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  1. Now that I think about it, the product of the first 23 is, as you say, 223092870. Now, the number of ways in which you can sum two (arbitrary) natural numbers to give N is just 111'546'435, because 223'092'870 is even. So the problem reduces to finding how many numbers there are between 1 and 111'546'435 that are not divided by 1, 2, 3, 5, ..., 23 (the 1st 23 primes). The only thing I can say is that's not an elementary problem. How did you get your conjecture @Tinacity? Counterexample: \( \pi \) is irrational; \( 1-\pi \) is irrational too. but \( \pi + 1- \pi = 1 \).
    1 point
  2. Respectfully where possible. Recognize and stop the political weaponization of it. One can call out white supremacy without calling everyone who might consider voting for Trump as supporting it, and one can embrace diversity without condoning or participating in the worst aspects of it. Democrats using identity politics rings hollow for you because you feel the Republicans do it more?
    1 point
  3. To start off. 1 / Gamma = √ 1 - v^2 c^2/ c^2 = c / Gamma = √ 1 - v^2 +v^2 You have to multiply all the factors under the radical by c^2 if you want to move c to the other side of the equation This leaves c/Gamma =√ (c^2 - v^2) And since c^2 ≠ 1+v^2 you can't get to where you got. And at the end, your answer is not a multiple of c, so that right there should have been a tip-off that you did something wrong along the way. To solve for v from 1 / Gamma = √ 1 - v^2/c^2 You first square both sides: 1/Gamma^2 = 1- v^2/c^2 (you square both the 1 and gamma, but since 1^2 = 1...) v^2/c^2 = 1-1/gamma^2 v^2 = c^2(1-1/gamma^2) take the square root of both sides: v= c√(1-1/gamma^2) Thus if v = 0.6c Then Gamma = 1/√(1- 0.6c^2/c^2) = 1.25 and v = c√(1-1/1.25^2) = 0.6c
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  4. I'm thinking that once the sub got to supersonic under water ( 1500 m/s ), the shock cone would actually become a vapor cone, with liquid water on the outside of the cone, and an immediate change to vapor inside the cone, due to vastly decreased pressure. The cavitation wouldn't be behind the sub, but behind the shock cone and all around the sub. That would really make it interesting. You often see jets with moisture condensation inside their shock cone due to decreased pressure … ( the shock starts at subsonic speeds at 1/4 chord because local airflow, at the wing, is supersonic ) Looking forward to other members' input, and corrections.
    1 point
  5. Interesting you ask- I actually have read one book too many, Trul. I am an old scientist, with multi disciplinary background. Thats all I can say so far on the internet. I should have qualified my question as "what positive, beneficial contribution has Religion made in 3000 years". As of yet, you have not provided any answer. You did however mention education. You mean Sunday School? Where "teachers" teach how Adam and Eve were the 1st man/woman on Earth? And how Moses met God on Mt Sinai via a burning bush? Do you actually believe Religion spawned the Renaissance? Then how did we manage to produce a Galileo whos discoveries about astronomy challenged and threatened the Catholic Church DURING that Renaissance? No one can prove exactly how/what spurred on the Renaissance. Our Constitution was written mainly by Deists (Jefferson, Washington, Monroe, etc) , not exactly a religious cult (you can google it). Either way, IMO, the Constitution is not perfect, and written by at least some hypocrites, albeit, masterful writers (thing all men are created equal- except leave my slaves out of it so I alone can benefit from them). Again, I offer two of the most stark examples of the contribution of science without which, in a few short weeks you would be dead- the disinfection of water throughout the modern world and the Haber Process. There are many more examples. Religious Cult "leaders" only have offered the idea of prayer, penitence, the misguided hope of eternal salvation, and false hope. And let's not forget the vile wicked sexually disfunctional priests who pervert sexual desire/urge itself by appearing to practice abstinence as some sort of reverence to be admired.
    1 point
  6. its such a pity that andromeda doesnt actually look like this to the naked eye
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  7. There are two types of fluid flows in aero/hydrodynamics, compressible and incompressible. They can both be modelled by little springs between each fluid particle; when you push against one particle, it pushes against the next via the little interconnecting springs, and the fluid, in effect, compresses. If you push too fast, the little springs reach maximum compression, and the particles begin to 'pile up' into a bow wave. For air, this happens at Mach 1, and the air effectively becomes incompressible. Water is nearly incompressible from the get-go ( also, liquids and solids have transverse 'sound' waves as well as longitudinal ). That's why you see a bow wave on a boat doing 10 mph. That wave is the 'shock' of the particles bunching up because they can't move out of the way fast enough. Another ( huge ) problem would be cavitation. This is usually seen in pumps/propellers where the fluid can't flow fast enough into the area behind the pump/propeller blades, creating a low pressure area ( or even vacuum ) which tends to destroy equipment. For a plane the shock is the separation where supersonic air is drastically decelerated to subsonic ( inside the shock cone ), and it carries a lot of momentum/energy which is dissipated in the 'sonic boom'. If the 'sub' was at a shallow depth, with the surface close by, the spray pattern of the water shock into the air would be extremely interesting. to say the least. So the shock wave of travelling through water would be no different than through an incompressible fluid such as supersonic air, except for the cavitation problem, which I didn't consider on Sunday ( and which may make this idea a non-starter ).
    1 point
  8. Swansont, after pondering about the interesting point you mentioned, "shock waves in water", I've come to the conclusion that supersonic submarines can't be compared to supersonic aircraft. For this reason: Aircraft fly through the Earth's atmosphere - ie, through a mixture of gasses. And gasses can be readily compressed, and pushed aside. Thus generating a Mach "shock-wave" in the atmosphere. The atmosphere absorbs and dissipates the shockwave, turning it into a "sonic-boom". Which may annoy remote ground-based residents. But doesn't molest the aircraft. However - water is a different matter. Water absolutely cannot be compressed. It retains its volume no matter how much it's squeezed. This is indeed, why hydraulic machines work. Therefore, it seems to me, that if a submarine accelerated underwater at ultra-high speed, then when it reached under-water Mach -1, the outcome would be crushing disaster for the sub. Can you fault my reasoning?
    1 point
  9. Great days... Cruising the stores and filling all the screens with <insert inappropriate sentence here>.
    1 point
  10. That "Narrow band" is a lot wider than it looks to the naked eye. You are only seeing that part that is bright enough. As an example, consider the Andromeda galaxy. To the naked eye it looks like a small fuzzy spot, but if you could see it in full, it would appear like this in the sky. Several times wider than a full Moon. What we see by naked eye is just the nucleus of the galaxy. But just because we don't see the disk by naked eye doesn't mean that it doesn't hide the light from galaxies behind it.
    1 point
  11. I truly have no idea what this refers to. If you want me to understand what you're saying, can you please supply enough context so that I know what "it" refers to? Nothing to do with intelligence. Just subject-specific education and study. I myself am right at the ragged edge of my own competence in the topics we're discussing and usually have to look things up to respond to your questions. It's just a matter of learning the material.
    1 point
  12. Why is it always barriers imposed by, or the fault of society, when someone fails ? What part does personal responsibility play in this ? Markus Hanke taught himself GR ( and many other aspects of Physical Science ). It was not provided for him, but he wanted it and he got it. Barriers did not hinder him. You, yourself, have displayed a questioning attitude. One of the best ways to learn about things you know little about. Yet others come here with the attitude that what little knowledge they have , is all there is. They ask no questions, but make conjectures and proclaim results which more learned members quickly dismiss. And yet their attitude, not barriers, allows them to double down and insist they are right ( until they are banned ). A good attitude, and a willingness to learn, go a long way in these days of internet access and on-line courses.
    1 point
  13. I remember our Primary School teacher telling us that we needed basic English and Maths so that we could get jobs in factories. My response was to do anything to prove her wrong. Most of my colleagues accepted her view without comment. I feel terrible when teachers say this stuff to people. As a teacher (now out of retirement) in my whole teaching career of 22 years, I have never told a child they could not do something. I have always stressed that they could do anything that they set their mind towards. I apologise on behalf of teachers. Sorry about your friend's son, that appears to be a mindset. However, a person has only failed when they admit it to themselves, in my opinion. I have taught in an area which can be described as an equivalent of the projects, and the mindset of a significant minority of students was exactly the same as the one that I viewed as a child. I take your point about generalisations and I did mention that doctors and other professionals came out of the same tough environments. It would appear that the successful minority of people have a different mindset and that mindset is maintained despite external circumstances. So, in my opinion, the rest of the people who are stuck in the ghetto have a mentality that is a story that they relate to themselves to keep them stuck in their circumstances. I have read your reply and the link. I take the point, underfunding and racism do contribute to negative attitudes. I also take the point that ghettoes exist in geographical location from deliberate Governmental legislation and decades of maladministration, and that other people have a mentality of what is expected from ghettoes. Despite those points, I can state that I am working with a teacher who was educated at primary level under a tree. Under a bloody tree! Yet she showed an aspirational mindset and is now the best Science teacher in my school, by some margin. The keyword in my opinion is aspiration. It was aspiration that took me out of Glasgow, took you out of Edinburgh and took that teacher out of a small village in Pakistan. Aspirational mindset disregards environment, in my opinion, regardless of what racists and class supremacists do in any part of the world. A person fails and stays in a stagnant situation when they relate the story of their failure to themselves. It normally starts when they blame others for all their problems...
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  14. I think there is no universal answer, for some people this may be true for others not. I have a friend whom I've met 40 years ago when we were sat besides each other on our first day in first grade primary school. He ended up solely owning an industrial manufacturing company worth more than 100mln USD right now, his 21 year old son just left the psychiatric hospital again last week - drugs, street life, severe depression, suicide attempts, etc. Is this caused by a mindset? Probably, partially yes but there are so many angles and factors to take into account that this kind of generalization is only good for rap songs imo.
    1 point
  15. Or, stupid is an aspect of behavior, or cognitive choices, but NOT an aspect of humans themselves. People can do and say many stupid things without being intrinsically stupid. In fact, by labeling the whole person, you're discriminating against groups you've judged as "stupid". You should stop that. "Money so they can be happy" is hideously short-sighted, imo. We should give a basic universal income so after several generations we'll see less ignorance and more educated people. Education and improving job skills are high priorities when people get past paying for the necessities. It should be money available to every citizen over a certain age so it will be supported by every citizen. I know it sounds petty, but if you don't give it to everyone, the wealthy will eventually resent it and work to take it away from those who rely on it. That's what they do with public parks, museums, swimming pools, healthcare, social security, and libraries, because they don't use them. But tie the basic income to citizenship, and they'll defend it as their right.
    1 point
  16. It isn't as simple as that, because intelligence (which I assume is the 'observable' you are quantifying here) isn't a linear thing, it is multi-dimensional. What I mean by that is that most people are differently abled in different areas of life. For example, I have a friend who is absolutely useless in maths and most other academic subjects, but a brilliant artist, and earns a decent living by producing art. I myself am very intellectual-minded, and thus perform well in academic subjects such as maths and physics, but I am useless when it comes to social skills, so I'd be a miserable failure if I were to go into (say e.g.) politics. So what does it mean for someone to be 'stupid' or 'intelligent'? These terms are meaningful only in a specific context. You don't need to have book smarts to be successful in life, and conversely plenty of book-smart people never do particularly well in the competitive world of business. So no, we shouldn't give money to people purely for lack of intelligence, unless of we are dealing with a recognised intellectual disability. What would be a far better thing to do is provide an unconditional universal basic income for everyone, because that would give people a better chance to develop their full potential in life without having to worry about their basic survival, even if that potential cannot be immediately quantified in terms of monetary value.
    1 point
  17. I don't think it will be the end of the NRA, but maybe it will be the beginning of the end. It's not my field; are there any "competitor" organisation? If there was an organisation that could say "We are a bit like the NRA, but less corrupt", they might do well enough to take over.
    1 point
  18. That doesn’t support the claim. (though “most rape victims, who don't know their attacker, are attacked out of the blue and usually from behind“ is ambiguous. Is the claim that most rape victims don’t know their attacker, or of the small fraction that don’t, are attacked from behind? The former is debunked, the latter isn’t supported)
    1 point
  19. You assume I presented an argument, or/and entertained conversation.
    -1 points
  20. https://www.cnn.com/2020/08/07/us/allan-lichtman-trump-biden-2020-trnd/index.html https://markets.businessinsider.com/news/stocks/stock-market-correctly-predicted-next-president-biden-donald-trump-election-2020-6-1029351214?op=1
    -2 points
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