Category Archives: Extended writing

Cats and butterflies: 2 misunderstood analogies in scientistic discourse

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Butterfly effect and Schrödinger’s cat are 2 very common ways of signalling one’s belonging to the class of the scientifically literate. But they are almost always told wrong. They were both constructed as illustrations of paradoxes or counterintuitive findings in science. Their retelling always misses the crucial ‘as if’.

This is an example of metaphor becoming real through its sheer imagistic and rhetorical power. But it also underscores the need to carefully investigate both domains being mapped onto each other, as well as the act of mapping. Metaphors used generatively are only useful if they are abandoned quickly enough. In this case, the popular imagination not only did not abandon the metaphor, it made it into a literal statement with practical consequences.

The way the two narratives are constructed is usually in the form of:

Science shows us that

  1. Cats can be both dead and alive in a box with an aparatus controlled by superimposed quantum states.
  2. Butterflies can cause hurricanes on the other side of the world.

But the actual formulation should be:

Science produces a lot of counterintuitive and (seemingly) paradoxical results some of which are at odds with each other and/or our experience of the world. For instance:

  1. If we were to apply Heisenberg’s quantum uncertainty principle to the world we know, we would have to admit that a cat in a box with a quantum killing machine is dead and alive at the same time. And that is obviously nonsense.
  2. If we were to apply what we know about chaos theory to the world of causes and effects, we would have to admit that a butterfly flapping its wings on one side of the world, can cause a hurricane on another side of the world. And that is obviously nonsense because butterflies have no real impact on the world on scales larger than a flower.

Both Schrodinger and Lorenz were trying to illustrate the counterintuitive conclusions of their respective scientific fields – quantum mechanics and dynamic (chaotic) systems. And in both cases, it badly backfired.

Although Schödinger’s dilemma was much more foundational to the structure of our universe, it was Lorenz, whose funny paper to an obscure symposium did the more lasting damage.

It is of no practical consequence whether or not in the retelling of Schrödinger’s paradox, we omit the word ‘paradox’ and assert that ‘science tells us that there are machines that can make cats alive and dead at the same time.’ This is merely par for the course in the general magical nature of the public scientific discourse. And it can even spur the development of new models of the physical universe.

But the ‘butterfly effect’ is more dangerous because it seems like it could have practical applications. Lorenz was not stating a paradox per se, only a counterintuitive conclusion that goes against our most common scenarios of causal relations. Our basic experience of the world is that big things move big things and small things don’t. So any suggestions we can make small things move big things seems intriguing. We know levers and pullies can get us some of the way towards that, so the dream of a magical lever is always there. Homeopathy “works” on the same magical principle. But this is not the lesson of complexity.

The most common reformulation of the ‘Butterfly effect’ is: ‘small actions can have a big impact’. However, this confuses sensitivity to initial conditions with a cumulative cascade effect. Every single snowflake contributes equally to an avalanche as do all the other aspects of the environment. Although none of them individually have any effect on the world at human scale, when combined, they can move much larger objects. But it is that combination (into a larger whole) that has the impact.

Whether any particular snowflake is the last to fall or somebody clapped loudly near a snow drift just before the avalanche fell says nothing about the ability of small things to have big effects. Only about our inability to measure small variations in big things accurately enough.

It is not true that a butterfly’s wings cause anything but minute variations of air right next to them. But it may be true that they are one of the infinite variations of the whole weather system that is simply impossible to measure with finite precision. It’s not that it is hard to calculate all the variations, it is that there are more variations than we have atoms to calculate them with.

Sure, we can talk about proximate and ultimate causes, but that again hides the problem of calculation. And if we ignore the practical problems of measuring the infinite with finite tools, we only get mired in philosophical musings on prime movers and free will. And these have yet to lead anywhere in two and a half millennia.

The only thing we can learn from the butterfly effect is that we cannot measure complex systems accurately enough to predict their behavior over the long term with enough precision. The big mismatch is that while the variation in ‘initial conditions’ is too small to measure, the variation in the outcomes is not. And that feels wrong.

Complexity is unsurprisingly too complicated to be captured by a single metaphor. The ‘butterfly effect’ is a good metaphor for the sensitivity to initial conditions aspect of it. But only if we understand that it is a metaphor that illustrates the counterintuitive nature of complexity and not complexity itself.

The larger lesson here is that metaphor is a process. It doesn’t just lie in a bit of text waiting for us to encounter it and understand it. It is picked up as part of stories. It is told, retold, reexamined, abandoned, readopted, and so on. If you unleash a generative metaphor on the world, you should keep an eye on it to make sure it’s still doing the job you meant it to do. That means a lot of talking and then more talking. Just like with butterflies, the ultimate outcome is never certain. That is fine. Metaphors are supposed to open up new spaces. But some of those spaces may have lions in them and we do know that lions have big impacts on human scales. Bon appetit!

3 burning issues in the study of metaphor

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I’m not sure how ‘burning’ these issues are as such but if they’re not, I’d propose that they deserve to have some kindling or other accelerant thrown on them.

1. What is the interaction between automatic metaphor processing and deliberate metaphor application?

Metaphors have always been an attractive subjects of study. But they have seen an explosionof interest since ‘Metaphors we live by’ by Lakoff and Johnson. In an almost Freudian turn, these previously seemingly superfluous baubles of language and mind, became central to how we think and speak. All of a sudden, it appeared that metaphors reveal something deeper about our mind that would otherwise remain hidden from view.

But our ability to construct and deconstruct metaphors was mostly left unexamined. But this happens ‘literally’ all the time. People test the limits of ‘metaphor’ through all kinds of dicoursive patterns. From, saying things like ‘X is more like Y’ to ‘X is actually Y’ or even ‘X is like Y because’.

How does this interact with the automatic, instantaneous and unconscious processing of language. (Let’s not forget that this is more common)

2. What is the relationship between the cognitive (conceptual) and textual metaphor?

Another way to pose this question is: What happens in text and cognition in between all the metaphors? Many approaches to the study of metaphor only focus on the metaphors they see. They seem to ignore all the text and thought in between the metaphorical. But, often, that is most of goes on.

With a bit of effort, metaphors can be seen everywhere but they are not the same kind of thing. ‘Time is money’, ‘stop wasting my time’, and ‘we spent some time together’ are all metaphorical and relying on the same conceptual metaphor of TIME IS A SOMETHING THAT CAN BE EXCHANGED. But they are clearly not doing the same job of work for the speaker and will be interpreted very differently by the listener.

But there’s even more at stake. Imagine a sentence like ‘Stop wasting my time. I could have been weeding my garden spending time with my children instead of listening to you.’ Obviously, the ‘wasting time’ plays a different role than in a sentence ‘Stop wasting my time. My time is money and when you waste my time, you waste my money.’ The coceptual underpinnings are the same, but way they can be marshalled into meaning is different.

Metaphor analysts are only too happy to ignore the context – which could often be most of the text. I propose that we need a better model for accounting for metaphor in use.

3. What are the different processes used to process figurative language

There are 2 broad schools of the psychology of metaphor. They are represented by the work of Sam Glucksberg and Raymond Gibbs. The difference between them can be summarised as ‘metaphor as polysemy’ vs ‘metaphor as cognition’. Metaphor, according to the first, is only a kind of additional meaning, words or phrases have. While the second approach sees it as a deep interconnected underpinning of our language and thought.

Personally, I’m much closer to the cognitive approach but it’s hard to deny that the experimental evidence is all over the place. The more I study metaphor, the more I’m convinced that we need a unified theory of metaphor processing that takes both approaches into account. But I don’t pretend I have a very clear idea of where to even start.

I think such a theory would also have to account for differences in how inviduals process metaphors. There are figurative language pathologies (e.g. gaps in ability to process metaphor is associated with autism). But clearly, there are also gradations in how well individuals can process metaphor.

Any one individual is also going to vary over time and specific instances in how much they are able  and/or willing to consider something to be metaphorical. Let’s take the example of ‘education is business’. Some people may not consider this to be a metaphor and will consider it a straightforward descriptive statement along the lines of ‘dolphins are mammals’. Others will treat it more or less propositionally but will dispute it on the grounds that ‘education is education’, and therefore clearly not business. But those same people may pursue some of the metaphorical mappings to bolster their arguments. E.g. ‘Education is business and therefore, teachers need to be more productive.’ or ‘Education is not business because schools cannot go bankcrupt’.

Bonus issue: What are the cognitive foundations shared by metaphor with the rest of language?

This is not really a burning issue for metaphor studies so much as it is one for linguistics. Specifically semantics and pragmatics but also syntax and lexicography.

If we think of metaphor as conceptual domain (frame) mapping, we find that this is fundamental to all of language. Our understanding of attributes and predicates relies on the same ability to project between 2 domains as does understanding metaphor. (Although, there seems to be some additional processing burden on novel metaphors).

Even seemingly simple predicates such as ‘is white’ or ‘is food’ require a projection between domains.

Compare:

  1. Our car is white.
  2. Milk chocolate is white.
  3. His hair is white.

Our ability to understand 1 – 3 requires that we map the domain of the ‘subject’ on to the domain of the ‘is white’ predicate. Chocolate is white through and through whereas cars are only white in certain parts (usually not tires). Hair, on the other hand, is white in different ways. And in fact, ‘is white’ can never be fully informative when it comes to hair because there are too many models. In fact, it is even possible to have opposite attributes mean the same thing. ‘Nazi holocaust’ and ‘Jewish holocaust’ are both use to label the same event (with similar frequency) and yet it is clear that they refer to one event. But this ‘clarity of meaning’ depends on projections between various domains. Some of these include ‘encyclopedic knowledge’. For instance, ‘Hungarian holocaust’ does not possess such clarity outside of specialist circles.

It appears that understanding simple predicates relies on the same processes as understanding metaphor does. What makes metaphor special then? Do we perhaps need to return to a more traditional view of metaphor as a rhetorical device but change the way we think about language?

That is what I’ve been doing in my thinking about language and metaphor but most linguistic theories treat these as unremarkable phenomena. This leads them to ignore some pretty fundamental things about language.

3 “easy” things that are hard for both humans and AI

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Everybody is agog at what AI systems can do. Nobody thought even 10 years ago that machines could be trained to recognise images or transcribe natural speech as well as they do now. And because of this leap forward everybody has started worrying about AI taking over the world because it will soon be able to do everything people can but better.

On the other hand, there are AI naysayers who point at incredible feats of human creativity and ingenuity and say ‘no machines will ever be able to write a poem’ or ‘manage a company’.

While I’m more than skeptical about the true possibilities of AI, I am equally ekeptical about this supposed limitless human creativity that is beyond the bounds of computation.

I think we can reveal more about the limits and nature of human intelligence and thus the targets (possible limits) for AI development, if we look at very simple things with which both humans and AI struggle albeit in different ways.

Machines are often thought of as capable only of algorithmic processing (such as adding lots of numbers) and humans are thought to excel at massively parallel tasks – also known as intuition (such as telling part dogs from cats). But we will see that they seem to trade these roles in the ways they approach and fail at these appartently simple problems.

I call these problems ‘easy’ because they can be broken into very easy and straightforward components. But they are hard if not impossible in reality because of the curse of dimensionality. Even the slightest variation in those simple components, will grow into an exponential mess.

1. Figuring out time zones

Apple Watches recently stopped working because of Summer Time in Australia. And just the other day, Outlook asked me if I wanted to switch to a continental time zone in Europe. After I said yes, it started scheduling all meetings 2 hours off.

On the other hand, I’ve been arranging meetings between 2 time zones 1 hour apart for 20 years and I still get it wrong about 3 times out of 10.

So what gives? Time zones are conceptually very straightforward. You just have a database of times and places with notes on what time it is when and where relative to some fixed point. Then all you do is subtract anywhere between 1 and 12. What could be easier?

Well, you have to add in change of dates, so you have to switch between today, tomorrow and yesterday quite a lot. But still. There is a finite number of times and places and their combinations, so how hard can it be for human programmers to sit down and write all the code once and for all? Turns out, incredibly hard. There are just too many permutations and they keep changing as the database of times and places is being updated with new information.

So, the magnitude of the problem seems to be too great for humans to come up with exhastively detailed algorithms to deal with it. (To be clear, the core has been solved, but we don’t seem to be able to nail all the edge cases. Things would be a lot worse without computers.)

So why don’t we unleashe machine deep learning on the problem? Well, partly because there’s no good data for a machine to learn on. This is mostly an algorithmic problem. But the inputs of the algorithm come from very human perceptions of how time relates to cyclical things like days and relationships like comparing states between time zones with respect to days. Again, none of this is all that complex. But the algorithmic part is too complex for humans to describe as a series of if-then commands to a computer without making lots of mistakes. And the perspective and context part seems to be completely outside of what any ML algorithm can access at the moment.

So we’re stuck with something that mostly works but not always and is mostly understood but also always confusing.

2. Scheduling a meeting

Scheduling meetings is another simple algorithmic problem related to time. Simply compare two series of numbers, find where they differ and spit out the result. But all of this starts interacting with a lot of human complexities that make the problem completely intractable if what we wanted to do is write a series of commands in the form of ‘if you see this, do that’.

That’s why the work of the human assistant handling the scheduling for a busy person (who rates an assistant) is not just to provide her intelligence or understanding of calendars. It involves conversations with the person whose calendar is being managed about their priorities, options, possible scenarios, conversations with other people, other assistants, eventually arriving at some compromise which is then entered into the straightforward if-then format of a calendar.

It is this conversation with other people that is often overlooked (“tell your people to call my people”). In the case of the assistants of the other busy people who rate an assistant also have to synthesize the priorities and value of their charges through the same process of conversations and adjustments.

The final matching algorithm is very simple – so simple that it seems like noone should need a human assistant any more. But the inputs into the algorithm need to come from sources that are too rich and complex to treat algorithmically or through some multi-dimensional analysis of hidden regularities (like deep neural nets). The inputs require either a fairly general artificial intelligence (although not full blown AGI) or that everyone keeps their calendar in the same way. (Even then we’d probably have to deal with travelling-salesman problems – but at least we have some ideas about the limits on the computability of those.)

There are many individual components of this process that could be algorithmically assisted. But often the simpler algorithms and heuristics such as preference polls and shared calendars are more effective aids than opaque machine learning output.

So although, this looks like a problem that should be solvable through ML, early attempts have been less than impressive.

3. Importing data about people into a table (deduplication)

Computers are great as aids to managing structured data. But the input into the structure has to be provided by humans. Can AI help here?

Imagine you’re organising an event and you want people to tell you if they’re coming. You can just ask and keep in your head who said yes. But that soon becomes too much. As a next step, you ask them to email or to send an RSVP so you can look at the messages and remind yourself who said yes. But even that becomes difficult soon, so you start a list. And the more people and events you need to manage, the more complicated the list is and the more time you have to spend structuring your data and inputing it into some sort of a table for managing and reviewing the data.

The world is littered with Excel sheets kept by event organisers. Now imagine you wanted to feed all the idiosyncratic Excel sheets with event information at a large organisation into a machine learning algorithm and get one number of the total number of participants or the total cost of lunch breaks.

If everybody kept their spreadsheets exactly the same way, this would be trivial. But they don’t. Computers make the task of managing this kind of structured data much easier but they constantly struggle with errors in the input from busy, overworked and cognitively limited humans.

On the surface of it, there’s nothing to prevent this part (ie participant registration and management) of event management from being completely automated. But there’s always a person involved in dealing with this. So could there be an AI system that does all of this? So far we’re not even very close to this. A system that processes some RSVPs via email, others via forms, and others from other sources (“Hi, Clare, Frances told me she was coming to your party!”) does not exist.

So let’s simplify the task even more. Take data from one table of a system (let’s say a registration table) and put it into another table on a different system (let’s say account creation). All the AI system would have to do is figure out what is important to one system and get the right data from another system. At the moment, humans are involved. In better cases by creating an API and programming algorithms to transfer data between systems. In the worse case, they download a spreadsheet from one system, modify it, if needed, and upload it into another system.

This is trivial if you’ve designed both systems and know they have to integrate. But the permutations get out of hand surprisingly quickly when you take any 2 random systems designed by different people for a similar purpose but without the intention to integrate. Is ‘Last name’ always the ‘Second name’, when the full name is in one column, is first name always first? Any one difficulty is easy to spot for a human and disambiguate. But it gets very error prone at scale and there are always some unexpected edge cases.

Even such a simple thing as contact deduplication between two devices of one person is not a completely solved problem.

Why isn’t there an AI system that can evaluate the data and transfer it as appropriate but at scale and without the errors human data processors or programmers or data processing algorithms make?

As always, even the most trivial algorithms require very complex inputs. And with even minor variation in the possible inputs, the if-then logic becomes too unweildy. Although computers in general are great at pursuing if-then logic chains regardless of complexity (within limits), AI algorithms are not. They provide guesses with probabilities. In certain areas, most notably speech and image recognition, their guesses are becoming very good and resembling humans. They may even outperform humans at scale.

But all the if-then part of what to do with these guesses is still handled by if-then algorithms designed by humans. There’s some talk of ‘Programming 2.0’ but nobody seems to be applying it to some of the day-to-day simple problems with complex scaling. Because even small errors in the inputs result in big aggregate problems and AI systems have no way of assessing whether their guesses ‘make sense’.

Is AI impossible?

Maybe AI is just too hard. But these examples don’t claim it’s impossible, they just show that some difficult problems are just difficult. Even if they appear straightforward on the surface.

I have learned not to bet against engineers’ ability to figure out solutions in the long run. It’s not always clear what is solvable by AI and what is not ahead of time. Sometimes, specialised ML systems can be developed to solve problems that don’t generalise (e.g. GO or chess machines). But I would have expected more people to deal with these problems, if there was an easy solution to be found. And there hundreds more similar task-based problems that just won’t be magicked away by slapping the label ‘AI’ on it. Individual ones may be solved by one way or another. Perhaps by breaking them into component parts. But I’m not seeing any specific steps being taken to create general purpose Machine Learning that would deal with all of them. Just wishful thinking about AGI (Artificial General Intelligence) emerging to solve these problems without regard to the actual complexity of some of them or the complexity of the intermediate steps it would take to get there.

Innovation is bad for business: 3 more ‘I’ words to compare innovation to

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Innovation is the ‘in’ thing. Innovate or die is the buzz up and down the hive mind. Everybody is feeling like they must innovate all of the things all of the time. But is the incessant innovation the right mode of approaching this?

We constantly spin up stories of the intrepid innovator and the change they bring about in the world. But is that what is really happening on the ground? I think we can bring up some metaphors to bear on this that may open up some different possibilities of conceptualizing innovation.

Note: I’m writing this as an early adopter and some time professional innovator. But despite a personal drive to constantly try new things, I find that approaching innovation uncritically and without regard to the full diversity of its instantiations is counterproductive. Therefore, this is meant to be a corrective as much to myself as others.

Infection as metaphor of innovation

When an innovation spreads through an institution, it does so just like an infection. It starts attacking existing systems who then have to spend time and resources on averting the damage done by the attack. We only tell the stories where the attack led to the strengthening of the system – like with childhood maladies or inoculation. But chronic disease and death of the system are also not uncommon – we just don’t tell them in association with innovation.

This weakening happens through many processes that every innovator and innovatee (and this covers most people in one way or another) will have direct experience of. Innovators have experienced resistance, doubt, slow response times. Those are all defense mechanisms the disease of innovation has to overcome.

The people who experience the innovation as the infected cells, can attest to lower productivity because of the need to learn new things, endless meetings on how to implement the new thing keeping them from doing the job, miscommunication and misunderstanding leading to higher error rate (be it in production or management).

Where this metaphor breaks down is that if the innovation is successful, the system is transformed. Almost, as if instead of a tumor killing us it would grow us a new useful organ while others may fall off without much harm to the organism as a whole.

On the other hand, the success of the system in extinguishing a malignant innovation can make it more resilient to innovation in the future. And this may lower its chances of survival in the face of environmental changes that make it easier to thrive for those where innovation took the system over. This latter aspect is what proponents of innovation as an unalloyed good point to. But that is a backward perspective. From the ground, the system as an organism will always have to start by defending against innovation as infection no matter how well-intentioned everybody involved may be.

Ignorance as metaphor of innovation

Innovation is often equated with knowledge. People research new ways of doing things, they bring together existing strands of knowledge and weave from them beautiful tapestries of brighter futures. But in practice, innovation almost always benefits from ignorance. Or even depends on it.

Ignorance by inventors is a well-known companion to some of the biggest inventions and discoveries. When Morse set out to create the telegraph system, it was received wisdom that what he was trying to do was physically impossible but he did not know that. Columbus is often given as the example of the innovator who was right and pursued his correct knowledge in spite of ridicule. But the truth was he was a zealot crank and completely wrong about everything. Everybody had known the Earth was round for over a thousand years by the time of Columbus and they also knew how large it was. He did not doubt it was round but he subscribed to a crank theory that it was much smaller than it was. He just got lucky there was a continent in the way.

This ignorance-of-the-impossible narrative can be applied to many of the other famous inventors. But this story is often told with the naysayers as hidebound blocks to progress and inventors as courageous pursuers of the truth. But this way the narrative misses the overwhelming majority of ignorant would-be inventors being simple cranks. For every clueless Morse and cranky Columbus, there were thousands of unknown failures who did not know or believe something truly impossible was impossible (just like most random mutations do not win the natural selection lottery). The correct response to somebody claiming they are able to do something known to be impossible is to doubt it. The trick is being able to update one’s priors in a way that helps us better judge the signs of success.

But we should also not overlook the ignorance among the adopters of innovations. The lack of information on the side of adopters of innovation is another necessary ingredient to success. Every innovation is too uncertain and often unreliable in its earliest stages to be considered by the well-informed other than as a bet. This ignorance is partly a result of pure uncertainty as to the viability of something new. But much more commonly, it is just ignorance of how the new thing works, what are its limitations – and how it truly differs from the old. This results in Potemkin innovations like the original Mechanical Turk. The innovations or their effects are often too complex to be fully understood (even by their inventors). This then leads to the creation of a zeitgeist (a sort of general framing) which provides the innovation with enough vectors for infection and the possibility for improvement.

But it also makes it very easy for impostors to sneak in. At present, there are many examples of companies simply labeling products with ‘machine learning’ or ‘blockchain’ and selling it to credulous investors and customers even if the underlying technology is not actually using anything that could be meaningfully described that way.

Imitation as metaphor of innovation

Innovation is associated with inventiveness and creativity. Strokes of brilliance and flashes of genius. But almost all of the great innovations were imitating a previous less successful attempt. It is well known that great inventions and discoveries often appear multiple times simultaneously as different people synthesize available information into similar outcomes. Perhaps the most famous examples are Newton and Leibniz for calculus and Darwin and Wallace for natural selection. But this holds true for almost all the great inventions. Either somebody figured it out as well, or was getting very close.

But more importantly, by the time we get to talk about almost any innovation, it will have reached us through a long chain of imitations. Novel ways of thinking or doing things really only become innovations when somebody copies them.

This process of imitation is similar to that of natural selection, so it usually leads to refinement and strengthening of the original idea. But let’s not forget that natural selection is based around the idea of imperfect copies (random mutations) finding uses that increase their chances of spreading (reproduction). So as part of this metaphor, innovation without copying would just be lots of random ideas that go nowhere.

Not only is innovation the result of imitation, without imitation, there would be no point to it in the first place.

Conclusion

There is not meant to be conclusion here. Investigating metaphors just opens up new prisms that slightly change the way we look at things. Sometimes, it’s the process of thinking through mappings in the metaphor that forces you to investigate one of the domains more closely. And that’s what this is all about.

Does machine learning produce mental representations?

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TL;DR

  • Why is this important? Many people believe that mental representations are the next goal for ML and a prerequisite for AGI.
  • Does machine learning produce mental representations equivalent to human ones in kind (if not in quality or quantity)? Definitely not, and there is no clear pathway from current approaches to a place where it would. But it is worth noting that mental representations in humans are also not something straightforward to identify or describe.
  • Is there a currently viable approach to ML that could eventually lead to mental representations with more engineering? It appears not but then again, no one expected neural nets would get so successful.

Update: Further discussion on Reddit.

Background

Over the last few months, I’ve been catching up more systematically on what’s been happening in machine learning and AI research in the last 5 years or so and noticed that a lot of people are starting to talk about the neural net developing a ‘mental’ representation of the problem at hand. As someone who’s preoccupied with mental representations a lot, this struck me as odd because what was being described for the machine learning algorithms did not seem to match what else we know about mental representations.

So I’ve been formulating this post when I was pointed to this interview with Judea Pearl. And he makes exactly the same point:

“That sounds like sacrilege, to say that all the impressive achievements of deep learning amount to just fitting a curve to data. From the point of view of the mathematical hierarchy, no matter how skillfully you manipulate the data and what you read into the data when you manipulate it, it’s still a curve-fitting exercise, albeit complex and nontrivial.”

He continues:

“If a machine does not have a model of reality, you cannot expect the machine to behave intelligently in that reality.”

What does this model of reality look like? Pearl seems to reduce it to ‘cause and effect’ but I would suggest that the model needs more than that (Note: I haven’t read his book just the interview and this intro.)

What are mental representations?

Mental representations are all sorts of images (ranging from rich to schematic and from static to dynamic) in our mind on which we draw sometimes consciously but mostly unconsciously to deal with the world. They are essential for producing and understanding language (from even the simplest sentence) and for basic reasoning. They can be represented as schemas, rich images, scenarios, scripts, dictionaries or encyclopedic entries. They can be in many modalities – speech, sound, image, moving picture.

Here are some examples to illustrate.

Static schemas

What does ‘it’ refer to in pairs of sentences such as these (example from here):

  1. The trophy wouldn’t fit into the suitcase because it was too big.
  2. The trophy wouldn’t fit into the suitcase because it was too small.

It takes no effort at all for a human to determine that it in (1) refers to trophy and in (2) to suitcase. Why, because, we have schemas of containment and we know almost intuitively that big things don’t fit into smaller things. And when we project that schema onto trophy and suitcase we immediately know what has to be too big or too small in order for one not to fit into the other.

You can even do it with a single sentence as in Jane is standing behind Clare so you cannot see her. It is clear that her refers to Jane and not Clare but only because we can project a schema of 2 similar-sized objects positioned relative to the observer’s line of sight.

So we also know that only sentence 1 below makes sense because of the schema we have for things of unequal size being positioned relative to each other and their impact on our ability to see them.

  1. The statue is in front of the cathedral.
  2. The cathedral is in front of the statue.

However, unlike with the trophy and suitcase, it is possible to imagine contexts in which sentence 2 would be acceptable. For instance, in a board game where all objects are printed on blocks of the same size and positioned on a 2D space.

This is to illustrate that the schemas are not static but interact with the rich conceptualisations we create in context.

Force dynamics

This is a notion pioneered by Leonard Talmy that explains many aspects of cognitive and linguistic processes through dynamic schemas of proportional interaction. Thus we know that all things being equal, bigger things will influence smaller things, faster things will overtake slower things, etc.

So we can immediately interpret the it in sentences such as:

  1. The foot hit the ball and it flew off.
  2. The bird landed on the perch and it fell apart.

But we also apply these to more abstract domains. We can thus easily interpret the situations behind these 2 sentences:

  1. The mother walked in and the baby calmed down.
  2. The baby walked in and the mother calmed down.

If asked to tell the story that led to 1 or 2, people would converge on very similar scenarios around each sentence.

Knowledge of the world

Sometimes, we marshall quite rich (encyclopedic) knowledge of the world in understand what we hear or see. Imagine what is required to match the following 2 pairs of sentences (drawing on Langacker):

  1. The Normans conquered England with …
  2. The Smiths conquered England with …
  1. … their moody music.
    b. … their superior army.

Obviously the right pairings are 1b and 2a. But none of this is contained in the surface form. We must have the ‘encyclopedic’ knowledge of who The Normans and The Smiths were but also the force dynamic schemas of who can conquer who.

So on hearing the sentence ‘Mr and Mrs Smith conquered Britain’, we would be looking for some metaphorical mapping to explain the mismatch between the force we know conquering requires and the force we know a married couple can exert. With sufficiently rich knowledge, this is immediately obvious as in ‘John and Yoko conquered America.’

How does machine learning do on interpreting human mental representations?

For AI, examples such as the above are a difficult challenge. It was recently proposed that a much more effective and objective Turing test would be to ask an AI to interepret sentences such as these under the [ Winograd Schema Challenge] (https://en.wikipedia.org/wiki/Winograd_Schema_Challenge).

A database of pairs of sentences such as:

  1. The city councilmen refused the demonstrators a permit because they feared violence.
  2. The city councilmen refused the demonstrators a permit because they advocated violence.

This has the great advantage of perfect objectivity. Unlike with the Turing test, it is always clear which answer is correct.

The best machine learning algorithms use various tricks but they still only do slightly better than chance (57%) at interpreting these schemas.

The only problem is that it is quite hard to construct these pairs in a way that could not be solved with simple statistical distributions. For instance, the Smiths and Normans example above could be easily resolved with current techniques simply by searching which words occur most frequently together.

Also, it is not clear how the schematic and force dynamic aspects interact with the encyclopedic aspects. Can you have one without the other? Can we classify the Winograd schema sentences into different types, some of which would be more suspectible to ML approaches?

Do mental representations exist?

There is a school of thought that claims that mental representations do not actually exist. There is nothing like what I described above in the brain. It is actually just a result of perceptual task orientation. This is the ecological approach developed in the study of perception and physical manipulation (such as throwing or catching a ball).

I am always very sceptical of any approach that requires we find some bits of information resembling what we see stored in the brain. Which is why I am quite sympathetic to the notion that there are no actual mental representations directly encoded into the synaptic activations of our brain.

But even if all of these were just surface representations of completely different neural processes, it is undeniable that something like mental representations is necessary to explain how we think at speak at some level. At the very least to articulate the problems that have to be solved by machine learning.

Note: I have completely ignored the problem of embodiment which would make things even more complicated. Our bodily experience of the world is definitely involved. But to what extent are our bodies actually a part of the reasoning process (as opposed to the brain as an independent computational contrl module) is a subject of hot debate.

How does machine learning represent the problem space?

Now, ML experts are not completely wrong to speak about representations. Neural nets certainly build some sort of representation of the problem space (note, I don’t call it world). We have 4 sources of evidence:

  1. Structure of data inputs: Everything is a vector encoded as a string of numbers.
  2. Patterns of activation in the neural nets (weights): This is where the ‘curve fitting’ happens.
  3. Performance on real world tasks: More reliable than humans on dog breed recognition but penguins can also be identified as pandas.
  4. Adversarial attacks: Adding seemingly random and imperceptible noise to a image or sound can make it produce radically different outputs.

If we take together the vector inputs and the weights on the nodes in the neural net, we have one level of representation. But that is perhaps the less interesting and as complexity increases, it becomes impossible to truly figure out much about it.

But is it possible that all of that actually creates some intermediate layer that has the same representational properties as mental representations? I would argue that at this stage, it is all inputs and weights and all the representational aspects are provided by the human interpreting the outputs. But if we only had the outputs, we could still posit some representational aspects. But the adversarial attacks reveal that the representational level is missing.

Note: Humans can also be subject to adversarial attacks with all sorts of perceptual and cognitive illusions. They seem to be on a different representational level to me but they would be worth exploring further in this context.

Update: A commenter on Reddit suggested that I look at this post on feature visualisation and I think that mostly supports my point. It looks like there are lots of representations shown in that article, but they are really just visualisations of what inputs lead to certain neuron activations on specific layers of the neural net. Those are not ‘representations’ the neural net has independent access to. I think in the same way, we would not think of Pavlov’s dogs salivating on the sounds of the bell as having ‘mental representation’ of the ‘bell means food’ causal connection. Perhaps we could rephrase the question of whether training a neural net is similar to classical or operant conditioning.  and what that means with respect to the question of representation.

Can we create mental representations in machines?

Judea Pearl thinks that nothing current ML is doing is going to lead to a ‘model of the world’ or as I call it ‘mental representations’. But I’m skeptical that his solution is a path to mental representations either:

“The first step, one that will take place in maybe 10 years, is that conceptual models of reality will be programmed by humans.”

This is what the early AI expert systems tried to do but it proved very elusive. One example of manually coding mental representations is FrameNet, a database of words linked to semantic frames but it barely scratches the surface. For instance, here’s the frame for container which links to suitcase. But that still doesn’t help with the idea of trophy being sometimes small enough to fit and sometimes too big. I can see how FrameNet could be used on very small subsets of problems but I don’t see a way for scaling it up in a way that could take into account everything involved in the examples I mentioned. We are faced with the curse of dimensionality here. The possible combinations just grow too fast for us to compute them.

I’m also not sure that simply running more data through bigger and bigger RNNs or CNNs will get us there either. But I can’t rule out that brute force won’t get us close enough for it not to matter that mental representations are not involved.

Perhaps, if label enough text of some subdomain with framenet schemas, we could train a neural net on this. But that will help with the examples where rich knowledge of the world is not required. We can combine a schema of a suitcase and a trophy with that of ‘fit’ and match ‘it’ with the more likely antecedent. Would that approach help with the demonstrators and councilmen? But even if so, the Winograd Schema Challenge is only an artificially constructed set of sentence pairs designed for a particular purpose. The mental representations involved crop up everywhere all the time. So we not only need a way of invoking mental representations but also a way to decide if they are needed and, if so, which ones.

Machine learning fast and slow up the garden path

Let’s imagine that we can somehow engineer a solution that can beat the Winograd Schema Challenge. Would that mean that it has created mental representations? We may want to reach for Searl’s ‘Chinese Room Argument’ and the various responses to it. But I don’t think we need to go that deep.

One big aspect of human intelligence that is often lumped together with the rest is metacognition. This is the ability to bring the process of thinking (or speaking) to conscious awarenes and control it (at least to a degree). This is reminiscent of Kahneman’s two systems in ‘Thinking Fast and Slow’.

Machine learning produces almost exclusively ‘fast thinking’ – instantaneous matching of inputs to outputs. It is the great advance over previous expert system models of AI which tried to reproduce slow thinking.

Take for instance the famous Garden path sentences. Compare these 2:

  1. The horse raced past the barn quickly.
  2. The horse raced past the barn fell.

Imagine the mental effort required to pause and retrace your steps when you reach the word ‘fell’ in the second sentence. It is a combination of instantanous production of mental images that crash and slow deliberate parsing of the sentence to construct a new image that is consistent with our knowledge of the world and the syntactic schema used to generate it.

Up until the advent of stochastic approaches to machine learning in the 1990s (and neural nets in 2010s), most AI systems tried to reproduce the slow thinking through expert systems encoded as decision trees. But they mostly failed because the slow thinking only works because of the fast thinking which provides the inputs to it. Now neural nets can match complex patterns that we once thought impossible. But they do it very differently from us. There doesn’t seem to be much thinking about how to go about developing the sort of metacognition that is required to combine the two. All of the conditional decisionmaking around what to do with the outputs of ML algorithms has to be hardcoded. Alexa can recognize my saying ‘turn on bedroom light’ but I had to give it a name and if I want to make it part of a more complex process (make sure bedroom light is off when I leave home), I have to go to IFTTT.

I don’t see how Pearl’s approach will take us there. But I don’t see an alternative, either. Perhaps, the mental representations will emerge epiphenomenally as the neural nets grow and receive more sophisticated inputs about the spatial nature of world (rather than converting everything to vectors). Maybe they will be able to generate their own schemas as training inputs. I doubt it, but wouldn’t want to bet against it.

What is just as likely is that we will reach a plateau (maybe even resulting in a new AI winter) that will only see incremental improvements and won’t take the next step until a completely new paradigm emerges (which may not happen for decades if ever).

Conclusion

It is not always obvious that more in-depth knowledge of a domain contributes to a better model of it. We are just as likely to overfit our models as to improve them when we dive too deep. But I think that mental representations at least reveal an important problem domain which should be somehow reflected in what machines are being taught to learn.

Update

In response to a comment on Reddit, I wanted to add the following qualification.

I think I ended up sounding a bit more certain than I feel. I know I’m being speculative but I note that all the critics are pointing at hypotheticals and picking at my definition of mental representation (which is not necessarily unwarranted).

But what I would like to hear is a description of the next 5 specific problems to be solved to get nearer to say 75% on the Winograd Schema Challenge that can then be built on further (ie not just hacking around collocation patterns Watson style).

I also wanted to note that I omitted a whole section on the importance of collocability in language with a reference to Michael Hoey’s work on Lexical Priming, which I think is one of the 2 most important contributions to the study of language in the last 20 years, the other being William Crofts Radical Construction Grammar. The reading of which would be of benefit to many ML researchers along with Fauconnier’s and Turner’s The Way We Think.

Not ships in the night: Metaphor and simile as process

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In some circles (rhetoric and analytics philosophy come to mind), much is made of the difference between metaphor and simile.

(Rhetoricians pay attention to it because they like taxonomies of communicative devices and analytic philosophers spend time on it because of their commitment to a truth-theoretical account of meaning and naive assumptions about compositionality).

It is true that their surface and communicative differences have an impact in certain contexts but if we’re interested in the conceptual underpinnings of metaphor, we’re more likely to ignore the distinction altogether.

But what’s even more interesting, is  to think about metaphor and simile as just part of the process of interpersonal meaning construction.  Consider this quote from a blog on macroeconomics:

[1a] Think of [1b] the company as a ship. [2] The captain has steered the ship too close to the rocks, and seeing the impending disaster has flown off in the ship’s helicopter and with all the cash he could find. After the boat hit the rocks no lives were lost, but many of the passengers had a terrifying ordeal in the water and many lost possessions, and the crew lost their jobs. [3] Now if this had happened to a real ship you would expect the captain to be in jail stripped of any ill gotten gains. [4] But because this ship is a corporation its captains are free and keep all their salary and bonuses. [5] The Board and auditors which should have done something to correct the ship’s disastrous course also suffer no loss.

Now, this is really a single conceptual creation but it happens in about 5 moves which I highlighted above. (Note: I picked these 5 as an illustrative heuristic but this is not to assume some fixed sequence).

[1] The first move establishes an idea of similarity through a simile. But it is not in the traditional form of ‘X is like Y’. Rather, it starts with the performative ‘Think of’ [1a] and then uses the simile ‘as’. [1b]. ‘Think of X as Y’ is a common construction but it is rarely seen as an example in discussions of similes.

[2] This section lays out an understanding of the source domain for the metaphorical projection. It also sets the limit on the projection in that it is talking about ‘company as a ship traveling through water’ in this scenario, not a ship as a metonym for its internal structure (for instance, the similarities in the organisational structure of ships and companies.) This is another very common aspect of metaphor discourse that is mostly ignored. It is commonly deployed as an instrument in the process of what I like to call ‘frame negotiation’. On the surface, this part seems like a narrative with mostly propositional content that could easily stand alone. But…

[3] By saying, ‘if this happened to a real ship’ the author immediately puts the preceding segment into question as an innocent proposition and reveals that it was serving a metaphorical purpose all along. Not that any of the readers were really lulled into a false sense of security, nor that the author was intending some dramatic reveal. But it is an interesting illustration of how the process of constructing analogies contains many parts.

[4] This part looks like a straightforward metaphor: ‘the ship is a corporation’ but it is flipped around (one would expect ‘the corporation is a ship’. This move links [2] and [3] and reminds us that [1].

[5] This last bit seems to refer to both domains at once. ‘The board and the auditors’ to the business case and ‘ships course’ to the narrative in the simile. But we could even more profitably think of it as referring to this new blended domain in which we have a hypothetical model in which both the shipping and business characteristics were integrated.

But the story does not end there, even though people who are interested in metaphors often feel that they’ve done enough at this stage (if they ever reach it). My recommended heuristic for metaphor analysts is to always look at what comes next. This is the start of the following paragraph:

To say this reflects everything that is wrong with neoliberalism is I think too imprecise. [1] I also think focusing on the fact that Carillion was a company built around public sector contracts misses the point. (I discussed this aspect in an earlier post.)

If you study metaphor in context, this will not surprise you. The blend is projected into another domain that is in a complex relationship to what precedes and what follows. This is far too conceptually intricate to take apart here but it is of course completely communicatively transparent to the reader and would have required little constructive effort on the part of the author (who is most likely to have spent time on constructing the simile/metaphor and its mappings but little on their embedding into the syntactic and textual weave that give it its intricacy).

In the context of the whole text, this is a local metaphor that plays as much an affective as it does a  cognitive role. It opens up some conceptual spaces but does not structure the whole argument.

The metaphor comes up again later and in this case it also plays the role of an anaphor by linking 2 sections of the text:

Few people would think that never being able to captain a ship again was a sufficient disincentive for the imaginary captain who steered his boat too close to the rocks.

Also of note is the use of the word ‘imaginary’ which puts that statement somewhere between a metaphor (similarity expressed as identity) and simile (similarity expressed as comparison).

There are two lessons here:

  1. The distinction between metaphor and simile could be useful in certain contexts but in practice, their use blends together and is not always easy to establish boundaries between them. But even if we could, the underlying cognition is the same (even if truth-conditionally they may differ on the surface). We could even complicate things further and introduce terms such as analogy, allegory, or even parable in this context but it is hard to see how much they would help us elucidate what is going on.

  2. Both metaphor and simile are not static components of a larger whole (like bricks in a wall or words in a dictionary). They are surface aspects of a rich and dynamic process of meaning making.  And the meaning is ‘literally’ (but not really literally) being made here right in front of our eyes or rather by our eyes.  What metaphor and simile (or the sort of hybrid metasimile present here) do is  help structure the conceptual spaces (frames) being created but they are not doing it alone. There are also narratives, schemas, propositions,  definitions, etc. All of these help fill out the pool of meaning into which we may slowly immerse ourselves or hurtle into headlong.  This is not easy to see if we only look at metaphor and simile outside their natural habitat of real discourse. Let that be a lesson to us.

Therapy for Frege: A brief outline of the theory of everything

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Frege’s trauma

I found the following quote from Frege on the Language goes on holiday blog and it struck as the perfect starting point for this essay which has been written for a while now:

“Frege (“Logic in Mathematics”): Definitions proper must be distinguished from elucidations [Erläuterungen]. In the first stages of any discipline we cannot avoid the use of ordinary words. But these words are, for the most part, not really appropriate for scientific purposes, because they are not precise enough and fluctuate in their use. Science needs technical terms that have precise and fixed Bedeutungen, and in order to come to an understanding about these Bedeutungen and exclude possible misunderstandings, we provide elucidations. Of course in so doing we have again to use ordinary words, and these may display defects similar to those which the elucidations are intended to remove. So it seems that we shall then have to provide further elucidations. Theoretically one will never really achieve one’s goal in this way. In practice, however, we do manage to come to an understanding about the Bedeutungen of words. Of course we have to be able to count on a meeting of minds, on others’ guessing what we have in mind.”

Duncan Richter’s commentary then follows:

“Frege’s problem is of a different kind [from Mill]. There is something wrong with what he wants. He sees the problems himself, but still, apparently, goes on wanting the same thing. So pointing out the problems won’t help at all. We might say he needs a kind of therapy, although this won’t be regular psycho-therapy.”

Well, I have been thinking about the need for exactly such a therapy and it must stem from an understading that Frege was wrong about the extent to which we can in practice determine the precise Bedeutungen of our terms. As I hope to show below, the infinite regress of elucidation intrudes on our every day thinking in many ways that make even relatively simple communication or understanding difficult (a never ending process of negotiation). Difficulties stemming from what I call below the impossibility of perfect reference are not a matter of some distant perifery of hypothetical paradoxes, they make themselves known as insurmountable obstacles in seemingly innocuous. Or in other words, it is Erläuterungen all the way down.

And this problem does not have an epistemological solution (even if we don’t have to go as far as Rorty in rejecting epistemology as a beneficial enterprise altogether). Our only course of action is acceptance and making peace with the fundamental indeterminacy of reference. The acknowledgment of the need to make peace is the therapeutic part because the alternative is dissolution into madness of circularity or arbitrary absolutism (which is a kind of madly willful blindness, in itself).

Halting Problem of Rationality

The original impetus for these notes was reading a recent review of Elezier Yudkowsky’s new book on Inadequate Equilibria by Scott Alexander. Yudkowsky and Alexander’s review seem to me an object study of what I’ve come to thinking about as the halting problem of rationality.

This problem has many formal kindred spirits in the form undecidability, computability (P=NP), etc. From everything we know, we should be exteremely skeptical of rationality to solve its own problems without any appeal to a sort of axiomatic arbiter (a Godelian ‘because I said so’, perhaps.)

Scott Alexander shows the infinite regression of the process of finding the final level at which to decide which perspective is valid (or even useful). Based on Yudkovsky’s book, he arbitrarily (or perhaps magically) uses two perspectives but they are clearly just points on a continuum which itself is on an infinite plane rather than just a neat straight line.

Now, Yudkowsky does not seem to be bothered by the infinity of it all. He uses a whole lot of Bayesian heuristics to build up a priors machine that spits out one good decision after another. Prior ex machina, if you will. And it’s not always good. That’s why Alexander calls the book’s core argument ‘theodicy’. And that’s how most rationalist epistemological arguments strike me. They are the same sort of hermeneutics performed on the Bayesian heuristic canon that biblical scholars engaged in with the Bible. Read the text and its understanding will reveal THE truth.

The impossibility of true hermeneutics

My arguement is that hermeneutics (in this sense) is impossible and always the wrong goal. What’s more it is very easy to mistake our heuristics for hermeneutics. In other words, it is almost an instinct to assume that the analytic instruments we use to handle the world around us for specific (if often implicit) purposes are isomorphic with the world. And the more successful the instrument, the more likely it is we will assume it reflects the actual ‘true’ and complete image of the world. So computers, have been hugely influential and successful in emulating (and enhancing) some previously difficult mental processes and therefore the world is made up of information and our minds are just computers. We can control so much of the world around us by manipulating chemical elements, and therefore everything we are is really chemistry and our goal in describing the human condition should be a transcription into chemical notation because only that is the language in which a true image of the world can be captured. We can describe a sentence with a transformational rule and therefore the true representation of language is a formal description. We can design precise logical proofs for truth conditions, and therefore all that a meaning of a word or a statement is, is its conditions for truth. We can describe the utility of an economic transation by its marginal value and therefore all that defines value is the margin. And so on.

Richard Rorty pretty much showed how this works in Philosophy and the Mirror of Nature and later on also showed how to deal with it through his ironist approach. But rationalists are too cool to read Rorty. Wittgenstein and Derrida saw the problem and instead of talking about it, they tried to reveal it through cryptic koans.

I’d like to go about this differently and offer an outline of what a proof might look like that there is no ultimate external referent available for adjudication of referential problems. I also show that this causes problems not just on the edges but all the time across all aspects of academic and daily life.

Outline of the theory of everything

Lets start with a key assumption from which everything else derives:

Everything exists!

On the word ‘exist’

Now, the word exist obviously has multipe meanings. I’m obviously not saying that everything exists as an object in the world. So I’m perfectly happy with the statement ‘Unicorns don’t exist’. I’m using it in the most universal sense similar to the logical notation E. In this sense it is impossible for something I can refer to with the word ‘something’ or even think about not to exist. But I don’t have to have a word or a thought for something to exist. In facts, words make it seem as if everything existed as some kind of entity. But those words and thoughts themselves exist and so does the relationship between them and the things they refer to as well as my reference to that relationship and my reference to that reference. And so on ad infinitum. In fact, the very act of naming brings things into existence. Existence in this sense is a Parmenidian totality – it is not temporal. Everything includes past and future. It is not dimensional – if it turns out there are infinite parallel worlds, everything will still exist. Parallel words are also part of everything. And if it turns out there’s no such thing, everything will still exist. The parallel worlds will just exist as an idea that turned out not to have identifiable external correlate. Everything does not require finiteness nor infinity. Infinity is still everything. But even if it turns out that infinity is just a mathematical construct and the physical world is actually finite in the shape of some bizzare multidimensional space-time sphere, that’s still everything. When Wittgenstein said ‘That of which I cannot speak, I must stay silent’, he was alluding to the same concept of everything. If it can exist it does exist, if it cannot, it does not. Everything exists. Anything that does not exist does not exist. What it means that there is nothing outside of existence in the sense of x E everything. There is no such special mode of being as metaexistence – existence beyond existence, existence about existence. Now, this is not the proof, this is the Cartesian axiom abstracted – X exists, therefore X exists.

Impossibility of perfect reference

The key consequence of everything existing is the impossibility of perfect referrentiality. This presents a problem because our entire epistemology is built on the assumption of referentiality. If something exists, we can refer to it with a concept, word, label, or at least point at it. In other words, signifier vs signified. We cannot speak or think without relying the perfect applicability of this abstraction. And most of the time it sort of works. In ‘Pass the salt’, ‘pass’ refers to an action, ‘salt’ to an object, ‘the’ to a relationship between the object and our perception of it. The ‘sort of’ refers to the fact that even simple sign/meaning pairings get very complicated very fast. Semioticians have been dining out on this since at least Peirce. (But medieval logicians and Indian ones before that have also taking this complexity apart as far as it can be taken apart.)

But it stops even sort of working very soon when we get even close to any attempt at metareferentiality. Just look what sort of verbal gymnastics I had to go through to even hint at what I mean by a simple statement ‘everything exists’. The problem is that referentiality is not a passive fact outside of existence. Every act of reference creates a new relationship between the refered, referee, and reference (at its most oversimplified). And that’s something we can then go and refer to, thus creating an infinite regress, that’s not linear but exponential. Because any new act of reference creates not one but at least four potential things to refer to. 1. The act of reference itself, 2. the referee in the act of reference, 3. the referent as being referred to, 4. the signfifier being used for that reference. Most often we can multiply that by referring to other participants in the act of reference, the relationship of that act to prior acts and their relationship to this act. In short, it’s not a pretty picture.

Borges in his psychedelic ways showed how the quest for perfect reference falls on its face in his short story about the mapmakers trying to create an ever better map but making it more and more closely resemble reality until it became as big as the land it was representing. By the end of his story, it simply lay abandoned on the edge of town. But the mapmakers did not even come close to achieving perfection. Because in the perfect representation of the world, the map itself would have to be included as well. But then an even bigger map would have to be created to capture the map, the reality and their relationship, but then we’d need another even bigger map to capture the previous relationships. And so on. A perfect map is a physical impossibility. Even in an infinite universe, there’s not enough transfinity to hold it.

There’s nothing new about this. Zeno, Russell, Goedel, Turing, Mandelbrot are just the most famous of the names who dealt with this problem in one way or another in the formal realm of mathematics. And Rorty did it for philosophy – while of course all the major philosophers of the last 300 years had hints of it, as well. Hume, Kant, Hegel, Marx, Nietsche, Heidegger, Wittgenstein, Rorty, Feyerabend. Of the western ancients Parmenides. But of course, so called eastern philosophy is rife with this, as well.

Meaning without perfect reference

So what does this mean? Is meaning impossible? Can we not speak? No. Meaning is obviously possible. But not in the way it suggests itself to us. When we say something means something we are implying a perfect one-to-one mapping of symbol to entity. But this is a false implication. When I point at an object and say this is a ‘chair’, I have a feeling that I have thus exhaustively described that object. That I engaged in perfect reference. But because everything about that chair exists, not just it chairness, I have simply pointed to a whole complex of existence and the word ‘chair’ only describes one of its infinitely many dimensions. When I set the chair on fire, at what point does it stop being a chair? When does it start being a chair during the contruction process? When the tree’s cut down with the intention of making furniture? When the last bit of varnish dries? Or somewhere in between? Maybe when it takes on the recognizable shape of a chair or when it can start functioning as a chair. What if it is a modernist chair and I can only recognize it as such when somebody puts a label on it? What if it is a chair in a picture? The label chair can do a lot of this work but it is not a perfect reference that maps nicely onto a thing.

This is all kind of obvious, so obvious that we take it all in our stride in our everyday acts of reference. But it starts causing problems as soon as we try to pin it down in the assumption that if we only stop being everyday about our reference, we can easily identify the ‘real’ referent exactly in the way our usual every-day unthinking reference suggests we are doing already. Oh, we’re just being sloppy thinkers, taking quick shortcuts for convenience. But if we sacrifice some of that convenience, take a bit more time, we will be able to stop the infinite referential regress. There has to be an end to it. But there cannot be. Not within the system of reference itself. Every moment we take to try to nail down the reference, creates another referent for us to refer. It just never ends.

Infinite perfect reference is impossible in principle. And we cannot resolve this by stepping outside the system of reference as we can do with maths in Godel’s theorem. Because, we can only consider reference using referential tools. This is so crazy-making and frustrating that generations of great thinkers simple assumed that it cannot be so. But in fact, it cannot be otherwise. Or if you think, it can. Show me how! I’ve been wrong before. (Obviously the Augustinian God who is outside of time – and presumably reference, or Buddhist karma – the extinguishment of existence itself – are pretty good conceptual exits out of the worry but they don’t provide any usable heuristics for dealing with the paradoxes of reference within the referential model itself.)

Summary of the key consequence

In summary, there’s a paradoxical consequence of the theory of everything. Beause everything exists, perfect reference is impossible, and therefore nothing exists in the way our words and thoughts make it seem it does. Or in a pithier (but less accurate) heuristic I recommend to all philosophers and rationalists:
“Just because there’s a word for it, it does not mean it exists.”

Edge cases in our midst

So what? Who cares about some edge cases on the margins of infinity? We can just happily go on to use our ‘ordinary’ language and take care of the really important problems like designing more efficient energy storage.

If only it were that easy. But as the example with the chair showed, the problems of reference are all around us. They pop up all the time in daily conversation or in basic academic discourse. They are not just something people in the most abstract domains have to deal with on their darker days. They are something we all deal with everyday – all of us – from Socrates to the Macedonian swineherd.

Lets take energy storage. It is a perfect way of thinking about batteries or pumping up water on an incline. But is there really a thing called energy we are storing the same way we may be storing bags of dried beans in a cupboard? Is there even such a ‘thing’ as energy? Well, there’s a whole lot of maths used to describe the measurements in the physical world that make it easy to think about a lot of things in terms of energy. Not only can we think of the world that way, we can all of a sudden compare things like burning fire and the rubbing of hands and the running of horses, pile of coal and pile of dinosaurs, etc. But what is happening when we say X is releasing energy? Is the pumping of water up a hill the same thing as a burning fire? What is it that we’re describing with the math? It is certainly not a given that energy is always a useful concept. People say things like, because everything is energy, I don’t believe in God but in universal energy that connects us all. We may laugh at charlatans like Deepak Chopra, but what is the mathematics describing energy really referring to? Is that one example of perfect reference? There is one energy and one value of energy in the world? Further indivisible? The ultimate building block of our semantics?

No. Theory of everything does not claim that no reference is possible. Or even that it is impossible to have one perfect one to one relationship between a signifier and signified. Just that that sort of atomic reference is not very useful. I can agree with my fellow referees that henceforth ‘dog’ refers to Spot at 5pm on July 23, 2011 in my living room (with the rest of the infinite specification taken as read). But that will render the word completely useless. I will have to then come up with a new word to refer to Spot at 5.01pm or Spot who’s wondered into the garden. Or I may choose the much more sensible option of refering to the fuzzy and ever changing universe of dogness. That word will be imprecise and fuzzy but that will make it useful. We will have broad agreement and negotiate around the edges.

So I can equally say, the word energy refers only to a set of mathematical formulae. But then I severly constrain what I can do with it. Which (in the case of physics) maybe exactly what I want. But it is a solution that does not scale as every effort to come up with a precise language has demonstrated and even if it did, it would necessarily run into paradoxes predicted by the theory of everything.

Possible objections

What are some possible objections to the theory of everything? I can think of several.

  1. The premise is wrong. Everything does not exist. There is a mode of metaexistence (for instance, human consciousness or a state of nirvana) that will make it possible to know all.
  2. There’s no problem. We just need an alternative epistemology which does not rely on reference.
  3. So what if perfect reference is impossible. We just need to come up with simpler formulae that will describe more complex ones and build a perfect reference by proxy.
  4. How does this apply to the theory of everything? How can you say everything exists when by your definition you should not be able to make any statements like that?
  5. You made a logical mistake and it is indeed possible to have perfect reference even when everything exists.

Re 1: Many years ago I read about a Buddhist school of semantics that claimed that the meaning of anything is everything that it is not. And the way Buddha himself was able to confirm that something does not exists was by looking at everything and finding that nothing was it. (This was a long time ago and I’m probably mangling this but it will suffice for illustration.) So is it possible that we can achieve some alternate level of consciousness – perhaps even stepping outside the ‘karmic wheel’ on which everything turns and grasping the whole world non-referrentially as one or simply being aware of everything through a vastly expanding consciouness where the limits of infinity don’t apply. Every mystical tradition would have you believe that you can.

But even if you could (and why not), it wouldn’t solve any of the problems in the here and now. Maybe we should realign our goals and instead of striving for accumulating ever more referential possessions, seek this new alternative consciousness. Sure. But again, this does not solve the problem for this consciousness.

re 2. Well, if you can come up with an epistemology not based around some notion of reference I’d like to see it. Now, there are many philosophical approaches that take the very impossibility (or at least great difficulty) of perfect (or even very good) reference to heart and integrate it into its epistemological toolbox. Zen Koans are one example, floating signifiers of post-modernist semioticians are another. But these approaches don’t actually transcend referentiality. They merely break it and through that breakage reveal the boundaries that reference imposes on us. The best Zen masters such as Derrida in his postcards or Wittgenstein in his investigations do a great job.

But, again this only exarcebates the problem rather than resolve it. There is no bulshit filter on koans. I can just as easily remain clueless as englightened and I have no way of knowing which one I am. Most of the reference transcending statements are as likely as not interpretted as if they are referential and simply referring to something not yet seen. Well, that does not help anyone.

re 3. The whole point of reference is that it simplifies the world. Who cares about perfection. As long as we can come up with simple and beautiful mathematics to describe the complex world, we’ll be in good shape. I call this generative referentiality. And if it could get us out of the jam, it would be nice. But it fails on two counts.

Count 1: Assume you come up with a nice function to describe a chunk of the world. Now, if you plug it into a computer, it will eventually spit out a perfect image of that chunk of the world. But then you’ve created a new object that needs to be generated by another function, including that function itself. Now, you might think that you could Cantor your way out of this. Just map one to one until infinity – no problem if it seems that one set should be smaller than the other. Yes, but Cantor never worried about everything. Russell did and look where that got him.

Count 2: But even if we assumed that generative referentiality can solve this problem, it is still arguable that it actually does do the job we assume referentiality does. Look at Madelbrot’s set. It is a dead simple formula (albeit with complex numbers) that generates infinitudes of self-similar shapes when plotted in a 2D space. But does knowing the formula actually constitute knowing the set? Can we know the set without knowing the formula? Do we need to know both? We can certainly take the formula as the signifier of the whole complex thing. But then it would seem to be mostly doing a job of referring to something complicated and calling it Bob (or Madelbrot’s set) would be just as good. There is something magical about knowing the names of things but knowing the names is not knowing the things. Generative referentiality is extermely useful and we might say it provides the foundations of our current civilisation. But confusing it with perfect referentiality has caused a lot of problems.

re 4. How do the epistemological limitations of the theory of everything apply to the theory itself? This is a typical worry of any foundational epistemological theory that tries to encompass all of cognition. How do you deal with self-referentiality without running into a paradox? The strictures are even more severe on any theory that tries to deal with self-referentiality itself. The limits on perfect reference of course apply to anything I say just as much as anything else. However, there is a small reprieve for reference that does not try to do anything useful. The whole point of reference is that it allows us to grasp something external to us. And the hidden strength of reference (at least hidden from most mainstream logicians) is that it is profoundly simplifying. It only works because it ignores almost everything and only zooms in on what is most important. However, there is a kind of perfect reference that is profoundly useless except as a foundational axiom. And that is tautology.

I can in fact avoid all the problems with chairs, love, kings of France or anything referentiality struggles with if I just say they are exactly what they are. So instead of positing that X = a, I simply say X = X. I can thus refer to everything as being everything and be quite happy that that reference includes itself and everything that surrounds it. Just like I can say that a set of all sets is a set of truly all sets including itself. The problems start when I try to build a non-selfreferntial system out of this assumption. Because I can’t.

I would say that the foundation of the theory of everything is purely therapeutic. It points to some fundamental impossibilities of our system without saying ‘and for my next trick, I will now show you how to simply resolve it’. There is no next trick. However, I will try to outline some heuristics that can be used to get around this. Deconstruction is one such approach – Derrida’s horizons come to mind here (but not something I know a lot about.) But even very simple rationalist heuristics will do as long as we don’t assume that they are external to the limits on perfect reference.

re 5. It is possible that I made a mistake somewhere. In fact, I would not be surprised in the least if I did – this kind of thinking is hard and not my strong suit. But what remains is the empirical fact that perfect reference is nearly impossible. It is so hard that nobody has yet managed to crack it in any system capable of expressing something like language. Even algebra. I never quite managed to understand the details of Goedel’s proof but this is what I imagine he was after. But for him, undecidability was an internal problem for any system with an outside observer. But with everything there is no outside observer. (Or at least not any outside observer we have access to.)

Words-as-models heuristic and the halting problem

So what are we to do? Perfect reference is impossible but our language-thought processes behave as if all reference was perfect. Is there a way out? No, there is no way out. You cannot be out of everything but there’s a way of living with this limitation.

One simple heuristic I suggest is to think of anything we say or think as a model. Each word, sentence, concept. It is a model of the thing it refers to. Then we can then go on and live with the statistician’s dictum: All models are wrong, but some are useful.

Of course, the world does not need me for this. Those assumptions have been around for a long time. But what has been missing is the next step. Ok, so some models are useful, how do we know which ones? Can we come up with a universal procedure for determining usefulness of models? And here the analogy with the halting problem comes in.

Models are a type of (by definition) imperfect reference. So, if we could get a perfect procedure for identifying the utility of models, we could build out a model of the whole world just based on utility. But utility of models is itself a mode and, therefore, by its nature imperfect. Which means we cannot have a perfect external procedure for identifying utility. So, what can we have?

As always, we need to remind ourselves of the heuristic ‘just because there’s a word for it, does not mean it exists’. We have a notion and a word of utility but that does not mean that there is a nice monadic entity of utility floating around in the world that we can attach that word to. We can pretend there is (just like the utilitarians) but that is not going to help us avoid paradoxes and other odius conclusions (just like the utilitarians). We don’t know whether a model is useful until we have examined all of its aspects with respect to all aspects of reality. But that is no more possible than it is possible to examine all steps of an infinitely recursive algorithm. At best we can follow the line of steps as far as the eye can see and say, well, it seems like it will continue for a while. Let’s go get a sandwich.

But with utility, things are even more difficult because it is not intrinsically a point on a simple scale from less useful to more useful. To simplify dealing with utility, we may convert it into a unidimensional scale of ‘utils’ spanning from negative to positive infinity. But that only makes the calculations of utility themselves easier by pushing all the difficult work one step down the line. We still have to decide in every case how to map the utility we perceive onto that scale. And we also have to decide how to measure that mapping. So by committing to a simple scale we have simplified one part of the process but we didn’t solve any of the problems. We simply pushed them upstream to the foundational issues.

How do we halt the infinite regress if we don’t know whether there is an actual end to it? In practice, we already do the only thing we can do. We give up when it feels right. Or when we’re exhausted. Or when we’ve reached a point of some sort of equilibrium or conversely leverage. Our only sane option is to do what we’re doing and not pretend that we’ve cracked the halting problem. Pretend (with conviction to the point of self-delusion) that we’ve come to a decision because a decision at that point makes sense. Dance as if noone is watching and there’s an externally arbitrated rational reason for stopping. Or a common sense one. But those are just pragmatic, ad hoc (or as Rorty insists contingent) decisions. The assumptions of external rationality are therapeutic ones, not epistemological.

Dealing with imperfect reference through heuristics: rationalists, postmodernists and pragmatists

Now, given we know all of the above and assuming we want to be reasonably honest about acknowledging there’s a problem, how do we go about continuing to speak and reason referentially while knowing that the reference we are working with as real is actually impossible? The postmodernists have suggested provisional knowledge. And they’re not wrong. All knowledge has to be provisional. The rationalists have come up with the Bayesian ‘strong opinions weakly held’ and updating priors. And they’re not wrong. And the Pragmatists have come up with conflating epistemology with ethics. I like these the most.

But these are just the general slogans of intent. What is really interesting (and actually useful) are the heuristics developed by each of these traditions.

The rationalists assume (implicitly) that perfect reference is indeed possible but very hard. They have come up (as the scholastics – Western and Eastern – before them) with a number of heuristics in the form of logical fallacies that help point out some of the paradoxes. They sort of present them as if avoiding these fallacies would avoid all problems. But while they help avoiding a lot of problems, they don’t avoid all or even most and they also create new ones. But simply dismissing them because of this would be foolish.

The postmodernists, on the other hand, focus on the impossibility of perfect reference and emphasize the provisionality of knowledge. They have developed a lot of deconstructive techniques to direct the mind to the boundaries of possibility. They almost write poetry about the abundance of everything and the futility of its conquest (Feyerabend being one of the most eloquent here). But they tend to reject even some of the more useful heuristics and are very likely to drown in bulshit. The rationalists are prone to non-sense, as well, but I think the profound embarassment of the Sokal hoax is unique to the postmodernists. The rationalists just assume that the infinite regress can be halted if we put up enough barriers of logic in its way, but postmodernists are sometimes all too happy to see something rhyme and don’t care if it could be made reasonable sense of (albeit provisionally) with some simple rationalist heuristics.

Then, there are the pragmatists. They are closest to my heart and I think Rorty pretty much said everything that I ever wanted to say. They emhasize the contingency of knowledge on situation and social commitments. But unlike the postmodernists, they are happy to take provisional stances for something and do something specific with them. When James spoke about the importance of commitments to others as being the foundation of epistemology, he touched on something fundamental. I came up with the slogan ‘epistemology is ethics’ without knowing about James or the details of Rorty’s analysis but when I read Philosophy and the Mirror of Nature, I knew Rorty and I were soul mates.

But I think Rorty was too quick to dismiss epistemology. He rightly took it down a lot of pegs and showed the impossibility of an ultimate epistemological theory. But he did not give it enough credit in thinking through some of the impossible problems while asssuming they are merely very hard. His ‘liberal ironist’ stance in later essays is a good practical application of the core insight but again, it does not give enough room to the basic heuristics.

That makes it much easier for the traditional epistemologists and scientists to dismiss him as irrelevant. While in fact, he speaks to the very core of their enterprise. But it feels to them like he is taking away the very foundations on which all of their heuristics stand and somehow invalidates them along with it.

But Rorty should be viewed as therapeutic. If I can hope to add anything to Rorty, it is this. Similar to the New Wittgenstein studies. Everytime we run into a referential paradox, we can take solace in its totality and turn away from the brink. We can also just simply save time and not worry about justifying stopping following the referential regress. But we can also let ourselves an out by remembering that we stopped simply for pragmatic reasons. And if new reasons (contingencies) appear, we can resume our journey along the infinite refrential web.

Serenity through disciplined conversation

What I am ironically calling ‘theory of everything’ is designed to do just that. Acknowledge that there is a problem and that there’s nothing that can be done about it.

Very much like Alcoholics Anonymous. The difference is that the wisdom to tell the difference between things we can and cannot do something about is not revealed by a deity but is a constant subject of disciplined conversation. Conversation that reflects the contingencies of the present as much as those of the past. A conversation that cannot have an end but which we must inevitably take part in. The serenity one hopes to get out of this will not come from resignation but from embracing of the totality without assuming that we can grasp its every possible aspect.

This is the therapy Frege needs. As do we all.

How to read ‘Women, Fire and Dangerous Things’: Guide to essential reading on human cognition

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Note:

These are rough notes for a metaphor reading group, not a continuous narrative. Any comments, corrections or elaborations are welcome.

Why should you read WFDT?

Women, Fire, and Dangerous Things: What Categories Reveal About the Mind is still a significantly underappreciated and (despite its high citation count) not-enough-read book that has a lot to contribute to thinking about how the mind works.

I think it provides one of the most concise and explicit models for how to think about the mind and language from a cognitive perspective. I also find its argument against the still prevalent approach to language and the mind as essentially fixed objects very compelling.

The thing that has been particularly underused in subsequent scholarship is the concept of ‘ICMs’ or ‘Idealised Cognitive Models’ which both puts metaphor (for work on which Lakoff is most well known) in its rightful context but also outlines what we should look for when we think about things like frames, models, scripts, scenarios, etc. Using this concept would have avoided many undue simplifications in work in the social sciences and humanities.

Why this guide

Unfortunately, the concision and explicitness I extolled above is surrounded by hundreds of pages of arguments and elaborations that are often less well-thought out than the central thesis and have been a vector for criticism (I’ve responded to some of these in my review of Verena Haser’s book).

As somebody who translated the whole book into Czech and penned extensive commentary on its relevance to the structuralist linguistic tradition, I have perhaps spent more time with it than most people other than the author and his editors.

Which is why when people ask me whether to read it, I usually recommend an abreviated tour of the core argument with some selections depending on the individual’s interest.

Here are some of my suggestions.

Chapters everyone should read

Chapters 3, 4, 5, 6 – Core contribution of the book – Fundamental structuring principles of human cognition

These four chapters summarize what I think everybody who thinks about language, mind and society should know about how categories work. Even if it is not necessarily the last word on every (or any) aspect, it should be the starting point for inquiry.

All the key concepts (see below) are outlined here.

Preface and Chapter 1 – Outline of the whole argument and its implications

These brief chapters lay out succinctly and, I think very clearly, the overall argument of the book and its implications. This is where he outlines the core of the critique of objectivism which I think is very important (if itself open to criticism).

Chapter 2: Precursors

This is where he outlines the broader panoply of thinkers and research outcomes in recent intellectual history whose insights this books tries to systematise and take further.

The chapter takes up some of the key thinkers who have been critical of the established paradigm. Read it not necessarily for understanding them but for a way of thinking about their work in the context of this book.

Case studies

The case studies represent a large chunk of the book and few people will read all 3. But I think at least one of them should be part of any reading of the book. Most people will be drawn to number 1 on metaphor but I find that number 2 shows off the key concepts in most depth. It will require some focus and patience from non-linguists but I think is worth the effort.

Case study 3 is perhaps too linguistic (even though it introduces the important concept of constructions) for most non-linguist.

Key concepts

No matter how the book is read, these are the key concepts I think people should walk away with understanding.

Idealized Cognitive Models (also called Frames in Lakoff’s later work)

I don’t know of any more systematic treatment of how our conceptual system is structured than this. It is not necessarily the last word but should not be overlooked.

Radial Categories

When people talk about family resemblances they ignore the complexity of the conceptual work that goes into them. Radial categories give a good sense of that depth.

Schemas and rich images

While image schemas are still a bit controversial as actual cognitive constructs, Lakoff’s treatment of them alongside rich images shows the importance of both as heuristics to interpreting cognitive phenomena.

Objectivism vs Basic Realism

Although objectivism (nothing to do with Ayn Rand) is not a position taken by any practicing philosophers and feels a bit straw-manny, I find Lakoff’s outline of it eerily familiar as I read works across the humanities and social sciences, let alone philosophy. When people read the description, they should avoid dismissing it with ‘of course nobody thinks that’ and reflect on how many people approach problems of mind and language as if they did think that.

Prototype effects and basic-level categories

These concepts are not original to Lakoff but are essential to understanding the others.

Role of metaphor and metonymy

Lakoff is best known for his earlier work on metaphor (which is why figurative language is not a key concept in itself) but this book puts metaphor and metonymy in perspective of the broader cognition.

Embodiment and motivation

Embodiment is an idea thrown around a lot these days. Lakoff’s is an important early contribution that shows some of the actual interaction between embodiment and cognition.

I find it particularly relevant when he talks about how concepts are motivated but not determined by embodied cognition.

Constructions

Lakoff’s work was taking shape alongside Fillmore’s work on construction grammar and Langacker’s on cognitive grammar. While the current construction grammar paradigm is much more influenced by those, I think it is still worth reading Lakoff for his contribution here. Particularly case studies 2 and 3 are great examples of the power of this approach.

Additional chapters of interest

Elaborations of core concepts

Chapters 17 and 18 elaborate on the core concepts in important ways but many people never reach them because they follow a lot of work on philosophical implications.

Chapter 17 on Cognitive Semantics takes another more deeper look at ICMs (idealized cognitive models) across various dimensions.

Chapter 18 deals with the question of how conceptual categories work across languages in the context of relativism. The name of the book is derived from a non-English example but this takes the question of universals and language specificity head on. Perhaps not the in the most comprehensive way (the debate on relativism has moved on) but it illuminates the core concepts further.

Case studies

Case Studies 2 and 3 should be of great interest to linguists. Not because they are perfect but because they show the depth of analysis required of even relatively simple concepts.

Philosophical implications

Lakoff is not shy about placing his work in the context of disrruption of the reigning philosophical paradigm of his (and to a significant extent our) day. Chapter 11 goes into more depth on how he understands the ‘objectivist paradigm’. It has been criticised for not representing actual philosophical positions (which he explicitly says he’s not doing) but I think it’s representative of many actual philosophical and other treatments of language and cognition.

This is then elaborated in chapters 12 – 16 and of course in his subsequent book with Mark Johnson Philosophy in the Flesh. I find the positive argument they’re making compelling but it is let down by staying on the surface of the issues they’re criticising.

What to skip

Where Lakoff (and elsewhere Lakoff and Johnson) most open themselves to criticism is their relatively shallow reading of their opponents. Most philosophers don’t engage with this work because they don’t find it speaks their language and when it does, it is easily dismissed as too light.

While I think that the broad critique this book presents of what it calls ‘objectivist approaches’ is correct, I don’t recommend that anyone takes the details too seriously. Lakoff simultaneously gives it too little and too much attention. He argues against very small details but leaves too many gaps.

This means that those who should be engaging with the very core of the work’s contribution fixate on errors and gaps in his criticism and feel free to dismiss the key aspects of what he has to say (much to their detriment).

For example, his critique of situational semantics leaves too many gaps and left him open to successful rejoinders even if he was probably right.

What is missing

While Lakoff engages with cognitive anthropology (and he and Johnson acknowledge their debts in the preface to Metaphors We Live By), he does not reflect the really interesting work in this area. Goffman (shockingly) gets no mention, nor does Victor Turner whose work on liminality is pretty important companion.

There’s also little acknowledgement of work on texts such as that by Halliday and Hasan (although, that was arguably still waiting for its greatest impact in the mid 1980s with the appearance of corpora). But Lakoff and most of the researchers in this areas stay firmly at the level of a clause. But give that my own work is mostly focusing on discourse and text-level phenomena, I would say that.

What to read next

Here are some suggestions for where to go next for elaborations of the key concepts or ideas with relevance to those outlined in the book.

  • Moral politics by Lakoff launched his forays into political work but I think it’s more important as an example of this way of thinking applied for a real purpose. He replaces Idealized Cognitive Models with Frames but shows many great examples of them at work. Even if it falls short as an exhaustive analysis of the issues, it is very important as a methodological contribution of how frames work in real life. I think of it almost as a fourth case study to this book.
  • The Way We Think by Gilles Fauconnier and Mark Turner provides a model of how cognitive models work ‘online’ during the process of speaking. Although, it has made a more direct impact in the field of construction grammar, its importance is still underappreciated outside it. I think of it as an essential companion to the core contribution of this book. Lakoff himself draws on Fauconnier’s earlier work on mental spaces in this book.
  • Work on construction grammar This book was one of the first places where the notion of ‘construction’ in the sense of ‘construction grammar’ was introduced. It has since developed in its own substantive field of study that has been driven by others. I’d say the work of Adele Goldberg is still the best introduction but for my money William Croft’s ‘Radical Construction Grammar’ is the most important. Taylor’s overview of the related ‘Cognitive Grammar’ is also not a bad next read.
  • Work on cognitive semantics There is much to read here. Talmy’s massive 2 volumes of ‘Cognitive Semantics’ are perhaps the most comprehensive but most of the work here happens across various journals. I’m not aware of a single shorter introduction.
  • Philosophy and the Mirror of Nature by Richard Rorty is a book I frankly wish Lakoff had read. Rorty’s taking apart of philosophy’s epistemological imaginings is very much complementary to Lakoff’s critique of ‘objectivism’ but done while engaging deeply with the philosophical issues. While I basically go along with Lakoff’s and later Lakoff and Johnson’s core argument, I can see why it could be more easily dismissed than Rorty. Of course, Rorty’s work is also better known for its reputation than deeply reflected in much of today’s philosophy. Lakoff and Johnson’s essential misunderstanding of Rorty’s contribution and fundamental compatibility with their project in Philosophy in the Flesh is an example of why so many don’t take that aspect of this work seriously. (Although, they are right that both Rorty and Davidson would have been better served by a less impoverished view of meaning and language.)

What language looks like: Dictionary and grammar are to language what standing on one foot is to running

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Background

Sometimes a rather obscure and complex analogy just clicks into place in one’s mind and allows a slightly altered way of thinking that just makes so much sense, it hurts. Like putting glasses on in the morning and the world suddenly snapping into shape.

This happened to me this morning when reading the Notes from Two Scientific Psychologists blog and the post on Do people really not know what running looks like?

It describes the fact that many famous painters (and authors of instructional materials on drawing) did not depict running people correctly. When running, it is natural (and essential) to put forward the arm opposite the leg that’s going forward. But many painters who depict running (including the artist who created the poster for the 1922 Olympics!) do it the wrong way round. Not just the wrong way, the way that is almost impossible to perform. And this has apparently been going for as long depiction has been thing. But it’s not just artists (who could even argue that they have other concerns). What’s more when you ask a modern human being to imitate somebody running in a stationary pose (as somebody did on the website Phoons­) they will almost invariably do it the wrong way round. Why? There are really two separate questions here.

  1. Why don’t the incorrect depictions of running strike most people as odd?
  2. Why don’t we naturally arrange our bodies into the correct stance when asked to imitate running while standing still?

Andrew Wilson (one of the two psychologists) has the perfect answer to question 2:

Asking people to pose as if running is actually asking them to stand on one leg in place, and from their point of view these are two very different things with, potentially, two different solutions. [my emphasis]

And he prefaces that with a crucial point about human behavior:

people’s behaviour is shaped by the demands of the task they are actually solving, and that might not be the task you asked them to do.

Do try this at home, try to imitate a runner standing up, then slowly (mime-like), then speed it up. Standing into the wrong configuration is the natural thing to do. Doing it the ‘right’ way round, is hard. It’s not until I sped up into an actual run that my arms found the opposite motion natural until I could keep track of what was going on any more. I would imagine that this would be the case for most people. In fact, the few pictures I could find of runners arranged standing at the start of the race have most of them also with the ‘wrong’ hand/leg position and they’re not even standing on one leg. (See here and here.)

Which brings us back to the first question. Why does not anybody notice? I personally find it really hard to even identify the wrong static description at a glance. I have to slow down, remember what is correct, then match it to the image. What’s going on. We obviously don’t have any cognitive control over the part of running that controls the movement arms in relation tot he movement of legs. We also don’t have any models or social scripts that pay attention to this sort of thing. It is a matter of conscious effort, a learned behaviour, to recognize these things.

Why is this relevant to language?

If you ask someone to describe a language, they will most likely start telling you about the words and the rules for putting them together. In other words, compiling a dictionary and a grammar. They will say something like: “In Albanian, the word for ‘bread’ is ‘bukë'”. Or they will say something like “English has 1 million words.”, “Czech has no word for training.” or “English has no cases.”

All of these statements reflect a notion of language that has a list of words that looks a little like this:

bread n. = 1. baked good, used for food, 2. metaphor for money, etc.
eat v. = 1. process of ingestion and digestion, 2. metaphor, etc.
people n. plural = human beings

And a grammar that looks a little bit like this.

Sentence = Noun (subj.) + Verb + Noun (obj.)

All of this put together will give us a sentence:

People eat food.

All you need is long enough list of words and enough (but not as many) rules and you got a language.

But as linguists have discovered through not a bit of pain, you don’t have a language. You have something that looks like a language but not something that you can actually speak as a language. It’s very similar to language but it’s not language.

Kind of like the picture of the runner with the arms going in the opposite direction. It looks very much like someone running but it’s not it’s just a picture of them running and the picture is fundamentally wrong. Just not in a way that is at all obvious to most people most of the time.

Why grammars and dictionaries seem like a good portrait of language

So, we can ask the same two questions again.

  1. Why does the stilted representation of language as rules and words not strike most people (incl. Steven Pinker) as odd?
  2. Why don’t we give more realistic examples of language when asked to imitate one?

Let’s start with question 2 again which will also give us a hint as to how to answer question 1.

So why, when asked to give an example of English, am I more likely to give:

John loves Mary.

or

Hello. Thank you. Good bye.

than

Is it cold in here? Could you pass the sugar, please. No no no. I’ll think about it?

It’s because I’m achieving a task that is different from actually speaking the language. When asked to illustrate a language, we’re not communicating anything in the language. So our very posture towards the language changes. We start thinking in equivalencies and left and right sides of the word (word = definition) and building blocks of a sentence. Depending on who we’re speaking to, we’ll choose something very concrete or something immediately useful. We will not think of nuance, speech acts, puns or presupposition.

But the vast majority of our language actions are of the second kind. And many of the examples we give of language are actually good for only one thing: Giving an example of the language. (Such as the famous example from logic ‘A man walks’ which James MacCawley analysed as only being usable in one very remote sense.)

As a result, if we’re given the task of describing language, coming up with something looking like a dictionary and a grammar is the simplest and best way of achieving fullfilling the assignment. If we take a scholarly approach to this task over generations, we end up with something that very much looks like the modern grammars and dictionaries we all know .

The problem is that these don’t really give us “a picture of language”, they give us “a picture of a pose of language” that looks so much like language to our daily perception, that we can’t tell the difference. But in fact, they are exactly the opposite of language looks like.

Now, we’re in much more complex waters than running. Although, I imagine the exact performance of running is in many ways culturally determined, the amount of variation is going to be limited by the very physical nature of the relatively simple task. Language on the other hand, is almost all culture. So, I would expect people in different contexts to give different examples. I read somewhere (can’t track down the reference now) that Indian grammarians tended to give examples of sentences in the imperative. Early Greeks (like Plato) had a much more impoverished view of the sentence than I showed above. And I’m sure there are languages with even more limited metalanguage. However, the general point still stands. The way we tend to think about language is determined by the nature of the task

The key point I’ve repeated over and over (following Michael Hoey) is that grammars and dictionaries are above all texts written in the language. They don’t stand aprt from it. They have their own rules, conventions and inventories of expression. And they are susceptible to the politics and prejudices of their time. Even the OUP. At the same time, they can be very useful tools to developing language skills or dealing with unfamiliar texts. But so does asking a friend or figuring out the meaning in context.

Which brings us to question 1. Why has nobody noticed that language doesn’t quite work that way? The answer is that – just like with running – people have. But only when they try to match the description with something that is right in front of them. Even then, they frequently (and I’m talking about professional linguists like Stephen Pinker here) ignore the discrepancy or ascribe it to a lack of refinement of the descriptions. But most of the time, the tasks that we fulfil with language do not require us to engage the sort of metacognitive aparatus that would direct us to reflect on what’s actually going on.

What does language really look like

So is there a way to have an accurate picture of language? Yes. In fact, we already have it. It’s all of it. We don’t perhaps have all the fine details, but we have enough to see what’s going on – if we look carefully. It’s not like linguists of all stripes have not described pretty much everything that goes on with language in one way or another. The problem is that they try to equate the value of a description to the value of the corresponding model that very often looks like an algorithm amenable to being implemented in a computer program. So, if I describe a phenomenon of language as a linguist, my tendency is to immediately come up with a fancy looking notation that will look like ‘science’. If I can make it ‘mathematical’, all the better. But all of these things are only models. They are ways of achieving a very particular task. Which is to – in one way or another – model language for a particular purpose. Development of AI, writing of pedagogic grammars, compiling word lists, predicting future trends, tracing historical developments, estimating psychological impact, etc. All of these are distinct from actual pure observation of what is going on. Of course, even simple description of what I observe is a task of its own with its own requirements. I have to choose what I notice and decide what I report on. It’s a model of a sort, just like an accurate painting of a runner in motion is just a model (choosing what to emphasize, shadows, background detail, facial expression, etc.) But it’s the task we’re really after: Coming up with as accurate and complete a picture of language as is possible for a collectivity of humans.

People working in construction grammars in the usage-based approach are closest to the task. But they need to talk with people who work on texts, as well, if they really want to start painting a fuller picture.

Language is signs on doors of public restrooms, dirty jokes on TV, mothers speaking to children, politicians making speeches, friends making small talk in the street, newscasters reading the headlines, books sold in bookshops, gestures, teaching ways of communication in the classroom, phone texts, theatre plays, songs, blogs, shopping lists, marketing slogans, etc.

Trying to reduce their portrait to words and rules is just like trying to describe a building by talking about bricks and mortar. They’re necessary and without them nothing would happen. But a building does not look like a collection of bricks and mortar. Nor does knowing how to put a brick to brick and glue them together help in getting a house built. At best, you’d get a knee-high wall. You need a whole of other knowledge and other kinds of strategies of building corners, windows, but also getting a planning permission, digging a foundation, hiring help, etc. All of those are also involved in the edifices we construct with language.

An easy counterargument here would be: That’s all well and good but the job of linguistics is to study the bricks and the mortar and we’ll leave the rest to other disciplines like rhetoric or literature. At least, that’s been Chomsky’s position. But the problem is that even the words and grammar rules don’t actually look like what we think they do. For a start, they’re not arranged in any of the ways in which we’re used to seeing them. But they probably don’t even have the sorts of shapes we think of them in. How do I decide whether I say, “I’m standing in front of the Cathedral” or “The Cathedral is behind me.”? Each of these triggers a very different situation and perspective on exactly the same configuration of reality. And figuring out which is which requires a lot more than just the knowledge of how the sentence is put together. How about novel uses of words that are instantly recognizable like “I sneezed the napkin off the table.” What exactly are all the words and what rules are involved?

Example after example shows us that language does not look very much like that traditional picture we have drawn of it. More and more linguists are looking at language with freshly open eyes but I worry that they may get off task when they’re asked to make a picture what they see.

Where does the metaphor break

Ok, like all metaphors and analogies, even this one must come to an end. The power of a metaphor is not just finding where it fits but also pointing out its limits.

The obvious breaking point here is the level of complexity. Obviously, there’s only one very discretely delineated aspect of what the runners are doing that does not match what’s in the picture. The position of the arms. With language, we’re dealing with many subtle continua.

Also, the notion of the task is taken from a very specific branch of cognitive psychology and it may be inappropriate extending it to areas where tasks take a long time, are collaborative and include a lot of deliberately chosen components as well as automaticity.

But I find it a very powerful metaphor nevertheless. It is not an easy one to explain because both fields are unfamiliar. But I think it’s worth taking the time with it if it opens the eyes of just one more person trying to make a picture of language looks like.

Anthropologists’ metaphorical shenanigans: Or how (not) to research metaphor

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Over on the excellent ‘Genealogy of Religion’, Cris Campbell waved a friendly red rag in front of my eyes to make me incensed over exaggerated claims (some) anthropologists make about metaphors. I had expressed some doubts in previous comments but felt that perhaps this particular one deserves its own post.

The book Cris refers to is a collection of essays  America in 1492: The World of the Indian Peoples Before the Arrival of Columbus (1991, ed. Alvin Josephy) which also contains an essay by Joel Sherzer called “A Richness of Voices”.  I don’t have the book but I looked up a few quotes on metaphor from the book.

The introduction summarizes the conclusion thus:

“Metaphors about the relations of people to animals and natural forces were essential to the adaptive strategies of people who lived by hunting.” (p. 26)

This is an example what Sherzer has to say about metaphor:

“Another important feature of native vocabularies was the metaphor – the use of words or groups of words that related to one realm of meaning to another. To students they provide a window into American Indian philosophies. … The relationship between the root and the derived form was often metaphorical.” (p. 256)

The first part of both statements is true but the second part does not follow. That is just bad bad scholarship. I’m not a big Popperian but if you want to make claims about language you have to postulate some hypotheses and try really really really hard to disprove them. Why? Because there are empirical aspects to the questions that can have empirical support. Instead the hypotheses are implied and no attempt is made to see if they work. So this is what I suggest are Sherzer’s implicit hypotheses that should be made explicit and tested:

  1. American Indian languages use metaphors for essential parts of their understanding of the world. (Corollary: If we understand the metaphors, we can understand the worldview of the speakers of those languages.)
  2. American Indian language use of metaphors was necessary to their survival because of their hunter-gatherer lifestyles.
  3. American Indian languages use metaphor than the SAE (Standard Average European) languages.

Re 1: This is demonstrably true. It is true of all languages so it is not surprising here. However, exactly how central this metaphorical reasoning is and how it works cognitively is an open question. I addressed some of this in my review of Verena Haser’s book.

As to the corollary, I’ve mentioned this time and time again. There is no straightforward link between metaphor and worldview. War on poverty, war on drugs, war on terror all draw on different aspects of war. As does Salvation Army, Peace Corps and the Marine Corps. You can’t say that Salvation Army subscribes to the same level of violence than a ‘real’ Army. The same goes for metaphors like ‘modern Crusades’ or the various notions of ‘Jihad’. Metaphor works exactly because it does not commit us to a particular course of action.

That’s not to say that the use of metaphor can never be revealing of underlying conceptualizations. For instance, calling something rebellion vs. calling it a ‘civil war’ imposes a certain order on the configuration of participants and reveals the speaker’s assumptions. But calling one ‘my rock’ does not reveal any cultural preoccupation with rocks. The latter (I propose) is much more common than the former.

Re 2: I think this is demonstrably false. From my (albeit incomplete) reading of the literature, most of the time metaphors just got in the way of hunting. Thinking of the ‘Bear’ as the father to whom you have to ritually apologise before killing him seems a bit excessive. Over metaphorisation of plants and animals has also led to their over or under exploitation. E.g. the Nuer not eating birds and foregoing an important source of nutricion or the Hawains hunting rare birds to extinction for their plumes. Sure, metaphors were essential to the construction of folk taxonomies but that is equally true of Western ‘scientific’ taxonomies which map into notions of descent, progress and containment. (PS: I’ve been working on a post called ‘Taxonomies are metaphors where I elaborate on this).

Re 3: This is just out and out nonsense. The example given are stuff like bark of the tree being called ‘skin’ and spacial prepositions like ‘on top of’ or ‘behind’ being derived from body parts. The author obviously did not bother to consult an English etymological dictionary where he could discover that ‘top’ comes from ‘tuft’ as in ‘tuft of hair’ (or is at the very least connected). And of course the connection of ‘behind’ to body part (albeit in the other direction) should be pretty obvious to anyone. Anyway, body part metaphors are all over all languages in all sorts similar but inconsistent ways: mountains have feet (but not heads), human groups have heads (but not feed), trees have trunks (but not arms), a leader may have someone as their right arm (but not their left foot). And ‘custard has skin’ in English (chew on that). In short, unless the author can show even a hint of a quantitative tendency, it’s clear that American Indian languages are just as metaphorical as any other languages.

Sherzer comes to this conclusion:

“Metaphorical language pervaded the verbal art of the Americas in 1492, in part because of the closeness Native American had always felt to the natural world around them and their social, cultural, aesthetic, and personal identification with it and in part because of their faith in the immediacy of a spirit world whose presence could be manifest in discourse.”

But that displays fundamental misunderstanding of how metaphor works in language. Faith in immediacy has no link to the use of metaphors (or at the very least Sherzer did not demonstrate any link because he confused lyricism with scholarship). Sure, metaphors based on the natural world might indicate ‘closeness to the natural world around’ but that’s just as much of a discovery as saying that people who live in an area with lots of oaks have a word that means ‘oak’. The opposite would be surprising. The problem is that if you analyzed English without preconceptions about the culture of its speakers you would find as much of a closeness to the natural world (e.g a person can be ‘a force of nature’, ‘eyes like a hawk’, ‘dirty as a pig’, ‘wily as a fox’, ‘slow as a snail’, ‘beautiful as a flower’, ‘sturdy as a tree’, etc.).

While this seems deep, it’s actually meaningless.

“The metaphorical and symbolic bent of Mesoamerica was reflected in the grammars, vocabularies, and verbal art of the region. (p. 272)

Mesoamerica had no ‘symbolic bent’. Humans have a symbolic bent, just like they have spleens, guts and little toes.  So let’s stop being all gushy about it and study things that are worth a note.

PS: This just underscores my comments on an earlier post of Cris’ where I took this quote to task:

“Nahuatl was and is a language rich in metaphor, and the Mexica took delight in exploring veiled resemblances…” This is complete and utter nonsense. Language is rich in metaphor and all cultures explore veiled resemblances. That’s just how language works. All I can surmise is that the author did not learn the language very well and therefore was translating some idioms literally. It happens. Or she’s just mindlessly spouting a bullshit trope people trot out when they need to support some mystical theory about a people.

And the conclusion!? “In a differently conceptualized world concepts are differently distributed. If we want to know the metaphors our subjects lived by, we need first to know how the language scanned actuality. Linguistic messages in foreign (or in familiar) tongues require not only decoding, but interpretation.” Translated from bullshit to normal speak: “When you translate things from a foreign language, you need to pay attention to context.” Nahuatl is no different to Spanish in this. In fact, the same applies to British and American English.

Finally, this metaphor mania is not unique to anthropologists. I’ve seen this in philosophy, education studies, etc. Metaphors are seductive… Can’t live without them…

Image by moune.drah CC BY NC SA