Saturday, January 1, 2022

Sailing from Ensenada, Mexico to Oahu



It’s 2am.  I am cold. It is pitch black. A strong wind is blowing in my face. The deck on which I stand lurches up and down. My legs are splayed wide for balance. I am wearing orange rubber foul weather gear which is bulky and odd feeling. Before me is a glowing green globe within which lies a compass bobbing in the darkness, spinning clockwise, passing the number 260. 

I have no idea what is ahead but the empty ocean for thousands of miles. Disoriented and nauseated I have both hands on a wheel nearly as tall as me. Hoping to keep the ship on course I swing the wheel to the left to counter wind and waves.  A few seconds pass and the compass slows and reverses, heading back down to 245. I cannot see the bow of the ship I am helming. But I can see reflections of the green and red navigation lights which occasionally wink out as a wave breaks on the bow, obscuring them with spray.  Clouds hide the night sky and there is no moon. It is pitch black. 

To my right, illuminated by the compass’s green glow, stands the captain. She is encouraging me to stay on course.  Is she insane, I think, trusting this 70 foot yacht to my seasick brain? 

My time on this watch doesn’t end for another two hours. I don’t know if I can last that long. But I know I will, because I chose this. I question my judgement.


I am aboard Sea Dragon, a steel-hulled, fractionally rigged cutter sailboat en route from Ensenada, Mexico to Hawaii. I embarked to learn to sail long distances, passage-making they call it. I dream of sailing around the world. I paid around $5000 to do this. Just had to work as a crew.  I've done two other liveaboard sail courses, but those were day sail trips only and the difference is stark, like the difference between a casual day hike and an Appalachian Trail section hike.

It’s the second time I’ve had the midnight to four am watch in the few days since we left Ensenada. I will have several more before we reach our destination. Two other guest-crew and the ship’s captain are on deck with me. It’s my turn at the helm.  We are close-reaching, meaning we are heading into the wind. The sails, which I cannot see in the blackness, act as vertical wings, pulling the boat forward.  The waves, driven at us, break on the bow.

The mast is somewhere ahead, stretching ninety five feet above the deck. The ocean is all around but I cannot see my own feet. It’s disorienting and other-worldly.  There’s no references for my mind to grasp.  Just darkness and wind and the eerie green glow of the floating compass. 

Wave after wave pushes the bow off course and I have to swing the wheel hard left or right. I am uncomfortable with this and I often over-correct. The sails flap violently, snapping displeasure as I steer us wrong and then they snap back with a pop as the ship shifts to a better angle to the wind. Eventually I sit huddled in the cockpit while another crewmate handles the pressure better.  I look at the foaming water over the gunwale and it doesn’t look like we are moving very fast.  

At 4am the next watch team rises like spectres through the companionway. I stand to exit and I fumble to open the locking carabiner on my tether that will keep me attached to the boat should I fall over.  Going overboard on a night like this, cloudy, moonless, black, could be death. There’s a light on my PFD, but the chance of being found in the roiling ink is slim. 

I climb awkwardly down the swaying stairway into the cabin.  Low level red lights illuminate us.  I am queasy as the floor and walls and ceiling veer around me. I unclasp the three connection points of my pfd. I take off my headlamp. I take off my hat. My neck warmer. My foul weather top. My shoes. My foul weather bottom. My sweater.  



I head to my cubby hole that has a plastic crate with my gear.  I get my toothpaste and toothbrush bag. To get to the head, which is 60 feet forward, I navigate through the salon. I lurch against a pole. I slam into a wall. I bounce against a doorway. I give in and slide on my shoulders wallside the rest of the way.  The head door is latched open. In the dim light I cannot unlatch it.  I press and push while leaning against the lurching wall.  I consider using the toilet with the door open. The latch comes undone and the door and I twist into the head. 

I latch the door closed and  am thrown over the sink as the boat hits a wave.  The forward part of the ship moves more than the aft. The head is forward.  I put my toiletry bag on the counter and it slides off and lands on the floor. I reach to get it and  my head hits a handrail, temporarily alleviating my seasickness by replacing it with pain.  I consider bawling. I hold the handrail in one hand and my toiletries in the other.  I have to pee. I see a hook and hang my toiletry bag where it proceeds to swing wildly, banging against the wall with each wave. 

There is a sign above the toilet asking men to sit to pee.  I look at the toilet.  I look at my crotch. I lift up the toilet seat with one hand. I put both hands on my belt to pull down my pants.  I am thrown against the door and put my hands against the wall to brace myself. I try again to take down my pants. Something something repeating the same actions expecting different results.  The same thing happens.  I am a stupid person I realize. 




Several minutes of impasse.  I have to pee.  The boat continues to lurch. I look at the toilet. I look at my crotch. I consider options. A mad dash up the companionway and I could probably jump overboard before I am stopped by my fellow crew.  Then I could pee before I drown in the dark. 

Finally I lean forward over the sink and use my weight to hold myself there.  I tentatively let go of the handrail and quickly pull down my pants.  I am not in a dignified position.  Nevertheless, I feel positive about this. I push myself and twist at the same time in a move I doubt I could repeat and for a moment I am a free spirit not touching walls or doors or handrails and I sit down quickly on the toilet, though for a moment I am sure I am going over, to be found crumpled and broken,covered in my own pee, when my next watch starts. 

I pee. 

The process needs to be reversed.  I should have studied harder in Mr. Reynolds PE class. I should have made better decisions in general.  I have made a terrible mistake. 

To flush, the toilet must be pumped. I figure it’s now been several hours and I won’t get to sleep before my next watch. I hold onto the handrail and pump the toilet.  Twenty times to pump and then a few more to empty.  My pee is emptied into the pacific. Fuck you pee. 

I turn to the prospect of brushing my teeth and I am overcome by doubt. I feel sorry for one handed people on boats. I rue my own birth.  I curse my decisions. If I could howl at the moon I would, but there is no moon tonight. 

I do the thing where I am leaning over the sink bracing myself on the handrail with my waist. I manage to get toothpaste on my toothbrush.  There is a foot pump for water.  I wait for a lull in the waves, which have not stopped, no siree, and I stomp around the floor until my foot finds the pedal. Water courses from the faucet and I can wash my hands and then wet my toothbrush. 

After brushing I want to rinse. I realize I have no cup. I cannot get my mouth near the faucet and pump with my foot.  I try to contort my hands into a cup shape while pushing the foot pedal. After several attempts I am soaked. 

I have no towel. 

I am sure there is toothpaste on my mouth.  

On the way back to my bunk a wave hits while I’m mid stride and I have the moment of feeling like when you are leaning back on a chair and suddenly you are falling backward. I slam into a doorframe. This will bruise. 

My bunk is the middle of three. To get into it there is a rope hanging from the ceiling. I grasp it and swing my feet up. For a moment I am swinging the wrong way and I may just fall to the lurching floor.  I hold on and the boat swings back, bringing my bunk with it.  I squeeze on, my glasses pulled off my face by the bunk above.  

I lie there.  I am confused by how this happened.  Maybe I was a bad person in a past life. Maybe I wronged someone in a position of authority.  Maybe I broke a mirror. Spilled salt. Walked under a ladder with a black cat. Ate pineapple pizza on Friday the thirteenth. 

Eventually I fall asleep. I momentarily wake thinking I am on a bus careening and rolling down a hill.  I am disoriented and confused.  Then I realize. I am in the Pacific Ocean on a boat. 



My transformation to sailor is thence rapid but the week is torturous.  Dramamine. Walking slowly. Using the leeward side head. Never taking a step without a hand firmly grasping anything solid.  Wearing a headlamp. Learning. Not being a dick. Praying to Neptune.  Apologizing for unknown slights to those I’ve harmed. All these together. 

@travailingman

♬ original sound - travailingman

It is many days later.  We are a thousand miles from land. We have sailed 24/7.  I have never been this far from civilization and nobody but ocean mariners and a few lunar astronauts can say the same. I am at the helm of Sea Dragon. It is a night shift again.  For the time being I am not seasick because I can see the dim horizon in the dark. Seeing stationary objects fixes the brain problem that causes seasickness in most people. 

The stars glitter, thousands of bits of salt sprinkled in a negative sky. Orion is overhead and the Pleiades and many other constellations I don’t know. In front of me, a diaphanous butterfly, eight stories tall, rises from the deck. Two massive triangular sails spread out to each side of the ship.  Tina said the square footage of one is more than her apartment. Getting the sails up took five of us directed by the Australian first mate, her sing-song voice carrying over the deck. “Grind on.” “Hold.”  “Lock it off.” “Ease.” The foresail or yankee is attached to a great stainless steel wire on the front of the boat, a forestay, and its clew, or corner, is held out from the boat by a great boom, mounted 30 feet up the mast and pointing 90 degrees abeam. This is what took five of us to set up. I am sure Maggie and Anna could do it just the two of them.

Sailing 24/7 for a week we have reached the trade winds and a breeze fills the sails from our aft, pushing us westward towards Oahu. 



It’s daytime and I comment to Anna that we haven’t seen any other boats for many days, basically since we left the Mexican coast. “We won’t,” she says. She explains that the horizon is maybe 5 or 6 miles away from our deck. So all around us we only see 30 square miles.  Even the superstructure on a big tanker will only be visible 12 miles or so away.  Basically we are blind. In the middle of the ocean we are a dot and the area we can see with the naked eye is a slightly larger dot. I knew this information, but somehow, it strikes home at this moment.  We are alone. 

It is nighttime again. The giant white sails in front of me glow from the brilliant quarter moon in front of them.  Below the sails I can see the water and a river of moonlight that is streaming from our bow to the dark line of the horizon, a silver pathway on the sparkling black sea. 

I steer the boat down this moonlight highway. My hands confidently pushing the wheel. The creaking of the rigging and the splash of the waves and the clangs of shackles are soundtrack. Only occasionally do I glance at the compass. 

Next to me stands the captain, silent. It is sublime 


It is more days later.  My team is on the 4 am til 8 am watch. A favorite watch. Sunrise. But now it is still dark.  We are motoring because the wind has died. The engine is noisy below but on deck the only sound is a gurgling from aft. The ocean is calm. Waves are long, low hills that approach us from behind slowly raising the stern then rolling under us, lifting and lowering the ship. A lazy swing. It is still a predawn velvety dark. I am navigating at 245 degrees magnetic by keeping Orion in between the weaving mast shrouds. I sometimes check the compass but I can navigate mostly by the stars, like thousands of sailors before me. 

Around 5 am the Eastern sea turns the color of shifting mercury. Behind us and to port, a paleness spreads, gauzing over the stars. We swing on the waves.  Gary, Tim, Samantha and I sit silently. Each are facing a different direction while I helm in the gloom.  

The light grows. Pink tinges the eastern clouds. My watchmates as one turn to aft to watch the coming dawn. It is a show. The pink grows and adds golds and yellows. The clouds right above the horizon are gilded with sparkling edges. Streaks of light pierce between, streaming toward us like flaming arrows from gods. I am glancing over my left shoulder to watch. It is the most glorious sunrise I have ever witnessed. 

Tim heads down the companionway and returns with a medicine bottle. He’s like me, I think, with the daily medicine regimen of middle aged men. Gary glances at the bottle.  

“My daughter’s ashes,” says Tim. He heads aft and empties memories of her into the glittering dawn sea. 

Later, Gary, barely above a whisper, “That was pretty emotional.”  I only nod, my throat constricted. 

That afternoon and evening, I am blessed to be again at the helm for the sunset watch. After the sun falls behind the horizon and the iPhones are put away, the crew departs through the companionway for dinner and I am uncharacteristically left alone.  I believe there is a rule against anyone being alone on deck. I tether myself in and do not bother calling down the hatchway for a crewmate.  I want this alone time.  The sunset isn’t finished. The highest cirrus clouds are peach streaks, fading to gray.  I struggle to read the compass under the darkening sky. I have ten more minutes of solitude before the next watch arrives and I selfishly want it. 

We are 900 odd miles from Oahu and the wind has not picked up. The sky is a Robin’s egg.  The sea is a deep blue disc under it. Word gets around that at nine am we will stop and swim. 

We are all on deck for a safety briefing. Call out for sharks, says the captain. “What do we yell?” Someone asks. “Shark!” Is the reply. 

We are children, jumping off the bow, playing in the water. I jump wrong and my nose is filled with salt water.  Samantha has on a mask and snorkel and lazily swims around in the ocean.  She is furthest from the boat. Hugh does a backflip. Gary and Rick compete with cannonballs.

“That’s quite a bruise you have on your back,” says Anna. And Hugh. And Gary. Figures. 

I have on goggles as I awkwardly dog paddle, trying to see the keel under the boat. I look down. There’s nothing but total blue with golden streaks of sunlight fading to the distance. It’s five miles to the bottom. 



What was old is new again. I’ve mis-timed my Dramamine and I’m feeling queasy.  And to make matters worse I have the midnight to four am shift again.  And to make matters worse it is predicted to be rainy and thus pitch black and thus no visible cues and thus seasick. I am dreading this watch. 

But it has been ten days and the moon is waxing and gibbous. I am pleased I know this phrase and repeat it often. I am sure my crewmates tolerate me because they have no choice, we being alone in the middle of the Pacific and all.  Though hidden by clouds the night is not pitch but gray. I can see the horizon in the dimness and the boat and my crew mates. Sea sickness is avoided. In the dark we can make out the shapes and splashes of dolphins playing in our bow wake. They stay with us for a long time.  Bucket list item “night dolphins” revealed and checked off. 

Among us are those who like to fish.  They like it a lot.  The boat has a vegetarian larder so any desire for animal protein must be satisfied by catching it. Two poles are mounted aft and lures are attached to lines and cast out, trailing behind. 

I’m ambivalent about fishing.  I have an underlying suspicion that the end of mankind will come with the death of the oceans, probably via a major toxic event. Overfishing isn’t helping. But I’m not so fundamental on this point to bring it up. Plus I am a hypocrite. I reap the result when my fishing crew mates land a mahi-mahi and a tuna.  Our multi-talented captain also knows how to fillet and a sushi spread is prepared that may be the best I’ve ever had. The situation certainly added to its attractiveness. 

We are running behind schedule. At the start of the trip we actually went back to Ensenada after a day at sea because a crew member’s diabetes was acting up.  The change in diet, he said. So we are still many days out from Hawaii. We need some wind.

We get wind. A squally patch of 25+ knot breezes whip the sea into a leaden froth. The waves grow to two meters and you can look at them face to face as they approach the ship. Sometimes the very top of a wave stretches thin enough to see through and the wave gets a brilliant aquamarine hat before it melts into another shape. 

Sea Dragon is a former racing yacht and it’s hull is sleek and fast. The bow is a vertical shear. The keel is shaped like a tongue depressor, a long vertical plate of steel sticking straight down from the ship’s bottom. This gives the ship better speed heading into the wind and more maneuverability as it can pivot on that narrow keel.

But it also means that Sea Dragon sways from side to side more than full-keel cruisers. In these wave-riddled seas with the two sails wing on wing, we bob right to left constantly, the mast swinging like a pendulum as we fly down, around, up and over the waves. 


In our bunks we roll side to side.  Sleep is fitful and scarce. In the salon we bounce against the walls, the table, each other. Getting to and using the head is more adventure than ever. I use extra clothes to make a cradle for my head so I don’t roll so much.  

We make great speed. We go more than 200 miles in a day. 

Six hundred miles from Hawaii I wake up at 5 am. I am starving. I don’t have watch for three hours but I can’t wait.  I didn’t eat dinner due to seasick. I put on my headlamp, turn it to red and go to the salon. I hear the watch crew on deck talking and laughing.  Nobody is stirring below. I’m sure many are awake in their beds as the rolling is significant. I get a plate from the cupboard. It has a rubber bottom so it won’t slide as the boat heels side to side.  I carefully get peanut butter and I knife some on the plate. Then some jam. I make my way, one hand on grab bars, to the table, scooping up the last of the saltines on my way. After I sit I see I didn’t latch the cupboard door fully and it swings wildly as the boat pitches to and fro. I can’t leave the knife because it will slide off the plate. I traverse the salon, peanut buttery knife in my hand and close the cupboard door.  I do this with surprising confidence. That I can enjoy my snack alone on such a crowded boat is really a marvel. 

We play games with numbers. Who will be on watch when the log reads “23456”?  When the log reads "24000"? Who clocked the fastest speed? (Isaak and Samantha tied at 13.3 knots). When will we arrive? 

Between watches I try to sleep in my bunk but sometimes I cannot. I have written a long poem about the trip. I fantasize that I will read it at our final dinner.  I reread it to myself and some of it is funny. I believe Hugh sees me silently reciting my poem, and gives me a funny look. I am not capable of alleviating his fears about my mental health. I know I will not actually read it to anyone. 


Example:  

At night the watches were rough

The 2am helming was tough

Tired and blind 

If you could, do you mind?

Take the wheel, I’ve had quite enough.


Two of the crew live in Hawaii. They are asked to divulge every secret about the islands, the best food trucks and best hikes and favorite candies. 

It’s my second to last midnight to four am watch, the most painful time for me. Again I struggle looking at the compass, my eyes water and swim searching for stability in a constantly moving world. The wind has picked up and we need to reef the mainsail. The helm is handed off. I accompany Maggie and Gary forward, in the dark. The boat is pitching because it is overpowered in 30 knot gusts. I am crouching on the foredeck. The wind is tropical and moist in my face. I am clumsy as I unclip and reclip my tether to port. We yell back and forth with the other crew aft, the wind and waves howling above us, following Maggie’s directions. I’ve been given simple tasks befitting my skill set. I operate clutches labeled “topping lift”, “reef 1” and the like that hold tight various lines after they’ve been winched to the right length. After the main sail has been shrunk a bit to match the stronger winds, Gary and I remain in the area called the snake pit filled with a dozen thick lines and we coil them neatly for their next use.

Just a few hours later the next watch will remove that reef as the wind falls off. 

We are 350 miles from Hawaii. Half of us are lounging around deck in the tropical sun as we motor during a lull in the wind. First Mate Maggie pops her head up through the companionway and hands captain Anna a notebook sized American flag and a similar sized yellow quarantine flag. We will fly both when we enter US waters.  Anna tells us that before the cause of scurvy was known, ships with scurvy-riddled sailors would wait in quarantine offshore not realizing the cure was the good food dockside denied them. Many died waiting. Until covid, the standard yellow quarantine flags were an anachronism for nearly 100 years. Not anymore.

Quarantine Flag


Nearly there, I am finally in a routine. I know the watch schedule by heart.  I can get into my bunk like Roy Rogers on Trigger.   I can pee in the head without fear or bruising. 

The wind has died again. I recall from a sailing story of the nineteenth century (Before the Wind by Charles Tyng) the author spends two months trying to sail west through the English Channel before giving up and sailing north entirely around Great Britain. 

At night when motoring the prop will stir up bioluminescent sea life. The boat wake is a mirror of the night sky with sparkling aqua stars and swirls and glowing blobs. We stare aft at the light blobs and sparkles in our wake and call out to each other. “Wow, that was a big one!”

It is Thursday. Some guest crew have flights out of Hawaii on Saturday.  We are motoring fast to make it to Oahu tomorrow.  We must clear customs because we are arriving from Mexico.  We hope we can clear in time for a landside meal with alcohol and meat. Maggie sticks her head out of the companionway and tosses three older cabbage heads into the sea. We can’t bring any fresh food into Hawaii.  We’ve been rapidly consuming everything and nearly all that is left are the cabbages and some sad limes.  Hopefully the sea life will appreciate them. 

We caught two more mahi-mahi yesterday. Gary and Tim filleted them. We are going to make fish tacos and maybe sashimi.

I wake early on Friday, just after dawn, having slept a few hours, and I exit to the deck. Tina, Rick and David are on deck staring south at The dim shape of Molokai to the south. 

The clouds are light and as dawn fully takes hold Oahu rises dead ahead.  A rainbow forms over the Oahu coast, pointing out our course. I take the helm around 9 am and guide us past Koko Head. Someone yells out “whale!” as we approach Diamond Head and I am instructed to briefly change course to both see them better and avoid them. "Let's not hit any whales," says the captain.

I am blissful as the beauty of Hawaii takes over our vision. Verdant valleys with cottony clouds. More rainbows appear and disappear over Oahu as we approach. We had hoped to sail gloriously around diamond head but the wind is weak so we are instead motoring just as gloriously. 

Honolulu is magnificently backdropped by green mountains and ubiquitous clouds.  Other sailboats and pleasure craft float in the waters off Waikiki.  Gary points out landmarks he knows. I pass off the helm to Tim as we consume the mahi-mahi caught the day before and the last of the vegetables we can’t bring into Hawaii. 

We turn the boat in a lazy circle as we lower the massive mainsail and prepare the fenders and dock lines. 

Finally ready, Captain Anna takes the helm of Sea Dragon and we pull up dockside in Honolulu.  Gary wins the contest for closest guess for our arrival time. 

That afternoon I am walking from the marina to the tourist areas in Waikiki. It has been 18 days since I walked on land. The ground shifts unsteadily as my brain continues to expect sudden movements.  I almost forget my wallet at the Surfrider Hotel bar where I watch the sunset and babble to the person sitting next me about sailing to Hawaii.  It will take me a full week before my hotel bed doesn't move while I sleep.

I meet my crewmates for final dinner and like old friends we toast each other and the three professional crew for getting us to Hawaii. 

I am infinitely more confident about my sailing and boat handling.  I’m considering chartering a catamaran in the Caribbean this summer. 

Fair winds and following seas, as they say.



Wednesday, November 10, 2010

English Subjunctive - Pet Peeve

The subjunctive tense in English is not used very often.  However, it does exist. And when it is not used it annoys me.  Why? Because I'm perhaps a bit weird.


The Fiddler on the Roof song "If I were a rich man..." is often mistakenly quoted as "If I was a rich man..."    And since I'm not a rich man (well, richer than many, but not really rich) it's even more annoying.  These errors occur with frequency.  The Joan Osburne song One of US (good video, BTW, and pretty good song) contains the line  "If God was one of us..." It should be "If God were one of us..."   And many folks often use the phrase "If it was up to me..." It should be "If it were up to me..."

And big shoutout and kudos to Rooney who has a song correctly titled "If it were up to me".

And so, if it were up to me, nobody would forget their English subjunctive.

Thursday, November 4, 2010

Should I go ahead and build PillMinder.me?

I've got some flows done for PillMinder.me, but I'm not sure if I should pull the trigger on a CrowdSpring design or just go with a vworker developer?

Decisions...

Why 1,000,000 > 1,000,000 - a note on weird math

So I posted previously about the math behind bit.ly. This brings up a minor point that made me want to post again at 5:30am today.

When we talk about numbers, the number 1000000 is pretty big.  But the number 0000000 is pretty small.  However, the number 0 is the same numerically as 0000000.  But in a database they are different, if the field is a non-numeric field.

This means that the actual number of outcomes that comprise all the possible combinations from 0 to 0000000 is greater than 1000000.   If you have a single digit number, the possible number of outcomes is 10 (0,1,2,3,4,5,6,7,8,9).  If you have a two digit number, the possible number of outcomes is 100 (01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 11, ...)  If you consider "6" different than "06" then the actual possible number of outcomes is 110 with a two digit number.

So with an 8 digit number, the possible number of outcomes is as follows:


And this is why 1,000,000 can be greater than 1,000,000.

Wednesday, November 3, 2010

Begin the submission process

Does applying for a job really require us all to be beaten down?

I have no problem with "submitting an application" but this is kind of harsh.

Monday, November 1, 2010

Automatic continuously updated web design - the site is alive...

So I have an idea...don't we all?

Ever since adwords was able to automatically optimize the display of ads based on click-through rates I've been curious about automatic content and web design.

Shouldn't web widgets, such as those at jquery automatically rotate through colors, size and perhaps even functionality from the moment they are launched?

This way they would be regularly updated and improved.  Some of the website control would be turned over to an optimization program that would cycle through a predefined range of options (colors, size, location, functionality) which would then feedback and choose the best combination set.


I can see one bit of the admin console that looks something like this:

Each in this way, multi-variate testing becomes even more scalable so that widget option rotations could be linked. The purple button rotates into orange when the content switches to internal vs. external.

In its simplest form a button is optimized with no input from the site editor. In it's most complex form, the entire size can morph and change based on site visitor behavior....


The site responds to traffic and builds itself in a way that optimizes whatever goal is set...

Saturday, October 30, 2010

The math behind bit.ly and other url-shortening services and other numbers on the web

My son, who is 12 years old, was recently assigned homework dealing with outcomes.  These are the calculations that feed into probability calculations. We use outcomes all the time to calculate our chances of an event occurring given a predetermined number of possibilities surrounding prior events.

If Janie has a red blouse, a blue blouse and a green blouse and she also has blue jeans, khaki shorts and black capri pants, how many outfits can she create?
Aside from the  possible Glamour donts that Janie could create, we can calculate Janie's number of outfits by multiplying the number of blouses (3) times the number of leg-wear (3) and get 9 total outfits.  This can be generalized by saying that the number of outcomes is the product of the total possibilities of each subsequent event.  This can be represented by a tree diagram as well.


This math is actually the basis of our numbering system. Every number we use every day from our age to our shoe size can be represented as the outcome of a tree diagram.  Each digit in any number is represented by one of 10 possible characters 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9. (These are called Arabic numerals.)  The second digit of a two-digit number can also have 1 of these 10 different characters.  Each digit in a number has 10 possibilities. If we draw a tree diagram for a 2 digit number, it has 100 possible branches.  Below is a tree diagram for a 2 digit number (I left out 2,3,4,5,6,7,8 for space reasons).

Each additional digit increases the number of possible outcomes by a factor of 10.  So a 3 digit number has 10^3 possibilities or 1,000.

You may see numbers mixed with letters on the, such as FF6.  This is a number, but instead of using 10 Arabic numerals for each digit, the character set has been expanded by 6 to include A, B, C, D, E, and F.  This yields a total of 16 characters for each digit.  This is called "base 16" or "hexadecimal". Our out numbering system is "base 10" or "decimal". Each additional digit in a hexadecimal number increases the number of outcomes by a factor of 16.

Anyone who has some knowledge of Cascading Style Sheets or HTML has come across hexadecimal in color codes.  All colors on the web can be represented by numbers and those numbers are often represented in hexadecimal instead of decimal. You can see breakdowns of the colors in both numbering systems on many websites. (for example, http://html-color-codes.com/ and http://www.december.com/html/spec/colorhex.html)

The reason behind this has to do with how computers think and how early computers stored numbers in memory.  Computers at their simplest operate in base 2 meaning they have two options, off and on. This is typically represented by the numbers 0 and 1.   Each on/off digit was called a "bit" and in fact on/off fields database tables are still called bit field.  Early computers, notably the 6502 microprocessor (which ran the Apple ][+), used 8 bits together to process calculations.  Half a byte was 4 bits. And with a 4 digit number in base 2, you have a total of 2x2x2x2 or 2^4 combinations or 16 total.  And instead of writing out 4 digit numbers, computer memory was often represented in base 16. (The name of this blog, FF69g, is the computer instruction that the original Apple ][+ used to exit from machine language mode and it refers to memory location FF69, which is a hexadecimal number)

Let's take a moment and talk about what Bit.ly and other url shortening services do.  They are very simple services in concept.  With an url shortening service you can take a long web address and shrink it down, like putting a wool sweater in a dryer, only when you put the sweater back on it magically returns to its correct size. Say you have a very long web address, for example if you search for "what is the capital city with the longest name?" on Google the actual results are in this web address:

http://www.google.com/search?q=what+is+the+capital+city+with+the+longest+name%3F&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

But wit an url shortening service, that search becomes

http://bit.ly/db3e3Q

The longer url can be hidden on a web page using the tag.  That search is linked here, for example. But with non-HTML services, such as text emails and text messages and Twitter, the longer url is simply inconvenient or impossible.  So url-shortening services evolved and now there are hundreds of them. They generally have short domain names such ".ly" or ".co".  (See recent controversy surrounding ".ly")

So bit.ly and other search services save the long url in a database table and assign a code to it. And when your browser requests a bit.ly url, the code that looks random (db3e3Q in this case) is used to look up the correct url in the table and redirect your browser to the destination, in this case a Google search.

Each url that bit.ly stores get it's own unique lookup code.  And sinceI assume bit.ly stores billions of urls, the lookup codes could get very long (and I'm assuming there are billions since I don't really know).

So a 10-digit lookup code using Arabic numerals would have about 10 billion possible outcomes  from 0000000000000 to 9999999999999.  In the computer world and the search world, that's not that much.  That means if everyone in China searched 10 times the service would run out of lookup codes if they wanted to use only 10 digits.

In order to increase the number of possible outcomes without increasing the number of digits, bit.ly added upper and lower case letters to each digit.  So instead of 10 possible characters each digit has 62, because there are 10 Arabic numerals, plus 26 lower case letters and 26 upper case letters. The number of possible outcomes for a 1 digit code with 62 characters is 62.  The number possible outcomes for a 10 digit code with 62 possible characters in each digit is 62 to the 10th power or 839,299,365,868,340,000 or, in words,  eight hundred thirty nine quadrillion two hundred ninety nine trillion three hundred sixty five billion eight hundred sixty eight million three hundred and forty thousand.




Now, math purists (and bit.ly mathematicians) may say I've actually undercounted the possibilities because not all 10 digit numbers are used, so, in fact, the remaining digits in any combination could be 63.  For example, 0000000000 and 0 could be considered different lookup codes by the bit.ly servers (and they probably are).

This means that the actual number of outcomes is the sum of the various-length codes from 1 digit (62 codes) to 10 digits (the aforementioned long number).

I've never seen a bit.ly url that has only one digit in the lookup code, so perhaps they've limited the number of digits in their lookup codes. And in fact I have no idea if they even use 10 digits.

In fact, I don't know anything about how bit.ly works at all. I'm just assuming this since I had to create a similar system for my QR code tracking service that I built for fun (http://www.bloty.com) which might one day become a way for people to tell you that your lights are on in your car or that you are illegally parked while sitting at a restaurant (http://www.notesonawindshield.com, but it's in beta, so apologies for errors).

My code to generate the look-up using 62 possible digits is written in PHP and I've cut and pasted it below. No apologies if it doesn't work for you, I only recently learned PHP and it may or may not work exactly as planned. "UUID" stands for universal unique identifier.

  function uuid()
  {
//62 ITEMS IN THE ARRAY
  $arr = array(0=>0,1,2,3,4,5,6,7,8,9,0,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z);
  $uuidtemp='';
 
  $i=1;
    while($i<=12)
          {
          $uuidtemp = $uuidtemp . $arr[mt_rand(0,61)];
          $i++;
          }
  return $uuidtemp;
  }