the definition of a transcendental number:

transcendental number: a real number that is not the root of any polynomial with integer coefficients.

TT and e are transcendental.

they also can't be represented by a ratio (i.e., they are 'irrational')

√2 is irrational and is a root of the polynomial equation x2 − 2 = 0.

Here is some more on irrational numbers.

The nonexistent world of ideas, numbers, abstractions, algorithms, et cetera, is very interesting indeed.

I would say that thinking and counting and otherwise imagining stuff can sometimes be a positive experience

And as we know, experiences are things that, like atoms, exist.

'experiences' aren't things like atoms, but both atoms and experiences really happen

I think they're things. Not like atoms in many ways, but things just the same. What's missing is a physical theory for them.

to me, things are 'out there', while quales are 'in here'. The mathematics of things is 1+1=2 while the mathematics of quales is 1+1=1 or something like that

Dan, I missed it. What the... is a quale?

The only quale that I know of looks and tastes like bar clams.

quale - luid?

Experiences are the electrical activity that occurs at the molecular level, when certain clumps of physical material (atoms) combine and do their thing.

I wonder then, are #'s made up of atoms?

http://plato.stanford.edu/entries/qualia/

The Four Fources

listed in decreasing strength:

Nuclear 10^3 1,000
Electromagnetic 1
Weak 10^-11 1/100,000,000,000
Gravitational 10^-39

These are the 4 ways in which the various particles that make up the universe can interact with one another.

Each interaction creates a force.

Every particle in the universe is the source of one or more of these forces.

Each particle serves as the center of a volume of space in which that force exists.

A force feild is the volume of space in which that force is felt.

If a particle can serve as the source of a particular field it will respond to such a field set up by another particle.

The response is generally one of movement where the particles move toward one another (attraction) or away from each other (repulsion).

Unless physically restrained from doing so...

...and it is only in the nucleus, the center of an atom, in the immediate neighborhood of isolated particles, that these forces exist.

Particles are not likely to respond to all 4 forces.

For instance, only hadrons produce and respond to the nuclear force.

hadron - from the Greek for 'strong', since the nuclear is the strongest.

The two nucleons (the proton and the neutron) are the most common and most important to the structure of the universe.

Ernest Rutherford, a British physicist, discovered the proton in 1914, and its name comes from the Greek for 'first' because at the time of its discovery it was the smallest object known to have a positive electric charge.

James Chadwick, also an English physicist, discovered the neutron in 1932. It carries no electric charge, neither positive nor negative, so it is essentially neutral electrically, hence its name.

The atom contains almost all of its mass in a very small region at the center in the nucleus.

The proton is a 'relatively' massive particle that must be located in the nucleus.

Each atom type contains a different # of protons in its nucleus.

Hydrogen 1
Helium 2
lithium 3
....
uranium 92

So what holds all of these protons toghther in tight proximity inside the nucleus?

The gravitational force is to weak to hold the protons together.

The electromagnetic force?

Yes, it is strong enough, however it can only manifest itself as either an attraction or as a repulsion. Between two particles of opposite electric charge (+ & -) their occurs attraction and when two particles exhibit the same electric charge (+ & +, - & -) their occurs repulsion.

Protons are all positively charged and therefore must repel each other and the repulsion must be more intense the closer the proximity of the atoms.

In the nucleus of an atom, where protons are squeezed together until virtually contact, the electromagnetic repulsion must be enormously strong. And the protons still hold strong.

Now, neutrons are also present, however since they have a neutral electric charge they can neither repel or attract notta. Therefore they will neither hold the protons intact nor accelerate breakup.

In 1935, Jap physicist Hideki Yukawa showed that it was possible for protons and neutrons when very close to each other to produce an attractive force a thousand times greater than the electromagnetic repelling force, the nuclear force.

What the nuclear force holds together the electromagnetic force cannot blow apart.

both protons and neutrons are composed of 3 quarks
a proton is composed of 2 'up' quarks of charge +2/3 and 1 'down' quark of charge -1/3 to give it a total charge of +1
a neutron is composed of 1 'up' quark and 2 'down' quarks giving it a total charge of 0
for reference, an electron carries a charge of -1

Yeah, I'm just trying to get to the bottom , or should I say center, of what is, and I feel that one would be better informed and equiped to philosophize on reality if one knew the fundamental structure of the atom, the basic building block of everything.

Yes, the electron, the most important lepton (from the Greek for 'weak'), sources of and responds to the weak force but never the nuclear force. Some leptons are electrically charged though and are a source of and respond to the electromagnetic force, as well as the weak force.

The negatively electric charged electron was discovered in 1897 by the English physicist Joseph John Thompson, and it recieved its name because it was the smallest unit of electric charge known.

Good call!

I've just been getting aquainted with it indepth since '02.

strange, but true

I bet there's a 'funk' field out there somewhere, just waiting to be discovered

Define funk.

funk is crazy cool, you dig?

The cool thing about "cool" is that it's been cool for over 50 years now. I used the term as a kid in the 1950s.

sweet

Totally, dude!

I figured only slang like nifty and neat came out of the fifties.

That's the bomb!

Ooooohhhh, that's hot.

I'll let you know when I get back.

The set of all transcendental numbers is one-to-one with the real continuum R. This arises from that fact that you can prove that the set of all algebraics is Aleph null, and thus the set of all transcendentals must be c in order for transcendentals U algebraics = R.

I can get the proof that the set of algebraics is aleph null if anybody is interested. (It involves setting up a correspondence between all polynomials and the rationals by invoking the properties of finite cont'd fractions)

I can see that the set of algebraics is Aleph null. An open question: is R really continuous?

Lol well maybe you can explain then how it ever caught on (I admit, I have fallen victim to the tem myself). Where did the term originate? I suspect cool is going to be a thing of the past soon, "chill" is the new "cool". I guess my generation just needed a slightly different twist

Depending upon what you think of as continuous.

Another very very open question: the continuum hypothesis. It's entirely independent of ZFC

I'd guess continuous means "without a break." For example, if we take a line in space composed of a continuous set of real numbered points, and remove one of them, say the square root of two, then the resulting "punctured" line is discontinuous, assuming the reals are continuous.

According to Wolfram's Website, the continuum hypothesis has been shown to be undecidable.

Rudy Rucker worked on it for a while without results.

I think jazz musicians in the 50s referred to certain flavors of jazz as "cool" and it took off from there. It was just part of the child culture for me. Meme reflection, like neutrons bouncing around in a light water reactor.

Undecidable as in independent of most widely accepted axioms. (Like ZFC)

The ideas of "continuity" and "brokenness" are very subjective. Is the set of rationals, Q, continuous? Well, between any two there are another infinity of them... as well as another uncountably many irrationals.

Q is dense in R, even though R is uncountable and Q is countable. This seems ironic, but it is true.

Hard stuff to imagine..

A bit like "now".

There is only now. Time does not exist (as a physical dimension).

Matter exists in different places in space, and at any point in time we could say that there is matter. It doesn't seem to me to have any contradictions by thinking of time as a dimension; it in fact fits up nicely with lots of phenomena involving matter and position.

But of course, if we think of it that way, it is obvious that time is a unique dimension as it is along this axis that our perception/change occur, and it is central to many descriptive equations which are not symmetric over a supposed 4 dimensions.

The fundamental indication of time is our own memory, which for the most part assumed objective, thereby establishing information which we can think of as an abstract structure involving time, with similarities to our idea of dimensions.