Tuesday, July 29, 2014

No prime preference?

As hard as number theory can be there are areas where you can stumble across simple ideas which have HUGE consequences, especially for generating controversy. Oddly enough it's easy to find raging arguments over seemingly basic things, where I stumbled into one by speculating about prime residues.

And it's easy enough to talk about it using 3 and some other primes. For instance 5 mod 3 = 2, while 7 mod 3 = 1. And if you're a coder you may be more used to seeing something like 5 % 3 = 2, and 7 % 3 = 1. And I use that so it may look familiar as I use "mod" all over the place, but now you should have the idea.

Well, I'm like, why should 3 have any particular residue modulo a larger prime? And "modulo" is just the more precise way to say what I showed above. And it turns out that's not a new thing to ponder and don't worry, we're close to one of the biggest raging arguments you can face if you dare.

For instance 101 is prime, and 101 mod 3 = 2. Think anyone could predict that without checking? Let's go higher. And 1621 is prime and 1621 mod 3 = 1. And no, wasn't trying to get that as just randomly went up to a higher prime. But it is convenient as you can have 1 or 2 as the residue, and why should it matter?

Well accepted number theory is that there is some very complicated mathematics which yup, does involve the Riemann Hypothesis, which says it DOES matter and is not random. While I suggested it WAS random and ran into some of the hugest arguments I've ever faced.

So I'm like, why should primes care what their residue is modulo 3? And extrapolated to primes in general modulo a larger prime and came up with some rules, and even came up with a prime gap equation. Did that years ago and turns out I have things I worked on years ago lying around that I just think about again now and then. Found the prime gap equation is in a post on my math blog from 2006:

If you're bored and like playing with numbers and don't care if it's using ideas supposedly incorrect, you can code it. Mainly just need to know what a prime is, and have a list of primes to plug into this probability equation. Hardest thing to figure out is the correction.

Some may wonder why is it so controversial and why would primes supposedly have a preference. Why would 3, you could say, care whether any particular prime has 1 or 2 as a residue?

Well if there is no mathematical reason then it's random.

Turns out you could define "random" using prime numbers. Which I've done, but yanked it as too controversial.

But it turns out you could solve some currently considered unsolved math problems like the Twin Primes Conjecture and the Goldbach Conjecture. Easy.

So yeah, no way it's accepted mathematics in this day and age! And in fact if I were a mathematician I'd probably not even dare bring it up for fear of destroying my career immediately. Turns out I'm not the first person to come up with these ideas. But I remember finding out about some controversial mathematician who put this notion forward years ago, and later when making a post about it, couldn't find his name again. Otherwise I'd give it here.

Later I decided that I would go even further and conclude I'd actually found a prime residue axiom.

An axiom is a really cool thing where most people believe they were all found long ago. It's something believed to be self-evident. That is, its truth is supposed to be so obvious as to be not in doubt.

Turns out mathematics is built on axioms. Without them, we wouldn't have mathematics! These are the foundation level things, where there is no proof, just the sense these things must be true.

And I decided this no preference of prime ideas was an axiom I guess in 2010 based on the date of the post.

Since I made that up, if you web search on prime residue axiom, it's about my ideas, including people trying to convince they are wrong!

So much fun! Here we started with this simple idea about the prime number 3, and its residues, considered with other primes, and I've managed to take you through a journey through some of the most controversial territory in all of number theory. Managed to put forward the idea that randomness itself can be defined using prime numbers. And let you in on the possibility of a simple resolution to supposedly open problems like Goldbach's Conjecture all in one little post.

And I remind you, officially from mathematicians, there is no acceptance of a prime residue axiom. There is no accepted resolution of the Twin Primes Conjecture or Goldbach's Conjecture. And randomness is not considered to be well-defined through prime numbers.

But if I'm right, and in the future what I say is accepted then these are some of the most important ideas of all time. Just defining randomness changes how we look at random processes, including, yup, the Big Bang itself.

And getting back to the beginning of the universe looks like a good place to stop.

To me this example is one of the most fascinating you can come across to show how easily controversy can be found and to raise questions about what happens as a result. Am I right about prime preference? Let's say for the sake of argument I'm not. But isn't it fascinating to play with such ideas regardless?

Some would say no. And I think here you can see how that kind of pressure can remove from others even the knowledge of a thing.

But if it turns out I'm right then that's huge! If I'm wrong, no big deal really, for me. So for others I think it important to emphasize I'm going against the official position of mathematicians. And I'm NOT a mathematician.

I came into these ideas out of curiosity and discovered I wasn't the first person. But even finding that out can be difficult as mathematicians seem to prefer such things not even be mentioned.

Luckily, I'm not a mathematician, which I like emphasizing, so I am willing to take you on a journey from a seemingly simple idea to the edges of human knowledge and into some of the most controversial ideas in mathematics itself.

I love talking about ideas! And sometimes it's fun to take you to the edge, and show you how close it is! For me, it's where I often have traveled, in journeys for me that feel like a long time ago.

Now, most of the time, I prefer to stay firmly on accepted ground.

James Harris

Monday, July 28, 2014

Is science hard?

The idea of conceptualizing science simply intrigues me and I have attempted to do so with the following basic statement:

Now I want to address common attitudes around science, which may make that seem too simple, as many may believe science is hard, but I say you do it, if you flip on a light switch!

And if you watch babies you may notice they stick lots of things in their mouths, which requires watchful parents and caretakers, as they're doing scientific experiments. This scientific activity of babies helps them rapidly learn their world, and eventually they can predict with great accuracy: like fruit is sweet!

As we grow older the childlike experimental side begins to fade as we learn social rules, and eventually with a personality well established we focus more on our place in our world, and eventually, most focus on procreation and then taking care of children before sliding into old age.

But some retain that childlike need to experiment, and we call those most obsessed, scientists.

So why might people think science is hard if everybody starts doing it as babies?

Well the art of prediction requires figuring out fundamental rules, and eventually those rules can become more difficult or the consequences of those rules are more complex. So, yes, fruits tend to be sweet. But the action of electricity for instance, can be predicted using mathematics that is challenging for most.

What science allows us to do is expand our realm of certainty. 

The more we move that realm of certainty beyond relatively simple things, like those most children learn, we start encountering greater difficulty in comprehending those rules, or their consequences. 

So scientists are in a way adult-babies, which may sound funny, but it best explains the childlike wonder that can drive certain people to keep expanding the realm of certainty, while most are involved with other things.

To the extent that we extend the realm of certainty we are doing science. And in fact plenty of people do science, but it can feel to be very difficult as certainty is actually kind of hard.

Of how many things are you certain in your life?

Remarkably enough, many people believe in endless shades of grey. While some claim absolute certainty, but primarily in a religious context.

Yet who, would argue with you that flipping a light switch and having a light come on is a matter of faith? Or shades of grey?

For many people you might as well call it magic, but we don't! We understand there are underlying rules which humanity has learned to understand so that it can predict with great accuracy what electricity will do.

Few people in the modern world marvel at the wonder of flipping on a light switch and having a light come on.

Maybe we all should.

Those who seek certainty are a different type of human. While most people are more focused on living their daily lives.

So science in and of itself is not hard, and we all start out as little scientists, learning some ability to predict in our world. But that ability to predict, like predictably setting a broken bone with medical science can get harder and harder to have, or can require learning a lot of difficult to understand rules.

So science covers a lot of territory where yeah, it can be really hard in certain areas, like at the limits of human certainty, but to some extent we all get to try our hand in some way shape or form, with the art of prediction. It's just part of the human experience to try and use those advanced brains of ours to try and gain some sense of certainty in our world.

And luckily we get lots of certainty, and next time someone tries to argue against that position with you?

Flip a light switch.

James Harris

Monday, July 21, 2014

Sharing ideas as part of sharing economy

Idea quality is something I think about a lot. Maybe that's a moving target so it's best to just try. Looking over lots of ideas and having my own ideas I like talking about sharing ideas as part of the sharing economy.

To some extent that's obvious, like with an open source application you have a product which people can use to do things, but it's just completely shared with all the ideas within it available to others.

This blog has evolved in my mind into an arena where I can share ideas, where some will be related to my open source application, but I doubt that hampers the ability of others to appreciate it.

Seems to me that can be a fascinating thing as well, as I am a single developer of a small open source project with downloads worldwide. There are decisions I make and things I share which have to do with what it's like to be in this position, and I think a lot of it is accessible to people with no interest in learning to code or administer an open source application, who might nevertheless be curious.

And I have over a decade now with it.

One of the things I like to do is tag certain posts as marketing. The idea though isn't conventional marketing but posts with the goal of clarifying social goals. For instance with this post I want to make clear that idea sharing is important to me, as a goal in and of itself. For me there is a strong sense of what I like or don't like while out there on the web in terms of pushing things on people. I don't like things pushed on me, and see no reason to push. Interesting quality content is a pleasure. You don't have to push quality, if you have it!

And if something is interesting to them, by definition that means people will be drawn to it. Not dragged.

My intent is for the bulk of posts here to be on a broad range of subjects. The Google Translate tool on the blog fascinates me as it opens up the potential for people in a vast array of languages to understand. Which helps with my software as well.

For years I've puzzled how best to use blogs, which is part of the reason I have more than one.

Blogs I think are evolving in terms of their use. I can compare how I use my blogs with how I use other tools like Twitter, and think you can see a specific way in which blogs are becoming more of a natural part of how people and organizations are interacting.

Here I want to talk about things I believe are beyond mundane which is very subjective to me. Of course, whether others agree is entirely up to them.

James Harris

Tuesday, July 15, 2014

Opening a Java file with Class Viewer

One of the features of my latest version of Class Viewer is the ability to open a local Java file. The way it works is that you have the packages for your classes setup in ClassViewerConfig.xml as usual, but the Local option should be set to "Yes", where the case does not matter, if you wish to open files rather than go to javadocs.

Now if you double-click on a method in the Results pane, or click on the Documents button, the application will go find the Java file, relying on your classpath so that must be set properly, look into the file to find the line number of the method, and call your preferred text editor.

If your preferred text editor takes a line number argument then it will get the call and you should have the file opened to that line number. Which I think is really cool. Well, it's fun to me.

If your text editor does NOT take a line number argument when called, Class Viewer will open up a pop-up window telling you the line number of the method. But you tell Class Viewer whether it does or not, in ClassViewerConfig.xml, so if you say it does take a line number then it will try that call with the line number.

If your text editor just opens the Java file and doesn't go to the method, you can assume it doesn't take the line number argument, or you do not have it set to take a line number argument in the ClassViewerConfig.xml file. Remember editing that file is easily done with a text editor, which is how I always do it.

The default text editor in ClassViewerConfig.xml is gedit as I think that one is well-known and it does take a line number in the argument! So I consider it a recommended text editor. It takes the line number with a parameter which is "+". So a call is like gedit +151 to go to line number 151 in as an example. That parameter is set in the config file as well.

Was almost tempted to write my own text editor to add this capability and realized that was silly, when Class Viewer could just call one. I think applications have great potential in calling other applications.

Class Viewer started in that direction by calling the browser anyway, and it's natural to continue down that path.

It's just so simple to let the application do it.

James Harris

Sunday, July 13, 2014

What intellectual property?

One of the most contentious areas out there is the arena of intellectual property where I like to ponder my default position of simply giving ideas away. Of course the most visible is with my open source, but I do have other ideas I've simply put out there.

With one idea I DID first pursue a patent, and did so back in the 1990's without success. That idea was for computers to use a generated password that cycled on the basis of connection time. I came up with it for cellphones, so that they would generate a new password with each connection invisible to the user. The telecommunications industry wasn't interested in my idea and that was when it was switching to digital instead of analog (yup that wasn't that long ago), and moved to digital encryption.

I resurrected the idea a couple of times on this blog, with the most recent asking a simple question:

Giving that idea away makes sense to me but it's also just easier than worrying about how to make money with it.

Also I updated recently an idea I had for storing encrypted files as copy protection. I labeled that idea Digital Media Equipment Self-Encryption.

Maybe that one could have made money for me, but I don't care that much. There were multiple problems I wanted to solve where the biggest was being able to make a copy of a movie that I bought. I figure that issue is being resolved.

Problem solving to me is for a purpose. If I simply want something then the problem is still solved if putting out an idea satisfies that want. And I think that as we move forward into a world where people can easily share ideas globally that viewpoint will show up more and more.

Why? Well for me ideas are like my buddies. I have lots of them. They come and go easily, and we have good times. That enjoyment is meaningful in and of itself. Sure I'd like some money but don't need a lot. And am terrified of getting too rich! Yup, I am terrified of getting too rich. Show me a single extremely wealthy person on the planet who can just casually walk down any street in America to go to a coffee shop say, and sit and chat with strangers.

One of my all time favorite ideas can't be patented anyway, though I'm not certain it's completely mine! But I know I am someone who has publicized it, which is about science, one of my favorite subjects.

I put forward the following:

Science is the art of prediction.

If correct that could be one of the most powerful concepts in all of human history, and if science can be encapsulated so succinctly it could be one of the coolest things ever: the greatest driver of human progress also capable of easy description.

Yeah, but I don't get to decide any of the above.

I have an entire recent blog post dedicated to explaining for the people who DO help decide:

And maybe that helps explain the concept of giving away ideas even better than some recent attempts I have on this blog. Can you imagine? If just that little idea is accepted then it could change the lives of billions of people by helping science get done better. It does matter when we're talking about it, to actually know what it is!

But, my opinion actually doesn't matter at all. That is the great beauty of the web--the collective opinion of so many people that make it work.

That's how people find my content. Not because I'm out there yelling to please read my blog, but because others have found an interest here. If we have a simple way to talk about science then it's not just about me stating some simple sentence. And I really doubt I'm the first to think science is the art of prediction.

If that concept changes the world it will be because a LOT of people found it useful.

Like I said, with me problem solving is for a purpose. I'm practical. If it isn't useful, why try to use it?

And finding use in ideas is a group thing. Like, imagine an individual with an idea he LOVES and no one can convince him there's anything wrong with it, but no one else thinks it useful! He's in his own little happy world then, by himself.

To me ideas are like these little gems that you get excited about when you find them and show them to people. But these gems of knowledge reproduce endlessly and travel the world. It's so beautiful and it's all about people.

So this post is about showing some ideas I find fascinating. But others decide whether or not those ideas work for them.

So YOU are the difference that makes it matter. Your opinion and that of so many others, rules.

What I get to do is share. And it's so easy to share what you think is a gem of knowledge these days.

Our ideas fly around the world. Zipping through borders. Able to touch as many lives as need them.

So is the concept of intellectual property dead? I don't think it is, but I think it has to evolve as reality is I can toss something up on my blog and not worry a lot about legalese. What good is that legal framework for me anyway? Do you think anyone is really going to steal any of these ideas from me? Guess we'll see, eh? And for people not money motivated, it can be a lot more fun, as generating ideas is just a natural thing for them.

And the web seems designed for them.

Others may fear the web. They may get angry or frustrated at the idea of losing their ideas to it. Desperately worry about how to protect themselves from it.

But I feel like it's an ocean of information, where finally I am free, and so are my ideas.

Here on the web they can fly around the globe, and carry me and as many who wish.

James Harris