Algorithms. By definition, a process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer. The word of focus here is ‘especially’. Doesn’t mean we can’t use them in our daily lives. There are splendid examples of when humans applied something way out of context to a situation and got amazing results.
It includes a lot of thing, SR71 Blackbird Jets, Burj Khalifa, Bullet trains, Your modern metropolis. All of these have one thing in common, biomimicry. That is, all of them are inspired by or has components that are heavily inspired by nature. Who would’ve thought that modern day buildings are something that termites came up with. Or that earthworms and other creatures have so much to contribute to maths. Similarly, we need to understand, some algorithms can give us a sanity check about a lot of decisions in our life. Am I trying to put maths to places where it shouldn’t be? ABSOLUTELY. And this is exactly the reason I despise modern day self improvement cult so much. It’s all rinse and repeat of very fundamental things. Let’s take some of those one by one.
Chips to the ceiling and all in(mostly)
People who want numbers and symbols go ahead. This team from Cambridge explains it very well. Otherwise,
WSLS algorithm and Gittin’s index. People who are into exploration(can range from choosing a cafe for a meetup to marketing startegies to stock market portfolios) would have heard of both of these. WSLS(Win stay, lose shift). As the name suggests, algorithm is pretty straight forward. If a choice leads to a favorable outcome, stick with that choice (Win-Stay); if the outcome is unfavorable, switch to a different choice (Lose-Shift).
The foundation for WSLS lies in the study of repeated games, where players engage in a sequence of interactions over time. In the early to mid-20th century, pioneers in game theory such as John von Neumann and Oskar Morgenstern laid the groundwork for understanding strategic decision-making.
Why am I telling you about it? Imagine this,
Consider the stock market, where investors employ WSLS in making trading decisions. If a particular stock proves profitable, investors might decide to stay invested, expecting continued success. Conversely, if a stock consistently underperforms, the algorithm advises investors to shift their investments to minimize losses. This adaptive strategy helps in optimizing investment portfolios over time.
And imagine meeting people. The most optimal approach here is not investing our energy,time and resources into people we don’t like. But for some reason, it’s a matter of aesthetic. People don’t like it when we perpetuate this behaviour because it hurts them. It’s not your duty to make everyone feel good, save your resources, time and energy for the people who you genuinely want to be with(and that is the reason we shall work on ourselves as much as we on/for others, because our situation shall not decide what we like.) Sounds like toxic advice, no problem, it’s backed by maths.
And then the gittin’s index.
The Gittins Index doesn't provide odds; rather, it offers the value of trying a new option. For instance, a 70% index reflects the belief that although this new option might not be perfect, it's worth exploring because of the chance that it could be excellent. In the context of decision-making, the Gittins Index is particularly useful when faced with the choice between "sticking with something known" and "trying something new."
Consider a dating scenario: if you've had one successful date with Sakshi and haven't dated anyone else, Sakshi is 1-0 (0.8001), and others are 0-0 (0.7029) according to the Gittins formula, indicating that going out with Sakshi again is a sensible choice.
Now, if another date with Sakshi goes well, and she becomes 2-0 (0.8452), the Gittins Index suggests sticking with her. However, a bad date changes her standing to 2-1 (0.7072), still slightly better than 0-0, prompting the Gittins formula to recommend staying with Sakshi. If there's another bad date, bringing her to 2-2 (0.6010), the formula suggests considering other options, as there's a reasonable chance of finding someone better.
It's essential to note that Gittins Indices also take into account the time factor, incorporating the concept of discounting. This means that finding the ideal person at a younger age is more valuable than finding them later in life. Different Gittins numbers may result from using various discount values.
For instance, Wikipedia's example involves choosing between wind power and wave power, and the Gittins Index advises trying one and sticking with it as long as it performs well. Up and Atom on YouTube explores using this concept in restaurant decisions, deciding whether to stick with a favorite or try something new. The key is to switch to something different as soon as your favorite falls below the 0-0 index, indicating a decline in its performance. If it consistently stays above this index, it's a good indication to stick with it and enjoy the experience.
“…younger age is more valuable than finding them later in life….”, I used this line, Now let’s talk about BRAKES!
37%
Life is a series of decisions, each with its unique set of challenges and opportunities. The optimal stopping problem, a classic concept in decision theory and mathematics, sheds light on the dilemma of choosing the best option among a sequence of possibilities, emphasizing the delicate balance between exploration and exploitation. At its core, the optimal stopping problem poses the question: When is the right time to make a decision and commit to a particular option, considering the uncertainty of future outcomes? This dilemma is pervasive in various aspects of life, from job interviews and dating to selecting the ideal house or car. In a simplified mathematical model, the optimal stopping problem involves evaluating a sequence of options, with each option revealing its quality only when chosen. The challenge lies in deciding whether to accept or reject an option based on the information available at each step, knowing that once rejected, an option cannot be revisited.
Again, for the maths, UCLA and Towards Data Science article. Other’s, follow me,
Imagine you're in the process of searching for your dream home. The optimal stopping problem comes into play as you encounter a series of potential houses, each with its unique features and drawbacks. The challenge is to decide when to make an offer and commit to a particular property, knowing that once you move on to the next option, you can't return to a previous one.
The first step in applying the optimal stopping strategy to house hunting is to establish criteria based on your preferences, needs, and deal-breakers. This could include factors such as location, size, price, amenities, and the overall condition of the property.
Initially, explore the market without making immediate commitments. Attend open houses, gather information, and get a feel for the available options. Resist the temptation to make an offer too soon, as this prevents you from fully understanding the range of possibilities.
As you explore different houses, use the information gained to establish a benchmark. This benchmark represents the minimum criteria that a house must meet for you to consider making an offer. For example, if a house exceeds your benchmark in terms of price, size, and location, it becomes a candidate for serious consideration.
The optimal stopping problem requires you to set a decision threshold. This threshold represents a point at which you commit to making an offer on a house that meets or exceeds your benchmark. Until you reach this threshold, your goal is to gather as much information as possible and refrain from making premature decisions.
Once a house surpasses your decision threshold and meets your established criteria, it's time to make a commitment. Submit an offer, negotiate terms, and proceed with the purchase process. This ensures that you capitalize on the best option available to you based on the information you've gathered so far.
The optimal stopping problem acknowledges that perfection may be elusive, and waiting for the ideal house may lead to missed opportunities. The strategy encourages you to balance the desire for the perfect home with the need to avoid regret. By setting realistic criteria and a decision threshold, you increase the likelihood of finding a home that aligns with your preferences and meets your needs.
According to the 37% rule, you should set a decision threshold of approximately 37% of the total number of options. This means that during the exploration phase, you don't make any decisions but carefully observe the first 37% of the options.
How we came to the number 37? Not explaining it here, try the proof.
At this point, you must be thinking. Although it makes sense(Would feel like an epiphany for 10 minutes then it would make so much sense), why complicate things? Let’s go for a party now,
Plato’s RAVE
Imagine you and your friends like to play with shadows on the wall with a flashlight. It's so much fun! But one day, someone tells you that there's a big world outside the room you're in.Plato, a very smart person from a long time ago, talked about something like this. He said it's like people sitting in a dark cave, watching shadows on the wall. These shadows are made by things outside the cave, but the people inside can't see the real things, just the shadows.
So, it's like your friends and you are in this dark cave, having fun with the flashlight and making shadow animals on the wall. But outside the cave, there's a big, bright world with real animals and trees and so many exciting things.
Plato wanted us to think about how sometimes we might only see a little bit of the world, like the shadows on the wall, but there's a whole big world out there to explore and learn about. The cave is like our little world, and going outside is like discovering new and amazing things beyond what we already know.
But, what if you don’t like the outside world? What’s stopping you and your friend’s to go back to plying with your flashlights in the cave again?
Two conditions here,
First let’s discuss that the cave(personal rave party), is going good. Is it sustainable for you to continue and keep the snacks running? Are you capable enough to keep the party running when you know there are outside factors that might come for you? Obviously, ignorance is bliss. Until it slaps you in the FACE.
Second being you have to take up things from outside the cave. Are you humble enough to give up on your prejudices and accept what other people and the world has to offer? Think about it, even a sunrise is going to be something very new to you. But, it’s the sunrise, something very absolute that you didn’t know about for a really long time. And will the people in your cave allow you to go out?
Ponder about these in your context. What exactly stops us(You and me) from doing things that we need to do and more importantly, getting to know of things that we need to do?
How sure we are(and should be),about so many things that we hold so dear. Principles, values, everything. Not like we don’t have any. Most people do, and you have a bestfriend(maybe) because your beliefs align. You don’t (and don’t want to) be around people who say things that don’t align with your world view. Does that mean you are in a echo chamber(Your own party)? Well, let’s do some maths again,
Bayesian Epistemology
I swear it’s not about maths, but grab a pen and paper and bear with me. You are in a hospital and doctor says you have a disease that hails on 0.1% of the population, the tests came out to be positive. But you ask “Doctor, how sure are you about the test?” 99! Does that mean you are dead? well , let’s stop panicking for once,
This is the Bayes theorem, the cornerstone in mathematics to calculate conditional probability. And here’s where the life part starts, so bear with me
When you plug the numbers like this, it’s just 9%. Just nine percent, and why do we have that low number, because the number of people affected vs. how accurate the test is huge, so in layman terms, out of a 1000 people, the test would falsely identify 10 people as sick and one person would actually be sick. So 1/11, roughly 9%. But you were not content with the result so you consult your second doctor and you ae positive again, let’s plug in the numbers again, where the probability of you having the disease is 9%, the new probability is 91%!!!, which is logical when you think about it.
Now the conclusion,suppose a caveman comes out of his cave for the first time and sees a sunrise, can he say, with 100% assurance that this is how the world works? Well , he can’t. He would have to see it for more than one time. And everyday he can be a bit surer that there’s a thing called sunrise. Our beliefs need to be updated systematically. This highlights the importance of challenging our beliefs and experimenting, because you cannot be one hundred percent certain about things just because they seem intuitive.
But what if you are 100% certain? Let’s plug 100% into the equations, and we find out that no amount of experimentation can change your mind. So another thing that we can take from this experiment, dogmas are never good. Having yourself open to new possibilities is far better than sticking to the same ideals and never learning.
This section was actually inspired by Vertasium’s this video.
I came around this really song this week, an indian hip-hop artist who’s got insane bars, doing my part by trying to promote him.
That was all for this week! be mindful of your decisions. Go venture into the greatest dephts of what world has to offer, and I would wish you very best in dveloping the acumen to do so, because there are obviously going to be reppercussions.
Adios!