Leg #3, Hawaii to San Francisco Single-Handed

Daily updates from a first-time captain sailing across the Pacific

See leg one (San Francisco to Tahiti) and two (Tahiti to Hawaii)

And then there was one

Jun 22, 2024

I’m still docked in Honolulu. My father went home last week. We rented a car and drove around Oahu. We hiked the first few miles up the trail to the highest mountain here. We packed a lunch of musubi and played in the waves at a remote beach. And then, after 100 days together, I called an Uber to the airport and waited on a busy street in Waikiki, vacationers in swimsuits streaming by, until his car came. 

My father is happy to be home. This was a wonderful experience for both of us, and it was also hard. Now he’s back to his comfortable bed (no leecloth required to keep him in), his oatmeal for breakfast (made on a stove without gimbals), his daily walk around the farm (without the deck moving under his feet). Since retiring, my father has dedicated himself to nonviolence programs in prisons. He’s right back to it, taking part in a program at Albion prison this weekend. 

My brother Eli and his family came to Hawaii to visit me and see the boat, so I was not immediately alone. We sailed from Honolulu around the island to Kaneohe bay. Surfing is far more popular in Hawaii than sailing, and it ends up there’s a reason for that. Trade winds and open ocean swell, funneled and concentrated in the channels between the islands, give rise to  world-class breaks. They don’t create the best environment to introduce your nieces to sailing. On our way to Kaneohe, everyone got sick. Let’s just say that a through deck wash down was required on arrival. 

Still, I had a great time with Zora and Sofia. They may not have loved the sailing, but they did love the beaches. We swam and snorkeled and body boarded. We made north carolinian sonker (an obscure dessert). We played cards. 

But yesterday, they too left. Now it’s just me. I will be sailing singlehanded back to San Francisco.

Hawaii is high contrast. It’s swamped in tourists, but even here in Oahu (by far the most populous island) there is undeveloped wilderness. Luxury travel contrasts against what is actually one of the poorer regions of the US. The mix of cultures—Japanese, Hawaiian, Portuguese—is notable. And while Honolulu’s beaches are certainly a major focus of visitors, they’re also a gathering place for residents. Yesterday I was watching a father teach his 4-year-old to surf. This is an interesting place. 

But my mind is not in Hawaii. Nurcan is in San Francisco. I miss her. She’s planning our wedding, looking for a house, starting to build our life. It’s time for me to go home. 

Between me and Nurcan is 2200 nautical miles of ocean. I will sail back to her. I’m getting the boat ready now. The weather looks favorable. I plan to depart on Tuesday.

I’ll write more about solo sailing. It’s going to be intense.

-Ammon

I’m off!

Jun 25, 2024

21°12’N 157°45’W

I’m 8 miles of Waikiki, heading east around Oahu. Making 6.5 knots close hauled in 18 knots of wind with 2 reefs in the main and 3/4 jib. It’s a bright, sunny day. 

Well, it’s me and the boat and the deep blue sea. This is going to be my reality for a while now. I’m pretty keyed up. I went over my prep checklist multiple times (with a bit of an obsession). And I could not sleep well last night because of nerves. 

Leaving the dock went well. The Marina in Honolulu is super tight. We were “parallel parked” between two other boats (along the side of a relatively narrow channel). There’s a technique for situations like this (spring lines). But it normally needs crew to set then release the lines while I drive the engine. Luckily wind was light, so I was able to run back and forth, setting a spring line, back to the helm to control the boat, back to the line to cast it off, back to the helm.

Then I motored slowly out of the marina, turned the boat to calibrate the compass, put away dock lines and fenders, raised the sail, set the windvane, and here I am. I’ve been sailing alone before. The difference is that this will be ~20 days alone. My body does not believe it yet.

As soon as I round the east eastern point of the island (Makapuu point) I’ll tack and head north. San Francisco is east-northeast of here. The problem is that the trade winds blow directly from San Francisco to Hawaii. If I tried to sail the great circle route (straight line) to SF, I’d have to tack into the wind all the way and it would take much too long. Instead, I plan to sail due north from Hawaii for 700 to 1000 miles, until I am out of the tropical trade winds and into the mid-latitude westerlies. There, I will have winds out of the west to carry my east to home. This is made more complicated by the pacific high (a zone with no wind right on the middle of the northeast Pacific). Sailors call it the “parking lot”. I need to go north of the high. If I turn east too soon, I could be stuck with no wind (one person I spoke to spent a week and a half adrift in the high). 

My largest concern right now is sleep management. Because I’m still close to Hawaii (with the potential for fishing boats without AIS beacons) I want to get up and look forward every 30 minutes tonight. Later in the trip (farther from land) I’m going to relax this to every 60 minutes. I’ve made up a bed in the center of the cockpit so I can scan the horizon without really getting out of bed.

We’ll see how this goes!

My second concern is boredom. Time can pass slowly when you’re alone, and I’m looking at a lot of time. It can be  harder to find joy in an activity when there’s no one to share it with. My hope is that I will find the experience peaceful. Many sailors report this. In case that’s not enough, I’ve downloaded hundreds of episodes of trashy reality TV. So imagine me either sitting in awe, pondering the beauty of the sea and reading classic literature, or rotting my brain, blinking blearily over my 5th episode of Storage Wars. It’ll probably be a mix. 

I’ll send another update tomorrow! Wish me luck, 

-Ammon

Day 2 alone

Jun 26, 2024

23°10’N 157°30’W

I’m about 116 miles north of Oahu. With the tacking, I ran 120 miles in the first 24 hours. Winds have for once been lighter than forecast. We’re currently making 5.8 in 11 knots of wind, under full genoa and one reef in the main. Conditions might call for full sail, but I’m trying to be conservative. We left Tahiti for Hawaii (with Gurney and Stuart) around the same time as another, larger boat sailing the same course. We stayed in email contact with them, and Little My (despite a 3-foot shorter hull) was makings about 20% more miles every day. The difference was sail selection. They were flying storm sails the entire time, while I was rolling out a real genoa, sometimes making 8 knots. This is to say, I like pushing the boat and going fast, perhaps more than some skippers. However, I’m fighting that impulse now. If we make 5, 5.5 knots, that’s plenty good enough.

Last night was… beautiful and really exciting! I am certainly tired. I got up every 30 minutes from about 10pm to 9am. But it was just so beautiful to lie in the cockpit under the stars as the boat zoomed along and fall asleep. It felt like one of the most adventurous things I’ve ever done. And it’s a good thing I liked it because I got to do it again, and again, and again. I’m going to switch to 1h sleep periods tonight, which should feel luxurious by contrast.

I’ve not seen another boat since turning north yesterday. The weather has been squally, but pretty benign squalls (wind up to 17 or 18 knots). The principal problem with the squalls is that they show up on radar and thus trigger my radar alarm. On top of the 30-minute timers, I got up 3 times with radar alarms as squalls passed. I could try to tune the radar to not show weather, but I’m afraid of missing a small boat in that case. I’ll just hope the weather calms down and lets me sleep more.

The propane controller has been malfunctioning. This is a system with a solenoid valve to control the flow of propane and keep it from building up in the boat. Propane is heavier than air, and a boat is necessarily a watertight convex vessel. Thus it can just fill up with propane in a way that a normal house can’t. To protect against this, we have a propane sensor controlling a solenoid shutoff valve. However, the sensor suffered water damage and has been sporadically giving false positives. This morning I had to power cycle the system 3 times before it let me make coffee. If it keeps doing this, I’ll have to give it the fridge controlled treatment (cut out the controller and replace it with a manual switch). BTW, my friend William helped me figure out what type of industrial controller was inside the fridge unit, Eli brought a new one from Boston, and after much paining over documentation, I was able to get it programmed! So the fridge is back to controlling itself.

In any case, I’m feeling good—better than I expected! So far I’ve only watched one and a half episodes of reality TV. A trio of masked boobies is following Little My. Oh, the agility with which they dive towards the waves, roll and swerve, just over the surface. Masked boobies are often pelagic, but we also saw them right at the shoreline. I wonder if these three birds will fly back to Hawaii to roost or stay out here with me.

-Ammon

The first night

Isolation, beauty, and lassitude

Jun 27, 2024

25°38’N 157°01’W

140 mile noon-to-noon run today. Hawaii is 280 nautical miles behind me. The evening is noticeably cooler. The weather today was ideal—bright sun, long swells, 14 knots of wind carrying us north. We’re still close hauled, but it was about as mild as sailing upwind in the open ocean can be. On a day like this earlier in the trip, we’d have all been excited about the blue, blue water and how peaceful it was.

But I’m in a strange state of mind. There are moments where I feel the beauty (the isolation even intensifies it). Just a few minutes ago, as the final light of the day was fading, a night bird flew by and circled us. I could hear the beat of its wings. But there are other moments where I stick my head out of the boat briefly to make sure everything is safe, then go right back to eating cheese sticks under a blanket on the settee. I think I ate more snacks than were good for me today. From talking to other solo sailors, I think this is normal. Lassitude from sleep deprivation is just part of what you go through.

I’m trying to slow down all maneuvers and keep the lines extra tidy to reduce the chance of making a mistake. I had to put in a reef at 3am last night (a squall was approaching). I spent 20 minutes doing what would normally be a 5-minute job. This does mean that I put more wear on the sails. Damage to sails comes mostly from them “luffing” or shaking in the wind when they are not properly adjusted (trimmed). So you want to limit how long you leave a sail out of trim as you maneuver the boat. Well, there’s just no way for me to do this well single handed. I can’t be in two places at once, and I can’t safely rush. So more wear on the sails it is.

I think I need more to keep me busy. Tomorrow morning, I’m going to put a fishing line out. If I catch even a medium sized fish, I won’t be able to eat it by myself. But coming home with a freezer full of fish is not a bad thing.

The long-range weather forecast is not looking great for my plans. Currently, the models show disorganized, variable westerlies next week (when I’ll be arriving at 37N and looking for steady winds). I do have the luxury of 200 gallons of fuel (~800 nm range under engine), however, so I can motor my way through some light winds if I need to.

-Ammon

In memory of Bernard Moitessier

Jun 28, 2024

27°15’N 156°50’W

Sight on the raising sun and setting moon at 0900 this morning. The declination of the sun right now is 23N. This is too close to our latitude for me to get good crossing LOPs from sun sights alone.

June 28th is a special day in sailing. In 1968, a British newspaper sponsored a non-stop, single-handed, around-the-word sailing race. This was the “Golden Globe Race”, and before it was held, no one had ever successfully circumnavigated non stop and single handed.

The race captured the world’s attention in a way that was only possible in simpler times when we all read the same newspapers. Reporters all over the world covered the prep, the departure, updates on each boat. It was a breakout story.

There were only a small number of competitors, and most of the few that there were dropped out early in the race. Sailing non-stop around the world with 1960s technology was a HARD thing to do. Most of the boats were made of wood. There was no electronic navigation. I’m not sure if steering windvanes had been invented (I’m writing this from memory, and they came along right around then). There was of course no weather forecasting (so sailors were just rolling a die as they crossed the southern ocean). Think of what they were doing as 100 times harder and more dangerous than what I am doing now.

In any case, as the race came to a close, there were three boats still in contention.

Leading the pack by more than 1000 miles was French sailor Bernard Moitessier in a steel ketch he’d built himself (named Joshua after Joshua Slocum). He took working boat building conventions of the time, and just made everything twice as thick and twice as strong. The masts were telephone poles. This was a boat that could survive the southern ocean.

Behind Moitessier was the American Donald Crowhurst. He was an engineer with no sailing experience prior to this race. His boat was a plywood catamaran. Both plywood and catamarans were new technologies, and on paper (under engineering analysis) his boat was the fastest of the three by a significant margin. But could it handle the open ocean? And could Crowhurst manage the boat with no experience? He also, crucially, was the only one of the three to carry a long-range radio.

In 3rd place as the race drew to a close was Robin Knox Johnston, Johnson was British and a traditionalist. He was in a wooden boat with canvas sails, caulked with hemp and tar. Think of him as John Henry vs the machine.

I’ll give away the outcome. Johnston would go on to win the race. This, however, makes him only the 3rd most interesting sailor of the three.

As the three boats finished their circumnavigation of the southern ocean, they were still in the order outlined above. Moitessier was ahead by 1000 miles. All he had to complete was the far simple and safer run up the Atlantic to the finish line. Papers were already calling him the winner.

And that’s when Moitessier became a legend. He did not have a radio. He communicated with the outside world by firing paper messages at cargo ships with a slingshot (really!) So Moitessier sailed up to a cargo ship in the southern Atlantic, and let fly a message telling the world that he’d liked non-stop circumnavigating so much that he was not done. He was going to keep going around the world a 2nd time! (He actually ended his voyage in Tahiti, having sailed a time and a half around the world.)

This left Crowhurst in first place. But Crowhurst had a secret. He did not know how to sail, and when he departed on the race, this deficiency had become painfully obvious to him. He could not do it. But unable to admit defeat, he came up with a plan. Crowhurst sailed his catamaran to an obscure island in the Caribbean, anchored, went ashore, and proceeded to live a good life on land, all the while going back to his boat from time to time to report fake positions via his long-range radio. He was going to hang out in the Caribbean, and only sail back to the finish line once his fake position made it back to the Atlantic. He was not trying to “win” the race. He seems to have been intentionally faking a 2nd place finish that would not subject him and his logs to scrutiny. Crowhurst was not well, and this story has a sad ending. With Moitessier out of the race, Crowhurst was going to “win” the race and in all probability have his fraud discovered. Unable to face this, he took his own life.

This left stodgy Robin Knox Johnston to sail to victory, the only finisher and the first person to sail solo non-stop around the world.

Why am I writing all this? Because Bernard Moitessier had a predilection for nudity (I bet you did not see that coming)) He listed “naked yoga” as one of his favorite ways to pass the time at sea, and would reportedly go days without putting on a shred of clothing.

In honor of Bernard Moitessier, then, contemporary sailors have named June 28th “Sail Naked Day.” And so it is, following the sacred tradition of sailors before me, that I have spent all day wandering about my boat unclothed. There’s something hilarious about it. I’m so far from anyone who could see or care. The problem, however, is sunscreen. I can’t reach the center or my back. So I must hide from the sun.

-Ammon

To be like a seabird

Jun 29, 2024

30°01’N 157°04’W

Sun-run-sun fix as of 1530. I said yesterday that we were too close to the sun’s declination to get crossing lines of position from two sun fixes. But the moon was obscured by clouds this morning, and we are moving north of the sun rapidly now. So I tried to do a sun-run-sun, and it came out well!

I think I’ve mastered the art of sleeping single handed! I’m feeling much less tired. The trick is to stay 80% asleep during the 1h checks of the boat / horizon. I only turn on a dim red headlamp, and I keep one eye closed! That way I’m still in bleary sleep mode and can go straight back to sleep. Last night, on one of my checks the steering system was making a noise I did not like. So I had to wake up a d look at it (salt had accumulated in a turning block for the vane lines, so I just had to pour fresh water on it then spray oil). In any case, all the other checks scarcely woke me up. Sea birds sleep while flying by sleeping one half of their brain at a time (again, I lack internet, but I think this is non-apocryphal). I just need to be like a sea bird!

Long-range weather models are starting to look a little better for me. I expect to be at 37 north in 3 or 4 more days, and (depending on which model I look at) I might then have a shot at sailing east.

I made a mistake today. I opened a 2-kilo bag of grocery store Madelines (from Tahiti). The first scary thing is that they are shelf stable. Never trust a shelf-stable pastry. But the real problem is that in this environment, I lack all self-control. I am going to eat all 2-kilos of Madelines. It’s going to happen.

-Ammon

Bliss and (boat) hypochondria

Jun 30, 2024

31°44’N 156°04’W

Sight on the sun and upper limb of the crescent moon at 10:40 this morning. I recorded video of myself taking the sights, doing the reduction, and plotting on the passage chart.

Today we encountered a slight current from the west. The currents in the trade belt go the same way as the prevailing winds (with the exception of the equatorial countercurrent). But a current from the west is a sign that we’re approaching the northern edge of the trades! The usual advice when sailing from Hawaii to CA is to hold the northern course until you’re truly in the westerlies, then turn 90 degrees. However, the westerlies are all jumbled up with the pacific high right now. Purely to avoid a dead patch in front of us, I’m now steering 020. We’re beginning a gentle curve to the east.

Winds are light. I’m under full sail for the first time since leaving Hawaii. I spent an hour on the foredeck today. I went forward to shake out a reef in the main, but it was so beautiful up there I just sat in front of the mast and watched the water go by. Somehow, sailing solo involves more leisure than sailing with a full crew. Yes, I’m in one sense always on watch. But because of the impossibility of actually keeping an active, forward-looking watch 24 hours a day, I have to trust my alarms (and perhaps accept more risk). But once I’ve done that, I’m free to lie on my back in the cockpit, listen to music, and watch the sky go slowly from day to night. I did this last night. There’s a good chance I remember this as the most intense natural beauty I experience in my life.

Then there are the fears. Today I watched a horror movie set on a sailboat. But even without the movie, I’m a boat hypochondriac. Being alone seems to increase this. With every groan of the stays, I fear the mast is falling down. A wave smashes the side of the boat, and I wonder about cyclic metal fatigue and aluminum boats (hey, it was a thing in airplanes in the 80s). The woodwork is making a new sound. Is the hull flexing more than it should?

Net, I am glad that I’m here. What a privilege to be able to do this. I am going to remember this trip.

I’ve been eating bean chili for the last few days. I just made a large pot of Senegalese maffee. That’ll be dinner for the next few days.

-Ammon

Readers write

Jul 1, 2024

33°48’N 155°16’W

Another sight on the sun and moon at 1100 this morning. The moon is down to just a sliver. It’ll be too close to the sun for me to use soon, and I’ll have to go back to sun-run-sun sights. Correcting for the parallax of the moon is more work than doing a running sight in any case. I think I’m going to use 100% celestial navigation from here back to SF.

It’s been mostly cloudy and raining on and off since last night. It’s amazing how big an impact that has on me. It’s much less nice out here when it rains. Somehow the ocean feels more threatening, especially now that it’s cold outside. The wind’s also been highly variable. I’ve been putting in and shaking out reefs all night and day.

However, sustained rain is more evidence that we’re out of the trades! You get rain squalls in the trades, but full days of rain and clouds are rare! I’m now on a courses of 045, directly northeast. With a penalty of only 1/sqrt(2), I’m headed home!

Today, I’m going to share things that you (recipients of these updates have sent me).

My brother Eli fills in details on the Golden Globe race.

I am not aware of Crowhurst living on land (I thought he went in circles in the atlantic). You forgot Nigel Tetley, who legitimately completed a circumnavigation in a plywood trimaran (he crossed his own incoming path), and would have beat Knox-Johnston's time (there were separate prizes for first back and fastest time). Thinking Crowhurst was hot on his heels, he pushed his boat too hard and sank in the north atlantic not far from home and when the boat started coming apart.

And finds an abstract of a paper on unihemispheric sleep in frigatebirds. It’s a thing! So frigatebirds, like me, are getting by but fundamentally fatigued.

Here, using electroencephalogram recordings of great frigatebirds (Fregata minor) flying over the ocean for up to 10 days, we show that they can sleep with either one hemisphere at a time or both hemispheres simultaneously. Also unexpectedly, frigatebirds sleep for only 0.69 h d−1 (7.4% of the time spent sleeping on land), indicating that ecological demands for attention usually exceed the attention afforded by sleeping unihemispherically. In addition to establishing that birds can sleep in flight, our results challenge the view that they sustain prolonged flights by obtaining normal amounts of sleep on the wing.

My friend John imagines a transparent ocean.

If you're looking for maritime horror, I recommend the fiction of H.P. Lovecraft and the genre of "Cosmic Horror" that he inspired

The core concept is that the sea is the unknowable. It represents the limit of what humans can understand, or indeed of sanity itself.

As a scientist, I can't help but optimistically assume that there is no such thing as unknowability.

Whenever I'm on the sea, I imagine flipping a light switch that turns the water as transparent as air on a bright sunny day.

Rather than floating on the surface of a black opaque ocean, I am flying like a bird over a landscape.

There's nothing special about that landscape below. It has mountains and plains, canyons and deserts.

And I'm not alone in flight. Made suddenly visible is every fish in the sea. The big things catch my eye first, of course. The whales, sharks, and large predatory fish.

But also look there, it's a nuclear submarine thinking it's being oh so sneaky. It looks like a small blimp, gently drifting through the air.

Suddenly the sea isn't so mysterious and dangerous. It's just a watery quirk of a planet with this particular mass and composition at this distance from its star.

And my brother Gurney (in another Lovecraft reference) imagines how we’d report a Cthulhu encounter to the Coast Guard.

“Coast Guard sector Honolulu, Coast Guard Honolulu, this is sailing vessel Little My, Little My. Do you copy?”

“Little My, switch to channel two two alpha”

“Coast Guard, this is Little My. We’ve got….ah… a Cthulhu approximately 2 miles off our port bow”

“How many people are on your vessel, and are they all wearing PFDs?”

The joke being that if you spend much time on marine radio, you’ll hear that the Coast Guard always responds the same way.

Keep writing to me! You can just reply to this email as it goes straight to me.

-Ammon

Cake or a broken gooseneck?

Jul 2, 2024

36°01’N 154°06’E

Sun / moon sight at 1130 this morning. There’s hardly a sliver of moon left and it’s converging on the sun. I won’t be able to do any more morning moon sights on this trip.

We’re sailing course 045 true now! Wind is forecast to drop to nothing tonight, stay low all tomorrow, and then, starting Thursday morning, I should have the northwest winds that will carry me home. I sailed 1000 miles north from Hawaii (close hauled all the way) to find these winds. I’ll be unhappy if they don’t show! We’re at least on a beam reach now. It’s already much more comfortable.

There was a small amount of salt water in the bilge this morning. I followed the wet trail back, and it seems to be a cooling water plumbing leak. I tightened a hose clamp and I’m monitoring. Only about 1 quart of water leaked in 24 hours, so I am not too concerned right now.

I’ve been at sea for 1 week! There’s a cake in the oven (molasses spice cake or “moles’-asses cake” as my mother used to call it). I even have whipped cream! This was my favorite when I was a boy.

There’s been a dull thudding sound on the boat for several weeks. I could not find the cause (Gurney and Stuart watched me hunt for it last leg). It was happening on the foredeck and only in rough conditions. There’s so much going on in those conditions (flying water, lines whipping, the boat trying to throw you off) that I could not isolate the sound when above deck (only below, when the hull of the boat acts like a guitar body and amplifies the sound to a resounding crash). Anyway, I camped out on the foredeck today until I heard the sound. We’re having gooseneck issues! This is the joint where the boom attaches to the mast. (Yes, everything on a boat has a name.) It seems the aluminum castings have worn, and now there’s much too much play in the joint. I am worried the dynamic loading could break the casting. I was not hearing this sound until recently, so the wear is recent. For now, I smothered the joint in lashings. I hope this will immobilize it or at least soften the smashing side to side.

I was going to write about Captain Bligh today. But the sun is about to set directly into the water. I’m going to set up my fancy camera (not my phone) and try to get footage. Expect my hot take on Captain Bligh tomorrow!

-Ammon

Taking a sight and working a fix

Why I’m sailing without a crew

Jul 3, 2024

37°44’N 151°54’W

To mix things up, I did a noon sight for latitude, and crossed that with a regular sun sight at 4pm. A noon sight does not require an accurate chronometer (but only yields latitude, not longitude). It was the most important tool in the navigator’s toolbox until quite recently.

The wind died today, as expected. I motored some in the afternoon (I’d not run the engine in a week, and I like to make sure it’s still in order). Then I hove to and went for a swim. Wind is forecast to arrive in a few hours.

I also took advantage of the break to replace a block and chafed line in the windvane.

So, today I am going to write about the mutiny on H.M.S. Bounty. My sources are a copy of “Mutiny on the Bounty” in front of me, memory from reading the trilogy 15+ years ago, and a small amount of internet research my brother Gurney and I did on Tahiti. So I’m probably wring about details. With that said…

In 1787, H.M.S. Bounty set sail from Portsmouth, England on a voyage to Tahiti (then known in English as Otaheite) with the goal of collecting bread fruit saplings, bringing them to the Caribbean, and establishing low-cost orchards to feed slave laborers on sugar plantations. Bounty was a military vessel, captained by Lieutenant William Bligh with a crew of 44 enlisted men. This voyage would not go as planned. After successfully collecting breadfruit in Tahiti and setting a course for the Caribbean, much of the crew (led by officer Fletcher Christian) staged a mutiny and took control of the ship.

Captain Bligh and 18 loyal men were put adrift in the middle of the Pacific in an overloaded open boat with little food or water (close to a death sentence). However, Bligh and his men went on to successfully sail 3600 miles to safety in present-day Indonesia.

Fletcher Christian and the mutineers returned to Tahiti. Some of them remained there (and were latter arrested and returned to England by a subsequent British military vessel). Christian and 8 other mutineers, however, collected a group of Polynesians women (more on this later) and sailed away. Nothing was heard from this group for 18 years.

In 1808, an American sealing vessel (apparently sealing was a thing) landed on thought-to-be-uninhabited Pitcairn Island, deeply isolated in the southeastern pacific, only to find a thriving, mixed-race settlement. One living mutineer remained (more on this later).

These events are famous because of the Bounty Trilogy by Nordhoff and Hall. Especially in decades past, theses were classics of adventure literature. However, Hall himself calls the books historical novels in their introduction. They contain factionalized characters, factionalized dialog, and factionalized details.

In the book, Captain Bligh is a tyrannical master who’s asking for mutiny. He cuts rations for no reason. He throws men into chains for daring to question his command. Yes, he’s the hero of book two (about Bligh’s open boat journey across the Pacific). But in totality, the picture is a brilliant sailor but abusive leader with no business leading men.

Christian and the mutineers, in contrast, are hard working men pushed into a corner. The book stops short of condoning the mutiny (the fictional narrator does not take part) but its sympathy is with Christian. It’s an easy reading book, and it uses words like “measured” and “understanding” for him, and “rash” and “irate” for Bligh.

The settling of Pitcairn is presented largely as a homesteader story, almost heartwarming, people from diverse backgrounds coming together to carve out a life.

I think it was all far darker than this. Points to that effect.

1. There’s a lack of specific allegations of abuse by Bligh. The book contains many, but the book is fiction. Gurney and I could not find other sources for almost any of these. And, interestingly, Bligh was progressive in some ways. He ran a 4 on 8 off watch schedule (rather than 4 on 4 off which was more common at the time)

2. Bligh and Christian had a long running personality conflict. There seems to be more documentation of this than there is of abuse by Bligh.

3. The crew of Bounty was having a great deal of sex on Tahiti. Pre-missionary Polynesia seems to have had relaxed sexual mores. On top of this, Bounty was toasted by the King of the island and the crew were perhaps seen as special or high status. Regardless of the reason, while on the island, most of the crew of H.M.S. Bounty had taken Tahitian sexual partners, in some cases multiple. Gurney and I were unable to find any documentation of how the Tahitians viewed this. An unwillingness to leave this (and some religious moralizing by Bligh) seems to have contributed to the conflict.

4. Christian all but tried to kill Bligh and 18 men. Think whatever you want of how Bligh ran the ship, but putting 19 men into an open boat with scant water has to be as bad an abuse.

5. Christian kidnapped 18 Tahitians. The book is vague about how the mutineers got 18 Tahitians (mostly women) to join them. The answer is that they kidnapped them. They organized a social event on the ship with free food, and after everyone came aboard, they raised anchor and left. They dumped the older women on Moorea as they passed.

6. Once on Pitcairn, the mutineers quickly started killing each other, mostly in conflict over (kidnapped) women. By the time the Island was discovered by an American ship all but one had died in violence (there were however children who continued the lineage).

7. Contemporary Pitcairn also has had sexual violence problems. In the early 2000s, a large portion of the adult male population was convicted (by the British government) of sexual abuse of children. Their defense was that adults having sex with children was part of their culture. This did not stand up in British court. Britton constructed a prison on the island so the men could serve their sentence close to home.

I’m probably making too many excuses for Bligh. The contrarian in me wants to be on his side. But abuse of crew on sailing ships was common. So Bligh was probably guilty. It’s not a stretch. However, there does seem to be more to the mutiny than simple abuse. And there are more documented misdeeds by Christian than by Bligh. If there’s a villain in this story, I think it’s Fletcher Christian.

Really, all I’m saying is that an adventure book from the 1930s was not entirely accurate, and that English sailors on one of the first European ships to arrive in Tahiti behaved atrociously. I guess none of that is too surprising.

-Ammon

Down with King George!

Jul 4, 2024

38°35’N 150°51’W

Sun-run-sun sight through cloud cover at 1304. I was trying to do a noon sight, but the sun was not visible at the right time. So I waited a few minutes for the clouds to thin, and worked it as a regular sight. The only advantage to a noon sight is that you don’t need a chronometer (you watch the sun as it rises and begins to fall, record the maximum observed altitude, and that gives you a latitude).

The forecast north winds have arrived! I’m making 6.6 knots right now, straight for Nurcan. I could feel the temperature drop as the north winds arrived. I’m wearing long underwear for the first time in a long while. (Eli, tell Zora that the tights do indeed fit me.) I also saw as whale this morning! (Actually, only the 2nd of the trip. We’ve suffered a low WPD.)

I think that the lack of sleep is getting to me. Last night I had a headache and a hard time focusing. I felt intoxicated. I was not hallucinating, really, but my brain did seem to want to interpret non-human sounds as voices. The squeak of a winch sounded just like a kid saying “hi, hi”. The groan of a sheet under load sounded like a man yelling. I wonder if this is how auditory hallucinations start.

I went to bed early and I extended my sleep periods from 60 to 90 minutes. I feel mostly but not entirely better today.

I saw my first ship since leaving Hawaii (a 500-foot container vessel headed for China). It passed 5 miles from me, but I took the opportunity to adjust the thresholds on my alarms and make sure they’re working. They were. This far out (I’m about 1100 miles each from Hawaii, California and Alaska right now) I feel pretty safe that most boats will have AIS or be large enough to trip my radar alarm. Trusting the alarms more lets me sleep longer. I felt pretty broken last night, so I need to change something.

Today is the 4th of July—America day! Right now, the American continent is 1000 miles to my east, over the horizon, the place I’ll get to sleep. I’m down to celebrate that!

Comments on H.M.S. Bounty

My brother Kai, a librarian, adds

I think that the story was already well known in the English speaking world prior to the publication of the novels. Numerous nonfiction works had been published, starting with Bligh's journals. Bligh was originally seen as the hero and the novels were being somewhat contrarian themselves. Most people today know the story from the movies rather than the novels. They dramatize Bligh's tyranny even more.

-Ammon

Hyperactive rodents — a deep dive part 1

Jul 5, 2024

38°15’N 146°49’W

Sun-run-sun sight at 1300 through clouds.

Conditions were aggressive today. We were close hauled going into 17 knots most of the time. This means groaning stays and water washing over the boat. There’s a stark beauty in watching the boat push through cold, dark waves. She’s built to do this. But I find I am a little on edge.

I saw two more ships today. I need to keep a good watch tonight. We must be close to a common shipping route.

The course is almost due east now. We’re already north of SF. But I need to go a bit farther north to get over the last remnant of the Pacific high.

I had several mechanical issues today. A freshwater leak (loose hose clamp, ~ 2 gallons of fresh water lost) and chafe on the genoa furling line. I installed a temporary fairlead that should fix the problem for now. I should replace the line as well, but I’m going to wait for calmer conditions (installing the fairlead on the foredeck today was… wet)

So, here, sequestered on my boat, I recently received impactful news from the outside world. Did it involve a debate and an aging president? The US Supreme Court? Genetically engineered laser sharks? (Some of my sources may be more reliable than others.) No. It was about beavers. Busy beavers specifically. BusyBeaver(5) has been calculated and has the value 47,176,870! What does that mean, you ask? Why, let me tell you! Hold on to your hats. I’m going to try to explain the BusyBeaver function for an audience with no background in math or computational theory. This might be… wide-ranging.

How do we know which mathematical statements are true and which are false? Well, we have proofs. Mathematicians (and undergrad math majors everywhere) slave over them. What is a mathematical proof? Well, it’s an attempt to express the truth or falsehood of a mathematical statement (a theorem) in terms of other, already established facts or theorems. More generally, we start with a small set of “axioms”. These are basic statements taken to be self-evidently (or definitionally) true. Next, we agree on a set of logic rules. These are things like “if (A or B) and not A, then B”. Finally, we apply the rules to the axioms with a little creativity(this is what mathematicians do), and out pops all of mathematics!

That sounds really nice! But I did smuggle something along in the last paragraph. We agree on self-evident axioms and rules of logic. Can it really be that simple? Do we always agree? Do we know what the “right” axioms and logical rules are to produce the one“true” mathematics?

No. The answer is we don’t. But as the 20th century began, we were pretty sure we were close.

Bertrand Russell and David Hilbert (mathematical giants) both did work in this area. Principia Mathematica was Russell’s attempt. The work is 3 exhaustive volumes, and he worked on them over a 13 year period (and published in 1913). This was a time of much technological optimism. The age of mechanical computation was on the horizon. If mathematics could be established atop a secure axiomatic foundation, who was to say whether human mathematicians were needed at all? Could a machine, armed with the requisite axioms, simply directly tell mathematical truth from falsehood?

That’s when one Kurt Gödel arrived and messed everything up. Gödel was a 25-year-old PHD student. And he did not simply find a flaw in Principia Mathematica. He did not just show that Russell had taken a wrong turn. No, Gödel proved that no finite axiomatic system can ever be capable of proving all true statements about natural numbers. Russell’s task was simply not possible.

Gödel published his result in 1930, and it went off like a bomb in the worlds of both math and philosophy. Popular science accounts sometimes say that Gödel “proved that there are true facts that can’t be proven.” Mathematicians hate this (I recall a professor of mine taking umbrage). The result IS more narrow than that. Recursive axiomatic system, natural numbers, etc. However, axiomatic proofs were previously put forward as the very definition of truth. That’s a philosophical position. And Gödel incompleteness challenges that. Something big had changed. We previously lived in a world where whether the axiom of choice (a controversial axiom in set theory) should be included in the foundations of math was a question with an answer (one we just did not yet know the answer to). Post Gödel, we know that there is no answer, just two different mathematics (one with the axiom of choice, one without). Which is true? Well, how are you defining true?

Ok, Gödel proved that finite recursive axiomatic systems are not capable of representing all of mathematical truth. So what about other types of formal systems? What about languages (formal or human), computer programs, or human brains?

To answer that question, we need to move out of number theory and into the mathematical subfield of computational theory.

And I need to go to bed. I’m going to pick this up here tomorrow. Expect many strange and wonderful things, and eventually some beavers!

-Ammon

It’s all about self reference, part 2

Jul 6, 2024

38°41’N 144°17’W

As of 1245 today. Early sun sight crossed with local apparent noon sight. I’m getting pretty fast at the sight, reduction, plot process.

Today was clear! The wind slacked to a civilized 13 knots and rotated to a reach. Really a beautiful day. I have 1000 miles to go to Nurcan! I expect to arrive between Saturday and Monday next week.

Three ships passed this morning. The closest was 2 miles from me. This was close enough that I hailed them as they approached to make sure they saw me (they are going enough faster than I am that I’d struggle to get out of the way if they turned towards me). It’s funny. In the ocean sailing mindset, 2 miles away is uncomfortably close.

The other thing that happened today is that… I now have two small spinnakers rather than one large! I flew the spinnaker for the first time singlehanded. The part I was worried about went fine (keeping it off the forestay). But then, suddenly, as we were humming among, a gust hit and it ripped right down the center. I don’t think I did anything wrong. It probably luffed a bit more than if I’d had a crew. But I think the problem was fatigued fabric. Anyway, I feel a bit bad about this (expensive thing to destroy). So it goes.

— amateur computational theory blogging begins! —

Ok, picking up where where I left off, Kurt Gödel publishes his incompleteness theorem and shows that the millennium-long quest to build an unimpeachable foundation for mathematics via an axiomatic system was not possible.

Before I talk about what comes next, I want to briefly touch on how Gödel achieved his result. The central issue is self reference. Think about the famous lier’s paradox: “This sentence is false.” While it may seem a rather shallow thing (just a linguistic oddity that children toy with) it’s a serious problem for logicians. You see, any formal logical system that allows the construction of a lier’s paradox begins to fall apart. Such a statement is self contradictory. And once you have one self-contradictory statement in an axiomatic system, you can prove anything. So the core thing Bertrand Russell was trying to do was to come up with a logic without the possibility of self reference. What Gödel did, then, was sneak it back in, over the walls Russell had built. He showed that the natural numbers *themselves* can be interpreted in a self-referential way, and thus any axiomatic system capable of proving all true statements about the natural numbers will necessarily allow self reference. Full stop.

Ok, so we know that axiomatic systems can’t represent all of mathematical truth. What about other types of formal proof systems? Computer programs? Linkages of gears and cams?Human brains? Well, enter the computational theorist!

These include Alonzo Church, Stephen Kleene, and most famously Allan Turing. Interestingly, they did much of their work in the 1940s and 50s, before the introduction of electronic computers. They were mathematicians, and they confronted the problem I asked in the previous paragraph. How can we reason about the capabilities of machines? Are there problems that a finite, discrete process is simply incapable of solving? If we reach a result for one specific machine (from now I’ll call it a computational model) does it hold for a different computational model?

Yes. A result proven for one computational model does apply, in most cases, to other computational models. To understand why, consider the following question. Is the set of problems which can solved in Python (a popular computer programming language) the same as the set which can be solved in C (a less popular computer programming language)? Yes, we know that they are. The reason is that the most popular Python implementation is itself written in C. And many students have written C compilers in Python. More generally, if any two computational models are capable of mutually simulating each other, then there can be no difference in the problems each can solve. Also notice that even if a computational model seems simple or limited, if it can simulate a more complicated model, then suddenly it “inherits” the power of that seemingly more complex model. What this implies is that all computational models above some threshold of power are capable of mutual simulation and thus compute the same set of problems. This threshold is called Turing-completeness. It follows that proving that a problem cannot be computed on one Turing-complete model is sufficient to prove that it can’t be computed on ANY Turing-complete model.

Two asides
1. The bar for a model being Turing-complete is actually surprisingly low (that is, rather simple systems can be so). There’s a funny blog called “accidentally Turing-complete” which lists things not intended as computational systems that have the property that they could become the sole way we think about computation. One I remember is the game Magic the Gathering.
2. There’s not actually any proof that there is not a higher class of computational model which all Turing-complete models are simply unable to simulate. Quantum computers are NOT such a model, however (they are easily simulated). And most theorists doubt the existence of such a class.

Ok, so all Turing-complete models compute the same set of problems. The question that jumps right to mind is…. are the axiomatic systems that Gödel and Russell were working with Turing-complete? If so, our work is done, and no computational model can better model mathematical truth! The answer is… I don’t know. I have not studied any of this in 15 years! Perhaps one of my readers knows? Regardless, we don’t need that result. There’s a more satisfying way to show the limitations of computational models. And we’ll get there. It involves Beavers and really big numbers. Like, really big. You think you know big, kid? You haven’t seen anything yet. I’ll pick this up tomorrow. Time to make dinner on Little My!

-Ammon

A flood of gratuitous math (and also sea water)

Jul 7, 2024

39°26’N 142°01’W

Sun sights as of 1233. Only 900 miles to go!

Today has been absolutely gorgeous. Not a single cloud in the sky, flat seas, and 13 knots of wind from the south. We’ve been making 7 knots on a beam reach all day with minimal heel. I’m writing this as the sunset fades to black. There’s a sliver of a crescent moon, silver in the sky. A flock of storm petrels is following the boat, flitting around me in the near dark. I’m going to sleep under the stars in the cockpit tonight.

Not everything was wonderful today. I had a crisis this morning. I went to shutoff the seacock (valve) that takes in engine cooling water. The valve is under the engine, so I have to reach through the floor into the bilge of the boat. Well, I put my hand down there and, it was full of water! 5 or 6 inches. It felt like the entire bilge of the boat up to the floor boards was flooded.

Flooding is one of the emergencies I’ve trained for. There’s a card on the wall with steps. So I followed them.

1. Close all seacocks coming into the boat. I did.

2. Turn on all pumps. I switched on the main pump. A little water came out, a few quarts, then nothing. Was it clogged? Shorted? Well, I can’t take it apart now. To the manual bilge pump! I pumped that. Still no water coming out. Could that be clogged too? The rubber looked a bit old. Had it lost suction? I was shaken at this point. I remember thinking, well, if I can’t keep the boat afloat, at least it’s beautiful weather to hang out in a life raft!

3.Taste the water. It was salt, meaning sea ingress not failed water tanks.

4.Look for the leak. At this point, I had a few reassuring thoughts. There had not been any high water alarms (and I have two alarms for redundancy). Also, I do have a reserve high capacity pump I can set up if needed (would take 5 minutes). So I decided to take up more floor boards and inspect. There was not any water in the main bilge! That was why the pumps were not doing anything. Normally, water runs from the back of the boat into the bilge. But it passes through two small holes in a bulkhead. Those holes were clogged. Only the back of the boat was flooded. That made me feel better, and also gave a clue. The leak had to be in the back of the boat.

I had engine work done in Hawaii. A mechanic there took apart the engine cooling system. So the first thing I did was inspect that. And there it was. He’d failed to tighten one of the hose clamps! You could see the salt deposits where water had leaked out onto the engine.

After that, I was not hard to fix. Tighten the clamp. Clear the bulkhead so water runs back to the pumps. It did overflow the bilge and set off both high water alarms, however! Consider that a test.

I’ve had water in the boat before. But it’s always been in the “slow leak” category, never something worthy of the name flood. This felt like flooding. The awkward thing is I really liked the mechanic who forgot to tighten the clamp! Ultimately, it seems, you have to be responsible for your own boat. The $200/hour electrician I hired ran a battery cable in contact with the propeller shaft! Both riggers I hired made significant mistakes. I wonder why this is more true for boat work than other areas.

— math—

Ok, picking back up… To take this further, we’re going to need a specific computational model to reason about. Academics today use a model known as a Turing machine. Now, Turing machines are NOT the electro-mechanical machines that Allan Turing built to break the German enigma code during WWII. Those were “Turing bombes”. The Hollywood movie “The Imitation Game” used the word Turing machine instead of Turing bombe, leading to much confusion. In any case, a Turing machine is a computational model just complex enough to be provably Turing complete, but simple enough to reason about mathematically.

We’re not going to use Turing machines. The definition would scare non-math people. We’re going to use CYOAMs, or choose your own adventure style computational models. What’s a CYOAMs? It’s a book with numbered pages of instructions. To “run” one, you open it up to page one and do what it says. You’ll also need a pad of paper open in front of you. Instructions in the book include things like “turn to page 7, “write the letter ‘a’ to the pad front of you”, or “read the number written on the pad in front of you, and turn to that page”. Finally, pages may have a “halt” instruction. If you get to a “halt” instruction, the program is done.

Ok, how does a CYOAM compute? Well, Remember that pad of paper you have in front of you? Whatever is written on that pad when you start is the input to the computation. For example, if we have a CYOAM that tests whether a given number is prime, we would start the process by writing the number to be tested on our pad. And how does a CYOAM produce output? The last thing it has you write to the pad (before reaching a halt instruction) is the output. Our prime testing model might have you write “prime” or “composite”, for example, before halting.

Ok, a CYOAM is a Turing complete model (I know this because it’s just folksy description of a Turing machine). So, if we can show that a specific problem can’t be solved on a CYOAM, then we know that it can’t be solved by ANY form of computational process. But how can we show the limitations of a CYOAM?

Well, we need to introduce self reference. Imagine if a computational model could somehow inspect itself (its own instructions or “source code”) and then be programmed to just do the opposite of what its own instructions say it’s going to do. It would be a high-tech version of the lier’s paradox. “This program does the opposite of the very thing this program does.” Is this really something that we can program a CYOAM to do? Yes, but we need two more pieces of background to understand how.

Backup. Think about what happens when we run a CYOAM. There are one of two outcomes. Either the CYOAM runs forever (e.g. page 1 says “go to page 2” and page 2 says “go to page 1”) or the CYOAM eventually reaches a “halt” instruction (e.g. the prime tester I brought up earlier that always outputs “prime” or “composite”). Ok, time to get meta. I want to propose the idea of looking at a CYOAM and determining whether that CYOAM will run forever or eventually halt. Now, I just made this exact determination for two simple examples above. But can it be computed in every case? That is, is it possible to create a CYOAM (call it A) that takes another CYOAM (call it B) as input, and determines whether the input CYOAM will halt? A takes B as input, and tells us whether B would run forever or eventually halt. Read that a few times if you have to. This is a famous problem from computer science known as the halting problem.

Ok, back to self reference. I’m going to define self reference in a computational model as the ability of a model to compute a description of its own instructions. Is this possible? Well, there’s a game programmers play called Quine (I think the name is some witty reference, but I don’t remember the specifics). They try to write a program that prints its own source code to the screen. Let me show you an example Python program.

> print(“Hello World!”)

This is valid Python, and when run will print the text “Hello World”. Ok, but I want it to print the entire program, not just some text. What about

> print(“print(“Hello World!”)”)

Ok! We’re getting somewhere! That (I’m ignoring the issue of nested quotes to make this simpler) will print the first program. But unfortunately it’s not the first program. What about

> print(“print(“print(“Hello World!”)”)”)

Will, that will print the 2nd program. But it’s not the 2nd program! I think you understand problem. There’s a self reference problem. Can it be solved? Yes, it can. It just requires more complex logic and a trick where you interpret the same piece of data in two different ways (there are also some “cheating” to do it in Python, but I’m trying to describe a more general solution). As an aside, there is a wonderful 22 language Quine cycle on GitHub. This is a program in one language, which, when run, outputs a program in a 2nd language. Run that one and you get a 3rd language. This goes all the way through 22 different programming languages. And when you run the 22nd program? Well, it, of course, outputs the first program again. Wrap your head around what it would take to create that!

Ok, back self reference. So programmers entertain themselves with quines. But is it always possible to create a quine in any Turing- complete model? Can we create a CYOAM quine?

Stephen Kleene was a professor at the university of Wisconsin in the mid 1950s. In his 2nd recursion theorem, Kleene proved that the answer is yes. This is highly analogous, in my opinion, to Gödel’s proof. Gödel showed that any axiomatic system powerful enough to model the natural numbers admits self reference. Kleene showed that any computational model above the threshold of Turing-completeness admits self reference. I suspect the results are deeply isomorphic.

Gödel want on to use self reference to show that there are true facts about numbers that no axiomatic system can prove. Can we do the same using Kleene’s result? An we prove that there are problems no computational model can solve?

Let’s go! Proof by contradiction. Assume (for the propose of contradiction) that the halting problem is computable. Then we have a CYOAM (called A) which when given as input the instructions of any other CYOAM (B) tells us whether B (when run with no input) will halt or run forever. Ok, consider a 3rd CYOAM C. C first acquires its own instructions as allowed by Kleene, then gives those instructions as input to A. If it gets back “halts” from A, it goes into a “page 1, page 2” loop and never halts. If it gets back a “does not halt” it immediately halts.

Does C halt? Well, we have a contradiction! It does the opposite of whatever A says will do. But A is a decider for the halting problem!

Given that we reached a contradiction,
our assumption is false. There can be no decider for the halting problem. The halting problem is not computable. QED.

Ok, I’ll leave it there for today! The sun is setting and I want to try to get images of it sinking into the ocean. Nurcan is a fan of these moments.

-Ammon

Here be beavers (the final installment)

Jul 8, 2024

39°42’N 139°03’W

Early sun sight crossed with local apparent noon sight. 730 nautical miles to go!

I’m trying to record video of myself taking a pair of sights, working the reduction, and plotting the result on a chart. I keep messing it up. The hard part is where to put the camera to record the paperwork. I’ve tried a bunch of things. What works the best is taping the camera to the end of a stick then c-clamping the stick to the top of a locker. Video composition is hard!

I washed clothing and bathed today, and also did a tuneup on the wind vane. I’m taking advantage of the mild weather. I’m struggling less than I was expecting to with the passage of time. There always seems to be enough to do.

I turned slightly south today. This is probably the northernmost point in the trip. The forecast is for light winds tomorrow and Wednesday, and then, as we approach the final 300 miles, 25 to 30-knot winds out of the north with 10-foot seas. The North Pacific off the CA coast is actually a rather rough stretch of ocean. It’ll be funny if I sail 10,000 miles and the worst conditions I experience are within spitting distance of home. I’m trying to stay north right now, and do most of the run south in the strong winds. A broad reach will be better than a beam reach in those conditions.

Ok, to the beavers! Let’s just jump right in.

— beavers —

There are a finite number of possible books under a given length. This is true because there are only 26 letters in English (plus a few symbols) and only a fixed number of letters can fit on one page. A CYOAM is a book. Therefore, there are a finite number of CYOAMs with 10 or fewer pages. Consider all these CYOAMs. As we discussed yesterday, some of them halt when run with no input, and some run forever. Discard the ones that run forever. Consider only the CYOAMs that halt. Ok, each of these has you flip the pages a certain number of times before it halts. Because the set is finite, there has to be some CYOAM in the set (or perhaps a tie between multiple) that has you flip the pages more times than any other. And that, any reader who has made it this far, is BusyBeaver(10)! It’s the maximum number of page flips possible in a 10-page CYOAM that eventually halts. More generally, BusyBeaver(N) is defined for all natural numbers N as the maximum number of times a CYOAM with N pages can have you flip the pages and still halt (not run forever).

Why? What’s interesting about this crazily meta function? Two things:

1.It’s not computable. No computational process can calculate all values of BusyBeaver. How do we know this? Because the halting problem is not computable, and calculating BusyBeaver would let us solve the halting problem. How? Imagine we have an N-page CYOAM. If we could calculate BusyBeaver(N), we could just run the CYOAM for that number of page flips, and if it had not halted yet, we’d know that it never would. We’d have solved the halting problem. This is not possible. Therefore, BusyBeaver can’t be computed.

2.BusyBeaver values get big—really, really, mind bendingly big. Let’s take a tiny detour.

There’s a game mathematicians play (when they’re feeling excluded from the programmers’ hardcore quine parties) where they compete to write the largest number possible on a small scrap of paper. Think about this for a second, if you never have before. What would you write? Small children might just fill the page with 9s. (Interestingly, filling the page with 1s would be a better strategy. More fit.) Older children might throw in a multiplication (9999999*999999). This is also not very helpful (multiplying two numbers produces a number of the same order of magnitude as concatenating their digits). The page full of 1s is still ahead. Now, an adult is likely to try up exponentiation. There’s the famous story about the rice on the chess board. Even with the small numbers 2 and 64, 2^64 yields more grains of rice than there are grains of sand on all the world’s beaches. Wow! 10^80 is a common estimate of the number of subatomic particles in the universe. Double wow!

But we can do better. What if I told you exponentiation was nothing? Have you ever thought about how they teach multiplication to kids? They explain that 3*5 means to add 3 to itself 5 times, or 3+3+3+3+3. Ok, and what about exponentiation? 3^5 means to multiple 3 with itself 5 times, or 3*3*3*3*3. But why stop there? Why not define an operator # where 3#5 means 3^3^3^3? And $ where 3$5 yields 3#3#3#3#3? This is called operator iteration. The normal syntax is a small arrow pointing up (I can’t type one my phone without internet, so I’m going to use exclamation marks). Ok, 3!5 is the same as addition (3+5). If you want, you can think of that as an incrementation operation iterated 5 times. 3!!5 is iterated addition, aka multiplication. 3!!!5 is iterated multiplication, aka exponentiation. But we can keep going. 3!!!!5. 3!!!!!!!!!!5. But where it really gets crazy is if we parameterize the up arrows. 3!(7)5 means seven arrows or 3!!!!!!!5. Once we admit that, the scale goes off the rails. Consider 2!(2!!!46)64. The inner term is 2^64 (the chessboards number). That numbed is big. Really big. We got it using 2 and 46 and only the 3rd operator on our sequence. But then we used that to jump far, far, far up the operator sequence. I promise you, you are under appreciating the scale of the result. You don’t have the capacity.

That’s where conventional math syntax leaves it. But we can take it further! We can define iterated, parameterized application of our up arrows as many times as we like. What if f(2, 64, n) is defined as nested sequence of up arrows? Thus f(2, 64, 2) is 2!(2!!!46)64, but f(2, 64, 3) is 2!(2!(2!!!46)64)64. Then we can consider f(2, 64, 2!!!64). I think you get the picture. There would seem to be no limit.

Except, there is a limit! There is. And what do you suppose it is? It’s Busy Beaver! The Busy Beaver function provably increases faster than ANY computable sequence! Why! Well, if we had any computable function greater than Busy Beaver, then we could use that it BB’s place to solve the halting problem (as a limit behind which you do not need to test a CYOAM to know whether it will halt). So if you ever need to write a big number, just go with BB(20).

Ok, my final section! Why is Busy Beaver so hard to compute? After all, a team spent 30 years and only just calculated the 5th number in the sequence. What you need to understand is that computing a Busy Beaver value requires proving something about EVERY CYOAM (well, really every Turing machine) of that size. And computation is powerful. For example, we know that there’s a Turing machine of 6 states (state count is what the N in BB(N) really references) that computed the Goldbach Conjecture. So we know we can’t calculate BB(6) until we solve the Goldbach Conjecture (famous unsolved math problem). Calculating Busy Beaver numbers involves solving non-trivial subsets of all possible computational problems (not just the ones we happen to have discovered already, all that can ever exist). Busy Beaver is a beast. And that’s why it’s impressive that a team spent 30 years calculating BB(5).

-Ammon

Wing on wing across a placid sea

Jul 9, 2024

39°24’N 137°03’W

Moon / sun sight at 1212. The moon is far enough behind the sun now that I can do simultaneous sun / moon sights again.

We only ran 88 miles noon to noon today. I think this might be the shortest daily run of the entire trip! I guess that’s part of being out of the trade winds. The wind went to near 0 in the night. And when I finally decided to start the engine, it would not start! (Rather, it started, but died after 5 minutes). So we bobbed on the waves while I slept, and I began this morning elbow-deep in diesel. The problem ended up being that the fuel filter was full of air! I think there’s an air leak somewhere in the fuel line, and the air is accumulating in the filter. After I bled the filter and all the lines, the engine started! I really should find and fix the air leak, but I think it takes long enough to cause a problem that I can just bleed the filter every time I start the engine. That should get me home.

I did have a scary moment when working on the engine. This engine for some reason switches the starter (and all electronics on the engine) on the negative side of their circuit. This means that the positive terminals are all at 13 volts at all times (and exposed on engine). On top of this, the engine block itself is the common ground for all systems (AC and DC) on the boat. So there’s short circuit potential. I had to loosen a bunch of fuel bleed nuts on the engine, so diesel was dripping everywhere. That’s when I shorted one of the nuts (dripping fuel) with my wrench to a positive terminal for a starter relay. There was a huge spark, and the wrench stuck to the terminal, still shorted. I had to run to the master battery cutoff switch and throw it. There was a bunch of smoke. I’m just glad it was diesel. If it were gas everywhere, I’d have had a fire.

I put the genoa to windward on a whisker pole this morning. This is known as sailing “wing on wing”, where you are going downwind and have the main to one side of the boat and the genoa to the other. It’s quite beautiful. I spent most of the afternoon reading in the cockpit. The wind is only 7 or 8 knots. So I’m drifting along, gently, on the bright, placid ocean.

It won’t stay placid for long. The wind should start to pickup tomorrow afternoon. The forecast is now for 11-foot waves on an 8.5 second period by Friday.

-Ammon

Single-handed fishing

Jul 10, 2024

39°10’N 143°34’W

Sun run sun sight at 1300.

I set my clocks back to UTC-8. I’m a bit of a slave to my watch. Setting the time back will help me go to bed early (start my night routine). On an iPhone, you can’t just set a timezone directly. You have to pick a city in that timezone. I guess someone thought that was simpler. Well, SF in the summer is UTC-7. Anchorage Alaska is UTC-8. What’s UTC-9? It’s kind of an empty stretch of the world. Nurcan had to assist me. ImAdak Alaska is! My guess is Apple only included it in the city list so they have something in each timezone.

We ran 101 miles noon to noon today (and I guess that was in only 23 hours because of my time change). The wind has been building since midmorning. Tomorrow the fun begins. I have 530 nautical miles to go. If I can average 6.3 knots over this timeframe, I’ll pass under the golden gate late Sunday morning. That’s now my goal!

I’ve had a fishing line out most days on this passage. Today, a fish bit! I had to rush to get set up to bring it in (get my harness on, gloves, the gaff ready, water, a knife). Before I was ready to do anything, it escaped. Well, I put the link back out and decided to leave all my gear set up just in case. And, bam, 20 minutes later there was another fish on the line, an 8lb big eye tuna.I’ve got more tuna in the freezer for Nurcan, and I dined on fresh Ceviche this evening.

I’m almost home. My mind is there already—imagining the homecoming, hugging Nurcan, what we’ll eat. It’s harder for me to get excited about the sailing or catching a fish.

This sailing trip has been my focus for almost 2 years now. I shut my company down in the end of 2022. Since then, this has been my thing—taking offshore sailing classes, crewing for other people, learning about diesel engines, helicopter rescue protocol, how to calibrate a compass, buying and fixing a boat, preparing.

I like being busy and having goals. For most of my life, that’s been work. More recently, it’s been this.

Well, in just a few days, I’ll need to figure out what my next goals are. I am a little afraid of the transition.

-Ammon

I try my hand at fiction, pure fiction

Jul 11, 2024

38°59’N 131°23’W

No sun visibility, even through clouds. Dead reckon position as of 1453.

The foul weather has arrived. 22 knots, 8 foot seas, building through tomorrow afternoon.

Read in the style of a boxing announcer

Weeeelcome to the exciting world of… ACRO-TOILEEEET!

In the red corner, we have our intrepid sailor, soaking wet, clad in a full set of offshore foul weather gear, bladder full.

And in the blue corner, we have one standard Raritin hand-pump saltwater marine toilet!

Round one, FIIIIGHT!

What’s this? The sailor is trying to remove his harness, jacket and bibs! Everyone knows, it’s not safe to pee standing on a pitching boat, so the bibs don’t even have a fly. But, as our sailor takes his hands off the boat, trying to operate the buckle in the harness, the boat lurches, throwing him against a wall. He tries again, using a single hand, but the buckles are not designed for one-handed operation. By sitting and bracing with his legs, he’s able to get the harness and jacket off, but then the same problem repeats with the bibs. You can’t take off overalls while sitting and you can’t balance on one leg during a storm! All the while, the toilet hasn’t broken a sweat.

Round one winner, TOILEEEET!

Round two begins. Our sailor has somehow shimmied out of his bibs and is atop the toilet. He’s braced himself with one leg against the doorframe. And that’s when toilet makes its first move. It leaps off the crest of an 8-foot wave, entering free fall. But our sailor anticipated this! He’s been operating the hand pump non-stop. The bowl is empty. There’s nothing to slosh. But the toilet is not over. As it lands with a tremendous “bang” in the trough of the next wave, it tilts forward, forward until the sailor’s center of gravity is above his bracing leg. He’s in danger of pitching forward, off the toilet, headfirst into the door. But the sailor is quick! Out shoots an arm. A nook for a handhold is found. The fall is prevented.

Round two winner, SAILOR!

Round 3 begins. Back and forth they go. Locked in an embrace. Sloshing, pumping, yawing, bracing. A stalemate seems likely. And that when the toilet shows its winner’s mentality. It changes the parameters of the game. For the first time in acro-toilet history, toilet springs a leak! Suddenly, with each jab the hand pump, unknown fluid spritzes into the air, into the floor, misting our sailor’s leg.

And that’s it. Sailor has no defense. Victory TOILEEEET!

Our sailor is left rummaging for paper towels and sanitizing spray.

—————

I’ve sailed through conditions as rough as are forecast here before. However, never on a beam reach. My course back to San Francisco is mostly across the wind / waves (a shallow broad reach). Sailing more downwind (with the wind and waves) is more gentle. For one, the motion of the boat is subtracted from the apparent wind (the wind you feel). More importantly, the boat is better equipped to handle waves approaching end on.

So, my plan is to sail slightly upwind and hold this long as I can (I’m on a close reach right now). This should buy me space to turn downwind whenever I need to. Of course, if it’s a matter of safety, I’ll turn down regardless of where I’m tracking re San Francisco.

One good definition of storm conditions on a sailboat is, it’s a storm when you set the course for the safety of the boat rather than arriving at your destination. We’ll see whether this is a storm.

I was afraid of the dark last night! I’m not sure why. Everything feels much more in control when I can see the sea, the horizon. As the light fades away, it becomes a threatening place. The groaning and slapping and screeching of the boat become all I can hear (some people recommend earplugs or music during a storm, just for your mental health). I did not fear the night when there were other people on the boat. In fact, I looked forward to it. Beautiful solitude. Intensity of the ocean. Well, I’m maxed out on beauty, solitude, and intensity during the day now. More at night is just too much.

-Ammon

Untitled

Jul 12, 2024

38°32’N 127°42’W

I got one sight on the sun today, but not two for a fix. The one was hilariously hard (12-foot waves, smacked by water, sun only visible for brief periods). So position is a DR updated to one solar LOP.

These conditions, single handed, are a test of endurance. The boat is cold, wet, a little scary, and throwing itself left, right, up, down. It’s a wild motion, and loud! This is not a place to live. It was high octane exciting for the first few hours. But I’m on hour 36. I just want it to stop so I can sleep.

I was on a close reach last night, trying to buy as much distance to the north as possible. I held that until 4am. At that point the wind was up to 25 knots, maybe 10-foot seas, and we were slamming into each wave with a jarring smash. I turned 30 degrees downwind. It’s amazing what a difference that makes. No slamming, far less water on the deck. I’ve held that course since. Wind has been steadily building. I see 30 knots on my instruments right now, gusts to 35. Waves are probably 12 feet, with an occasional 15 footer. The period of the waves makes a big difference. These waves are big, but the wind has been blowing long enough that they are long-period. Our course takes us nearby beam on, and I was more concerned the smaller shorter-period waves this morning.

But you should see what it looked like today! Looming walls of water. Froth blowing. Patches of turquoise against the gray ocean. This is the sea in its wild state, with no regard for us. And there in the middle of it, Little My, heeled over 30 degrees, postage stamps for sails, sliding sideways, waves rolling over the bow, but always emerging to press on.

I *think* I’m experiencing close to the worst that will come. The forecast calls for conditions to calm, quite abruptly, around 8am tomorrow.

Only 210 miles to go! I’m within helicopter rescue range. This trip is ending.

-Ammon

9 hours later

I was so tired I forgot to add a subject! How about “storm fatigue.” In any case, I just unrolled a bunch of genoa. It’s still blowing 22 knots, but that’s just a fresh breeze! Heavy weather is over.

It’s not over

Jul 13, 2024

37°57’N 124°06’W

Heavy overcast for most of the day. I could not get a single sight. Because we’re so close to the shore, I’ve switched back to GPS navigation. It’s a bit of a shame. I had a goal of making it to sight of land by celestial. But I made it close.

I’m writing this paragraph early Saturday morning. The storm is over. The wind started to ease around 3:30am. It was still blowing 25 knots, but after 35, that was tranquility. I rolled out more genoa every hour as the wind dropped. By 7:30, the wind was 12 knots and I went to full sail on main and genoa. It’s a cold, foggy morning. The wind has dropped, but it takes longer for the waves to calm down. The sea has inertia. So we’re sailing through aimless, disorganized but still rather large waves. The boat is still a mess - everything damp, spilled corn chips pushed by heel into a line among one wall, tangled floor towels and foul weather hanging from every perturbance. I need to coil lines and clean the cabin. But instead, I’m in my corner, under a sleeping bag. I’m waiting for sun.

Ok, I’m writing this at 10pm. I need to grab sleep when I can, so will be brief. Basically, we had another flooding situation. I was wrong about the cause last time. The mechanic had left a hose clamp loose, but that was not where the water came from. It came from the prop shaft gland beginning to fail. I know this because it failed more fully this afternoon. This is the most scary bellow waterline fitting to fail, because there’s no seacock (valve) to shut it off. I made an emergency call to one of my mentors (a deeply experienced delivery captain). He helped me debug and get a jury rigged fix in place. This is not over till I’m tied up at the dock. I’m pressing harder now and I think I can still make 12 pm tomorrow under the golden gate. But man am I tired. Starting my sleep periods (shorter because I’m close to shore)

-Ammon

Laaaand ho!

Jul 14, 2024

North Farallon is clearly visible. Point Reyes is obscured by fog. I’ll arrive at the golden gate at noon.

Home is the sailor

Jul 15, 2024

I made it safe to the dock in Sausalito yesterday, into the waiting arms of Nurcan! 

I’ll write a final update in a few days with more thoughts. But for now, it’s good to be home, with people I love and a full night’s sleep in a bed.

The final update

Jul 15, 2024

Hello everyone!  Let's start with the trip by the numbers:

• 9923 nautical miles sailed

• 122 days away 

• 70 days underway 

• 5.9 knots average boat speed 

• 40% of sailing downwind

• 45% of sailing on a beam reach  

• 15% of sailing upwind 

• 180 gallons of diesel burned 

• 138 hours under engine (8% of total time)

• 8 fish on our line

• 4 fish landed (one mahi mahi, three tuna)

• 15 foot largest waves encountered 

• 43 knots highest wind speed observed

• 11.6 knots highest boat speed observed

• 10 days longest period without seeing another vessel

• 46 celestial fixes calculated

• 40 minutes average time to work and plot one celestial fix 

• 30 hours spent performing celestial navigation 

• 4 whales seen

• 7 days under spinnaker

• 10 loaves of bread baked underway

• 71 daily updates written

• 28 pounds of cheese consumed     

• 45 pounds of granola and breakfast cereal consumed  

• 6 times swimming from the boat offshore

• 357 watches stood while sailing multi-handed  

• 126 times waking at night to check boat while singlehanded  

When I left on this trip, I had a fear that I would not enjoy it. Spending 4 months trapped inside a 46 by 10-foot box might not be fun. The small disk of ocean visible from the boat--my eyes to the horizon--might become monotonous. Did I really want to drink warm water out of a fetid tank? Eat canned food? Would tying myself that closely to my father be good for our relationship?        

Well, it's over. I've been home for more than a week now. And while there was boredom and, no, I don't want to make sailing my life and depart around the world for years, this trip was one of the most memorable and beautiful things I've experienced. In my updates, I often focused on what was going wrong. I want to make this final email a recap of why I enjoyed the trip. 

First, the ocean is a wild, untouched wilderness. You feel the remoteness. It's the same feeling you have when you hike into the backcountry in Yosemite or the Adirondacks--awe at the beauty of nature and your own smallness. It's perhaps the closest I can come as an atheist to an experience of religious exaltation. And there's the sky! At sea, you experience zero light pollution--not even airplanes. And the sky extends to the horizon in every direction. The night sky at sea is the void of space, frozen, eternal, uncountable points of light, and each point a distant sun, a world, reaching out across a vastness, making the gentlest of contact. 

Second, there's a wonderful simplicity to sailing. Keep the boat pointed in the right direction with sails trimmed for speed and comfort--that's the mandate. Keep the boat happy. And if the boat's happy, I am happy. The work to be done is physical and the results are clear and satisfying (lines coiled, the boat moving faster, a refrigerator running again). When it's time to sleep, I am tired. Like the swaying of a train, the motion of a sailboat underway is a soporific. It rocks you to sleep. (There are exceptions, but most of the time, I sleep very well on a boat.) Sailing a boat is everything running a tech startup is not--an escape to a simpler life.  

Third, it's a chance to spend time with people you love. The element of boredom even helps with this. When did I last sit next to my brothers and father and simply talk, see where our conversation takes us? When did I last share the rhythms of domestic life--coffee in the morning, washing clothing, dinner in the cockpit as the sun goes down, games? My father is 77. There's a limit to how much time I have left with him. This trip gave us a large chunk of time. Sharing something so adventurous with Nurcan was an excellent start for our marriage. We're The Owl and the Pussy-Cat.  

Finally, going on this trip meant I got to come home! I guess that's not a reason by itself to do something. But seeing Nurcan after 3 months apart, coming back to friends, finding my old life waiting--these are intensely positive experiences. I love cooking and could not do it justice on the boat. A few days ago, I made fresh cavatelli with uni and Turkish butter, orange-pepper romesco sauce, sour cherry bread pudding, plum ice cream from the tree in the backyard. I ate it with Nurcan and friends around me.  

I wrote a bunch about bioluminescence early in the trip. I stopped mentioning it because I did not want to bore you all with repetition! But the wonder did not go away. My central memory of this trip is me, alone on Little My, the void of the night sky overhead split by the river of the milky way, the boat buoyed on adventurous waves, and all around me, the water, a plane mirroring the sky, marked by one million points of dancing light.  

-Ammon