Skip to main content

You need to jump dimensions to solve certain problems

 


In the image caption above you see the solution to the equation given in the first line in the second line. A simple looking innocuous equation doesn't have a solution in the real line. In order to solve it, we have to jump into the imaginary line. 

I am always amazed by this equation because it informs us of certain deep realities that we might not usually contemplate when we are going about finding the solutions to other problems we encounter in daily life.

While the typical definition of dimensionality involves the length of a vector, I think jumping from the reals to the imaginary is a dimensional jump in some sense.

So why is it important to put this in mind? There are many scenarios where one can solve a problem in the same plane where the problem is found like there are many equations for which there is a solution in the real line. But one must be vigilant about those problems that require a dimensional jump because every now and then they will crop up in all kinds of systems.

The main motivation for this post is because I think the stagnation we are experiencing in deep learning research despite inventions like GPT-3 requires a massive dimensional shift to overcome. 

We might need to use the tools of pure mathematics to really understand more of what deep learning systems are doing and thus make the needed jump or else we will eventually use the whole planet as a computer to run very weak algorithms. 

Comments

Post a Comment

Popular posts from this blog

Next Steps Towards Strong Artificial Intelligence

What is Intelligence? Pathways to Synthetic Intelligence If you follow current AI Research then it will be apparent to you that AI research, the deep learning type has stalled! This does not mean that new areas of application for existing techniques are not appearing but that the fundamentals have been solved and things have become pretty standardized.

Virtual Reality is the next platform

VR Headset. Source: theverge.com It's been a while now since we started trying to develop Virtual Reality systems but so far we have not witnessed the explosion of use that inspired the development of such systems. Although there are always going to be some diehard fans of Virtual Reality who will stick to improving the medium and trying out stuff with the hopes of building a killer app, for the rest of us Virtual Reality still seems like a medium that promises to arrive soon but never really hits the spot.

What is Intelligence: Software writing Software

Sometimes I wonder why programmers are hell-bent on writing programs that can communicate in natural language and not even putting adequate effort into writing programs that write other programs. Maybe is because of the natural tendency to protect one's source of livelihood by not attempting to automate it away or maybe because writing programs is hard enough such that contemplating of writing some program that writes programs might be even harder.