• 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.

• 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.

• 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.

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.

• 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 x^th 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’s 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.

• 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…

Download Mantissa Chords for Uke!

• 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!

• 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...

• 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!

• 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.

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.

• 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.

• 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.

• 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.

• Yocto,
• Zepto,
• Atto,
• Femto,
• Pico,
• Nano,
• Micro,
• Milli,

• Unity.         One Thousand Times More.

• Kilo,
• Mega,
• Giga,
• Tera,
• Peta,
• Exa,
• Zetta,
• Yotta!