jgill

What do you mean? The ratio "of"? Take a square with sides =1. The 1/1=1. Are you talking about the hypotenuse of a right triangle? Like each side = s...

You ask, and it shall be so . . . http://www128.pair.com/r3d4k7/LBEXP334b.jpg I work with this sort of thing all the time. Later: Interesting, my imag...

It should please you to know that you are at the point mathematicians were at two and a half centuries ago as they pondered what infinite sums meant. ...

Not so for Planck Time. You'll need a real, live physicist to discuss this properly. It used to be that this limit was variable according to some phys...

I'm sure he's found something else to fill those lonely hours.

Wow. This goes on forever, doesn't it? \underset{x\to {{0}^{+}}}{\mathop{Lim}}\,\tfrac{1}{x}\text{ }=\text{ }+\infty 1/0 undefined. Suggest you move o...

Each point corresponds to a specific real number. How many real numbers are there in the unit interval? I would question whether "happy" is the approp...

"points" are an intriguing notion aren't they? Like "lines" with no thickness. There are theories of time that posit the non-existence of a "present p...

If you google supertopo forum and go to "what is mind" you will find 25K posts that circle around this question.

Wiki: "The mathematical universe hypothesis suggests a new paradigm, in which virtually everything, from particles and fields, through biological enti...

The axiom of choice in theory allows one to decompose into pieces a solid sphere of diameter one foot, then reassemble those pieces into a solid spher...

It appears this concept overlaps with weak and strong emergence.

It's true. My graduate degree says "philosophy" Oh dear . . .

It all breaks down as limits are approached: Wiki: "The term Planck scale refers to the magnitudes of space, time, energy and other units, below which...

Factoid: The harmonic series (1 + 1/2 + 1/3 + ...) diverges to infinity so slowly that the sum of the first six million terms is less that 21. Another...

I'm 82. Oh, for the days of youth (77)! :cool:

Any open line segment is in one-to-one correspondence with the entire real line, thus the points on it are uncountable.

Indeed. I had trouble with it when I first encountered it in 1962. :yikes:

Actually they don't. You are very wrong. But that's OK, carry on. :scream:

Why Philosophy? To staff philosophy departments. I do think, however, that philosophy pertaining to human behavior and societal matters is appropriate...

With the right parents CT can be cultivated at an early age, I suspect. Of course, such parents probably have the abilities by nature and thus impart ...

And I look forward to the day. Spacefoam anyone? :nerd:

Maybe we haven't tried hard enough? I've seen arguments like this many times, projecting past failures to future attempts.

Were you aware there is a one-to-one correspondence between any interval on the real line, no matter how small, and the entire infinite real line? It'...

The mathematics of analogous dynamic systems is fun to play with, but social sciences are messy, even economics and history where one looks backward r...

What is a particle in a continuum? So .25 =.2500000... Only the first two decimal places have information worth having. I assume you are thinking of a...

Wiki: "In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequali...

There was no "before the big bang." The north pole of the Riemann sphere. So there. :cool:

If you say so. :roll:

Well, I can't argue with that. Above my pay grade. :brow:

The reality you are aware of, perhaps. Is there nothing else?

I agree with the first four sentences. Physicists that I have known are interested in results, in the predictive power of their processes. I don't kno...

I don't know about cosmology, but in mathematics I don't know where you get the "huge" from; most mathematicians sail along successfully oblivious to ...

Why not? You are making it axiomatic that this cannot happen. Is your axiom true or false? How can you tell?

Not at all. There are mathematicians whose expertise lie in set theory and foundations. Let them do their job. Non-standard analysis lives within a ma...

Sometimes metaphysical concepts are so poorly defined it's hard to get started toward a consensus. Look at the tens of thousands of pages devoted to "...

I'm not convinced that metaphysics can determine anything and I'm not sure what is meant by the "truth" of axioms. This is an interesting discussion a...

Context means everything: (1) a=a+1 (no finite solution. In complex analysis a would be the point at infinity - corresponding to an actual point at th...

Manifest=clear or obvious to the eye or mind. And does the eye or mind unravel every detail of the universe? If there are features of reality we canno...

I'm not aware of any real applications along these lines, meaning predictive power. And keep in mind, economics is called the "dismal science" because...

I'm not so sure of this, but prefer not to argue the point. When I taught college algebra courses some of the word problems went back very far in time...

OK, might want to jettison calculus then . . .and all the technology we use as a result. (This thread demonstrates why one of my profs sixty years ago...

Human bodies age at different rates according to genetics and other factors. In high school at the age of 17 I could barely grow enough facial hair to...

And yet it can be dealt with as a dimension in mathematics and physics and predict observed results. Why not? Just curious.

\int\limits_{0}^{1}{\phi (z,t)dt={{\lambda }^{2}}} Aha! The Wikipedia cut/paste on Mathtype with square vs angle "math"

It's true. These forums require some sort of balance between intellect and babble. I was a climber for many years and on a great climbers site called ...

Just looking at this it appears you are rearranging a conditionally convergent series and expecting the same sum. If this is the case you can draw no ...

Complex time, t=x+iy , is productive in certain settings in physics, and its metaphysical interpretations seem immaterial to those who simply want ans...

Strong attractors are fixed points (FPs) of functions that, upon iteration, draw a given initial point towards the FP. But there are other FPs that ei...

I think the word "negligible" should not be used in the context of chaotic dynamical systems. Clearly if a slight variation at the beginning of an ite...