The nature of math came up in our embodied cognition discussion. Here is a presentation by Dehaene on the topic followed by comments from The Reality Club: George Lakoff, Marc Hauser, Jaron Lanier, Rafael Núñez, Margaret Wertheim, Howard Gardner, Joseph Traub, Steven Pinker, Charles Simonyi. A few brief, edited Lakoff excerpts follow from that discussion. Note that this is a discussion from 1997, so a lot of confirming science has happened since then.
” [Dehaene] has made it clear that our capacity for number has evolved and that the very notion of number is shaped by specific neural systems in our brains. […] We understand the world through our cognitive models and those models are not mirrors of the world, but arise from the detailed peculiarities of our brains.”
“Mathematics is not ‘abstract’, but rather metaphorical, based on projections from sensory-motor areas that make use of ‘inferences’ performed in those areas. The metaphors are not arbitrary, but based on common experiences: putting things into piles, taking steps, turning around, coming close to objects so they appear larger, and so on.”
“Dehaene is right that this requires a nonplatonic philosophy of mathematics that is also not socially constructivist. Indeed, what is required is a special case of experientialist philosophy (or ’embodied realism’). […] Such a philosophy of mathematics is not relativist or socially constructivist, since it is embodied, that is, based on the shared characteristics of human brains and bodies as well as the shared aspects of our physical and interpersonal environments. […] On the other hand, such a philosophy of mathematics is not platonic or objectivist. Consider two simple examples. First, can sets contain themselves or not? This cannot be answered by looking at the mathematical universe. You can have it either way, choosing either the container metaphor or the graph metaphor, depending on your interests.”
“Dehaene is by no means alone is his implicit rejection of the Computer Program Theory. Distinguished figures in neuroscience have rejected it (e.g., Antonio Damasio, Gerald Edelman, Patricia Churchland). Even among computer scientists, connectionism presents a contrasting view. In our lab at the International Computer Science Institute at Berkeley, Jerome Feldman, I, and our co-workers working on a neural theory of language, have discovered results in the course of our work suggesting that the program-mind is not even a remotely good approximation to a real mind.”
Pinker of course also comments and takes issue with Lakoff’s depiction of him. Dehaene also responds to the comments at the end.
A Nieman Reports article highlights four startups seeking to improve public discourse. Let’s hope efforts to create methods and technologies along these lines accelerate and succeed in producing positive outcomes.
This article was originally published at Aeon and has been republished under Creative Commons.
Cassandra woke up to the rays of the sun streaming through the slats on her blinds, cascading over her naked chest. She stretched, her breasts lifting with her arms as she greeted the sun. She rolled out of bed and put on a shirt, her nipples prominently showing through the thin fabric. She breasted boobily to the stairs, and titted downwards.
This particular hyperbolic gem has been doing the rounds on Tumblr for a while. It resurfaced in April 2018, in response to a viral Twitter challenge posed by the US podcaster Whitney Reynolds: women, describe yourself the way a male writer would.
The dare hit a sweet spot. Many could summon up passages from books containing terrible, sexualised descriptions of women. Some of us recalled Haruki Murakami, whose every novel can be summarised as: ‘Protagonist is an ordinary man, except lots of really beautiful women want to sleep with him.’ Others remembered J M Coetzee, and his variations on the plot: ‘Tenured male professor in English literature sleeps with beautiful female undergraduate.’ It was a way for us to joke about the fact that so much great literature was written by men who could express perfectly detailed visual descriptions of the female body, and yet possessed such an impoverished understanding of the female mind.
This is why the philosophical project of trying to map the contours of other minds needs a reality check. If other humans are beyond our comprehension, what hope is there for understanding the experience of animals, artificial intelligence or aliens?
I am a literature scholar. Over thousands of years of literary history, authors have tried and failed to convey an understanding of Others (with a capital ‘O’). Writing fiction is an exercise that stretches an author’s imagination to its limits. And fiction shows us, again and again, that our capacity to imagine other minds is extremely limited.
It took feminism and postcolonialism to point out that writers were systematically misrepresenting characters who weren’t like them. Male authors, it seems, still struggle to present convincing female characters a lot of the time. The same problem surfaces again when writers try to introduce a figure with a different ethnicity to their own, and fail spectacularly.
I mean, ‘coffee-coloured skin’? Do I really need to find out how much milk you take in the morning to know the ethnicity you have in mind? Writers who keep banging on with food metaphors to describe darker pigmentation show that they don’t appreciate what it’s like to inhabit such skin, nor to have such metaphors applied to it.
Conversely, we recently learnt that some publishers rejected the Korean-American author Leonard Chang’s novel The Lockpicker (2017) – for failing to cater to white readers’ lack of understanding of Korean-Americans. Chang gave ‘none of the details that separate Koreans and Korean-Americans from the rest of us’, one publisher’s letter said. ‘For example, in the scene when she looks into the mirror, you don’t show how she sees her slanted eyes …’ Any failure to understand a nonwhite character, it seems, was the fault of the nonwhite author.
Fiction shows us that nonhuman minds are equally beyond our grasp. Science fiction provides a massive range of the most fanciful depictions of interstellar space travel and communication – but anthropomorphism is rife. Extraterrestrial intelligent life is imagined as Little Green Men (or Little Yellow or Red Men when the author wants to make a particularly crude point about 20th-century geopolitics). Thus alien minds have been subject to the same projections and assumptions that authors have applied to human characters, when they fundamentally differ from the authors themselves.
For instance, let’s look at a meeting of human minds and alien minds. The Chinese science fiction author Liu Cixin is best known for his trilogy starting with The Three-Body Problem (2008). It appeared in English in 2014 and, in that edition, each book has footnotes – because there are some concepts that are simply not translatable from Chinese into English, and English readers need these footnotes to understand what motivates the characters. But there are also aliens in this trilogy. From a different solar system. Yet their motivations don’t need footnoting in translation.
Splendid as the trilogy is, I find that very curious. There is a linguistic-cultural barrier that prevents an understanding of the novel itself, on this planet. Imagine how many footnotes we’d need to really grapple with the motivations of extraterrestrial minds.
Our imaginings of artificial intelligence are similarly dominated by anthropomorphic fantasies. The most common depiction of AI conflates it with robots. AIs are metal men. And it doesn’t matter whether the press is reporting on swarm robots invented in Bristol or a report produced by the House of Lords: the press shall plaster their coverage with Terminator imagery. Unless the men imagining these intelligent robots want to have sex with them, in which case they’re metal women with boobily breasting metal cleavage – a trend spanning the filmic arts from Fritz Lang’s Metropolis (1927) to the contemporary TV series Westworld (2016-). The way that we imagine nonhumans in fiction reflects how little we, as humans, really get each other.
All this supports the idea that embodiment is central to the way we understand one another. The ridiculous situations in which authors miss the mark stem from the difference between the author’s own body and that of the character. It’s hard to imagine what it’s like to be someone else if we can’t feel it. So, much as I enjoyed seeing a woman in high heels outrun a T-Rex in Jurassic World (2015), I knew that the person who came up with that scene clearly has no conception of what it’s like to inhabit a female body, be it human or Tyrannosaurus.
Because stories can teach compassion and empathy, some people argue that we should let AIs read fiction in order to help them understand humans. But I disagree with the idea that compassion and empathy are based on a deep insight into other minds. Sure, some fiction attempts to get us to understand one another. But we don’t need any more than a glimpse of what it’s like to be someone else in order to empathise with them – and, hopefully, to not want to kill and destroy them.
As the US philosopher Thomas Nagel claimed in 1974, a human can’t know what it is like to be a bat, because they are fundamentally alien creatures: their sensory apparatus and their movements are utterly different from ours. But we can imagine ‘segments’, as Nagel wrote. This means that, despite our lack of understanding of bat minds, we can find ways to keep a bat from harm, or even nurse and raise an orphaned baby bat, as cute videos on the internet will show you.
The problem is that sometimes we don’t realise this segment of just a glimpse of something bigger. We don’t realise until a woman, a person of colour, or a dinosaur finds a way to point out the limits of our imagination, and the limits of our understanding. As long as other human minds are beyond our understanding, nonhuman ones certainly are, too.
Kanta Dihal is a postdoctoral research assistant and the research project coordinator of the Leverhulme Centre for the Future of Intelligence at the University of Cambridge.
This article was originally published at Aeon and has been republished under Creative Commons.
Our discussions all, to some extent, relate to cognition. An important area of inquiry concerns whether some form of physical embodiment is required for a brain to support cognition in general and the self-aware sort of cognition we humans possess.
Philosophy In The Flesh: The Embodied Mind And Its Challenge To Western Thought, by George Lakoff and Mark Johnson. Please note, while the title includes “Philosophy,” we are not a philosophy group and the book and discussion will revolve around scientific concepts and implications, not spiritualistic or metaphysical ideas.
– Amazon (used copies in the $6 range, including shipping)
RSVP by email to email@example.com if you plan to attend our discussion on the afternoon of Saturday, November 3, 2018.
While our group enjoys socializing and will plan other events to that end, this meeting is for focused discussion among people who invest the time in advance to inform themselves on the topic. As a courtesy to those who will do their ‘homework,’ before the meeting please read and consider Part 1 (the first eight chapters) of the book. As you read, jot down your thoughts and questions on the book’s claims, supporting evidence, and implications for our core topics–brain, mind, and artificial intelligence. If you are not able to invest this effort prior to the meeting, please do not attend. Thank you for your understanding.
Will new readers develop the more time-demanding cognitive processes nurtured by print-based mediums as they absorb and acquire new cognitive capacities emphasized by digital media? For example, will the combination of reading on digital formats and daily immersion in a variety of digital experiences — from social media to virtual games — impede the formation of the slower cognitive processes, such as critical thinking, personal reflection, imagination, and empathy, that are all part of deep reading?
Wolf first addressed the evolution of reading and its implications in her earlier book, Proust and the Squid: The Story and Science of the Reading Brain. She summarizes her thesis in this interview (14 min video).
Stanislas Dehaene, an author whose work we’ve discussed, also investigated the brain circuits involved in reading. Hear him speak on the topic in this video (33 min).
For something a little different to start your weekend, here is a glimpse into one man’s subjective world. He asks himself what consciousness is. He observes, “Life is fear,” yet his mind has found a way to peace. What is the adaptive significance of magical thinking? What is the value of cozying up to ambiguity?
Indeed we should according to this recent Scientific American article. One thing I learned from Dennett in his new book is that according to him the scientific image uncovers an objective, underlying reality, while the manifest image is corrupted by our personal ontology. Not so according to quantum mechanics, which operates on the premise that our scientific results themselves are tied to our perceptions and constructed categories, not “a purely objective world out there.” There is a paradigm shift in science itself in accepting this understanding, given quantum anomalies described in the link. It’s time to update your scientific (and manifest) image Professor Dennett.
From the introduction to Chapter 9 of his new book The Strange Order of Things.
“The term ‘consciousness’ applies to the very natural but distinctive kind of mental state described by the above [subjective] traits. The mental state allows its owner to be the private experiencer of the world around and, just as important, to experience aspects of his or her own being. For practical purposes, the universe of knowledge, current and past, that can be conjured up in a private mind only materializes to its owner when the owner’s mind is in a conscious state, able to survey the contents of that mind, in his or her own subjective perspective.” This perspective is combined with “integrated experience, which consists of placing mental contents into a more or less unified multidimensional panorama” (143- 44).
Also of note is that consciousness is not located in any particular brain area but “it is possible to identify several brain regions and systems that are unequivocally related to producing key ingredients of the process as outlined earlier: perspectival stance, feeling and experience integration” (154). But “still, the panoramic integrated experience […] is not to be found in one single brain structure but rather in more or less numerous time series of frames being activated piecemeal” (156).