1 + 1 = 2

[Piero]

6/2(1+2) = 9
or
6/2(1+2) = 1
?
The answer depends on your calculator...

Maybe I'm missing something, but if calculator respects parenthesis, isn't it always 9?

[Olli]

Heh... isn't that really great? I read a wonderful explanation of how he got the equation (deducting from sin/cos formulas) but cannot remember the book

+

6/2(1+2) = 9
or
6/2(1+2) = 1
?
The answer depends on your calculator...

Maybe I'm missing something, but if calculator respects parenthesis, isn't it always 9?

=



for piero : on 4th minute and 17th second, when the guy starts to shoot the e exponential symbol, cos and sin appear !!
Else you have this :
e^(ix) = cos(x) + iSin(x)

and if you want to see a simple man who walks, here is a link..

[Piero]

6/2(1+2) = 6*1/2*3

[Olli]

Note :

i is considered as a vector.

i is defined as i * i = (-1)

As (-1) * (-1) = 1,
i * i * i * i = 1

And i * i * i * i is also considered as a vector
This vector is as i / i.

If we represent the two vectors i and i / i on a right plane, we can consider that, if i^(4*k) = 1 (k being a relative integer number), then there are 4 directions for the vectors i^(4*k). i is constant. So the 4 angles between the 4 directions are the same ones. So, the vectors i^1 and i^0 are perpendicular on this right plane.

By extension, if we consider :
i * i = -1
j * j = -1
k * k = -1
In a space, where we forget i^0 as a vector, there is a mechanic to find several relative directions for i, j and k in this space (as i * i * i * i = 1) from this : i * k * j / 1 = 1.

[Piero]

from this : i * k * j / 1 = 1.

[Olli]

Nice tribute! Note that the notion of using three distinct imaginary numbers i, j and k to apply 3 directions in a space, had its first hours in Hamilton's mind.

What it is off topic, but it surprises me a lot, is the death we give to this brilliant mind :
<< He [Hamilton] died on 2 September 1865, following a severe attack of gout. >>

I am very surprised, because Jacques Psychriste discovered that colchicum was an antidote for gout attacks, 1300 years earlier !

Plus colchicum appears naturally in Europa every year on September, since the greek gold age !

I am subject to this disease, and never I will die by this disease, even if it would be 100 times more strong on me. Colchicum acts two hours after a taken, and we must calculate precisely and beforehand according to its weight (else it's a very powerful poison).

Hamilton was however a mathematician...

[Piero]

Note that the notion of using three distinct imaginary numbers i, j and k to apply 3 directions in a space

I'm not practical with vectors, even less if imaginary, but sounds like Riemann geometry, and that has to do with prime numbers, right?

[Piero]

I am very surprised, because Jacques Psychriste discovered that colchicum was an antidote for gout attacks, 1300 years earlier !

I'm not, being what happened recently...

[Olli]

Personal hypothesis: there was an error in the supply chain of the plant. Someone confused a colchicum drying time. A dose, for a plant dried since the Fall of 1864, was prepared, when the plant had been dried for a week (August 1865).

The alkaloid concentration in a drying plant approximately follows the curve of an inverse function.
(Image source site - pedagogic site about maths
So, he has maybe absorbed a quantity 100 times above the wanted quantity...
The disease is painful. But too much colchicum is very painful too.

Anyway, his math demo was a breakthrough.

[Piero]

the plant had been dried

You made me remember the interesting (forgive me Fred) story of the "cannabis" plant...
Math: try to calculate how much money they "stole" by suppressing it (you can even make car bodies and fuel out of it... no pollution……)

[Olli]

Today, the cannabis is used for its isothermic properties. Imagine you build your house. And there has been a problem of genetic in the cannabis you used in the architecture of your house.

Let's imagine you are parent and married. And there is a fire in the house.

Imagine the stoned brains of the firefighters who have to brave the flames to save your baby. Four tons of thermal insulation that burns out in an hour. Not sure the rescue mission will succeed.

400mg = you discover colors that are not in the user manual.
4 tons = 10 000 000 times the 400mg = I fully ignore the biologic effects on the brain of a guy which take such a quantity. Anyway if you give to only one person a quantity which send a whole country in the dreams of woodstock, the final human configuration and the final administrative configuration wont allow you to give an opinion.

[CDXbow]

Personal hypothesis: there was an error in the supply chain of the plant. Someone confused a colchicum drying time. A dose, for a plant dried since the Fall of 1864, was prepared, when the plant had been dried for a week (August 1865).

The alkaloid concentration in a drying plant approximately follows the curve of an inverse function.
(Image source site - pedagogic site about maths
So, he has maybe absorbed a quantity 100 times above the wanted quantity...
The disease is painful. But too much colchicum is very painful too.

Anyway, his math demo was a breakthrough.

I think the colchicine degradation is irrelevant. Gout doesn't kill you unless is causes a complication like kidney stones and renal failure. So the story he died after an episode of heavy drinking and acute gout is rubbish. The comment in this link discusses the original source of the story, which appears to be a fabrication. https://seamusdubhghaill.com/2021/09/02 ... -hamilton/
He suffered severe 'bronchitis', which in mid 19th century could be one of many chronic lung diseases. If he died with a big red swollen foot the diagnosis would be more likely to be septic arthritis or osteomyelitis than gout.

[DarkDragon]

i² + j² + k² = ijk = -1

What about octonions and sedenions ?

[Olli]

(www.pypi.org)

[Olli]

A succinct answer for DarkDragon: a human being can imagine, in his head, the quaternion mechanism. But the octonion mechanism is impossible to imagine in the head. Rare people achieve this on paper. But it is really the computer tool that makes it possible to affirm the existence of these more complex algebraic generations.

I think the colchicine degradation is irrelevant. Gout doesn't kill you unless is causes a complication like kidney stones and renal failure. So the story he died after an episode of heavy drinking and acute gout is rubbish [...]

I find your version of the end of Mister Hamilton, is real.

I thank you for the less incredible details you mention above, and I thank you also, for the data source.

I recall them again here :
Death of the mathematician Sir William Rowan Hamilton, by Jim Doyle

[...] He [Sir Hamilton] suffered severe 'bronchitis', which in mid 19th century could be one of many chronic lung diseases. If he died with a big red swollen foot the diagnosis would be more likely to be septic arthritis or osteomyelitis than gout.

I recall also an math historic scale :

1 : REAL
2 : COMPLEX
4 : QUATERNION (discovered by Hamilton in 1843)
8 : OCTONION (unable to be rightly studied without computing tool)
16 : SEDENION
32 : PATHION* (Mul table from Canada)
64 : CHINGON*
128 : ROUTON*
256 : VOUDON*

(*) I absolutely actually ignore which math tools are usable for these numbers.