Κυριακή 13 Ιανουαρίου 2013
Σάββατο 12 Ιανουαρίου 2013
The logarithm the difference of the difference and the division of the division
Through another more careful analysis you will notice that since we have 1/n n has to be above 0
so the sum
is actually
or
going back
In any case we arrive at logarithm and i should have expected it since 1/n and log(n) are somehow related
as you cut down the unit into smaller and smaller pieces you get to something (if you add them together) we call the logarithm
What is the division? the difference of the difference
if you divide 8/2 it's like subtracting 2 until you get to zero
now what is the logarithm? the division of the division
or more compactly
and that's natural since the exponent is the multiplication of the multiplication
unfortunately it seems we stopped there
there is no widely known name for the logarithm of the logarithm - there is of course polylogarithm but that's not a completely new name
or the power of the power
and the abstraction continues
[ i really enjoy these equations
so it's more like me doing these
and in the meantime seeing the progression of folding and moving on
]
is actually
or
going back
In any case we arrive at logarithm and i should have expected it since 1/n and log(n) are somehow related
as you cut down the unit into smaller and smaller pieces you get to something (if you add them together) we call the logarithm
What is the division? the difference of the difference
if you divide 8/2 it's like subtracting 2 until you get to zero
now what is the logarithm? the division of the division
or more compactly
and that's natural since the exponent is the multiplication of the multiplication
unfortunately it seems we stopped there
there is no widely known name for the logarithm of the logarithm - there is of course polylogarithm but that's not a completely new name
or the power of the power
and the abstraction continues
[ i really enjoy these equations
so it's more like me doing these
and in the meantime seeing the progression of folding and moving on
]
Σάββατο 5 Ιανουαρίου 2013
The z-transform as an Appropriation Technique
you know all those fourier and all those fancy smanchy transforms
are none but weighted summations
so z-transform is one of my favorite ( i don't know why it stuck with me probably the name of it and it is concrete i.e. it mostly applies to concrete sequences that is discrete
whereas Mr. Fourier is all over the place and nobody knows what he means
so here's your z transform
if you choose your pieces in this form 1, 2, 3, ...
which comes out in a nice form such as
and since i'm in good spirits i'll do the derivation which is
where we disguised 1/z as a in some point for easy manipulation
that's what we do in everyday life
[and this is how you avoid aggravation
hearing everybody's opinion and flub]
so you cut your original piece into little pieces and voila off you go
isn't that what we did in the first place?
are none but weighted summations
so z-transform is one of my favorite ( i don't know why it stuck with me probably the name of it and it is concrete i.e. it mostly applies to concrete sequences that is discrete
whereas Mr. Fourier is all over the place and nobody knows what he means
so here's your z transform
which comes out in a nice form such as
and since i'm in good spirits i'll do the derivation which is
where we disguised 1/z as a in some point for easy manipulation
that's what we do in everyday life
[and this is how you avoid aggravation
hearing everybody's opinion and flub]
so you cut your original piece into little pieces and voila off you go
isn't that what we did in the first place?
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