29 May 2016

Lakoff: Math is made up by your brain

Tonight I was on YouTube, and in my 'recommended videos' section there was a selection from the channel Closer to Truth asking physicist Max Tegmark the old granddaddy of questions, "Why is there something rather than nothing?" Tegmark goes on to expound on his view that the universe is fundamentally mathematical and that mathematics are discovered, not invented.

Tegmark's view is an example of a view called mathematical Platonism, a form of mathematical realism which holds that:
  • There are mathematical objects
  • Mathematical objects are abstract
  • Mathematical objects are independent of intelligent agents and their language, thought, and practices.
There are several difficulties that this point of view faces, both conceptually (what, exactly, is an "abstract object" and how does it causally interact with the brain?) and given what we actually observe here in the physical universe. Alexander Vilenkin touched on Tegmark's ideas in his book Many Worlds In One:
The number of mathematical structures increases with increasing complexity, suggesting that “typical” structures should be horrendously large and cumbersome. This seems to be in conflict with the simplicity and beauty of the theories describing our world.
It just so happens that in the 'related videos' sidebar, YouTube recommended this vid from George Lakoff on embodied mathematical cognition — a condensed version of his book Where Mathematics Comes From. It's a scientific alternative to folk theories of mathematics like mathematical Platonism and though it's a relatively nascent field with plenty of challenges ahead, there's growing evidence that it's correct [1, 2, 3]. It's not without controversy, but challenging intelligent people to case aside philosophies entrenched in academia for centuries is inevitably going to meet resistance.

My take is that the conceptual ambiguities intrinsic to mathematical realism put it at a disadvantage to embodied mathematical cognition, which builds on research from the broader field of embodied cognition. Is it true? I don't know. And as a non-mathematician, some of this stuff is over my head. But I think it's fascinating as hell, and the fact that it grounds conceptual abstraction within the purview of scientific inquiry instead of mysterious 'metaphysical realms' is a big reason why I'm such a fan of Lakoff's work.

Anyway... here's the lecture. 

20 May 2016

The Oklahoma State Legislature makes me embarrassed to live in the state

Just this week, the legislature in my state of Oklahoma has:

And just a couple of months ago, the passed legislation that would ask voters to restore the 10 Commandments monument to the Capitol after the state supreme court ruled it unconstitutional.

Now look, this is bad enough. Most of this legislation is flagrantly unconstitutional. Our governor Mary Fallin, by most accounts an incompetent stooge, at least had the foresight to veto the abortion law and save the state hundreds of thousands in legal fees from a sure-loss court case. 

But here's what really grinds my gears: shit is bad in Oklahoma, and a good deal of it is the legislature's fault. Years of Laffer-Curve economics has led the state to a record budget shortfall that is threatening funding for medicaid, teachers, schools, public attorneys, and much much more. And Oklahoma is just one of many GOP-led states whose Laffer-Curve policies have led to steep red ink.

You'd think this would lead to a little introspection among the legislature: Golly, maybe supply-side economics aren't working! Pfff. Of course not. Tax cuts have become such a central part of the GOP milieu that it's unfathomable that a candidate would campaign without them. Conservatives love to chide Bernie Sanders supporters for wanting "free stuff", while presumptive GOP nominee Donald Trump offers a tax-cut plan that would cost nearly $10 trillion over the next decade, with most of the cost coming from cuts to top earners. But hey, I guess that's just "free stuff", right? 


Teachers are losing their jobs. Schools are facing closings, 4-day weeks, larger class sizes, and reduced bus routes because of massive shortfalls in education funding. Public attorneys aren't getting funding. The House passed a bill cutting 111,000 people from medicaid

At a time when the state legislature should be hard at work on solutions to these problems, they're passing frivolous laws and pandering to the most extreme of their constituency. Unsurprisingly, the non-profit Center for Public Integrity and Global Integrity gave Oklahoma an "F", citing a lack of transparency, corruption, inequality, and access to public information. The one bright spot is in the state's auditing office, which independently found "fraud and waste across a broad spectrum of public bodies".

It's not entirely clear what can be done in the short term. I just hope that the widespread knowledge of the legislature's incompetency inspires more urban young people to get out the vote.

Robert Epstein: Your brain is not a computer

For decades, the neurocomputational metaphor has been an integral part of research that attempts to bridge the gap between the biological structure of the brain and cognition. But it is, alas, only a metaphor. In an essay for Aeon, psychologist Robert Epstein argues that your brain does not process information, store knowledge, or retrieve memories. In short: it is not a computer.

Some choice quotes:
We don’t store words or the rules that tell us how to manipulate them. We don’t create representations of visual stimuli, store them in a short-term memory buffer, and then transfer the representation into a long-term memory device. We don’t retrieve information or images or words from memory registers. Computers do all of these things, but organisms do not.
[The] IP metaphor is, after all, just another metaphor – a story we tell to make sense of something we don’t actually understand. And like all the metaphors that preceded it, it will certainly be cast aside at some point – either replaced by another metaphor or, in the end, replaced by actual knowledge.
Misleading headlines notwithstanding, no one really has the slightest idea how the brain changes after we have learned to sing a song or recite a poem. But neither the song nor the poem has been ‘stored’ in it. The brain has simply changed in an orderly way that now allows us to sing the song or recite the poem under certain conditions. When called on to perform, neither the song nor the poem is in any sense ‘retrieved’ from anywhere in the brain, any more than my finger movements are ‘retrieved’ when I tap my finger on my desk. We simply sing or recite – no retrieval necessary.

It's a fascinating and provocative essay. I'd be very curious to hear thoughts on it from writers I follow like Steve Novella (neuroscientist) and George Lakoff (cognitive linguist).

However, there are a few issues that I'd raise with this essay.

The first is that while metaphor is of course not literal — computers don't literally store and process information — metaphors are nonetheless integral to our human process of reasoning. As counter-intuitive as it might be, we literally cannot reason without the use of metaphor. These range from primary metaphors like big is important ("tomorrow is the big day!") or love is closeness ("we grew apart over the last year") and many more, to conceptualizations of time as spatial movement ("the holidays are approaching quickly") or causation as motion ("FDR's leadership brought the country out of depression"). The fact that we conceptualize the brain using the neurocomputational metaphor is not in itself fault, such that it allows us to understand and predict states of cognition. But Epstein is likely correct in that the metaphor is inherently limited. That's why we need a cross-disciplinary study of the mind and brain from neurobiology, neurocomputation, and cognition.

I'm also skeptical of this claim:
[There] is no reason to believe that any two of us are changed the same way by the same experience. If you and I attend the same concert, the changes that occur in my brain when I listen to Beethoven’s 5th will almost certainly be completely different from the changes that occur in your brain.
Our shared biology constitutes a reason to think that responses to similar experiences are at least somewhat the same. Perhaps Epstein simply means that the configurations of neurons that change over a lifetime are inherently widely varied due to our vastly varying experiences; but we don't have to throw the baby out with the bathwater — the same parts of the brain likely undergo similar structural changes in response to similar stimuli, simply because our brains are — by our shared, human DNA — very similar organs.

Those are my thoughts, at least. But it's a provocative topic, certainly.

Full essay: The Empty Brain

18 May 2016

Humans of New York, and thoughts on childhood cancer

Christian theodicies contend that God has a Divine Plan, and thus morally sufficient (if inexorably mysterious) reasons for allowing this child to suffer. (Click to embiggen...)

His story is one of many. If there's anything that convinces me a theistic god — one who is invested in human affairs — does not exist, it's childhood cancer. And the weaselly rationalization that it's a necessary part of God's unknowable, mysterious, yet presumably perfect plan just strikes me as the most blind and desperate kind of faith. 

16 May 2016

Galen Strawson: Consciousness Isn't a Mystery

Galen Strawson, professor of philosophy at the University of Texas at Austin, writes in a New York Times op ed that the "mystery of consciousness" isn't really so mysterious:

Consciousness Isn't a Mystery. It's Matter.

In his own way, he argues for non-eliminative physicalism:

Those who make the Very Large Mistake (of thinking they know enough about the nature of the physical to know that consciousness can’t be physical) tend to split into two groups. Members of the first group remain unshaken in their belief that consciousness exists, and conclude that there must be some sort of nonphysical stuff: They tend to become “dualists.” Members of the second group, passionately committed to the idea that everything is physical, make the most extraordinary move that has ever been made in the history of human thought. They deny the existence of consciousness: They become “eliminativists.” 
This amazing phenomenon (the denial of the existence of consciousness) is a subject for another time. The present point — it’s worth repeating many times — is that no one has to react in either of these ways. All they have to do is grasp the fundamental respect in which we don’t know the intrinsic nature of physical stuff in spite of all that physics tells us. In particular, we don’t know anything about the physical that gives us good reason to think that consciousness can’t be wholly physical. It’s worth adding that one can fully accept this even if one is unwilling to agree with Russell that in having conscious experience we thereby know something about the intrinsic nature of physical reality.

I don't think his take on it is as illuminating as Lakoff's, but for a quick op-ed it does the job.

09 May 2016

Sean Carroll's new book is (apparently at least partly) about model-dependent realism

Salon has an interview with Sean Carroll in which he discusses his new book, The Big Picture, which releases tomorrow (May 10th). Readers of this blog will no doubt be aware of my fondness for Hawking's model-dependent realism or what I consider to be a cognitive-science-based variation, Lakoff's embodied realism. And while I've often referenced Carroll's old blog post about free will as evidence he shares the basic ideas, some of his comments in the Salon interview certainly have a ring about them that should be familiar to anyone versed in those empirically responsible epistemologies:

Naturalists don’t all agree with each other. On the one end of the spectrum you have the most hard-core variety, who claim that only the most deep-down fundamental description of nature can be said to describe something “real.” They might say that consciousness, or morality, or free will, are all just illusions. On the other end of the spectrum you have naturalists who believe in only the natural world, but are willing to ascribe objective reality to various extra properties it might have – moral judgments, for example, or inner states of conscious experience.
Poetic naturalism sits in between. There is only one world, but we have many ways of talking about that world. And if a particular way of talking gives us a useful handle on what the world is and how it behaves, it’s completely appropriate to consider the concepts it evokes as “real.” Air is really made of atoms, but its temperature and pressure are real, even though the individual atoms don’t have temperatures or pressures. Human consciousness and free will are real, even though they’re not present in the individual particles or cells of which we are made.
Whether he ever mentions model-dependent realism by name in the book, I don't know yet (obviously); but he's certainly in the ballpark. Stephen Hawking essentially says that the question of what is 'real' is meaningless; what matters is the utility of a model in its ability to reliably describe and predict phenomena. Lakoff, similarly, suggests that we consider something to be 'real' when it has a theoretical ontology necessary to explain phenomena. I think Carroll is in good company.