Saturday, May 21, 2016

Epstein's Dollar Bill and What it Doesn't Prove About the Brain

I hate to pick on poor confused Robert Epstein again, but after thinking about it some more, I'd like to explain why an example in his foolish article doesn't justify his claims.

Here I quote his example without the accompanying illustrations:

In a classroom exercise I have conducted many times over the years, I begin by recruiting a student to draw a detailed picture of a dollar bill – ‘as detailed as possible’, I say – on the blackboard in front of the room. When the student has finished, I cover the drawing with a sheet of paper, remove a dollar bill from my wallet, tape it to the board, and ask the student to repeat the task. When he or she is done, I remove the cover from the first drawing, and the class comments on the differences.

Because you might never have seen a demonstration like this, or because you might have trouble imagining the outcome, I have asked Jinny Hyun, one of the student interns at the institute where I conduct my research, to make the two drawings. Here is her drawing ‘from memory’ (notice the metaphor):

And here is the drawing she subsequently made with a dollar bill present:

Jinny was as surprised by the outcome as you probably are, but it is typical. As you can see, the drawing made in the absence of the dollar bill is horrible compared with the drawing made from an exemplar, even though Jinny has seen a dollar bill thousands of times.

What is the problem? Don’t we have a ‘representation’ of the dollar bill ‘stored’ in a ‘memory register’ in our brains? Can’t we just ‘retrieve’ it and use it to make our drawing?

Obviously not, and a thousand years of neuroscience will never locate a representation of a dollar bill stored inside the human brain for the simple reason that it is not there to be found.

Now let me explain why Epstein's example doesn't even come close to proving what he thinks it does.

First, the average person is not very good at drawing. I am probably much, much worse than the average person in this respect. When I play "pictionary", for example, people always laugh at my stick figures. Yet, given something to look at and copy, I can do a reasonable job of copying what I see. I, like many people, have trouble converting what I see "in my mind's eye" to a piece of paper. So it is not at all surprising to me that the students Epstein asks to draw a dollar bill produce the results he displays. His silly experiment says nothing about the brain and what it "stores" at all!

Second, Epstein claims that the brain stores no representation of a dollar bill whatsoever. He is pretty unequivocal about this. So let me suggest another experiment that decisively refutes Epstein's claim: instead of asking students to draw a dollar bill (an exercise which evidently is mostly about the artistic ability of students), instead give them five different "dollar bills", four of which have been altered in some fairly obvious respect. For example, one might have a portrait of Jefferson instead of Washington, another might have the "1" in only two corners instead of all four corners, another might have the treasury seal in red instead of the typical green for a federal reserve note, etc. And one of the five is an ordinary bill. Now ask them to pick out which bills are real and which are not. To make it really precise, each student should get just one bill and not be able to see the bills of others.

Here's what I will bet: students will, with very high probability, be able to distinguish the real dollar bill from the altered ones. I know with certainty that I can do this.

Now, how could one possibly distinguish the real dollar bills from the fake ones if one has no representation of the real one stored in the brain?

And this is not pure speculation: thousands of cashiers every day are tasked with distinguishing real bills from fake ones. Somehow, even though they have no representation of the dollar bill stored in their brain, they manage to do this. Why, it's magic!


Michael Anes said...

Well, psychologists for years have known that even in a recognition task we don't do very well identifying, for example, a penny (Nickerson and Adams, 1979) and recently with the Apple logo (Blake, Nazarian and Castel, 2015

This doesn't take away from your points in the main post, which I agree with.

Thanks for your writing on this subject.

petros diveris said...

I am afraid Epstein's point is more about memory's accuracy, than artistic merit. If Jinny was a computer, and if her "drawing" was a 204xx87 pixels greyscale bitmap facsimile no one would challenge its accuracy or relative merit, the techies would just call for more resolution and better printers. Furthermore, the ability of people to pick the correct dollar bill out of a pile of modified/wrong ones doesn't prove Epstein either correct, or wrong. It certainly doesn't prove in any meaningful way that somewhere in our brains there is a dollar bill. I am sure there are people there who know what a dollar bill should have on it without ever having seen one, as well as people who use them every day, and yet they'd fail this test.

Jeffrey Shallit said...

Furthermore, the ability of people to pick the correct dollar bill out of a pile of modified/wrong ones doesn't prove Epstein either correct, or wrong. It certainly doesn't prove in any meaningful way that somewhere in our brains there is a dollar bill.

Nobody says "somewhere in our brains there is a dollar bill", so you're attacking a straw man. Somewhere in our brains there is a representation of a dollar bill; for otherwise how could we know which one is real and which one fake? This applies equally well to people who have never seen a dollar bill but know what it "should have on it". Such people have a representation which is not as detailed as those who see and handle it every day.

Simple information theory, combined with some experiments along the lines of what I described, can even estimate how many bits of representation the average person would have about a dollar bill.

Jeffrey Shallit said...

Thanks, Michael, for these interesting studies.

From personal experience I know that I have a pretty good internal representation of a US one-cent coin. When the one-cent coin was redesigned very slightly in 1969, I showed a new one-cent piece to my 6th grade teacher and pointed out how it differed from the one dated in 1968. My teacher was very skeptical of the differences I pointed out, but soon enough the Mint acknowledged they had redesigned the coin in exactly the ways I had seen. Of course, I imagine coin collectors have much more detailed representations of the coins they collect than the average person.

In contrast, for the Google logo, recently on a trivia contest we were asked what the colors of the standard logo were; in particular, what color are the G's? Nobody at our table was really sure, although I thought it was blue. And even though I was right about the G's, I definitely could not have told you the color of the other letters. Somehow I notice blue things more than other colors.

Andrew Wilson said...

OK; let's grant that this $1 bill thing is not a particularly convincing argument for anything. But I want to walk through it a little for a moment to try something out.

You argue that anyone with any experience of the $1 bill has a representation (with varying quality) of that bill. Representations are supposed to do work, specifically they implement the mental/cognitive processes that create functional behaviour.

I will grant the issue of drawing competence. But even given that, that drawing behaviour was supposedly generated with ongoing access to and reference to a representation of a $1 bill. And yet this representation, which is apparently good enough to support recognition of the bill is unable to support anything close to recall of the bill? Put another way, even taking drawing ability into account, if the drawn product is generally this sparse and inaccurate, how is it possible for the representation that supported that (poor) behaviour to also support another excellent behaviour? Why the huge disconnect?

Jeffrey Shallit said...

And yet this representation, which is apparently good enough to support recognition of the bill is unable to support anything close to recall of the bill?

That is a common feature of human memory. There are apparently special machinery, like the "Fusiform Face Area", which is devoted to recognition things. It does not necessarily translate to the ability to describe the thing recognized or draw it. I can recognize faces easily, even people I have not seen in 20 years, but ask me to draw them or describe them and I am handcuffed by my own neural circuitry.

I don't know why you would find this surprising. Surely you can think of similar examples in your own experience. I am sure you can also think of good evolutionary reasons why the circuits for recognizing faces might be more competent than the circuits for describing the faces.

Paul C. Anagnostopoulos said...

Certainly there are many factors that contribute to my ability to draw a dollar bill from memory. My "drawing ability" is one factor. The detail level of my internal representation is another. Here is an interesting article on drawing ability:

And then there's this fellow:

Apparently Epstein believes that what's going on is that some chunk of my brain is changing so it can drive my motor neurons to cause my hand to draw a dollar bill, but that chunk of brain should not be said to contain a "representation."

~~ Paul

JimV said...

Some people don't seem to be able to generalize or analogize. So if the human brain doesn't store a dollar bill as 24-bit colored pixels at 300 DPI (like a typical contemporary computer would) then it doesn't act like a kind of computer, as they see it.

In 1980 I had an Apple II+. In its low-resolution mode it would only have been able to store a dollar bill as about 40x15 large pixels, each being one of only eight colors. It might not have been recognizable as a dollar bill to most people, but that was the best it could do. Yet it was called a computer.

Different computers have different capabilities. Some have more memory than others and some have more bandwidth of colors than others (as birds do compared to humans). A computer could be developed to store graphic information in an incomplete way focusing on a few important characteristics, to save memory and processing time. In fact it has been (by evolution).

Daniel Copeland said...

What does it mean to have poor "drawing ability" -- assuming that one has functional eyes and steady hands? It means that, somewhere between eye and hand, the recognisable image is being converted into a set of symbols. A tabletop forms a trapezium on your retina but you draw it as a rectangle because you know tabletops are rectangular. A person's eye forms a complex crescent on your own, but you draw it as a pointy-ended oval with a circle in the middle because that's the shape you know for eyes. I've never seen an American dollar bill but I'm betting Americans encode it in their brains as an array of symbols rather than a visual representation.

Neal Z said...

Not to get too technical, but the recognition/recall dichotomy exists in computer science as well, and at times it's even more stark than it is in human memory. Yes, I'm talking about hash functions.

Hash functions basically allow a computer to recognize something without recalling it. Generally a hash is smaller - often much smaller - than the thing it is checking. Sometimes a hash can be used to identify if one thing is another thing without actually storing the second thing at all.

For example, most secure authentication systems do not actually store your passwords in memory. Instead, they add your password to some random string of characters (called "salt") and then use a hash function to convert this to a secure code. The code is secure because it cannot be converted back to the original password - the hash function has actually lost information. However, when you type in your password, the computer repeats the salting/hashing process and compares the new hash to the old hash. It is theoretically possible for another password to generate the same hash as yours but it is astronomically unlikely.

There's also file verification, which can be done with hashes or checksums. Both of these methods allow you to quickly and accurately verify file integrity after downloading - that is, to recognize that the file downloaded correctly. However, neither the hash nor the checksum contains all of the information contained in the file - that is, it's not a one-to-one comparison. Instead, you're comparing specific, well-chosen features of the files which are highly likely to differ if the files differ.

So with that in mind, we can think of the dollar bill problem this way: how many features of the dollar bill do you have to verify to guess that the bill is authentic? Ten? Twenty? But how many would you need to reproduce the bill with high fidelity? Possibly thousands or millions. The brain evolved to be efficient. It isn't efficient to store high-fidelity copies of everything to be recalled in case a misguided professor smugly asks you to draw it on a whiteboard. It's much more efficient to use a small collection of unique details to recognize objects.

philosopher-animal said...

Hm! Another anti-representationalist. I should have known ...

Dynamical systems approaches work for motor skills and so on, but I haven't been able to figure out how one gets "memory" back out, ironically.

(Also, has Epstein never *heard* of the "marketing" remarks about ANNs? Something about degraded input and sampling?)

This bit about "computers have to store everything exactly" is a science fiction trope (think Data, from ST:TNG), not an actual engineering (never mind scientific) feature!

JimV said...

Someone linked to the Epstein article in the current comment thread at Scott Aaronson's blog (Shetl-Optimized). I don't know how to link to the specific comment that contains Dr. A's reply, so I'll paste the whole comment here (he strongly agrees with you, of course):

Scott Says:
Comment #99 June 4th, 2016 at 2:19 am
Peter Byrne #97: I didn’t find that article cogent at all. In fact, the entire thing seems based on a trivial language confusion.

In saying that “your brain is not a computer,” Epstein turns out to mean something true but pedestrian: namely, that the brain isn’t organized the way existing digital computers are organized. Nowhere does he even try to show why the brain couldn’t be simulated by a computer—i.e., why the brain violates the Physical Church-Turing Thesis. That’s what we’d need for the brain to be genuinely non-computational, i.e., for reproducing its behavior on a suitably-programmed computer to be impossible rather than merely complicated or hard. Worse, Epstein gives no indication of understanding what computational universality or the Church-Turing Thesis even are—meaning that the actual questions at stake here, the ones that Roger Penrose realizes he needs to answer for the brain-is-not-computational thesis to stand a chance, never even cross the horizon of Epstein’s consciousness.

Related to that, Epstein never even tries to grapple with deep learning algorithms, which do have a vaguely brain-like organization, and which of course have enjoyed spectacular successes over the last five years. It’s as if someone published a philosophical article, in June 2016, entitled “Why American Democracy is Inherently Stable Against Authoritarian Demagogues,” without even showing awareness of any potential recent counterexample, let alone trying to explain it away. I’d call that borderline intellectual dishonesty, if not for my suspicion that Epstein really does have no more awareness about machine learning than about other parts of CS.

Purple Neon Lights said...

Hi Jeffrey. This is Purple Neon Lights. I just posted an essay about James Randi and the mind-body question. I hadn't realized there is a limit on the length of a post. So, I initially cut it into 3 pieces so it would fit. However, as I was posting the pieces, I discovered that I actually needed to have it be in five parts to fit in. Thus, the numbering scheme that I put at the beginning in the end of the posts, is inconsistent. At first, I was mentioning that there are three parts, then later that changed to being 5 parts.

I don't know if you care about this essay, but if you do, is there some way I can tweak that numbering system, or could you do it for me?

Thank you for your blog. I appreciate anyone who is interested as in this area as you are. It's that kind of impetus and initiative that makes the world go round. Peace.:)