Sedenion
In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the reals obtained by applying the Cayley–Dickson construction to the octonions. The set of sedenions is denoted by 
.
The term "sedenion" is also used for other 16-dimensional algebraic structures, such as a tensor product of 2 copies of the biquaternions, or the algebra of 4 by 4 matrices over the reals, or that studied by Smith (1995).
Arithmetic
Like octonions, multiplication of sedenions is neither commutative nor associative.
But in contrast to the octonions, the sedenions do not even have the property of being alternative.
They do, however, have the property of power associativity, which can be stated as for any element x of , the power 
is well-defined. They are also flexible.
Every sedenion is a linear combination of the unit sedenions e0, e1, e2, e3, ...,e15, which form a basis of the vector space of sedenions. Every sedenion can be represented in the form
Addition and subtraction are defined by the addition and subtraction of corresponding coefficients and multiplication is distributive over addition.
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Tragicomic
by: Pseudo NeinWhen everything is black
And the clowns have all gone home
You're left standing in the middle of the stage
And you know that you're all alone
The clouds are made of acid and the rain is coming down
And the puddle that you stand in is the only one around
Then the colors start to fade and the blue will turn to grey
And you should run away
In the darkness
The relentless alcoholics
Are the solace that you seek
And the smile that you see is
The blinding parody
Of the soulless life you lead
And you know that you are not asleep
When everything is fading
And the clowns are all that remain
In your tragicomic life you know
It's driving you insane
The clouds are made of acid and the rain is coming down
And the puddle that you stand in is the only one around
Then the colors start to fade and the blue will turn to grey
And you should run away
And the road you're walking
Is a dead end waiting
When the life you're leading
Is the path you're taking...
And when all that's left is
All that you're making
You kick and scream but
You're still not waking.
Deep in the darkness
The relentless alcoholics
Are the solace that you seek
And the smile that you see is
The blinding parody
Of the soulless life you lead
And you know that you are not asleep
Deep in the darkness
The relentless alcoholics
Are the solace that you seek
And the smile that you see is
The blinding parody
Of the soulless life you lead