# DrRocket

Senior Members

1566

1. ## Prime Numbers in the Frequency Domain

Right. An awful lot of what is being said here violates the prime number theorem.
2. ## Prime Numbers in the Frequency Domain

You are correct. I overlooked the obvious.
3. ## Science Club advisor seeks information relevent to Zoology

What part of the country are you in ? The options for a school in the Bromx will differ ffrom those of a rural school in Montana.
4. ## Do all things fall at the same rate?

Short answeer -- The gravitational force exerted on a body is proportional to its mass, but the resulting acceleration is inversely proportional to its mass and the net result is that the acceleration is independent of the mass. This is basically what DJBruce told you. Longer answer -- The short answer works so long as the mass of the object is sufficiently small relative to the Earth that the movement of the Earth can be neglected. In reality you have a two-body problem, and both bodies accelerate towards their combined center-of-mass according to Newton's law of universal gravitation. A somewhat heavier body will approach the Earth very slightly more rapidly than a light body. A really really heavy body will move the Earth with appreciable acceleration and then things are very different from everyday experience. If the orange were the mass of the sun, it would appear to an outside observer that the orange was fixed and the Earth moved.
5. ## Prime Numbers in the Frequency Domain

It doesn't say much, and it is false. Read what I said. I don't care what wiki said. The difference between two numbers of the form '6k±1' is at least 4. If all primes (>3) were of the form '6k±1' there could be no twin primes other than 2 and 3. There are lots of them. Note in edit: This is still incorrect.
6. ## Time Traveling - Impossible?

Nearly all of the participants in this thread know better than you what you do and do not understand. The basic problem is that you do not understand that you do not understand. As a result you argue against a strawman -- your misconception of the content of fundamental physical theories.
7. ## Time Traveling - Impossible?

As usual you are arguing about something that you don't understand. This has nothing to do with Einstein. Newtonian mechanics can be formulated, quite trivially, in terms of spacetime. It is simply a flat spacetime with a different metric. The past, present and future are all in the spacetime manifold, but they do not exist "simultaneously", because "simultaneously" means at the same time. The issue is really one of determinism versus non-determinism. Newtonian mechanics and general relativity are deterministic. That is what permits all of time and all of space to be described in terms of a single manifold. Quantum mechanics is non-deterministic. That is a fundamental difference between general relativity and quantum field theories. We do not have a single theory that encompasses gravitation and quantum theory -- yet. Until such a theory is constructed, no one can say whether Einstein was "right". Most people would bet that in the end general relativity will give way to a non-deterministic theory. But some pretty smart guys, like Roger Penrose and Gerard 'tHooft, take possible deterministic theories seriously. The jury is out.
8. ## Prime Numbers in the Frequency Domain

This is not even close to correct. If primes >3 were of thev form 6k ± 1 the minimun separation between those primes would be 4. Twin primes are primes of the form N and N+2. Here is a list of 100,00 twin primes http://primes.utm.ed...l/100ktwins.txt The twin prime conjecture -- that there are infinitely many twin primes -- is an open problem. Note in edit: This is incorrect as shown by uncool below.
9. ## Group theory problem 2

Since this problem is unrelated to earlier problems posted by Obelix, and since he has been silent for a couple of days (in at least two forums where this same problem was posted) I will assume that it is too late for a solution to be used in a manor contrary to academic ethics. Also, it is quite clear that Obelix cannot produce a proof himself. So, for those who might find this problem a bit interesting here is a solution. It assumes some elementary facts regarding topological groups. Proof: Since $G(T)$ has non-empty interior and since $G$ is continuous homomrphism we can, by translation if necessary, assume that $G(T)$ contains a neighborhood of the identity. Since $G$ it is a group homomorphism $G(T)$ contains the subgroup of $H$ generated by that neighborhood. But a connected group is generated by any neighborhood of the identity. QED For anyone interested in pursuing the topic of topological groups I recommend the classic treatise by L.S. Pontryagin Topological Groups. For any electrical engineering control theory types, this is the Pontryagin of "the Pontryagin maximum principle". For any interested in harmonic analysis, this is the Pontryagin of "Pontryagin duality". For those interested in vector bundles this is the Pontryagin of "Pontryagin classes". He did rather well, as a mathematician at least (not necessarily as a nice guy), for someone who was blinded at age 14.
10. ## Good book on quantum mechanics?

That book is not Hawking's best. It is extremely speculative. In fact bloody awful. For a nonmathematical treatment of QM try Quantum Mechanics and Experience by David Z. Albert. Then learn the necessary mathematics and try something like Introduction to Quantum Mechanics by David J. Griffiths.
11. ## Will the Universe exist forever?

It will last until the end of time. We won't.
12. ## Are most atheists just hypocrites?

You made the statement "The question to wether or not life can exist is defiantly not 0." Prove it. The existence of life on Earth is NOT proof. Probability zero events can occur. They just correspond to sets of probability measure zero. If you intend to use the theory of probability, use it correctly. Start with a probability space. Justify it as a model of the physical system at issue. Proceed from there.
13. ## Infinity

Belief has nothing to do with it. Infinite sets are a logical consequence of the fundamental axioms that underly mathematics. If you accept them (in essence if you accept the counting numbers 1,2,3,... ) then infinite sets and infinite cardinal numbers are part of the package.
14. ## Are most atheists just hypocrites?

Prove it. No unsupportable assumptions allowed. Hint: To even begin such an argument you need to have a supportable value for the "probability" that life emerges under some specified circumstances. There is no way to assign such a value given the current state of ignorance. Probability theory is the most commonly misapplied branch of mathematics. Ophiolite is correct.
15. ## Time Traveling - Impossible?

You need to brush up your history and dial down the paranoia. "Nuts" was the exact response of General Anthony McAuliffe when presented an unreasonable position by the Geremans during the Seige of Bastogne during the Battle of the Bulge.. It is simply a categorical denial.
16. ## Can we use probability distributions to work out the likelyhood of only 1 planet having life?

In order to apply probability theory you need two things; 1) A probability space and 2) rationale for why that space applies to the issue at hand. You have only the second.. No one has any quantative model for abiogenesis. Qualitatively it would seem that in a universe as large as this one life ought to arise elsewhere. But to make quantitative arguments without any basis is just fooling yourself. Note that in your model you get the same probability for life nowhere. Does that seem reasonable ?
17. ## Missing mass of the universe found with x-rays

Here's the preprint. http://arxiv.org/abs/1104.0711
18. ## Time Traveling - Impossible?

"Nuts" -- Anthony C. McAuliffe
19. ## What to do when you feel like you've wasted your life

Eugene Wigner once remarked that "One of the marks of genius is that when you try something and it doesn't work the next time you try something different." If math doesn't work for you, then try something different.
20. ## Are most atheists just hypocrites?

I suggest that you do some research, and form an opinion on the basis of original-source data and documented historical studies. Read the scholarly biography of Joseph Smith, No Man Knows My History, by Fawn Brodie. You might also look at the text of some of the revelations (available at the official site), say the one calling on Emma Smith by name, to accede to Joseph Smith's participation in plural marriages (Doctrine and Covenants 132): " 54And I command mine handmaid, Emma Smith, to abide and acleave unto my servant Joseph, and to none else. But if she will not abide this commandment she shall be bdestroyed, saith the Lord; for I am the Lord thy God, and will destroy her if she abide not in my law."
21. ## Time Traveling - Impossible?

You are missing the fact that time is not universal. Time is a local concept and two accurate clocks can measure very different "proper time" intervals between two given points in spacetime. Time neither "speeds up" nor "slows down" -- speed presupposes ability to reckon time and "time per unit time" is meaningless. Time is NOT Newton's "flowing river" that is the same everywhere for everyone. Relativity was a revolutionary theory of the very nature of space and time. The result is that neither space nor time are global. There is no way to understand or explain this without recourse to abstract mathematics. Should you ever want to try to understand, Gravitation by Misner, Thorne and Wheeler is the classic source.
22. ## Prime Numbers in the Frequency Domain

No. http://en.wikipedia.org/wiki/Prime_number_theorem If you have a healthy skepticism for Wiki you can find this theorem proved in any good book on number theory, say Hardy and Wright's An Introduction to the Theory of Numbers. Rudin's Functional Analysis also contains a proof.
23. ## Advice needed for giving a conference presentation

I know of talks where the speaker was shown to be wrong, but no horror stories outside of folklore. At a special session of the Annual American Mathematical Society/Mathematical Society of America Meeting (I gave a talk in this session also) I saw a gentleman who is now a full professor at Purdue be shown by another gentleman in the audience, that his theorem was incorrect. It was all very polite, and the fellow who gave the talk told me quite honestly that the gentleman in the audience was absolutely correct. There was no animosity and they still get along very well. The fellow who was corrected felt a bit embarrassed, but there was no lasting damage. The audience was not large, but included several "big shots" -- Lou Auslander, Cal Moore, Joe Wolf, Roger Howe, .... None of them seemed to considered the mistake a tragedy or to think less of the presenter. Anyone who has not made a mistake has probably never tried anything difficult or produced anything of note. Einstein made lots of them.
24. ## Metaphysics and Science

If all the philosophers who ever lived were laid end to end they would not reach ...............................................a conclusion.
25. ## Can we do a Masters in Physics after a bachelors in Engineering?

If you have the necessary ability you can change disciplines as late as you please. Eugene Wigner earned a Dr. Ing. in chemical engineering, and a Nobel Prize in physics.
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