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Why are background noises from cars louder at night than during the day? It is because nights are quieter as there aren't as many people outside. When people are outside making sounds like voices, machines, etc.; those sounds are effective at blocking background noises from cars, but don't travel as far, that's a reason why days are often quieter, that's my opinion. Upon hearing cars loudly at night, I can picture the outdoor as a giant dome! At the time of this writing, I had a window opened next to me at night and heard those background noises somewhat loudly. PlanetStar 02:28, 11 October 2016 (UTC)[reply]
I think you definitely have at least "part" of the answer. Our ears are very good at attenuating sounds and a clue is that decibels are a logarithmic scale. This means you roughly need ten times the sound energy to make something sound twice as loud. Without "loud" sounds to drown them out, you can hear the quiet sounds a lot better. I've noticed pretty much the same effect when I listen to music or a podcast on the train, I don't listen to it loud, just a comfortable level like someone speaking to me, when the doors open and I step out of the train it easily gets drowned out by the noises outside of the train in particular as the train takes off. Even though without headphones at all the train doesn't actually sound that loud at all, subjectively one at a time the train sounds doesn't seem nearly loud enough to drown out what's coming out of my headphones, but in actual fact when you have both sounds at the same time, I have to increase the volume substantially on my headphones to be able to hear over the sounds of the train. Vespine (talk) 02:57, 11 October 2016 (UTC)[reply]
There is also another effect called sound refraction, when there is a layer of cold air above or below a layer of hot air, (which typically happens at night as the earth cools and the warm air rises, but also happens on hot days when the earth heats up but the air above is still cool) sounds do actually travel further and therefore would seem louder from farther than normal. So cars on a road nearby could be heard from further away, for example. Vespine (talk) 03:02, 11 October 2016 (UTC)[reply]
In my above opinion, quieter IS louder would be a paradox. Sound behaves like light that there is refraction you mentioned as well as reflection. There is also sound fog, sound glare, and even colors of sound. So sound have all the characteristics that light has, except that sound does not travel in outer space like light. Also hearing background car sounds is often louder on rainy days. Sometimes though, car noises are only slightly audible at night, possibly due to minimal air temperature differences by layer, don't you think? PlanetStar 04:39, 11 October 2016 (UTC)[reply]
Maybe cars just make more noise when moving on a wet road? PiusImpavidus (talk) 10:02, 11 October 2016 (UTC)[reply]
That's certainly true in my experience. Also wet surfaces reflect sound more easily, and so transfer sound farther. SemanticMantis (talk) 13:04, 11 October 2016 (UTC)[reply]
[citation needed]The first part is believable, after all, splashing water makes a lot of noise. But I don't buy that wet roads reflect sound better than dry roads. Please provide a source for that. StuRat (talk) 22:21, 11 October 2016 (UTC)[reply]
I have no problem proving sources upon polite request. You could learn from my example. Here are two references that support my claim that wet surfaces generally have higher reflectivity in the audible range [1][2]. It's also true that wet surfaces reflect radar better [3][4]. I hope you are as responsive and successful at providing citations to support your own claims in the future. SemanticMantis (talk) 01:54, 13 October 2016 (UTC)[reply]
The first ref is about wet sand, loess (sediment), and clay, not roads, and the closest comparison, with dry and wet compacted clay, actually shows more absorption of sound when wet. The 2nd ref is behind a paywall, but nothing in the abstract suggests that it supports your assertion. The two refs of reflectivity of radar are completely irrelevant. If you have some actual proof that wet roads reflect SOUND better, please provide quotes and page numbers, not just irrelevant refs. And when people ask nicely, I tend to give USEFUL refs, but you started by being extremely sarcastic, rather than asking for a ref politely. StuRat (talk) 13:07, 13 October 2016 (UTC)[reply]
Thanks for providing references. Keep in mind that your own impoliteness tends to breed impoliteness from others. ←Baseball BugsWhat's up, Doc?carrots→ 07:17, 13 October 2016 (UTC)[reply]
He's very adamant about demanding sourcing, but "in his experience" is apparently adequate sourcing for... his experience. ←Baseball BugsWhat's up, Doc?carrots→ 00:07, 13 October 2016 (UTC)[reply]
According to you, that's a personal attack. Stop trying to be "clever" and WP:pointy and start being useful, or, failing that, at least stop being so disruptive. SemanticMantis (talk) 01:50, 13 October 2016 (UTC
It's often very evident that it's currently raining or has been raining, as you can hear the splashing as the cars plow through the layer of water on the roadway. Whether the roadway is otherwise "reflecting" more sound than a dry road could be hard to measure. ←Baseball BugsWhat's up, Doc?carrots→ 07:33, 12 October 2016 (UTC)[reply]
I believe for awhile that we hear sounds more loudly in the dark than in the light because light interacts with sound. I looked up in Yahoo Answers and reported to be true. The darkness of night may have minutely contributed to cars heard more loudly than during the light of day. PlanetStar 04:39, 11 October 2016 (UTC)[reply]
I'm going to assume good faith here but the above answers are nonsense. Sound and light do not interact at all, one is a physical propagation of vibrations through a medium (like air) and the other is electromagnetic radiation. That yahoo answer is preposterous, I very strongly suspect it's only got "up votes" by people who think it's "so ridiculous it's funny", not because anyone has verified it as true. It would be trivially easy to prove, does the sound of ANYTHING change when a cloud blocks out the sun? Clouds block 50%-80% of the photons reaching the earth but nothing gets quieter louder when a cloud goes overhead. Vespine (talk) 06:13, 11 October 2016 (UTC)[reply]
Also, color of sound is purely a metaphor, you can just as validly call it "flavor of sound" it does not mean you can literally "taste it" with your tongue. Vespine (talk) 06:20, 11 October 2016 (UTC)[reply]
Sound and light are both waves. Both are described by the physics equations for wave propagation, which describe how waves are reflected or refracted when their speed changes depending on the medium where they move. That's about all they have in common. Light is an electromagnetic wave, sound a pressure wave.
There are indeed reasons why sound seems louder at night. In the dark you see less, so you pay more attention to what you hear. At night, the air close to the ground cools. This leads to a warm layer on top of the surface layer, known as an inversion, and this warm layer refracts sound back to the ground. And at night, there's less background noise. PiusImpavidus (talk) 10:02, 11 October 2016 (UTC)[reply]
1) One obvious reason is that you have a window open at night, and presumably not during the day.
2) Another could be rush hour, with more cars on the road from around 5 or 6 AM, which could still be called "night".
3) As for the effect of darkness, that brings lower temperatures, and potentially fog. Both effect sound propagation. I think sound travels better in cold air, but high frequencies are blocked by fog (hence low frequency fog horns). So, if cars make more low frequency sounds, they may then stand out better, due to a lack of competing high frequency sounds. StuRat (talk) 12:42, 11 October 2016 (UTC)[reply]
Speed of sound as a function of temperature in dry air, especially for Stu."I think sound travels better in cold air" Why do you think that? [citation needed]SemanticMantis (talk) 15:44, 11 October 2016 (UTC)[reply]
[5] says, on page 156: "...the maximum value of absorption increases with increasing temperature". Therefore, sound is absorbed less at lower temps. StuRat (talk) 22:17, 11 October 2016 (UTC)[reply]
Here are a few research papers on noise pollution that you might be interested in [6][7]. SemanticMantis (talk) 13:04, 11 October 2016 (UTC)[reply]
See Psychoacoustics, especially the subsection titled "Auditory masking" and the article titled Auditory masking. To wit "Auditory masking occurs when the perception of one sound is affected by the presence of another sound." Also very relevant is the article titled Loudness, again to quote the relevant part "loudness is a subjective measure, often confused with physical measures of sound strength such as sound pressure, sound pressure level (in decibels), sound intensity or sound power." --Jayron32 13:20, 11 October 2016 (UTC)[reply]
The speed of sound link isn't relevant, but the second link is. Also note that my foghorn link does state that low frequencies travel better through fog. StuRat (talk) 15:09, 11 October 2016 (UTC)[reply]
not references or answers
Shall I box this up as a non-answer? Speed of sound most certainly talks about effects of temperature. Maybe you're having some problems with reading comprehension, in addition to having problems with scientific facts and references? SemanticMantis (talk) 15:43, 11 October 2016 (UTC)[reply]
"Sounds travels better" could mean speed, in which case it goes up with temperature (at constant pressure though, methinks), or attenuation factor, in which case it goes down with temperature (at least for some non-irrealistic range).
Of course, you both knew it - but StuRat wouldn't explain, and SemanticMantis would pretend not to have understood, because it is so much funnier to be confrontational. TigraanClick here to contact me 16:24, 11 October 2016 (UTC)[reply]
I'm not sure I know what you're talking about. I have never pretended not to understand anything on these pages. I make it a point to provide as little as possible other than the references I cite. I admit my (now removed) sarcastic confrontation was not ideal. However, since I cannot delete Stu's misleading and incorrect posts, and he adamantly refuses to properly cite references, I have little recourse other than posting correct information, and challenging his guesswork. SemanticMantis (talk) 16:51, 11 October 2016 (UTC)[reply]
I was hoping you were just pretending not to understand, but, just in case you really don't understand, I will patiently explain. This Q is about why cars seem louder at night. Loudness is volume, and attenuation of that volume is therefore the issue here. Loudness is not related to the speed at which sound travels (unless you are talking about sonic booms). Frequency and wavelength are related to the speed at which sound travels, but this Q is not about that.
As for references, my fog horn ref was good one, and I've added another good one, while you had some good refs, some bad refs, and some missing refs, so don't get all "holier than thou" on me. StuRat (talk) 22:05, 11 October 2016 (UTC)[reply]
I'll stop criticizing you when you learn how to properly reference your claims. I'm fucking thrilled that you managed to find a decent ref to support your claim above. Good job. Next time, do it without being asked, and you'll be on the path to being useful here. SemanticMantis (talk) 13:38, 12 October 2016 (UTC)[reply]
I did provide a useful ref, the fog horn one. You provided at least one USELESS ref, about the speed of sound, wasting the OP's time, and failed to provide any ref for your claim that wet roads reflect sound better. Stop criticizing others and try to do better with your own refs. StuRat (talk) 16:45, 12 October 2016 (UTC)[reply]
This is not exactly rocket science. Atmospheric conditions could be a factor, but keep in mind that what you can hear often depends on what other noises there are. Vespine's original answer pretty well explains that part of it. As a simple example, when you're driving in your car with your radio at what seems like an optimal level, if you stop the car and turn off the engine, the radio will seem louder, even though you have not increased the volume of it. Why? Because the engine noise is no longer there. Another practical example is attending a game in a domed stadium filled to capacity with spectators. When your team scores, the crowd's roar is very loud and that's about all you can hear. But when there's nothing going on, you can hear a lot more of the "quieter" sounds that Vespine points out. ←Baseball BugsWhat's up, Doc?carrots→ 06:40, 12 October 2016 (UTC)[reply]
I believe the OP is not necessarily claiming car sounds are objectively louder at night but seeks an explanation why they seem (subjectively) louder. Consequently it may be unnecessary to look for explanations based on the physics of Sound or on human hearing physiology. Under the article heading Neural adaptation we have a short section Neural adaptation#Auditory that may be relevant to the OP (though it is not as detailed as the one devoted to visual adaptation.). There are articles on preoccupation of general attention in some specific abnormalities e.g. BDD (own appearance), Egomania (own importance), Hypochondriasis (own sickness), etc., but no article about preoccupation in healthy people by multiple distractions that may be present in greater strength during the day than during the night. Such daytime distraction might decrease the sensitivity of hearing and this idea seems straightforward to test by controlled experiment.AllBestFaith (talk) 00:44, 13 October 2016 (UTC)[reply]
Vespine's explanation pretty well covers it. If there are fewer other sounds, the sounds you hear will tend to seem louder. ←Baseball BugsWhat's up, Doc?carrots→ 07:20, 13 October 2016 (UTC)[reply]
Hearing fewer other sounds would make the other sounds already present seem louder. That is similar to what I mentioned in my first comment of this section. PlanetStar 23:45, 13 October 2016 (UTC)[reply]
Assuming Vespine's answer about sound refraction, sounds not just from cars and other vehicles in the background can be heard more loudly at night, but of any sound. For example, we could hear the music playing from down the street more loudly at night than during the day, even though the source is at same distance and same volume. PlanetStar 23:45, 13 October 2016 (UTC)[reply]
What plants are these (the ones in the foreground)?edit
(regarding the first image) A variety of Dracaena fragrans Massangeana? The shading of the leaves looks different in that article, but see here for example ---Sluzzelintalk 02:37, 11 October 2016 (UTC)[reply]
Hi I remember asking a question about mind uploading a few weeks back. If mind uploading were not possible, would there be other possible ways for humans to become immortal?Uncle dan is home (talk) 08:12, 11 October 2016 (UTC)[reply]
We have an article on immortality which includes some notable theories. Why don't you start there, and then let us know if you have any more specific questions. Someguy1221 (talk) 08:16, 11 October 2016 (UTC)[reply]
Immortality is a philosophical problem, not a physical one. The atoms that make up the body endure. The fundamental essence of consciousness (Atman) is arguably universal and immortal. Even the information learned in a lifetime accumulates in some sense, whether transmitted recognizably as text or whether it disperses and affects future events in unpredictable ways. Even particular aspects of the genome are long-lived - though the precise combination of genes may not occur again, the individual alleles likely remain present in the gene pool for a very long time. And this is even before we broach such issues as parallel universes and whether they contain copies of ourselves, or the related quantum immortality. And then there are creepy misgivings regarding qualia, such as Nietschze's notion of "eternal return". Now all these things are uncertain, but is it certain that who you were five minutes ago was you, rather than just a memory? Let alone a robotic effigy or an imperfectly cell-printed copy! So outside the very narrow sense of trying to put off disease a little longer, the fundamental issue of what the human being is and whether or how long he remains is a far voyage beyond all we understand. Wnt (talk) 10:30, 11 October 2016 (UTC)[reply]
Woody Allen was once asked if he wanted to achieve immortality through his film work. He said, "I would rather achieve immortality by not dying." ←Baseball BugsWhat's up, Doc?carrots→ 10:50, 11 October 2016 (UTC)[reply]
Plus I'd want good health! Not as a Struldbrug. :) Dmcq (talk) 11:55, 11 October 2016 (UTC)[reply]
Wave some philosophy at it. When you're dead, you don't exist. At the moment of death, you're dead. Therefore, you never experience the moment of death; hence, you never die. Q.E.D. :) Wnt (talk) 12:34, 11 October 2016 (UTC)[reply]
There's the possibility of some type of suspended animation, like being frozen. Of course, there's not much point in living forever if you aren't aware of any of it. But the hope is that eventually mind uploading will be possible, then you could be revived and live again. Other life extension techniques, like replacing failing organs with those cloned from your own stem cells, may also keep you alive until that time. StuRat (talk) 12:29, 11 October 2016 (UTC)[reply]
@StuRat: The issue with "mind uploading" is that you're in a lump of live neurons doing action potentials, and your "alter ego" is in a bunch of integrated circuits carved into silicon. How can the essence of yourself be in that thing, but not be in some five-year-old who lives in Ethiopia? Yeah, yeah, I know, you taught it some lines. I know some folks who can quote every line in Monty Python and get the accents right, does that mean the actors have uploaded their minds to them? Wnt (talk) 16:09, 13 October 2016 (UTC)[reply]
Sometimes the actors are no different than the character, so what's important to one's identity and ego would be a period of integration. If one can create a cyborg AI for which experiences can be transferred from organic form to the other and vice versa, then one will come to identify with both even if the transistor copy version is imperfect and so one may eventually not "mind" making a complete transition to a hardwired life because you will have, in critical ways, remembered experiencing both forms of consciousness during the transition. --Modocc (talk) 18:15, 13 October 2016 (UTC)[reply]
Are you worried that your ants are aging too slowly ? :-) StuRat (talk) 15:12, 11 October 2016 (UTC) [reply]
There are only a finite number of physically distinguishable states your brain can be in. This means that an immortal brain would eventually have to experience the same things over and over again, ad infinitum. Anything that this brain experiences will involve only a finite recollection of a "past" (which in most cases will be an artifact of false memories). The more you try to evade these limitations by using a system that can access larger and larger number of states, the more different persons with different experiences you'll end up producing. Count Iblis (talk) 17:19, 11 October 2016 (UTC)[reply]
@Count Iblis Would your hypothesized immortal brain discover a repetition in the decimal expansion of Transcendental numbers such as π and e or in an inward zooming animation of the Mandelbrot set ? AllBestFaith (talk) 15:15, 12 October 2016 (UTC)[reply]
Not a full repetition as these are irrational numbers, but the Mandelbrot set does contain exact copies of itself. Count Iblis (talk) 17:38, 12 October 2016 (UTC)[reply]
There is no finite number of repetitions of a digit that will not eventually occur in the expansion of a transcendental number. Your hypothetical immortal-but-capacity-limited brain will be unable to decide whether very long-cycle repetitions it sees are infinite or finite patterns. Scientific method for us mortals relies on experiments that are sufficiently replicable, where sufficiency is a criterium related to an intellectual's life resource. Example: I have seen the demonstration that a lead ball and a feather fall at the same rates in a vacuum a couple of times and I regard that demonstration as such conclusive evidence for Newton's laws for falling bodies that I regard them as indisputable, and won't "waste" my time repeating the ball and feather test whose result is to mortal me highly predictable. In contrast, the immortal brain lacks the option of dismissing any result as too unlikely to happen to seriously consider, hence if it is honest about its own finite capacity, it can suffer the uncomfortable awareness of inability to discover (know) anything scientifically.
While some fractals are exactly self-similar such as the Koch snowflake, a deep animation[11] of the Mandelbrot fractal (warning: big file 146 MB, chosen for beauty) suggests the supply of fresh contexts for the reappearing kernel is inexhaustible. Perhaps you will draw on the argument that images digitized in a finite number of bits inevitably repeat after 2bits images. AllBestFaith (talk) 18:59, 13 October 2016 (UTC)[reply]
@Count Iblis: AI is not limited to our brains, but, in any case, our universe would need to be eternal and with my modeling of its underlying physics I have reason to believe that it is. --Modocc (talk) 18:31, 13 October 2016 (UTC)[reply]
If you had cancer, could you treat it by going into outer space, which I've heard is full of high levels of radiation.
NOTE: I am not asking if this is a sensible, feasible, cost-effective or risk-free way to cure cancer. Just wondering if it could cure cancer.--Captain Breakfast (talk) 16:22, 11 October 2016 (UTC)[reply]
Radiation is such a vast, complex idea, you can't make general statements about "radiation" as though it were some tiny little thing that always does the same thing. It's like asking "Is eating good"? Eating what? When? How much? --Jayron32 16:35, 11 October 2016 (UTC)[reply]
Okay. Thank you for your exteremely helpful comment. Radiation is not "some tiny little thing that always does the same thing." Glad we cleared that up. Can any of the kinds of radiation you would be exposed to in outer space cure cancer?--Captain Breakfast (talk) 16:41, 11 October 2016 (UTC)[reply]
Jayron32 is helpfully pointing out that this topic is incredibly broad. It might take weeks of reading background science to bring you up to the point where you are phrasing your question in a way that a scientist could actually answer. But here at the reference desk, we aren't here to provide you with a definitive "yes" or "no" to your question: our role is just to point you in the right direction towards great encyclopedic resources.
Proper medical professionals rarely talk about curing cancer; they use words like "treatment," "prevention," "remediation," "remission." Even our encyclopedia editors have decided that cure for cancer ought to redirect to our article on cancer research - because this is how well-informed individuals actually speak about cancer.
So - where do you want to begin? Jayron32's advice was much briefer than mine - but he's making the exact same point: your question, as it is worded, cannot be answered with scientific rigor.
Radiation therapy works by focusing a beam of ionizing radiation onto a localized area of cancer, to kill the cancer cells. The radiation must be carefully directed so that it hits the intended target (the cancer) without affecting very much of the surrounding noncancerous tissue. Exposing the entire body to radiation at a level that would kill cancer cells would most likely kill the patient, by killing large amounts of normally functioning cells. Exposing the body to lower, non-lethal, levels of radiation would be more likely to cause cancer than to cure it. CodeTalker (talk) 16:44, 11 October 2016 (UTC)[reply]
(edit conflict) Radiation can kill cell, even cancerous ones. Dead cells don't reproduce. So yes, it "can".
Now, either the probability of that happening without killing the patient is ridiculously small, or radiotherapists with access to precise levels of radiation and focusing the rays at some places are desperately incompetent.
What Jayron32 said is actually very relevant, because (to take his example) your answer amounts to "glad that we cleared up that the safety of food depends on its type" - if you ask an imprecise question, people are not going to assume you are an expert in the subject. In addition to "it depends on radiation", I would add "it depends on cancer", because there are plenty of "cancers" out there and some of them are completely different. TigraanClick here to contact me 16:53, 11 October 2016 (UTC)[reply]
"Treat" also implies survival of the patient generally. A shotgun cures cancer quite effectively otherwise. Likewise radiation - it may well stop the cancer, the tricky bit is not making the side-effects worse than the initial disease. Marvel Comics are not a competent guide to medical physics and the therapeutic uses of radiation, even when administered via the spider-bite mechanism. Chemotherapy is already a matter of deliberately poisoning the patient and hoping that the cancer is slightly more poisoned than the rest of the patient. We have some hope that the next generation of cancer treatments will be more self-targeted themselves.
Historically radiotherapy has largely been a matter of three dimensional geometry and cooking the patient along a line through their body, repeating treatments at different angles to repeatedly dose the cancer site whilst irradiating other parts only once. This relies on radiation as narrow collimated beams, and accurate positioning relative to the patient. Neither of these would arise from the "cook in space" approach. Andy Dingley (talk) 17:17, 11 October 2016 (UTC)[reply]
Adding to what the others have said, there are many ways radiation is used in oncology. Its almost always used to cook the cancer more than the tissue we don't want to kill. The typical question is how you concentrate the radiation. Chemotherapy generally assumes that tumors get more blood flow that healthy tissue so adding a bit of radioactive material to the blood will hurt the tumor more than the rest of the body. Beams of radiation (Cyberknife) where you fire from many directions at one point are another way to get the local concentration. Yet another way is via radioactive seals (brachytherapy) placed near/around the tumor. This is common for prostate surgery. Springee (talk) 17:57, 11 October 2016 (UTC)[reply]
Nothing personal, but your terminology is incorrect. Chemotherapy refers to the use of cytotoxic drugs. Administering radioisotopes is known as radioisotope therapy. Also chemotherapy isn't really based on tumors having increased blood flow, though that does help. Rather, it's based on the tendency of cancer cells to divide rapidly. Most chemotherapy drugs interfere with cell replication, and thus affect rapidly-dividing cells more. This also accounts for their most common side effects. --47.138.165.200 (talk) 19:44, 11 October 2016 (UTC)[reply]
Total body irradiation generally involves 10-12 Gray given in "fractions" so the patient can recover from shorter term effects in between. Honestly I have not bothered to learn the exact protocol which sounds like some kind of semi-fictional horror story about the Dark Ages. The Apollo astronauts received 0.86 Gray during the outbound transit through the Van Allen belts, according to [12]; the inbound was much less though, presumably since they could use the atmosphere to slow down more at the end? So it seems plausible that a nice leisurely orbit through the Van Allen belts can deliver the same total radiation dose in as many fractions as desired, though the profile of how long each treatment takes will be forced to be longer. I don't know if that matters. I would presume there is no FDA approval or Cochrane review about doing total body irradiation using a space capsule, so there is a certain level of guesswork here. :) One good thing is that potentially the capsule may have been very well disinfected prior to launch, making recovery safer from infection. The astronaut might shield his lungs per the current irradiation protocol, and of course you'd best shield the bone marrow to be transplanted afterward! You might cure leukemia with something like this. Wnt (talk) 20:24, 11 October 2016 (UTC)[reply]
Feynman Lectures. Lecture 30. 30–1The resultant amplitude due to n equal oscillators [13]edit
I'm trying to check formulae 30.1 and 30.2 in Mathcad:
PNG xmcd
So according the image we see that two formulae give different graphs. But it looks like the derivation of 30.2 is correct. How is it possible?
@Username160611000000: It looks to me like one is finding R and one is finding AR. If I had to take a guess, I'd say AR is the amplitude of R, perhaps the absolute value? In any case, I notice AR (the second) hits its low points everywhere R (the first) passes through zero. Catch is, the graph makes it look like AR goes slightly negative, so I should see if that's real or not. (As it happens I just rehabilitated the copy of R I have here, so if I get a chance I'll put it to the test) Wnt (talk) 16:18, 13 October 2016 (UTC)[reply]
Thank you. Now I see that R is a projection of AR on X-axis (or x-component of the vector AR). Besides the angle OQT (Fig. 30–1) is not always equal to nφ , sometimes it is equal to (2π - nφ). When I found y-component and length of the vector, it became equal to modulus:
Compared to plot(phi, abs(sin(n * phi / 2)/ sin(phi / 2)), type="l")
for ARWnt (talk) 02:42, 16 October 2016 (UTC)[reply]
@Username160611000000: I'll also mention that the reason for these nodes is that at regular intervals the polygon segments sum up to form regular polygons or stars. These can be drawn in R by taking rvc = function (wt, phi, n) { i = 1 : (n + 1); sapply(i, function (i) { sum(cos(angles(wt, phi, i))) }) } and the equivalent sine and plotting them. The repetition of the main peak every 2pi units is trivial though, since these are angles modulo 2pi. Wnt (talk) 09:15, 16 October 2016 (UTC)[reply]
What matches the density of air compressed by a factor of one trillion? — Melab±1☎ 21:35, 11 October 2016 (UTC)[reply]
The density of air at ordinary temperatures and pressures is around 1.2 kg/m3, or about 830 times less dense than liquid water. Something a trillion times more dense than air would be about 1.2 billion times more dense than water, which is denser than the core of the sun (150x that of water). In fact, the only place in the universe you find material this dense is inside a neutron star. Someguy1221 (talk) 21:58, 11 October 2016 (UTC)[reply]
