Hello, friend.

Welcome to another issue of Mind Macros - I hope you find something of value.

Food for Thought

I.  Reference frames

"In more abstract terms, we can think of reference frames as a way to organize any kind of knowledge. A reference frame for a coffee cup corresponds to a physical object that we can touch and see. However, reference frames can also be used to organize knowledge of things we can’t directly sense. Think of all the things you know that you haven’t directly experienced. For example, if you have studied genetics, then you know about DNA molecules. You can visualize their double-helix shape, you know how they encode sequences of amino acids using the ATCG code of nucleotides, and you know how DNA molecules replicate by unzipping. Of course, nobody has ever directly seen or touched a DNA molecule. We can’t because they are too small. To organize our knowledge of DNA molecules, we make pictures as if we could see them and models as if we could touch them. This allows us to store our knowledge of DNA molecules in reference frames—just like our knowledge of coffee cups.

"Reference frames are not an optional component of intelligence; they are the structure in which all information is stored in the brain. Every fact you know is paired with a location in a reference frame. To become an expert in a field such as history requires assigning historical facts to locations in an appropriate reference frame. Organizing knowledge this way makes the facts actionable.

"A well-known trick for remembering a list of items, known as the method of loci or sometimes the memory palace, is to imagine placing the items you want to remember at different locations in your house. To recall the list of items, you imagine walking through your house, which brings back the memory of each item one at a time. The success of this memory trick tells us that recalling things is easier when they are assigned to locations in a familiar reference frame. In this case, the reference frame is the mental map of your house. Notice that the act of recalling is achieved by moving. You are not physically moving your body, but mentally moving through your house." — From A Thousand Brains by Jeffrey Hawkins (view my three takeaways).

Joshua Foer won the 2006 USA Memory Championship using the method of loci, memorizing 52 cards in 1 minute and 40 seconds, a U.S. record. A year earlier, Foer regularly forgot where he left his car keys and had no intention of ever participating in a memory championship. Foer's book, Moonwalking with Einstein, documents his journey while exploring how techniques like mnemonics and the method of loci (memory palaces) can help anyone improve their memory.

Foer's example is anecdotal and may be domain-specific, i.e., Foer can memorize lists by using these tricks but can’t apply them to everyday life (he might still forget his keys). This is an example of domain dependence, where a person understands a concept or skill in one domain but fails to apply it to another. Yet, despite these objections, Foer's story showcases the malleability of memory.

According to Hawkins' research, if we wish to recall information at scale or achieve expertise in a field, we should assign knowledge pieces to a map (reference frame). I've used the analogy of a tree in previous issues to represent a knowledge map, where we can hang novel concepts on existing branches of knowledge. Now let's explore how building such reference frames (or maps) can help us learn complex concepts.

II. Frameworks for learning

"If all knowledge is stored this way, then what we commonly call thinking is actually moving through space, through a reference frame. Your current thought, the thing that is in your head at any moment, is determined by the current location in the reference frame. As the location changes, the items stored at each location are recalled one at a time. Our thoughts are continually changing, but they are not random. What we think next depends on which direction we mentally move through a reference frame, in the same way that what we see next in a town depends on which direction we move from our current location.

"But what kind of reference frame should the brain use for concepts like economics or ecology? There may be multiple reference frames that work, although some may be better than others. This is one reason that learning conceptual knowledge can be difficult. If I give you ten historical events related to democracy, how should you arrange them? One teacher might show the events arranged on a timeline. A timeline is a one-dimensional reference frame. It is useful for assessing the temporal order of events and which events might be causally related by temporal proximity. Another teacher might arrange the same historical events geographically on a map of the world. A map reference frame suggests different ways of thinking about the same events, such as which events might be causally related by spatial proximity to each other, or by proximity to oceans, deserts, or mountains. Timelines and geography are both valid ways of organizing historical events, yet they lead to different ways of thinking about history. They might lead to different conclusions and different predictions.

"My point is that becoming an expert in a field of study requires discovering a good framework to represent the associated data and facts. There may not be a correct reference frame, and two individuals might arrange the facts differently. Discovering a useful reference frame is the most difficult part of learning, even though most of the time we are not consciously aware of it. I will illustrate this idea with the three examples I mentioned earlier: mathematics, politics, and language.

"Say you are a mathematician and you want to prove the OMG conjecture (OMG is not a real conjecture). A conjecture is a mathematical statement that is believed to be true but that has not been proven. To prove a conjecture, you start with something that is known to be true. Then you apply a series of mathematical operations. If, through this process, you arrive at a statement that is the conjecture, then you have succeeded in proving it. Typically, there will be a series of intermediate results. For example, starting from A, prove B. From B, prove C. And finally, from C, prove OMG. Let’s say, A, B, C, and the final OMG are equations. To get from equation to equation, you have to perform one or more mathematical operations. To a mathematician, equations are familiar objects, similar to how you and I see a smartphone or a bicycle. When mathematicians see a new equation, they recognize it as similar to previous equations they have worked with, and this immediately suggests how they can manipulate the new equation to achieve certain results. It is the same process we go through if we see a new smartphone. We recognize the phone is similar to other phones we have used and that suggests how we could manipulate the new phone to achieve a desired outcome." — From A Thousand Brains by Jeffrey Hawkins.

Having a well-stocked storehouse of mathematical equations in one's memory can be an invaluable asset for problem-solving. These equations can be utilized as a blueprint to bring insight and direction to new material. Instead of starting from square one, past equations can lay the groundwork for approaching future problems. Solving mathematical equations requires more than just memory, but I'd like to explore this aspect in another domain, chess.

The current world champion and widely considered the greatest player of all time, Magnus Carlsen, is often praised for his memory. Dubbed the Mozart of chess, Carlsen holds the highest rating in history and is the youngest player to rank number one in the world, a title he's held for the last 11 years.

Carlsen estimates he’s memorized 10,000 chess games. This encyclopedic knowledge of past games has been tested on multiple occasions with impressive results. One video shows chess grandmaster David Howell (ranked 96th in the world) challenging Carlsen by setting up historical positions on a board and asking him to name the game. Not only does Carlsen get every single one, he often does so before Howell has finished setting up the board. Several times in the video, Carlsen volunteers the continuation (the next handful of moves for both sides). He can even remember games taking place on the table next to him (while engaged in his own) from 19 years ago.

Levy Rozman, an international chess master and content creator, believes that Carlsen's memory is his standout ability, stating on a podcast:

Carlsen might get the [strategic complexity of positions] from an enormous database within his brain of historical games with similar structures or just sheer genius; we won't know. It's probably a mix of the two. The younger you are, you can't remember a game played in 1951 in some bar in the Soviet Union, but [Carlsen] does because he read it in a book or magazine, and he just remembers it.

When asked what makes Carlsen so good, Rozman answered:

"I think it's the memory, and he seems to just 'get' the game better than anyone else."

Rozman's example of the 1951 game may appear to be an exaggeration. However, in the abovementioned video, Howell throws Carlsen a curveball, presenting a chess game from the first Harry Potter movie. To everyone's surprise, Carlsen remembers the game and can recall the next several moves. It’s unlikely this would have been a game he studied nor attempted to commit to memory, showcasing his ability to absorb games without effort. This aligns with Carlsen’s preferred method of practice which involves reading books and studying historical games rather than the conventional approach of drilling moves, solving puzzles, and using AI engines.

My hypothesis (from my limited knowledge of this field) is that Carlsen has absorbed the entire history of chess games (that he can access) and uses that database to act as scaffolding for his dominance over the board. Rather than drilling purely theoretical moves, he absorbs experience, heuristics, and practical tricks from historical games.

Nassim Nicholas Taleb, a mathematical statistician and essayist observed that classroom knowledge is fragile, while real-life knowledge combined with a library is antifragile. A fragile system breaks under uncertainty, whereas an antifragile one strengthens under the same circumstances. Fragile knowledge is pure theory, while antifragile knowledge is experience meets wisdom. A theoretical approach to chess might seem like the ideal strategy, but Carlsen notes that at his level, often making suboptimal moves to throw your opponent off is more effective. These are the sorts of practical tricks Carlsen can absorb from historical games rather than the pure theoretical moves of the AI engines (that most players use for practice). 

This line of reasoning leads to the age-old debate between rationalism and empiricism. In philosophy and science, rationalism is knowledge derived from theory, reason, and logic, while empiricism is knowledge derived from experience, observation, and experimentation. Carlsen leans toward empiricism, with his love of books and historical chess games combined with mental experimentations. All of this preparation builds out Carlsen's reference frames and provides him with a database that informs his own ingenuity, creativity, and perhaps, dare I say it, genius. [1]

Quotes to Ponder

I. Epictetus on our lives being the result of how we spend our attention.

"You become what you give your attention to...If you yourself don't choose what thoughts and images you expose yourself to, someone else will, and their motives may not be the highest."

II. Richard Feynman on following our curiosity.

“Study hard what interests you the most in the most undisciplined, irreverent, and original manner possible.”

Wishing you and yours a happy holidays.

Thank you for reading,

Matthew Vere

‍

[1] Carlsen doesn't literally think this way. He has stated several times that he 'just knows what to do' instantly and spends his time mentally reviewing the move when in matches. Nevertheless, I believe that the extent of his reference frames influences the mechanisms informing his innate senses.