This is a great video.

To summarize:

Digital signatures are a way to verify that you wrote a message. Ordinarily I of the public private key communication as giving out the public key so that people can encode messages that I decrypt with the private key. This is the opposite. I lock up the message with the private key and people can unlock/verify it with the public key. It is difficult for people to find a way to lock up a message that will decrypt with that same public key.

Cryptographic Hash functions make a summary of a small number of bits that is difficult to find a message that makes the same summary hash.

Your bitcoin address is the public key. I think you have a wallet that can manage multiple public/private pairs. Possibly transferring money between them.

Bitcoin has the miners append a number to the end of the transaction list trying to find a hash that has a long string of zeros. Since you’re just basically randomly trying numbers anyway, it doesn’t hurt you to add in more transactions as they come in I think.

The blocks form kind of a funky linked list, where instead of a pointer you have the hash of the previous block. People trust the longest chain they can find, which was really hard to compute.

Miners can be incentivized to include transactions into their block. In general it seems like the protocol is a bit extendable by the consensus of the community. You can sort of vote on changes to the protocol by including your vote in the the hashed block.

Euro Trip Post Analysis

I fell off the bandwagon posting day by day due to technical difficulties at first and then because I felt so behind.

After Berlin we got on a very hot overnight bus to Warsaw. Warsaw was pretty great. It had good food. There was this restaurant called Zapiecek where I got this kind of pork stew on a potato pancake dish. Best meal of the entire trip in my opinion. Got it AGAIN the second night, not quite as amazing. Also got interesting desert pierogies with seeds, blueberries and vanilla cream. They were weird and ok. We also got lots of 4 Zloty Lody (ice cream). The hostel may have been our last true free breakfast on the trip. I love breakfast.

The museums were interesting. The Jewish history museum took a surprisingly long view history, not hyper focussing on the last 100 years. The Warsaw uprising museum was also very interesting. Some highlights were the home made guns, how much they hate Stalin now, and the exact equivalent advertising for their special forces as we would have for our seals.

We flew down to Athens. The ancient sites were impressive. They are so OLD it’s nuts. The Parthenon is ridiculous. We walked roughly the same paths Aristotle did, which was a strange sensation. The views you can find from the tops of hills are gorgeous. Gyros were good and cheap. The bakeries there have great stuff too, lots of flaky savoury pastry like spanikopita and others. We also got laughed at for trying so many cookies.

We took an overnight ferry (where we made a buddy) to Santorini, which was the best day of the trip. We rented an ATV and scooted all over the island, which is just naturally beautiful. I like nature a lot, probably more than the great buildings we’ve been seeing if I had to pick. The architecture is also unlike any I’ve seen. Saw a number of the famous blue topped churches. It was too bad maybe that we didn’t schedule more time here.

We then took another ferry to Crete. We went to this restaurant called Amalia’s, which was really excellent and friendly. The temple of knossis was disappointing. Unfortunately, the archeologist from the 1920s reconstructed a bunch and it looks like a putt putt course. It took away from the stuff that was original because I had to always be guessing if it was original or a lie. The archeological museum was great though and the Venezian fortress was also great. We wandered the streets that night and slept in the airport. Matt was in great discomfort.

We scooted on over to Rome. Matt loved Greece so much that I think he got a bug in his butt about Italy and came in with kind of a bad attitude. Rome was very crowded and dirty. I remember looking over and seeing this old woman peeing on the tracks at the train station in the middle of the day with hundreds of people around. It’s not like that only happens in Rome, but it kind of feels characteristic.

We stumbled into a concert the first night

The vatican museum was the best museum I saw the whole trip. The painted rooms were huge wow factors, Sistine chapel, and I really liked the contemporary art section. Matt didn’t come for ethical reasons, which was interesting. He may have a point. A trade off is that I didn’t have time to wait in line for St. Peter’s

The Colosseum was nice but I was somewhat underwhelmed by the forum. That was a long day.

We made a day trip to Pompeii. It really brought home that these other ruins were actually just cities, because Pompeii is almost perfect. Put some roofs on things and you’re good to go. It was kind of spooky to see recognizable hearths and stuff from people 2000 years ago. At that train station, I got this ham and cheese calzone. 3 Euros, up there for best food on the trip, alongside Stockholm’s cheese sandwich and Zapiecek

Naples had good pizza. We were only there for a couple hours scooting between Rome and Pompeii.

The last night in Rome, we slept on the streets. It wasn’t that bad actually. Pretty warm.

We took a train to Florence. The church here was the coolest one in Europe basically. Well, in the running with Notre Dame. And the one in Ghent.

The Galileo museum reminded or taught me how much time and difficulty occurred in the early history of science. I kind of don’t think about much before 1800, but there was plenty happening. The handmade brass apparatus was fun.

We saw the leaning tower of Pisa, which is surprisingly tilted. There wasn’t much else in Pisa though, so we went on a to a beach. I wasn’t feeling the ocean on this trip. I think I was scared of having the skin on my thighs wrecked, which has happened before, and we were walking so much that it would have been miserable.

We hung out with this Australian dude one day.

Then another train off to Venice. Venice also didn’t feel like it had too much going on. The canals are neat but there isn’t that much else. I think my opinion is heavily influenced by Europe fatigue though. If it was your first or only location you’d probably think it was great. Started eating lots of peanuts.

Then a plane ride up to Paris. Saw the main sights, The Arc, The Eiffel, Notre Dame. Got some Vietnamese that night with Ben and Derek.

Baguettes are fine. Crepes are good. French coffee is a bit better than other coffee because it got the closest to American coffee.

Went into the Louvre. It was just too much.

Then took my flight to NYC and dumped the night in Matt Wiener’s swinging pad. Got a huge American breakfast to celebrate being back in the motherland. Was filled with more love of my country than I can recall feeling. Breakfast is the thing we do best. It is the quintessential American dish that everyone else screws up and we didn’t borrow. Got on a bus and I’m back, ready to figure it all out.

What is the takeaway from the trip?

I guess I was kind of hoping for a transformative experience, but maybe I’m too old, or Europe isn’t weird enough, or I’m not that kind of person. Even over there I was basically me. It was neat though and I had a blast. The time flew.

Maybe I stayed too connected. I was chatting with Connie and all my friends, checking my emails, and browsing Reddit and bullcrap almost every night.

I had lots of time to contemplate what I want and what I should do, which was good, but I think figuring that stuff out is more of an active seeking and trying process. I was coming up with more and more project ideas or things to look up, but i couldn’t really act on them because we were always on the move and I didn’t have a computer or equipment, which was sometimes frustrating.

In particular in regards to what I can do for a living, I don’t think there is too much I could do in a vacuum. I cannot just know what people would want to hire me for, and cockamamie self employment schemes need to be tried to know if they’ll even remotely work

I did learn that I probably could live in a foreign country, although it is not preferable. Everyone basically speaks english, but it does add a small extra layer of hesitancy to every interaction, even buying gum.




we made a quick stop in Antwerp on the way to Amsterdam. Not so much to see there really. Cool train station. Got some subway. Chicken teriyaki

amsterdam was neat

we were there for a day.

we didn’t really go into any museums but we walked by them.

the Anne frank house and van gig museum

I saw a guy trying to steal a bicycle


Berlin: Sausages, Spetzle and Nazis

Berlin has the overcast of its history hanging over its tourist experience.

We visited the holocaust memorial, and the topography of terror, checkpoint charlie, the Stasi museum, and the wall in various spots. Very sad and disturbing. Very recent. Not clear to me that it can’t happen again. Not to be alarmist, but I do see parallels to early thirties Germany and the US now. The nazis were very shitty for a long time before It’s crazy that the wall fell.

On a lighter note, we went out to a techno club and regular club on Tuesday night. They stay open all night, which is pretty neat. I got the closest I’ve ever been to getting in a fight as an adult with two British? jerk offs.

there are big cool buildings. Reichstag, victory column, Brandenburg gates, big tv tower thing, museum island.

we also went on a graffiti walking tour. Berlin does have tons of graffiti, some of which is very good.

we ate lots of sausage. Why not. The pretzels were just pretzels.

Ghent: Disneyland?

Today we arrived in Ghent. We’re staying on this eco hostel boat. It’s really nice.

We wondered around the old city. It’s like boom boom boom down there. The churches are bonkers.

I feel like there kind of was less interesting going on. Yes the old buildings were insane and nonstop, but that got a touch old? Am I already getting blasé about Europe shit?

Despite that misgiving, again it was basically the most gorgeous city I’ve ever seen.

had waterzooi for linner. Very good. It’s like a creamed chicken soup with lots of veggies. Matt is freaking out (in a positive way) about his.





Brussels: a hell of a town

so we spent today exploring Brussels.

Coming in last night, I noticed a lot of homeless sleeping in the train stations.

It seemed like there was just endless stuff to see. We walked over ten miles.

the grand place was impressive. The whole square is kind of guilds and the town hall building has a huge ornate spire and statues all over it. That stuff dates to 1690 ish

The churches are hue and impressive and kind of blur together.we only went inside one. Again, very impressive.

he pissing boy is fun. Shows a sense of humor on everyone’s part. We showed up for some kind of Ethiopian celebration thing. The boy was dressed up and Ethiopian dancers were dancing to music.

i don’t know why there as graffiti, shitty graffiti on this really awesome domed building on top of the hill. It seemed like a shame.

Butotherise there was some really awesome graffiti all over the city.

We went to a sewer museum and walked in the operating sewer of Brussels. It smelled like shit. We were kin of confused by people living in tent outside of most of the doors of the museum blocking it off. The museum was in these somewhat small fancy columns stone buildings.

we had vol au vent (chicken pot pie kind of)  and carbonnade (beef stew) for linner. It was a touch pricey but very good.

then we got some touristy waffles for desert.

one of the top cities so far.

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Copenhagen: Babies Bikes and Smorresbrod

After a long night we arrived here in Copenhagen on Sunday.

We’re staying at matt’s friend’s place, Sam. He is very nice to do so, since we are disgusting animals.

The sink here has been filling up with the upstairs neighbors dirty water so draining it into the toilet has been a theme.

The first day, Matt arranged all the travel. Buses places trains etc. That really took all day. I feel kind of bad about being a hanger on piece of crap who isn’t helping with the planning really.

The second day we walked all over town. Saw the harbor, Christiana, the weird commune thing in a park where they sell weed and/or declared themselves independent from Denmark? Saw Bohrs birthplace and the institute where he worked. Pretty cool. Also saw the requisite mermaid statue and a star shaped fort.

We went to aamans, a pretty fancy place, for some smorresbrod, the danish thing. It’s various things placed on a piece of rye bread. It’s good. I got boring choices, pig ,beef, fish, while Matt went for more exotic liver, steak tartare, and pickled herring.

I stopped fighting my coffee urges on day 3 in the museum Louisiana which was awesome. The exhibit on William Kentridge was particularly cool. He loves megaphones. The other main exhibit on Tal R, some danish artist, was more underwhelming.  I’m just a crass bore so whatever. The view of the sea was great. Also just generally the museum looked good. The building and grounds and scattered sculpture of shape.

after another chill day,we’re off to Brussels.



Euro trip Start

So I took a mega bus to JFK on June 1. Penn Station at rush hour was a vision of Hell. I watched some Lenny Suss on the ride. Damn, that guy knows what’s up. Then an all nighter to Stockholm and arrived around 2. I’m not built for planes. Is anybody? Tiny little things? It makes my hips feel like their falling out of their sockets and my feet spasm.

I exude a gelatin so that I can crawl over the knife.

Swedes have bird noises in their elevators instead of Muzak at least in that one elevator to the Atlanta Express. That’s nice.

We ordered something in Swedish. Everybody here speaks English basically so we didn’t have to. Matt in a happy accident ate fish eggs. I got some kind of herring.

We eventually got some meatballs. They were ok. Kind of like round Salisbury steak? They were good because it was a nice place.

we also saw this outdoor concert and the Swedish Bruce Springsteen.

Went to the Nobel museum. Saw that kosterlitz thouless plot in the case like I saw at the colloquia. Also went to the fotogratiska or something. It was a cool photography museum with an exhibit “like a horse”. Highlights include the bowcoy, the skinned horse face and the guilded poop.

we also were outside the abba museum and saw the YouTube stars of Sweden walk a red carpet. Gold tubes 2017 Woooooooooooo!

it turned out that we arrived the weekend of the Stockholm marathon. And we hadn’t pre booked a hostel, probably because when we were doing our big planning session we thought we might be staying with Matt’s family and then never thought about it again. We lucked out to get a room that cancelled the first night. The second night we kind of gave up on and resigned ourselves to an all nighter on the streets of Stockholm

Max burger as pretty good. Stayed there’s most of the night when the clubs wouldn’t let our schlubby selves in.

The swedes do not let you lie down in train stations. Cops woke me up twice.

Slept on the train toCopenhagen on Sunday morning and here we are.img_0285 img_0286 img_0287 img_0289 img_0291 img_0292 img_0294 img_0296 img_0298 img_0299 img_0301 img_0302 img_0303img_0301img_0298img_0287img_0285img_0299

Contracts and Category Theory

Contracts are both less cryptic and less impressive than a type system.

A type system somehow proves that things will never happen at compile time. You’ll never get a string when you expected an int or even more powerful facts. Contracts just guarantee that at least if certain problems occur at least the program will freak out and tell you at runtime.

I had been vaguely aware of contracts which I considered to be kind of a band aid Racket thing that is their solution to type safety (besides typed racket), but I did not go into depth. And I kind of viewed the thing more as a methodology for showing loop invariants and algorithmic correctness rather than type correctness. I do not know if this is an accurate portrayal of what is in Racket and I’m pretty sure contracts do not actually originate there (Eiffel?).

Mike Stay (who you may know as the co-author of the Rosetta Stone paper a bunch of videos which I don’t know how I didn’t come across before (they’re kind of old by skateboarding millennial mountain dew front end developer standards. Did Node even exist? Barely.). Javascript (well maybe after python) was my language of greatest comfort a couple years ago and I would have loved this. I absolutely loved Bartosz Milewski’s Category Theory for Programmer’s series. There is a crap-ton of line noise  that kind of muddies the waters though in javascript. I wonder if it makes sense to me because I mostly already understand what he’s going for from a Haskell context. He has some cool patterns here like using objects as typeclasses/interfaces.

The really neat thing he discusses is higher order contracts which I’d bet is a central piece of contract based programming but I had never gotten that far.

I’m still skimming over the vids, but nice job.


Convolution and Tensor Product

I realized a relation the other day that made me feel like a doof.

The tensored H\otimes I +I\otimes H extension of a 1-particle operator H occurs often. This is also the form of a laplacian of many variables

One of the most fantastic properties of the exponential and tensor product is

e^{H\otimes I +I\otimes H}=e^{H}\otimes e^{H}

I guess that looks okay but it is worth remarking that kron multiplication meshes well with exponential.

While this is easy, the inverse is not. You can’t write the inverse simply in terms of the inverses of H, as you can write the exponential in terms of the krons of e^H.

At the same time, This operator is roughly the propagator e^{tH}, which often you use the Laplace transformed version of G(E)=\frac{1}{H-E}. But that right there gives you an interesting integral expression for the inverse of the tensor extension of H.

e^{t H\otimes I}e^{t I\otimes H} is a product in the time domain. Hence it becomes convolution in the Fourier domain.

G(E) =\frac{1}{H-E} (*) \frac{1}{H-E}=\int dE' \frac{1}{H-E'}\otimes\frac{1}{H-(E-E')}

Where that star is some kind of kroneckerized convolution. It makes sense that kronecker product in the time domain becomes a kronecker convolution in the Fourier domain. If you do the integral out in an eigenvalue expansion you can see that it does work.

This suggests a kind of interesting method for finding the tensorized sum (I’m having a hard time knowing what to call it, but sums of the form A\otimes I+I\otimes B ) in terms of their original using a numerical integration.