the product. Lo and behold Abstract Algebra (AA) does affirm this and leaves out analysis of the inverse operators. It turns out that these inverse operators are not universally available... nor are they necessarily simple. In the case of subtraction, should an additive inverse exist, then all is well, and so it seems easily dismissed, yet then is subtraction really an operator at all? Since it will be defined by the sum it seems much wiser and simpler to regard the sum as supreme and along with it comes quite a lot that is supreme such as the integral and the sigma notation; along with reality itself, where we see objects are superposed with each other and universally so.

This distinction between operator and value is really of great significance. A choice to draw a hard line here puts things like the square root of two in a nonfundamental position, whereas standard real analysis builds a numerical branch of the real number around this concept. The whole idea that a pure and fundamental number would have such sects built into it is obnoxious by today's structured thinking. This step is quite easy, yet what follows next is quite a bit more difficult to swallow: the rational value is as well compromised.

[Julio Di Egidio]

On Wednesday, 7 December 2022 at 16:01:07 UTC+1, timba...@gmail.com wrote:
> On Wednesday, December 7, 2022 at 7:47:18 AM UTC-5, ju...@diegidio.name wrote:
> > On Tuesday, 6 December 2022 at 17:10:33 UTC+1, timba...@gmail.com wrote:

<snip>

> > > The possibility of
> > > a purely mathematical basis then is available but goes
> > > ignored this day.
> >
> > But the very opposite is true: logic has been obliterated
> > and what we globally have is the triumph of the lying with
> > numbers. (As far as what we are talking about is concerned:
> > of course there is more and even worse than just that to
> > the global situation.)
> >
> > Anyway, that much as for my science. (I start owing to
> > myself at least that much.) Thank you for your ideas and
> > feedback and let's keep in touch.
>

> I am not a Jordan Peterson fan, but his guest here is new to me
> and goes right down the alley of discussion:
> https://www.youtube.com/watch?v=FEh5JyZC218&t=1h13m

Where we still see the tyranny of self-referencing utter cluelessness,
to put it charitably.

> Anyway, I don't think much of field theory, and it does tie back to your OP here.
> Some of it arguably stems from polysign notation, but I don't mean to push that here.
> The issue is logically distinct and has to do with operators versus values.

But indeed scalars vs vectors in other places and in so many places.
And that's where, if there is something useful with Polysigned, I guess
it's in the arithmetic, the numbers and numerics, not the algebra.

> subtraction, should an additive inverse exist, then all is well, and so it seems easily dismissed, yet then is subtraction really an operator at all? Since it will be defined by the sum it seems much wiser and simpler to regard the sum as supreme and along with it comes quite a lot that is supreme such as the integral and the sigma notation; along with reality itself, where we see objects are superposed with each other and universally so.

Besides that, at least in numbers, it's subtraction, i.e. difference, that is
more fundamental (and predecessor over successor), as well as the
notion of divisibility over that of product. But, overall, that is yet another
fallacious reductionism, what is really fundamental is *duality* (Yin and
Yang, man)... but the globalized man just can't look past its own nose.

> A choice to draw a hard line here puts things like the square root of two in a nonfundamental position

Which is an utter and fundamental mistake, then the standard fraud,
that of pretending that we can get anything infinite without limits, i.e.
without some primitive infinity to begin with.

> the rational value is as well compromised.

The *standard* natural numbers are to begin with.

Julio

[Timothy Golden]

On Wednesday, December 7, 2022 at 10:31:45 AM UTC-5, ju...@diegidio.name wrote:
> On Wednesday, 7 December 2022 at 16:01:07 UTC+1, timba...@gmail.com wrote:
> > On Wednesday, December 7, 2022 at 7:47:18 AM UTC-5, ju...@diegidio.name wrote:
> > > On Tuesday, 6 December 2022 at 17:10:33 UTC+1, timba...@gmail.com wrote:
> <snip>
> > > > The possibility of
> > > > a purely mathematical basis then is available but goes
> > > > ignored this day.
> > >
> > > But the very opposite is true: logic has been obliterated
> > > and what we globally have is the triumph of the lying with
> > > numbers. (As far as what we are talking about is concerned:
> > > of course there is more and even worse than just that to
> > > the global situation.)
> > >
> > > Anyway, that much as for my science. (I start owing to
> > > myself at least that much.) Thank you for your ideas and
> > > feedback and let's keep in touch.
> >
> > I am not a Jordan Peterson fan, but his guest here is new to me
> > and goes right down the alley of discussion:
> > https://www.youtube.com/watch?v=FEh5JyZC218&t=1h13m
> Where we still see the tyranny of self-referencing utter cluelessness,
> to put it charitably.

I'll have to be honest with you: I'm looking into Matt Ridley as a fraud right now.
The interview is a bit too clean, isn't it? One who is plain spoken is not generally quite so well spoken.
Of course I take Peterson as a fraud already, but as I see it his followers here are brought right up to the line of enlightenment.
The problem lays mainly in the entrainment of the two horse race that continues to go on in our media. Free thought leads elsewhere with at least one other option that is undiscussable. So these figures have really raised the quality of the game, eh? Not so fast.
Ridley is portrayed as Pinker cutout on his own website. I have to say I like the guy and his statements, but these days my scrutiny and skepticism leads the way. I do not have any extensive proof, and probably never will, but the agglomeration of details often enough tells of diversionary tactics. Here: https://www.pnas.org/doi/10.1073/pnas.2214427119 we see a doubling down from one of the originators of the natural origin thesis. For the moment pnas is down here, as I try to dig back a little farther.

> > Anyway, I don't think much of field theory, and it does tie back to your OP here.
> > Some of it arguably stems from polysign notation, but I don't mean to push that here.
> > The issue is logically distinct and has to do with operators versus values.
> But indeed scalars vs vectors in other places and in so many places.
> And that's where, if there is something useful with Polysigned, I guess
> it's in the arithmetic, the numbers and numerics, not the algebra.
> > subtraction, should an additive inverse exist, then all is well, and so it seems easily dismissed, yet then is subtraction really an operator at all? Since it will be defined by the sum it seems much wiser and simpler to regard the sum as supreme and along with it comes quite a lot that is supreme such as the integral and the sigma notation; along with reality itself, where we see objects are superposed with each other and universally so.
> Besides that, at least in numbers, it's subtraction, i.e. difference, that is
> more fundamental (and predecessor over successor), as well as the
> notion of divisibility over that of product. But, overall, that is yet another
> fallacious reductionism, what is really fundamental is *duality* (Yin and
> Yang, man)... but the globalized man just can't look past its own nose.

No, I'm sorry. This is an inauthentic fend away from obvious and simple logic.
The logical consequences of rejecting the rational value as fundamental do not actually go so far as you might think.
The decimal point as an indicator of unity in an otherwise natural values system holds up just fine.
This means, though, that we've added a bit of structure to the type of number that came before. The natural value is devoid of that decimal point. It is discrete in nature, and its form of unity is a basis. Should we opt for a 'u' as unity we can primitively apply a codex to our digits:
1 : u
2 : uu
3 : uuu
and so forth, and sadly what we expose is yet another failed portion of mathematics, for we treat this form of superposition as a product. This is not fail, but it may be a conundrum none the less. On the one hand we might claim that uuu is u in the product form while it is three in the natural superposed form, and then of course the value 111 as one hundred and eleven is as well a superposed form. It's all an aside, honestly, but that when we dig down into fundamentals that we may wind up having to go over our notational system in pursuit of the truth is acceptable imo. As we put the lens upon the operator versus the value then the conflict really ensues. Your own inability to use the language of the operator and the value is indicative of your own commitment to the blurred state that is modern mathematics. Isn't it clear that operators work upon values? That there is a process of evaluation or computation that takes place and that values do not possess these attributes? Then when I build an expression that contains operators clearly something has gone unevaluated and I certainly am not looking at a simple value. The sqrt(2) is one of these. So is three fifths. Plus three is not one of these, but then if you want to treat that plus sign as an operator I might be wrong. So is sign an operator or is it a value? This is the discussion I'd rather be having.

> > A choice to draw a hard line here puts things like the square root of two in a nonfundamental position
> Which is an utter and fundamental mistake, then the standard fraud,
> that of pretending that we can get anything infinite without limits, i.e.
> without some primitive infinity to begin with.
> > the rational value is as well compromised.
> The *standard* natural numbers are to begin with.
>
> Julio

As you have fit in a rejection of the naturals here and infinity all in a quick little paragraph that is all quite some cud you are chewing.
How are the *standard* natural numbers compromised? By the ellipses? 1,2,3,...
I tend to agree, and that natural analysis on those terms is starkly different from digital analysis on its terms.
Especially in the reach toward the infinite we see that a repetitious digital value in its progression:
3, 33, 333, 3333, ...
reaches so much farther than the natural analysis which has only gotten to four at this stage, that the abysmal growth in its ellipses should hardly be confounded with infinity. Particularly the ability to perform computations on a value such as x=333...33 exposes the problem. And another thing: the b-adic people have it wrong. x*x=111...10888...89; and as well claims that two-aleph is one-aleph do not hold up in this digital analysis. The square of a one-aleph value is a two-aleph value. The product has always been thus: you will need to provide twice as many digits to get your square on. That computability does exist for specific infinite values is a new concept afaict.

[Ross A. Finlayson]

What standard natural numbers?

What if they're always an extension or fragment, the copy of them you intend?

[Julio Di Egidio]

On Wednesday, 7 December 2022 at 19:07:34 UTC+1, timba...@gmail.com wrote:

> As you have fit in a rejection of the naturals here and infinity all in a quick
> little paragraph that is all quite some cud you are chewing.
> How are the *standard* natural numbers compromised? By the ellipses? 1,2,3,...

Jesus Christ, I have been fighting around here for a decade at
least for proper infinities and against a broken standard: calling
me a finitism... what the fuck are you even talking about.

Julio

[Julio Di Egidio]

On Thursday, 1 December 2022 at 22:20:09 UTC+1, Julio Di Egidio wrote:

> Of course logic is not mathematics. Unless you
> ask Hilbert in spite of Goedel. Indeed "Euclidean
> geometry is a mathematical system", courtesy
> WP, is simply *false*, to say it is not easy to find
> links on what *logic* or the geometric methods
> of Euclid and postera actually are all about, and
> as opposed to mathematics in particular.

Here is one, Archimedes and the Law of Lever:

<< Whereas the Newtonian mechanics gives us a
proof, we will see how this proof was presented
first. The proof is by Archimedes. [...]

The answer known to almost all students of physics
is that the products wd and WD should be equal.
Archimedes did not give a proof to this law in this
form. For it is said he would have been offended by
multiplying two entirely different quantities such as
weight and length. The balance is expressed by him
in terms of equality of two proportions W : d = D : w.
The statement is that the weights balance at
distances inversely proportional to their magnitudes.

Archimedes made some assumptions, which were
supposed to be self evident. [...] Archimedes uses
this assumptions to prove propositions which lead
us to the law of the lever. **The point in the proofs
is that the assumptions should not contradict each
other.** >> (emphasis is mine)

<https://damitr.org/2008/08/24/archimedes-and-the-law-of-lever/>

And, for reference, see how that gets typically
reframed, indeed with how cogent an argument...

<https://www.math.nyu.edu/~crorres/Archimedes/Lever/LeverLaw.html>

Julio

[Mostowski Collapse]

> in terms of equality of two proportions W : d = D : w.

You sure?

[Timothy Golden]

Indeed. We are none the wiser in the moment to the man's falsification, but to understand that the establishment of a vague unit, whose application goes so far as to allow a comparison between men and grains of sand, relies upon the sensibility of that unit. To what degree that unit is vague versus precise: this is a reversal to the continuum, and to admit that the continuum came first in sensibility, then to push into the discrete countable form, and yet to overlook the means of counting: this part to me is suspect. If another wise man could sum it up as such in his own terms then we'd be having a discussion rather than an insult contest. The standard natural analysis runs out of numerical glyphs without engaging the radix. That the radix is left out of natural analysis then is a sore spot that nobody will escape. The freedom to pick n, and never actually pick an n: instantiation and the lack thereof are problematic too. Hand the man a bag of bb's and tell him "there's your n, sir." and what, he'll count them out? He's too good for that. Give him a bb counter and we'll see the little wheels go spinning and levers go clicking and popping and whirring about. All that left out of natural analysis, of course.

Julio dumps the leather bag of bb's into the funnel; resets the counting wheels to zero; puts the now empty bag into the machines good sort output; hoping that he's got enough digits cause it's a big bag of bb's... hoping halt at zero is within the counting machine's logic what, so he can count them himself? The human form becomes a mere doorman to the machine.

[Julio Di Egidio]

On Saturday, 10 December 2022 at 15:19:47 UTC+1, timba...@gmail.com wrote:
> On Wednesday, December 7, 2022 at 8:09:44 PM UTC-5, Ross A. Finlayson wrote:
> > On Wednesday, December 7, 2022 at 7:31:45 AM UTC-8, ju...@diegidio.name wrote:
> > > On Wednesday, 7 December 2022 at 16:01:07 UTC+1, timba...@gmail.com wrote:

<snip>

> > > > A choice to draw a hard line here puts things like the square root of two in a nonfundamental position
> > >
> > > Which is an utter and fundamental mistake, then the standard fraud,
> > > that of pretending that we can get anything infinite without limits, i.e.
> > > without some primitive infinity to begin with.
> > >
> > > > the rational value is as well compromised.
> > >
> > > The *standard* natural numbers are to begin with.
> >

> > What standard natural numbers?
> > What if they're always an extension or fragment, the copy of them you intend?
>
> Indeed. We are none the wiser in the moment to the man's falsification,

Mine is to begin with a *construction*. That I have meanwhile to
point out that our standard is fundamentally broken and how, that
is, strictly speaking, just an unfortunate incident.

> that unit is vague versus precise: this is a reversal to the continuum,

Aka, you keep looking the other way.

> Julio dumps the leather bag of bb's into the funnel; resets the counting

[...]

> can count them himself? The human form becomes a mere doorman
> to the machine.

Julio is rather puzzled that you keep putting in his mouth all the opposite
of what he's been saying, here and elsewhere: and I won't add for you if
to just keep distorting. Even less I now feel like trying to explain proper
vs broken infinities, which is something I have been *regularly* talking
about around here *for ages*, and that I am talking about yet again right
now in another thread...

Be serious, man: that's all I am saying, in my poor English.

Julio

[Mostowski Collapse]

Here is a counter model:

w=2 d=6 W=4 D=3

We have:

wd = 2*6 = 12 = 4*3 = WD

But we don't have:

4 : 6 = 3 : 2

Its even not a ratio between same sorts.

[Julio Di Egidio]

On Sunday, 11 December 2022 at 05:44:46 UTC+1, Mostowski Collapse wrote:

> Here is a counter model:

It's just a typo, you other spamming nazi-retard.

*Spammer/troll alert*

Julio

[Ross A. Finlayson]

I've been enjoying your recent style,
I hope it's the result of your own personal
enjoyment of your findings and personal development,
as opposed to feelings from a bottle.


You'd deserve your mathematical self-esteem from
your thoroughness and conscientiousness, earned.

Foundationalists are conscientious formalists 24/7.

[Julio Di Egidio]

On Sunday, 11 December 2022 at 14:27:12 UTC+1, Ross A. Finlayson wrote:
> On Saturday, December 10, 2022 at 6:46:10 AM UTC-8, ju...@diegidio.name wrote:
> > On Saturday, 10 December 2022 at 15:19:47 UTC+1, timba...@gmail.com wrote:

<snip>

> > Be serious, man: that's all I am saying, in my poor English.
>

> I've been enjoying your recent style,
> I hope it's the result of your own personal
> enjoyment of your findings and personal development,
> as opposed to feelings from a bottle.

All and only about "feelings" is yet another side of the
same poisonous coin.

> You'd deserve your mathematical self-esteem from
> your thoroughness and conscientiousness, earned.

The neurotic removal and/or denial...
I am in fact *the sloppiest* of mathematicians and
I am rather explaining *logic* around here and what
to lie with numbers actually means. But no level of
emphasis can anymore breach through the rubber
wall that wraps your skull and soul.

> Foundationalists are conscientious formalists 24/7.

Sure, keep dreaming your inverted dreams...

*Plonk*

Julio

[Ross A. Finlayson]

Ah, but, haven't you, not lied?

Truth is discovered / ....

I enjoy your opinion either way,
usually in terms of its honesty.

[Timothy Golden]

Likewise, I consider Julio to be in the smart bunch here; as if we were in a gradeschool classroom.
I do think he has some wisdom to impart, but I don't see him imparting it at the moment.
We don't seem to be able to coax it out of him, either.
This world is a disappointing place for most of us in the ordinary times say of pre 2016.
Now, with the exposure of just how rigged society is; the possibility that this place, in particular, is not the bastion of free speech that I once thought it was, is looming. The lengths that the deep state has gone to are extraordinary.

I value the presence of Julio here though we may disagree on the mathematics.
I have no recollection of his writings and they are easily lost but as well easily found... one hopes.
As to numbers as lies: In the physical sense every number contains a lie in that it is merely the representative for something else.
One hundred sheep may be in the field, but giving me the number versus giving me the sheep are two different things.
In this way those focused purely on mathematics are a bit gone in my opinion.
Sadly, I can be one of these goners too.
I think the healthy space is to arrive at a sense of unification which does not sequester your spirit to one of the three branches, let's say, of philosophy, physics, or mathematics. That these things are ultimately wrapped up into one thing is the truth of the matter. Sadly as well as we approach these topics as humans practicing them great confounded problems arise. We suffer from the accumulation of the past, and habituation, under threat of failure from academic institutions if we do not mimic; and we pay for it all, too. What a luscious piece of cardboard we are left chewing on; thrilled about the next layer of flavenoids, and now along come polysign numbers to challenge it all. They do in fact challenge much of mathematics and they do so of their own free standing qualities. There is cause to go back and review, and oh, pew! The stench and the drivel and the sects that intersect all the way down through seem confused and ambiguous and that's what we did chew? Did you?

[Julio Di Egidio]

On Sunday, 11 December 2022 at 15:23:32 UTC+1, Ross A. Finlayson wrote:

> Truth is discovered / ....

Truth does not belong to mathematics as even
the mathematician should know. And it is not
discovered anyway, not per chance we are an
inductive civilization "altogether and in principle":
e.g. indeed "induction", as a philosophical then
logical principle, is the very basis for the validity
of the deductive and mathematical methods
(mathematical induction included, should you
wonder).
<https://web.maths.unsw.edu.au/~jim/williams.html>
<P.F. Strawson, Introduction to Logic Theory>

An induction principle not so much justified by
the fact that the Universe does appear rational,
which would be an inductive belief in itself hence
circular, but rather from the purely logical fact
that no other approach to reality yields anything
sensible.

That said, and mainly to the die-hard Platonist:
in terms of the simplest cosmic duality matter-
mind, there is a substrate to mind as there is
one to matter, like fields of potential. But do
not conflate the substrate, i.e. the realm of
"potentially infinite possibilities", with what
we do with it: e.g. "truth", the very notion, as
every notion, is our own invention.

/ Now let me regret that...

Julio

[Timothy Golden]

I have to admit that I had to look up what a Platonist looks like.
How's this for a semiclassical interpretation:
That which is tangible requires adjacency.

When you use the term inductive it may be a bit more strict than I use it as.
If we take the root 'induce' then the connotation of generalization is not so far away.
In that natural valued analysis is n-ary at its heart then the applicability of this n-ary stance could vary more broadly than the natural number allows.
Thus full generality is not so much important at large values but at smaller values, where say for instance humans are locked onto a binary relationship that might exclude the possibility of a trinary relationship. Then too, what of the unitary form?

In terms of thought processing we have to grant ourselves constructive freedom. We are caught in a progression that does not deny the possibility that something quite good has gone overlooked and especially due to academic training is getting filtered out of the possibility space of most who ascribe to a nearly universal curriculum. That certain constructions come out of thin air and then upon exploring them yield physical correspondence... this is the gap between theoretical and empirical work. The two should join, but not too early. The system we have now pulls spacetime out of a hat, and so all work thereupon can be cast into the realm of empirical, but for the fact that many confuse their work with theoretical. If curve fitting is all there is to the theoretical then philosophy be damned... just as the quantum folks would like it to be. Supposedly the quantum gravity people are astutely interested in emergent spacetime, and perhaps there is a cult of them who know of polysign numbers now, but they won't be joining us here any time soon.

The notion that we are humans practicing these things is awfully important. What we see now on the global stage is little better that a tribe of baboons. That this is as well what we witness here on usenet is entirely consistent. The ideals of altruism and integrity do not actually bear out on the human race. Particularly capitalism is bereft of these qualities. That it should not be the final say in global identity I find believable. That it may have its place... but not take the table over... this I find more likable. Meanwhile a curtain of lies which require the populace to line up on one side or the other of a fraud is hardly a meaningful play in any game other than one of pure fiction. It really is a mind numbing process that they have deployed. If only the lies were more carefully constructed at least then we could be cleanly fleeced.

A look at https://en.wikipedia.org/wiki/Induction shows an unusually long list. This is as I suspected and really I think your usage of the term deserves specification beyond the broad usage. Even inside of mathematics I suspect this is true. The inseparability of the ellipsis usage from induction exposes that the ball used across different games. As to which ball you mean or how you hit it I'd say you are still being vague.

I've found a very simple usage in that 4, 44, 444, 4444 are getting to infinity quite rapidly; much faster that the ordinary natural value does. So when I tack the ellipses on the end of that progression, and it is about the simplest progression you could ask for, now setting x=444...44 we have
x*x= (197530864)...1(580246913)...6
and so computability of infinite values can be achieved, but it is only via induction that this can be claimed. In the mathematics application sage I have:
sage: x=444444444
sage: x*x
197530863802469136
sage: x=4444444444
sage: x*x
19753086415802469136
sage:
sage: x=44444444444444444444444444444444444444444444444444444444444444444444444
....: 4444444444444444444444444444444444444444444444444444444444444444444444444
....: 4444444444444444444444444444444444444444444444444444444444444444444444444
....: 4444444444444444444444444444444444444444444444444444444444444444444444444
....: 44444444444444444
sage: x*x
19753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086419753086415802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469136
sage:

There is a bit of slop, but the slop does resolve, so I believe that the claim is true. Some values are easier than others. One thing is for certain: digital inductive infinity gets there far faster than any natural analysis. In that attempts to claim infinity are divergent the most divergent form I suppose wins. Beyond this computability is not such a bad feature. These infinities are just as untouchable yet their multiplicity and their natural form are established, with some backlash onto natural analysis.

The junction of notation and interpretation onto the issues and the usages of terms such as 'induction', along with the realization that we are basically just a bunch of chimps, leaves me trying to be plainspoken, and many in the past did try to go from scratch on their mathematics, and I suppose that is what we ought to be doing here. If we are engaged in a progression then it is by such variations that progress will be made.

In fact I happily can reject the school of thought of infinity. Along with it though goes a bit more. Did your real value have infinite precision? Does this construction have implications on the continuum? How did we get there? Upon generalizing sign it always did feel as though magnitude were next on the chopping block.

[Julio Di Egidio]

> I have to admit that I had to look up what a Platonist looks like.
> How's this for a semiclassical interpretation:
> That which is tangible requires adjacency.

Sure "locality/causality" and yet the same pile of fraudulent
mangled bullshit: physicalism and being unable to see past
that point...

> When you use the term inductive it may be a bit more strict than I use it as.
> If we take the root 'induce' then the connotation of generalization is not so far away.

LOL, the dictionary objection... I said "induction *as a
philosophical then logical principle*" and even what that is,
not just any other use of "induction" by the layman, or by the
physician, or by any Collins... not to mention again the level
of fraud and abuse that is inscribed in our received views,
and how nonsensical anyway is to reinject just the very
things I have been debunking...

Which is really about how to study and think critically: you
guys literally have no clue how to actually read and think.

Seriously.

Julio

[Timothy Golden]

Well, I'll concede that you did qualify it. I'm disappointed you won't criticize my application.
Hey, concessions on usenet are far and few between. This is progress.

[Julio Di Egidio]

On Wednesday, 21 December 2022 at 00:33:16 UTC+1, timba...@gmail.com wrote:
> On Tuesday, December 20, 2022 at 12:53:05 PM UTC-5, ju...@diegidio.name wrote:
> > On Tuesday, 20 December 2022 at 16:26:57 UTC+1, timba...@gmail.com wrote:
> > > On Sunday, December 11, 2022 at 10:01:08 AM UTC-5, ju...@diegidio.name wrote:
> > > > On Sunday, 11 December 2022 at 15:23:32 UTC+1, Ross A. Finlayson wrote:

<snip>

> > > > / Now let me regret that...
> > >
> > > I have to admit that I had to look up what a Platonist looks like.
> > > How's this for a semiclassical interpretation:
> > > That which is tangible requires adjacency.
> >
> > Sure "locality/causality" and yet the same pile of fraudulent
> > mangled bullshit: physicalism and being unable to see past
> > that point...
> >
> > > When you use the term inductive it may be a bit more strict than I use it as.
> > > If we take the root 'induce' then the connotation of generalization is not so far away.
> >
> > LOL, the dictionary objection... I said "induction *as a
> > philosophical then logical principle*" and even what that is,
> > not just any other use of "induction" by the layman, or by the
> > physician, or by any Collins... not to mention again the level
> > of fraud and abuse that is inscribed in our received views,
> > and how nonsensical anyway is to reinject just the very
> > things I have been debunking...
> >
> > Which is really about how to study and think critically: you
> > guys literally have no clue how to actually read and think.
> >
> > Seriously.
>

> Well, I'll concede that you did qualify it. I'm disappointed you
> won't criticize my application. Hey, concessions on usenet are
> far and few between. This is progress.

Your "The inseparability of the ellipsis usage from induction" and
similar amenities only "expose" the fact that you don't know what
you are talking about. And how many times do you want me to
repeat just that??

I just give up on you: you guys are too compromised to even read,
and, what's worse, too hypocritical and vile to ever assume even
just an inch of your own responsibilities...

EOD.

Julio

[Timothy Golden]

Well, I feel very humbled in your presence and no doubt your superiority is well felt throughout the world. The only problem that I see is that without any instantiation there really has been no topic of conversation. As you picked on physicality earlier with dismissal: that I would say is the first order of a staging ground that we build up from. Going then to a level of abstraction arguable we reach the second order of discussion, which is far less tangible than the first. Upon entering the third order I believe the situation is garbage. I do accept that plenty of third order garbage has been produced by the human race. Look at the piles of fiction; it's clearly quite a draw and an efficient escape.

Now I suppose you could argue that a very good piece of fiction is so good as to be indistinguishable from reality, but you see, the valuation implies something quite relevant: without any harkening back to the first order or even the second order the third order is lost. Not even lost in space, for that is harkening back to the first order.

That said this season of depression in the Northern hemisphere must be felt particularly hard this year. The veil of lies that society has been exposed to is boiling over now, and the burns are going to be felt inside and out. Drink it and choke; Push it off the burner and suffer again. Those that live the lies have been living the lies for so long now that they will not necessarily turn back, and so the zombie state has begun. With burned throats and burned hands somehow they carry on. For how long can they though? Numb as a box of rocks is just how they'd like us to be. Here we are on the shortest day of the year. Normally a time to make a happy wish and greeting. Not really feeling it this year though. This new year promises more darkness ahead.

[Timothy Golden]

I found the problem with the value 444...44. To what degree is the ellipsis an operator? Clearly it is! Not only that it is an operator which fails to halt. So, again, the criticism which alleviates the irrational value as a worry thence exposes the fraud of the rational value, goes on to destroy my new form of infinity. All such expressions, and I must use this terminology for the term 'value' is quite specific, as is the term 'operator', and those who wish to blur the two are obviously practicing mathematicians; oh good gravy, have we got to term the new philosophy under a different heading? A fourth branch? No. We just have some very grotesque ambiguities to resolve. What mathematician cannot understand the boundary between an operator and a value? An important blur seems to take place with sign, actually. To what degree is sign an operator or is it a value? Or rather should an instance such as -1.234 be treated as a product? Then the sx form is approached, and those seeking generality will shortly have polysign numbers. Those who restrict sign to a modulo two system are mistaken, and that covers the entire human race but for a few brave souls.

[Julio Di Egidio]

On Thursday, 22 December 2022 at 16:48:21 UTC+1, timba...@gmail.com wrote:

> I found the problem with the value 444...44. To what degree
> is the ellipsis an operator? Clearly it is!

No, the ellipsis in a first instance is just a piece of syntax, it is
up to you/us attaching any operational or other meaning to it.

In fact, it is also the case that in standard mathematics (as well
as in common thinking, which is finitary thinking) all you can say
is "and so on", which is what the ellipsis means in that context,
and you cannot get to talk of the "last digits" of a (standardly)
infinite sequence as there is no such thing as the "last digits"
to begin with: so, again, rather up to you to explain what what
you wrote means and how it is useful.

Julio

[Timothy Golden]

This is very sad analysis on your part, J. The last digits are in fact the first digits in any large value. The fact that we end at the start could be exposed as another ambiguity of mathematics, and that might be quite right, but to admit that values are two sided would not be a bad leap either. Could you ever have a large value without having expressed its lesser digits? Within digital analysis you won't be able to get very far. I am sure that this awareness is only vague to the natural analyst, for their sense of number is a badly neutered thing. Zelensky once played the piano with his dong, you know. And what the natural analysis gets up to with it; just incredible, eh? https://www.youtube.com/watch?v=oua0Puihrkc

[Julio Di Egidio]

On Sunday, 25 December 2022 at 17:06:08 UTC+1, timba...@gmail.com wrote:
> On Thursday, December 22, 2022 at 11:17:56 AM UTC-5, ju...@diegidio.name wrote:
> > On Thursday, 22 December 2022 at 16:48:21 UTC+1, timba...@gmail.com wrote:
> >
> > > I found the problem with the value 444...44. To what degree
> > > is the ellipsis an operator? Clearly it is!
> >
> > No, the ellipsis in a first instance is just a piece of syntax, it is
> > up to you/us attaching any operational or other meaning to it.
> >
> > In fact, it is also the case that in standard mathematics (as well
> > as in common thinking, which is finitary thinking) all you can say
> > is "and so on", which is what the ellipsis means in that context,
> > and you cannot get to talk of the "last digits" of a (standardly)
> > infinite sequence as there is no such thing as the "last digits"
> > to begin with: so, again, rather up to you to explain what what
> > you wrote means and how it is useful.
>

> This is very sad analysis on your part, J. The last digits are in fact the first digits in any large value. The fact that we end at the start could be exposed as another ambiguity of mathematics, and that might be quite right, but to admit that values are two sided would not be a bad leap either. Could you ever have a large value without having expressed its lesser digits? Within digital analysis you won't be able to get very far. I am sure that this awareness is only vague to the natural analyst, for their sense of number is a badly neutered thing. Zelensky once played the piano with his dong, you know. And what the natural analysis gets up to with it; just incredible, eh? https://www.youtube.com/watch?v=oua0Puihrkc

Sad is you, your abysmal ignorance, and even more the vileness
of your mental insanity, you fucking nazi retards...

Get extinguished already.

*Plonk*

Julio

[Timothy Golden]

I could understand a criticism of Quixoticism, say, but naziism is not at all my theme. I don't see nationalism as an answer for anybody. It's everybody's problem, and how far you will go for your nation is a mark of your own nazi meter. Of course these days most are simply doing it for pay; just doing their job, so to say. Possibly even on a need to know basis, which means you don't know shit. Brings a whole new meaning onto operators and values doesn't it? Your lack of mathematical falsification suggests that I am onto something. In terms of pinning the tail on the nazi; I'll just add one simple link from the past: https://www.youtube.com/watch?v=5SBo0akeDMY

In terms of the mathematics we do understand that numbers have a head and a tail, or at least these labels could be meaningfully applied, and that without this order their meaning could be taken either way. With numbers that which matters most is built upon that which matters least. In terms of natural progression it could be said that mathematicians have their numbers backwards notationally. But I'm not really making this claim; simply noting that the situation may have some side-effects. Your own language is falsifiable in this way, as you focus on 'last digits'. Without addressing whether the last digits are in fact the first digits, or the other way around, or back to where you started; we simply land in an ambiguity that continues to go unadressed. That such simple ambiguities can be exposed within mathematics I find interesting.

That the inductive value is available and computable will rely upon this head and tail awareness, for the computations will require such flexibility. Any claim of an infinite value under digital analysis will certainly require that the early digits (the tail) be well specified. That this is consistent with natural analysis, or at least not in conflict with it, is apt, and that these lesser digits, little as they matter, must be present in order that the greater digits can take their places. That all of these may be interconnected like wheels with linkages at the carry or the borrow; this is somewhat the natural perspective of the successor, though it is married to the radix form. It is only by limiting the glyphs and developing the series that number is fully born. It's status is pre-polynomial, yet its roots are common with the latter. Yet what was to be plugged into any polynomial but a number? Well then where the cart is ahead of the horse, you can expect a catastrophe to happen. The bits perhaps should be dismantled and remantled so to speak, and that is roughly what I am trying to do.

Suppose x=333...338 .
x / 2 = 1666...669 .
x * x = 111...114222...2244
and all this done by the simplest of inductive steps. It's almost like there is nothing to do. No decent falsification has landed on this analysis yet. It can be criticized for lack of an aleph mark, and that is a point of interest, but until it is necesary it is somewhat like the zero sign. Yes, it is an important realization, but it can be done without as well for a bit.

In the end I can rest easy letting go of the infinite analysis. Where the game gets even more interesting is where an omega and an aleph lay buried in the beginnings of number theory. These things I don't really even value that much, but there they are in the polynomial form upon disambiguation. Engaging schools of number becomes one option to recohering the mess. That would be the remantling effort to date down low. I'm sure that would be cryptic but to a well read fellow. The structure of the thing is what matters most. A reuse of a lesser concept in a higher concept as if the low level usage never occurred is a sure mistake that I think is best to simply declare as open and gaze upon it as such. Philosophically speaking there is as well a grandiose (quixotic perhaps) notion that a true basis will form. By this I do in fact mean a physical basis. This is how theory was to be done, but in the modern realm so much has been laid over the feet of the empirical in the guise of theoretical that the theoretical lays compromised at every turn. The simple question of what it means to have a basis at all is opened, then. To cower under the accumulation that is present is basically everybody's position. It is too much. To return to the fundamentals; as if RxRxR was any basis at all; to seek emergence down here in the bottom of things would be ideal. Of course polysign have a lot to say through the modulo usage of sign, but they may be but a stepping stone under the rotten bridge.

[Augǝl]

Putting together little facts can produce knowledge, that is beyond belief......




ju...@diegidio.name kirjutas Esmaspäev, 28. november 2022 kl 10:30:44 UTC+2:
> Little facts that make my head spin.
>
> Shifting two numbers by 't' units.
>
> Can you say *why* their sum is not
> translation invariant while their
> difference is? Namely,
>
> a+b = a-(-b) = a-B, yet:
> a+b = (a+t)+(b+t) - 2t
> a-B = (a+t)-(B+t)
>
> Julio

[mitchr...@gmail.com]

How are you a fact maker?
Who made you that?