DrRocket

Time is what clocks measure. No kidding. There is no more fundamental definition or deeper understanding. If you find one, publish it immediately.

In mathematics, groups in the sense that you mean are rare. There are certainly collaborations, but good research tends to follow tastes of the indvidual with collaborations being informal and often for short periods of time focusing on a single specific issue. Papers with a large number of authors (say more than three) are very rare indeed. There tend to be more men than women, but no particular bias that I have noted. People are noted for what they accomplish. Plumbing is a non-issue.

Mathematics is learned by doing. Most college algebra and trigonometry books (the same as high school algebra and trigonometry) are equivalent. I would suggest getting a copy of whatever books you used in the past (if you don't remember get any book with a title like college algebra or trigonometry) and do a large number of the exercises in the book). Such books should be readily available and affordable on the used book market at amazon.com, alibris.com or abebooks.com. Even a Schaum's outline should suffice. BTW what you are proposing is a VERY good idea in preparation for a calculus class. Your biggest hurdle in making the transition to calculus will be making the adjustment form "solving the equation and finding the number" to and estimating a solution and refining the approximation until it becomes exact. Calculus is philosophically different, and making the algebra and trig "old hat" will let you focus on that difference and not "miss the forest for the trees".

Noting that all of the above statements are true we then see from the OP' date=' after a bit of gibberish and argument:[/font'] Bold added It can be difficult to distinguish among crackpots, trolls, and fools who do not listen. One suspects that many apparent crackpots and fools are really just trolls.

Any charged particle has associated with it an electric field, which depends on the magnitude and sign of its charge. The charges on a proton and an electron are of equal magnitude but opposite sig. Any charged particle in an electric field "feels" a force bthat is proportional to the strength of the field, proportional to the vharge on the partivcle and in a direction either of the applied field or opposite to it depending on the sign of the charge on the particle. The electron and proton in your scenario each feel a force attracting them to the other particle, of equal magnitude. Because it is much more massive, the proton will move less than the electron, but each will move toward the other. Once in motion, the charged particles will also create magnetic fields, and that too will result in forces on moving charged particles (Google "Lorentz Forcce"). There is no "sucking" going on.

Virtual particles are, by definition, undetectable. Their "existence" comes from the perturbative nature of current quantum field theories.

Depends on the subject matter. What math class do you have in mind ?

No one knows the limits. Many share your thoughts. I think the Pioneer anomaly has been explained conventionally. The neutrino expereiment is still up in the air, but most people suspect that there is an error in the experiment. It is known that general relativity and quantum theory are not compatible. Most, but not all (e,g. Roger Penrose), think general relativity will give way to a theory of quantum gravity. To really determine the limits we will need a new and better theory. There is a lot of ongoing research to develop such a theory, but it does not yet exist. GR may break down at the Planck scale, but so far that is just speculation. You can find all sorts of rank speculation stated as fact in popularizations. No one really has a clue what goes on at that scale.

There is something called St. Venant's Principle that roughly states that stresses at points significantly distant from one another are essentially independent. To punch a hole requires application of a load that results in the local shear stress exceeding the material allowable. So to punch 11 holes (simultaneously) in your saituation you will need to apply 11 times the force necessaer to punch one hole. If you stagger the punches as suggested earlier the necessary force will be the same, but the required travel will increase by a factor of 11, plus some tolerance slop.

Pi can be, and is, defined in modern mathematics independently of any geometric construction, though pi is the ratio of the circumference of the circle to its diameter. Herewith is the modern analytic definition: The complex exponential function defined by the power series [math] e^{z} = \displaystyle \sum_{n=0}^\infty \frac {z^n}{n!}[/math] can be shown to be periodic (see e.g. Rudin's Real and Complex Analysis for an elegant proof). [math]\pi[/math] is defined to be the period of this function divided by 2i. This gives you a definition traceable to the Zermelo Fraenkel axioms and quite independent of Euclidean geometry. If this is not familiar, recall the Euler formula [math]e^{i \theta}= cos \theta \ + \ i \ sin \theta [/math] .

Those were available for hP calculators 25 years ago.

The big bang hypothesis says no such thing. Stephen Hawking and Roger Penrose proved theorems showing that, if general relativity is correct, then given a currently expanding universe and a minimal amount of mass in it, that spacetime is singular in the sense that timelike geodesics cannot be continued infinitely into the past. This does not in any way mean that "a singularity is needed to create the universe". In fact, the spacetime manifold (aka the universe) contains no singular points. Not everything that smart people have stated is correct. Einstein made major errors himself. The next prediction from Quantum Loop Gravity will be the first one. Presumably it will come after someone can actually state in clear rigorous terms exactly what Quantum Loop Gravity is.

rubbish

Go right ahead. No one is stopping you.

Wrong. Go read what I said and also read up on cardinal numbers. Naive Set Theory by Halmos is a good source.

Since x=0 is not a zero of [math]4x^2 + \frac{1}{x^2} - 4 = 0[/math] or of [math]4x^4 + 1 - 4x^2 = 0[/math] you have not changed the zeros of the original rational function. In many cases multiplying by [math] x^2[/math]ould add a zero at [math] x=0[/math], but in this case you have simple eliminated the pole due to the [math]\frac {1}{x^2}[/math] term. But you have dramatically changed the general character. [math]4x^2 + \frac{1}{x^2} - 4 = 0[/math] is very large near 0 because of the [math]\frac{1}{x^2} [/math] term and grows quadratically for large values of x, while [math]4x^4 + 1 - 4x^2 = 0[/math] is approximately 1 near zero and grows like a quartic.. Note that [math]4x^4 + 1 - 4x^2 = 0[/math] is quadratic in [math] x^2[/math] so you should be able to find the zero.

Try Classical Dynamics of Particles and Systems by Marion

I have been studying all my life at the highest level that i can handle.

No quantum theory of gravity currently exists. If and when such a theory is developed, we have a name already chosen for the particle that mediates the gravitational force -- the graviton. So, nobody knows if gravitons are real. If they are then, yes, by definition, they "control" gravity.

In the theory of cardinal numbers there are LOTS of infinite cardinals. They can be added and multiplied, but addition and multiplication do not follow the rules that you are used to seeing for integers. While you can certainly utter the phrase "never ending amount instantaneously which cannot be matched in counting speed 0 times is 0", I doubt that anyone, including you, will understand it. In the extended real numbers [math] 0 \times \infty [/math] and [math] \frac {1}{0}[/math] are meaningless.

Curvature, not "warpage" is a property of the spacetime manifold, and it is invariant in general relativity. Curvature of spacetime has nothing whatever to do with acceleration. Curvature is determined by the stress-energy tensor. In GR there is no such thing as "gravity" other than an effect of spacetime curvature. Curvature results in geodesics diverging, which is what results in "tidal forces" and gravitation. There is no such thing as "inertial acceleration" and insofar as one might try to make sense of such a term it is an oxymoron. There is an "equivalence principle" that guided Einstein philosophically under which gravitation and acceleration are taken as indistinguishable, but it has little import in modern geometric formulations of the theory. So, no you don't see, and "orthodox interpretation" has nothing to do with it. For a nice geometric treatment of GR see Gravitation by Misner Thorne and Wheeler. To see SR treated geometrically see The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of Special Relativity by Naber.

No. Violation of causality is not randomness and randomness is not violation of causality. A baseball player hitting a pitch before it is thrown is not random. It is bizarre, but not random. Go read the post again. Pay attention to the mathematics.

"You can observe a lot by watching" -- Yogi Berra A verifiable source.

The next prediction from Quantum Loop Gravity will be the first one.

There are apparently non-local phenomena in quantum mechanics that result in "instantaneous" effects -- this is the issue of entanglement. However, these effects do not permit the instantaneous transmission of an information-bearing signal. To do so would create issues of causality violation within the context of special relativity. IF the current issue with superluminal neutrinos happens to be resolved in favor of superluminal speed for such particles, then the very logical foundations of relativity will have been violated, the basis for superluminal signal transmission violating causality is invalidated, and all bets are off.