It’s Not That Easy Seeing Green

From an article in yesterday’s New York Times:

Take again the case of color and wavelength. Wavelength is a real, physical phenomenon; color is the brain’s approximate, slightly incorrect model of it. In the attention schema theory, attention is the physical phenomenon and awareness is the brain’s approximate, slightly incorrect model of it. In neuroscience, attention is a process of enhancing some signals at the expense of others. It’s a way of focusing resources. Attention: a real, mechanistic phenomenon that can be programmed into a computer chip. Awareness: a cartoonish reconstruction of attention that is as physically inaccurate as the brain’s internal model of color.

The crucial point, in one sentence:

The brain computes models that are caricatures of real things.

Of course, many Buddhists and mystics and philosophers and others have been saying this for centuries (only they say it in Sanskrit instead of scientific language, which makes it easier to read), but it looks like science is rapidly catching up.

Question Two: What Rule of Sanskrit Grammar Is Being Violated in the Following Line of Javascript?

A question in a physics textbook I’m looking at:

A psychic conducts seances in which the spirits of the dead speak to the participants. He says he has special psychic powers not possessed by other people, which allow him to “channel” the communications with the spirits. What part of the scientific method is being violated here?

The answer is supposed to be that the results aren’t reproducible by others, but unless the psychic is claiming to be doing a scientific experiment, how is any part of scientific method being violated?

If the reasoning were valid, it would be valid even if we changed the nature of the claim itself. So rewrite it a little and see if it still makes sense:

A singer holds concerts in which words sung to musical accompaniment convey emotion to the participants. She says she has special performance powers not possessed by other people, which allow her to move the participants to a “standing ovation” whenever she sings a particular combination of words and notes bearing the title “People”. What part of the scientific method is being violated here?


A couple of weeks ago I was at the Millbrae BART station and a young man asked me if I knew how to get to Slim’s in San Francisco. I didn’t, but I had my iPhone on me so I used Google Maps and showed him how to get there. After we got on the train we chatted some more, and he mentioned that he maybe shouldn’t be going to this event at Slim’s, because he had homework to do in probability and statistics. I told him I knew something about that stuff, and he showed me his homework.

One of the problems he hadn’t been able to solve concerned 25 letters and the 25 differently addressed envelopes that they were supposed to go into. The letters are shuffled and randomly stuffed into the envelopes. What are the odds that no letters at all wind up in their proper envelopes?

I told him I thought this was an awfully hard problem to be giving to an introductory class, but we weren’t going anywhere anyway, so we got out pen and paper and we tackled it. We (mostly me) came up with a plausible looking formula for the solution, but when I calculated it, it all reduced to (24/25)25, and I knew that that couldn’t be the correct answer. (That would be the answer if each pairing of a letter to an envelope was a completely independent event from the others; but they aren’t, because each pairing takes a letter and an envelope out of the game, and that I knew that that just had to affect the odds in some way, even though I couldn’t figure out how to figure out exactly how it did. I give myself partial credit, though, for at least recognizing that our answer could not possibly be right.)

When I got back home I did some online research and discovered that there’s a special name for a permutation (that is, a shuffling of ordered objects) that does not leave any object in its correct place in the order: a derangement. It seems inconceivable that I haven’t come across this term before at some point, but I don’t have any memory of it; maybe something I encountered in college and not since.

There’s a very tidy little formula for getting the number of possible derangements of n objects: dn = n!/e rounded to the nearest integer. And therefore the probability that a random permutation will be a derangement (that every letter ends up in the wrong envelope) is the number of derangements divided by the number of permutations, or dn/n!. This is very close (just a rounding error away) to (n!/e)/n!, which cancels out neatly to 1/e, which is about 0.368 (or 36.8%), and in fact as n increases, the probability converges toward precisely 1/e very, very rapidly.

It’s neat and counterintuitive, then, to consider that the odds don’t change significantly whether you’ve got 25 envelopes to stuff or 25 trillion.

Thing is, I got all this off a website, and the calculations needed to get that simple-looking formula for dn are pretty darned long and involved. So I have to wonder what it’s doing on the homework for an introductory class. Maybe it was meant as an exercise in Internet research?

Sorry, Wrong File Packet

Good and important story in the Machinist,’s tech blog, about Associated Press’s discovery that Comcast is selectively interfering with its user’s data transfer.

Comcast, the AP determined, actively manages data on its network by using software to essentially masquerade as its subscribers’ machines. When non-Comcast Internet subscribers request files from your Comcast-connected machine — as happens in peer-to-peer file-sharing applications — Comcast’s technology steps in and tells the non-Comcast subscriber you’re not available.

No one disputes that Comcast has the right to manage data transfer to increase performance for all its subscribers. The objection is that the method is dishonest. According to the AP story, Comcast’s software inspects data coming into the network, and if the data appears to be peer-to-peer file transfer between a subscriber and a non-subscriber, the software sends out forged data packets to the two computers.

Each PC gets a message invisible to the user that looks like it comes from the other computer, telling it to stop communicating. But neither message originated from the other computer — it comes from Comcast. If it were a telephone conversation, it would be like the operator breaking into the conversation, telling each talker in the voice of the other: “Sorry, I have to hang up. Good bye.”

Of course, Comcast doesn’t mention in its advertising or in its contract that it is blocking this kind of use of its service. In both, Comcast emphasizes the high speeds and the unlimitedness of its services, and the company is perfectly happy to take the money from subscribers who want the service precisely in order to use peer-to-peer file sharing.

I’m already down on Comcast from my experiences trying to email their subscribers. I am a technical editor for a small publisher, and as a result I send and receive a lot of attachments, mostly Word docs and PDF files, to and from authors. Well, now and then when I email an attachment to an author on Comcast, I get a message back saying that the message couldn’t be delivered because my company has been identified as a spammer.

A spammer. Right. You may have noticed what a problem you have been having lately with all that unsolicited email in your inbox urging you to buy study materials that are claimed to help you pass your licensing exam in structural engineering. You know the ones: Get stronger, deeper understanding — fast! Last longer under time pressure! Insert joke about stress analysis of steel members here!

Turns out, we get on this list because from time to time we send out email promotions to people who have signed up to receive them, and these promotions keep triggering whatever spam detection software Comcast has set up. It never seems to trigger anybody else’s, just Comcast’s, and they respond by blocking all messages over a certain very small size. Whenever this happens, I usually just forward the attachment to one of my several personal email accounts and then send it along from there, but it’s a pain in the butt.

Well, our marketing director calls Comcast up and says, look, we’re a small company and everyone who receives our promotions has signed up for them, please take us off your list of blocked addresses. And they do, and after a half a day or a day passes, I can send attachments again. Until the next time it happens again. And again. And again.

iTopia, Limited

I learned a new word the other day: iPerbole.

This review of the iPhone (plus this addendum) seems more cool-headed than most, though — neither all gee-whiz about it nor venting hatred of everything Apple just because it’s Apple.

They tell me a few things about the iPhone that make me more certain that I’m better off without one, though, at least until some improvements are added.

The iPhone can display, but not edit, Microsoft Word and Excel documents and Portable Document Format files. Conversely, iTunes doesn’t provide you with a computer-editable copy of any notes you jot down in the iPhone’s Notes program (although it does back them up automatically).

One of my main uses for a PDA is as a portable notepad, but I have to be able to send my notes back and forth between the PDA and my laptop and modify them in either place, or it’s not any more useful to me than carrying around a paper notebook and pen (which I often do anyway).

Switching between iPhone programs happens almost instantly, but moving data between them is just about impossible without copy or paste commands.

Ugh. For me, anyway, an important part of processing my email is quickly filing away any info I may want to refer to later, which means cutting and pasting into my note organizing software or into Address Book or whatever, so that I can get the email message out of the inbox and into the archives.

Spending time online will, however, expose the sluggishness of AT&T’s barely-faster-than-dialup Edge data service.

The USB modem I bought to use with my laptop uses 3G, which is much faster, about as fast as a low-end DSL connection.

Typing a Web address or an e-mail message reveals another awkwardness: text entry. Without a real keyboard, you have to tap on an onscreen substitute that offers no tactile feedback and puts punctuation and letters on separate screens.

I’m a touch typist and have found that I get frustrated writing on a PDA, whether it’s by way of Graffiti or a touch-screen keyboard or whatever.

An awful lot of my computer time is spent during my long commute by way of BART and CalTrain, or while sitting at a café somewhere, where opening up my laptop usually isn’t any hassle. So as beautiful a piece of equipment as the iPhone certainly is, it doesn’t seem to suit my needs right now well enough for me to justify the price and the two-year commitment.