Bertrand's postulate
 

[QUOTE=aketilander;290540]Well I would like to expose my ignorance, but I have been wondering one thing:

There is a proof that there are at least 1 prime between X and 2X. If the distribution of primes were a true Poisson Distribution there would be a very, very, very small porobability that there were 0 primes between X and 2X.

So my question is: Is this not a proof that the distribution of primes is not a true Poisson Distribution only a distribution very similar to a Poisson Distribution?

I suppose to a matematician this is a dumb question, but even though I would like to pose it and hopefully learn someting from the answer.[/QUOTE]

I think there must be something left out of that first sentence, for brevity perhaps, such as for integer x > some minimum value. (Because otherwise the disproof by example would be so trivial even I could do it; let x=1; the interval 2x > y > x contains no prime integers, and also no integers.) Ok, a bit of searching yields [URL]https://en.wikipedia.org/wiki/Bertrand%27s_postulate[/URL]

civility
 

[QUOTE=Uncwilly;290501]Firstly astrology is not a physics issue per se, it is an astronomy and medical/psychological issue.
Secondly, did not astrology (which should have been the proper term for astronomy) lead to astronomy?
Just be cause it seemed to you to be astrology, does not mean that it is of no value as a step to learning for the presenter. It is the duty of the more knowledgeable, [B][U]if and [COLOR=DarkRed]only if[/COLOR] they [COLOR=darkred]choose[/COLOR] to speak up[/U][/B], to shepherd the presenter to a position of knowledge, knowledge sufficient so that they understand why astrology is wrong. Part of this self-assigned duty is to present the teaching in such a way that the newbie does not become so offended that they shut down to instruction.

I would ask Bob that he practice biding his time and let others the first couple of chances with newbies like Emily.[/QUOTE]

Amen. I understand it can sometimes be irritating to cover again the same introductory ground with yet another novice lacking background, yet I think it sad that RDS appears to have driven emily off in well under a day elapsed time. How much better to be welcoming and pleasant to share what one loves with others. How did those who taught RDS act? How did any of math, science, or technology get developed, except by people paying attention, wondering, employing curiosity, coming up with hypotheses, trying things, talking with each other, and eventually teaching each other? Numbers can be used and enjoyed and puzzled over by people without the deep background in that specialty held by a rare few, just as music can be enjoyed without being a member of the London Philharmonic. I'd bet there are also few if any of us that could design and build an entire car or computer or house, much less invent a new better way of doing any of those, but enjoy their ready availability. RDS may have had as much to learn from emily or Dale Carnegie, about being civil and positive to people regardless of circumstances, as emily may have had to learn from RDS or Euler, about math, if measured by life impact.

One of the things that has impressed me and clearly others about some of the authors of current world class software in number theory is the decency, tact and courtesy with which they respond on forums or in email to anyone no matter what. (A skill I'm working on.) Carnegie teaches among other things that tone is more important than content, since it can help content be welcomed, or work against content being heard or accepted, or motivate active resistance to the content (to the possible detriment of both the recipient and sender). Carnegie teaches in effect to wrap the message like a present. Excelling in any field has perhaps more to do with people skill than technical skill.