My thoughts…

• Remember, you are special—just like the sauce.
• I find it more often the case that it is six of one or a half dozen seven of the other.
• It’s best to have more than you need, but less than you want.
• But it’s also good to, at least once, have less than you need and more than you want to appreciate the previous statement.
• Nobody was ever decades ahead of their time. Their successors were decades too late.
• Encourage others to do the impossible. It’s so satisfying to watch them fail. (this should be taken as humor)
• I believe what I do know is infinitely less than what I do not know.
• At risk of offending the oxymorons, political correctness is an oxymoron.
• Remain open to the possibility that it is you who is primitive, not your ancestors.
• Fact is rarely what you know to be true, but more often what you trust another has declared to be true.
• You cannot approach infinity, but you can infinitely approach.
• The foundation of security is trust.
• Sometimes a win-win scenario is just a disregard for the two losers.
• Give things worth having.

From others…

• “Time is an illusion. Lunchtime doubly so.” – Ford Prefect (Douglas Adams)
• Writer 1: “I’m writing a book.” Writer 2: “Neither am I.” – Peter Cook
• “If you want something done, ask a busy person to do it.” – Laura Ingalls Wilder
• “The lack of money is the root of all evil.” – Mark Twain
• “There are three kinds of lies: lies, damned lies, and statistics.” – Mark Twain (among others)
• “It is better to remain silent at the risk of being thought a fool, than to talk and remove all doubt of it.” – Maurice Switzer?

Maybe you should stop reading here…

You might find logical flaws ahead. I will try my best not to care so much about that.

I always had a hunch that rotation was strange and special.

I wonder if space is one dimensional and I just can’t see it. Consider the following very loose analogy: The color of light is measured using wavelength, but we perceive the color of light through a combination of three filters on a singular wavelength. We measure space with distance, but we perceive space within a framework of three independent axes. [Now, of course there’s a difference here because spatial axes are each measured with distance, but the individual components of a single color/wavelength don’t each have their own individual contributing wavelength]. Is our real-world, three-dimensional space just a filtered perception like color? Does all of space fit into a linear “spectrum” like color? Maybe space is one-dimensional after all and humans are just messy filters. Other properties of perceived reality which I can think of are associated with single axes – properties like time, temperature, mass, or energy are measured with a single value. But distance is the oddball with its three axis combination yielding three-dimensional space as we perceive it. I’ve always wondered if time existed in multiple axes as well. It seems like in science, ideas are often broken down into their simplest components – like a real world object being made of smaller parts, and then those parts being made of molecules, made of atoms, made of subatomic particles, etc. The macro being the sum of the micro. But with space being composed of one-dimensional distance components, it would seem that every possible combination of reality might be measured as a combination of singular values of distance, time, mass, energy, etc. Three dimensional space is weird.

Both happiness and sadness offer clarity. Each discovers both truth and lies. And truth can even yield happiness as lies yield sadness. Sometimes I think happiness more easily discovers truth, and sadness more easily discovers lies. I’ve felt in the past that the edge to clarity might go to sadness, and that happiness sometimes feels like a distraction for sadness.

Recursive mathematical functions have been pestering my brain since I was about 19 or 20. Consider a function F with one parameter x such that F(x) = x + 1. F(4) is therefore 5. Now consider F(F(x)). F(F(4)) would be F(4 + 1), or F(5) which yields 6. Simplifying F(F(x)) gives F(x + 1) –> (x + 1) + 1 –> x + 2, so F(F(x)) = x + 2. Given this F(F(x)) = x + 2 as an initial statement, how would you find an original F(x) to satisfy this? (Note that there could be multiple solutions) Or in other words, solve for F(x). Take a slightly more convoluted initial statement with F(F(x)) = x^3 – 2x. Now what is F(x)? Although we’re trying to find an F(x) equation to satisfy the recursive equation, and you might stumble upon one, the real question is not “What is an answer that satisfies F(x),” but rather “How exactly do you approach the problem?” Are there any methods available to help unravel this? The whole concept reminds me of one-way hash functions commonly used in encryption.