Dr. Igor Halperin On Physics, Ai & Their Unexpected Interplay With The World Of Finance
A Mental Walk With Dr. Igor Halperin!
Rebellion Research: How has your background in theoretical physics influenced your approach to quantitative finance and modeling in the financial markets? Are there specific principles or methodologies from physics that you find particularly relevant in the field of finance?
Igor: To answer this, let me start with my story. After I got my Ph.D. in theoretical particle physics and did two postdocs, my second postdoc time was probably the worst time for those in particle physics. This is because, during these years, there was a huge project called Superconducting Super Collider (SSC) that was supposed to be funded by Congress to the tune of approximately $400 million. If the project went through, it would have provided plenty of projects and work for physicists like me. During my second postdoc, this project was shut down, and many people found themselves without jobs. In my particular field, there were only a few faculty jobs in physics departments in the US, and they all went to folks working on string theory. So I decided to leave physics and change my career path. I had a strong math background because theoretical physics uses lots of math and I wanted to utilize it, but beyond this point, I did not have any clear idea what to do.
I then started to think about what I could do next. At first, I considered electrical engineering since it used math. But I quickly found that the math they used was mainly just the Fourier Transform and nothing else, so it looked boring to me. But then what really shaped my thinking was that I saw many physicists turning to finance and starting to apply methods from physics to finance.
During my postdoc, the first thing I would do in the morning to start my day would be to check out the most recent papers on ArXiv.org. That is when I first came, around 1998, across papers written by physicists who applied techniques that I already knew to finance problems. I kept reading these papers offering alternative financial models, even before learning anything about the original finance models themselves. So, in a sense, I entered finance through the backdoor, instead of the front door.
When I discovered these papers, I thought finance is very interesting for physicists, as we have our own methods to look into complex systems such as financial markets, and with particular methodologies that are absent in classical finance. In particular, physicists are skilled in constructing mathematical models that focus on the most essential parts of dynamics of complex systems and strip unessential details, and then in accessing these models by considering their various theoretical limits. A great physicist Paul Dirac, who was one of the creators of quantum mechanics, once said that if you are humble and patient, then your equations will lead you by the hand to the right answer. My other hero in science, Richard Feynman, said once that the best way to understand something is to try to explain it or teach it. Which I found to be exactly right. I did find interesting scientific questions when I was trying to conceptualize and explain things that I discovered.
So in my case, I worked on my models, and then tried to understand what they imply. After this, I was able to identify major issues with almost all of the standard financial models used by practitioners in the field. I am not talking about all existing models, because obviously there is a rich academic literature, and it would be impossible to grasp everything that exists out there. However, I know which models people use in practice, and this research led me to identifying a major issue with all of these models.
Dr. Halperin debated Exodus Point’s Head Quant Peter Cotton at Cornell School of Financial Engineering’s 2023 conference. Moderated by Databento CEO Christina Qi.
The major issue is this: as financial engineering students, you learn about Black-Scholes, diffusion models, and stochastic differential equations which are given by drift and diffusion terms: a drift term is the deterministic part, and a diffusion term is the stochastic part. The most famous model of this sort is called the Geometric Brownian Motion (GBM) which is considered the most foundational model, and is the same model used to model stock prices in the Black-Scholes model.
All models that came after the Black-Scholes extended the GBM dynamics by modifying only its diffusion term. In the original Black-Scholes model, volatility is a constant parameter, but this model does not fit the market data.Then people said, we can make the diffusion/volatility term more complex by introducing local volatility that depends on the stock price, or by making volatility itself a stochastic process. The latter models are called stochastic volatility models.
What is the problem here? I think the problem is this: All modifications of the Black-Scholes model focused on the diffusion term in the dynamics, but totally missed the importance of the drift term. Black, Scholes and Merton even doubled down in a sense on this point, by claiming that the drift term is not important altogether. But this is again a wrong conclusion that follows from taking a continuous-time limit which is fine mathematically, but not financially or physically justified. Still, these are a bit more technical points. Most importantly, in all these models, the drift term can be of only two types. The first type is the standard form of GBM which gives you a linear drift term which is a linear function of the stock price. You can work instead with logarithms of stock prices instead of prices. In these transformed variables, the linear drift of the GBM becomes simply a constant drift. These are essentially the only two choices for the drift in these models: you have the drift term either as a constant term that does not depend on the underlying stock price, or as a linear term which is a linear function of the underlying. Now I am saying this is wrong.
To explain why I think this is wrong, let me first note that the GBM model is a special case of a more general family of models which is called Ito’s diffusion. Ito’s diffusion has the same structure with a drift term and a diffusion term. Both can be arbitrary functions of the underlying stock price in the general case. But in the particular case of the GBM model, both these functions are linear.
The critical observation here is this: you can definitely view Ito’s diffusion as a mathematical equation with certain drift and diffusion functions. In mathematics, both are some functions of the underlying stock price. However, if we turn to physics, we find that we can give a very particular physical meaning to the drift term. This is because Ito’s diffusion is mathematically equivalent to a well-known equation in physics called the Langevin equation. This observation provides valuable insights about what form the drift term should have in order to provide realistic dynamics.
Here is a story. It is well known that it was Louis Bachelier who came up in 1900 with the first theory of Brownian Motion, to apply it to modeling of stock prices. Albert Einstein came up with his theory of diffusion 4 years later, in 1904. The math of both models was the same. This fact is well known in the financial mathematics community, and is often recalled in various talks devoted to the history of the profession.
What however strongly surprised me was that while everyone in quantitative finance have heard of Bachelier and Einsteins theory of diffusion, most of the researchers (or maybe even all of them) missed another groundbreaking work that was done in 1908, only 4 years after Einstein, by the French physicist Paul Langevin. Langevin extended upon Einstein’s theory which is a theory of free Brownian particles. Langevin explored what happens if these particles also experience an influence of some external field created by large molecules, or a magnetic field, or something like that. In this case, we don’t have free diffusion anymore, but instead we have diffusion in an external potential field.
Strikingly, the Langevin equation has the same mathematical structure as Ito’s diffusion, i.e. it has a drift and diffusion terms. But this means that any particular Ito’s diffusion can now be interpreted in physics terms as a Langevin equation. The value of this interpretation is that it provides insights into the drift term. Specifically, the drift term now is not just a general mathematical function, but rather a negative gradient of the potential function of the Langevin equation. This means that if you have a potential function as a function of the stock price, you take a partial derivative of this function with respect to stock price and flip the sign of the whole expression to get the drift term of the price dynamics.
Now recall that the GBM model has a linear drift. Now we understand that linear drift should be the negative gradient of a potential. the function should be quadratic to get a linear function after differentiation. You also have to flip the sign since we are concerned with a negative gradient. If we do that, we can now identify the potential function corresponding to the GBM model. The resulting potential is an inverted parabola – a quadratic function of the price with a negative coefficient. In physics, this potential is sometimes referred to as an inverted harmonic oscillator potential, or a ‘negative mass’ harmonic potential.
So by a simple side-by-side comparison of two very well known equations, the GBM model and the Langevin equation, I found that the GBM dynamics corresponds to the dynamics of an inverted harmonic oscillator in a noisy environment. The keyword here is ‘inverted’, because this system has unstable dynamics, and can never reach any equilibrium state.
What does this tell me as a physicist? It immediately tells me that the GBM model, and all its offspring, simply cannot be complete and self-consistent models, similar to how classical mechanics is not a complete model, and should be replaced by quantum mechanics for very small distances, or by relativity theory for very high velocities. This is because all of these models inherit the same drift – which implies unlimited unstable dynamics which are not stopped at any point according to the model.
Dr. Halperin & long-time collaborator Dr. Matthew Dixon won Quants of the Year for 2022!
But as a physicist, I also know that unbounded instability never ever occurs in the Universe. There are some physical systems that become unstable but only for a short period of time, and never indefinitely. And yet, if you look at financial models through the lens of physics, you can immediately see that something is wrong with all of these models. All of them end up with a linear (or constant) drift which implies globally unstable dynamics. Also, a linear drift implies that we deal with a linear physical system. We have heard many times that financial markets are highly complex, nonlinear systems, and yet we describe the price dynamics using models with a linear drift? What is going on here?
Obviously, if you make volatility stochastic, you can get quite complex patterns of the price dynamics that may look fancy. But in physics, we have a great way to explore our theories by considering various theoretical limits. For example, we can analyze the limit when volatility goes to 0. In this limit, the model becomes completely trivial, because the drift is linear, and thus no interesting dynamics can be established. Many people believe that it is enough to consider complex volatility dynamics to make models consistent with market data. But I am convinced that when people miss nonlinear effects in their models, they are ‘fooled by randomness’, using Nassim Taleb’s expression.
But I found a remedy for this. I know how to construct better models that appeal again to ideas from physics, namely physics of open and nonlinear systems. I am saying that what was missing in the previous models are two things. First, everyone knows that there are money flows into the market, and the major source of money flows are pension plans such as the 401k plans. Second, money flows into the stock market produce financial frictions. While commonly known, these two things are not taken into consideration in the standard models. But these are exactly the two things that together produce a potential for the drift that I expected on the general ground using physics principles. More precisely, incorporating these two phenomena in the modeling framework produces a quartic polynomial in the stock price as a model for the drift potential. If we have a quartic potential, then our drift term must be a cubic function of the stock price, and this cubic drift function is what eventually stabilizes the dynamics.
Rebellion Research: Thanks for that fantastic response. Now why don’t we pivot towards machine learning and AI in finance? What specific challenges or problems in finance do you think AI and machine learning have been most effective in addressing?
Dr. Halerin & Dr. Dixon debating at the MIT Quant & Ai Conference.
Igor: When people talk about AI in finance, they usually refer to Large Language Models. The very definition of what we call AI is continuously changing. Until very recently, when people discuss AI, they usually meant deep learning and various supervised learning algorithms. More recently AI in finance became associated with reinforcement learning thanks to work from DeepMind and OpenAI. And since ChatGPT, when my colleagues talk about AI, they often mean Large Language Models (LLMs). LLMs are useful as a way to process information, and interact with the computer to explore documents, transcripts, databases, and knowledge graphs. That’s where they are useful. But they can’t reason well enough to replace human asset managers who plan for long time horizons. On this, Andrew Ng once said that AI gradually replaces humans in all tasks, but starting with tasks with very short time horizons. Examples of such short-horizon tasks in finance are high frequency and intraday automated trading and optimal execution tasks.
Consider for example the latter problem of optimal trade execution, where the problem of the trader is to buy or sell a specific number of shares during a certain time window, e.g. a day, such that to minimize the negative market impact from the trade, In general, this problem is a perfect use case for reinforcement learning (RL), where our time horizon would be one day. We are reasonably confident that ‘features’ needed for such RL formulation would only use data from the limit order book (LOB), and not, say, the Treasury rates or the inflation rate. The reason is that the latter factors do not show any significant changes at the daily scale, and hence simply can be viewed as constants and dropped from the modeling framework, when dealing with such short-time problems.
On the other hand, for other financial problems our time horizons can be weeks, or months, or even years. Certainly, factors such as Treasury rates, GDP, inflation rate etc. become very important for such long time horizons. On top of this, there are other risk factors that do not necessarily get incorporated into models, such as geopolitical risk or epidemiological risk. All this makes problems of portfolio management with long time horizons more difficult than problems with short horizons.
This is why in my view, what we need to do is to work towards some sort of symbiosis between AI and human intelligence. We are not trying to build fully autonomous systems. It is more about developing helpful tools that will allow us to more efficiently do what we do. And there is no limit on this front.
You asked me where I see AI being most useful in finance. I see two such areas. Firstly, AI and machine learning methods enable flexible extensions of traditional quant models, and their improvements by better handling of non-linearities and co-dependencies in the data. In this direction, we do not expect any revolutionary changes. It is highly unlikely that by data crunching, someone will be able to develop a super-duper algorithm that will make them all the money in the world. The second area is of course the language models that facilitate a more natural interaction of humans with computers, and can even help with writing code. But what we do with LLMs in finance is not much different from what people do in other industries. We just tune LLM using our vocabulary, terminology, and documents.
Rebellion Research: I’m glad you brought up reinforcement learning. I know you are a big advocate for it and I would love to touch on it later on after a few more general questions. You have spent much time applying machine learning to portfolio modeling. Can you explain how machine learning is used in portfolio modeling and portfolio optimization?
Igor: The traditional approach to portfolio management involves essentially two steps. First, we get trading signals. These trading signals go into your portfolio model. For example, you can use the Black-Litterman model which is a Bayesian model for portfolio investment. It works by saying that we have two types of trading signals: common signals known to everyone, and private signals only known to us. Now we can make some inferences. If we take the market portfolio as given, we can invert our model, and get ‘implied’ common signals that are available to everyone. Then we can add our private signals to our portfolio model, and find a new portfolio that is hopefully better than the market portfolio. This is how most of the models work. The role of machine learning with these approaches amounts to finding informative trading signals.
Rebellion Research: Great, so why don’t we dive into reinforcement learning and how it connects to portfolio management?
Igor: Vladimir Vapnik, one of the fathers of modern machine learning who invented support vector machines, once formulated his principle, now commonly referred to as Vapnik’s Principle, which I found a great motivation for reinforcement learning. Vapnik’s principle says that if you have a main goal, it is not optimal to first try to solve an intermediate problem, especially when such an intermediate problem is itself hard.
Reinforcement learning is actually an implementation of this very idea. Indeed, finding good trading signals is a hard problem. You construct them in order to plug them back into your original model and make your decisions based on these predictive signals. From the perspective of Vapnik’s principle, this is your intermediate process. You only need this step of building predictive signals just because of your framework. You don’t need it on its own. We are not in the business of exploring the world for the sake of exploration; we are in the business of trading. Our main task is action – which is exactly reinforcement learning.
Having said that, there are many approaches in reinforcement learning. RL is a framework that works with problems of optimal control, rather than a particular numerical approach. There are versions of RL that do more or less similar things to what we just described. They use external trading signals, along with some internal models of the world, to find optimal investment decisions. Such methods are known as model-based RL.
But it is not the only way, and other, model-free RL methods such as e.g. Q-learning may proceed without any external signals or a model of the world. Essentially, they say that as long as we have an informative set of features, any trading signals would be found using the same features.
So why do we split our main task artificially into sub-tasks? Why do we first use some set of these features to construct signals and then bring them back, run the model, and then decide what to do? Because there is something called model risk in the first step – the first step of constructing signals.
Instead of splitting all available features into features used to construct signals and features used to make decisions, we can bypass this and use reinforcement learning via a model-free approach where we don’t try to do these steps. Of course, nothing comes for free – model-free RL methods require much more data than model-based RL, where the above steps are required. But these are details – I like RL in general because it is essentially about what we do in finance. Indeed, at least conceptually, finance is all about acting on information, but this is exactly the problem addressed by RL. Everything else can be used but only as components for an RL framework. There is a place for supervised learning, unsupervised learning, and language models in this framework. Conceptually, all of quantitative finance is reinforcement learning.
Rebellion Research: You have also mentioned inverse reinforcement learning and discussed a combination of both reinforcement learning and inverse reinforcement learning. Can you elaborate on this?
Igor: Inverse reinforcement learning (IRL) is an inversion of the problem of reinforcement learning. In IRL, you observe actions of a human or robot agent, and then you try to explain this observed behavior in terms of agent’s optimization of a total reward function. The reward function is what defines a reinforcement learning task, as it specifies the objective of the agent. In many cases, we observe the behavior of an agent, but we do not know the reward function that the agent tried to maximize. The task of inference in IRL is to recover the reward function from the observed behavior of an agent.
IRL is used in situations when the agent’s reward is unknown, but also in cases when finding a good reward function is feasible in theory but cumbersome in practice.
For example, consider a task in robotics where you have to teach robots to move a glass of water from one table to another one. With RL, you have to decompose the motion of the robot’s arm into small steps, and design a reward function to encourage the correct arm’s move for each time step. This problem itself is super hard. Instead, what people proposed is that we can just demonstrate to the robot what to do by literally taking it by its arm and showing it how to do the task. One can then rely on IRL to infer a good reward function that the robot could use going forward to perform its task.
Dr. Halperin after lecturing at Cornell Financial Engineering.
More generally, IRL is appropriate when you see some behavior of an agent, but you don’t know what reward function was used by the agent. This is obviously a much more common situation in real life than the setting of direct RL that assumes that the reward function is known. This is also why IRL is more interesting than RL, because there are so many cases in life where you learn from seeing someone doing something.
Let me give you a practical example of IRL in finance. Let’s say you have a history of trades made by a trading desk, storing the state of your portfolio over a specific time, trade made, and profit-and-loss (P&L) changes of the portfolio. But P&L itself is not yet a proper reward function, which is the important point to understand. A more useful definition of the reward function would be risk-adjusted returns. But you can also go further, and incorporate other elements of the practice of portfolio managers into the design of a reward function. In particular, a paper that I wrote with my colleagues proposed a two-step procedure that combines IRL and RL. It goes as follows. First we design a simple reward function that mimics what the portfolio manager actually does. Even though our reward function is very simple, it captures the most essential task of what portfolio managers do. Obviously, portfolio managers have a lot of things in mind, but we simplify our model, and condense what they do into a very simple reward function which has only 4 easily interpretable parameters. We then use this reward model and the actual trading data within IRL to find parameters of this reward function from data.
This is interesting for two reasons. First, once we infer the reward function from data, we can use our results to implement an RL agent that would mimic what the portfolio managers do. To this end, we use the direct RL. But what is even more interesting is that we found that our RL agent can not only mimic the human traders, it can also improve their strategies! How it improves is also important. For groups of individual portfolio managers that have similar benchmark indexes and similar investment philosophy, our algorithm was able to beat them on average, though it still was not able to beat the best performers in each group. But this is still a very encouraging result, as it demonstrates how IRL and RL can work together jointly.
Rebellion Research: Do you believe there are cases when using RL or IRL individually would be better than using the 2 algorithms together?
Igor: Whether to use them separately or jointly depends on the problem you solve. People rarely use IRL on its own, but people do use RL on its own. If you believe in the particular form of the reward function that you should use, then you don’t need IRL. But if you don’t know the appropriate reward function for your problem, then you cannot move forward without IRL. On the other hand, for certain applications, inference of the reward itself may be sufficient, if for example we use the inferred rewards for classification tasks.
Rebellion Research: Now a more specific question for you. When researching how to approach the issue of retirement planning, you introduced “G-learning – a probabilistic extension of a common reinforcement-learning algorithm known as Q-learning. G-learning is designed to work with “noisy” data, such as financial data. It is also stable because it is guaranteed to converge and produce a unique result.” Can you elaborate more on G-learning?
Igor: Q-learning became very famous after a paper from DeepMind that showed that they can train reinforcement learning agents to play many Atari video games simultaneously using Q-learning. So they combined Q-learning and neural nets to make them more flexible. Q-learning produces deterministic policies, which means that a Q-learning agent will always take the same action in the same state of the world.
G-learning was proposed later by other researchers who proposed that in certain systems, especially noisy systems like those in finance, stochastic policies should work better than deterministic policies, because they can better accommodate the noise in the data and make the model more robust. If you have stochastic policies like those produced by G-learning, it will no longer be the case that every time your system is in the same state, then it will do the same action. This is due to the stochasticity involved. When you work with stochastic policies, when the system finds itself again in the same state, its action might be different from the previous action taken in the same state due to stochasticity. Stochasticity is what provides both exploration and stability in G-learning. In my other work, I used G-learning for portfolio optimization as a tractable way to handle multi-asset portfolios with randomized allocation policies.
But what does a randomized policy mean? It doesn’t mean that your allocations are decided by flipping a coin. You look at your policy as a distribution, and you usually take the maximum point of this distribution as your final allocation decision. But in addition, you take the width of the distribution to assess uncertainty of your decision-making. So in the end, your decision is still deterministic, but there is important extra information in G-learning that is missing in the previous Q-learning approach. With Q-learning, your optimal action is deterministic, but don’t know how accurate your solution is. What happens when your input is a little bit different? Will your actions change a little bit or a lot? In noisy environments, Q-learning may become quite fragile, while G-learning performs better.
Rebellion Research: How would one train reinforcement learning models or other ML models to predict black swan events like COVID-19 and events like wars and other geopolitical conflicts?
Igor: There are certain large and rare market fluctuations such as e.g. large market moves. These fluctuations are called “instantons”, from the word ‘instant’. They are called instantons because they happen very quickly. However, what sometimes takes very long is to wait until these instantons actually happen. You can predict that an instanton fluctuation will happen with a certain probability over a time horizon. However, you can’t predict when the moves will happen, as the theory only gives you the probability that it will happen at the given time interval. Forecasting the timing of such large moves is a different story that I do not know how to solve.
Now with regard to Black Swan events, I do have a little bit to add. I think sometimes what we mean by Black Swan events is a matter of how information is set. For example, in the case of COVID-19, it was not a black swan event for epidemiologists, biologists, etc. because they monitored it. But for some folks on the finance side, who only monitored the market, COVID-19 could count as a Black Swan event. So I believe that events like COVID-19 are not really Black Swan events, because it depends on who is looking into it, and how they look into it. Another example is the 2008 market crisis. There were people who warned about it, and there were also folks who made tons of money by playing against the market during this period. For them, it was not any sort of Black Swan event, since they actually anticipated it. Truly Black Swan events I think do exist, but it might be still tricky to find a good example. For example, would a comet approaching Earth and threatening to destroy it be a Black Swan event? The answer is no, because we would see it coming. So I am not really sure what constitutes a true Black Swan event. Usually, you do have some expectations or indications that a Black Swan event is coming.
Rebellion Research: I do like the perspective that nothing really is a Black Swan event because there are always certain groups of people who can see things coming before most of us. Perhaps expanding on that, how would one tap into the kind of information that these groups of people possess?
Igor: One way which I already mentioned is that you can use models that predict the likelihood of these events, even though they are not able to predict the exact timing of these events. Physicists have previously found some success in predicting the timing of earthquakes, which have highly complex dynamics and are not easily predictable. But when the same group of physicists tried to use similar methods to predict large market movements, this work was more controversial. This shows that predicting the timing of Black Swan events in finance is very hard.
Rebellion Research: Now, where do you see the future of machine learning and AI heading in the next 5-10 years in both finance and in general? Are there any emerging trends or technologies that you find particularly promising in the finance industry?
Igor: It is my long-held view that reinforcement learning as a concept and as a framework is the right framework for most of finance. Having said that, the framework is not yet a tool. I have had many conversations with folks who tried various deep reinforcement learning algorithms for different trading settings. Sometimes it works and sometimes it doesn’t. Sometimes people don’t understand when it works and when it doesn’t. This is mostly because the deep RL algorithms are kind of black boxes methods. Many people in finance just take generic deep RL algorithms from robotics or video games, and make minor adaptations to them by simply changing the format of the data or hyperparameters etc. I have heard many times people say “Oh, we’ve tried reinforcement learning, and it did not work”. What does that even mean? To me, it is the same as if someone tried integral calculus and said it doesn’t work. If you can’t compute integrals, it doesn’t mean that integral calculus doesn’t work. So it’s the same thing here. Don’t blame a particular algorithm that was used. It can fail, but don’t confuse it with the general conceptual framework of reinforcement learning. It is not the same thing.
So I don’t see how reinforcement learning can fail as a concept. It is not the same as saying that a particular algorithm for a particular problem can fail. With regards to the methods of machine learning that I am involved with, like RL and everything that RL uses, my expectation is that things will continue to evolve along these lines, progressively becoming more realistic and more adaptive and perhaps a little more autonomous to a degree. So an ideal situation in the future would be a system that does its job but with few humans who monitor it, so that if anything goes wrong they can intervene.
To sum up, I expect things will become more flexible, better, and more interactive. We want to have AI tools that help us.I don’t mind, and I don’t think anyone minds if we get replaced by AI for certain sub-tasks. It’s not that we have to compete with AI.
Also, it is important to remember that AI in finance doesn’t learn from scratch, but rather can leverage the existing financial models as long as not all of them are wrong, and some are useful. So we should think of AI models as a gradual tuning of previous models that provides their nonlinear or non-parametric extensions. These are gradual improvements and not a revolutionary jump.
Rebellion Research: What advice do you have for individuals looking to become AI/quantitative researchers? What are the most important skills?
Igor: You need to have three sets of skills: math skills, coding skills, and soft skills, mainly presentation skills. Sometimes it takes a lot of effort to understand what people are trying to say. This happens when they don’t know how to structure their thoughts or presentation either in the oral or written form – especially in the written form. Many people don’t have good discipline when it comes to writing documents. This sometimes becomes a major pain when you have to read documents written by such folks – you will waste tons of time trying to understand what is being written.
But above all, self-education is most important. My academic specialization was in experimental physics in my master’s degree, but I self taught myself first theoretical physics, then finance, and then AI. It is hard to develop self-education skills, but once you have it, it becomes a very good weapon for you. For me, when I encounter a new field or topic, I usually perform a Google search, find the most recently reviewed article on the topic, jump into there and if needed, work backward. If I find something I don’t understand, then I go back and try to understand what they meant, and then move forward again. The advantage of studying things this way is that it brings me near to the cutting edge – provided I understand what is being discussed. If you are able to understand a topic, at least in theory you can know almost as much as the people who have spent many years researching it, because they brought you to their cutting edge research.
An advice that stuck with me throughout college is that when you start working on a problem, first spend a couple of days on your own thinking about it. You will definitely be able to make some progress but then you will get stuck. It is when you get stuck that you should turn to external sources of information like Google. When you understand some parts and then start to have specific questions, you will then look for answers to these specific questions. So you end up drilling deeper into these questions, and then develop a deeper understanding. It is also a more economical and efficient way of learning as a result.
Rebellion Research: Thank you for a fantastic interview! It was truly an enlightening experience and I was able to learn a lot. It was truly a pleasure and honor of mine to be able to talk to you and walk through your mind!
Igor: Thank you very much for this interview and great questions!
Written by Max Ong
