On Monday, April 25, 2022 at 5:39:32 PM UTC-5, Archimedes Plutonium wrote:
> Alright, so, if we take all of Special Relativity to mean-- it makes no difference if the coil in Faraday law is moving and magnet is stationary or vice versa. Plus the idea that speed of light is a maximum.
>
> So the idea of speed of light a maximum must link up with the idea that there is a maximum finite number-- 1*10^604 where Huygen's tractrix area converges upon the associated circle area. Where pi has 3 zero digits in a row..
>
> So, I have never tried to assemble the speed of light with the number 1*10^604. I may as well get started.
>

This is a good idea to tackle. For the speed of light has all the hallmarks of a boundary line, a borderline between finite and infinite.

So in the Huygens proof of tractrix area under the curve, equals the associated circle area at infinity borderline. That is a geometry example of unbounded in reach, yet finite in area.

Same thing with speed of light-- a maximum speed and no speeds faster allowed.

So what is the connection if any between 1*10^604 and 3.16*10^8 meters/second ?

Well we can consider either 1*10^604 or its algebraic closure of 1*10^1208. With 1208 exponent we see 10^8 divides evenly 1208/8 = 151.

We presume meters is a unique distance measure, and that can easily be supported along with seconds.

Now one of my proofs that infinity borderline was 1*10^604 dealt with the fact that all the regular polyhedra divide evenly into 604.

As I wrote in my TEACHING TRUE MATHEMATICS textbook
-- quoting --
The infinity borderline is derived in two methods, one, by algebra it is derived from where pi digits are evenly divisible by 120=5! = 5x4x3x2x1 and second, is derived from the fact that when pi has its first three zeroes in a row, 10^-601, 10^-602 and 10^-603, place values, and this is where the area of the tractrix equals for the first time, the area of the associated circle, and since Huygens proved the area of tractrix equals associated circle at infinity, we have a borderline.
--- end quote --
How I achieve that borderline from regular polyhedra is the idea that 120 = 5! encompasses all the 6 regular polyhedra (AP found a 6th regular polyhedra in 2021) "The 6th Regular Polyhedron-- hexagonal faces at infinity// Math proof series, book 12"
by Archimedes Plutonium; in that we have even division by 2, by 4 by 6, by 8, by 12, by 20 at the pi digits at the 604th digit being 0.

On Monday, April 25, 2022 at 7:07:16 PM UTC-5, Archimedes Plutonium wrote:
> On Monday, April 25, 2022 at 5:39:32 PM UTC-5, Archimedes Plutonium wrote:
> > Alright, so, if we take all of Special Relativity to mean-- it makes no difference if the coil in Faraday law is moving and magnet is stationary or vice versa. Plus the idea that speed of light is a maximum.
> >
> > So the idea of speed of light a maximum must link up with the idea that there is a maximum finite number-- 1*10^604 where Huygen's tractrix area converges upon the associated circle area. Where pi has 3 zero digits in a row.
> >
> > So, I have never tried to assemble the speed of light with the number 1*10^604. I may as well get started.
> >
> This is a good idea to tackle. For the speed of light has all the hallmarks of a boundary line, a borderline between finite and infinite.
>
> So in the Huygens proof of tractrix area under the curve, equals the associated circle area at infinity borderline. That is a geometry example of unbounded in reach, yet finite in area.
>
> Same thing with speed of light-- a maximum speed and no speeds faster allowed.
>
> So what is the connection if any between 1*10^604 and 3.16*10^8 meters/second ?
>
> Well we can consider either 1*10^604 or its algebraic closure of 1*10^1208. With 1208 exponent we see 10^8 divides evenly 1208/8 = 151.
>
> We presume meters is a unique distance measure, and that can easily be supported along with seconds.
>
> Now one of my proofs that infinity borderline was 1*10^604 dealt with the fact that all the regular polyhedra divide evenly into 604.
>
> As I wrote in my TEACHING TRUE MATHEMATICS textbook
> -- quoting --
> The infinity borderline is derived in two methods, one, by algebra it is derived from where pi digits are evenly divisible by 120=5! = 5x4x3x2x1 and second, is derived from the fact that when pi has its first three zeroes in a row, 10^-601, 10^-602 and 10^-603, place values, and this is where the area of the tractrix equals for the first time, the area of the associated circle, and since Huygens proved the area of tractrix equals associated circle at infinity, we have a borderline.
> --- end quote --
> How I achieve that borderline from regular polyhedra is the idea that 120 = 5! encompasses all the 6 regular polyhedra (AP found a 6th regular polyhedra in 2021) "The 6th Regular Polyhedron-- hexagonal faces at infinity// Math proof series, book 12"
> by Archimedes Plutonium; in that we have even division by 2, by 4 by 6, by 8, by 12, by 20 at the pi digits at the 604th digit being 0.

Looking up Planck's constant and I became fascinated with the fact that 604/ 23 = 26.260869...
and 604/ 26 = 23.230769...

Fascinating.

AP

On Monday, April 25, 2022 at 9:03:52 PM UTC-5, Archimedes Plutonium wrote:
> On Monday, April 25, 2022 at 7:07:16 PM UTC-5, Archimedes Plutonium wrote:
> > On Monday, April 25, 2022 at 5:39:32 PM UTC-5, Archimedes Plutonium wrote:
> > > Alright, so, if we take all of Special Relativity to mean-- it makes no difference if the coil in Faraday law is moving and magnet is stationary or vice versa. Plus the idea that speed of light is a maximum.
> > >
> > > So the idea of speed of light a maximum must link up with the idea that there is a maximum finite number-- 1*10^604 where Huygen's tractrix area converges upon the associated circle area. Where pi has 3 zero digits in a row.
> > >
> > > So, I have never tried to assemble the speed of light with the number 1*10^604. I may as well get started.
> > >
> > This is a good idea to tackle. For the speed of light has all the hallmarks of a boundary line, a borderline between finite and infinite.
> >
> > So in the Huygens proof of tractrix area under the curve, equals the associated circle area at infinity borderline. That is a geometry example of unbounded in reach, yet finite in area.
> >
> > Same thing with speed of light-- a maximum speed and no speeds faster allowed.
> >
> > So what is the connection if any between 1*10^604 and 3.16*10^8 meters/second ?
> >
> > Well we can consider either 1*10^604 or its algebraic closure of 1*10^1208. With 1208 exponent we see 10^8 divides evenly 1208/8 = 151.
> >
> > We presume meters is a unique distance measure, and that can easily be supported along with seconds.
> >
> > Now one of my proofs that infinity borderline was 1*10^604 dealt with the fact that all the regular polyhedra divide evenly into 604.
> >
> > As I wrote in my TEACHING TRUE MATHEMATICS textbook
> > -- quoting --
> > The infinity borderline is derived in two methods, one, by algebra it is derived from where pi digits are evenly divisible by 120=5! = 5x4x3x2x1 and second, is derived from the fact that when pi has its first three zeroes in a row, 10^-601, 10^-602 and 10^-603, place values, and this is where the area of the tractrix equals for the first time, the area of the associated circle, and since Huygens proved the area of tractrix equals associated circle at infinity, we have a borderline.
> > --- end quote --
> > How I achieve that borderline from regular polyhedra is the idea that 120 = 5! encompasses all the 6 regular polyhedra (AP found a 6th regular polyhedra in 2021) "The 6th Regular Polyhedron-- hexagonal faces at infinity// Math proof series, book 12"
> > by Archimedes Plutonium; in that we have even division by 2, by 4 by 6, by 8, by 12, by 20 at the pi digits at the 604th digit being 0.
> Looking up Planck's constant and I became fascinated with the fact that 604/ 23 = 26.260869...
> and 604/ 26 = 23.230769...
>
> Fascinating.
>

So, I am trying to obtain the infinity borderline from that of speed of light constant. The infinity borderline is 1*10^604 from Huygen's tractrix and from AP's regular polyhedra existence coming from 120 = 5! of all possible angles at infinity border represented in the 6 regular polyhedra.

So I notice that 604/23 and 604/26 are connected.

I note that speed of light is 3.16*10^8 meters/second
I note that Planck's constant in ev*Hz^-1 and in eV*seconds is 4.135*10^-15 and 6.582*10^-16eV*second respectively.

So I divide both by 3.16*10^8 and obtain in the first 1*10^-23 and 2*10^-24 in second.

And my interpretation of this is that Planck's constant is the curvature of the front end tip of the closed loop pencil ellipse of the light wave (Planck's constant is not the silly idea of 0.5MeV particle jumping orbits).

And so when I divide the two constants I end up with an exponent between 23 and 26. And my interpretation of that is the idea that the size of the Cosmos at infinity borderline is a sphere of surface area 1*10^604. Physics stops at this surface area borderline of a gigantic sphere.

On Monday, 25 April 2022 at 23:40:24 UTC+2, Archimedes Plutonium wrote:
> On Monday, April 25, 2022 at 8:00:54 AM UTC-5, ju...@diegidio.name wrote:
> > On Monday, 25 April 2022 at 01:00:21 UTC+2, Archimedes Plutonium wrote:
<snipped>

> > > Question please, for Julio.
> >
> > Is that even you? I don't think so, for a couple of years now.
>
> The same person who writes science books.

All right, I suppose that's you. ;)

> > > If all valid and true functions are only Polynomials
> >
> > Would you discard stuff as simple as f(x) = sqrt(x)?
> >
> Yes, that maybe the most simple equation discarded Y = x^-1/2.

You are not just discarding an equation, you are discarding (to begin with) the very possibility that there exists a number representing the ratio of the diagonal of a square to its side: i.e. a perfectly elementary geometric construction for a perfectly elementary mathematical question. (The answer I grant you is not trivial, we immediately get into limits: but even that, if you ask me, is mainly because standard infinity isn't the last natural number...)

> Now can we take the Power Rules to coax out a derivative or integral? Y' = -1/2 (x^-3/2)

Derivatives and integrals are defined in terms of limits, and things like the power "rule" are in fact proven to hold based on that foundation: so, if you discard the foundation, you cannot rely on those "rules". Indeed, a discreet set is not even continuous, and I think that's the keyword: *continuity* and whether a mathematical system can handle it or not. (Sure, "continuity" is an idealization, but then even "square" or "circle" or even "length" is, and any "science" whatsoever really and intrinsically.)

> Old Math allowed admittance and entry of anything, and called it mathematics. New Math has a prime essential concern-- it has to be Logical and simple.

Logical necessarily, and simple as much as possible, but not too simple: in fact too simple becomes illogical.

> a borderline exists between finite and infinite.

Beyond that borderline there is nothing: I call the borderline Infinity. Indeed, I see significant similarities in our approaches (as soon as I use it as a "scale factor"), I think the main difference is that I try and keep the interval [0,MAX] closed all the way to the limit.

> Thanks Julio for my book 240 is launched all because of your question in sci.math.

Ah, I am glad to hear that! Thank you,

Julio

On Sunday, 24 April 2022 at 17:32:19 UTC+2, Julio Di Egidio wrote:
> On Sunday, 24 April 2022 at 16:22:40 UTC+2, Julio Di Egidio wrote:
<snip>
> In fact, here is a simpler form of the same problem:
>
> Say I have the relation y = m x for m any real number.
>
> I could rewrite it as x = (1/m) y, and now it is not defined for m = 0.
>
> But, it occurs to me, if I need to express x in terms of y, I should rather write:
>
> R := [x = (1/m) y] if m=/=0, else [y = 0]
>
> and I suppose, modulo the clumsy notation, that's it: rather than "eliminable discontinuity" I need "definition by cases".
>
> Correct?
> > Do we just say/imply that "the discontinuity is eliminable at t=0" or something of that sort (since m is defined and constant everywhere except at t=0)? Otherwise, how do we correctly find/express the slope of a straight line given parametric equations, or state what we have found?
> >
> > Thanks in advance for any help,

Thanks everybody for the feedback so far.

At this point, I can try and reformulate the question more precisely:

Say I have a problem parametrized on b, a real number in [0, 1], and
a derived quantity g_b = 1/sqrt(1-b^2), which blows up for b = 1.
Assume g_b is the only quantity that directly blows up, while I can
write all remaining quantities of my problem as (g_b^k)*Q, for k an
integer (positive or negative) and Q an expression that stays finite
for all values of b.

Now, in order to make the whole thing finite, I just consider the highest
power of g_b that appears in any quantity I have in the problem, call
that K, then I scale down all quantities by g_b^K (sure, all quantities with
k<K go to zero for b=1). In fact, I also now write g_b in [0, b_1]...

But there's the problem, how to justify that division by g_b^K if g_b can
blow up?! And now that I look at it again, I'm thinking I am just back to
good old limits and, here, an application (several) of L'Hopital's rule...

That is looking good to me, but comments, especially from actual
mathematicians :), remain quite welcome.

Julio

On Tuesday, 26 April 2022 at 19:08:07 UTC+2, Julio Di Egidio wrote:
> On Sunday, 24 April 2022 at 17:32:19 UTC+2, Julio Di Egidio wrote:
> > On Sunday, 24 April 2022 at 16:22:40 UTC+2, Julio Di Egidio wrote:
> <snip>
> > In fact, here is a simpler form of the same problem:
> >
> > Say I have the relation y = m x for m any real number.
> >
> > I could rewrite it as x = (1/m) y, and now it is not defined for m = 0.
> >
> > But, it occurs to me, if I need to express x in terms of y, I should rather write:
> >
> > R := [x = (1/m) y] if m=/=0, else [y = 0]
> >
> > and I suppose, modulo the clumsy notation, that's it: rather than "eliminable discontinuity" I need "definition by cases".
> >
> > Correct?
> > > Do we just say/imply that "the discontinuity is eliminable at t=0" or something of that sort (since m is defined and constant everywhere except at t=0)? Otherwise, how do we correctly find/express the slope of a straight line given parametric equations, or state what we have found?
> > >
> > > Thanks in advance for any help,
> Thanks everybody for the feedback so far.
>
> At this point, I can try and reformulate the question more precisely:
>
> Say I have a problem parametrized on b, a real number in [0, 1], and
> a derived quantity g_b = 1/sqrt(1-b^2), which blows up for b = 1.
> Assume g_b is the only quantity that directly blows up, while I can
> write all remaining quantities of my problem as (g_b^k)*Q, for k an
> integer (positive or negative) and Q an expression that stays finite
> for all values of b.
>
> Now, in order to make the whole thing finite, I just consider the highest
> power of g_b that appears in any quantity I have in the problem, call
> that K, then I scale down all quantities by g_b^K (sure, all quantities with
> k<K go to zero for b=1). In fact, I also now write g_b in [0, b_1]...
>
> But there's the problem, how to justify that division by g_b^K if g_b can
> blow up?! And now that I look at it again, I'm thinking I am just back to
> good old limits and, here, an application (several) of L'Hopital's rule....

Eh, it's not even l'Hopital, those factors just simplify in the limit, but I do
not remember the name if any of that rule right now...

> That is looking good to me, but comments, especially from actual
> mathematicians :), remain quite welcome.

Julio

On Tuesday, 26 April 2022 at 00:14:17 UTC+2, Archimedes Plutonium wrote:

> Math is easy, but given the centuries after Newton,
> math was made more and more crazy with every math professor
> wanting fame and leaving math a tangled mess of illogical methods.

Newton is the one who started the mathematical treatment of physics
in the modern sense, whence the need for, and his early contributions
to calculus (together and in contrast with Leibniz, but that's another
story), i.e. a solid foundation for taking what now is limits, derivatives
and integrals.

> with Planck's Quantum of Quantum Mechanics means math had to
> be discrete, not continuous. Yet there are the bozo the clowns Cohen
> pursuing ever more continuity when physics found discreteness.

FWIW, here are my comments on this matter:

Besides that physics has no import on mathematics, whatever either
of the two is actually talking about, physics is and remains continuous
all over the place, even quantum physics despite some popularizations
seem to suggest otherwise. For example:

- The levels of energy of a particle system, e.g. the hydrogen atom
are indeed "quantized", but that specifically means that they come
in integer multiples of some "ground energy", and that itself is not
an integer.

- The uncertainty principle (roughly speaking) says that we cannot
measure complementary quantities with absolute (i.e. arbitrarily good)
accuracy *at the same time*, but it puts no limits on the accuracy with
which we can measure a single quantity at any time. In practice, we
can indeed measure the position of a particle with as much accuracy
as we like and can, just in the process we will make the momentum
more and more uncertain. So, not even here there is any actual
discreetness of quantities.

- The Plank length/time/mass put limits on what we can observe/
measure, not on the granularity of the physical reality itself. And,
if I am not too mistaken, these limits have more to do with gravity,
i.e. the fact that when we go to too minuscule a scale/high an
energy of our probes, we rather blow the region into a black hole
as big as the energy employed makes it.

- The primary parameter of a dynamical system is time, which was,
is, and forever will be a continuous quantity...!

And there is also that thing called quantum information theory,
whose "atoms" are the q-bits, but that's even more remote from
reality, indeed patently something to do with (the limits of) what
we can say about it: again, it's the granularity of our observations
and descriptions, not that of reality per se. But, in fact, even
there, a q-bit is quite more than just a 0/1 value...

Have fun,

Julio

Julio Di Egidio presented the following explanation :
> On Tuesday, 26 April 2022 at 19:08:07 UTC+2, Julio Di Egidio wrote:
>> On Sunday, 24 April 2022 at 17:32:19 UTC+2, Julio Di Egidio wrote:
>>> On Sunday, 24 April 2022 at 16:22:40 UTC+2, Julio Di Egidio wrote: <snip>
>>> In fact, here is a simpler form of the same problem:
>>>
>>> Say I have the relation y = m x for m any real number.
>>>
>>> I could rewrite it as x = (1/m) y, and now it is not defined for m = 0.
>>>
>>> But, it occurs to me, if I need to express x in terms of y, I should rather
>>> write:
>>>
>>> R := [x = (1/m) y] if m=/=0, else [y = 0]
>>>
>>> and I suppose, modulo the clumsy notation, that's it: rather than
>>> "eliminable discontinuity" I need "definition by cases".
>>>
>>> Correct?
>>>> Do we just say/imply that "the discontinuity is eliminable at t=0" or
>>>> something of that sort (since m is defined and constant everywhere except
>>>> at t=0)? Otherwise, how do we correctly find/express the slope of a
>>>> straight line given parametric equations, or state what we have found?
>>>>
>>>> Thanks in advance for any help,
>> Thanks everybody for the feedback so far.
>>
>> At this point, I can try and reformulate the question more precisely:
>>
>> Say I have a problem parametrized on b, a real number in [0, 1], and
>> a derived quantity g_b = 1/sqrt(1-b^2), which blows up for b = 1.
>> Assume g_b is the only quantity that directly blows up, while I can
>> write all remaining quantities of my problem as (g_b^k)*Q, for k an
>> integer (positive or negative) and Q an expression that stays finite
>> for all values of b.
>>
>> Now, in order to make the whole thing finite, I just consider the highest
>> power of g_b that appears in any quantity I have in the problem, call
>> that K, then I scale down all quantities by g_b^K (sure, all quantities with
>> k<K go to zero for b=1). In fact, I also now write g_b in [0, b_1]...
>>
>> But there's the problem, how to justify that division by g_b^K if g_b can
>> blow up?! And now that I look at it again, I'm thinking I am just back to
>> good old limits and, here, an application (several) of L'Hopital's rule...
>
> Eh, it's not even l'Hopital, those factors just simplify in the limit, but I
> do not remember the name if any of that rule right now...

Power rule?

On Tuesday, April 26, 2022 at 7:29:06 AM UTC-5, ju...@diegidio.name wrote:
> On Monday, 25 April 2022 at 23:40:24 UTC+2, Archimedes Plutonium wrote:
> > On Monday, April 25, 2022 at 8:00:54 AM UTC-5, ju...@diegidio.name wrote:
> > > On Monday, 25 April 2022 at 01:00:21 UTC+2, Archimedes Plutonium wrote:
> <snipped>
> > > > Question please, for Julio.
> > >
> > > Is that even you? I don't think so, for a couple of years now.
> >
> > The same person who writes science books.
> All right, I suppose that's you. ;)
> > > > If all valid and true functions are only Polynomials
> > >
> > > Would you discard stuff as simple as f(x) = sqrt(x)?
> > >
> > Yes, that maybe the most simple equation discarded Y = x^-1/2.
> You are not just discarding an equation, you are discarding (to begin with) the very possibility that there exists a number representing the ratio of the diagonal of a square to its side: i.e. a perfectly elementary geometric construction for a perfectly elementary mathematical question. (The answer I grant you is not trivial, we immediately get into limits: but even that, if you ask me, is mainly because standard infinity isn't the last natural number...)
> > Now can we take the Power Rules to coax out a derivative or integral? Y' = -1/2 (x^-3/2)
> Derivatives and integrals are defined in terms of limits, and things like the power "rule" are in fact proven to hold based on that foundation: so, if you discard the foundation, you cannot rely on those "rules". Indeed, a discreet set is not even continuous, and I think that's the keyword: *continuity* and whether a mathematical system can handle it or not. (Sure, "continuity" is an idealization, but then even "square" or "circle" or even "length" is, and any "science" whatsoever really and intrinsically.)

Hi Julio,

I make a distinction between an equation and a function. Those are separate entities to me. For Calculus, only functions count. For graphing, you can graph either a equation or graph a function.

To me, only valid functions are polynomials. This allows all of Calculus to be rendered simple and easy with Power Rules. If you want to enter a equation such as Y = x^-1/2 , the square root of x, then, you have to translate that equation into a polynomial over an interval using the Lagrange transform.

This keeps all of Calculus as polynomials only.

As for equations, well, you can graph them all you please or manipulate all you please. But equations are not functions until they are polynomials.

Calculus needs discreteness, calculus cannot exist in a continuum as a geometry proof of Fundamental Theorem of Calculus shows. No FTC is possible if you insist on continuity, as my diagram of a rectangle as integral and you slice off a right triangle, lift it up at midpoint and you have derivative.

Well, it says that-- if you have a rectangle with a midpoint on its top side.

__m__
|         |
|         |
|         |
---------

That you can cut a right triangle from the midpoint

__m__
| /      |
|/       |
|         |
---------

Cut that right triangle and swivel it up to make the trapezoid

        B
        /|
      /  |
 m /----|
  /      |
|A      |
|____|

Or, you can start with that trapezoid and swivel the right triangle downwards to make the rectangle

__m__
| /      |
|/       |
|         |
---------

And, basically that is the Calculus at its most simple form.

Julio, I do not know when in math history, that such a mix up occurred where no-one in mathematics realized they had two separate beasts on their hands. And since no-one noticed, they melted them together into one toxic pot.

On Tuesday, April 26, 2022 at 1:20:20 PM UTC-5, ju...@diegidio.name wrote:
> On Tuesday, 26 April 2022 at 00:14:17 UTC+2, Archimedes Plutonium wrote:
>
> > Math is easy, but given the centuries after Newton,
> > math was made more and more crazy with every math professor
> > wanting fame and leaving math a tangled mess of illogical methods.
> Newton is the one who started the mathematical treatment of physics
> in the modern sense, whence the need for, and his early contributions
> to calculus (together and in contrast with Leibniz, but that's another
> story), i.e. a solid foundation for taking what now is limits, derivatives
> and integrals.
> > with Planck's Quantum of Quantum Mechanics means math had to
> > be discrete, not continuous. Yet there are the bozo the clowns Cohen
> > pursuing ever more continuity when physics found discreteness.
> FWIW, here are my comments on this matter:
>
> Besides that physics has no import on mathematics, whatever either
> of the two is actually talking about, physics is and remains continuous
> all over the place, even quantum physics despite some popularizations
> seem to suggest otherwise. For example:
>
> - The levels of energy of a particle system, e.g. the hydrogen atom
> are indeed "quantized", but that specifically means that they come
> in integer multiples of some "ground energy", and that itself is not
> an integer.
>
> - The uncertainty principle (roughly speaking) says that we cannot
> measure complementary quantities with absolute (i.e. arbitrarily good)
> accuracy *at the same time*, but it puts no limits on the accuracy with
> which we can measure a single quantity at any time. In practice, we
> can indeed measure the position of a particle with as much accuracy
> as we like and can, just in the process we will make the momentum
> more and more uncertain. So, not even here there is any actual
> discreetness of quantities.
>
> - The Plank length/time/mass put limits on what we can observe/
> measure, not on the granularity of the physical reality itself. And,
> if I am not too mistaken, these limits have more to do with gravity,
> i.e. the fact that when we go to too minuscule a scale/high an
> energy of our probes, we rather blow the region into a black hole
> as big as the energy employed makes it.
>
> - The primary parameter of a dynamical system is time, which was,
> is, and forever will be a continuous quantity...!
>
> And there is also that thing called quantum information theory,
> whose "atoms" are the q-bits, but that's even more remote from
> reality, indeed patently something to do with (the limits of) what
> we can say about it: again, it's the granularity of our observations
> and descriptions, not that of reality per se. But, in fact, even
> there, a q-bit is quite more than just a 0/1 value...
>
> Have fun,
>
> Julio

Julio, I am not going to argue with you, that continuity is a sham. The only thing I will say is -- give me a geometry proof of Fundamental Theorem of Calculus, not a limit analysis, for it is funny that many mathematicians equate analyzing something, equate that analysis to proving something. Why heck, I analyzed 20 things today, not proving a single one of them.

But anyway, Julio, here is a picture diagram of a geometry proof of fundamental theorem of calculus, and it is only possible with discrete numbers, no continuum.

Well, it says that-- if you have a rectangle with a midpoint on its top side.

__m__
|         |
|         |
|         |
---------

That you can cut a right triangle from the midpoint

__m__
| /      |
|/       |
|         |
---------

Cut that right triangle and swivel it up to make the trapezoid

        B
        /|
      /  |
 m /----|
  /      |
|A      |
|____|

Or, you can start with that trapezoid and swivel the right triangle downwards to make the rectangle

__m__
| /      |
|/       |
|         |
---------

And, basically that is the Calculus at its most simple form.

On Tuesday, April 26, 2022 at 3:34:37 PM UTC-5, Archimedes Plutonium wrote:
> On Tuesday, April 26, 2022 at 1:20:20 PM UTC-5, ju...@diegidio.name wrote:
> > On Tuesday, 26 April 2022 at 00:14:17 UTC+2, Archimedes Plutonium wrote:
> >
> > > Math is easy, but given the centuries after Newton,
> > > math was made more and more crazy with every math professor
> > > wanting fame and leaving math a tangled mess of illogical methods.
> > Newton is the one who started the mathematical treatment of physics
> > in the modern sense, whence the need for, and his early contributions
> > to calculus (together and in contrast with Leibniz, but that's another
> > story), i.e. a solid foundation for taking what now is limits, derivatives
> > and integrals.
> > > with Planck's Quantum of Quantum Mechanics means math had to
> > > be discrete, not continuous. Yet there are the bozo the clowns Cohen
> > > pursuing ever more continuity when physics found discreteness.
> > FWIW, here are my comments on this matter:
> >
> > Besides that physics has no import on mathematics, whatever either
> > of the two is actually talking about, physics is and remains continuous
> > all over the place, even quantum physics despite some popularizations
> > seem to suggest otherwise. For example:
> >
> > - The levels of energy of a particle system, e.g. the hydrogen atom
> > are indeed "quantized", but that specifically means that they come
> > in integer multiples of some "ground energy", and that itself is not
> > an integer.
> >
> > - The uncertainty principle (roughly speaking) says that we cannot
> > measure complementary quantities with absolute (i.e. arbitrarily good)
> > accuracy *at the same time*, but it puts no limits on the accuracy with
> > which we can measure a single quantity at any time. In practice, we
> > can indeed measure the position of a particle with as much accuracy
> > as we like and can, just in the process we will make the momentum
> > more and more uncertain. So, not even here there is any actual
> > discreetness of quantities.
> >
> > - The Plank length/time/mass put limits on what we can observe/
> > measure, not on the granularity of the physical reality itself. And,
> > if I am not too mistaken, these limits have more to do with gravity,
> > i.e. the fact that when we go to too minuscule a scale/high an
> > energy of our probes, we rather blow the region into a black hole
> > as big as the energy employed makes it.
> >
> > - The primary parameter of a dynamical system is time, which was,
> > is, and forever will be a continuous quantity...!
> >
> > And there is also that thing called quantum information theory,
> > whose "atoms" are the q-bits, but that's even more remote from
> > reality, indeed patently something to do with (the limits of) what
> > we can say about it: again, it's the granularity of our observations
> > and descriptions, not that of reality per se. But, in fact, even
> > there, a q-bit is quite more than just a 0/1 value...
> >
> > Have fun,
> >
> > Julio
> Julio, I am not going to argue with you, that continuity is a sham. The only thing I will say is -- give me a geometry proof of Fundamental Theorem of Calculus, not a limit analysis, for it is funny that many mathematicians equate analyzing something, equate that analysis to proving something. Why heck, I analyzed 20 things today, not proving a single one of them.
>
> But anyway, Julio, here is a picture diagram of a geometry proof of fundamental theorem of calculus, and it is only possible with discrete numbers, no continuum.
> Well, it says that-- if you have a rectangle with a midpoint on its top side.
>
> __m__
> | |
> | |
> | |
> ---------
>
> That you can cut a right triangle from the midpoint
>
> __m__
> | / |
> |/ |
> | |
> ---------
>
> Cut that right triangle and swivel it up to make the trapezoid
>
> B
> /|
> / |
> m /----|
> / |
> |A |
> |____|
>
> Or, you can start with that trapezoid and swivel the right triangle downwards to make the rectangle
>
>
> __m__
> | / |
> |/ |
> | |
> ---------
>
>
> And, basically that is the Calculus at its most simple form.

You cannot do a geometry proof of calculus FTC in a continuum. Only discrete numbers for sides and top of rectangle -- the integral, can you do a geometry proof of calculus.

And strangely enough, Polynomials are discrete as functions.

This is why, Julio, Polynomials bypass the question of slope being 0.

On 4/25/2022 4:29 PM, Chris M. Thomasson wrote:
> On 4/24/2022 5:12 PM, Chris M. Thomasson wrote:
>> On 4/24/2022 7:22 AM, Julio Di Egidio wrote:
[...]
>> Probably misunderstanding you here... Think in terms of two 2d
>> vectors, and the angle between them. atan2(0, 0) is undefined when x
>> _and_ y are both zero. So, taking the angle between points:
>>
>> vec2 p0 = {0, 0}
>> vec2 p1 = {0, 0}
>> vec2 dif = p1 - p0
>> angle = atan2(dif.y, dif.x)
>>
>> angle is undefined. So you can get zero radians, or undefined. Depends
>> on what the implementation decides to do.
>
> One p0 is no longer equal to p1, everything works.
^^^^^^

The word 'One', should be 'Once'. Damn typos!

Feel the need to clarify just in case it caused any confusion to readers...

If the vectors p0 and p1 are no longer equal to each other, we can find
the angle between them. Actually, we can find the angle to any single
vector with a non-zero component wrt using the origin point at the
center of the plane.

Give me a point P, I can tell you the angle from origin. atan2 is
wonderful, just remember to swap the components. atan2(y, x), not
atan2(x, y), bad... ;^)

If the point P is at the origin where the difference vector is zero with
respect to the origin, then we can define it as, zero radians, or
anything we want to simply because it is undefined to begin with...

Julio's thread caused me to consider parametric equations once again. I remember several years back, perhaps 5 perhaps 10 years ago that I raised the question of why have parametric equations at all. And some polite poster tried explaining the "why?". Although, he knew, and I knew I was not buying it.

The prime essential math of the entire 20th and 21st century was basically a single question, a single question that puts the entire subject of mathematics on a correct footing and cleans out some 90% or more of all of mathematics.

The question is simple-- you know calculus is geometry. Therefore-- you are required to do a geometry proof of Fundamental Theorem of Calculus. Not bickering or wavering but forced and required to do a geometry proof of FTC.

A limit analysis is not proof at all for FTC. Analyzing something is not proving something. Why today I analyzed some 20 or 30 things around the house, which is not proving 20 or 30 things.

To prove FTC with geometry requires you to throw out the continuum. You cannot prove FTC if numbers and graphs are continuous. The true numbers of mathematics are Grid numbers that get finer and finer-- so fine that at 10^-604 they are the fine holes between one finite number and the next finite number. You need holes in between the last number and the next number in order to have Calculus exist. Calculus cannot exist in a continuum.

So the true numbers of math start with 10 grid, then 100 grid, then 1000 grid,each time the holes get smaller.

To prove geometrically that of FTC is simple in the diagram sketch I gave earlier-- rectangle is integral and a slice off the midpoint of a right triangle hinged up or down at the midpoint is the derivative. Hinge it up and you have derivative, hinge it back down and you have integral.

This is a geometry proof of FTC. In fact, in the entire history of mathematics there was never a VALID proof of FTC until my geometry proof of 2015. For limit analysis is not a proof.

And the moment that mathematicians start to do a geometry proof of FTC, they well understand why so much of Old Math was con-art fakery. We throw out rational numbers, irrationals, complex, Reals, every number is thrown out and only Grid numbers remain. We use the Grid to whatever accuracy we need. No-one on Earth needs 10^604 accuracy, but generally 10^4 or 10^5 is the usual precise accuracy.

So, well, does math need Parametric equations or was that more con-art fakery? In the geometry proof of FTC, we have to sharpen our definition of what is a function, and so, only polynomials can be true valid functions of mathematics. And anything not a polynomial has to be transformed into a polynomial over a specific interval so the Power Rules can grind out the derivative and integral.

Thus, well, parametric equations were a fool's game in mathematics, just another con art that continuum was a con-art.

I invite all mathematicians to do a Geometry proof of Fundamental Theorem of Calculus and clear your heads and minds as to what true math really is. And see for yourself all the con-art side show gimmicks were infused into mathematics that was outright fakery. The continuum, the rationals which are unfinished divisions, the irrationals are only insane never completed numbers-- tell me what the length of sqrt2 ruler is--for the boogar never stops moving. Sqrt2 is not a learned person of math or logic, but sqrt2 is the fool that was con-arted to death and proud of being a fool.

AP, King of Science-- especially physics-chemistry

On Tuesday, 26 April 2022 at 19:08:07 UTC+2, Julio Di Egidio wrote:
> On Sunday, 24 April 2022 at 17:32:19 UTC+2, Julio Di Egidio wrote:

> Now, in order to make the whole thing finite, I just consider the highest
> power of g_b that appears in any quantity I have in the problem, call
> that K, then I scale down all quantities by g_b^K (sure, all quantities with
> k<K go to zero for b=1). In fact, I also now write g_b in [0, b_1]...

That should read g_b in [0, g_1].

Julio

On Wednesday, 27 April 2022 at 06:04:42 UTC+2, Chris M. Thomasson wrote:

> Give me a point P, I can tell you the angle from origin. atan2 is
> wonderful, just remember to swap the components. atan2(y, x), not
> atan2(x, y), bad... ;^)

"Swap here, or swap there, or do whatever you like": that's not
mathematics Chris, that's bad poetry, and it doesn't work in general
anyway, which is the point of asking the questions I am asking and
proposing the constructs i propose...

No, you won't get it, you'll just come back somehow offended, and
then even add to it.

*Plonk*

Julio

On 4/26/2022 11:59 PM, Archimedes Plutonium wrote:
> Julio's thread caused me to consider parametric equations once again. I remember several years back, perhaps 5 perhaps 10 years ago that I raised the question of why have parametric equations at all. And some polite poster tried explaining the "why?". Although, he knew, and I knew I was not buying it.[...]

I remember back when you inspired to me to create a parametric that
creates two semi-circles. Thanks again!:

https://pastebin.com/raw/mGar95sa

Result:

https://youtu.be/4VrMT18Rr84

My code for Processing:
__________________________________
/*
Alien Code?
First try by: Chris M. Thomasson
____________________________________________________*/
float g_pradius = 200;

void setup()
{ size(800, 800);
noFill();
noLoop();
background(0);
colorMode(RGB, 255);
translate(width / 2, height / 2);
ct_alien_code_render(0, 2, 0, 0, 100);
saveFrame("ct_alien_code.jpg");
}

void ct_alien_code_render(
int irecur,
int irecur_max,
float ox,
float oy,
int imax
) {
if (irecur >= irecur_max) return;

float angle_start = 1 / (imax - 1.0) * (PI*2);

float ptx = 1;
float pty = 0;

float ptx_x = (cos(angle_start) + floor(sin(angle_start)) * 2 + 1) * .5;
float ptx_y = sin(angle_start) * .5;

float dif_x = ptx_x - ptx;
float dif_y = ptx_y - pty;

float dis = abs(dif_x * dif_x + dif_y * dif_y);

for (int i = 1; i < imax; ++i)
{
float ir = i / (imax - 1.0);
float angle = (PI*2) * ir;

float np_x = (cos(angle) + floor(sin(angle)) * 2 + 1) * .5;
float np_y = (sin(angle)) * .5;

np_x += ox;
np_y += oy;

float dif_np_x = np_x - ptx;
float dif_np_y = np_y - pty;
float ddd = abs(dif_np_x * dif_np_x + dif_np_y * dif_np_y);

if (ddd <= dis && i > 1)
{
// line in.plot.line(pt, np, CT_RGBF(0, 1, 1));

float proj_pt_x = ptx * g_pradius;
float proj_pt_y = -pty * g_pradius;

float proj_np_x = np_x * g_pradius;
float proj_np_y = -np_y * g_pradius;

stroke(255, 255, 0);
line(proj_pt_x, proj_pt_y, proj_np_x, proj_np_y);

stroke(255, 0, 0);
line(-proj_pt_x, -proj_pt_y, -proj_np_x, -proj_np_y);
}

ct_alien_code_render(irecur + 1, irecur_max, np_x, np_y, imax);

ptx = np_x;
pty = np_y;
}
} __________________________________

On 4/27/2022 12:15 AM, Julio Di Egidio wrote:
> On Wednesday, 27 April 2022 at 06:04:42 UTC+2, Chris M. Thomasson wrote:
>
>> Give me a point P, I can tell you the angle from origin. atan2 is
>> wonderful, just remember to swap the components. atan2(y, x), not
>> atan2(x, y), bad... ;^)
>
> "Swap here, or swap there, or do whatever you like": that's not
> mathematics Chris, that's bad poetry, and it doesn't work in general
> anyway, which is the point of asking the questions I am asking and
> proposing the constructs i propose...
>
> No, you won't get it, you'll just come back somehow offended, and
> then even add to it.
>
> *Plonk*
>

Have you ever had to use atan2 before?

On Wednesday, 27 April 2022 at 10:14:45 UTC+2, Chris M. Thomasson wrote:
> On 4/26/2022 11:59 PM, Archimedes Plutonium wrote:
> > Julio's thread caused me to consider parametric equations once again.
> > I remember several years back, perhaps 5 perhaps 10 years ago that I raised
> > the question of why have parametric equations at all. And some polite poster
> > tried explaining the "why?". Although, he knew, and I knew I was not buying it.[...]
>
> I remember back when you inspired to me to create a parametric that
> creates two semi-circles. Thanks again!:
<snip>

> void ct_alien_code_render(
> int irecur,
> int irecur_max,
> float ox,
> float oy,
> int imax
> ) {
> if (irecur >= irecur_max) return;
>
> float angle_start = 1 / (imax - 1.0) * (PI*2);

Whence (I'll have to surmise, in that sense your code is redundant/opaque)
you just skip the case imax==1 (where you'd have to return an "undefined",
just your function of corse returns void), which, if you notice, is the very
motivating example for my question. Have you seen how I "fix" it? Would
you be able extend your code to use that method? Would you like some
help in that sense? I have nothing to do myself.

Julio

On Wednesday, 27 April 2022 at 09:10:27 UTC+2, Julio Di Egidio wrote:
> On Tuesday, 26 April 2022 at 19:08:07 UTC+2, Julio Di Egidio wrote:
> > On Sunday, 24 April 2022 at 17:32:19 UTC+2, Julio Di Egidio wrote:

> > Now, in order to make the whole thing finite, I just consider the highest
> > power of g_b that appears in any quantity I have in the problem, call
> > that K, then I scale down all quantities by g_b^K (sure, all quantities with
> > k<K go to zero for b=1). In fact, I also now write g_b in [0, b_1]...
>
> That should read g_b in [0, g_1].

That should actually read g_b in [1, g_1]. Apologies...

Julio

On Tuesday, 26 April 2022 at 20:27:44 UTC+2, FromTheRafters wrote:
> Julio Di Egidio presented the following explanation :

> > Eh, it's not even l'Hopital, those factors just simplify in the limit, but I
> > do not remember the name if any of that rule right now...
>
> Power rule?

Nah, this is just simplification of factors by the "just how limits work" rule.

I don't think I can explain it properly, anyway it's by definition of limit that
whatever is in the limit behaves as if the limit is not actually reached, hence
we can do e.g. lim_{x->oo} 2x/x = lim_{x->oo} 2 = 2. And that's where the
definition of limit is a higher order operation, i.e. to begin with more of an
algebraic operation than an arithmetic one... or something along that line.

Julio

Ha Ha, dream on with your Nazi mathematics and cleansing.
AP brain farto, Putler of sci.math and sci.physics.
Not a single line of math in 30 years.

Archimedes Plutonium schrieb am Mittwoch, 27. April 2022 um 08:59:14 UTC+2:
> The prime essential math of the entire 20th and 21st century was basically a single question, a single question that puts the entire subject of mathematics on a correct footing and cleans out some 90% or more of all of mathematics.

On Wednesday, 27 April 2022 at 14:26:46 UTC+2, Julio Di Egidio wrote:
> On Tuesday, 26 April 2022 at 20:27:44 UTC+2, FromTheRafters wrote:
> > Julio Di Egidio presented the following explanation :
> >
> > > Eh, it's not even l'Hopital, those factors just simplify in the limit, but I
> > > do not remember the name if any of that rule right now...
> >
> > Power rule?
>
> Nah, this is just simplification of factors by the "just how limits work" rule.
>
> I don't think I can explain it properly, anyway it's by definition of limit that
> whatever is in the limit behaves as if the limit is not actually reached, hence
> we can do e.g. lim_{x->oo} 2x/x = lim_{x->oo} 2 = 2. And that's where the
> definition of limit is a higher order operation, i.e. to begin with more of an
> algebraic operation than an arithmetic one... or something along that line.

Let's try and broaden the spectrum here.

Can we define the limit of a function as a specific operator on functions?
(So not relying on, rather recovering, the standard, first-order, set-based
formalization: indeed, that remains after the fact, we "guess" results to
begin with, or something along that line...)

Of course it's not just:
Lim_{x->a from /dir/}(f( x, y, z...)) = f(Lim_{x->a from /dir/}(x), y, z...)
but what is it if anything?

Julio

Mostowski Collapse wrote:

> Ha Ha, dream on with your Nazi mathematics and cleansing.
> AP brain farto, Putler of sci.math and sci.physics.
> Not a single line of math in 30 years.
>
> Archimedes Plutonium schrieb am Mittwoch, 27. April 2022 um 08:59:14
> UTC+2:
>> The prime essential math of the entire 20th and 21st century was
>> basically a single question, a single question that puts the entire
>> subject of mathematics on a correct footing and cleans out some 90% or
>> more of all of mathematics.

AP forget twice as much mathematics you think you can do.

Putin promises ‘lightning’ response to strategic threats
President warns that Russia won’t hesitate to use ‘weapons that no other
country’ possesses to defend itself.
https://www.rt.com/russia/554619-putin-strategic-threat/

“If someone decides to intervene in the ongoing events from the outside
and create unacceptable strategic threats to us, they should know that our
response to those oncoming blows will be swift, lightning-fast,” he
explained.

“We have all the tools to do this. Tools that no one except us can brag
about. But we’re not going to brag. We’ll use them if such a need arises,”
the president added, without specifying which tools could be deployed.

On Wednesday, April 27, 2022 at 3:01:04 PM UTC-5, Hugh Itoh wrote:
> Mostowski Collapse wrote:
> AP forget twice as much mathematics you think you can do.
>

In my college training of Logic, formal logic, two years of logic. We had lessons in which we take sentences and transcribe them into mathematical logical quantity formulas.

So let me see if I can transcribe Hugh's sentence which was meant to be:

AP forgot twice as much mathematics, that Jan Burse will ever do in his entire lifetime.

So if I can remember back to 1970, over 50 years ago. Interesting and let us give it a try. And by the way, the DC Dan Christensen poop crap certainly cannot do anything remotely like this-- quantify a sentence of a language into math.

Let me denote these:

AP_t.k. = AP's total knowledge
AP_f.k. = forgotten AP knowledge

JB_t.k. = Jan Burse's total knowledge

Do I need a forgotten knowledge of Jan Burse? I do not think so, at this moment anyway.

So we have AP_t.k. = Summation of every piece of knowledge for 72 years subtract AP_f.k.

For Jan Burse we have JB_t.k. = 1/2 (AP_f.k.)

Now I should be able to make this more detailed.

So in every year that AP gains knowledge we have 72(AP_t.k.)

And let us say that AP forgot in those 72 years, let us say he forgot 2 years worth of logic.

So we have 72(AP_t.k.) - (2)

That would leave the total knowledge accessible for the brain of Jan Burse would be 1/2(-2).

In other words, the brains of Jan Burse, Swiss Zurich ETH, are brains that can accummulate in his lifetime of the knowledge that AP picked up in 1 year time.

So the brains of AP would be a graph of Y = 72x while the brains of Jan Burse would be a graph of Y= 1

AP brains graphed would look like this:
knowledge gained
| /
|/
|/__________

While Jan Burse brains graphed for 72 years would look like this:

|
| |--------------------_________________knowledge gained

No, definitely the DC Dan Christensen nutjob proof machine could never give pictures or formulas

Calling on failure of Logic Dan Christensen with his failed machine of DC proof. Yoo, Dan, you logic failure, how do you translate the below, with or without your failed DC proof. I am sure I made errors, for the below was my first take on "AP forgot more math than twice the amount of math Jan Burse will ever learn in his entire lifetime".

DC how do you quantify that into logic, you ignorant waif with your AND truth table of TFFF when it is actually TTTF.

On Thursday, April 28, 2022 at 1:01:01 AM UTC-5, Archimedes Plutonium wrote:
> On Wednesday, April 27, 2022 at 3:01:04 PM UTC-5, Hugh Itoh wrote:
> > Mostowski Collapse wrote:
> > AP forget twice as much mathematics you think you can do.
> >
> In my college training of Logic, formal logic, two years of logic. We had lessons in which we take sentences and transcribe them into mathematical logical quantity formulas.
>
> So let me see if I can transcribe Hugh's sentence which was meant to be:
>
> AP forgot twice as much mathematics, that Jan Burse will ever do in his entire lifetime.
>
> So if I can remember back to 1970, over 50 years ago. Interesting and let us give it a try. And by the way, the DC Dan Christensen poop crap certainly cannot do anything remotely like this-- quantify a sentence of a language into math.
>
> Let me denote these:
>
> AP_t.k. = AP's total knowledge
> AP_f.k. = forgotten AP knowledge
>
> JB_t.k. = Jan Burse's total knowledge
>
> Do I need a forgotten knowledge of Jan Burse? I do not think so, at this moment anyway.
>
> So we have AP_t.k. = Summation of every piece of knowledge for 72 years subtract AP_f.k.
>
> For Jan Burse we have JB_t.k. = 1/2 (AP_f.k.)
>
> Now I should be able to make this more detailed.
>
> So in every year that AP gains knowledge we have 72(AP_t.k.)
>
> And let us say that AP forgot in those 72 years, let us say he forgot 2 years worth of logic.
>
> So we have 72(AP_t.k.) - (2)
>
> That would leave the total knowledge accessible for the brain of Jan Burse would be 1/2(-2).
>
> In other words, the brains of Jan Burse, Swiss Zurich ETH, are brains that can accummulate in his lifetime of the knowledge that AP picked up in 1 year time.
>
> So the brains of AP would be a graph of Y = 72x while the brains of Jan Burse would be a graph of Y= 1
>
> AP brains graphed would look like this:
> knowledge gained
> | /
> |/
> |/__________
>
>
> While Jan Burse brains graphed for 72 years would look like this:
>
>
> |
> |
> |--------------------_________________knowledge gained
>
>
> No, definitely the DC Dan Christensen nutjob proof machine could never give pictures or formulas