Log: A Rhythm

by icanhasmath

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    15 original songs focused on Exponents and Logarithms! Including scientific notation, base 2, geysers, and find out who saved us from the Ultraviolet Catastrophe!

    This CD comes with a colorful 16 page booklet of lyrics and illustrations.
    AND two music videos!

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released October 17, 2011

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Track Name: Log: A Rhythm.
The brightness of a star,
The shaking of the ground,
Computational complexity,
The power of a sound.

The acid in your jar,
The measurements are found
On a logarithmic scale,
The only way I’ll be allowed,

To see the different sizes when the range is just too great,
From super small to super large, is hard to contemplate,
But log base ten will strike and then it’s quite appropriate,
One millionth is negative six, a hundred million’s eight.

See, a logarithmic scale is most concerned with magnitude,
at log base ten the jump is ten times from the one to two.
And two to three and three to four each step is ten times more.
And when we get to sixty-three we’ll fill space universally
with grains of sand the hand of Archimedes’ mind has reckoned
that to find a beach this large without an ocean is a crime,
like every passive second spent in haste!
Desert the massive massive waste of space– time to realign
less focus on the sand, more focus on mankind.

As population rises in an exponential manner,
Like markets do though they seem too prone to constant disaster,
A logarithmic scale will help us see the patterns faster,
at last a graph so prone to change, becomes a graph so rearranged
to lines and planes these simple gains brought to us by a man so strange:

A marvel of a Scotsman and a real necromancer,
kept a spider in a box like any real techno-dancer.

Named John Napier of Merchistoun, of which he was the laird.
Invented bones. wrote tomes of logarithmic prose.
Promoted points alone in action, Decimals to pwn the fractions!
Simon says, “I miss the circles - but - I think that’s just my first reaction.”

The brightness of a star,
The shaking of the ground,
Computational complexity,
The power of a sound.

The acid in your jar,
The measurements are found
On a logarithmic scale,
An exponential turnaround.
Track Name: Crosshairs
When you say, “I love you,”
you know that I’ll say it back.
When we are escaping,
you know that I’ve got your back.

Peas in pods, and bees in bonnets,
mathematics psych –
Psychoanalytic math of
what I think we’re like:

We’re like a power distribution over multiplication.
Combinations aren’t required, complications won’t arise,
but I fear I see addition symbols floating in your eyes.

Side by side we’re simple;
you are A and I am B.

Raised to any power:
A to P times B to P.

Don’t misunderstand me.
Don’t expect me.
Don’t expand me.
Extra coefficients only serve to make me antsy!

If you and I were added and
then love was multiplied,
love of you plus love of me.
Simplicity.

When operation levels
jump inside to the outside,
they strain they very fabric
of this weak analogy!

We could add another
member to our tiny crew,
Wonder-twins can not form Voltron
it takes more than two.
Three would clarify the nature
of association.
You and me are two,
but three would have the same relation!

‘cause we‘re a power distribution over multiplication.
Combinations aren’t required, complications won’t arise,
but I fear I see addition symbols - crosshairs - floating in your eyes.
Track Name: e
I crossed seven bridges to be here to day,
to bring you this important notation.
Not Functions, or Sigma i fear,
though my vision is fading, my voice is still clear.

Not U-ler but Euler.
Euler? I barely know how much I’d have if,
I added, reciprocals of all of the factorials,
turns out it’s the number of nature.
Presenting now for all to see
the main event named after me:

it’s
e! the number e, more than 2, less than 3.
e! the number e, a constant transcendentally

One plus 1 over n, all in parentheses,
to the power of n, take n to infinity.

Describe the growth of things, compounded continuously,
or half-life the radiation decays exponentially.

Edges plus two is Faces plus the Vertices.
Off topic, I’m sorry, just came to me, apologies.

The function e to the x - A.K.A. the exp().
Its inverse - the log base e
or natural log naturally.

it’s
e! the number e, more than 2, less than 3.
e! the number e, with beautiful Taylor series.

it’s
e! the number e, more than 2, less than 3.
e! the number e, a constant transcendentally

e to the i x is, cosine x plus i sin x,
it is imperative that you catch what happens next,
you see x - is measured in the radians and not degrees
using my formula it is plain for all to see
that e to the pi times i, plus one makes the quantity of zero.

Abstract I know – but still used to this very day,
when engineers transform the waves, to phasors,
not the kind that blaze, just electricty.

You see it’s

e! the number e, more than 2, less than 3.
e! the number e, as seen on x k c d.

e! the number e, more than 2, less than 3.
e! the number e:

Two point seven one eight two eight one eight two endlessly.
Infinitely continuing streaming irrational
e.
Track Name: Rules of Powers
x to the A times x to the B
is x to the A plus B
Exponent addition is the action.

x to the A over x to the B
Can always be x to the A minus B
Dividing make subtraction.

And x to the A all to the B
Oddly is x to the A times B

And x to the power of One over B
Is really a Root, The Bth root it be!

x to the Zero Always One

Negative exponents are Un-
Necessary, if you like the fractions,
Don’t leave I know you hate fractions!
I just thought this time that maybe,
It would be alright if maybe we used fractions.

x to the power of A over B
The Bth root of x to the A, you See?

x to the power of A over B
Can also be x to the A then root of B.

And x to the A all to the B
Oddly is x to the A times B

And x to the power of One over B
Is really a root, The Bth root it be!

x to the Zero always One

Negative exponents are Un-
Necessary, if you like the fractions,
Don’t leave I know you hate fractions!
But I thought this time that maybe,
You could really get over your fear of fractions.
Track Name: Napier's Curse
To the power of x,
you never seen it before,
much less solved it,
but you’re like fo-sho,
‘Cause you have ideas that won’t be denied,
You take the xth root of both sides,
But you’re scratching your head, ‘cause that didn’t help,
If the object is to get the x all by itself!

You see,
the only way to get that exponent down to earth,
for what it’s worth, there’s nothing worse,
And it is called inverse.

In this case the Logarithm’s your hearse,
use Napier’s curse to help you switch it around,
And move that exponent a whole six feet under the ground.

So use it, abuse it, apply it, remove it.
Use it, abuse it, apply it, remove it.

So why is it there - still?
Looking down laughing, deriding while you’re
crying buckets over your spilled poten-
Shall you stand this power drilling into your mind,
Kinda like the fleeting feeling that you’re dealing with Pi-
rotechnic visions of a exponential monster unwind.

Untie the lies of your lofty tormentor,
resent the disguise and embrace the inventor:
Here’s Johnny with a mantra that will cut to the center
As HE applies the inverse - exponential descenter.

Clear your mind, lift the fog,
the base of the power is the base of the log.

Clear your mind, lift the fog,
The base of the power is the base of the log.
The base of the power is the base of the log.
The base of the power is the base of the log.
The base of the power is the base of the log.

No more exponential messes for you, the essential message to you,
Be the change you want to see, apply Logs to both sides of the
Equation that’s distressing, and oppressing and depressing,
And after all the messing, and the stressing, and the testing.
I suppose logs are a blessing, but they maybe not the best thing.
Track Name: Geyser
The water at the bottom
heated up by molten rock
Is under lots of pressure
from the water at the top.

The water at the bottom
heated up by molten rock
Is under lots of pressure
from cold water at the top.

And So,
And so it doesn’t boil.
And so
it just gets really really hot!

The water at the top is warmed
and slowly turns to steam,
Releasing lots of pressure
from the water underneath.
And when the pressure’s low enough
it happens suddenly.
The super-heated water boils,
erupting fervently!
Until...until all the water’s spent!
And then,
and then the cycle starts again!
The water at the bottom
heated up by molten rock
Is under lots of pressure
from the water at the top.
WATER! BOTTOM! HEATED BY THE ROCK!
Is under lots of pressure
from the water at the top.
And So,
And so it doesn’t boil.
It just,
it just gets hotter than normal.

The water at the top is warmed
and slowly turns to steam,
Releasing lots of pressure
from the water underneath.
And when the pressure’s low enough
it happens suddenly.
The super-heated water boils,
erupting fervently!
Until...until all the water’s spent!
And then…
Track Name: Mantissa
Now I’m not killing time,
but I gotta find the place I signified,
Not a character, I stick around
don't miss the point I'm on the right
At an estimate, I vaporize.
No ghostly trace. I'm outasight.
But fill that space don't zorak me
Ya need me, I keep things tight.
Cause I’ma Mantissa!
A minor addition
written in the table
With decimal precision
I’ma Mantissa! The accuracy!
Tight as a lock, when precision’s the key...
Six hundred thousand, six, or sixty, point oh oh oh six,
When log base ten is on the scene to me it makes no diff,
exponents build characteristics the big intense,
Then I glance at the significand and chippy my 2 cents
Cause I’ma Mantissa!
A minor addition
written in the table
With decimal precision
I’ma Mantissa! The accuracy!
Tight as a lock, when precision’s the key.
I’ma Mantissa!
A minor addition
written in the table
Sittin’ with Clark Gable.
Mantissa! The decimal part!
Breakin’ your heart,
Breakin’ my heart!
Track Name: Bring It Round
You gotta bring it round,
For the exponent,
You gotta make a Sound,
For that exponent,
You see that log,
With the exponent,
Now free that log,
Of the exponent,
A constant now is found,
It was the exponent,
The constant stands its ground,
The stubborn exponent!
Unless you need,
Another exponent,
So send with speed,
To make an exponent.
You gotta bring it round,
For the exponent,
Around and round, and round
whatever your intent!
You gotta bring it round,
For the exponent,
Around and round, and round...
Track Name: Get By My Side
I got a base…and you got a face,
and I want… to use… my base…to get to your face.
2 to the 4…is multiplied by 2 to the 5,
Result …2 to the nine.
And I find…the same is…true about
Us logs…but inside out.
Plus is to times as Minus to Divide,
I got the base to get you by my side…
so get by my side.
Plus is to times as Minus to Divide,
sharing a base will get you by my side…
now get to my side.
You’re log x, and I’m log y:
And added we will simplify to
Log of x times y. I’m so inclined.
‘Cause I know, your base’s the same as mine,
At least that’s what I hope, so we combine.
Plus is to times as Minus to Divide,
I got the base to get you by my side…
so get by my side.
Plus is to times as Minus to Divide,
sharing a base will get you by my side…
now get to my side.
If perchance we are to be
subtracted then you’re x
up on my y.
Oh so sublime.
Get intertwined.
You’re so fine, that I’ll take either sign,
So please don’t be unkind, time to combine!
Track Name: Change of Base
Every Log must have a base it’s often e or ten,
Input number into place: It's x the Argument.
Awful bases cause a frown,
Shake you up an' slow you down.
But turn the corners of your mouth,
as I make the case

Change of face.
Change of pace.
Change of base.
Change your base.

Mystery Ternary Tree with
Two Hundred Forty-Three Leaves
Use logarithm at base three.
How many branches do you see?
But log base three can be replaced!
To hasten matters: Calculate!
Log 243 over Log 3,
at any equal base.

Change of face.
Change of pace.
Change of base.
Change your base.

When change of base has been invoked any base is game.
Just log of x: the argument, over log of b :base.
The bases can be anything as long as they’re the same.
So take your place, the adaptation will not hesitate!
I said the adaptation will not hesitate!
Space. It’s the place.
For your base. All your base.

Change of face.
Change of pace.
Change your base.
Change your base.
Change your.
Track Name: The Base 2
Four ones were being bullied around,
By a mean Five who hung out at
The same play ground.
The four ones were scared
for no matter the weather,
Oh, the Five was very big,
More than all of them together.
Oh four ones, there’s gotta be a way,
to beat a wicked Five at his dirty game
the situations pretty grim,
but there’re four of you,
and one of him.
One day our four heroes
were hiding from the Five.
When they met four Zeroes,
Just glad to be alive.
Together they knew
that they could put him in his place.
When one of the zeroes
got a smile across his face.
His dad had told him this once:
“All you need’s a little space,
For some zeroes and a one
to make a number to amaze.”
So the eight of them united
and decided...to build a base.
They worked out,
If - they built a base ten,
They‘d be over a million!
But that seemed a bit beyond them.
So after careful research planning and review,
they began to build a small base two.
For three Tuesdays, the ones and zeroes stayed up late.
Their base had four seats numbered:
One, two, four and eight.
And so the time had come,
but they could find no trace.
Of that bully five whom they
had plans to utterly disgrace.
They split to look for him,
imagine their surprise,
When two ones saw their base two
bein’ accosted by the Five.
He tried to sit in it,
but in base two Five don’t fit.
The two ones ran back to the base
and in its seats did sit.
They pressed the big blue button
which was labeled activate,
The base it sprang to life,
as they stepped up to the plate,
But five just ran and decked them
knocking ones and the base free
Cause one and one in a base two
still only act as three.
Another one ran to the base
but never made it there,
Cause Five had thrown her
to the ground but she was still aware,
Her actions were distractions,
Now her friends had all arrived,
And they had climbed into the base
to finally challenge five!
Five laughed in their collective face,
“I’m fighting with halfwits!
Three Zeroes and a One,
About to be bashed into bits!”
But what he didn’t realize,
when they hit Activate,
1 0 0 0 in base two’s the same as eight.
Not much more to say,
but that five got it in the face,
He woke up ten times weaker,
feeling somewhat out of place,
He vowed that he’d get even,
at least until he had spied,
The decimal point that the ones
affixed to his left side.
Track Name: Scientific Notation
A toast to numbers great and small,
Like Avogadro’s number holy moley!
It’s six hundred two quintillion
and some change.

The speed of light roughly
let c three hundred million meters
to the second though we think it might be slowing which is strange.

Also of course minute amounts,
Mu–naught magnetic constant counts for this
You thought four π (two τ) divided by ten million small,
But then you walked the Planck’s length blind:
At one point six decillionth of a meter, mind
the gap the edge was quite a way before.

These numbers all are useful, but essentially reducible
to make us able to compute them, keep us up to pace,
for trillion and quintillionth, are both hard to picture when
you know what’s really the important thing is the decimal place.

AND SO…
A necessary explanation, of Scientific Notation.
Big Significand times ten and exponential indication,
Whether minute or immenser, extra Large or quite condenser,
50 cents or 50 grand: a change of five in power land.

C three hundred million transformed into something brilliant,
As the photon glides through space at three times ten to the
eighth. Scientific haven, with an exponential heaven
Magnetic constant: four π (two τ) - times ten to negative seven.

Scientific Notation
It separates computation.
Significand fracas! Look right!
Exponent vs. Exponent
Multiply / divide Miss Siggy
Add / subtract the exponent
Respectively as I have said,
Now simplify the exponent.

Slide around the decimal
Until there is only a single digit to it’s left
There is only one step left.
For each slide left add one,
To the exponential sum,

When sliding right, you take away,
Since Sixteen-thirty-seven when
Descartes figured a significant method
Leading to invention of convention,
And you need no invitation, for the mention
Words become undone

Vive! Scientific Notation.
Track Name: Dax Axlna (The Loge)
Dax Axlna Private Eye,
and the case of the loge!
Which is over an x!

Meet Miss Ellen X! -
She has one over ex–tremely
important task, to find the LOGE!

Dax Axlna hired by Miss Ellen X,
Daughter of, The Famous Mr. X!

The Mister X! He’s the one,
who has left us to solve
the Mystery of the Loge!

And what is this Loge?
Well it’s made from a log,
ex- perts know it -
to be over an x!

And where is this Loge?
When it’s found they all will know
Up above the glow of - Mr. X’s base.

Mister Saul Nadu,
is here, here to manage the funds,
of the Famous Mr. X
Mister Saul Nadu is here,
here to handle the gold. AKA – Au!

But who is Saul Nadu!
The man who betrayed you!
By you I mean the Famous Mr. X!

He’s cooked all your books,
and the dinner he cooked laced with strychnine,
He told you it was thyme.

Dax Axlna, and Miss Ellen X
race against time,
to discover the loge.

Dax Axlna, and Miss Ellen X
Up on the roof,
which is shaped like an x!

The Loge now is Sighted!
Our heroes are frightened,
By the plight of bullets flying through the night!
But no one is faster than Dax, the Master blaster,
Disaster! for Saul Nadu’s been outclassed!

Dax Axlna Private Eye, has recovered the loge!
Which was over an x!

For Miss Ellen X! She had one over ex-tremely
important task. The case is closed!

Dax Axlna, and Miss Ellen X up on the roof,
in the midst of the night.

Dax Axlna, and Miss Ellen X up on the roof,
in the midst of the night.
Track Name: UV Catastrophe
Rayleigh-Jeans you must be kidding,
Wilhelm Wien is dead to me.
When you write equations they should work at every frequency.

Measured wavelengths radiating from an ideal blackbody,
At a given temperature show me your inconsistency.

And who the h is he?
A man appearing on the scene.
A man of great discretion sees,
To make the laws complete,
You gotta be discrete.

MAX PLANCK!

Who will save us from the ultraviolet catastrophe? MAX PLANCK!
Who will save us from the ultraviolet catastrophe? MAX PLANCK!

In the middle 1890’s Planck was tryin’ to maximize,
The light emitted by a bulb, to ultra-fy efficiency.
So he wrote a small equation based on ideal oscillation.
But to his intense frustration, it still failed for the UV!

In an act of desperation he accepted an assumption,
(for the sake of innovation) that he might not be correct.
Now released from prior notions, he was free to revelations
Contradicting current thinking in ways he could not project.

Statistical mechanics leads,
Him to quantize the energy.
Planck’s constant times the frequency,
Discreet levels of energy,
No more UV catastrophe!

MAX PLANCK!

Who has saved us from the ultraviolet catastrophe? MAX PLANCK!
Who has saved us from the ultraviolet catastrophe? MAX PLANCK!

Planck didn’t stop at energy, no unit has immunity,
when physical relationships can be expressed more succinctly.
Mass, Length, Charge Time, Temperature,
reduced as small as they can be,
Analog is out, the dawning of Quantum Reality.

He has saved us from the ultraviolet catastrophe. MAX PLANCK!
He amazed us with his plan to quantize the energy. MAX PLANCK!
He has saved us from the ultraviolet catastrophe. MAX PLANCK!
Playin’ violin with Einstein in pre-war Germany. MAX PLANCK!
Nobel Prize for Physics, in a state of constant hardcore! MAX PLANCK!
Six point six two six times 10 to negative thirty four! MAX PLANCK!

Saved us from the catastrophe. MAX PLANCK! MAX PLANCK!
Saved us from the catastrophe. MAX PLANCK! MAX PLANCK!
Saved us from the catastrophe. MAX PLANCK! MAX PLANCK!
Saved us from the catastrophe.
Track Name: Giga-Bit Pico-Chip
Yocto,
Zepto,
Atto,
Femto,
Pico,
Nano,
Micro,
Milli,
Unity. One Thousand Times More.
Kilo,
Mega,
Giga,
Tera,
Peta,
Exa,
Zetta,
Yotta!