Log: A Rhythm.

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Log: A Rhythm - Download at thesixtyone.com
  • 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.

     Record Scratch by Luffy at freesound.org.
Crosshairs - Download at thesixtyone.com
  • 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.

e - Download at thesixtyone.com
  • 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.

Rules of Powers - Download at thesixtyone.com
    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.

Napier's Curse - Download at thesixtyone.com
  • 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’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.

Geyser - Download at thesixtyone.com
  • 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…

Mantissa- Download at thesixtyone.com
  • 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!

If you update your web browser there will be exciting things in this spot!

Bring it Round! - Download at thesixtyone.com
  • 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...


Get by my Side. - Download at thesixtyone.com
  • 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!

Change of Base - Download at thesixtyone.com
  • 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.

The Base 2 - Download at thesixtyone.com
    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.

Scientific Notation - Download at thesixtyone.com
  • 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
D[ax] = axln(a)

Ellen X. (one over x)
D[ln(x)] = 1/x

Mr. X. (the one)
D[x] = 1

Mr. Saul Nadu. (AU)
auln(a)du = au + C

The Loge (Which is over an x)
D[log(x)] = log(e)
              x


Dax Axlna - Download at thesixtyone.com
  • 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.

UV Catastrophe - Download at thesixtyone.com
  • 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!

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Content by Sadie Bowman and Marc Gutman.     © Matheatre 2011     ^Top^