If we had a Marriage, These Would be its Thoughts

Illegal Numbers and the Dangers of Banned Information

October 15, 2013 3:07 pm

Did you know that some numbers are illegal? It’s true.

No, there isn’t a law somewhere that says the numbers 745, 1,889, and 131,101 are illegal. In fact which numbers are illegal isn’t even known a priori. And there’s an unbounded (and possibly infinite) number of illegal numbers! It’s crazy!

So how are some numbers illegal?

It all started with the invention of digital storage mediums (i.e., the computer). You may have some notion about computers operating entirely on 0s and 1s. That is, they use a binary number system. Physically, these values are usually stored as a high or low voltage (electrical storage, like a USB thumb drive), the direction of magnetization (magnetic storage, like a hard drive or floppy disk), or as actual pieces of material (physical and optical storage, like a punch-card/CD/DVD/Blu-Ray). These physical representations are interpreted as either a zero or a one.

Since every piece of data on your computer is stored in some fashion and then interpreted, every piece of data on your computer is represented by a series of zeros and ones. Any series of zeros and ones in a binary system represents a specific number. In binary, 01101 is the decimal value 13. Therefore, every piece of data on your computer has a corresponding number that exactly represents that data.

Take this image for example:

It’s just a 64×64-pixel square with bands of red, green and blue. The number that is stored on the computer to represent this image is:

1238301683640466317815934360806135690116434697154877923
4494792367923755906673163981641861895458337604702343466
2810700348261887772411034091469320270991594673908631991
5844885402876248165441943076299189588485408932698051652
9274954637784672242688658729288559072939506175348618889
6499525714591179951958772678400887694932269665261700174
3252008568133749407688395385589539990171146138088533455
4251168727225022618657147246713345507166265266049883607
2457758487000098535759665677768294453081438629169206933
668292205864758173826

In any sense that matters, this number and that picture are equal—with the important understanding that I told the computer to treat that number as if it were a picture (specifically a png file). I could just as easily tell the computer to interpret that number as audio, or video, or text (but it would appear to be garbage if interpreted in any of those ways).

That picture is this number and this number is that picture. It has to be so in order for computers to work.

Now here’s where this gets interesting and a little bizarre.

There are many laws that make certain physical objects illegal to possess under many circumstances (drugs, explosives, etc.). But our legal system has also made certain types of information illegal to possess. One such category is child pornography. To my understanding it is illegal to possess any instance of child pornography, regardless of intent. If such an instance exists on a computer then the number that represents that illegal information is itself illegal, for the number and the image are one and the same.

Other types of information are legal to possess, but illegal to share with others. The DMCA makes it illegal to provide to others any tool which is capable of circumventing any measure designed to prevent access to a copyrighted work. Meaning I could write a piece of software to copy DVDs, but it’s illegal for me to use it or give it to anyone else.

This seems like it creates some real legal challenges.

I don’t think anyone would disagree that a website dedicated to posting and sharing child pornography would be illegal. But suppose that instead of pictures a website is set up dedicated to posting numbers. The only things posted are numbers and discussion of those numbers. Surely there’s no harm in a website dedicated to numbers.

Now suppose during the discussion of some number, someone suggests that people tell their computers to interpret that number as an image (create a file, load in the binary form of the number, set the file extension to .jpg or .png, or .gif). And suppose that the resultant image is illegal as described in the previous section. Who, if anyone, is legally liable for possessing or sharing this illegal number?

This is a theoretical practice as far as I’m aware, but let’s take another step anyway. MIT hosts a site with the first 1 billion digits of Pi. The current record for calculating Pi is just over 10 trillion digits (though not posted for viewing). Surely if pi continues on forever and never repeats it would have to eventually include all illegal numbers.

Suppose someone sets up a website that says start at the 19,995th digit of Pi, take the next 3,021 digits and interpret it as an image or run it as a program. And again, suppose that interpretation is illegal. Is anyone at fault? Should they be?

This is the trouble that occurs when information itself is made illegal.

This referencing is how your computer works though. You can consider your hard-drive as an incredibly long list of zeros and ones and through some conventions your computer looks at one set of numbers which tells it how to interpret the other numbers (go to the 1,313,163rd bit, take 766,122 bits and treat them as a picture).

So, given an illegal number sitting on your hard-drive, is the number itself illegal, or is it the other numbers elsewhere on the hard-drive that tell the computer how to treat the first number? Or is it only the pair together that’s illegal?

How many steps out do we go before illegal numbers are no longer illegal? Can I break up the numbers into parts and have people add them back together? Can I tell you to get X numbers from pi and then use those numbers to look up in pi the illegal number?

We can sort of borrow a concept from quantum mechanics to describe the situation: A number is a superposition of information. It only takes on definite meaning once a specific interpretation is applied. So is it the person applying or sharing the specific interpretation that is at fault?

Kyle’s Hypothesis

Using this superposition idea, I propose the following hypothesis:

A number exists which represents a perfectly innocuous piece of data but when interpreted in another format (e.g., image) is illegal.

What happens if some particularly popular number (e.g., a song in mp3 format) turns out to be the same number that represents something illegal?

In this case, it’s only the other numbers on the hard-drive that specify how to interpret the mp3 as either a song or something illegal. Is it then illegal to suggest to other people to interpret the same number they already have in a different way?

Once you start making information itself illegal to possess or distribute, you start creating some really bizarre corner-cases for the legal system.

(For the technically minded: For simplicity I’m ignoring the scenario where magic-number headers may be used to suggest file format within the file itself.)

Update to answer Megan’s question:

Megan asked what

846513265498765646454545431313

15464875465134876532165400014654684

would look like as a picture. As my parenthetical at the end the post alluded to, it’s not quite as simple as I made it sound.

There is this notion of “magic-number” headers. Which is really just a convention that computer scientists use that says when I want this data to be treated as a BMP file, the very first thing in the file will be the number “16973” which stands for the letters BM. There are similar magic numbers (or “fingerprints”) for many different file formats. Many programs that know how to open a BMP file, won’t even try if the magic number doesn’t match.

So by directly dumping Megan’s number into a file and trying to open it as various image formats I only got error messages. So I used the simplest file format with which I’m familiar (pbm) and added the proper magic number (P3) and header (which describes the width and height of the image; I chose both to be 5 arbitrarily).

The resultant number is now

6086291824888092467866770275946841

3783905258129499855885219551478363

6286731887369226

And the image itself is just a smudge. The pbm format is black and white only, no grey. And I’ve blown the image up to 65×65 pixels so you could actually see something (remember it was only 5×5 to start with):

I did not change anything about the number Megan provided, I simply added the necessary information that tells the computer how to interpret that number into an image.

If I change that interpretation to expect a very simple color image (a PPM file with magic number P6, 4×4 pixels with only 8 possible colors) then the image looks like this (blown up to 64×64 pixels):

Most of the image is white, so you can’t really see it against the white background.

Firsthand Knowledge

September 24, 2013 11:39 pm

Things you never wanted to learn firsthand: The people who design car-seats have clearly never needed to clean copious amounts of vomit out of them on the side of the highway 50 miles from the closest exit in middle-of-nowhere Nevada. Why are there so many crevices?!

(Sigh) The other side of parenthood. Luckily it was still daylight, traffic was light, and nothing but the seat and Heather’s clothes got contaminated.

Heather was apparently not feeling well, but after giving up most her lunch she seemed to improve dramatically. Unfortunately, now the car has a lovely eau de sick.

Hopefully a thorough washing of the car-seat will fix that.

Had we any safe way of transporting Heather without it, I may have been tempted to leave the car-seat in the desert–it was pretty gross.

Best Early Birthday Gift EVAR

September 19, 2013 8:25 pm

I went visiting teaching tonight, so Kyle was responsible for getting Heather to bed. I guess she was pretty distraught about my absence at key points in the process. But Kyle managed to calm her and get her down.

So I get home and he’s telling me about how upset she was, and I kind of wished I could go in and give her a hug and snuggle. Kyle pointed out that she was still wide awake…and then remembered he had forgotten to put an overnight diaper on her. So I went in to change her and show her that I did, in fact, come back. While I was changing her, she kept babbling something around her binkie that I could not understand at all. Kyle finally realized what it was: “Happy birthday, Mama.” He had taught it to her and told her to say that to me in the morning (but not really thinking at all that she would remember to do so). But she did! How cute is that?!

It’s Not Apathy, It’s Despair

September 8, 2013 1:20 pm

Germans are protesting in the streets about the NSA. Americans are doing nothing. Why?

OK, yes, I think apathy does play a role. I think there are a lot of Americans who have their bread and circuses and just don’t care about anything else. I also think there are a lot of Americans who think, “This only affects bad guys” and haven’t studied enough history to realize why that is a dangerous assumption.

But for me, and I think many others, it’s not apathy. I care. I care a great deal about the usurpation of civil rights that has occurred in this country since the end of 2001. And not just the loss of civil rights but the abandonment of any moral high ground we may have held on the international stage.

I haven’t flown since 2010 and I won’t fly until the TSA is reigned in and passengers are treated with some modicum of respect and aren’t assumed to be terrorists. I wrote to all the airlines explaining why I would no longer be a customer. They didn’t seem to care.

I don’t vote for Republicans or Democrats (if possible). I vote for, and donate money to, third-party candidates. They never win.

I donate money to the Electronic Frontier Foundation and the Electronic Privacy Information Center. They file lawsuits that get thrown out of court because “National Security” which apparently also means “end of discussion.”

I’ve written actual paper letters to my Congressional representatives and the President with my positions. The only response is a form letter with no indication anyone bothered to read the message.

So I promise it’s not apathy. I previously wrote about Outrage Fatigue and what follows fatigue is despair. I think for those of us that do care, our lack of action is mainly due to despair.

What can we honestly do as average citizens that will make any difference?

I may despair in what I can do next to help fix things, but I’m not without hope. I think we are making a difference, though slow. And I think we will eventually rein in the egregious abuses we’ve seen.

I think, or at least hope, we’ll look back on 2001-2020 the same way we look at 1950-1956 and the abuses that were McCarthyism.

Then the important question will be: what can we do to prevent it from happening again?

Dickerson Family Reunion 2013 – Cedar City, UT

August 26, 2013 8:16 pm

The Dickerson family had a reunion this year in Cedar City, UT. We stayed in the dorms at Southern Utah University and just happened to be there during the first stage of the Tour of Utah bicycle race which ended right in town and went past our apartments three times.

Throughout the trip I took over 900 pictures, so I did a lot of culling to get it down the 15 I’m using in this post, so don’t complain about too many pictures.

The reunion ran from August 4 through August 9. The 4th and 5th was just people arriving and wandering about doing whatever.

The Tour of Utah stuff on was the 6th. As the race wound its way through the mountains there was stuff going on downtown including a booth for the Shakespeare Festival with various costumes and props to try on. Heather fit perfectly in the jester’s hat.

The racers got into town in the late afternoon. Here’s the main group of racers coming down the road:

Here’s the crew that stayed up in the apartment watching on:

That evening a group of us went to watch Peter and the Starcatcher. It’s a retelling of the origin of Peter Pan. A little odd at times, but enjoyable.

On Wednesday, the 7th, we went to Frontier Homestead State Park where Heather sat on a horse (statue, obviously). It’s a bunch of old-timey machinery and buildings and stuff to look at.

That evening obligatory family fun & games were held, of course. Here’s Evan in his cowboy getup enjoying Bingo (run by Megan & Chad) after he won some honey-roasted peanuts:

Erin ran The Price is Right complete with Plinko, which Megan and Chad played:

On Thursday we took a horse- (and mule-) back ride through Bryce Canyon (thanks again Mike!). Mike’s mule was appropriately named “Porky” as he took every opportunity to graze at the side of the trail.

From left to right: Megan, Mollie, Jess, Mike, and Tina.

Here we are at our rest stop. Left to right: Evan, Tina, Mike, Mollie, Megan, Chad, and Jess.

Jess had a blast. I have a bunch of pictures of her riding with a great big smile on her face.

Riding and taking pictures is easier said than done for someone with very little riding experience. We weren’t allowed to take anything with us except a camera, so I picked my 50-200mm zoom lens with a polarizer and hoped for the best. I probably should have taken the 18-55mm instead as with the 50mm widest angle I wasn’t able to get any grand panoramic shots, however with the 200mm telephoto I was able to get closer-up pictures of everyone else riding.

The biggest issue was trying to look through the viewfinder to take a shot with the horse bouncing around and me trying to hold on. To compensate, many of my pictures were taken Rambo-style just aiming in the general direction and hoping for the best.

Here’s my favorite picture of the few hundred I took while on the ride. I think it’s neat how clear the various layers of rock are across the hoodoos.

The next day was checkout so we all spent the morning trying to get packed up and out the door. After checking out we tried to take some family pictures.

Here’s the Dickerson grandchildren of 2011. Heather, born in October. Charlie, born in December. And Addie, born in August.

After family pictures we had a round of bowling to celebrate Evan’s birthday (with requisite cream-cheese pie).

From there the party broke up and went separate ways. We went up to Provo along with most of the rest for Will’s baptism on Saturday. After the baptism and lunch it was time to head home. Heather was starting to not feel well and didn’t much like adjusting to hotel rooms so we decided to drive straight through and just get home. So we got home at around 4:30am Sunday completely exhausted.

And if you don’t come home in the middle of the night completely exhausted then you’re not doing your family vacations right; at least that’s what my childhood memories suggest anyway.