Euler problem 41

Project Euler is a pretty good way to exercise your programming muscles. I tend to think that the hardest part is usually the math.

So when I figure one of them out in minutes, I’m pretty happy about it.

library(gtools)
library(numbers)
pandig <- function(n){
x <- permutations(n,n)
x <- apply(x,1, function(x) paste(x, collapse=""))
return(x)
}
y <- as.numeric(pandig(7))
max(y[isPrime(y)])

The surprising thing is that largest pandigital prime does not begin with either 8 or 9.

Practical project management

Project management is not easy. A handfull of practical hints from ~20 years of experience:

  • Dont ask for more ressources. Ask for the ressources you were promised, but never got.
  • Dont ask for an extension on deadlines. Ask that the ones you got in the first place are not changed.
  • Never expect anyone to have heard of the iron triangle of project management.
    Even if they actually have heard of it before.
  • Never expect anyone to have any understanding of what the project is about.
    Even if they are in charge of managing it.
  • When, at the beginning of a project, estimations of the necessary ressources are deemed irrelevant by the steering commitee, buy antacids. You will get an ulcer.
  • When someone is given a budget – never expect them to stay within it.

 

Star Trek in stardate order

By popular demand: Star Trek in stardate order. Discovery is not in the list. I think we still have to figure out if it is a heretical series, or if it fits into the correct, and only true timeline.

Series Season Title Episode (Star)date(s) Stardate used for sorting
ENT 1 Broken Bow 1×01/02 4/16/2151
ENT 1 Fight or Flight 1×03 05-06-2151
ENT 1 Strange New World 1×04 Unknown
ENT 1 Unexpected 1×05 Unknown
ENT 1 Terra Nova 1×06 Unknown
ENT 1 The Andorian Incident 1×07 Unknown
ENT 1 Breaking the Ice 1×08 Unknown
ENT 1 Civilization 1×09 7/31/2151
ENT 1 Fortunate Son 1×10 Unknown
ENT 1 Silent Enemy 1×12 09-01-2151
ENT 1 Cold Front 1×11 09-09-2151
ENT 1 Dear Doctor 1×13 Unknown
ENT 1 Shadows of P’Jem 1×15 Unknown
ENT 1 Sleeping Dogs 1×14 Unknown
ENT 1 Shuttlepod One 1×16 11-09-2151
ENT 1 Fusion 1×17 Unknown
ENT 1 Rogue Planet 1×18 Unknown
ENT 1 Acquisition 1×19 Unknown
ENT 1 Oasis 1×20 Unknown
ENT 1 Detained 1×21 Unknown
ENT 1 Vox Sola 1×22 Unknown
ENT 1 Fallen Hero 1×23 02-09-2152
ENT 1 Desert Crossing 1×24 02-12-2152
ENT 1 Two Days and Two Nights 1×25 2/18/2152
ENT 1 Shockwave 1×26 Unknown
ENT 2 Shockwave, Part II 2×01 Unknown
ENT 2 Carbon Creek 2×02 04-12-2152
ENT 2 Minefield 2×03 Unknown
ENT 2 Dead Stop 2×04 Unknown
ENT 2 A Night in Sickbay 2×05 Unknown
ENT 2 Marauders 2×06 Unknown
ENT 2 The Seventh 2×07 Unknown
ENT 2 The Communicator 2×08 Unknown
ENT 2 Singularity 2×09 8/14/2152
ENT 2 Vanishing Point 2×10 Unknown
ENT 2 Precious Cargo 2×11 09-12-2152
ENT 2 The Catwalk 2×12 9/18/2152
ENT 2 Dawn 2×13 Unknown
ENT 2 Stigma 2×14 Unknown
ENT 2 Cease Fire 2×15 Unknown
ENT 2 Future Tense 2×16 Unknown
ENT 2 Canamar 2×17 Unknown
ENT 2 The Crossing 2×18 Unknown
ENT 2 Judgment 2×19 Unknown
ENT 2 Horizon 2×20 01-10-2153
ENT 2 The Breach 2×21 Unknown
ENT 2 Cogenitor 2×22 Unknown
ENT 2 Regeneration 2×23 03-01-2153
ENT 2 First Flight 2×24 Unknown
ENT 2 Bounty 2×25 3/21/2153
ENT 2 The Expanse 2×26 4/24/2153
ENT 3 The Xindi 3×01 Unknown
ENT 3 Anomaly 3×02 Unknown
ENT 3 Extinction 3×03 Unknown
ENT 3 Rajiin 3×04 Unknown
ENT 3 Impulse 3×05 Unknown
ENT 3 Exile 3×06 Unknown
ENT 3 The Shipment 3×07 Unknown
ENT 3 Twilight 3×08 Unknown
ENT 3 North Star 3×09 Unknown
ENT 3 Similitude 3×10 Unknown
ENT 3 Carpenter Street 3×11 Unknown
ENT 3 Chosen Realm 3×12 Unknown
ENT 3 Proving Ground 3×13 12-06-2153
ENT 3 Stratagem 3×14 12-12-2153
ENT 3 Harbinger 3×15 12/27/2153
ENT 3 Doctor’s Orders 3×16 Unknown
ENT 3 Azati Prime 3×18 2154-01
ENT 3 Hatchery 3×17 01-08-2154
ENT 3 Damage 3×19 Unknown
ENT 3 The Forgotten 3×20 Unknown
ENT 3 3×21 Unknown
ENT 3 The Council 3×22 02-12-2154
ENT 3 Countdown 3×23 2/13/2154
ENT 3 Zero Hour 3×24 2/14/2154
ENT 4 Storm Front 4×01 Unknown
ENT 4 Storm Front, Part II 4×02 Unknown
ENT 4 Home 4×03 Unknown
ENT 4 Borderland 4×04 5/17/2154
ENT 4 Cold Station 12 4×05 Unknown
ENT 4 The Augments 4×06 5/27/2154
ENT 4 The Forge 4×07 Unknown
ENT 4 Awakening 4×08 Unknown
ENT 4 Kir’Shara 4×09 Unknown
ENT 4 Daedalus 4×10 Unknown
ENT 4 Observer Effect 4×11 Unknown
ENT 4 Babel One 4×12 11-12-2154
ENT 4 United 4×13 11/15/2154
ENT 4 The Aenar 4×14 Unknown
ENT 4 Affliction 4×15 11/27/2154
ENT 4 Divergence 4×16 2154-12
ENT 4 Bound 4×17 12/27/2154
ENT 4 In a Mirror, Darkly 4×18 1/13/2155
ENT 4 In a Mirror, Darkly, Part II 4×19 1/18/2155
ENT 4 Demons 4×20 1/19/2155
ENT 4 Terra Prime 4×21 Unknown
TOS 0 The Cage 0x01
TAS 1 The Magicks of Megas-Tu 1×08 1254.4 1254.4
TOS 1 Where No Man Has Gone Before 1×01 1312.4 – 1313.8 1312.4
TOS 1 Mudd’s Women 1×03 1329.8 – 1330.1 1329.8
TOS 1 The Corbomite Maneuver 1×02 1512.2 – 1514.1 1512.2
TOS 1 The Man Trap 1×05 1513.1 – 1513.8 1513.1
TOS 1 Charlie X 1×07 1533.6 – 1535.8 1533.6
TOS 1 The Enemy Within 1×04 1672.1 – 1673.1 1672.1
TOS 1 The Naked Time 1×06 1704.2 – 1704.4 1704.2
TOS 1 Balance of Terror 1×08 1709.2 – 1709.6 1709.2
TOS 1 The Squire of Gothos 1×18 2124.5 – 2126.3 2124.5
TOS 1 What Are Little Girls Made Of? 1×09 2712.4 2712.4
TOS 1 Miri 1×11 2713.5 – 2713.3 2713.5
TOS 1 Dagger of the Mind 1×10 2715.1 – 2715.2 2715.1
TOS 1 The Conscience of the King 1×12 2817.6 – 2819.8 2817.6
TOS 1 The Galileo Seven 1×13 2821.5 – 2823.8 2821.5
TOS 1 Court Martial 1×14 2947.3 – 2950.1 2947.3
TOS 1 The Menagerie, Part I 1×15 3012.4 – 3012.6 3012.4
TOS 1 The Menagerie, Part II 1×16 3013.1 – 3013.2 3013.1
TOS 2 Catspaw 2×01 3018.2 3018.2
TOS 1 Shore Leave 1×17 3025.3 – 3025.8 3025.3
TOS 1 Arena 1×19 3045.6 – 3046.2 3045.6
TOS 1 The Alternative Factor 1×20 3087.6 – 3088.7 3087.6
TOS 1 Tomorrow is Yesterday 1×21 3113.2 – 3114.1 3113.2
TOS 1 Space Seed 1×24 3141.9 – 3143.3 3141.9
TOS 1 The Return of the Archons 1×22 3156.2 – 3158.7 3156.2
TAS 2 The Practical Joker 2×03 3183.3 3183.3
TOS 1 A Taste of Armageddon 1×23 3192.1 – 3193.0 3192.1
TOS 1 The Devil in the Dark 1×26 3196.1 3196.1
TOS 1 Errand of Mercy 1×27 3198.4 – 3201.7 3198.4
TOS 2 The Gamesters of Triskelion 2×17 3211.7 – 3259.2 3211.7
TOS 2 Metamorphosis 2×02 3219.8 – 3220.3 3219.8
TOS 1 Operation — Annihilate! 1×29 3287.2 – 3289.8 3287.2
TOS 2 Amok Time 2×05 3372.7 3372.7
TOS 1 This Side of Paradise 1×25 3417.3 – 3417.7 3417.3
TOS 2 Who Mourns for Adonais? 2×04 3468.1 3468.1
TOS 2 The Deadly Years 2×11 3478.2 – 3479.4 3478.2
TOS 2 Friday’s Child 2×03 3497.2 – 3499.1 3497.2
TOS 2 The Changeling 2×08 3541.9 3541.9
TOS 2 Wolf in the Fold 2×07 3614.9 – 3615.4 3614.9
TOS 2 Obsession 2×18 3619.2 – 3620.7 3619.2
TOS 2 The Apple 2×09 3715.0 – 3715.6 3715
TOS 2 Journey to Babel 2×15 3842.3 – 3843.4 3842.3
TOS 2 Bread and Circuses 2×14 4040.7 – 4041.7 4040.7
TAS 1 The Slaver Weapon 1×14 4187.3 4187.3
TOS 2 The Doomsday Machine 2×06 4202.9 4202.9
TOS 2 A Private Little War 2×16 4211.4 – 4211.8 4211.4
TOS 2 The Immunity Syndrome 2×19 4307.1 – 4309.4 4307.1
TOS 3 Elaan of Troyius 3×02 4372.5 4372.5
TOS 3 Spectre of the Gun 3×01 4385.3 4385.3
TOS 2 I, Mudd 2×12 4513.3 4513.3
TOS 2 The Trouble with Tribbles 2×13 4523.3 – 4525.6 4523.3
DS9 5 Trials and Tribble-ations 5×06 4523.7 4523.7
TOS 2 By Any Other Name 2×21 4657.5 – 4658.9 4657.5
TOS 2 The Ultimate Computer 2×24 4729.4 – 4731.3 4729.4
TOS 2 Return to Tomorrow 2×22 4768.3 – 4770.3 4768.3
TOS 3 The Paradise Syndrome 3×03 4842.6 – 4843.6 4842.6
TAS 1 Mudd’s Passion 1×10 4978.5 4978.5
TOS 3 The Enterprise Incident 3×04 5027.3 – 5027.4 5027.3
TOS 3 And the Children Shall Lead 3×05 5029.5 5029.5
TOS 2 A Piece of the Action 2×20 Unknown 5101
TOS 2 Patterns of Force 2×23 Unknown 5102
TOS 2 The Omega Glory 2×25 5103
TOS 2 Assignment: Earth 2×26 Unknown 5104
TOS 1 The City on the Edge of Forever 1×28 Unknown 5105
TOS 2 Mirror, Mirror 2×10 Unknown 5106
TOS 3 Day of the Dove 3×11 Unknown 5108
TOS 3 That Which Survives 3×14 Unknown 5109
TOS 3 The Empath 3×08 5121.5 5121.5
TAS 1 The Survivor 1×06 5143.3 5143.3
TAS 1 Beyond the Farthest Star 1×01 5221.3 – 5221.8 5221.3
TAS 1 The Time Trap 1×12 5267.2 – 5267.6 5267.2
TAS 2 Albatross 2×04 5275.6 – 5276.8 5275.6
TAS 1 One of Our Planets Is Missing 1×03 5371.3 – 5372.1 5371.3
TAS 1 Yesteryear 1×02 5373.4 5373.4
TAS 1 More Tribbles, More Troubles 1×05 5392.4 5392.4
TOS 3 The Mark of Gideon 3×17 5423.4 – 5423.8 5423.4
TOS 3 Spock’s Brain 3×06 5431.4 – 5432.3 5431.4
TOS 3 For the World is Hollow and I Have Touched the Sky 3×10 5476.3 – 5476.4 5476.3
TAS 1 The Lorelei Signal 1×04 5483.7 – 5483.9 5483.7
TAS 1 The Ambergris Element 1×13 5499.9 5499.9
TAS 1 The Eye of the Beholder 1×15 5501.2 5501.2
TAS 1 The Infinite Vulcan 1×07 5554.4 -5554.8 5554.4
TAS 1 The Terratin Incident 1×11 5577.3 – 5577.7 5577.3
TAS 1 Once Upon a Planet 1×09 5591.2 5591.2
TOS 3 Is There in Truth No Beauty? 3×07 5630.7 – 5630.8 5630.7
TAS 1 The Jihad 1×16 5683.1 5683.1
TOS 3 The Tholian Web 3×09 5693.2 5693.2
TOS 3 Wink of an Eye 3×13 5710.5 – 5710.9 5710.5
TOS 3 Whom Gods Destroy 3×16 5718.3 5718.3
TOS 3 The Lights of Zetar 3×18 5725.3 – 5725.6 5725.3
TOS 3 Let That Be Your Last Battlefield 3×15 5730.2 – 5730.7 5730.2
TOS 3 Plato’s Stepchildren 3×12 5784.2 – 5784.3 5784.2
TOS 3 The Cloud Minders 3×19 5818.4 – 5819.3 5818.4
TOS 3 The Way to Eden 3×20 5832.3 – 5832.6 5832.3
TOS 3 Requiem for Methuselah 3×21 5843.7 – 5843.8 5843.7
TOS 3 The Savage Curtain 3×22 5906.4 – 5906.5 5906.4
TOS 3 Turnabout Intruder 3×24 5928.5 – 5930.3 5928.5
TOS 3 All Our Yesterdays 3×23 5943.7 – 5943.9 5943.7
TAS 2 How Sharper Than a Serpent’s Tooth 2×05 6063.4 – 6063.5 6063.4
TAS 2 The Pirates of Orion 2×01 6334.1 – 6335.6 6334.1
TAS 2 The Counter-Clock Incident 2×06 6770.1 – 6770.6 6770.1
TAS 2 Bem 2×02 7403.6 7403.6
MOV Star Trek: The Motion Picture 1 7412.6 7412.6
MOV Star Trek 2: The Wrath of Khan 2 8130.4 8130.4
MOV Star Trek 3: The Search for Spock 3 8210.3 8210.3
MOV Star Trek 4: The Voyage Home 4 8390 8390
MOV Star Trek 5: The Final Frontier 5 8454.1 8454.1
MOV Star Trek 6: The Undiscovered Country 6 9521.6 9521.6
TNG 1 Encounter at Farpoint 1×01/02 41153.7 41153.7
TNG 1 Encounter at Farpoint II 1×01/02 41153.7 41153.7
TNG 1 The Naked Now 1×03 41209.2 41209.2
TNG 1 Code of Honor 1×04 41235.25 41235.25
TNG 1 Datalore 1×13 41242.4 41242.4
TNG 1 Lonely Among Us 1×07 41249.3 41249.3
TNG 1 Justice 1×08 41255.6 41255.6
TNG 1 Where No One Has Gone Before 1×06 41263.1 41263.1
TNG 1 Haven 1×11 41294.5 41294.5
TNG 1 Too Short a Season 1×16 41309.5 41309.5
TNG 1 11001001 1×15 41365.9 41365.9
TNG 1 The Last Outpost 1×05 41386.4 41386.4
TNG 1 Coming of Age 1×19 41461.2 41461.2
TNG 1 Home Soil 1×18 41463.9 41463.9
TNG 1 Heart of Glory 1×20 41503.7 41503.7
TNG 1 When The Bough Breaks 1×17 41509.1 41509.1
TNG 1 Hide and Q 1×10 41590.5 41590.5
TNG 1 Skin of Evil 1×23 41601.3 41601.3
TNG 1 Angel One 1×14 41636.9 41636.9
TNG 1 We’ll Always Have Paris 1×24 41697.9 41697.9
TNG 1 The Battle 1×09 41723.9 41723.9
TNG 1 Conspiracy 1×25 41775.5 41775.5
TNG 1 The Arsenal of Freedom 1×21 41798.2 41798.2
TNG 1 Symbiosis 1×22 Unknown 41800
TNG 1 The Neutral Zone 1×26 41986 41986
TNG 1 The Big Goodbye 1×12 41997.7 41997.7
TNG 2 The Child 2×01 42073.1 42073.1
TNG 2 Where Silence Has Lease 2×02 42193.6 42193.6
TNG 2 Elementary, Dear Data 2×03 42286.3 42286.3
TNG 2 The Outrageous Okona 2×04 42402.7 42402.7
TNG 2 The Schizoid Man 2×06 42437.5 42437.5
TNG 2 Loud As A Whisper 2×05 42477.2 42477.2
TNG 2 Unnatural Selection 2×07 42494.8 42494.8
TNG 2 A Matter Of Honor 2×08 42506.5 42506.5
TNG 2 The Measure Of A Man 2×09 42523.7 42523.7
TNG 2 The Dauphin 2×10 42568.8 42568.8
TNG 2 Contagion 2×11 42609.1 42609.1
TNG 2 The Royale 2×12 42625.4 42625.4
TNG 2 Time Squared 2×13 42679.2 42679.2
TNG 2 The Icarus Factor 2×14 42686.4 42686.4
TNG 2 Pen Pals 2×15 42695.3 42695.3
TNG 2 Q Who 2×16 42761.3 42761.3
TNG 2 Samaritan Snare 2×17 42779.1 42779.1
TNG 2 Up The Long Ladder 2×18 42823.2 42823.3
TNG 2 Manhunt 2×19 42859.2 42859.2
TNG 2 The Emissary 2×20 42901.3 42901.3
TNG 2 Peak Performance 2×21 42923.4 42923.4
TNG 2 Shades of Gray 2×22 42976.1 42976.1
TNG 3 Evolution 3×01 43125.8 43125.8
TNG 3 The Ensigns of Command 3×02 43133.3 43133.3
TNG 3 The Survivors 3×03 43152.4 43152.4
TNG 3 Who Watches The Watchers 3×04 43173.5 43173.5
TNG 3 The Bonding 3×05 43198.7 43198.7
TNG 3 Booby Trap 3×06 43205.6 43205.6
TNG 3 The Enemy 3×07 43349.2 43349.2
TNG 3 The Price 3×08 43385.6 43385.6
TNG 3 The Vengeance Factor 3×09 43421.9 43421.9
TNG 3 The Defector 3×10 43462.5 43462.5
TNG 3 The Hunted 3×11 43489.2 43489.2
TNG 3 The High Ground 3×12 43510.7 43510.7
TNG 3 Deja Q 3×13 43539.1 43539.1
TNG 3 A Matter of Perspective 3×14 43610.4 43610.4
TNG 3 Yesterday’s Enterprise 3×15 43625.2 43625.2
TNG 3 The Offspring 3×16 43657 43657
TNG 3 Sins of the Father 3×17 43685.2 43685.2
TNG 3 Allegiance 3×18 43714.1 43714.1
TNG 3 Captain’s Holiday 3×19 43745.2 43745.2
TNG 3 Tin Man 3×20 43779.3 43779.3
TNG 3 Hollow Pursuits 3×21 43807.4 43807.4
TNG 3 The Most Toys 3×22 43872.2 43872.2
TNG 3 Sarek 3×23 43917.4 43917.4
TNG 3 Ménage à Troi 3×24 43930.7 43930.7
TNG 3 Transfigurations 3×25 43957.2 43957.2
TNG 3 The Best of Both Worlds 3×26 43989.1 43989.1
TNG 4 The Best of Both Worlds, Part II 4×01 44001.4 44001.4
TNG 4 Family 4×02 44012.3 44012.3
TNG 4 Brothers 4×03 44085.7 44085.7
TNG 4 Suddenly Human 4×04 44143.7 44143.7
TNG 4 Remember Me 4×05 44161.2 44161.2
TNG 4 Legacy 4×06 44215.2 44215.2
TNG 4 Reunion 4×07 44246.3 44246.3
TNG 4 Future Imperfect 4×08 44286.5 44286.5
TNG 4 Final Mission 4×09 44307.3 44307.3
TNG 4 The Loss 4×10 44356.9 44356.9
TNG 4 Data’s Day 4×11 44390.1 44390.1
TNG 4 The Wounded 4×12 44429.6 44429.6
TNG 4 Devil’s Due 4×13 44474.5 44474.5
TNG 4 First Contact 4×15 Unknown 44500
TNG 4 Clues 4×14 44502.7 44502.7
TNG 4 Galaxy’s Child 4×16 44614.6 44614.6
TNG 4 Night Terrors 4×17 44631.2 44631.2
TNG 4 Identity Crisis 4×18 44664.5 44664.5
TNG 4 The Nth Degree 4×19 44704.2 44704.2
TNG 4 Qpid 4×20 44741.9 44741.9
TNG 4 The Drumhead 4×21 44769.2 44769.2
TNG 4 Half a Life 4×22 44805.3 44805.3
TNG 4 The Host 4×23 44821.3 44821.3
TNG 4 The Mind’s Eye 4×24 44885.5 44885.5
TNG 4 In Theory 4×25 44932.3 44932.3
TNG 4 Redemption 4×26 44995.3 44995.3
TNG 5 Redemption II 5×01 45020.4 45020.4
TNG 5 Darmok 5×02 45047.2 45047.2
TNG 5 Ensign Ro 5×03 45076.3 45076.3
TNG 5 Silicon Avatar 5×04 45122.3 45122.3
TNG 5 Disaster 5×05 45156.1 45156.1
TNG 5 The Game 5×06 45208.2 45208.2
TNG 5 Unification I 5×07 45236.4 45236.4
TNG 5 Unification II 5×08 45245.8 45245.8
TNG 5 A Matter of Time 5×09 45349.1 45349.1
TNG 5 New Ground 5×10 45376.3 45376.3
TNG 5 Hero Worship 5×11 45397.3 45397.3
TNG 5 Violations 5×12 45429.3 45429.3
TNG 5 The Masterpiece Society 5×13 45470.1 45470.1
TNG 5 Conundrum 5×14 45494.2 45494.2
TNG 5 Power Play 5×15 45571.2 45571.2
TNG 5 Ethics 5×16 45587.3 45587.3
TNG 5 The Outcast 5×17 45614.6 45614.6
TNG 5 Cause and Effect 5×18 45652.1 45652.1
TNG 5 The First Duty 5×19 45703.9 45703.9
TNG 5 Cost of Living 5×20 45733.6 45733.6
TNG 5 The Perfect Mate 5×21 45761.3 45761.3
TNG 5 Imaginary Friend 5×22 45832.1 45832.1
TNG 5 I Borg 5×23 45854.2 45854.2
TNG 5 The Next Phase 5×24 45892.4 45892.4
TNG 5 The Inner Light 5×25 45944.1 45944.1
TNG 5 Time’s Arrow 5×26 45959.1 45959.1
TNG 6 Time’s Arrow, Part II 6×01 46001.3 46001.3
TNG 6 Realm of Fear 6×02 46041.1 46041.1
TNG 6 Man of the People 6×03 46071.6 46071.6
TNG 6 Relics 6×04 46125.3 46125.3
TNG 6 Schisms 6×05 46154.2 46154.2
TNG 6 True Q 6×06 46192.3 46192.3
TNG 6 Rascals 6×07 46235.7 46235.7
TNG 6 A Fistful of Datas 6×08 46271.5 46271.5
TNG 6 The Quality of Life 6×09 46307.2 46307.2
TNG 6 Chain of Command, Part I 6×10 46357.4 46357.4
TNG 6 Chain of Command, Part II 6×11 46360.8 46360.8
DS9 1 Emissary II 1×01/02 46379.1 46379.1
DS9 1 Emissary I 1×01/02 46379.1 46379.1
DS9 1 Past Prologue 1×03 Unknown 46400
DS9 1 A Man Alone 1×04 46421.5 46421.5
DS9 1 Babel 1×05 46423.7 46423.7
TNG 6 Ship in a Bottle 6×12 46424.1 46424.1
TNG 6 Aquiel 6×13 46461.3 46461.3
DS9 1 Captive Pursuit 1×06 46477.5 46477.5
TNG 6 Face of the Enemy 6×14 46519 46519
DS9 1 Q-Less 1×07 46531.2 46531.2
TNG 6 Tapestry 6×15 Unknown 46532
DS9 1 The Passenger 1×09 Unknown 46533
TNG 6 Birthright, Part I 6×16 46578.4 46578.4
TNG 6 Birthright, Part II 6×17 46579.2 46579.2
DS9 1 Move Along Home 1×10 Unknown 46580
DS9 1 The Nagus 1×11 Unknown 46581
TNG 6 Starship Mine 6×18 46682.4 46682.4
TNG 6 Lessons 6×19 46693.1 46693.1
DS9 1 Vortex 1×12 Unknown 46694
DS9 1 Battle Lines 1×13 Unknown 46694
DS9 1 The Storyteller 1×14 46729.1 46729.1
TNG 6 The Chase 6×20 46731.5 46731.5
TNG 6 Frame of Mind 6×21 46778.1 46778.1
TNG 6 Suspicions 6×22 46830.1 46830.1
DS9 1 Progress 1×15 46844.3 46844.3
TNG 6 Rightful Heir 6×23 46852.2 46852.2
DS9 1 If Wishes Were Horses 1×16 46853.2 46853.2
DS9 1 Dax 1×08 46910.1 46910.1
TNG 6 Second Chances 6×24 46915.2 46915.2
DS9 1 Dramatis Personae 1×18 46922.3 46922.3
DS9 1 The Forsaken 1×17 46925.1 46925.1
DS9 1 Duet 1×19 Unknown 46926
TNG 6 Timescape 6×25 46944.2 46944.2
DS9 1 In the Hands of the Prophets 1×20 Unknown 46945
TNG 6 Descent 6×26 46982.1 46982.1
TNG 7 Descent, Part II 7×01 47025.4 47025.4
DS9 2 The Homecoming 2×01 Unknown 47026
DS9 2 The Circle 2×02 Unknown 47027
DS9 2 The Siege 2×03 Unknown 47028
TNG 7 Liaisons 7×02 Unknown 47029
TNG 7 Gambit, Part I 7×04 47135.2 47135.2
TNG 7 Gambit, Part II 7×05 47160.1 47160.1
DS9 2 Cardassians 2×05 47177.2 47177.2
DS9 2 Invasive Procedures 2×04 47182.1 47182.1
TNG 7 Interface 7×03 47215.5 47215.5
TNG 7 Phantasms 7×06 47225.7 47225.7
DS9 2 Melora 2×06 47229.1 47229.1
TNG 7 Dark Page 7×07 47254.1 47254.1
DS9 2 Rules of Acquisition 2×07 Unknown 47255
DS9 2 Necessary Evil 2×08 47282.5-47284.1 47282.5
TNG 7 Attached 7×08 47304.2 47304.2
TNG 7 Force of Nature 7×09 47310.2 47310.2
DS9 2 Second Sight 2×09 47329.4 47329.4
DS9 2 Sanctuary 2×10 47391.2 47391.2
TNG 7 Parallels 7×11 47391.2 47391.2
DS9 2 Rivals 2×11 Unknown 47391.3
DS9 2 The Alternate 2×12 47391.7 47391.7
TNG 7 Inheritance 7×10 47410.2 47410.2
TNG 7 Homeward 7×13 47423.9 47423.9
TNG 7 The Pegasus 7×12 47457.1 47457.1
ENT 4 These Are the Voyages… 4×22 47457.1 47457.1
DS9 2 Armageddon Game 2×13 Unknown 47458
TNG 7 Sub Rosa 7×14 Unknown 47459
TNG 7 Lower Decks 7×15 47566.7 47566.7
DS9 2 Paradise 2×15 47573.1 47573.1
DS9 2 Whispers 2×14 47581.2 47581.2
DS9 2 Shadowplay 2×16 47603.3 47603.3
TNG 7 Thine Own Self 7×16 47611.2 47611.2
TNG 7 Masks 7×17 47615.2 47615.2
DS9 2 Playing God 2×17 Unknown 47616
TNG 7 Eye of the Beholder 7×18 47622.1 47622.1
DS9 2 Profit and Loss 2×18 Unknown 47623
TNG 7 Genesis 7×19 47653.2 47653.2
DS9 2 Blood Oath 2×19 Unknown 47654
TNG 7 Journey’s End 7×20 47751.2 47751.2
DS9 2 The Maquis, Part I 2×20 Unknown 47752
DS9 2 The Maquis, Part II 2×21 Unknown 47753
TNG 7 Firstborn 7×21 47779.4 47779.4
TNG 7 Bloodlines 7×22 47829.1 47829.1
DS9 2 The Wire 2×22 Unknown 47830
TNG 7 Emergence 7×23 47869.2 47869.2
DS9 2 Crossover 2×23 Unknown 47870
TNG 7 Preemptive Strike 7×24 47941.7 47941.7
DS9 2 The Collaborator 2×24 Unknown 47942
DS9 2 Tribunal 2×25 47944.2 47944.2
TNG 7 All Good Things… 7×25/26 47988 47988
DS9 2 The Jem’Hadar 2×26 Unknown 47989
DS9 3 The Search, Part I 3×01 48213.1 48213.1
DS9 3 The Search, Part II 3×02 48217.7 48217.7
DS9 3 The House of Quark 3×03 48224.2 48224.2
DS9 3 Equilibrium 3×04 Unknown 48225
DS9 3 Second Skin 3×05 48244.5 48244.5
DS9 3 The Abandoned 3×06 48301.1 48301.1
VOY 1 Caretaker 1×01/02 48315.6 48315.6
VOY 1 Caretaker II 1×01/02 48315.6 48315.6
DS9 3 Civil Defense 3×07 48388.8 48388.8
DS9 3 Meridian 3×08 48423.2 48423.2
VOY 1 Parallax 1×03 48439.7 48439.7
DS9 3 Defiant 3×09 48467.3 48467.3
DS9 3 Fascination 3×10 Unknown 48468
DS9 3 Past Tense, Part I 3×11 48481.2 48481.2
DS9 3 Past Tense, Part II 3×12 48481.2 48481.2
VOY 1 Time and Again 1×04 Unknown 48482
DS9 3 Life Support 3×13 48498.4 48498.4
DS9 3 Heart of Stone 3×14 48521.5 48521.5
VOY 1 Phage 1×05 48532.4 48532.4
DS9 3 Destiny 3×15 48543.2 48543.2
VOY 1 The Cloud 1×06 48546.2 48546.2
DS9 3 Prophet Motive 3×16 Unknown 48547
DS9 3 Visionary 3×17 48576.7 48576.7
VOY 1 Ex Post Facto 1×08 Unknown 48577
VOY 1 Eye of the Needle 1×07 48579.4 48579.4
DS9 3 Distant Voices 3×18 48592.2 48592.2
MOV 9 Generations 48593
VOY 1 Emanations 1×09 48623.5 48623.5
VOY 1 Prime Factors 1×10 48642.5 48642.5
VOY 1 State of Flux 1×11 48658.2 48658.2
DS9 3 Through the Looking Glass 3×19 Unknown 48659
VOY 1 Heroes and Demons 1×12 48693.2 48693.2
DS9 3 Improbable Cause 3×20 Unknown 48694
DS9 3 The Die is Cast 3×21 Unknown 48695
VOY 1 Cathexis 1×13 48734.2 48734.2
DS9 3 Explorers 3×22 Unknown 48735
VOY 1 Faces 1×14 48784.2 48784.2
DS9 3 Family Business 3×23 Unknown 48789
VOY 1 Jetrel 1×15 48832.1 48832.1
DS9 3 Shakaar 3×24 Unknown 48833
VOY 1 Learning Curve 1×16 48846.5 48846.5
DS9 3 Facets 3×25 48876.3 48876.3
VOY 2 Projections 2×03 48892.1 48892.1
VOY 2 Elogium 2×04 48921.3 48921.3
DS9 3 The Adversary 3×26 48959.1 48959.1
VOY 2 The 37’s 2×01 48975.1 48975.1
VOY 2 Initiations 2×02 49005.3 49005.3
VOY 2 Non Sequitur 2×05 49011 49011
DS9 4 The Way of the Warrior 4×01/02 49011.4 49011.4
VOY 2 Twisted 2×06 Unknown 49012
DS9 4 The Visitor 4×03 49034.7 49034.7
DS9 4 Hippocratic Oath 4×04 49066.5 49066.5
VOY 2 Parturition 2×07 49068.5 49068.5
DS9 4 Indiscretion 4×05 Unknown 49069
VOY 2 Persistence of Vision 2×08 Unknown 49070
VOY 2 Tattoo 2×09 Unknown 49071
VOY 2 Cold Fire 2×10 49164.8 49164.8
DS9 4 Homefront 4×11 49170.65 49170.65
DS9 4 Paradise Lost 4×12 Unknown 49171
VOY 2 Prototype 2×13 Unknown 49172
DS9 4 Rejoined 4×06 49195.5 49195.5
VOY 2 Maneuvers 2×11 49208.5 49208.5
DS9 4 Starship Down 4×07 49263.5 49263.5
DS9 4 Little Green Men 4×08 Unknown 49264
VOY 2 Resistance 2×12 Unknown 49289
DS9 4 The Sword of Kahless 4×09 49289.1 49289.1
DS9 4 Our Man Bashir 4×10 49300.7 49300.7
VOY 2 Death Wish 2×18 49301.2 49301.2
VOY 2 Alliances 2×14 49337.4 49337.4
DS9 4 Crossfire 4×13 Unknown 49338
VOY 2 Threshold 2×15 49373.4 49373.4
DS9 4 Return to Grace 4×14 Unknown 49374
VOY 2 Meld 2×16 Unknown 49375
VOY 2 Dreadnought 2×17 49447 49447
VOY 2 Investigations 2×20 49485.2 49485.2
VOY 2 Lifesigns 2×19 49504.3 49504.3
VOY 2 Deadlock 2×21 49548.7 49548.7
DS9 4 Sons of Mogh 4×15 49556.2 49556.2
DS9 4 Bar Association 4×16 Unknown 49557
DS9 4 Accession 4×17 Unknown 49558
VOY 2 Innocence 2×22 49578.2 49578.2
VOY 2 Tuvix 2×24 49655.2 49655.2
DS9 4 For the Cause 4×22 Unknown 49656
DS9 4 Rules of Engagement 4×18 49665.3 49665.3
DS9 4 Hard Time 4×19 Unknown 49666
DS9 4 Shattered Mirror 4×20 Unknown 49667
VOY 2 The Thaw 2×23 Unknown 49668
DS9 4 The Muse 4×21 Unknown 49669
VOY 2 Resolutions 2×25 49690.1 49690.1
DS9 4 To the Death 4×23 49904.2 49904.2
DS9 4 The Quickening 4×24 Unknown 49905
DS9 4 Body Parts 4×25 49930.3 49930.3
DS9 4 Broken Link 4×26 49962.4 49962.4
VOY 2 Basics, Part I 2×26 Unknown 49963
VOY 3 Basics, Part II 3×01 50032.7 50032.7
DS9 5 Apocalypse Rising 5×01 Unknown 50033
DS9 5 The Ship 5×02 50049.3 50049.3
DS9 5 Looking for par’Mach in All the Wrong Places 5×03 50061.2 50061.2
DS9 5 Nor the Battle to the Strong 5×04 Unknown 50062
DS9 5 The Assignment 5×05 Unknown 50063
VOY 3 False Profits 3×05 50074.3 50074.3
VOY 3 Remember 3×06 50203.1 50074.3
VOY 3 Flashback 3×02 50126.4 50126.4
VOY 3 The Chute 3×03 50156.2 50156.2
VOY 3 Sacred Ground 3×07 50063.2 50203.1
VOY 3 The Swarm 3×04 50252.3 50252.3
VOY 3 Future’s End 3×08 50312.5 50312.5
VOY 3 Future’s End, Part II 3×09 50312.5 50312.5
DS9 5 Let He Who Is Without Sin… 5×07 Unknown 50313
DS9 5 Things Past 5×08 Unknown 50314
VOY 3 Warlord 3×10 50348.1 50348.1
DS9 5 The Ascent 5×09 Unknown 50349
VOY 3 The Q and the Grey 3×11 50384.2 50384.2
DS9 5 Rapture 5×10 Unknown 50385
DS9 5 The Darkness and the Light 5×11 50416.2 50416.2
VOY 3 Macrocosm 3×12 50425.1 50425.1
VOY 3 Fair Trade 3×13 Unknown 50426
VOY 3 Alter Ego 3×14 50460.3 50460.3
DS9 5 The Begotten 5×12 Unknown 50461
DS9 5 For the Uniform 5×13 50485.2 50485.2
VOY 3 Coda 3×15 50518.6 50518.6
VOY 3 Blood Fever 3×16 50537.2 50537.2
MOV 9 First Contact 50538
DS9 5 In Purgatory’s Shadow 5×14 Unknown 50539
DS9 5 By Inferno’s Light 5×15 50564.2 50564.2
VOY 3 Unity 3×17 50614.2 50614.2
VOY 3 Darkling 3×18 50693.2 50693.2
DS9 5 Doctor Bashir, I Presume 5×16 Unknown 50694
VOY 3 Rise 3×19 Unknown 50695
DS9 5 A Simple Investigation 5×17 Unknown 50696
DS9 5 Business as Usual 5×18 Unknown 50697
DS9 5 Ties of Blood and Water 5×19 50712.5 50712.5
VOY 3 Favorite Son 3×20 50732.4 50732.4
DS9 5 Ferengi Love Songs 5×20 Unknown 50733
DS9 5 Soldiers of the Empire 5×21 Unknown 50734
DS9 5 Children of Time 5×22 50814.2 50814.2
VOY 3 Before and After 3×21 Unknown 50815
VOY 3 Distant Origin 3×23 Unknown 50836
VOY 3 Real Life 3×22 50836.2 50836.2
DS9 5 Empok Nor 5×24 50901.7 50901.7
VOY 3 Displaced 3×24 50912.4 50912.4
DS9 5 Blaze of Glory 5×23 Unknown 50913
DS9 5 In the Cards 5×25 50929.4 50929.4
VOY 3 Worst Case Scenario 3×25 50953.4 50953.4
DS9 5 Call to Arms 5×26 50975.2 50975.2
VOY 4 Day of Honor 4×03 Unknown 50976
VOY 3 Scorpion 3×26 50984.3 50984.2
VOY 4 Scorpion, Part II 4×01 51003.7 51003.7
VOY 4 The Gift 4×02 51008 51008
VOY 4 Nemesis 4×04 51082.4 51082.4
DS9 6 Rocks and Shoals 6×02 51096.2 51096.2
DS9 6 Sons and Daughters 6×03 Unknown 51097
DS9 6 Behind the Lines 6×04 51145.3 51145.3
DS9 6 Favor the Bold 6×05 Unknown 51146
DS9 6 Sacrifice of Angels 6×06 Unknown 51147
VOY 4 The Raven 4×06 Unknown 51148
VOY 4 Revulsion 4×05 51186.2 51186.2
DS9 6 A Time to Stand 6×01 Unknown 51187
VOY 4 Scientific Method 4×07 51244.3 51244.3
DS9 6 You Are Cordially Invited 6×07 51247.5 51247.5
VOY 4 Year of Hell 4×08 51268.4 51268.4
VOY 4 Random Thoughts 4×10 51367.2 51367.2
DS9 6 Statistical Probabilities 6×09 Unknown 51368
VOY 4 Concerning Flight 4×11 51386.4 51386.4
DS9 6 The Magnificent Ferengi 6×10 Unknown 51387
DS9 6 Waltz 6×11 51408.6-51413.6 51408.6
DS9 6 Resurrection 6×08 Unknown 51425
VOY 4 Year of Hell, Part II 4×09 51425.4 51425.4
VOY 4 Mortal Coil 4×12 51449.2 51449.2
VOY 4 Message in a Bottle 4×14 51462 51462
VOY 4 Waking Moments 4×13 51471.3 51471.3
DS9 6 Who Mourns for Morn? 6×12 Unknown 51472
DS9 6 Far Beyond the Stars 6×13 Unknown 51473
DS9 6 One Little Ship 6×14 51474.2 51474.2
VOY 4 Hunters 4×15 51501.4 51501.4
DS9 6 Honor Among Thieves 6×15 Unknown 51502
DS9 6 Change of Heart 6×16 51597.2 51597.2
VOY 4 Prey 4×16 51652.3 51652.3
VOY 4 Retrospect 4×17 51658.2 51658.2
VOY 4 The Killing Game 4×18 Unknown 51659
VOY 4 The Killing Game, Part II 4×19 51715.2 51715.2
DS9 6 Wrongs Darker Than Death or Night 6×17 Unknown 51716
DS9 6 Inquisition 6×18 Unknown 51717
DS9 6 In the Pale Moonlight 6×19 51721.3 51721.3
VOY 4 Vis à Vis 4×20 51762.4 51762.4
VOY 4 The Omega Directive 4×21 51781.2 51781.2
DS9 6 His Way 6×20 Unknown 51782
VOY 4 Unforgettable 4×22 51813.4 51813.4
DS9 6 The Reckoning 6×21 Unknown 51814
VOY 4 Living Witness 4×23 Unknown 51815
DS9 6 Valiant 6×22 51825.4 51825.4
VOY 4 Demon 4×24 Unknown 51826
DS9 6 Profit and Lace 6×23 Unknown 51827
VOY 4 One 4×25 51929.3 51929.3
DS9 6 Time’s Orphan 6×24 Unknown 51930
DS9 6 The Sound of Her Voice 6×25 51948.3 51948.3
DS9 6 Tears of the Prophets 6×26 Unknown 51949
VOY 4 Hope and Fear 4×26 51978.2 51978.2
VOY 5 Night 5×01 52081.2 52081.2
VOY 5 Drone 5×02 Unknown 52082
VOY 5 Extreme Risk 5×03 Unknown 52083
VOY 5 In the Flesh 5×04 52136.4 52136.4
VOY 5 Once Upon a Time 5×05 Unknown 52137
VOY 5 Nothing Human 5×08 Unknown 52138
DS9 7 Shadows and Symbols 7×02 52152.6 52152.6
DS9 7 Afterimage 7×03 Unknown 52153
DS9 7 Take Me Out to the Holosuite 7×04 Unknown 52154
DS9 7 Chrysalis 7×05 Unknown 52155
DS9 7 Treachery, Faith and the Great River 7×06 Unknown 52156
DS9 7 Once More Unto the Breach 7×07 Unknown 52157
DS9 7 The Siege of AR-558 7×08 Unknown 52158
VOY 5 Timeless 5×06 52164.3 52164.3
DS9 7 Image in the Sand 7×01 Unknown 52165
VOY 5 Thirty Days 5×09 52179.4 52179.4
DS9 7 Covenant 7×09 Unknown 52180
VOY 5 Infinite Regress 5×07 52356.2 52356.2
VOY 5 Counterpoint 5×10 Unknown 52357
DS9 7 It’s Only a Paper Moon 7×10 Unknown 52358
DS9 7 Prodigal Daughter 7×11 Unknown 52359
VOY 5 Latent Image 5×11 Unknown 52360
VOY 5 Bride of Chaotica! 5×12 Unknown 52361
DS9 7 The Emperor’s New Cloak 7×12 Unknown 52362
VOY 5 Gravity 5×13 52438.9 52438.9
VOY 5 Bliss 5×14 52542.3 52542.3
DS9 7 Chimera 7×14 Unknown 52543.3
VOY 5 The Disease 5×17 Unknown 52544.3
DS9 7 Badda-Bing, Badda-Bang 7×15 Unknown 52545.3
DS9 7 Inter Arma Enim Silent Leges 7×16 Unknown 52546.3
DS9 7 Penumbra 7×17 52576.2 52576.2
DS9 7 ‘Til Death Do Us Part 7×18 Unknown 52577.2
DS9 7 Strange Bedfellows 7×19 Unknown 52578.2
DS9 7 The Changing Face of Evil 7×20 Unknown 52579.2
DS9 7 When It Rains… 7×21 Unknown 52580.2
DS9 7 Tacking Into the Wind 7×22 Unknown 52581.2
VOY 5 Course: Oblivion 5×18 52586.3 52586.3
VOY 5 Dark Frontier 5×15/16 52619.2 52619.2
VOY 5 Dark Frontier II 5×15/16 52619.2 52619.2
VOY 5 The Fight 5×19 Unknown 52620.2
VOY 5 Think Tank 5×20 Unknown 52621.2
DS9 7 Extreme Measures 7×23 52645.7 52645.7
VOY 5 Someone to Watch Over Me 5×22 52648 52648
VOY 5 11:59 5×23 Unknown 52649
DS9 7 Field of Fire 7×13 Unknown 52739
VOY 5 Relativity 5×24 52861.27 52861.27
DS9 7 The Dogs of War 7×24 52861.3 52861.3
VOY 5 Warhead 5×25 Unknown 52862.27
DS9 7 What You Leave Behind I 7×25/26 Unknown 52862.3
VOY 5 Equinox 5×26 Unknown 52863.27
DS9 7 What You Leave Behind II 7×25/26 Unknown 52863.3
VOY 6 Equinox, Part II 6×01 Unknown 52864.27
MOV 9 Insurrection 52864.3
VOY 5 Juggernaut 5×21 Unknown 52865.3
VOY 6 Survival Instinct 6×02 53049.2 53049.2
VOY 6 Barge of the Dead 6×03 Unknown 53050.2
VOY 6 Tinker Tenor Doctor Spy 6×04 Unknown 53051.2
VOY 6 Dragon’s Teeth 6×07 53167.9 53167.9
VOY 6 Alice 6×05 Unknown 53168.9
VOY 6 Riddles 6×06 53263.2 53263.2
VOY 6 One Small Step 6×08 53292.7 53292.7
VOY 6 The Voyager Conspiracy 6×09 53329 53329
VOY 6 Pathfinder 6×10 Unknown 53330
VOY 6 Fair Haven 6×11 Unknown 53331
VOY 6 Tsunkatse 6×15 53447.2 53447.2
VOY 6 Blink of an Eye 6×12 Unknown 53448.2
VOY 6 Virtuoso 6×13 53556.4 53556.4
VOY 6 Collective 6×16 Unknown 53557.4
VOY 6 Memorial 6×14 Unknown 53558.4
VOY 6 Spirit Folk 6×17 Unknown 53559.4
VOY 6 Ashes to Ashes 6×18 53679.4 53679.4
VOY 6 Child’s Play 6×19 Unknown 53680.4
VOY 6 Good Shepherd 6×20 53753.2 53753.2
VOY 6 Fury 6×23 Unknown 53754.2
VOY 6 Live Fast and Prosper 6×21 53849.2 53849.2
VOY 6 Life Line 6×24 Unknown 53850.2
VOY 6 Muse 6×22 53918 53918
VOY 6 The Haunting of Deck Twelve 6×25 Unknown 53919
VOY 6 Unimatrix Zero 6×26 Unknown 53920
VOY 7 Unimatrix Zero, Part II 7×01 54014.4 54014.4
VOY 7 Drive 7×03 54058.6 54058.6
VOY 7 Repression 7×04 54090.4 54090.4
VOY 7 Imperfection 7×02 54129.4 54129.4
VOY 7 Critical Care 7×05 Unknown 54130.4
VOY 7 Inside Man 7×06 54208.3 54208.3
VOY 7 Body and Soul 7×07 54238.3 54238.3
VOY 7 Nightingale 7×08 54274.7 54274.7
VOY 7 Flesh and Blood 7×09/10 54315.3-54337.5 54315.3
VOY 7 Flesh and Blood 7×09/10 54315.3-54337.5 54315.3
VOY 7 Shattered 7×11 Unknown 54316.3
VOY 7 Lineage 7×12 54452.6 54452.6
VOY 7 Repentance 7×13 54474.6 54474.6
VOY 7 Prophecy 7×14 54518.2-54529.8 54518.2
VOY 7 The Void 7×15 54553.4-54562.7 54553.4
VOY 7 Workforce 7×16 54584.3-54608.6 54584.3
VOY 7 Workforce, Part II 7×17 54622.4 54622.4
VOY 7 Human Error 7×18 Unknown 54623.4
VOY 7 Q2 7×19 54704.5 54704.5
VOY 7 Author, Author 7×20 54732.3 54732.3
VOY 7 Friendship One 7×21 54775.4 54775.4
VOY 7 Natural Law 7×22 54827.7 54827.7
VOY 7 Homestead 7×23 54868.6 54868.6
VOY 7 Renaissance Man 7×24 54890.7 54890.7
VOY 7 Endgame I 7×25/26 54973.4 54973.4
VOY 7 Endgame II 7×26 54973.4 54973.4
MOV 9 Nemesis 10 56844

Clifford

I have a strange affinity for attractors, and has had it since graduating highschool, where I got a top grade in the final mathematics examination. That was under the old grading system. And the grade (13) was given to only two students in my high school that year. The examination centered on strange attractors. I’ve have not spend much time on it lateer. But there is a weird beauty in them.

Recently I discovered Clifford Attractors. Take a look at this page for some very nice examples. They look stunning, and are simple to handle. Lets play with them!

Clifford Attractors are defined by iteratively making these calculations: xn+1 <- sin(ayn) + ccos(axn) yn+1 <- sin(bxn) + dcos(b*yn)

Choose a, b, c and d between -2 and 2. Calculate x,y for n=0 to n=10.000.000 and plot them. It looks cool!

Lets begin by defining a function that takes four variables and a number of points, and calculate the points:

calcTrace <- function(a,b,c,d,numint){
  x <- y <- rep(NULL, numint) # initializing the vectors
  x[1] <- 0 # set the first point to (0,0)
  y[1] <- 0
  for (i in 2:numint){    # calculate the following points
    x[i] <- sin(a*y[(i-1)]) + c*cos(a*x[(i-1)])
    y[i] <- sin(b*x[(i-1)]) + d*cos(b*y[(i-1)])  
  }
  df <- data.frame(x=x,y=y)
  return(df)
}

Lets also define some parameters. I would prefer to choose the parameters at random. But there are a surprising number of instances where this lead to nothing. The formulas converges very quickly on just a few values, and I end up with a simple dot on the plot. I guess that is to be expected – but not what I am looking for. I want beautiful images!

a <- -1.8 
b <- -1.9 
c <- -1.7
d <-  1.9

points <- calcTrace(a,b,c,d,10000000)

That takes some time – I’ll get back to that. Lets plot it. I remove almost anything from the ggplot theme, and insert the parameters in the plot.

library(ggplot2)
opt = theme(legend.position  = "none",
            panel.background = element_rect(fill="white"),
            axis.ticks       = element_blank(),
            panel.grid       = element_blank(),
            axis.title       = element_blank(),
            axis.text        = element_blank(),
            plot.title       = element_text(size=9, face="italic", hjust = 0.5)
            )

p <- ggplot(points, aes(x, y)) + geom_point(color="black", shape=46, alpha=.01) + 
  opt +
  ggtitle(paste("a = ",a , ", b = ", b, "\n c = ", c, " d = ",  d))
print(p)

All right. It takes some time to do the calculations. There are ways to speed that up.

One way is to compile the function.

library(compiler)
compiled <- cmpfun(calcTrace)

According to the compiler packages, that should make the function faster. Lets test it:

library(microbenchmark) 
test <- microbenchmark(
    calcTrace(a,b,c,d,10000000),
    compiled(a,b,c,d,10000000) , times=3
)
print(test)

I am not impressed. This result might be caused by the fact that I am running Paperclips http://www.decisionproblem.com/paperclips in the background (almost ready to release the hypnodrones!) on a not particularly powerfull laptop.

What else could be done? I’m tinkering with this to hone my R-skills. But here might be a situation where it would be better to do it in another language.

The library Rcpp allows me to add C++ code. Lets try that:

library(Rcpp)
cppFunction('DataFrame cppTrace(double a, double b, double c, double d, int numint) {
            // create the columns
            NumericVector x(numint);
            NumericVector y(numint);
            x[0]=0;
            y[0]=0;
            for(int i = 1; i < numint; ++i) {
            x[i] = sin(a*y[i-1])+c*cos(a*x[i-1]);
            y[i] = sin(b*x[i-1])+d*cos(b*y[i-1]);
            }
            // return a new data frame
            return DataFrame::create(_["x"]= x, _["y"]= y);
            }
            ')

Lets see how quick that version is:

library(microbenchmark)
## Loading required package: microbenchmarkCore
test2 <- microbenchmark(
    cppTrace(a,b,c,d,10000000),
    times=3
)
print(test2)
## Unit: seconds
##                         expr     min       lq     mean   median       uq
##  cppTrace(a, b, c, d, 1e+07) 2.11005 2.122835 2.154553 2.135619 2.176804
##       max neval
##  2.217989     3

That was fast!

The plot still takes an awfull lot of time. I have not found a way to do anything about that.

Lets make a new plot, with different parameters.

a <-  1.7
b <-  1.7
c <-  0.7
d <-  1.3
points <- cppTrace(a,b,c,d,10000000)
q <- ggplot(points, aes(x, y)) + geom_point(color="orange", shape=46, alpha=.01) + 
  opt +
  ggtitle(paste("a = ",a , ", b = ", b, "\n c = ", c, " d = ",  d))
print(q)

Nice. Lets make one in green as well:

a <-  -1.6
b <-  1.2
c <-  0.1
d <-  -1.2
points <- cppTrace(a,b,c,d,10000000)
r <- ggplot(points, aes(x, y)) + geom_point(color="green", shape=46, alpha=.01) + 
  opt +
  ggtitle(paste("a = ",a , ", b = ", b, "\n c = ", c, " d = ",  d))
print(r)

 

How do you gauge a place to work

I’ve recently been involved in the recruitment of a mid-level manager in an organization I’m involved with. That got me thinking (always a good way to prepare for anything):

What questions are reasonable to ask? There are rules of course, but what kind of questions is it OK for the prospective new employee to ask.

There are all the professional questions. But you should also be interested in what kind of a workplace you are potentially entering.

I think a good question is: What kind of employee benefits do you offer? And why those?

The added question is important. I am not interested in knowing that you offer all the fruit I can eat. That is not what will decide if I want to take the job.

But it does make a difference if company A offers free coffee. And company B offers me all the water and electricity I will need to brew coffee on the brewer I have to bring myself, using coffee grounds that I will have to buy myself.

And it would be interesting to hear a manager reflect on why they offer free yoga, coffee or whatever.

I think it says a lot about how employees are viewed in a company.

Merging pdf-files

You may need to merge several pdf-files into one.

There are several tools. Some of them you have to pay for.

If you are in a linux environment, try this:

gs -dBATCH -dNOPAUSE -q -sDEVICE=pdfwrite -sOutputFile=final.pdf filea.pdf fileb.pdf

continue with filec.pdf etc.

Some say it is slow.

Others say, yes it is slow, but it produces smaller final files, and are able to handle “difficult pdfs”.

I say it is nice that it can be done from the command line.

Visualizing Pi

We celebrate Pi-day (3/14) every year at the library. And though it is december, and there is months to the big day, it is not too early to begin planning. This is something we do in the incredibly amounts of time we have left over when all the other tasks that also only take a tiny portion of the day are done. In other words, this is something we plan in our weekly lunchbreak.

Usually Henrik delivers a small talk about Pi. We eat some Pie, and there is much rejoicing.

But we would like to show something else. A cool visualization perhaps. There are several out there, but it is no fun just to show cool stuff. Its much cooler to understand how it is done.

One of the visualizaions we found on the net is this. https://www.visualcinnamon.com/portfolio/the-art-in-pi It is made by the extremely talented Nadieh Bremer. Take a look at her page. She does a lot of other cool stuff!

So. How to replicate this?

The idea is to take pi. Draw a line segment from 0,0 in the plane to a new point, determined by the first digit. Then we draw another segment from that point, to a newer point, determined by the second digit in Pi. Continue ad nauseam, or until your computer catches fire. Add colours, and make it look cool.

First item is to get pi to a million decimal places. Read it in, and make a vector containing all the digits. I’ll begin with a smaller string.

testnumvec <- "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679"

Not quite pi. But I can’t be bothered figuring out how many digits of pi I should use in order to get all the digits from 0 to 9. I want that to make sure that whatever I do, works on all the digits.

Next up is getting rid of the period.

numvec <- gsub("[[:punct:]]", "", testnumvec)

In Denmark we would use a “,” instead of “.” This removes all punctuation.

Now we convert it to a vector with individual digits. And cast them as integers rather than characters.

numvec <- as.integer(unlist(strsplit(numvec,"")))

We begin a (0,0). The next point is determined by the first digit i pi – 3. The number 3 should determine witch direction, angle, we should move. The new x-value will be cos(f(3)), where f(3) is some function, that converts 3 to the correct angle. That should be some fraction of pi. The new y-value is similarly determined by sin(f(3)).

What should f(x) be? Imagine a decimal clock, with the ten digits 0 to 9 positioned around the circle. In the original 0 is at top, at 12 o’clock. 5 is at 6 o’clock. And the numbers follow the circle clockwise. In the unity circle 0 is positioned at 1/2pi. 5 at 1 1/2 pi. So f(0)=1/2pi, f(5)=1 1/2pi.

This formula gives us the result we need: 5/2pi – z/5pi.

z is the digit in pi. For all of them, we can calculate the steps we need in this way:

x <- cos(5/2*pi - numvec/5*pi)
y <- sin(5/2*pi - numvec/5*pi)

So. Beginning at (x0,y0), we calculate the trig functions, add it to (x0,y0) and get (x1,y1). When we continue to do that, we notice, that xi is the cumulative sum of all the calculated x-values. If we calculate the trig functions for all of the digits in pi, and then calculate the cumulative sum, we get all the x-values. Similarly with all the y-values.

Thats neat, and thanks to Henrik, who pointed this out. We get the cumulative sums easily: And we can then get the cumulative sums with:

x <- cumsum(x)
y <- cumsum(y)

Thats it! There is just a little detail. The first value in x,y is the first step we need to take – or the second point if you will. We will need to add a 0 at the start:

x <- c(0,x)
y <- c(0,y)

Thats it! I should now be able to plot it. Lets just do a quick test:

plot(x,y, type="l")

That looks almost like what we need. The most notable difference is that Nadieh only plots the decimals. I include the “3” as well. We are going to test this, and it is cumbersome to do all the preceding steps. Let’s begin with defining the generation of points as a function, that takes a string. In just a little while I’ll invoke the magick of ggplot. So it would be convenient that the result is a dataframe:

piPoints <- function(piString){
  numbers <- gsub("[[:punct:]]", "", piString)
  numbers <- as.integer(unlist(strsplit(numbers,"")))
  x <- cos(5/2*pi - numbers/5*pi)
  y <- sin(5/2*pi - numbers/5*pi)
  x <- cumsum(x)
  y <- cumsum(y)
  x <- c(0,x)
  y <- c(0,y)
  df <- data.frame(as.integer(c(0,numbers)),x,y)
  colnames(df) <- c("num", "x", "y")
  return(df)
}

All right. We now have a dataframe with three columns. The number, and the x,y coordinates. We can plot that with ggplot:

df <- piPoints(testnumvec)
library(ggplot2)

ggplot(df, aes(x=x,y=y,group="1"))+
  geom_path(aes(colour=factor(df$num)))

Weird. Something is wrong. Look at the second linesegment. It goes up and to the right, just as it should, since this segment represents a “1”. But the color? It is green. It should be sorta orangy. The reason is that ggplot looks at the number, and by implication the color, at the origin of the linesegment. Not at the end. How to change that? What I really need to do, is shifting the number column one place relative to the x,y pairs. Simply done – remove the 0 at the beginning of the num-vector in the function. And the final digits in the x and y vectors. I really don’t like it, as it increases the size of the dataframe – but I add an id-column as well. Just a sequential number, to control the colouring:

piPoints <- function(piString){
  numbers <- gsub("[[:punct:]]", "", piString)
  numbers <- as.integer(unlist(strsplit(numbers,"")))
  x <- cos(5/2*pi - numbers/5*pi)
  y <- sin(5/2*pi - numbers/5*pi)
  x <- cumsum(x)
  y <- cumsum(y)
  x <- c(0,x)
  y <- c(0,y)
  id <- 1:(length(y)-1)
  df <- data.frame(as.integer(c(numbers)),x[-length(x)],y[-length(y)], id)
  colnames(df) <- c("num", "x", "y", "id")
  return(df)
}

Lets take another look:

df <- piPoints(testnumvec)
library(ggplot2)

ggplot(df, aes(x=x,y=y,group="1"))+
  geom_path(aes(colour=factor(df$num)))

Now we’re there. Two steps are missing: Adding more digits – I would like to get to one million digits. And getting it to look nice.

Lets try getting to the million. I don’t need to calculate pi to a million decimals. I can just download it.

library(readr)
storpi <- read_file("pi_dec_1m.txt")

df <- piPoints(storpi)
library(ggplot2)

ggplot(df, aes(x=x,y=y,group="1"))+
geom_path(aes(colour=df$id)) +
  scale_colour_gradient(low="red", high="green")