Smooth functions

It is funny how many people have opinions on how others should live, despite very different circumstances. It is also funny how good we are at internalizing other people expectations. This gets drilled very deeply especially through school.

A thought process could be:

  • what I want
  • what I have
  • what is the difference
  • how is the process of covering the difference

At the end, where we start and where we end doesn’t matter that much. It is the function that connects the two points the part that we call life. It is damn too easy to focus on the start and the end, and forget the rest. This is particularly bad if the fleeting happiness of the end point doesn’t backpropagate to the iterative process we call everyday life.

There is no better model for life, than a function that fits well on what we consider important, is smooth, and generalizes on unforeseen cases without the need of a large normalization factor.

Well, perhaps there is. Who am I too know any better? I also don’t want to contradict myself within a single blog post.

Shortcut to success

Having a strong interest in something can be a shortcut to being successful at it. This can be both an opportunity and a disaster in the long term. The difference may boil down to reflection.

Having the strong motivation on doing a task well, can lead to active thinking towards the topic, its properties and how these lead themselves to a solution. You may see variations of the same mantra under different phrasings: The customer is always right, focus on the user, or more academically, start by defining the problem and its desired properties.

This process also makes more effective the related communication with others. When everyone is focusing on the same topic, it becomes easier to fill in the gaps with the correct assumptions, as they arise from the understanding of the topic even if they are left unsaid. Fields develop their established lingo and culture in a kind of similar way, (but admittedly, in a larger scale).

Because of the strong inherent motivation, a generalisable methodological approach of the problem may be deemed superficial, bureaucratic and unnecessary. It may require much more time than it is really necessary when compared with an approach that takes advantage of the inherent structure of the topic at hand.

Our interest in a topic may be flickering. If it is connected in a naive way to satisfying curiosity (information gain) or monetary rewards, we may experience relatively soon a flattened curve. Some argue about the logarithmic return of money after a certain level or, many times what we experience as an exponential function may really be just a sigmoid.

This may have been less of an issue, if we didn’t have higher level abstraction capabilities or other external factors. Both may provide with, perhaps external to the topic itself, reasoning why insisting on it may make sense beyond the experienced naively defined returns discussed above.

Moreover, most likely at some point we will move towards a new task. The strong interest may be there or may need some time to be cultivated or it may be a coin flip and we got the wrong side of the coin. Then, we will find ourselves reflecting on our past experiences and if we rely too much on the presence and deeper understanding of the topic, we may find that our experience doesn’t count for much. In other words, I am talking about getting too used to the specifics of a situation (overfitting) to such a degree that we are not able to tackle other situations that may differ in a substantial way.

Thinking, to the external observer, may be glossed over as a waste of time. Why spend time on thinking, if you could have somehow the conclusion (could you?) and start executing faster? Even more strongly, reflective thinking almost by definition may seem redundant, unless your explicit goal is to generalize the knowledge of the task you are performing.

Experiencing success can be a blessing. You have the opportunity in first person to observe some of the qualities that help you do well what you are doing. Sometimes, that may also include some noise (lucky charms?) but it may also lead to establishing healthy habits.

Experiencing success can also be a curse. You don’t need to take a systematic approach and deeper look on what you are doing. The autopilot can do the work for you. The gaps are filled by your passion of focusing on the problem. A passion, which admittedly, is hard to be replaced by any system. Therefore, you may never establish the systematic approach that leads to success even when the intensive interest is lacking. You may also find that the established habits are built on shaky grounds leaving you without much.

Failure is an important component. Similar to success can come to two different flavors, leaving either a positive influence or a negative. Both can be based on the level of reflection that is induced. Nevertheless, here the situation may be different. Usually, the sentimental magnitude of an experienced failure may be stronger from the corresponding magnitute of a success. This quantitative difference may lead to qualitatively different results. People are usually more prone to introspection after a failure (or a perceived one). If done to an unhlealthy degree, this can be quite demotivating. Otherwise, in balance and in context, it can be the breeding ground of a systematic approach that coupled with some successful stories, leads to systems that decrease the variance between the two outcomes (failure and success) and also shift it to the right.

Having pondered during this blog post based on the assumption that there is a distinction both objective and subjective between success and failure, it would be unfair to call at this point on the reevaluation of this assumption. Nevertheless, its evaluation (both under personal and objective terms) is the critical final component that ties together the experiences and the systematic approach that may arise to the different context and lead to its transfer among tasks in something that we have the tendency to characterize as much as a part of our personality.

Having said that, it is very easy to observe the flip side of what I mentioned on tasks that we find both uninteresting and we have no external reasons to ever become good at them. Most likely, I will never get good at playing FIFA 98.

To bring this to a conclusion, perhaps a bit hastily, I am arguing for a more systematic approach of the things that we consider important. The shape of the system can differ. Reflection on the differences can reveal some of the underlying properties of the topic we are occupied with. Comparison with other systems we or others have followed in the past can lead to generilisable attributes that we may one day promote to what we feel defines us. Contemplation of what consists of success and what is a failure has the potentially of profoundly shaping our values. Observing the flip side of all that can reveal what is really what interests us and why, which is the long road of arriving to the first sentence of this blog post.

How to talk about FIRE at a party

This is a guide on how to try to sound smart at a party while talking about FIRE. Given that this is in the context of a party, half of it will be nonsense. You, as a reader, will decide which half. If you read it twice, you may realize that the other half is nonsense too.

Having said that, let me also increase the prestige of this blogpost by reminding you that I am not a financial advisor.

There will be two sides of the story, for and against the FIRE movement. If you feel neutral about either and you just want to impress someone at the party, voice the opinion that people have heard less but they can still confidently follow. If you have already form an opinion, just read the point of view that is closer to what you already believe, as we usually do on the web nowadays.

Having explained the setup, let’s proceed to the guide which is in the form a question/answer. It has the potential to significantly expand your social circle when you talk to your acquaintances about FIRE. And by saying potential, I mean it is very likely that it will do nothing. It definitely hasn’t helped me. At any party. Not that I am invited to any, anyways.

  • What is FIRE?

FIRE stands for Financial Independence, Retire Early. Sounds lit? It is basically the idea that you can make enough money at some point in your life so you don’t have to work again.

For: You save money. Put it in something that gives a high interest rate, and withdraw only once you reach a goal. People have done some maths (Trinity study, later studies) and it works. No need to rely on external factors or wait for an official retirement age. You can be free to do whatever your heart desires after you reach your goal.

Against: This is a DIY privatized retirement plan with uncompensated risk (you die early). A lot of the mechanics are heavily disputed (SWR — Safe Withdrawl Ratio) and essentially is for people who don’t know what to with their money.

  • What is Financially Independent?

Financially Independent is the person who doesn’t need to work for the rest of their lives. (Insert joke here “I have enough money if I die tomorrow”).

For: If you hate your job, you have the opportunity to do something else. Even if you like it, you don’t have to worry much about outside factors (what your boss thinks of you) that may diminish your motivation to do it properly.

Against: Being part of the society means also doing work that you don’t really enjoy. Even if you are financially independent, this moral obligation doesn’t change. At the end of the day, someone has to do the work that no ones wants to do.

  • What are the mechanics of FIRE? (practice)

There are long books that essentially will tell you things are complicated. Follow this strategy. They may also explain a little bit why they are complicated. Nevertheless, they are not THAT complicated, but in any case, not the most fun thing to explain in a party.


  1. Make sure you have no debt, unless that’s very cheap (mortgage).
  2. Save enough money in case of emergency (3-6 months).
  3. Buy the ETF called VT until you come close to (early) retirement.
  4. When you are getting closer to your retirement, start increasing your allocation to bonds (perhaps reaching 40%).


Live your life now. You may die sooner than you think. You will definitely never be as young as you are now. Your memories that you take in your retirement are more important than your money.

  • What are the mechanics of FIRE? (theory)

You save a lot of money. Saving money means that you earn more than you spend. If you have risk tolerance (e.g. you are young), you put your money in stocks which historically and averaging long enough periods of time have returns of about 7%. Otherwise, you put your money on bonds (2-3% returns) which are more stable. If you are really risk averse, you can have them even in cash in a bank account.

There are other strategies too, like using structured products, which usually make more sense for institutions because they involve fees that don’t scale well at individual level. There are also markets of other assets classes (precious metals like gold) or private companies that go beyond what is fun to explain during a party.

There are also strategies that are a mix of stocks, bonds, and cash.

For: You have worked harder or smarter than others. You take advantage of the exponential nature of the returns (compound interest) and you are being rewarded for being proactive and understanding our financial system with the option of being able to retire early.

Against: Your life is sustained by the work of others. The stock market is a way aggregates way too much capital back to the people who already have it, under the false pretense of return for assumed risk. The argument that capital allocation reflects prioritization to social beneficial initiatives is … (sip some drink here and quickly skip to another topic. If someone insists, see further points below. The trick is to not make your audience tired with too many financial details and you don’t want to sound like a communist. Waving hands can go a long way to a drunk audience. Much better than starting a 10 minute monologue.)

  • What is an ETF?

ETFs are stocks. Essentially ETFs are special companies that the only thing they do is to own shares in other companies. Because they also need to make some money, they charge you some fees, called TER. Because they also want to make some more money, they also lend their shares to short-sellers but that doesn’t really affect you.

By buying an appropriate ETF, you buy a little bit of many companies. A popular strategy is to buy a little bit of (almost) every company in the world. That’s what you do by buying VT. Of course, in practice it is impossible to buy a bit of every company in the world (due to lack of liquidity for small companies among other practical reasons) so they are some kind of approximation to that.

For: ETFs is the only investment that you need to make, apart from bonds. You don’t have to worry about companies going bankrupt or losing a lot of value, because you have a little bit from many of them. Just buy an ETF with low TER and you are set for life.

Against: ETF is one of the surest ways to make guaranteed money in the stock market… by creating them. By creating them, you charge the people who buy them, you make money by lending their shares and you also keep the voting rights for yourself (or charge extra to lend your shares to those who want the voting rights).

  • What is a bond?

Bond is a loan. There are bonds issued by governments and by companies. That means that a government (or a company) asks for some money now and promises that they will pay you back later. Bonds in theory help you diversify further and therefore decrease your systematic risk. Nevertheless, in practice their performance recently has a quite high correlation with stocks.

For: Bonds are more stable than ETFs because their return is guaranteed unless the government (or company) goes bankrupt. Nevertheless, their returns are smaller, especially nowdays.

Against: Bonds are an alternative way of financing a company without diluting the voting rights of the current stockholders or making them share with you their future profits. The company essentially bets that your return will be smaller compared to that of the current shareholders. You are fine with the smaller return only because you want to decrease its volatility.

  • Should I buy stocks?

Stock is a piece of a company. Buying a stock gives you (partial) ownership and with that some voting rights on the decisions that the company makes. By buying stocks to specific companies, you are exposing yourself to the risk associated with the destiny of that company.

For: Only buy ETFs. Buying a stock of a company is too much trouble and likely you will get it wrong. There are way too many stocks, you are competing with professionals and the chances that you can outperform them are minimal. That’s why choosing an ETF with a low TER and tracking error are so important.

Against: To replicate a market capitalization index fund can be done relatively easy with some automation if you care enough or alternatively manual rebalancing should be good enough for practical purposes. Nevertheless, it may be too tempting to spend time on things that make small difference to the world (or your world) that it may not be the most advisable path.

  • Should I do day trading?

Day trading is the activity of buying and selling stocks in short period of time. Some people call it speculation instead of investment because the time horizon makes a difference on the mentality.

For: No. Not worth the trouble or the fees that this may incur.

Against: No. Not worth it.

  • How does really buying a stock (or an ETF) work?

You open an account with a service called broker. This is a website (or an app) that shows you stocks, ETFs and other stuff you can buy (or sell). Once you choose something to buy, this service forwards your order to another service called wholesaler. A wholesaler aggregates many orders and tries to match them internally. That is, if for a stock they see an offer to buy for 200$ and to sell for 100$, they will execute internally. Then, they will split the difference with all participants (including them, the broker, you, your counterparty, the other broker…). If they don’t manage to do that for some reason, the order will go a stock exchange where it will be matched against other orders. On top of the fees that you pay based on the splitting of the spread difference, you also pay commission fees and taxes for your purchase (or sell). If you are interested in this topic more, you can search terms like “dark pool”, “odd lot” and so on.

For: It doesn’t matter. As long as you buy and hold, the mechanics of a single transaction don’t go beyond the level of noise.

Against: There are too many intermediates that make money out of a system that they purposefully keep obscure.

  • Amazing! How do you know all this stuff?

If we reached this part during a party, which I highly doubt since you are from the people who are still reading this blogpost, it means the above worked! Congrats! Now you have the self-confidence to also make up some financial “facts” to impress at a party!

For: What is your phone number?

Against: What is the phone number of your friend?

You may have noticed that above I didn’t include any links. That’s because I just made up this blog post. Don’t take it too seriously. Feel free to leave a comment with your opinion or made up facts in the comments though. I promise not to take them seriously.

Gnome vs KDE

Some pieces of software have an imaginary part and just like complex number, you can’t enforce an ordering. You may have infinite options with the same length (but only one with zero length).

I am tired of flame wars.

Long vs Short in investing

To long a stock, is to own one. That is, when it goes up, you make money and when it goes down you lose money.

To short a stock is about the opposite. That is, when it goes up, you lose money and when it goes down you make money.

That has an important consequence. Owning a stock has a lower bound on your losses (the stock becomes worthless) and theoretically no upper bound on wins. Shorting a stock is the opposite. You can win only up to the amount the stock has decreased in value but your losses are unbounded.

Moreover, shorting a stock, due to the mechanics (you have to borrow it from someone) also incurs higher costs.

Theory, theory and a bit of practice (On tiling planes and nanobots)

When I learnt about tilings as a complexity model, I thought that it was one crazy concepts that didn’t have any practical applications. I was wrong. There are as you can see on the wikipedia’s article.

I read about the movie created using atoms by scientists at IBM. That made me wonder, what could we create using atoms as the ingredients of building patterns in a plane. What kind of computations could we perform? Could we make the atoms to create self replicating nanobots with atomic precision? The answer, if we could model the atoms as Wang tiles, is yes.

There is a blog post about tilings (from a theoretical point of view) from Gödel’s Lost Letter and P=NP. The relevant material starts somewhere in the middle of the post.

Erste Schritte – Albert Goes

Klein ist, mein Kind, dein erster Schritt,
Klein wird dein letzter sein.
Den ersten gehn Vater und Mutter mit,
Den letzten gehst du allein.

Sei’s um ein Jahr, dann gehst du, Kind,
Viel Schritte unbewacht,
Wer weiß, was das dann für Schritte sind
Im Licht und in der Nacht?

Geh kühnen Schritt, tu tapfren Tritt,
Groß ist die Welt und dein.

Wir werden, mein Kind, nach dem letzten Schritt
Wieder beisammen sein.

I could not find a translation online, so I will provide my own (which may have a lot of mistakes).

You first step, my child, is small,
your last step will be small.
You will take your first steps with your mother and father,
you will take the last one alone.

When you are one year old, then my child, you will take
many unsupervised steps.
Who knows, what your steps will be for
In the light or in the night?

Go and take steps, take big steps,
the world is big and yours,
We will wait, my child, until your last step,
then we will be together.

GameStop short games

Gamestop is a public company. That means it is listed in a stock exchange and anyone can buy stocks. Its price has recently gone up. This post are some observations of story that is happening now. Quite likely it will be incomplete and perhaps even incorrect. Nevertheless, I find the story quite interesting.

Here is the graph behind the story.

The stock was trading at around 4 dollars 1 year ago. It is trading around 40 dollars now.

The price of the company didn’t go up (only) because an improvement in its fundamentals. GameStop is a company that is declining according to its income statements.

What is happening is that the stock is hyped on reddit. People on reddit are trying to cause a short squeeze. Assuming almost no background, I try to explain in simple terms what that means.

Let’s focus on short term investors. If someone believes that the price of a stock will be up in the near future, they want to buy the stock now so they can sell it afterwards at a higher price. Similarly, if they think it will go down soon, they want to sell the stock now, before it has a lower price.

But what happens if you believe a stock will go down but you don’t have it in order to sell it? You borrow it and then sell what you borrowed(!). Then, if everything goes according to the plan and the stock has a lower price in the future, you buy it from the stock market and return it to the person where you borrow it from. If, in contrast, the price goes up, and you are either asked to return the share or you can’t tolerate anymore the risk of the share price going even higher, then you are forced to buy it at a higher price and return it.

A short squeeze happens when someone has shorted a share, but the share is going up significantly. Then, that person is forced to buy the share in order to return it (=close their position) which makes the price go even higher.

What people on reddit are doing is they are trying to increase the price of the share, force a short squeeze and then sell their shares at an even higher price.

Simple, no? Here are some speculative factors that may have contributed this phenomenon by retail trading:

  • There are brokers (services where you buy/sell shares) with zero or almost zero commission. That is, they don’t make profit when you buy or sell shares through them. An example in US is Robinhood. The very low commissions encourage people to make many trades.
  • A way for these brokers to make money is to allow them to give your shares to people who want to short them. We explained above how people short a share: they borrow it and then they sell it. But where they borrow it from? That is where the brokers come in. If the owner of the shares allows it, the brokers can give it a short seller. Then the short seller will pay some interest which is shared between the broker and the owner of the shares. How much of the interest goes to the broker and to the owner depends on the agreement.
  • Due to the pandemic, many people have to stay nowadays at home. Some of them had to find new hobbies. One of these hobbies can be day-trading, increasing the volume of the so-called retail investors (=people who put relatively small amounts on the stock market but there are quite a few of them).
  • has created a quite strong community around day trading to the point that it has attracted interest from more traditional financial firms that monitor it for news. It is a place where some stocks are “hyped”.
  • There is a narrative on wallstreetbets that is quite appealing to some people. By buying the stock of GameStop, they hope to get paid by taking profit from traditional (or “boomer”) investors when they cause the short squeeze.
  • Quantitative Easing (=printing money) that is happening to the US (and in other countries) has pushed a lot of money in the stock market. This happens in two ways. First, there are more money now and people who have too much of them put them in the stock market. The second, is about bonds (=a big loan). The interest rates have fallen. That means if I borrow money, I have to pay less in interest. That makes a bond worth less. Because bonds are worth less, institutions (and other investors) are more inclined to put their money in the stock market and therefore pump it to higher prices.
  • As the stock market goes to higher prices, more often news and excitement about it find their way to more people which makes them buy more stocks and therefore increase their prices.

I am quite curious on what is going to happen on the stock price of GameStop in the next days/weeks.

Disclaimers: I won’t make a profit no matter how the stock price of GameStop moves. Very likely I paint an incomplete picture here due to my ignorance. Don’t take financial advise from me. I am not talking on behalf of anyone else. Just spectating something I find fascinating.


(This is an old post that was saved as draft but never published.)

Today I ran beyond what I thought I could, given that was my first try. It felt wonderful.