[MUSIC, Title: "Compression is the Name of the Game!"] [Beth] I'm telling you Barb, those links are declarative. [Barb] They're procedural. [Beth] No, they're declarative. [Barb] If I tell you enough times they're procedural, are they procedural? [Beth] Very funny Barb, but it's like we said in the previous video, if you do pretty much whatever enough times, procedural links will start to develop. But those initial declarative links can still be there, lurking in the background. Some activities especially lend themselves to becoming, or almost becoming, procedural links. Walking, biking or driving your way home— of course, once you repeat the trip enough times— change your thoughts from declarative, conscious effort (am I supposed to turn left or right here?), to procedural, unconscious activities. That's when you can find yourself arriving home without even being aware of how you got there. Hauling out information or thought processes through the procedural system makes things much easier on the brain. It's like you having a nice bag of marbles that you can easily grab instead of having to go and pick each marble individually. Think of the first time you tried to unlock a combination lock on a wall locker. It was tedious as you tried to remember the numbers and get the hang of how the lock works. But once you unlocked the combination lock enough times, the process became automated. You barely needed to even think about it and could unlock your padlock in seconds. [Barb] A key idea is that the procedural system likes to take over on activities performed repeatedly through TIME, such as, playing a snippet of song on the piano. Or reciting a poem you know by heart. Or saying "spaghetti!" (pronunciation of "spa-ghe-tti" occurs over time). Or any other word you know well in your native language. Or even learning math facts, such as 4 + 6 =10. You might think this all relates to rote, meaningless memorization of a response to a cue— like seeing the numbers 4 + 6 and responding with the word "ten." But it turns out that this process is not at all just rote memorization with no conceptual understanding behind it. In fact, there is evidence suggesting that both reading and math rely, at a foundational level, on simply being able to stimulate a response when given a cue. That's "psychology speak" for responding in the way you've been taught to respond. A student sees the letter B and they respond with a [b] sound. They see the numbers 2 and 3 connected with the multiplication sign and respond automatically by saying, or thinking, 6. This is an important skill and children who can't do it, experience dyslexia or dyscalculia. In fact, there's a 40% commonality between dyslexia and dyscalculia—meaning if the students experience one condition, there's a substantially increased chance they'll experience the other. More about this, in the next week as we talk about neuro diversity. Remember, the brain's watchdog, the prefrontal cortex, keeps a careful eye out for repeated physical motions or thoughts. [Beth] When we learn to play a musical instrument, for example, we often learn to play small snippets of a complex song. These song snippets are like subroutines. Eventually, these snippets are knit together as a full song. [MUSIC] [Terry] Similarly, learning to serve a tennis ball requires a dozen or more motor subroutines that have to be seamlessly integrated, from throwing up the ball, how to prepare your swing, aiming at the hit and the follow through, and all the bridges in between these steps. [Barb] Learning to pronounce words and sentences in a foreign language can also involve complex subroutines as you learn the skills needed to pronounce different sounds. Saying, "Hello, how are you?" may seem simple and it is simple for a well practiced English speaker. But try saying the Russian equivalent: "Здравствуйте, как вы поживаете?” and you can find yourself struggling. [Terry] Even advanced patterns of mathematical thinking can be automated and done unconsciously after they've been done so often. The higher math level is equivalent to the procedural learning of an eloquent piece of music. Or making a powerful serve in tennis. Or speaking flawlessly and intuitively in a second language. In math, we can learn how to prove theorems using the procedural system. Each proof may require a dozen different corollaries which are themselves smaller proofs. Each with its own specific way of setting it up for different types of problems. It takes a lot of practice to become fluent at these steps and knowing how to apply them. I remember learning to prove theorems and nucleus geometry slowly, one at a time. But eventually they became easy. But it took a lot of practice to get the hang of it, and eventually I could prove new theorems fluently. No wonder it's a struggle. It's the same as learning how to play tennis, but with your mental muscles instead of your body. One of the big differences between experts and novices is that, as researcher Miseom Shim and her colleagues note, quote: "Experts retrieve chunks, patterns or templates that are made of stimulus-response associations stored in long-term memory and apply them for their professional performance." Let me decode that for you. It means that experts, such as mathematicians studied by Miseom and her colleagues, appear to process key building blocks of their work in mathematics through links laid down by their procedural system. They do this instead of getting involved in the detailed actual calculations. In other words, as mathematicians acquire their expertise, they build sets of neural links that are accessible unconsciously through the mysterious box that is the procedural system. It's worth quoting William Thurston, winner of the Fields medal, the top award in mathematics. Quote: "Mathematics is amazingly compressible. You may struggle a long time, step by step to work through the same process or idea from several different approaches. But once you really understand it and have the mental perspective to see it as a whole, there is often a tremendous mental compression. You can file it away, recall it quickly and completely when you need it, and use it as just one step in some other mental process. The insight that goes with this compression is one of the real joys of mathematics. And you, too, can experience this by practice, practice practice. [Beth] I'm Beth Rogowsky. [Barb] I'm Barb Oakley. [Terry] I'm Terry Sejnowski. [All] Learn it, link it, let's do it!