Monday, December 2, 2013

Inheritance, templates, and database models

Some years ago (around 1991, as a matter of fact) I observed that object oriented programming, and C++ in particular, was following a path similar to that followed by databases decades before.

At the time, multiple inheritance had recently been added to C++. I noted that single inheritance corresponded closely to the hierarchical database model, and multiple inheritance corresponded closely to the network model.

As I'd guess most people reading this are well aware, most databases have long-since switched to (something at least intended to be similar to) the relational model and there are formal proofs that the relational model is strictly more powerful than either the hierarchical or the network model. That led to an obvious question: what sort of program organization would correspond to the relational model?

I would posit that C++ templates (especially function templates) correspond closely to the relational model. Rather than being restricted to situations like "X is derived from Y", we can instantiate a template over any type satisfying some relation--though in the case of a template, the relation is basically a set of operations that must be supported by the type rather than a set of values that must be stored in the database.

The major problem with templates (by themselves) is that we have very little control over how that matching is done. The matching criteria are difficult for most people to understand, and even harder to control. Even at best, the control currently available (e.g., via static_assert) is clumsy use and hard to read.

Concepts refine that capability considerably. Concepts are similar to defining foreign keys in a database. Right now, what we have is similar to a bunch of tables, with some fields (or sets of fields) in some of those tables used as foreign keys in other tables--but no declarations of what is supposed to be used as a foreign key, and therefore no way for the compiler to (a C++ equivalent of) enforce referential integrity.

As I'm sure most programmers are already well aware, a key (no pun intended) capability of a relational database is defining relationships between tables so the database manager can enforce referential integrity. That is similar to what C++ Concepts add--something at least roughly equivalent to foreign key declarations in a database, defining what relations are intended and should be enforced by the compiler.

Now don't get me wrong: I'm not trying to write a sales-pitch for Concepts, or anything like that. Rather the contrary, I think quite a few people have probably done a better job of explaining them and how they improve C++ than I've even attempted. What I find much more interesting is seeing (or maybe just imagining--others may disagree with my ideas) a fairly clear similarity between two types of programming that (I think) many probably see as quite unrelated or perhaps even directly opposed.

Sunday, August 11, 2013

When is a question about a puzzle, and when is it really about programming?

The following question was recently asked on Stack Overflow:
This is the problem: There are two players A and B. Player A starts and chooses a number in the range 1 to 10. Players take turn and in each step add a number in the range 1 to 10. The player who reaches 100 first wins.

In the program, player A is the user and player B is the computer. Besides that the computer must force a win whenever possible. For instance, if the player A reaches 88 at some point, the computer must choose 89, as this is the only way to force a win.

A user then voted to close the question, with the comment that it was about a logic or math problem rather than about programming.

Personally, I disagree with that. In fact, I think it's an unusually good example of a problem for learning to program.

Allow me to digress for a moment. The first step in learning to program is learning to take some algorithm, and transcribe it into the syntax of a chosen programming language. Now, it's certainly true that being able to express an algorithm in a chosen programming language is important. It's not just about syntax either. Just for example, expressing an algorithm well often involves knowing a great deal about the accepted idioms of that language as well. Nonetheless, the whole business of simply writing code is only the last step in a larger, usually much more involved process.

That larger, more involved process deals primarily with finding solutions to problems. Only once we've found a way to solve the problem can we write code in our chosen language to carry out that solution. Now, it's certainly true that in many cases, we want to use an iterative approach to a solution -- we don't expect the first code we write to be the final an ultimate solution to a real problem for real users. Nonetheless, when we write code, we need to write it to do something, and we need to decide on that something before we can write code to do it.

Now, the question already notes that 89 is a winning "position". That immediately leads us to two questions: 1) why is it a winning position? 2) Based on that, can we force a score of 89?

The answer to the first is simple: 89 is a winning position, because from there our opponent can't reach the goal of 100, but no matter what move he makes, in the subsequent move we can reach 100. That is so because 100-89 = 11. The smallest move the opponent can make is 1 and the largest is 10, so no matter what he chooses, the remainder will be between 1 and 10, and we can win.

That leads fairly directly to the next step: we can force a score of 89 if we can reach a score of 78 -- and we can force a score of 78 if we can reach a score of 67 (and so on, counting backwards by 11 until we reach 12 and finally 1.

Therefore, the first player can force a win if and only if he chooses 1 in his first turn. If he chooses anything larger, the second player can choose a number that gives a result of 12, guaranteeing himself the win.

This is a large part of why many of the better computer science programs have classically used (more or less) functional languages like Scheme, and emphasized recursion as a basic primitive. It's not really about recursion as a flow control primitive or anything like that. Yes, we've known for years that a for loop, while loop, etc. can be expressed via recursion (and likewise that anything we can do with recursion can also be done via other flow control primitives).

What's important isn't that recursion allows arbitrary flow control. What's important here is the way of thinking about and approaching the problem. Recursion just gives a simple and direct way to approach the problem: instead of solving for 100, if we know that 89 is a winning position we can solve for 89 instead. Note: we could just about as easily think of it mathematically. Instead of thinking of this as a case of recursion, we could think of it as an inductive proof. The steps I've outlined above are essentially the same as those for an inductive proof.

Now, it's certainly true that this approach isn't suitable for every programming problem. If you're dealing with something like: "why is this text field being computed as 134 pixels wide when it should be 135?", chances are recursion isn't going to enter into your thinking, and might not be a lot of help if it did.

Nonetheless, if you're trying to solve a problem, and can define one step toward a solution, chances are very good that an inductive/recursive approach will be useful in solving the whole problem. It's most obvious in a case like this where the problem and solution are mathematical, so we have a well-defined line from problem to solution, but it can also apply to quite a few other cases as well (including the previous problem about text width, which it's sometimes useful to think of in terms of "some arbitrary string followed by one character", and continue with shorter and shorter strings until we reach only one or two characters).

Thursday, January 24, 2013

Word frequency counting

Eric Battalio recently posted about Jumping into C++. Like many people who've written C++ at times, I found his post quite interesting and entertaining. A fair number of people posted their own ideas about how to accomplish the same task -- some concentrating on minimal source code, others on maximum speed, and so on.

After seeing his follow-up After the Jump, I decided one point could stand being addressed. In his followup, he says: "About reading a file using iostream. Don't. It is slower and difficult to manage for complicated file formats. This application was trivial but I will avoid in the future."

On this subject, I have to disagree. Iostreams do have some shortcomings, and some implementations are also (un-)fairly slow. Nonetheless, they also have some pretty major advantages if (a big if, here) you use them well. I hope he won't feel insulted if I point out that (at least in my opinion) there are better ways to use iostreams than the way he did it.

For those who haven't read his posts, the task he set was quite simple: count the unique words in a file. He decided to do a bit of parsing, however, so that something like "one,two" would not include the comma. Unfortunately, he didn't (IMO) do this very well, so that would be counted as "onetwo" instead of treating "one" and "two" as separate words.

That brings up the obvious question: can we read those correctly, without doing extra parsing to patch things up after the fact? Of course, there's not a whole lot of suspense -- pretty much anybody with an IQ higher than a mosquito's can probably figure out that I wouldn't ask the question in the first place unless the answer was yes.

The way to do this (or the way I'm going to advocate in this post, anyway) depends on part of how iostreams are designed. When you read a string from a stream, any leading whitespace characters in the stream are ignored, then non-whitespace characters are read into the string, and reading stops at the first whitespace.

About now, you're probably thinking: "Yes Jerry, we already got past the 'IQ higher than a mosquito's' question; I already knew that!" What you may not know, or at least may not have seriously considered (though a few of you probably have) is exactly how the iostream determines what is or is not whitespace. The answer to that is a little complex: the iostream has an associated locale. The locale, in turn, contains a ctype facet -- and the ctype facet is what determines classes of characters.

So, to ignore those commas (and hyphens, etc.) we simply need a ctype facet that classifies them as white space, tell the iostream to use a locale containing that ctype facet, and we can just read words. Since it seems reasonable to me that (for example) "Jerry's blog" should be read as two words, not three, I'll classify upper and lower case letters and apostrophes as "alphabetic" and everything else as "white space".

Using that, the code we get code that's fairly simple, readable, and as a bonus, even a bit faster (though that wasn't really the intent).

Friday, December 7, 2012

Heaps and heapsort

Like most programmers, quite some time ago I'd read about heaps and the heapsort. Being a dutiful student, I could quote the standard line, saying that a heap was an implicit tree where node N was less than (or greater than, depending on the type of heap) nodes 2N and 2N+1. Like (I think) most, I'd also implemented a heapsort -- but to be honest, most of really came down to a line by line translation from the description in Knuth Volume 3 into the syntax of the programming language I was using at the time (Pascal, the first time around, and later the same again in C).

For years, given that I'd written a Heap sort that worked, I considered my knowledge of heaps and the heap sort entirely adequate. To be entirely honest, however, during most of that time I never really fully understood heaps. In particular, I never really understood the 2N and 2N+1 -- why those particular numbers/nodes? What was the significance of 2N and 2N+1? Why not 3N or 1.5N+65 or something? In short, that "implicit tree" had never really gelled for me -- I'd read the words, but never truly understood what they meant or how the "tree" worked.

For some reason a few months ago my lack of understanding on that particular subject bubbled to the top of the heap (I know: puns are the death of real humor) and I decided to implement a heap (and heap sort) entirely on my own, based only on my recollection about 2N and 2N+1. Instead of going to the book and translating syntax, I sat down with a supply of paper and pencils (the most underrated programming tools ever) and re-invented the heap and the algorithms to create and maintain a heap from first principles.

So, what did I do to finally and truly understand a heap? It ultimately came down to one piece of paper:

And from there came true understanding at last. If we arranged the nodes by layers, it "just happened" that the children of every node N were nodes 2N and 2N+1. Better still, after three layers of the tree, it was pretty apparent that as/if I added more to the tree, the same relationships would hold. Only 30 years (or so) after I'd first written a heap sort, I finally understood what I was doing!

I finally also understood why people who understood heaps thought they were cool: since the "links" in the tree are all based on (relatively simple) math, it's a tree you can walk almost any direction you'd care to think about by simply doing the right math. Just for example, in a normal binary tree, the only way to get from a node to its parent is to traverse down the tree, and remember the parent on the way there so when you need it back, you can recall it from wherever you have it stored. Likewise, getting to the sibling of a node requires that you get back to the parent (see above) and then take the other branch downward to get to the sibling.

With a heap, however, both of these are simply trivial math: the children of node N are nodes 2N and 2N+1, so the parent of node M is node M/2 (using truncating/integer math). Likewise, the sibling of node N is either node N+1 or N-1 -- if N is even, the sibling is N+1, and if N is odd, the sibling is N-1.

So, for any given node, we can walk through the tree up, down, or sideways (literally) with a single, simple math operation. Better still, all the nodes are contiguous in memory, with no space used up on links, so it's also pretty cache-friendly in general.

There was one other point I ran into repeatedly as I worked at understanding what I was doing well enough to produce working code: the math all depends on 1-based indexing. Making it work right with 0-based indexing like most currently languages use was not trivial. In fact, I finally decided that for this purpose it was better to maintain the illusion of 1-based addressing for most of the code, and since I was writing this in C++, have a truly trivial class to handle the translation from 1-base to 0-based addressing (i.e., subtract one from every index I used). As simple of an operation as that seems like it should be, keeping it in one place still simplified the rest of the code tremendously (and made it much easier to see the relationship between the code and that fundamental 2N/2N+1 relationship that defines the heap).

Anyway, in case anybody cares to look at the resulting code, I've decided that trying to post significant amounts of code directly here is too painful to be worthwhile, so here is a link to it on ideone.com. I think this is long enough for now, but sometime soon I'll probably write a post going through that code in more detail, explaining how it works and why I did things the way I did.

Saturday, November 24, 2012

Adventures in monitors

Friday I broke with my usual habit of staying home on the big shopping days, and went to Best Buy. I had some store credit, and was (and should still be) working on a project where I'd get a pretty major benefit from having another monitor attached to my computer. Besides, while my current monitor was quite high-end when it was new (a LaCie 321), it was getting quite old -- something like 7 or 8 years, if I recall correctly. Over the last few years, nearly anytime somebody heard about my ancient monitor, they'd tell me about how much better monitors had gotten since then, so even a really cheap, entry-level monitor would be a huge improvement.

In terms of specs, almost an new monitor should be a pretty serious upgrade. Just for one obvious example, the LaCie is only rated at 500:1 contrast ratio. Definitely pretty unimpressive compared to the ratios claimed by nearly all new monitors (anymore, the bare minimum seems to be at least a few million to one, and five or even ten million to one isn't particularly hard to find). Granted, those are "dynamic" contrast ratios, but the static ratios are still better than my ancient LaCie

After looking around a bit, I found an HP W2071d, which is a 20" wide-screen monitor, that was marked down to only $79.95 (from a list price of $149.95, for whatever that's worth). Seemed like a decent enough deal, so I picked one up, brought it home, and connected it up. As usual for me, just about as soon as it was connected it up, I pulled out my trusty Eye-one display 2 and calibrated it so the brightness, contrast, color (etc.) should match up with the LaCie (in case anybody cares: 5200K whitepoint, 110 cd/m2 luminance, gamma of 2.2).

Anyway, let's get to the meat of things: just how big of an improvement did the new monitor bring? Well, let me show you a couple of pictures. The HP is on the left, the LaCie on the right:


Here, the two don't look drastically different -- the background in both is reasonably black (though in person, the background of the LaCie is definitely blacker). The picture on the HP is a bit dark, but not too terrible. But now look what happens when I quite crouching down quite as far, and aim the camera down at the screen at something like a 30 degree angle:


Now, especially toward the bottom right corner, the HP's background isn't even close to black. Despite a higher claimed contrast ratio (600:1 static, 5000000:1 dynamic) the contrast between the picture and the background on the HP is looking pretty minimal. Worse, while the picture looks pretty much the same from either angle on the LaCie, on the HP it's gone from a bit dark and shadowy to completely washed out -- to the point that the stripes on the sweater have almost completely disappeared!

My conclusion: both the specifications and people claiming current entry-level monitors have surpassed high-end monitors from yesteryear are basically full of crap1. The new monitor undoubtedly works for spreadsheets or word processing, but the LaCie retains a significant edge in contrast, color accuracy and ability to view from different angles.

1 No, I'm not accusing HP of lying in the specifications -- I'm sure under the right circumstances, it meets its specification. Nonetheless, even after years of regular use, the blacks on the LaCie look deep and rich, while those of the brand new HP look weak and wimpy at best.

Tuesday, October 9, 2012

Software patents, part II.

In my last post, I promised a post about what I think needs changing in the patent system. This necessarily gets considerably more detailed, so it's likely to be harder to apply it to different patent systems. Nonetheless, when people talk about problems with software patents, the US seems to be (by far) the most often cited culprit, so I doubt that being specific to it is really a major problem. Anyway, on with the show.

The first problem I see is that the US patent office is basically run as a business -- it's profitable to the government, and most of the profit comes from issued patents. Worse, what's really intended to be the primary job of the patent office (searching through prior art to figure out whether something is really original) is apparently run at a loss. The profit comes from "maintenance fees" on patents after they're issued.

The patent office has suggested a way to try to streamline the patent examination process that would involve the inventor either citing only a few sources of related art, or (if they know of too many) specifically pointing to those they think are most relevant, including specific citations of the parts they consider relevant.

At least to me, this seems utterly insane. First of all, it's simply attempting to shift the burden of the patent office's job from the patent office to the inventor. Second, it's asking the inventor to predict what the patent examiner will find the most useful. If, for example, the patent examiner looks at some other reference and finds it more relevant than the ones the applicant pointed to as most relevant, would the patent become invalid? If so, the patent system basically becomes a lottery. But, if there's no penalty, what's to prevent an applicant from citing something utterly irrelevant as the most relevant art related to his patent?

The simple fact is fairly simple: as it stands right now, the patent office simply isn't complying with the requirements of patent law. The law says the fees they charge should cover the cost of examining the patent. If their fees aren't high enough to do that, then the fees need to be raised. Another point that's routinely cited is that an examiner has only about 20 hours to examine a given application (there's some disagreement about the exact number, but at least it's at what I'd consider the noise level -- there's little question that it's between  15 and 25 in any case). Another common complaint is that patent examiners simply aren't competent -- that they often just don't know enough about the technology to sort out (for one example) truly new techniques from simply new and different terminology for existing techniques.

These have a simple solution though: simply increase the fees for a patent application to the point that they can/will cover the costs of hiring competent examiners, and giving them enough time to do a good job. Along with funding the process properly, higher fees, all by themselves, would probably do quite a bit to encourage companies to look more carefully at their applications before filing, to ensure that what they're filing is truly novel and useful, before wasting others' time finding prior art to show that it's invalid.

The second major problem I see is that it's much easier to get a patent granted than to get that same patent invalidated after it's been granted. The patent office has been taking some steps that attempt to balance this a bit better, but at least personally, I don't think they've done quite enough yet.

Classically, the situation was that the inventor filed his application, and the patent examiner (usually only one, though sometimes two) tried to find prior art. Under most circumstances, almost nobody else participated in the process at all. The patent office does now publish (most) patent applications, so normal people can review them, but it's still basically provided as a one-way communication -- if you look at an application on the patent office's web site, there's not (for example) a button on the page to let you send an email to that examiner citing what you think is prior art on that patent application. Right now, however, instead of treating prior art submissions as what they really are (normal people doing them a favor to make their job easier) they seem to treat it as if they're doing me a big favor by allowing me to submit anything at all, and it's perfectly reasonable to make me jump through flaming hoops before I can be granted such a privilege.

Even so, the patent office follows a "preponderance of the evidence" rule in deciding whether to issue the patent. That basically means only a simple majority of the evidence needs to point toward its being novel for the application to be accepted, and the patent to issue. If 51% of the evidence says it's original, and 49% says it's not, the patent can be issued. Keep in mind that in most cases, it's up to one person to find any and all evidence of invalidity (in roughly 20 hours of work or less), but a large company may easily have a dozen people working hundreds of hours (if necessary) to get the patent issued, and it's quickly apparent that the system is heavily loaded in favor of issuing the patent unless it's quite obviously bad (and sometimes even if it is quite obviously bad).

Once the patent issues, however, the courts are required to give the patent a presumption of validity. To invalidate the patent, you don't simply need to provide a preponderance of evidence in the other direction. It's not enough at that point to show that 51% of the evidence points toward invalidity, and only 49% toward validity -- instead, the courts require "clear and convincing" evidence that the patent is invalid before they will declare it invalid. I've never seen a court attempt to specify a percentage of the evidence necessary to meet the clear and convincing hurdle, but it's clearly a lot higher than a mere preponderance of the evidence. If I had to characterize it, I'd probably put the number at around 90% -- still somewhat short of the "beyond a reasonable doubt" (that's supposed to be) used in criminal courts, but much higher than than 51% used as the basis for issuing the patent in the first place.

We end up with a system that deprives most people of much ability to provide evidence that a patent application isn't valid, issuing the patent even when/if there's a substantial chance that it's not valid, and maintaining it as valid even when most of the evidence indicates that it's really not.

Though I don't think those are (probably) the only two problems with the patent system as it stands today, I think addressing those two points would go a long ways toward redressing much of the current imbalance in the patent system. Interestingly, neither of these requires any change to the actual patent laws at all, only changes in procedures about how the existing law is enforced. Over the past several years I've seen many proposals that included what initially seem like much larger changes (nearly all including substantial changes to the patent law itself). I believe most of these would do little to cure existing problems, and quite a few would add many more problems of their own as well.

From a programmer's point of view, most of the proposals strike me as doing nothing to try to find or fix actual bugs, and instead advocate changing indentation and naming conventions throughout the code. They'll change how the code looks, and might (conceivably) make it more readable, to at least some degree, but they're almost certain to introduce at least a few new bugs in the editing, but fail (except, perhaps incidentally) to fix existing bugs. Just as with code, to do real good, you need to identify the real problems, prioritize them, and (usually) attempt to make the smallest changes that fix those problems.

I'd also note that almost none of this is specific to software patents at all. Most of the problems I see apply at least equally to areas outside of software. As noted in my previous post on the subject, I think most of the arguments attempting to separate software patents from other patents lack merit.

Thursday, September 20, 2012

Why most programmers are wrong about software patents.

Many (probably most) computer programmers favor elimination of patents that apply to software. I believe, as is often the case, that they're well on their way to repeating a dark history they've blithely ignored.

Patents were invented as a service to society -- the basic intent was (and remains) fairly simple: give an inventor exclusive rights to his/her invention for some limited period of time in exchange for agreeing that as soon as that limited period of time expires, the invention goes into the public domain -- anybody can freely use it. By itself, that wouldn't mean much: after all, if the patent didn't exist to start with, anybody would be able to make free use of the invention immediately, instead of waiting for the patent to expire.

The benefit to society comes from another requirement for a patent: that the patent describe the invention so others can use it. The exact phrasing varies by country, but in the US the requirement is that the patent contain a description of the invention sufficient for a person of ordinary skill in the art to implement the patented invention.

Going a step beyond that, US patent law also includes a "best mode" clause that says the inventor must reveal what he believes to be the best method of implementing/deploying/using the invention. For example, if he's thought up a new type of oil for lubricating automobile engines, he can't patent it, but in the patent claim that it's intended to be used as cooking oil (which could deprive society of the benefit, because they ignore it after finding that it makes food taste terrible). Obviously the example of a cooking vs. lubricating oil is a bit extreme, and probably easily seen through -- most people would probably think something was a bit odd about Exxon patenting what they claimed was a cooking oil, for example.

Anyway, let's take at least a quick glance at that dark history they're ignoring. Before patents were invented, most crafts were governed by guilds. To learn how to carry out a particular craft, you had to be admitted into the proper guild. The guild guarded the secrets of its craft quite carefully in most cases -- to the point of sometimes murdering people who were suspected of revealing guild secrets, and refusing admittance to others because they were seen as too dangerous. In other cases, there were literally wars between competing guilds. These not only get people killed, but in some cases when a guild was destroyed, its secrets died with it. Archaeologists have found artifacts showing techniques we don't quite know how to duplicate to this day.

As many problems as they had, guilds were a substantial improvement over the previous system: one of individual craftsmen keeping secrets entirely to themselves, to be passed onto their children, sometimes on their deathbed -- or taking their secrets to the grave, if their children weren't handy at the right time, or were estranged, etc.

Most arguments programmers level against this fall into three broad groups. The first is that programming techniques (algorithms, protocols, etc.) get published even when there are no patents. The second is rarely quite so clearly articulated, but basically comes down to the notion that if one person invented something, they can invent something at least equally good when and if they need to. The third is that software moves so quickly that by the time a patent has expired, it's no longer of any value.

The first is partly true. They can point, for example, to the fact that European companies continue to publish despite the European policy against software patents. This, however, ignores reality. What's happening right now is that Europe is basically "freeloading" off of the patent systems of other countries (US, Japan, etc.) If, for example, Seimens or Philips wants a patent in the US and/or Japan, they need to publish all the details of that invention in their US/Japanese patent application. That means the invention is no longer secret -- and given current communications, the minor detail that it's published in the US/Japan instead of somewhere in Europe adds (at most) a few milliseconds for a European citizen to download the patent application. As such, Europeans enjoy the benefit of inventions being published, without (themselves) giving the inventor anything in return.

The second strikes me as simple conceit. Yes, there are patents running the gamut from utter stupidity to simply being something nobody else thought was important or original enough to bother patenting. Being at all honest, those constitute only a fairly small percentage of patents overall though. Much of this stems from a problem I've seen many times: somebody will draw a badly mistaken conclusion about what the patent covers, often based on looking at nothing other than the patent's title. They see a title that says something like "A method for run-length compression", and they think something like "good lord what insanity -- everybody's known about RLE for ages -- obviously the patent office is a bunch of idiots!" Though it's barely possible they're (at least sort of) correct, and this really is a patent on something everybody's known about for decades, chances are it's something else entirely -- some (possibly minor) improvement that allows the job to be done a little faster, or using a little less memory, etc. In a typical case, it's not earth-shaking, but is original and at least mildly useful.

The third argument may sometimes have some degree of validity as well, but often doesn't. This argument, however, ignores that fact that if the invention becomes obsolete quickly, the cost of the patent (to the people) is also low -- if an invention is only meaningful for a year or two, the cost to society of the fact that an inventor (theoretically) gets exclusive use of it for years afterwards costs society essentially nothing. At the same time, people have invented and patented algorithms that retain value well after the patent expires. An obvious case in point would be RSA encryption. The US patent on RSA expired well over a decade ago, but it's still almost certainly the most widely used from of PK cryptography. RSA remains (roughly) as valuable today as ever, although there are alternatives that could be used if RSA were not available.

Now, don't get me wrong: I don't think the US patent system (or probably any other) is anywhere close to perfect. Some time soon, I'll write a post about what I see as problems in the system, and at least some ideas about how to fix those problems. To give fair warning: I believe many of the problems can be fixed with much less drastic changes than most people seem to think are necessary. In fact, some of the changes are (or at least initially seem) so minor that they're probably almost invisible except to attorneys who specialize in intellectual property law. Nonetheless, I think some seemingly trivial modifications can have fairly serious consequences.