Archive for the ‘Mysteries’ Category

Wonder and Music

Thursday, December 18th, 2014

galaxySo many times I’ve felt like life was over.  That there was nothing to live for.

Don’t get me wrong — I’ve never seriously considered logging out of this cosmic videogame any earlier than I have to.  But often I’ve thought that the rest was going to be a slide into senility, nothing more than that.

Wonder always rescues me.

Life is infinitely precious, but it is Wonder that reminds me just how incredible it can be.

Have you stopped recently to consider what a miracle it is that atoms came together to make the living masterpiece of you? Have you paused to reflect on the incredible truth that something we call love exists? Maybe abstractions like truth, honor, justice, and love are human inventions. Maybe insects and worms know nothing of them. Perhaps ants and bees fight to protect their homes out of mere instinct. Maybe.

But unless you are truly soulless, truly dead inside, you have to be moved by the unbelievable beauty around you. Both the beauty that arises “naturally” in plants, animals, and geography…and the beauty that we as a species learn to create.

Do bird enjoy the sounds they make? Music has always been a powerful inspiration for me. I am mystified to find beauty in all kinds of music: so many infinite kinds of celebration - the “joyful noise” we humans make from sound and time, frequency and rhythm.

If you’ve read this far and you feel the need to escape from mere words back into the world of wonder, try this:

EPIC music with full cinematic eye candy.

I didn’t make it that beauty. But I enjoy it…and you might too.

—MRK

Twitter del.icio.us Digg Facebook linked-in Yahoo Buzz StumbleUpon

The Equations of Motion

Wednesday, November 27th, 2013

The equations of motion for a volume element of fluid, written in Exterior Calculus form, using a system of units which unitizes the distracting arbitrary constants such as the speed of sound, can be written (and translated)  as :

-"eqns

molecular displacement acceleration = opposite of the gradient of pressure change

pressure variation over time is opposite to the divergence of the molecular displacement  velocity

density variation over time is opposite to the divergence of molecular displacement velocity

Now you may well wonder why the mathematical form of these expression seems so opaque when it describes things so easy to say in English, such as the fact that when you crowd air molecules together, the density and pressure goes up, and vice versa.

One answer might be that to those who wish to formulate mathematical descriptions, such descriptions are only acceptable if they are sufficiently detailed to describe and account for all possible situations.  In other words, while “crowding raises the pressure” seems so obvious as to be trite, making this expression into a mathematical equation — involving vector expressions such as gradients and divergences expressed in some form of calculus or differential equation — makes the expression more useful in practical applications where it can be applied to unusual situations and unique geometries.

— MRK

Twitter del.icio.us Digg Facebook linked-in Yahoo Buzz StumbleUpon

Modal Logic and Quantum Mechanics

Wednesday, November 27th, 2013

meAnd here I am again.  Yes this is me today. It’s too late to hide now.

Today I’d like to talk about modal logic. My introduction to symbolic logic and the predicate calculus began in a philosopy & logic class in the late Seventies. But that was merely true-false logic.

Modal logic is a generalization of simple logic, going beyond whether statements are true or not, but whether it is possible for them to be true, or necessary that they be true.

modal1

The combination of these operators yields some interesting theorems:

modal2

If this sounds more like philosophy (epistemology) as well as Quantum Mechanics, then perhaps it is. For example, one way to state the principle of “mixed states” such as we find in the “uncollapsed state vectors” might be the following:

modal3

Conversely, if one passes a beam of spinning particles such as electrons through a magnetic field so as to cause the “spin up” particles to deflect one way and the “spin-down” particles to deflect the other way, then the states are no longer mixed. In this case, looking at either one of the diverged result beams, we find that it is no longer possible to observe both “up” and “down” states:

modal4

More on this later –MRK

Twitter del.icio.us Digg Facebook linked-in Yahoo Buzz StumbleUpon