Very Secure

Linear and Abstract Algebra - The Why

March 6th, 2025

As mentioned in my previous article, where I became aware of how the new language models fail at defining words, I've taken to studying algebra. The original motivation was to learn more about bitcoin's use of the elliptical curve digital signing algorithm. As I found myself reading about elliptic curve cryptography, I became acutely aware that I didn't have the necessary mathematical vocabulary.

This motivated me to start reading more about abstract algebra, which is a branch of mathematics that encompasses elliptic curves.1 As I started reading texts on the subject, I was reminded of my shaky linear algebra foundations, so I decided to add a linear algebra course2 to my study as well.3

I have my sights set on other branches of mathetmatics, such as complex analysis. The definition of an elliptic curve that I've come accross uses terminology explained in complex analysis. And how is one to know anything about a mathematical structure if they don't even have the tools to define what it is? I also am interested in retaking differential equations, even though that branch of mathematics is distant from anything related to ECDSA. Those two courses will have to wait though, as I already have a lot on my plate.

  1. Elliptic curves are ubiquitous. They were used, for example, to prove Fermat's last theorem. []
  2. From MIT's open courseware. []
  3. My brother was also interested in taking the course, so I am fortunate enough to have a classmate. []

ChatGPT Fail

March 5th, 2025

Use ChatGPT to learn math at your own peril.

I recently started a self study of linear and abstract algebra. I tried to use chatgpt in order to look up definitions. Look what I got1 :

Prompt 1: Define linear operator:

Definition of a Linear Operator

A linear operator is a mapping T between two vector spaces that preserves vector addition and scalar multiplication.

Formal Definition

Let V and W be vector spaces over a field {F}. A function
T: V -> W is called a linear operator if it satisfies the following properties for all u, v in V and all scalars c in {F}:

  • Additivity: T(u + v) = T(u) + T(v).
  • Homogeneity (Scalar Multiplication): T(cu) = cT(u).

Special Case: Endomorphism

If V = W, meaning the operator maps a vector space to itself, T is called a linear transformation or an endomorphism.

Matrix Representation

In the context of finite-dimensional vector spaces, a linear operator can be represented by a matrix, and applying the operator corresponds to multiplying the matrix by a vector.

Prompt 2: Describe the relationship between a linear transformation and a linear operator.

Relationship Between Linear Transformation and Linear Operator

Linear Transformation

A linear transformation is a function between two vector spaces that preserves vector addition and scalar multiplication.

T: V -> W

Linear Operator

A linear operator is a linear transformation that maps a vector space to itself:

T: V -> V

Key Relationship

  • Every linear operator is a linear transformation.
  • Not every linear transformation is a linear operator because a transformation may map between different vector spaces.

Conclusion

A linear operator is a special case of a linear transformation where the domain and codomain are the same vector space.

So is a linear operator a special case of a linear transformation or vice versa? Chatgpt gave me contradicting answers. Poking around other sources has led me to believe that the two terms are used interchangeably.

Here's wolframlpha's definition of a linear transformation. For the time being I'll be using that website as the resource for math related definitions. I noticed that they cite the contributor. Thanks Todd Rowland

  1. I had to fiddle with the latex response to make this somewhat html friendly, chatgpt gave me quality latex output that led me to have false confidence in the validity of that output []

One bitcoindexplorer mirror is down

March 2nd, 2025

http://mirror1.bitcoindexplorer.com/ is frozen at block height 883,682 due to being out of storage space. I rented 1.9 TB from a company in NZ and allocated 1.5TB to bitcoind + bitcoindexplorer. I could allocate the remaining .4TB to allow the mirror to continue, but I haven't decided if I am willing to because I pay roughly $1,500-$2,000 a year to keep that server running, and afaik no one uses it. My lease just expired and that mirror will likely be shutdown all together soon. If you have interest in it staying alive please leave a comment below.

Birding Guanacaste

February 26th, 2025

Below we have a peak at the airborne wildlife of Guanacaste, Costa Rica.

As I began my birding journey I was surprised to learn that there are only 10,000-12,000 species of birds1 known in the world. I'd hazard a guess that that means there is a maximum of 20,000 total species known and unknown and that the number is closer to 12,000-14,000.

The number 12,000 surprised me. I had suspected there was 1-2 order magnitudes more species. In the biologically diverse land of Costa Rica, there seems to be an infinite number. But that is not the case. And when my friend visited for 10 days and meticulously searched for every new bird he could possibly find - waking up at the crack of dawn armed with his notepad, binoculars, and merlin bird id app,2 hiking up to 30km a day, climbing trough mosquito filled mangroves, and then birding again at sunset - he found ~130 species.

Now indeed 130, 100 or so which were new to him, is a large number of species. But as his trip went on he went from finding 30-40 new birds a day to finding 1-4. And this made me realize that approaching the total enumeration of local birds is somewhat possible3, and that no, there obviously is not an infinite number of species of birds.

This realization of finiteness gave me an appreciation of the birds I see4 everyday.

These are the current finalists in the game of life, the ones that made it; all future generations will be their children. There's not endless variation, this is what is, if you want to see a magpie jay well those only come in blue with a white or black throat, no you cannot see one in red but if you want a red bird well a tanager does come in that color, those that peck wood look a certain way, parrots are never purple, hawks are never tiny, warblers are never large...

Here's what I've found sofar5, the shots were taken with a Sony A6400 with a 70mm-300mm Tamaron f/4.5-f/6.3 Lens.

A vulture takes a fishermen's catch.bird-3

Some snowy egretsbird-1


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These two seemed to have had a falling out.bird-10

The tricolored heronbird-11

My attempt at an inflight photo.bird-12

Tropical kingbirdbird-14

Streak-backed oriolebird-16

Scissor-tailed flycatcherbird-15


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A scissor-tailed flycatcher social hourbird-17

Scissor-tailed flycatcher in flight! bird-43


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Likely a juvenile common hawk bird-18

Some humming birdbird-20


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A great kiskadee or the pecho amarillo or the bienteveo común. One of Guanacaste's most fierce and common little guys. If you've lived here you've definitely heard them. De ta-dee! De ta-dee! These little dudes attack falcons and hawks. Dun fuck wit 'em.bird-25

I swear these guys knew they were in a photoshoot.bird-26

Alright it's time for our sand piper and turn section. Attention! Formation!bird-27

Pretend to be a stick! HOLD! bird-28

The guy in the back with a long beak is a whimbrel. bird-29

Zoom in and see all the fish they got.
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The majestic white-throated magpie-jay. They usually make an awful sound but they are indeed able to produce a beautiful chirp.bird-32

A woodpecker or as the hispanohablante's say, carpinterobird-33

Does this bird remind you of Donald Trump or is it just me?bird-34

This Osprey chills on this branch everyday.bird-35


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Black-crowned night heronbird-39


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Crested caracara with a little snack.bird-40

Find the hummingbird.bird-41

A blurry summer tanager, I believe`bird-42

Scrub euphonia, isn't this little guy just adorable?bird-44


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Can you find the woodcreeper in the below pic?bird-46

This may be a dove, I'm not sure.bird-49

The little blue heron!bird-50

Ok technically not a bird, but it's got a baby.bird-51

Yellow-crowned night heronbird-54


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The black and yellow crowned night herons get along, it seems.bird-56

A squirrel cuckoo's buttbird-57

Can you find the butterfly?bird-58

A few shots of the Elegant Trogon. This was from the Diriá National Park, an absolutely splendid place to visit primarily cuz no one is there yappin' and scaring away the birds.bird-59


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And now a black-headed trogon in my ~backyard
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Possibly a baltimore or bullock's oriole.bird-70


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Baltimore oriole bird-22

Blue-gray tanagerbird-72


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And we'll finish with a puffbird.
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  1. What defines a species? The answer is debatable, but the simplest idea - known as the Biological Species Concept - is a unique group that can interbreed to produce fertile offspring. The problem with this definition is some birds on the genetic periphery are able to breed with two otherwise disjoint groups. It's also, ya know, damn hard to figure out which other birds a given bird can impregnate with a fertile baby. []
  2. A tool by Cornell University that uses the phone's mic to identify birds by their chirps/songs []
  3. Local birds. Birds migrate to Costa Rica from all over North America so on any given day you may find a new bird that is passing by on its migration journey. []
  4. And for the most part previously ignored. []
  5. Actually, I have a lot more better pictures for a later article. []

Wandering Productively

June 29th, 2024

This is mostly a heartbeat article, to show signs of life, and provide a little update to others and my future self.

I've put a pause on playing bridge. I still love that game, but I was sinking too many hours into it. Instead I've been focused on the following: renovating/redecorating my apartment, starting a new business, studying Spanish, and saltmines work.

My hands are, as usual, feeling shitty. I'm working around it.. I probably should make more of an effort to keep fighting this terrible disease; I have just learned to accept the pain as part of life. It rarely bothers me on an emotional level anymore, but I must admit that the pain is slowly getting worse.

I've been to New York City twice recently; I had a great time both times. I particularly enjoyed myself at House of Yes's House of Love parties, I may have to post an entire article detailing my experiences there.

For now, I'm back in Guanacaste, and despite the tremendous amount of rain, it feels good to be home.

Wandering Aimlessly

March 2nd, 2024

I've started hitting the gym. While I am stoked about my progress,1 I'm embarrassed to say it has become my main, dare I say only, focus.

Other than my workout routine, I've been all over the place. I've been underperforming in my saltmines job and haven't managed to produce a plan of where I want to go with my career.

Speaking of which, I'm sick of the saltmines, even though I work so few hours.2 Nowadays my mind often goes through the following pattern:

Good morning Will, let's seize the day! Start off with a nice hard workout at the gym. Phew, that was exhausting. Nice work. Now let's eat a hardy meal. Okay. Let's get to some actual work. Wellllll why not enjoy the day a bit and play some bridge/hang out/etc. Boy I'm quite tired, let's lie down for a sec. Wow there's only like 1-2 hours left of the day, shit. Should we do what we are passionate about, something related to bitcoin? Wait, we really need to get some saltmines work done don't we? *Spins between the two options, gets nothing done.*

Despite this disastrous thought pattern, perhaps I shouldn't be hard on myself. I have made progress this year. The gym is certainly helping with my RSI. I'm back to writing. I got some work done on my blockexplorer.

But I don't have a clear vision. I jump from one random "productive" task to another. No plan, no lofty goals.

Putting in my notice for the saltmines job may be in order. Working for a US tax paying organization is soul crushing. And having saltmines on the TODO list distracts my mind overall.

Simultaneously I need to construct my plan for the next coming years so that I can wake up and live life to the fullest.

  1. Minus the injury I gave myself doing a calf raise, sigh. []
  2. RSI gives a constant reminder that the number of clicks one gets on the keyboard is finite. []

My level two Freediving course in the magical Cenotes of the Yucatán peninsula with Blackfin Freediving

February 18th, 2024

A long overdue article.

This epic journey started with a solar eclipse. My instructor took me to go buy obsidian stones. You can use these as shields to look at the sun. Shortly after we arrived at the cenote, the moon began to block the sun. This distorted our respective shadows. Check out the crescent shape of the leaves.


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Just after seeing this it was time to get in the water. For the first dives I was tripping out from anxiety. What can I say? Freediving is intense. Some people are naturals; there was a lovely mermaid who was able to get to 25m on her second day. I struggled to get to 15m. One must not compare themselves to mermaids.


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Mermaid mermaiding

When I got home my throat was sore. Something was wrong with my equalization technique. I was using too much effort, which manifested in a horrible noise.1 I learned from my Instructor that doing this can lead to a trachea squeeze as “shallow” as 20m.2

The next day, I went to another famous and beautiful cenote called Angelita. I was hesitant to dive given my sore throat. That said it was feeling a little better, and so I decided to make some conservative dives. My instructor gave me an excellent drill that allowed me to understand what I have been doing wrong with my equalization.

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Angelita entrance


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Wrapping up at Angelita

The drill was to fill my mouth with air and dive down and up with my glottis closed. The point of the exercise was to feel my cheeks compressing on the way down and expanding on the way up. I was stunned to see that I was able to make it to about 10m. Normally to get to 10meters I would have to recharge my mouth with air multiple times.

The drill taught me to keep my glottis closed. It became painfully obvious that my problem was that I was constantly opening my glottis, allowing the air in my mouth and nasal cavities to fall back into my lungs. This fault made me have to charge my mouth for every equalization.

My instructor also showed me that I could equalize my mask simply by relaxing my soft palate and unpinching my nose. Previously I had the misconception that I had to actively blow air from my nose into the mask. This misconception arises because you have to create pressure in order to open up the eustachian tubes. It may make one naïvely believe that equalization means pushing air into the middle ear. But once the tubes are open, there is no need for extra pressure. In other words, the pressure is used to open the valve but not to relocate the air once that valve is already open.

After the dive, I got home to rest. My next session was in the pool in the following afternoon. The 30 hours of rest got me worked up about the static apnea challenge. I was spinning thinking about how maybe I would somehow fail to even reach 2 minutes 30 seconds. Or maybe I would try to go for another shot at my PB of 4:40 and then I would black out. In retrospect, it was a silly thing to get worked up over, but my mind tortured me. I calmed myself down by doing 2min 40s static apnea on land.

Still, I was worrying so much about this that I forgot to pack my fins for the pool session. I took full responsibility for it, and it seemed my instructor did as well, so I think we both felt a little bummed out and slightly wishing the other person had not made their respective mistakes. It was not such a big deal, but that meant I would have to come back to the pool to do my 50m horizontal challenge… in any event the static apnea went fine, and I managed to last 3 minutes. At about that time I was dying to pee (a side effect of the mammalian dive reflex) so I was able to excuse myself from not pushing further because I did not want a warm current to brush the leg of my safeties. Lucky me.

The next day I went back to Maravilla, the first cenote. I was feeling confident. Still, I struggled to get to 15m. Even though I knew about my glottis problem, I was still accidentally opening it all the time. Also, my duck dive technique needed serious work. I was starting every dive terribly, causing stress that was fucking up my equalization. In the end, I managed to dive to 20m and see the beautiful cavern of Maravilla. I was high on life.

We were going to the pool that afternoon. During the downtime I managed to get myself into an anxious state. My mind started playing tricks on me, and I started to feel terrible. But it passed, and eventually we were back at the pool.

When we got there, my instructor gave us the drill to swim 200m free stroke and 200m breaststroke. As far as I know, one does not normally warm up for apnea with aerobic training. But I seriously needed to just swim and somehow my instructor knew this so I was so grateful for this warm up.

Then we did safety drills for horizontal apneas. This requires absolute focus. You need to stay right fucking next to your partner, and when they come up for air, you need to immediately tell them to breathe and be ready to catch them if they have an LMC.

While I was safetying, my partner did a turn and grabbed the pool ladder to get extra leverage. I thought this was hysterical. When he came up for air, I was laughing far away from him. My instructor scolded me, I did something incredibly fucking stupid and dangerous by letting the pool-ladder-grab make me laugh and lose focus. Grabbing the ladder might be the exact type of thing someone delirious from lack of oxygen would do.

When it was my turn to do my 50m horizontal distance, I was feeling not great, but not bad either. I did my breathe up and started the apnea. I had horrible technique. Nevertheless, I had my first contraction at around 40m. I think of the first contraction as about the half way point, so I felt confident that I could get to 75m. I sent it. When I came up for air the world seemed fuzzy. I realized that I had to do my hook breaths or I would faint. I recovered and was happy about the accomplishment. But I was stunned at how hypoxic I was.

I realize as I write this where my logic went wrong. When I had my first contraction at 40m I thought “I am halfway through my air and I have swam a pool length and a half, and then some. So certainly another pool length should be no problem.” It’s quite stupid but somehow my brain did not think about the 10 meters I had left to complete my second pool length. So I thought I only had 25m left after completing 50m. But in reality I had 35m left after completing only 40m.

Getting hypoxic when I didn’t expect it shook up my nervous system. I was sad and stressed for the next 24 hours. I still had 3 sessions booked and one more task needed to complete to get my certification, a mock rescue from a black out at 15m depth. I was stressed enough that I was contemplating calling everything off.

At the same time, I saw this as an opportunity to overcome adversity. So I decided to take a three day rest and then get back at it. I contacted the head of Blackfin and asked to push back my Friday session. Then I signed up for William Trubridge’s mental immune system course, and decided to use the time off to get my head in a good place. Learning how to handle myself during stressful times is one of the reasons why I decided to start Freediving.

I found the first few videos of William’s online video course to be helpful. He clearly has thought about the issue of anxiety from both a spiritual and biochemical perspective. There were a couple main takeaways that helped me get into a relaxed state. (1) rhythmic, diaphragmatic breathing.(2) viewing thoughts as an experience like a breeze of wind rather than something tied to one’s identity. The diaphragm breathing sends a signal to the brain that ‘all is good’ ; the dissociation of identity from thoughts takes away the power of intrusive thoughts to cascade into a downward spiral.

Armed with these tools I was feeling better. The head of Blackfin messaged me saying that they were gonna have a fun event and go to a great cenote on Friday and he asked me to change my mind about postponing my next session. I did and had a magnificent time.

We went to a lagoon that was roughly 75 m deep. We had to go to this place because of the caliber of divers that were present. There were national record holders, multiple people who have been deeper than 100m, and otherwise a cool cast of people. Everyone was friendly. The presence of all the talent and the camaraderie gave me a magnificent boost in confidence and relaxation.

I managed to repeatedly dive to 20m without any equalization problems.3 The head of Blackfin got some amazing videos, here are some stills. You can see the settlement layer between 0 and 7m. It was such an amazing feeling to break through the cloud and get to see the seawall.


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Diving along the seawall of La Laguna de Kaan Luum

The next day I was feeling high on life and went back to Angelita and again was able to dive to 20m without any problems. This cenote has a gorgeous tree coming out of her sulfuric acid cloud. The desire to see this tree in person got me to my happy place before I dived.

I did my 15m rescue and therefore finished the course and got my level two certification.

That was basically the end of the trip with regards to Freediving. I had one more day booked with Blackfin, but the plan was to go to some shallow cenote and have a free swim rather than dive with a line. I was relieved to be done diving, but there was a bitter taste in my mouth. Before coming on the trip I have been to 24.5 m, and I was slightly disappointed that I hadn’t matched or surpassed my PB. I knew my diving had improved, but I didn’t have the depth to show for it.

Well as things turned out, the fun dive got canceled. I had one more shot to go diving on the line and I took the opportunity. I went back to Angelita, the amazing Cenote with a tree coming out of a sulfur cloud.

I was feeling amazing and confident the morning of this last session. We did three warm-up dives to 10m. My equalization was working perfectly. I was ready to do 20m, then maybe 23m, and finally 25m.

Instead, the instructor said I should go to 25m right away while I had the most energy. My heart started racing. I was excited because I was feeling confident that I could do the dive and I knew how great it would be to end on a high note. I started my meditation and got myself to a state of serenity. I envisioned myself in the third person as if I had the perspective of a bird hovering over the Cenote. Then I zoomed out to the perspective of an astronaut in outer space looking down at me. Finally, I zoomed out “ all the way” to another galaxy, and just imagined myself as an infinitely small point. I let the image of Ganesh, the overcomer of obstacles, flash through my head.4

The dive was blissful. I performed the equalization exactly as I had planned it in my head.5 I got to see the beautiful tree and sulfur cloud up close. It was such a beautiful sight that later when I was retelling the story, I started crying.

When I came up from my dive my depth gauge read 25.1m. I was estatic, 25m has a much nicer ring to it then 24.5m. Everyone congratulated me on my personal best. But doing something once shows you have rather than you can. So I repeated the dive and I was later happy to find out that one of the diver friends I had made recorded it with a GoPro.

When I came up from the second 25m dive my instructor told me “you are on the other side.” It’s true, I know how to dive up to 25m and maybe even 30m now. I have a much better understanding of how to perform the necessary equalization, and I have much better control of the muscles necessary to do so.

The excitement of the trip didn’t end there, though. I had one more unwelcomed battle. After our diving session, as we were sitting down for lunch, I started to feel faint. I have neurocardiogenic syncope, which means that my blood pressure can drop dramatically during a fight or flight response, causing me to faint.6 I started to feel the symptoms of presyncope, and the people who were eating with me told me I turned white as a sheet. I knew there was a chance that I was going to go out and wake up on the floor. But I decided I’m going to fucking fight it and not faint.

The next two minutes were hell. My blood pressure must have dropped to an incredibly low level because I felt my whole arms and hands go numb. I started to use techniques I had learned to calm myself for Freediving. Specifically diaphragmatic breathing and focusing my mental effort on observing the sensations in my body and thoughts in my mind. I also kept drinking water with lime juice and salt as well as a Coca-Cola for sugar. My instructor who was with me helped me with all of this.

For the first time in my life, I endured pre-syncope without fainting. This was a big victory for me in that it taught me that it is possible to stop an episode. But it was maybe a pyrrhic victory because pre-syncope by itself is a fucking horrible feeling that I would very much like to never experience again. And I am concerned about Freediving being a potential trigger for an episode. The problem is that fainting is ultimately caused by lack of oxygen to the brain. This is usually because of low blood pressure, but apneas cause me to feel a similar sensation.

I think that I have developed a fear of the sensation of being close to fainting. This means that after a small amount of hypoxia, my body may start releasing adrenaline, causing the chemical cascade that leads to an episode of syncope. In order to enjoy Freediving, I’m going to have to figure this out. For now it’s time to rest and enjoy the accomplishments of the trip.

Since I wrote this months ago, I've continued to freedive and have achieved 30.9m or 101 ft. That's it for me for now though, I keep dealing with weird fatigue and headaches after diving and I simply cannot enjoy the sport since I always feel bad the day after. So that's it, the story of Will's freediving career and his journey to 30.9m. I'm going to leave my flag there and go find something else to do.

  1. Perhaps it was the infamous 'grouper call' noise. []
  2. This injury is considered minor when compared to a lung squeeze. But I’m not about to lose my squeeze virginity for no reason. []
  3. I did notice on one dive that, despite my supposedly relaxed state, I felt a contraction somewhere early in the dive. My instructor informed me that it’s possible that It was not a contraction. I’m really not sure because I think I felt it multiple times, which leads me to believe it was indeed a contraction. []
  4. To me it's all a bunch of mental voodoo, but if it works it works. []
  5. I charged at 5m., 10m, and 17m. I had told myself that if my 17m charge didn’t last until 25m I would just turn around instead of charging again. I equalized the mask at the same time as each charge as my first Instructor had taught me. []
  6. I have fainted ~6 times in my life, and this was one of my biggest fears going Freediving and the thing that was nagging in my head the entire trip. The first time I saw a doctor to get checked out if I could dive, I fainted discussing it. I was sure I would never be approve to dive, but I also thought that not diving would be giving into the fear and anxiety. Also, I always have pre-symptoms before an episode. so I could know when it’s not safe to dive. I spoke with my neurologist who diagnosed the condition in the first place, and he agreed with me and told me to go freedive. []

Understanding the Psyop that is the Segwit Softfork

February 5th, 2024

Segwit is an attempt to redefine the bitcoin protocol in a manner that drastically undermines the security of the network. Here’s an analogy to get a jist of what is going on.

Imagine a FIDE1 imposter attempted to add a new rule / restriction to chess, call this version chess2. Bishops are now only allowed to move a maximum of 4 squares diagonally from their current position. This new rule does not conflict with the original rules of chess.2 A chess player observing a game of chess2 would not necessarily know that a different game was being played. They would watch this ‘chess’ game and perhaps be perplexed as to why certain bishop moves weren’t played, but otherwise the game would look the same.

Imposter FIDE could slowly add new rules to chess2, all while maintaining an illusion of fidelity with the original game. Of course, the brazen FIDE impostor would not name their game chess2, and so their new game would be masquerading as chess itself.

This is the state of bitcoin. A group of ‘core devs’ have been chipping away at what the word bitcoin even means. They’ve made the kind of changes that are akin to removing the 20,999,999.9769 btc cap. 3 Yes, the situation is that bad. They are not only changing the rules of bitcoin, they are adding rules that poison it.

Chess2 is not chess and segwit is not bitcoin. If you want to use sound money you must use real bitcoin addresses that start with the character ‘1’.

  1. The major chess organization []
  2. Provided opposing kings do not move into a position 5+ diagonal squares away from a bishop. []
  3. Nope, it’s not exactly 21 million. And yes, this matters. Stating the precise cap illustrates that bitcoin adheres to a strict protocol, warts and all. []

Bitcoin Investment Strategy

February 3rd, 2024

Warts and all, bitcoin is the best money out there. It seems all but certain that it will take the dollar’s position as the reserve currency of the world. From napkin calculations that should put bitcoin at about $2,000,000-$4,000,000 per coin in today’s dollars, although the USD price per coin one day will be way higher than that due to inflation. All this to say, getting your hands on some coin is a very good idea.

So how do you buy some? Do you put away a paycheck each month or go all in with your savings right away? Well that depends on your risk profile. For the highest expected value, the best decision is to buy as much btc as possible all at once. This is because at time T+E it is always >50% that the price of btc will be higher than at time T. Of course you may have some insight that tells you the current price is at a local maximum, and thus you should ‘wait for the dip.’ But I seriously doubt you are privy to such information.

If you want to lower your EV for decreased variance, then you can consider dollar cost averaging. And if you’re new to using bitcoin, it is a good idea to practice buying, selling, trading, moving coins from one wallet to another, creating backup protocols, testing those backup protocols, etc. DCA is a good way to do this.

Lastly, if you want to put in a reasonable chunk of money in btc the only people in the consulting game are to be found at jwrd.net.

Happy investing. Rest with a smile on your face knowing that every buck you put into BTC takes some power away from the cursed governments of the world.

Hands Update

February 3rd, 2024

I’m pretty sick and tired of always avoiding activity in fear that I will incur further damage to my hands. I am also losing my mind from my inability/decision not to write. I would rather have flare ups than remain silent.

I am going to focus on physical therapy and typing technique retraining. Speech to text is no solution. Here’s to a revival of my textual output.