Debates - Potential Faulty Science

[talanum1]

We have: i^2=j^2=k^2=ijk=-1. Now set i=j=k=sqrt(-1) in the fourth equation:

sqrt(-1)*sqrt(-1)*sqrt(-1) = -1*sqrt(-1) not = -1, so it doesn't hold. What do I do wrong?

 

[FiestaST]

What does your ChatGPT and/or Claude say?

 

[now05ster]

What does your ChatGPT and/or Claude say?

What is wrong with Gemini?

 

[borro]

 

[Brian_G]

 

[Bewlen]

We have: i^2=j^2=k^2=ijk=-1. Now set i=j=k=sqrt(-1) in the fourth equation:

sqrt(-1)*sqrt(-1)*sqrt(-1) = -1*sqrt(-1) not = -1, so it doesn't hold. What do I do wrong?

Oh yes they can.

Listen carefully: "Yes. They. Can."

They can... and they will. "Can't hold"? What the hell man? Who are you to judge them?

 

[Brian_G]

 

[talanum1]

Poe says ijk relies on quaternion multiplication structure, not ordinary multiplication.

 

[airborne]

Poe says ijk relies on quaternion multiplication structure, not ordinary multiplication.

Why soo serious bro??

 

[talanum1]

It also implies i=j=k=sqrt(-1) is not valid.

 

[talanum1]

Why soo serious bro??

What makes you think I am too serious?

 

[Bliksis]

Your calculation is not a flaw in the quaternion definition; it is proof that \(i\), \(j\), and \(k\) cannot be equal. That is precisely why Hamilton needed three distinct imaginary units (and non-commutative multiplication) when he invented quaternions in 1843. The structure is consistent and extremely useful (e.g., in 3D rotations, computer graphics, and physics), but only when you keep \(i\), \(j\), and \(k\) distinct.

 

[RedViking]

Poe s.

Dis nie mooi nie.

 

[Brian_G]

What makes you think I am too serious?

 

[Prawnapple]

We have: i^2=j^2=k^2=ijk=-1. Now set i=j=k=sqrt(-1) in the fourth equation:

sqrt(-1)*sqrt(-1)*sqrt(-1) = -1*sqrt(-1) not = -1, so it doesn't hold. What do I do wrong?

Core issue

• The step “set i = j = k = √(-1)” is invalid.
  

Why

• In Quaternion algebra:
  • i,j,ki, j, ki,j,k are distinct basis elements, not numbers.
  • They behave differently from the complex unit −1\sqrt{-1}−1.
  • Multiplication is non-commutative (order matters).

Key properties

• i2=j2=k2=−1i^2 = j^2 = k^2 = -1i2=j2=k2=−1
• ij=k,  jk=i,  ki=jij = k,\; jk = i,\; ki = jij=k,jk=i,ki=j
• ji=−k,  kj=−i,  ik=−jji = -k,\; kj = -i,\; ik = -jji=−k,kj=−i,ik=−j

Why the substitution fails

• There is only one −1\sqrt{-1}−1 in complex numbers.
• Quaternions require three independent imaginary directions.
• Treating them as equal collapses the system → contradictions.

Correct interpretation

• ijk=−1ijk = -1ijk=−1 is consistent within quaternion rules, not under complex-number substitution.

 

[RedViking]

@talanum1 what is on the menu for today ?

 

[Brian_G]

@talanum1 what is on the menu for today ?

How much longer is this gonna be fun, (and maybe mildly interesting)?

Nah, he's neva gonna stop the BS theories, I say report the bugger

 

[RedViking]

How much longer is this gonna be fun, (and maybe mildly interesting)?

Nah, he's neva gonna stop the BS theories, I say report the bugger

It is not like all your posts are always better. Don't be like that. This is a community and everyone is equal.

 

[Brian_G]

It is not like all your posts are always better. Don't be like that. This is a community and everyone is equal.

Oh for sure, but he's making a big mess. Won't keep it in one thread :-/

He could call all of it "Muh Theories"

 

[talanum1]

Treating them as equal collapses the system

But their squares are equal. You are saying we cannot always draw the square root on both sides of any equation.