…Under Construction…

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Hi y’all,

We are under construction! I am working on retooling the site to be more focused on getting readable information about cognitive science, psychology, and education out to the public. There will be summaries of major scientific papers, introductory articles for those interested in the science of the mind, applications to current events, and, of course, my own crackpot theories on how it all works. On the launch page, you can expect:

• An introduction to embodiment from the Neural Theory of Language perspective,
• Musings on synesthesia, and the origins of Daniel Tammet’s savant-like mathematical abilities,
• Lockhart’s Lament and how Cog Sci can help,
• What Cognitive Science can tell us about concept learning,
• and an introduction to my hands-down favorite concept of all time, cognitive dissonance.

Later articles might include a summary of the Neural Theory of Language model of creativity, some advice and tools for those applying to graduate school, how to study optimally (according to science), why getting older doesn’t necessarily mean getting more absent-minded, and what neuroimaging can tell us about rewards and pleasure – and what that can tell us about happiness.

Overall, it will be more scientifically focused, with a eye to getting relevant information out. I’ve left a few articles up in the meantime for your reading pleasure. Thanks to everyone who’s read and commented so far, and please let me know if there’s anything you’re interested in reading about!

Frank

Learning and the Neural Theory of Language

Neurons!

Today I spent my morning prepping with my SAT students, and it got me thinking about why I want to study cog sci. So here we have an introductory post on The Neural Theory of Language and Why It is Important!

What I want to Study and Why

I first became interested in the study of cognition as an offshoot of my interest in how people learn and how people grow and develop personalities – how do you become who you are? This is due to a combination of genetics and environment, but that’s a topic for another time. As I worked with students, I became more and more interested in how we physically learn – how the information we take in gets encoded, and combined to create new ideas and new understanding. George Lakoff, Jerry Feldman, Srini Narayanan, and their colleagues at Berkeley’s NTL (Neural Theory of Language) project have an interesting answer that both stands up to Occam’s Razor and accounts for the powerful feats of memory and creativity that our brains are capable of.

The Neural Theory of Language

The Neural Theory of Language (NTL) has 2 main tenets: 1) we can only know what we have experienced; 2) we can only experience the world by means of the limited set of senses and emotions the brain possesses; and 3) all of these experiences are encoded in what we call language. 3) seems like the most radical claim of them all, so we will address that later. The rest of this post will address 1) and 2).

1) We understand in terms of what we’ve experienced

What does this mean? Let me ask you a question. What is a pomelo? Is it a piece of furniture, a type of horse-riding gear, or a fruit?

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Don’t know? It’s unlikely that you do unless you have had physical contact with a pomelo, or someone has described it to you before. If I then told you that a pomelo is an yellow-green citrus fruit with a hard peel and seeds, you might have a better idea of what I am talking about.* Similarly, if I asked you to describe a space alien to me, you might recount the blank eyes and grey skin of the ones you saw in Close Encounters of the Third Kind, or the feral, reptilian ones from Alien, or the humanoid eyes of E.T., but likely you would draw from your previous experience with aliens in the movies to tell me what an alien might be like.

This has an interesting corollary in that the same description of a novel object might give different ideas to different people. For example, an “alien” might look different from different people, and the “orange-colored fruit with a hard peel and seeds” might look like a lime to one, a green tangerine to another, or even an yellowish avocado to a third person. This tells us something interesting: that we draw on our previous experience to understand new ones. We mentally model new experiences in terms of old ones. For example, you will have a pretty solid understanding of a pomelo if I compared it to something you already understand: it’s a light green grapefruit.  In this scenario, and many others, we use our previous experience to understand what we are experiencing currently.

2) We can only experience the world by means of the limited set of capacities – senses, emotions, and movements.

If we can only know what we have experienced, we can only experience what we have the senses to do so.  We are not capable of echolocation, like bats are, nor are we capable of seeing heat, like bees do. We are only capable of sight, smell, touch, hearing, and taste, and even those are limited (consider a dog whistle, for example. It produces sound, but we can’t hear it!).

We also come with a set of basic emotions – sadness, anger, fear, happiness, disgust, and surprise**. These emotions, just like our senses, are wired within us, and we start feeling them the moment we are born (likely we cry because we are so overwhelmed by feeling!).

The combination of these senses and these emotions is what allows us to access the world. We are required to use them to translate what is going on in the outside world to something we can understand – for example, we translate light patterns into sight, and sound wave frequencies into tones we hear. We literally could not understand the world without these senses and emotions, and without them, we would not know what to do with the massive amount of stuff going on outside us at all times.

The NTL recognizes that, and takes it one step further. It says that not only do our senses and emotions determine how we understand the world, they literally are what we understand of the world. That is, what we remember of a dog we met at the park is not some abstract snapshot of a dog we created in our minds, but the concrete experience we had with him, what he looked like, what his bark sounded like, and how he felt to pet. What we remember when we think about him is actually those experiences, not some abstract idea of what a dog is. Conversely, our idea of what a dog is comes from our contact with actual dogs.

This fits current theories of concept learning in children. When children are first learning words, say the word “cow”, they at first call everything a “cow”. Birds are cows, fences are cows, horses are cows, and cows are cows. This is because they heard the word “cow” when all these things are around, and they don’t know which one is actually the cow. They applied the label “cow” to everything in their field of vision at the time they heard the word.  Once they gain enough experience with cows, once they have seen and heard one, or perhaps when a parent sits them down with a picture book and says, “This is a cow,” while pointing to the white-and-black spotted animal with horns and an udder, then the child understands that the sound “cow” refers just to that animal, and not to fences or birds or horses or any of the other things that were in his field of vision when he first heard the word “cow”.

So I like the NTL explanation particularly much here because it explains not only how we learn the meanings of words and the things we see in the world, but it also explains why we make the mistakes like we do, like calling horses and birds and fences “cows”. It is the same explanation – that we encode everything we experience, and make sense of it later – that tells us why we learn correctly, and also why we learn incorrectly. This fascinates me with its simplicity and its simultaneous predictive power. My hope is that, with a solid understanding of the processes by which people learn, we can create a more effective system of education, and solve problems like why our math curriculum works for only ~40% of students.

Hope you enjoyed! Next time, I will go further into how the NTL actually works in the brain, talk about mirror neurons, which are some of the most fascinating things to ever exist, and explain what the Neural Theory of Language actually has to do with language. Thanks for reading!

Frank

Footnotes:

* Pomelo example taken from Made to Stick, by Chip and Dan Heath.

** Though whether or not to include others, like love, content, anxiety, and embarrassment, is hotly debated among emotion researchers.

For more information,

• check out the Neural Theory of Language Project website at: http://icbs.berkeley.edu/natural_theory_lt.php,
• pick up Jerome Feldman’s easy-to-read primer on the subject, From Molecule to Metaphor,
• or read Feldman’s introduction and scientific paper on the NTL, cited 155 times so far.

It occurs to me that I should start looking at labs by the citations in that paper…hm…

Cog Sci and Mathematics

After yesterday’s post I had been discussing Michael Ramscar’s papers with some friends, including Alex Hartley, and I had some interesting thoughts on the applications of his research as related to mathematics. Today’s blog post will be a follow-up to yesterday’s, where I will ask a question and

Alex asked,

“So how would this affect color-word learning in languages (like French and Spanish) that put the noun before the adjective (la pomme rouge)? I wonder if any work has been done in that domain? ”

I think that would definitely speed up color word learning, assuming there is no utterance in French/Spanish that change the FL order. As far as I can remember, there exist “C’est une pomme rouge” and “La pomme est rouge” – both of which fit our feature-label order qualifications. A quick Google search for “rouge pomme” turns up only a trendy restaurant, which I am going to assume means that the LF order for colors in French is done for hipness and is not commonly used.

One point that I do want to point out is that this (LF/FL learning order) goes for everything, not just color words. In mathematics, if you take a student who sees just a soup of numbers when he looks at the page, and you ask him, “Which fraction is ‘one-fifth’?”, he will not be able to tell you, just like he can’t pick out which is “the blue ball”. He attends to ‘fractions’ first, and, seeing many, is not sure which you mean. If you say to him, “one-fifth is the same as what fraction?”, he will get it. (Here, “fraction” is the label and “one-fifth” is the object.) It’s a matter of what he attends to first – if he attends to “fractions” he gets confused, just like if he attends to “blue”. If he attends to “one-fifth”, he gets it, since there are few things called “one-fifth” around.

OH! This brings me to a realization – this is an instance of a fundamental problem we see in mathematics education often: we teach the outcomes of mathematics as if they were the mathematics itself.* What does that mean? I mean that we learn things like the long division algorithm without understanding how they work. This is dry and boring, because it has no logic to it. Real math involves proving concepts and putting together ideas to create new ones. It is exciting and creative. If that sounds foreign to your math experience, it’s because we don’t teach it that way. What we teach are the things that mathematicians discovered centuries before us, and we now have to memorize.

It seems to me that this is related to students’ trouble learning fractions. In the example above, “fractions” is the Label, and “one-fifth” is the Feature. That is, “one-fifth” is a concrete entity that you can touch, and “fraction” is more general, an abstract category label. But we persist in telling students that they are going to learn about “fractions”, without having anything concrete for them to match it with. What is the one, singular “fraction”? Can you point me to it without giving me an example? We tell students they are going to learn about “fractions” without first knowing about “one-fifth”, “one-half”, “one-eighth”, or “one-hundredth”. That’s like telling kids they are going to learn about “furniture” before they know about “chairs”, “tables”, or “beds”! There is no way that they can learn the general category of “fractions” or “furniture” before they understand the elements that go into that category.

Perhaps this is where the Feature/Label orientation actually comes from – it is a matter of abstractness of the quality. The Feature is concrete – if we point it out first, we can understand what is being talked about. But the Label is abstract – if we point it out first, we are not sure which of the many objects with that label to apply it to.

But we as adults can figure it out. How come? It is because we are capable of processing many other sources of information – social context, verbal cues, previous experience with “blue” and “balls” – that we are able to understand what the speaker is referring to with the “blue ball” or the “fraction that equals one-fifth”. But children, with their limited experience and limited processing capacity, do not understand what you are talking about. To understand it you must have an understanding of both “blue” and “ball” alone to be able to apply them together – so it’s a question of previous experience, and working memory, that create this understanding. It’s similar to the subitization of 2, 4, and 6 that Ramscar cites, in that you have to be able to recognize both objects independently before you can put them together. What’s exciting about this is that it’s kind of a scientific proof of scaffolding knowledge!

So to bring this full circle, this may be why fractions/decimals/percents may be so difficult for students to learn – because instead of showing them the examples (Features) and letting them fit them into a category (Label), we teach them the category and expect them to derive the examples! By doing this, we tell them that Fractions, Decimals, and Percents are actually very different things in very different categories — and then we throw them for a loop again when we tell them, whoa, wait, these different things are actually all equal! Small wonder they have such trouble getting it. To make it simple, we have to flip around the way we teach this to them – we have to start with concrete quanities they can touch, then show them how to represent each of those as a fraction, a decimal, and a percent. When they see that we started from a quantity (say, what we adults would call “half” a pie), then Label that quantity as “one-half”, “point five”, and “fifty percent”, they will have a much greater understanding of what is going on!

As always, thanks for reading and please leave any responses/challenges/academic trash talk for me in the comments. Thanks!

Frank

* PS — For a beautiful illustration of how we teach the outcomes of mathematics instead of the mathematics itself, mathematician Paul Lockhart tells a wonderful story where he compares it to music education gone wrong: http://www.maa.org/devlin/LockhartsLament.pdf.

“A musician wakes from a terrible nightmare. In his dream he finds himself in a society where
music education has been made mandatory. “We are helping our students become more
competitive in an increasingly sound-filled world.” Educators, school systems, and the state are
put in charge of this vital project. Studies are commissioned, committees are formed, and
decisions are made— all without the advice or participation of a single working musician or
composer.
Since musicians are known to set down their ideas in the form of sheet music, these curious
black dots and lines must constitute the “language of music.” It is imperative that students
become fluent in this language if they are to attain any degree of musical competence; indeed, it
would be ludicrous to expect a child to sing a song or play an instrument without having a
thorough grounding in music notation and theory. Playing and listening to music, let alone
composing an original piece, are considered very advanced topics and are generally put off until
college, and more often graduate school.”

Unbelievable…right?

BTW, this goes for everything, not just color words. if you take a student who is bad at math, and sees just a soup of numbers when he looks at the page, he is not going to be able to pick out the correct numbers to use in a problem, just like he can’t pick out which color word refers to what. Meaning, if you say to him, “what fraction equals one-fifth?” he will be confused, since he sees a lot of fractions; and if you say to him, “one-fifth is the same as what fraction?”, he will get it. It’s a matter of what he attends to first – if he attends to “fractions” he gets confused, just like if he attends to “blues”. If he attends to “one-fifth”, he gets it, since there are few things called “one-fifth” around.

(this appears to be a reversal of what they say, but I am thinking it’s the same since you are telling them to attend to the less common quality first, then narrow their scope. But I could be wrong!)

Then the interesting part comes with “blue ball” – this is a unified unit. To understand it you must have an understanding of “blue” and “ball” and be able to apply them together – so it’s a question of working memory as well as understanding. It’s similar to subitization in that you have to be able to recognize both objects independently before you can put them together. It’s kind of a scientific proof of scaffolding knowledge!

The scaffolding of the “blue ball” goes the same for fractions, which are super hard for kids to learn. First you have to understand what a fraction is. Then you can learn about the different kinds of fractions. Then you can learn about the different kinds of decimals. Then percents. Perhaps this is why fractions/decimals/percents are so confusing to students – because they appear to be in different categories, and it is not made clear that they are all a subinstance of the category “number”. It appears instead that the fractions/decimals/percents are all very different things in different categories, and then we tell them that they’re actually all equal! Whoa! No wonder they don’t get it…