Nice article about Algebra vs. Arithmetic

If you are anything like me, this is something you’ve try to articulate. Here’s a great article on that arcane topic!

What is algebra? | profkeithdevlin:

Is mastery of algebra (i.e., algebraic thinking) worth the effort? You bet — though you’d be hard pressed to reach that conclusion based on what you will find in most school algebra textbooks. In today’s world, most of us really do need to master algebraic thinking. In particular, you need to use algebraic thinking if you want to write a macro to calculate the cells in a spreadsheet like Microsoft Excel. This one example alone makes it clear why algebra, and not arithmetic, should now be the main goal of school mathematics instruction. With a spreadsheet, you don’t need to do the arithmetic; the computer does it, generally much faster and with greater accuracy than any human can. What you, the person, have to do is create that spreadsheet in the first place.  The computer can’t do that for you.

 

Fibonacci series and Photography

You can’t be a self-respecting computer or science geek and not have heard about the Fibonacci series. You know, 1-1-2-3-5-8… etc. How about Fibonacci’s Ratio? How about the Golden Mean or the Divine Proportion? Not sure, right?

Fibonacci, and its role in art, design and photography is a little less well known. As I continue to study photography and art I came across this excellent article about that very topic:

“Hopefully, this article has shed some light on a somewhat mysterious subject in the world of photography. Fibonacci’s Ratio is a powerful tool for composing your photographs, and it should’€™t be dismissed as a minor difference from the rule of thirds.

While the grids look similar, using Phi can sometimes mean the difference between a photo that just clicks, and one that does’€™t quite feel right. I’€™m certainly not saying that the rule of thirds doesn’€™t have a place in photography, but Phi is a far superior and much more intelligent and historically proven method for composing a scene.” (from Divine Composition With Fibonacci’s Ratio)

 

Patents and perpetual motion machines

An interesting commentary on a couple of patents that issued from the US Patent Office:

“The US patent office no longer grants patents on perpetual motion machines, but has recently granted at least two patents on a mathematically impossible process: compression of truly random data” (from Gailly.net)

Also you might be interested in the topic, there’s a second patent that seems also to be fatally flawed — It is analyzed here.

I am not opposed to software patents as a matter of principle. And of course a patent that describes something that is mathematically impossible is harmless inasmuch no one is forced to use it. But it does shine a light on the problems with Patents in general. Is it mathematically impossible though?

I wonder how the inventors of these patents would respond to the allegations above. Well it turns out that he has devoted a whole web site to the topic: “Michael Cole, Inventor of Recursive Data Compression Patent 5,488,364 created andy utilized a recursive data compression structure.” The site has lots of details and mathematical symbols. I have not taken the time to try to understand either his arguments or the counter arguments.

I mainly got fascinated by the conflict.

Mathematical Foundations of Consciousness?

Say what? I came across this paper; Mathematical Foundations of Consciousness. I generally love this stuff: Mathematics and writings on the nature of consciousness. When I saw this paper the title really intrigued me. Now my math is not strong enough to tackle anything like PhD level math (in fact my math knowledge beyond under graduate level is definitely uneven.)

“The self-referential qualities of consciousness place it outside conventional logic(s) upon which scientific models and frameworks have heretofore been constructed. However more contemporary mathematical development has begun to deal with features of self-reference. We shall address Schrödinger’s critique by assembling and extending such development thereby putting self-reference as a form of awareness into theory. In this way we shall frame mathematical foundations for a theory of consciousness.” (from Mathematical Foundations of Consciousnes)

As I said, my math is weak, so I am not appreciating it, but to me this paper came across as a bunch of fancy mathematics with only peripheral thinking about consciousness.

Two fun (to me) articles about arcane mathematical topics

Ok, probably to a mathematician these are not arcane, but to normal people (oops, sorry, I love mathematicians) I think they might be. Anyway, read and enjoy without any further commentary:

  • Needle-in-a-haystack Problems: “[snip…]A needle-in-a-haystack problem is a problem where the right answer is very difficult to determine in advance, but it’s easy to recognize the right answer if someone points it out to you. Faced with a big haystack, it’s hard to find the needle; but if someone tells you where the needle is, it’s easy to verify that they’re right[snip…]”
  • Needle-in-a-haystack Problems, and P vs. NP. “[snip…]Last week I wrote about needle-in-a-haystack problems, in which it’s hard to find the solution but if somebody tells you the solution it’s easy to verify. A commenter asked whether such problems are related tothe P vs. NP problem, which is the most important unsolved problem in theoretical computer science. It turns out that they are related, and that needle-in-a-haystack problems are a nice framework for explaining the P vs. NP problem, which few non-experts seem to understand.[snip…]”