No "Thanks" plz. But i will accept some Science(or other area) cool facts
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As current physics dictate, black holes with masses lower than 20 micrograms can not exist because their event horizon (Schwarzschild radius) would be smaller than their uncertainty in diameter (2x de Broglie wavelength). That's about the mass of a small grain of sand.
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That's actually really interesting,
Can you share some paper where i can look into the math involved?
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The fact can be derived from some well known text book formulas and the math is rather simple:
The Schwarzschild-radius R of a black hole can be calculated from its mass m alone:
R = 2Gm/c² ... with G being the gravitational constant and c the speed of light.
The diameter of a sphere (or circle) is two times its radius, thus the diameter d of a black hole is
d = 2 R = 4Gm/c²
De Broglie's Wave-Matter-Duality (from quantum mechanics) states that ALL things behave like particles and waves simultaneously. In photons (i.e. light waves), the wavelength lambda can be calculated from the photons momentum p and Plancks constant h. According to de Broglie's theory, this has to be true for all particles, too.
lambda = h / p
Using the four-momentum from special relativity of a non-moving particle (i.e. px=py=pz=0), one obtains
p = E / c
with E being the energy content of the relativistic rest mass m. Applying Einsteins famous formula E = mc² yields
p = mc (usually relativistic p = mc * gamma, with gamma = 1/sqrt(1-v²/c²), but since a non moving particle has v = 0 -> gamma = 1)
Thus, a black hole has a de Broglie wave-length (and therefor spacial uncertainty) of: lambda = h/(mc)
If we now equate the black hole's diameter d with its wave-length lambda, we know the minimal mass of a black hole: With less mass the event horizon gets smaller than its spacial uncertainty. Not only can nothing fall into the black hole, but it does not "know" if it is still "inside" of itself because of quantum mechanics.
d = lambda
4Gm/c² = h/(mc) | Multiply both sides with (mc)
4Gm²/c = h | Multiply with c and divide by 4G
m² = hc / (4G) | Take the square root
m = sqrt ( hc / 4G ) <- this only contains natural constants, plug it into Wolfram Alpha or a calculator
m = 27.278 μg
Rounding down to be on the safe side, you get the 20 µg mentioned above.
Divide by the density of quartz and you get an associated volume of sand.
Assuming a spherical grain of sand, calculate the radius from its volume.
Finally you end up with a diameter a little bit smaller than 1/4 mm, which classifies in the US as fine sand.
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Thank you for sharing your knowledge with the comunity :)
I will have a look with a fresh head tomorrow morning :)
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Have you had time to take a closer look ?
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Today, the Sun continues to fuse hydrogen atoms to make helium in its core. It fuses about 600 million tons of hydrogen every second, yielding 596 million tons of helium. The remaining four million tons of hydrogen are converted to energy, which makes the Sun shine.
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I'm not even doing the math of how much mass the sun has lost since it's formation since i don't want an existencial crisis atm ahaha
Thanks for the share :)
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No worries, I've calculated it for you.
If I am not mistaken, the sun should have lost about 97 earth masses or 0.30 Jupiters worth of hydrogen in its existence so far. That's about 0.03% of the sun's mass. Not really enough for an existential crisis.
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Given if
A/B = C/D, then multiply both sides by B/C
A/B × B/C = C/D × B/C, so rearrange
A×B / B×C = C×B / D×C, so rearrange
A/C × B/B = B/D × C/C, and since B/B=1 and C/C=1
A/C = B/D
This is a well known proof for a theorem that basically says you can transpose the denominator (ie B) on one side of an equation with the numerator (ie C) on the other side.
Now for the deeper part.
Given the mathematical laws that essentially
x / infinity = 0, and also 0 / y = 0, then if y=1
x / infinity = 0 / 1, then apply the theorem above to transpose the left hand denominator and right hand numerator, so
x / 0 = infinity / 1, then simplify the right side since z/1=z
x/0 = infinity
tl/dr your calculator may say dividing by zero is "undefined", but my theorem shows that it should be infinity.
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Thanks for the share.
I love math as well :)
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Unfortunately "infinity" is not a number, so you can't do it this way.
The better approach is to use limits, i.e. values that get bigger and bigger (or smaller and smaller towards zero), and have a look where the result is going to. In this way, no math is broken at any point.
If you do it this way, you can discover that for positive a and b with b going to zero quotients of the form a / b may go to infinity or zero or anything between, depending on how fast b is decreasing relative to the rate of a. Since all these results can equally be considered "divisions by zero", it is still not clear how one should define its meaning. Therefore it is undefined behavior.
If you are still interested in this topic, have a look here. There are special fields of mathematics and mathematical structures where a meaningful definition of "division by zero" exists.
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Ah, I knew I was forgetting something from memories of my teenage musings. This was something that I came up with in some high school math class, but of course it was before knowing anything about calculus.
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Thanks for the GA.
I want to advice that you set a minimum level for your future GAs because each one that gave one, not free, game is, at least, level 1.
Easy solution to hold the worst rulesbreakers, win resellers, autojoiner user and bots outside (40% of the level 0 accounts have infractions for unactivated or multiple wins + the ammount of used autojoiners are much more as in higher levels).
And besides that it lowers the cases of problems with your winners.
You can check accounts/your winners with:
http://www.sgtools.info/activation
http://www.sgtools.info/multiple-wins
If someone have red marks there request a reroll and put the link(s) into the support ticket.
https://www.steamgifts.com/stats/community/users
Scroll down to the bottom and look at the "per level" info and you see 970k are level 0, only around 165k have a level, 113k of them are level 1. So around 15% of the members from sg gave something and only 4% gave more as 5 games.
Have a nice day
Ps.: The autojoiner program have a thanks script that can be activated. So you will, partly, see, very easy, which ones use a autojoiner.
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Hello,
Thanks for the tip, i didn't knew about it,
I just use SG to give the community some unwanted bundle games or some game i was particulary fond off and i got an extra copy in promotion, so i never thought about that,
But i will have that into consideration in the future.
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Not a science fact, I'm more into paranormal stuff, creepy stuff, etc., but here goes some of what I can come up with:
According to the FBI, there are 25-50 active serial killers in the United States.
Most of the cruise liners have their own morgue on board for passengers that inevitably die on each trip.
The last execution by guillotine took place the same year the first Star Wars movie premiered (1977). It happened in France, half a year later after the Star Wars premiere.
Over 50% of commercial pilots have admitted to falling asleep while flying a plane.
Those are a little Science-based:
According to some studies, if you fall into a Black Hole, you could see the start and end of the Universe. Of course, you'd be dead, but still.
Apollo 11 only had around 20 seconds of fuel left when it finally landed.
If the Sun actually blew up, we wouldn't know it for another 8 minutes. Light that is emitted from Sun travels to Earth for approx. 8 minutes and 20 seconds.
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⚜️ Good luck to all 👍
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Thanks~
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Science fact;
The guy who actually made MS DOS working was backstabbed by IBM and Windows.
They just copied his working OS and sold it worldwide, just recently saw an article about it. can you believe this?
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I saw it on the movie "Silicon Pirates". If you are interested in that area, it can be a cool movie for you :)
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obrigado
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Mercii pour ce magnifique jeu. Et à plus dans le bus ^^
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Thanks! :)
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