Bonjour les amis !
I asked for the roots of the following equation on the French forums, I
only got one answer that didn't satisfy me, and the rest is just
contempt and insults.
So I'm trying my luck here.
y=f(x)=(x²)²+2x²+3
Il y a pour moi, deux racines très simples pour cette équation, dont
aucun n'est réelle.
Can the Anglo-Saxons find these two roots?
R.H.
Le 06/02/2025 à 20:15, sobriquet a écrit :
Op 06/02/2025 om 16:42 schreef Richard Hachel:
Bonjour les amis !
I asked for the roots of the following equation on the French forums,
I only got one answer that didn't satisfy me, and the rest is just
contempt and insults.
So I'm trying my luck here.
y=f(x)=(x²)²+2x²+3
Il y a pour moi, deux racines très simples pour cette équation, dont
aucun n'est réelle.
Can the Anglo-Saxons find these two roots?
R.H.
Actually there are four complex roots.
https://www.wolframalpha.com/input?i=x%5E4%2B2x%5E2%2B3
Yes, these are indeed the roots found in traditional development.
Mathematicians find four complex roots.
Personally, in this specific case, I only find two, because I think
there are only two.
But I use different concepts, and a different method.
For me, the roots are x'=-i and x"=i in this particular case, and I
place them on the y=0 axis, obviously, and on a simple Cartesian
coordinate system.
DON'T SHOUT!
I remind you that I use a different approach that I think is more
correct and in line with the very nature of i, and its precise
definition, which is not only i²=-1.
R.H.
Op 06/02/2025 om 16:42 schreef Richard Hachel:
Bonjour les amis !
I asked for the roots of the following equation on the French forums, I
only got one answer that didn't satisfy me, and the rest is just
contempt and insults.
So I'm trying my luck here.
y=f(x)=(x²)²+2x²+3
Il y a pour moi, deux racines très simples pour cette équation, dont
aucun n'est réelle.
Can the Anglo-Saxons find these two roots?
R.H.
Actually there are four complex roots.
https://www.wolframalpha.com/input?i=x%5E4%2B2x%5E2%2B3
But no one has ever explained where this being comes from, which, in its being,
is an entity whose square is equal to -1. It is a convention.
Ok, but that's a bit like people saying that 3 + 5 = 7 and then claiming
that usually mathematicians say that 3 + 5 = 8, but they have different concepts that are more correct.
Unless you're able to demonstrate that your alternative concepts are
superior than the conventional way of defining these concepts, it
seems a bit silly.
The concept of a complex number didn't fall from the sky.. it was
developed over many centuries by multiple generations of mathematicians.
So it seems unlikely that someone can come along and claim their way to conceive of a complex number is superior or more correct.
Le 06/02/2025 à 21:52, sobriquet a écrit :
Ok, but that's a bit like people saying that 3 + 5 = 7 and then
claiming that usually mathematicians say that 3 + 5 = 8, but they have
different concepts that are more correct.
Unless you're able to demonstrate that your alternative concepts are
superior than the conventional way of defining these concepts, it
seems a bit silly.
The concept of a complex number didn't fall from the sky.. it was
developed over many centuries by multiple generations of
mathematicians. So it seems unlikely that someone can come along and
claim their way to conceive of a complex number is superior or more
correct.
You may be right.
But I also know that mathematicians and physicists can also be wrong. Descartes' works are full of errors, Berkeley and Newton did not agree
on the calculation of an infinitely small increment (I think Berkeley
was right), Lorentz wandered for years on relativistic transformations
before Poincaré gave it to him.
If you observe carefully, you will realize that basically, the notion of complex numbers is very quickly presented, then very quickly skipped.
You are given an i²=-1, in order to square an awkward discriminant, and,
if the principle is correct (we multiply by 1, then we pose that i²=-1
by convention and this allows us to have a positive root).
But no one has ever explained where this being comes from, which, in its being, is an entity whose square is equal to -1. It is a convention.
Personally, I wish that we put this being under the microscope once and
for all, he fuuses imaginary.
It would seem that i is a special entity, which, like 1, can be used in
such a way that, whatever its exponent, it remains identical to itself
in its abstract being. -i is always equal to -i.
We can do as with 1^x give all the possible and imaginable powers to x, always, 1^x=1.
It seems that it is the same thing with i=-1.
i²=-1.
i^(-1/2)=-1
i^4=-1
i°=-1
etc...etc...etc...
So we have to define i, because then, in the calculations, big sign
errors can appear. The biggest one can be that, sometimes, depending on
the concept i²=-1 or i²=1 if we simplify too quickly.
Let's take z1=16+9i and z2=14+3i and make a product.
We have: aa'+i(ab'+ba')+(ib')(ib)
If we make the product as is, we see that if i=-1 then (-9)(-3)=+27,
but if we square it, we have i²=-1 and i²bb'=-27
The error is then colossal:
Hachel finds Z=251+174i.
Mathematicians find Z=197+174i
We need to think about this and check what is correct and why it is
correct.
R.H.
Op 06/02/2025 om 23:15 schreef Richard Hachel:
Le 06/02/2025 à 21:52, sobriquet a écrit :
Ok, but that's a bit like people saying that 3 + 5 = 7 and then
claiming that usually mathematicians say that 3 + 5 = 8, but they have
different concepts that are more correct.
Unless you're able to demonstrate that your alternative concepts are
superior than the conventional way of defining these concepts, it
seems a bit silly.
The concept of a complex number didn't fall from the sky.. it was
developed over many centuries by multiple generations of
mathematicians. So it seems unlikely that someone can come along and
claim their way to conceive of a complex number is superior or more
correct.
You may be right.
But I also know that mathematicians and physicists can also be wrong.
Descartes' works are full of errors, Berkeley and Newton did not agree
on the calculation of an infinitely small increment (I think Berkeley
was right), Lorentz wandered for years on relativistic transformations
before Poincaré gave it to him.
If you observe carefully, you will realize that basically, the notion of
complex numbers is very quickly presented, then very quickly skipped.
You are given an i²=-1, in order to square an awkward discriminant, and,
if the principle is correct (we multiply by 1, then we pose that i²=-1
by convention and this allows us to have a positive root).
But no one has ever explained where this being comes from, which, in its
being, is an entity whose square is equal to -1. It is a convention.
Personally, I wish that we put this being under the microscope once and
for all, he fuuses imaginary.
It would seem that i is a special entity, which, like 1, can be used in
such a way that, whatever its exponent, it remains identical to itself
in its abstract being. -i is always equal to -i.
We can do as with 1^x give all the possible and imaginable powers to x,
always, 1^x=1.
It seems that it is the same thing with i=-1.
i²=-1.
i^(-1/2)=-1
i^4=-1
i°=-1
etc...etc...etc...
So we have to define i, because then, in the calculations, big sign
errors can appear. The biggest one can be that, sometimes, depending on
the concept i²=-1 or i²=1 if we simplify too quickly.
Let's take z1=16+9i and z2=14+3i and make a product.
We have: aa'+i(ab'+ba')+(ib')(ib)
If we make the product as is, we see that if i=-1 then (-9)(-3)=+27,
but if we square it, we have i²=-1 and i²bb'=-27
The error is then colossal:
Hachel finds Z=251+174i.
Mathematicians find Z=197+174i
We need to think about this and check what is correct and why it is
correct.
R.H.
But what would be a compelling reason to accept one way to define multiplication of complex numbers over another way?
With the standard way of defining complex numbers, if we pick any point
on the unit circle and we multiply it with any other point on the unit circle, the result will end up on the unit circle. With your method,
this would fail (in the sense that the product would not end up on the
unit circle if the factors of the product are on the unit circle).
This seems like a compelling reason to me to prefer the standard way to define multiplication of complex numbers over your alternative way.
You might say it's irrelevant whether complex numbers on the unit
circle multiply in a way that ends up on the unit circle, but other nice properties also fail, like the way we can multiply complex numbers in
polar form by multiplying their modulus and adding their argument.
For some reason, "some" people seem to want to say complex numbers are
not "real" because of the word "imaginary" used to define the y axis?
No, such a "new approach" to complex numbers is not possible. You can
define what you like, but you are not free to call that "complex numbers" unless it conforms to actual complex number theory. You seem to be
ignorant of all mathematics, so you are not in a position to say what is possible, and what not.
Le 07/02/2025 à 01:24, sobriquet a écrit :
Op 06/02/2025 om 23:15 schreef Richard Hachel:
Le 06/02/2025 à 21:52, sobriquet a écrit :
Ok, but that's a bit like people saying that 3 + 5 = 7 and then
claiming that usually mathematicians say that 3 + 5 = 8, but they
have different concepts that are more correct.
Unless you're able to demonstrate that your alternative concepts are
superior than the conventional way of defining these concepts, it
seems a bit silly.
The concept of a complex number didn't fall from the sky.. it was
developed over many centuries by multiple generations of
mathematicians. So it seems unlikely that someone can come along and
claim their way to conceive of a complex number is superior or more
correct.
You may be right.
But I also know that mathematicians and physicists can also be wrong.
Descartes' works are full of errors, Berkeley and Newton did not
agree on the calculation of an infinitely small increment (I think
Berkeley was right), Lorentz wandered for years on relativistic
transformations before Poincaré gave it to him.
If you observe carefully, you will realize that basically, the notion
of complex numbers is very quickly presented, then very quickly
skipped. You are given an i²=-1, in order to square an awkward
discriminant, and, if the principle is correct (we multiply by 1,
then we pose that i²=-1 by convention and this allows us to have a
positive root).
But no one has ever explained where this being comes from, which, in
its being, is an entity whose square is equal to -1. It is a convention. >>>
Personally, I wish that we put this being under the microscope once
and for all, he fuuses imaginary.
It would seem that i is a special entity, which, like 1, can be used
in such a way that, whatever its exponent, it remains identical to
itself in its abstract being. -i is always equal to -i.
We can do as with 1^x give all the possible and imaginable powers to
x, always, 1^x=1.
It seems that it is the same thing with i=-1.
i²=-1.
i^(-1/2)=-1
i^4=-1
i°=-1
etc...etc...etc...
So we have to define i, because then, in the calculations, big sign
errors can appear. The biggest one can be that, sometimes, depending
on the concept i²=-1 or i²=1 if we simplify too quickly.
Let's take z1=16+9i and z2=14+3i and make a product.
We have: aa'+i(ab'+ba')+(ib')(ib)
If we make the product as is, we see that if i=-1 then (-9)(-3)=+27,
but if we square it, we have i²=-1 and i²bb'=-27
The error is then colossal:
Hachel finds Z=251+174i.
Mathematicians find Z=197+174i
We need to think about this and check what is correct and why it is
correct.
R.H.
But what would be a compelling reason to accept one way to define
multiplication of complex numbers over another way?
With the standard way of defining complex numbers, if we pick any
point on the unit circle and we multiply it with any other point on
the unit circle, the result will end up on the unit circle. With your
method, this would fail (in the sense that the product would not end
up on the unit circle if the factors of the product are on the unit
circle).
This seems like a compelling reason to me to prefer the standard way
to define multiplication of complex numbers over your alternative way.
You might say it's irrelevant whether complex numbers on the unit
circle multiply in a way that ends up on the unit circle, but other
nice properties also fail, like the way we can multiply complex
numbers in polar form by multiplying their modulus and adding their
argument.
I think a new approach to complex numbers may be possible, and it starts
by redefining what the imaginary i is.
It is defined in a dramatically stupid way.
And we say, stuttering: "it is the... the number... uh... that...
which... that if you square it, it becomes -1."
This is not very reasonable.
But this dramatic and narrow definition turns downright horrific when we
say: "Let's square the square".
Then everything becomes dreadful. We say (i²)(i²)=1 because (-1)(-1)=1.
And we attribute to an imaginary structure the same property as to a
real structure.
But, hold on tight, friends, this is false.
(i²)²=-1, and not 1.
And there, the whole structure that we thought we had defined by a
simple i²=-1, which was true, collapses for everything else.
R.H.
Le 07/02/2025 à 14:27, Alan Mackenzie a écrit :
No, such a "new approach" to complex numbers is not possible. You can
define what you like, but you are not free to call that "complex numbers"
unless it conforms to actual complex number theory. You seem to be
ignorant of all mathematics, so you are not in a position to say what is
possible, and what not.
:))
Richard Hachel <[email protected]> wrote:
(i²)²=-1, and not 1.
Where do you get that garbage from? i^4 = 1.
And there, the whole structure that we thought we had defined by a simple
i²=-1, which was true, collapses for everything else.
Garbage. Nothing "collapses". The theory of complex numbers is, as far
as mathematicians can determine, consistent. It is vast and fascinating
in its own right. It is also useful to scientists and engineers.
I suggest you make more humble efforts to learn and understand it.
R.H.
Le 07/02/2025 à 14:48, Richard Hachel a écrit :
Le 07/02/2025 à 14:27, Alan Mackenzie a écrit :
No, such a "new approach" to complex numbers is not possible. You can
define what you like, but you are not free to call that "complex numbers" >>> unless it conforms to actual complex number theory. You seem to be
ignorant of all mathematics, so you are not in a position to say what is >>> possible, and what not.
:))
Nothing is funny here, Richard. You're showing how a crank you are. It may have
been funny at first, it is not anymore.
Everyone noticed that you removes 90% of Alan's debunking of your claims. In addition to be a crank you have absolutely no intellectual integrity.
In addition to be a crank you have absolutely no intellectual integrity.
Richard Hachel <[email protected]> wrote:
[ ... ]
I suggest you make more humble efforts to learn and understand it.
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