Is it possible for a moon to stay on the same side of its planet relative to the sun?

Question: I'm building an earthlike world that has a moon orbiting a gas giant. Is it possible for the moon to always be between the planet and the sun? Also, is it possible for a moon to rotate around its own axis?
Comment: Welcome to worldbuilding SE! make sure you have read the rules and taken the tour.
Comment: It may be possible for the moon to never be in the shadow of the planet if it's in a sun synchronous orbit.
Answer: No, it's not possible for the moon to always be between the planet and the sun.
For the moon to be in a stable orbit around the planet, and always be in front of the sun, two things must be true (We'll ignore the situation of putting the Moon at the L1 Lagrange Point, it wouldn't be in orbit around the planet, and L1 is not long-term stable):

The Moon's sidereal orbital period around the planet must be equal to the planet's orbital period around the sun.
The Moon must be orbiting inside the Planet's Hill Sphere.

The Hill Sphere  is the region of long-term stable orbits around the planet, which is based on the mass of the planet, the mass of the star being orbited, and the distance between the two. Its radius can be estimated as follows.
$$r_h=a_p\sqrt[3]{\frac{m_p}{3m_s}}$$
Where $m_p$ is the mass of the planet, $m_s$ is the mass of the star, and $a_p$ is the semimajor axis of the planets orbit, or the radius, in the circular orbit case we'll be using for simplicity.
The Orbital Period of an object around another object can be determined by the following formula.
$$t=2\pi\sqrt{\frac{a^3}{GM}}$$
Where $a$ is the semimajor axis of the orbit in question in meters, $G$ is the Newtonian Gravitational Constant, and $M$ is the mass of the body being orbited. This assumes that the satellite is negligible compared to the mass of the central body.
When I started fooling around with the numbers determined by these values in a Desmos Graph, a curious relation emarged, that I'll have to take some time to work through the derivation of:
Regardless of the mass I chose for the Sun and the Planet, regardless of the semimajor axis of the planet, The Period of the largest Moon orbit that could fit inside the Planet's Hill Sphere was always 55.7% of the Planet's orbital period.
So, no. You can't have a Moon with a long-term-stable orbit around a planet that keeps it between the planet and the sun.
Comment: @novotny I do not have the math to calculate it, but my gut tells me (it is the fashion in the US!) that rather than a moon, a binary planet with equal sized partners could fulfill your conditions 1 and 2.   The orbital calculators I found all make your assumption that satellite is negligible & I am not sure Hill sphere calculation works for equal mass orbiting partners.
Comment: Here is a bounty in hopes that you will expand your answer to detail your use of the Desmos graph and also explore the case of a binary planet and orbital period.
Comment: I've come up with a derivation of the curious relation, if you'd like to see it - it's really just applying Kepler's third law. cc @Willk.
Comment: @HDE226868 - Go ahead and put up an answer, HDE.  The bounty is for whomever provides sweet math education & you have a fine track record in that regard.
Comment: @Willk Excellent, done.
Answer: This answer is meant as a supplement to notovny's. I agree with their conclusions (the scenario is impossible because of the instability of this Lagrange point, and the fact that the Hill sphere is too small), and I just want to derive the "curious relation" they came up with.
We start with Kepler's third law. $T_M$ and $T_p$ are the periods of the planet and the moon; $a_M$ and $a_p$ are their semi-major axes; $M_p$ and $M_S$ are the masses of the planet and the start. Let's write out Kepler's third law for both the orbit of the moon and the orbit of the planet:
$$T_M^2=\frac{4\pi^2}{GM_p}a_M^3,\quad T_p^2=\frac{4\pi^2}{GM_S}a_p^3$$
If we assume the moon is in its outermost orbit, we have
$$a_M=a_p\sqrt[3]{\frac{M_p}{3M_S}}$$
Now we substitute and our first equation is
$$T_M^2=\frac{4\pi^2}{GM_p}a_p^3\frac{M_p}{3M_S}$$
Finally, we divide by the equation for the planet's period:
$$\frac{T_M}{T_p}=\frac{M_S}{M_p}\frac{M_p}{3M_S}$$
and so $T_M\approx0.58T_p$, which is the result notovny found.
It's interesting to think about this in the case of a binary planet ($M_p\approx M_M$) or a binary star ($M_S\approx M_p$). Kepler's third law is easy to modify for both of those cases. However, the derivation of the Hill radius requires that $M_p\ll M_S$, and that the Hill radius $R_H\ll a_p$. If we get rid of that requirement, then I believe a general solution would require finding the roots of a fifth-order polynomial in $x\equiv R_H/a_p$, which unfortunately has no general solution. For particular values of $M_p$ and $M_S$, we may be able to find solutions, but we'd need to look at them on a case-by-case basis.
Comment: @Willk The big issue (so far) is that the expression for the Hill sphere assumes that $M_p\ll M_S$, so we would need to find a different equation for that equal-mass regime to think about that case. I'll have to think about it.
Comment: / and  are the periods of the planet and the moon;  and  are their periods;/. I think T is the period.  What is a?  Circumference?
Comment: @Willk Whoops, typo on my part - let me fix that.
Comment: I should just plug in numbers and try to do the math.  I may yet.  But consider your scenario where Mp is close to Ms.  That is like the situation in your question  https://worldbuilding.stackexchange.com/questions/71971/is-it-safe-to-orbit-hde-226868. If the ship plays the role of moon and "lunar period" is larger, can the orbiting ship orbit (the center of mass) so as to keep the black hole between itself and the super star?
Comment: @Willk Having done the algebra out, I believe there's no general solution because it would require finding roots of a fifth-order polynomial, and there's no algebraic formula for the roots of such a polynomial in the general case.
Answer: Not in practice, and yes, if you justify it.
If a moon is orbiting a planet, it has to go around the planet. To simplify, the movement around the planet is what keeps it from just falling onto the planet. Orbits are simple in principle, but those principles don't especially correspond to everyday ideas about moving objects. If you learned about orbits from films or TV, you likely have things to un-learn, because those sources tend to ignore how things actually work. The Wikipedia page about orbits is a good place to start.
There is a special case that looks as if it will solve your problem, but doesn't work in practice. That's the "L1" Lagrangian point. In that, the "moon" is not actually orbiting the planet. It's orbiting the sun, close enough to the planet that it gets dragged along by the planet's gravity, and is always approximately between the planet and the sun. The reason that this doesn't work in practice is that the position is unstable: the slightest disturbance of the moon's position, such as the gravity of another planet in the system, will set the moon drifting away from the L1 position.
Staying at L1 requires frequent course corrections. Humanity has several spacecraft at the L1 point between Earth and our Sun, but they all need to use small rockets ("thrusters") to stay there. The SOHO satellite is an example. However, any body big enough to retain an atmosphere and be habitable is too large for its position to be adjusted with any reasonable level of technology.
Moons always rotate, it's just that they usually do it in a time equal to the time they take to orbit their planet. This means they always show the same face to the planet, giving a false impression that they don't rotate. This is called "tidal locking," and it happens naturally with most moons.
To have a moon that is not tidally locked, you need some kind of explanation. The simplest way is to say that the moon collided with another sizable body, which can change its rotational speed and axis quite seriously, and provides a reason for exciting topography. You need to have this happen before life appeared on the moon, because such a collision is likely to kill all life on the moon.
Comment: Tidal locking is a very slow process. It may take several billion years for a moon to be perfectly in sync with its planet. This means that you can justify having a moon not in sync with its planet just by saying that tidal locking has not done its job yet. Their is no need for a celestial bodies to crash.


Wireless Keyboard Connection

Question: I have the wireless bluetooth connecting keyboard for the iMac and it continues to disconnect even when the batteries are brand new. Is there anyway to enhance the bluetooth connection so that it will stop disconnecting?
Comment: Try using 5GHz WiFi or LAN instead of 2.4GHz WiFi, this should lower the noise in the bluetooth spectrum.
Answer: I guess you are using the original Apple keyboard? In this case, you shouldn't have any problems with the bluetooth connections when the keyboard is in front of the iMac (and your Mac is located in a "normal" office, without lots of over the air devices that can cause a lot of noise).
To me, this sounds like a hardware defect. I would take the keyboard back to Apple/reseller to get a new one.

Wireless Keyboard Connection


Why isn't the symmetric twin paradox a paradox?

Question: Two twin sisters synchronize their watches and simultaneously (from the earth frame) depart earth in different directions. Following a predetermined flight plan, each sister accelerates identically to 99.9%c and then returns home at the same time (again in the earth frame). The observers on earth see each twin as having aged identically, as the symmetry of the problem dictates. Each twin however should see the other as having aged... What gives?
Comment: For more on this see [What is the proper way to explain the twin paradox?](http://physics.stackexchange.com/questions/242043/what-is-the-proper-way-to-explain-the-twin-paradox)
Comment: In a sense this is easier than the basic "paradox". It is sufficient to note that the difference of elapsed time observed by one twin must be equal to that of the other. To quantify it you use the same resolution as in the basic "paradox".
Answer: The resolution of this apparent paradox introduces no new ideas with respect to the canonical version of the paradox. As you point out, the journey of each twin is symmetric, and so each twin calculates that they will age the same amount by the time they return home.
If, instead of appealing to symmetry, you would like to do the calculation from the perspective of one twin reasoning about the passage of time of the other twin, the reasoning is as follows: During the outgoing phase of the journeys, each twin calculates that less time has elapsed on the other twin's clock than on their own. But during the turnaround, they calculate that the other twin ages rapidly to such an extent that, even accounting for the time dilation for the return journey, their ages will be the same when they meet up back at their starting point.
Answer: We can simplify the problem by assuming that the twin sisters leave Earth already at 0.999c and when they return to the earth they are still doing 0.999c. That means the only acceleration takes place when the sisters reverse speed at the halfway point of their journey.
We can all compare watches on two points that everyone is in the same place i.e. when the sisters leave Earth we can all synchronise watches so they read the same, and when the sisters return we can all compare the readings on the watches. The fact the sisters are moving at this moment doesn't matter as long as both the sisters and we are in the same place.
So consider what sister A sees: working forward from the start point, sister A sees sister B moving at 0.9999995c (relativistic addition of 0.999c to 0.999c) so the time dilation is 1,000. So sister A sees sister B aging at 1/1000 of the normal rate. Likewise for sister B.
Now take the end point, at which the sisters are the same age, and follow the sister's trajectories back in time. Again sister A will see sister B aging at 1/1000 of the normal rate, and again likewise for sister B.
If we follow the trajectories forward from the beginning, and backwards from the end, then obviously at some point the trajectories must meet, and this means the sisters must have changed from the initial to the final inertial frame i.e. they must have accelerated to change inertial frames. Lets consider this from sister A's point of view.
During the acceleration sister A feels a force, but considers herself not to be moving. So from her perspective sister B accelerated to change her speed from 0.9999995c to -0.9999995c and even though sister B was aging at 1/1000 of the normal rate, during the acceleration sister B's time catches up with and overtakes sister A's time. During the inbound leg sister A sees sister B aging slowly again, but the age jump during the acceleration makes up the difference. Sister B sees exactly the same, i.e. she sees sister A age during the acceleration.
So that's why the sisters end up the same age. They do indeed see each other aging more slowly, but it's during the acceleration between the outbound and inbound legs that each others time catches up.
I haven't attempted to do the sums because to be honest I've long since forgotten it and I'd have to go away and look it up, but you can probably find it on the web. Contrary to popular belief you don't need general relativity as special relativity is perfectly capable of handling accelerations, as long as you're content to treat acceleration as absolute. My recollection of doing the calculation at college is that it was messy and actually not very illuminating.
Comment: No you don't need GR--- the General Relativity is just ridiculous here. The proper answer is "draw the space-time diagram".
Comment: @user1247: This is not exactly true--- it is only true if there is a uniform constant acceleration for one of the twins, and then it is true that you can view it either in the constant acceleration frame or in the unaccelerated frame, and then you do get the same answer, and it's equivalent. But the reason it's ridiculous anyway is because you are looking at flat space and answering "why is this broken line a different length than this straight line"? You wouldn't answer that by making a curvilinear coordinate system in Euclidean geometry, so you shouldn't do that in space-time either.
Comment: Good explanation +1. But you _do_ need general relativity, to explain what happens in the acceleration phase. That is also why you elegantly skip that part. General relativity is also needed to explain the non-symetry of the normal twin paradox(one stays in the same inertial frame, and the other goes trough an acceleration at one point).
Comment: The problem with this answer is that the sister does not "see" the other sister age during the turn around, but the other sister "coordinate ages" because the coordinate now moves as the sister moves to a new reference frame. The whole thing is very simple if you look at the Euclidean geometry analog, as every other relativity paradox.
Comment: @Ron Maimon: the GR is not ridiculous. You can sit down and do the math from the perspective of one of the twins. During the acceleration due to the equivalence principle the twin sees a distance-dependent gravitational time dilation as causing the other twin to age. If you do the calculation you will see that you get the correct result. So your dismissal of this approach is unfair; it is a matter of personal/philosophical preference.
Answer: John Rennie's answer doesn't sound quite right. This problem can be restated with no acceleration. Suppose we have 4 sisters {A1,A2} and {B1,B2}.  Sisters A1 and B1 leave the earth simultaneously and agree to keep traveling on a non accelerated trajectory indefinitely. At the same time (from the earth frame) sisters A2 and B2 start traveling towards earth. Some where in the middle Sister A2 passes A1 and B2 passes B1. Sisters A1 and B1 transmit their current wallclock time to their respective sisters. Here there is no acceleration, hence acceleration can not be part of the problem.
Or what if the universe is closed and they meet at the starting point after a finite time. Again, no acceleration.
Comment: Closed universe is not relativistically invariant. As for the passing sisters, the "jump" comes from the changing frames, and is no more mysterious than when you rotate a frame that the y coordinate of something far away jumps.
Comment: Flat space with periodic boundary conditions is not invariant. When you boost, the boundaries become pasted with a time-jump. There is a preferred frame where the time-jump is zero, and this is the rest frame of the boundary conditions. There is nothing screwy--- draw the picture in space time and it will be obvious. Is it screwy that in a cylinder the path that wraps once around while going up is longer than the path that just went up? The cylinder is the Euclidean 2d periodic boundary in one of the dimensions.
Comment: Ok.. you don't like closed space... fair enough, how about flat space with periodic boundary conditions. That's invariant. Also, what jump are you referring to. I boosted no particles, I simply transmitted information between frames. And if both frames {A1,A2} are moving with the same absolute velocity (albeit in opposite directions) the time dilation should be constant from the perspective of other twins. There is no acceleration or boost. Something is screwy here.
Comment: +1 : The nice but wrong answer, together with @RonMaimon 's rebuttal helped me to understand the twin paradox better.
Answer: A simple explanation appears to be that each twin are the same age after the journey because they traveled paths of equal length through spacetime. In other words their perspective watches measured the same amount of proper time.
In the canonical version of the twin paradox the difference in age of the earth bound twin, and the space-traveling twin can viewed as that the earth bound twin followed an essentially straight line through spacetime, and the space-traveling twin followed a curved path through spacetime. In Minkowski space, unlike Euclidean space, a curved path is shorter than a straight path.
Comment: One poster commented that General Relativity was "needed to explain the non-symmetry of the normal twin paradox" since one twin accelerates. Special relativity can handle the case of accelerating objects (in this case a space-traveling twin). The key is to imagine the acceleration as a series of Lorentz transformations between inertial reference frames that differ infinitesimally in relative velocity.
Comment: See, for example, "Spacetime Physics" by Taylor and Wheeler. This "solves" the twin paradox taking into account acceleration, entirely using SR. Indeed GR reduces to SR in the absence of gravity, and as gravity doesn't enter into the problem, there is no need for GR.
Answer: I'd stick to simple for this one: Both twins accelerate and then decelerate equally, while the earth observer stays put with close to zero accumulated acceleration. So Minkowski's very first approach to answering this question -- "who is accelerating?" to paraphrase -- applies nicely. When everyone returns to the same location and velocity and compare clocks, the twins simply find they are the same (low) age, and that everyone on earth aged faster.
Incidentally, don't let discussions of "viewing" each other's ages through telescopes throw you off on this one. With enough data you can place brackets around permissible time deltas that way, but you can't give final answers because you don't know how much of the spatial distance between you may still end up converted into time distance. The shared location, shared frame finale in contrast gives answers that depend only on who spent more time accelerating.


What happened to Pandavas in future lives?

Question: Did the Pandavas eventually take rebirth? If they did, who were they and what happened to them?
Comment: They no longer exist as distinct beings, just as in the case of Karna; see my answer here: http://hinduism.stackexchange.com/a/6551/36
Comment: Bhima born as Madva Arjuna born as Jayatheertha of Madva sect Bhalika born as Raghavendra swamigal again of Madva sect shalliya born as jaggandha dasa
Answer: Arjuna was reborn as Kannappa Nayanar, one of the 63 great Shiva-bhaktas in South India.
When Arjuna fought with Lord Shiva as a Kirata to obtain the Pasupatastra, he had at first insulted him based on his caste (although later he admired the hunter). And after realising who He really was, Arjuna fell at Mahadeva's feet and repeatedly asked for his grace. Therefore, as a combined result of this, Mahadeva told Arjuna that he will have to take another birth, but will live only for sixteen years. He would perform Shiva-bhakti for six days, and return back to His abode. Thus, Arjuna was born as Kannappa Nayanar.
http://www.sacred-texts.com/hin/m03/m03039.htm
https://en.wikipedia.org/wiki/Kannappa_Nayanar
http://www.shaivam.org/nakannap.html
http://www.shaivam.org/nakanna1.html
Comment: where does it say shiva telling arjuna that he has to take another birth?
Comment: @Abhiram it is not found in the Mahabharata, but in the story of Kannappa Nayanar, as related by Upanyasakas.
Comment: yeah vyasa mahabharata is true mahabharata alright. arjuna was a portion of indra and was born on earth to kill asuras who were men on earth such as duryodhana and jarasandha alright. pandavas and krishna had a mission, slay large number of adharmis which they did in the war and restore dharma which they did after the war by performing ashwamedha yagya
Answer: No Arjun didn't take rebirth. In fact he attained Vaikunta , the highest of all positions . The Mahabharata itself clearly mentions it. In Gita Krishna himself describes that no one is dearer to him as Arjuna. In fact Krishna-Arjun were Nara-Narayana. There is no question of rebirth for Arjuna. The story of Kannappa is different . As per original Mahabharata, Arjuna attained Vishnu Loka

He beheld Govinda endued with his Brahma-form. It resembled that form of his which had been seen before and which, therefore, helped the recognition. Blazing forth in that form of his, he was adorned with celestial weapons, such as the terrible discus and others in their respective embodied forms. He was being adored by the heroic Phalguna, who also was endued with a blazing effulgence. The son of Kunti beheld the slayer of Madhu also in his own form. Those two foremost of Beings, adored by all the gods, beholding Yudhishthira, received him with proper honours.

From Section 4 Swargarohanika Parva.
Answer: It is detailed in the Bhaviṣya Purāṇa in this section:

....At this Shiv said - "Because you are all the devotee of Shree Krishna that is why I am protecting you otherwise you were all worth of being killed. You all will have to suffer for this by taking birth in Kali Yug." and he got disappeared....

... Although my words will not be a lie, still Pandavas and Kauravas will be born on Prithvi (earth) from their part and will be free soon. Yudhisthira will be the son of Vats Raaj (Bacchraj), his name will be Baalakhaani (Maalkhan) and he will the king of Shireesh (Sirsa) city. Although, he spoke bad languages, Bheem's name will be Veran and he will be the king of Vanaras. Whoever will take birth from Arjun's part, he will be my Bhakt and great intelligent. He will be born in Parimala's house and his name will be Brahmaananda. Nakula will be born as Ratnabhaanu (Raatibhaan)'s son in Kanyakubja and his name will be Lakshmana. Sahadev will be the son of Bheem
Sinh and his name will be Dev Sinh. Dhritraashtra's part will be born as Prithviraaj in Ajmer and Draupadi will be born as Velaa, the daughter of Prithviraaj. The great donor Karna will be born as Taaraka (Saadar/Tahaar). At that time I will also take Avatar in the form of Raktabeeja. Kauravas will be skilled in Maya war and Pandavas will fight according to Dharma."

It feels weird having to defend a text from the main canon, but the Bhaviṣya Purāṇa is affirmed in the Padma Purāṇa to be a Mahāpurāṇa, putting above even celebrated texts like the Devī Bhāgavata. Also, the people who refute it couldn't even figure out Gabriel's very obvious appearance and central importance to the plot, so they don't understand the story well enough to be an authority to refute it. They also always ignore that there are two very obvious references to Christianity and Islam at different points in the story, not one for each, so I really doubt they even read the thing.
P.S. Having read most of this section it seems like Harinagara is the avatar of Viṣṇu that was promised much earlier to Kali to protect the wicked Gabriel, after his ardent prayers (I am going to assume they are one and the same due to their extremely similar qualities and stories focusing on them neighboring each other). That seems like a fun pseudo-horror story to tell round a campfire.
Comment: Revised your answer by citing appropriate section from the Bhavishya Purana link provided in answer. Now it answers the question properly. Undeleted :)
Answer: https://www.sacred-texts.com/hin/m18/m18005.htm

Both Kshattri and king Yudhishthira entered into the god of Righteousness.

Yudhisthira, in the end, merged in to Yama.
https://sacred-texts.com/hin/m09/m09061.htm

"He also beheld the princess of Pancala, decked in garlands of lotuses. Having attained to Heaven, she was sitting there, endued with a form possessed of solar splendour. King Yudhishthira suddenly wished to question her. Then the illustrious Indra, the chief of the gods, spoke to him, 'This one is Sree herself. It was for your sake that she took birth, as the daughter of Drupada, among human beings, issuing not from any mother's womb, O Yudhishthira, endued with agreeable perfume and capable of delighting the whole world.

Drauapdi was in heaven and became Sri.

In another part he beheld Bhimasena of great puissance, sitting in the midst of the Maruts, and endued with a blazing form. He was sitting by the side of the God of Wind in his embodied form.

Yudhisthira sees Bhima with Vayu, meaning, he is in Vayu Loka.
Vaishampayana said, "King Yudhishthira, thus praised by the gods, the Maruts and the Rishis, proceeded to that place where those foremost ones of Kuru's race were. He beheld Govinda endued with his Brahma-form. It resembled that form of his which had been seen before and which, therefore, helped the recognition. Blazing forth in that form of his, he was adorned with celestial weapons, such as the terrible discus and others in their respective embodied forms. He was being adored by the heroic Phalguna, who also was endued with a blazing effulgence. The son of Kunti beheld the slayer of Madhu also in his own form. Those two foremost of Beings, adored by all the gods, beholding Yudhishthira, received him with proper honours.
Yudhisthira sees Arjuna and Krishna together in heaven.

In place belonging to the Ashvinis, the delighter of the Kurus beheld Nakula and Sahadeva, each blazing with his own effulgence.

Yudhisthira sees Nakula and Sahadeva with Ashvins
In the end, the Pandavas have attained to their highest end.

In Shanti Parva, Bhishma was blessed with the boon of knowing the past, the present, and the future by Krishna.
https://www.sacred-texts.com/hin/m12/m12a047.htm
"Learning by his Yoga prowess of the devotion of Bhishma, Madhava, otherwise called Hari, (entering his body) bestowed upon him heavenly knowledge compassing the Past, the Present, and the Future, and went away. "
Krishna did it for a reason.
"Subject to universal time, when the divine Surya turns to his northerly course, thou, O foremost of men, shalt go to those regions whence no man of knowledge ever returns to this earth! When thou, O Bhishma, wilt leave this world for that, all Knowledge, O hero, will expire with thee. It is for this, that all these persons, assembled together, have approached thee for listening to discourses on duty and morality. Do thou then speak words of truth, fraught with morality and Yoga, unto Yudhishthira who as firm in truth but whose learning has been clouded by grief on account of the slaughter of his kinsmen, and do thou, by this, quickly dispel that grief of his!'
Krishna also could have taught Yudhisthira the duties of king, dharma, and statecraft himself so why did he tell Bhishma to teach Yudhisthira and even Bhishma asked the same question to Krishna?
"Vasudeva said, 'Know, O thou of Kuru's race, that I am the root of fame and of everything that leads to good. All things, good or bad, proceed from me. Who on earth will wonder if the moon be said to be of cool rays? Similarly, who will wonder if I were described as one possessed of the full measure of fame?  I have, however, resolved to enhance thy fame, O thou of great splendour! It is for this, O Bhishma, that I have just inspired thee with great intelligence. As long, O lord of earth, as the earth will last, so long will thy fame travel with undiminished lustre through all the world. Whatever, O Bhishma, thou wilt say unto the inquiring son of Pandu, will be regarded on earth to be as authoritative as the declarations of that Vedas. That person who will conduct himself here according to the authority of thy declarations, will obtain hereafter the reward of every meritorious act. For this reason, O Bhishma, I have imparted to thee celestial understanding so that thy fame maybe enhanced on earth.
In Shanti Parva, hishma told the story of how Sanatkumaras told the greatness of Vishnu to Vritra and Vritra attained to highest station.
https://www.sacred-texts.com/hin/m12/m12b107.htm#fr_866

"Bhishma continued, 'Having said these words, O son of Kunti, Vritra cast off his life-breaths, uniting his soul (in Yoga, with the supreme Soul), and attained to the highest station.'

Yudhisthira then questioned Bhishma as to what will be the end attained by the Pandavas.

"Yudhishthira said, 'O thou that art conversant with the highest object of knowledge, I think that Vritra saw beforehand the excellent end that awaited him. It is for this, O grandsire, that he was happy and did not yield to grief (in view of his coming Death). He who is White of hue, who has taken birth in a pure or stainless race, and who has attained to the rank of a Sadhya, doth not, O sinless one, come back (into the world for re-birth). Such a person, O grandsire, is freed from both hell and the status of all intermediate creatures. He, however, who has attained to either the Yellow or the Red hue, is seen sometimes to be overwhelmed by Tamas and fall among the order of Intermediate creatures. As regards ourselves, we are exceedingly afflicted and attached to objects that are productive of sorrow or indifference or joy. Alas, what will the end be to which we shall attain? Will it be the Blue or the Dark which is the lowest of all hues?'

This is what Bhishma said about their end.

"Bhishma continued, 'Ye are Pandavas. Ye have been born in a stainless race. Ye are of rigid vows. Having sported in joy in the regions of the gods, ye shall come back to the world of men. Living happily as long as the creation lasts, all of you at the next new creation will be admitted among the gods, and enjoying all kinds of felicities ye will at last be numbered among the Siddhas. Let no fear be yours. Be you cheerful.'"


What kind of bushy plant is this?

Question: I found this bushy plant while walking through an urban area in New England. The majority of its branches were brown, except for the very tips which had a bright red color. It didn't have any flowers, and some of the tips had fallen on the ground which led me to suspect this is how it propagates. I searched online a bit, but I don't think it's a red twig dogwood because the leafs look different.
Comment: Do you have any more photos that show the whole plant? If not, roughly what size was it (height and spread) and did it have a woody base or stem/trunk, like a shrub, or soft stemmed?
Answer: The dogwoods are highly variable in form, but share that characteristic leaf veining (branching off from main vein and curving back in towards the tip) and propagation from stolons and stem tips. Where you find one dogwood generally you find a lot of them in the same area where they spread. This one seems to be Gray Dogwood (Cornus racemosa) which has rather unremarkable stems/twigs in comparison to other dogwoods but has the bright red flower/fruit stalks seen in this photo. Native to NE America.

What kind of bushy plant is this?


First science fiction story featuring super-intelligent character?

Question: I know of Odd John but probably much earlier. Not sure if Dracula's intelligence was supposed to be superhuman or his great age just made him wise -- same thing with The Wandering Jew, maybe. Frankenstein's Monster was very intelligent but not sure if that was due to the brain used or the process used.
Comment: "Yet across the gulf of space, **minds that are to our minds as ours are to those of the beasts that perish, intellects vast and cool and unsympathetic,** regarded this earth with envious eyes, and slowly and surely drew their plans against us." Sounds like those Martians were "super-intelligent"? Do they count?
Comment: Downvoted because you didn't define "super-intelligent" other than by comparison to other characters. I would vote to close as unclear if I could.
Comment: https://en.wikipedia.org/wiki/List_of_knowledge_deities - not Science Fiction, but that requirement is completely arbitrary anyways
Comment: Eve became super intelligent when she bit into that apple from the tree of super knowledge of good and evil...
Comment: Might be nice to link to Odd John, as you give him as an example. I, for one, have no clue who that might be. Can always Google of course, but a direct link to maybe the description you think is relevant, might help.
Comment: Many people consider Gilgamesh and Ramayana both works of science fiction. Both of these works feature super-intelligent gods in them. Both of these works are millennia old
Comment: @user14111: yes, that it a good example.
Answer: In terms of characters who are "superintelligent" for science fictional reasons rather than simply being exceptionally intelligent human beings, one early one is the 1879 story "The Ablest Man in the World" by Edward Page Mitchell, featuring a cyborg character who had a kind of clockwork computer, said in the story to be similar (but superior) to the real-life difference engine created by Charles Babbage, implanted into his skull (seemingly replacing his brain entirely rather than augmenting it), giving him superior mental abilities. The story can be read online at Project Gutenberg here. Here is the character Dr. Rapperschwyll describing the creation of the cyborg:

"My endeavors in mechanism had resulted in a machine which went far beyond Babbage's in its powers of calculation. Given the data, there was no limit to the possibilities in this direction. Babbage's cogwheels and pinions calculated logarithms, calculated an eclipse. It was fed with figures, and produced results in figures. Now, the relations of cause and effect are as fixed and unalterable as the laws of arithmetic. Logic is, or should be, as exact a science as mathematics. My new machine was fed with facts, and produced conclusions. In short, it reasoned; and the results of its reasoning were always true, while the results of human reasoning are often, if not always, false. The source of error in human logic is what the philosophers call the `personal equation.' My machine eliminated the personal equation; it proceeded from cause to effect, from premise to conclusion, with steady precision. The human intellect is fallible; my machine was, and is, infallible in its processes.
...
"Once more: a profound study of history from the sociological point of view, and a not inconsiderable practical experience of human nature, had convinced me that the greatest geniuses that ever existed were on a plane not so very far removed above the level of average intellect. The grandest peaks in my native country, those which all the world knows by name, tower only a few hundred feet above the countless unnamed peaks that surround them. Napoleon Bonaparte towered only a little over the ablest men around him. Yet that little was everything, and he overran Europe. A man who surpassed Napoleon, as Napoleon surpassed Murat, in the mental qualities which transmute thought into fact, would have made himself master of the whole world.
"Now, to fuse these three propositions into one: suppose that I take a man, and, by removing the brain that enshrines all the errors and failures of his ancestors away back to the origin of the race, remove all sources of weakness in his future career. Suppose, that in place of the fallible intellect which I have removed, I endow him with an artificial intellect that operates with the certainty of universal laws. Suppose that I launch this superior being, who reasons truly, into the burly burly of his inferiors, who reason falsely, and await the inevitable result with the tranquillity of a philosopher.
"Monsieur, you have my secret. That is precisely what I have done. In Moscow, where my friend Dr. Duchat had charge of the new institution of St. Vasili for hopeless idiots, I found a boy of eleven whom they called Stépan Borovitch. Since he was born, he had not seen, heard, spoken or thought. Nature had granted him, it was believed, a fraction of the sense of smell, and perhaps a fraction of the sense of taste, but of even this there was no positive ascertainment. Nature had walled in his soul most effectually. Occasional inarticulate murmurings, and an incessant knitting and kneading of the fingers were his only manifestations of energy. On bright days they would place him in a little rocking-chair, in some spot where the sun fell warm, and he would rock to and fro for hours, working his slender fingers and mumbling forth his satisfaction at the warmth in the plaintive and unvarying refrain of idiocy. The boy was thus situated when I first saw him.
"I begged Stépan Borovitch of my good friend Dr. Duchat. If that excellent man had not long since died he should have shared in my triumph. I took Stépan to my home and plied the saw and the knife. I could operate on that poor, worthless, useless, hopeless travesty of humanity as fearlessly and as recklessly as upon a dog bought or caught for vivisection. That was a little more than twenty years ago. To-day Stépan Borovitch wields more power than any other man on the face of the earth. In ten years he will be the autocrat of Europe, the master of the world. He never errs; for the machine that reasons beneath his silver skull never makes a mistake."
Comment: That is quite a find! cyborg 140 years ago -- never heard of this! he should have asked this cyborg for help with the title of the story, however. *Everyone* should look the author up -- he is somehow not very well known but you will be amazed about the ideas he had before Wells.
Comment: @kojiro It seems to be used here in a figurative sense, describing Napoleon's intelligence, since the next sentence says that "that little was everything". Using height as a metaphor may just be an unfortunate coincidence.
Comment: "Napoleon Bonaparte towered only a little over the ablest men around him." [What would possess an author to write this?](https://www.thoughtco.com/was-napoleon-bonaparte-short-1221108) Is it satire?
Comment: @kojiro Read in the context of the cited paragraph he is clearly referring to " ... his level of intellect ...".
Answer: Despite the possible identification of The War of the Worlds (1898), I'm going to suggest a slightly later work because I'm not sure that The War of the Worlds satisfies the character requirement.
The SF Encyclopedia entry on "Intelligence" notes:

the first of real importance was The Hampdenshire Wonder (1911; exp vt The Wonder 1917) by J D Beresford, in which the focus of interest is on the feelings of a superintelligent child growing up in a world of what seem to him subnormals.

On the basis of this, I'm going to suggest The Hampdenshire Wonder (1911) (gutenberg link) as the first story featuring a super-intelligent character (Victor Stott) who is actually developed and portrayed in the story.
As a four-and-a-half year old child, Victor reads the entirety of the Oxford English Dictionary (in 2 days) and the Encyclopaedia Britannica in the balance of 3 weeks.  In linear order, absorbing the material wholesale and filling in the gaps in the earliest readings with material from what is read later.  He reaches the encyclopaedia's index, recognizes that it is inferior to his internal cross-indexing and then starts trying to explain all the deficiencies in what he has just read.  "Trying" simply because - knowing the entire vocabulary of English and the technical subjects covered in the encyclopaedia - there are not words for the insights he has drawn.
Comment: @releseabe I can't find a reference at the moment, but I read an essay a couple of decades ago about the problem of writing a truly super-intelligent character; writing one _as a child_ was one of the handful of ways discussed to reasonably approach super-intelligence.  The problem being that no human author has any way of inserting themselves into the consciousness of a true super-intelligence to write it as a viewpoint character.  *Flowers for Algernon* subverts this by having Charlie write a journal that's (in-story) intended to be read by normal humans.
Comment: I note that Odd John's author was influenced by Beresford. Prodigies have always been of interest and so a science fiction story about one who is beyond what humanity has so far produced seems natural. I would guess that there were always kids who spoke really young and exaggerations about them might also be called fiction.
Comment: thanks. whether earliest example or not, never heard of it and i have been reading classic scifi for more than half a century in a family of science fiction readers. i will check it out.
Comment: @DavidW - two other works that take the child route are "Star Bright" and *Children of the Atom*.
Comment: @DavidW: Interesting and perhaps related to the idea that IQ tests were meant to identify students who might, due to being subnormal, need special help whereas at the top end, how could one write a test that reliably identifies people who are extremely able? You might note that some people have unusual digit span recall, etc. That is why I find discussions of Einstein's IQ (which seem to come up a lot) extremely cringey.
Answer: I'm tempted to include Jules Verne's stories here.
20,000 Leagues Under the Sea was first published in 1870. It is rather steampunk , which I consider a subgenre of sci-fi - though I believe the terms steampunk and science fiction did not exist back then.
The story features Pierre Aronnax and Captain Nemo, two huge nerds - the kind that would probably have multiple accounts in Stack Exchange network if they lived nowadays, probably with 100K+ reputation in the more science oriented sites.
Captain Nemo in particular was genius enough to build a futuristic submarine (for 1870's standards). He extracted all the materials he needed to fuel and maintain his submarine from the oceans, which involves huge feats of engineering, chemistry, physics and even biology. On top of that, the fictitious machine could perform better than real life submarines from the late 1900's in terms of maneuverability, endurance and navigation.
To add to Nemo's displays of genius, he also had a fully functional prosthetic hand,* could speak multiple languages (French, English, Latin, German and at least one language spoken in India (unspecified, could be Hindi or Punjabi for example)), collects art, discourses on philosophy and is an accomplished organ player.

Vernes had previously written From the Earth to the Moon, which also features people engineering hard to solve a problem. In it he basically figured a way to take people to the Moon in 1864. However, rather than feats of invention by geniuses in order to make the journey possible, the characters in this book merely used well-known Newtonian physics and scaled a canon up to shoot a manned bullet at the Moon. In my opinion that is not as clever as what Nemo did with his submarine.

* I had initially mentioned Nemo having a prosthetic hand. That was actually something done in a 1997 movie, but in the book Nemo does not have a prosthetic hand.
Comment: stories that include very bright people go all the way back to Greek mythology but that is different than having a character who is notable because of abnormal intellect. Odd John is about someone of superhuman genius who does accomplish things later whereas Nemo and other Verne characters are presented because of what they have already accomplished.
Comment: Hmm. There is nothing about him having a prosthetic arm in my edition which was translated from French at around 1945-50ies.
Comment: @Gnudiff you are right! I was actually remembering a movie, not the original book. I'll fix that.
Answer: Any advance on 1752: Voltaire's Micromégas?
It might even count as the first science fiction story, period.
Micromégas is a child only 450 years old from a planet that orbits Sirius, when he writes a heretical book about the insects on his planet, for which he is banished. He travels the universe to develop his intellect. He meets the secretary of the Academy of Saturn, and together they visit the Earth. Microgmégas is 37 km tall, his friend only 1.8 km tall.
On Earth, they first believe that there is no intelligent life, but eventually find a ship full of philosophers (scientists) returning from an Arctic expedition. They have no difficulty in creating a listening device so that they can hear the voices of the tiny humans, and they learn human language very quickly in order to communicate. They find it hilarious that humans think that the universe was created solely for the benefit of humankind.
Comment: Making a listening device out of fingernail clippings is not the sort of thing that your average, run of the mill, everyday super-intelligent hero does, is it?
Comment: @user14111 being called a heretic and then banished for doing science is something that happens to geniuses.
Comment: I was thinking about that one too, but I wasn't sure Micromégas was **super** intelligent.
Answer: Found an even earlier candidate than my last answer. On p. 186 of Science Fiction: The Early Years by Everett Bleiler, viewable on google books here, there is a synopsis for an 1854 book by C. I. Defontenay, the original French title is Star ou Psi de Cassiopée, histoire merveilleuse de l'un des mondes de l'espace, translated into English as Star (Psi Cassiopeia). The story deals with historical accounts of an alien planet called "Star" in the system of Psi Cassiopeia, records which were found in a meteorite on Earth. Several different types of intelligent beings live on the planet, including "humans" much like ourselves, but also a more intelligent species:

Superior to both humans and repleus are the Nemsedes or Longevouses, who amount to a rational version of culture heroes or demigods. They are very few in number, perhaps only a hundred at their most numerous period, nine-feet tall, blue-haired, sexless and nonreproductive, passionless, intellectually superior to man, and nearly immortal save by accident. They seem to have been a spontaneous creation during the period of the planet's greatest life force, for they all appeared at once and had no parents. The Nemsedes have had a long history in guiding Starian civilization.

I picked up an English translation on kindle and searched for the section on them--their name is here translated as "The Nemsèdes, or Longevites" and the account of them says:

Those people, who were endowed with superior reason, who had lived and reflected so long, were soon regarded with the utmost respect and admiration by all Starians. A great number of them decided to leave the island of Tastot in order to bring to the other peoples the lessons of their experience and wisdom. Among other humans, almost all the Longevites, incapable of physical passions, became enamored of an art or a science. Each of them pursued his preferred science or art without pause through the centuries; their influence on the progress of Star was great, and would have been even greater had it not been for the evils which later decimated the planet's people.

Perhaps "superior reason" is ambiguous--one might make a comparison to Spock on Star Trek, who often is shown having superior ability to make mathematical and scientific deductions along with other types, but probably would not be considerd "super-intelligent".


Sink Smell and Slimy P-Trap

Question: I have a sink which emits an odor from the drain.  I checked the p-trap and there was a pretty nasty buildup of black slime in it.  I'm cleaning that out, but find it strange that just this one drain has this problem.  Another right next to it is fine.  The drain with the problem is the highest drain in the house.  The vent for these drains seems to be fine, but sometimes I do smell the same odor coming from it.  Any ideas on the cause of the slimy buildup in the p-trap?
Comment: Is this two sinks in the same bathroom?  Has the smell always been a problem for this one sink or just this one time?  In this statement, "but sometimes I do smell the same odor coming from it. ", you are referring to the adjacent sink?  Can you post a picture of the P trap.
Comment: Is this the first time this P-trap was cleaned?
Comment: Did you ever get this resolved? If so, please give a check-mark to the answer that helped you the most, or write up your own answer explaining what you did to get it fixed and give yourself a check mark. That will help others with this kind of problem know that this has a resolution and is a good place to look for their answer.
Answer: Being the highest drain might cause a bit more water to be sucked out of the trap causing some odor to get past the remaining water. If it's a bathroom sink, they're prone to gross buildups due to soap scum, toothpaste, shaving cream and whatever. I have a brush from an aquarium that I run down my bathroom drain and trap regularly and it has helped a lot.
Comment: True if a double wide sink with 2 drains 1 usually has a horizontal run to the trap so there is more drain line exposed to air , this could also contribute to the smell.
Comment: Or if, because there are two sinks, that one doesn't get used and the water in the trap evaporates. That happens in our "guest" bathroom tub, I have to remember to run water into it about once every other month or so.

Sink Smell and Slimy P-Trap


I sleep with tzitzis on. Is there any part of the body they shouldn't touch?

Question: I sleep with my tzitzis on. Is there any part of the body the tzitzis should not touch?
Comment: Why would you think there are any limitations on what they can touch? It's one thing when you wear tzitzis by day - there are indeed different opinions and customs (this was once discussed here on m.y) about whether they can be worn directly on the skin; but at night it can't really be helped.
Comment: @alex if you dont wear pants while sleeping, then they can touch your thighs. my understanding was that the tzitzis can only touch those parts of the body that are not usually covered
Comment: I'm not sure that's the case. Consider when people wear their tzitzis tucked into their waistband (some do this always, but even those who usually wear them sticking out, have to tuck them in when they're visiting a cemetery); don't they inevitably touch one's legs then?
Comment: @alex yes they may touch it but that doesnt make it right
Comment: Related: http://judaism.stackexchange.com/questions/1703
Answer: This is sort of an argument from absence, but...
Shulchan Aruch (Orach Chaim 8:16) describes a case where a person sleeps at night wearing his tallis, as to whether he has to recite a berachah on it the next morning. If there were indeed any problem with what parts of the body the tzitzis strings touch, then I would think this would be a logical place for one or more of the commentaries to point it out. Since I haven't found any that do so, I would assume that this is not an issue. (Unless someone else can find sources that talk about this explicitly.)
Comment: לא ראינו אינו ראיה


Allow multiple windows to be opened if the windows don't already exist

Question: I have an application that opens a new window on clicking a button.
There are many buttons to open multiple windows if the windows don't already exist.
All the buttons and url are dynamic, therefore, I use a function to open window with the following codes:
function openwin(url, winname)
{
    var winRef = window[winname];

    if( typeof winRef =='undefined' || winRef.closed)
    {
        winRef = window.open (url, 'winname');
        winRef.focus();
    }
}

But there is problem/bug:
When I click on button A, it opens new window A.
When I click on button B, it "overwrite A" and the window become B.
When I click on button A again, it "overwrite B" and the window become A.
Therefore, I always open one new window.
Answer: winRef = window.open (url, 'winname');

should probably be
window[winname] = window.open (url, winname);


Can I use a NPT fastened device to vacuum or 10^-2 Torr?

Question: I am designing a flange to be use to maintain a pressure of 10-2 Torr for at least 3 months. I am using an o-ring seal from my (device) to the product weldment. I am looking for feedback on using NPT fittings in a vacuum system. I have heard it is unwise. However what I find readily available online is only NPT fitted gauges. I was thinking of using Teflon tape or Loctite. I should add there is a fitting I am using to adapt from NPT to conflat which will be welded.
Answer: Are you going to continue pumping or have intermittent pumping ?  As a engineering professor of sealing once told me "everything leaks, it is a matter of how much". Without continued pumping you will not hold that vacuum. For serious leak tight construction I have mostly seen Swageloc connections. NPT has no metal to metal seal , I think metal/metal will be necessary depending on pump.For a start use as many welds as possible to minimize the threaded connections. American Petroleum Institute (API) pipe dope has metal powders in it to seal threads like NPT for moderate pressures so it does not depend on grease-like stuff ( regular pipe dope) to stop leaks; it may not be easy for you to find.
Answer: TLDR: NPT and vacuum - no problem - use correct type. NPT and o-ring - possible (likely) problem landing o-ring if you use a tapered thread style.
Please post a sketch so we know the size of the thing and how the o-ring relates to your flange.
NPT can be one of a dozen or so thread types. Some make sense and some don't.
The most common NPT type is a tapered thread that has an interference fit on the crest/valley of the mating threads, but has a spiral leak path around the threads. It is also not produced accurate enough to land an o-ring due to differing thread depths cut into different parts. If you are making both mating pieces, this isn't really a problem - you can jig it up so you are consistent. But if you only have control over one of the pieces in the joint, no, go with a non-tapered thread style.
You can use any of several "dry seal" NPT styles intended for fuels which don't have the spiral leak path.
You can use any straight thread type plus your o-ring to accomplish the seal.


Can i ask a question about a problem i no longer face or have access to test?

Question: Is it okay to ask a question about a problem, for which I can't test the answers for, out of general curiosity ? Say I want to ask a question about a problem I would potentially face / I used to face when I was using a Server account, but I no longer have access to the said server account. Can I ask such a question without going out of the boundaries of what is allowed in ask ubuntu ?
Comment: One of the standard close reasons is pretty much "This problem can no longer be reproduced or went away on its own"
Comment: I suppose it depends on the problem. If, for example, some command output or logs are needed for the problem to be assessed and solved but you can't provide them, then there is no point in asking really. If on the other hand you can provide all the information needed, then ask about it. In my opinion (but you've better wait to see what other people say in order for you to decide), you can go ahead and ask the question either way. In the worst case it will be closed as needing more details. You risk of getting some downvotes however.
Answer: In general, no.

You might not be able to answer requests for detail
You might not be able to say what worked (if it's something that needs fixing)

It's hard to think of many examples of questions that can be asked in the abstract that are about an actual system. If you think you have one, be more specific in your question here, or just ask but make it clear that you cannot get more information.
It seems likely that the time spent answering this won't offset the limited reward of answering your curiosity, but also consider that we've no way to police any of these things. Just be conscientious with other people's time.
Comment: I have actually done something along these lines over on U&L: [Mysterious bash instances using a lot of CPU, how can I debug?](https://unix.stackexchange.com/q/81639). I asked the question, but then rebooted and the issue went away, but I was still interested in a solution for next time. I mentioned in the question that I could no longer test and still got some useful answers.
Comment: @Dan no, my question doesn't contradict Oli at all! I posted that as an example of "questions that can be asked in the abstract that are about an actual system". And the approach I had chosen at the time is what Oli is suggesting here for such edge cases: I clearly stated that I can no longer test in the question body, but went ahead and asked since the answers could still be useful.
Comment: I would consider these types of questions "unanswerable hypothetical questions" because you no longer can test, etc.  As such, it would be closed as "no longer reproduced or went away", and you can't really get more information for us when we need to debug things.  So, this is really a "Bad Fit" for the site.  As Oli said.


how to log in to WP if the "Log in" link under Meta is missing

Question: Help Please:  somehow I have stuffed up my WP site, now when I put in my URL and bring up my site there is no  Meta (word) or "log in link" option so I can access my "dashboard", so i cannot get into the back end of my site, can someone please help with directions as to how I can fix this.
Cheers
Cheryl
Comment: http://yoursite.com/wp-admin/ or http://yoursite.com/wp-login.php
Answer: In order to access the administration dashboard on your wordpress site, you can use the /wp-admin URL. For example, on http://example.org, one would use http://example.org/wp-admin to access the administration dashboard.


Determining the number of weak classifiers to use in adaboost without overfitting?

Question: I was thinking by using validation but not quite sure how to go with it. Please list some papers or ideas on how. This is for multi class problem (using one vs all approach). I think each class/category has its own speed in converging to a good strong classifier hence would need different number of weak classifiers to avoid overfitting.
Answer: You could use a hold-out validation set. Break your training data into two pieces, which we'll call the training and validation sets.
Run AdaBoost on the training set.
After each iteration of AdaBoost where a new weak classifier is generated, run the meta-classifier comprised of all currently created weak classifiers on the validation set.
If the performance on the validation set has dropped relative to the performance in the previous iteration, stop and use the meta-classifier from the previous iteration as your final classifier.
Or, if you're worried about local optima, just stop if it is much worse (whatever much means) than the best classifier you've seen so far.
Importantly, this approach will reduce the amount of training data available to you. There will be a trade off between reducing over-fitting (by taking a large, and thus representative, sample for the validation set), and under-fitting (since if your classifiers have less data to work with, they may not be able to learn all the patterns in the set).
Thus, picking the proper size of validation set is non-trivial. Some important considerations though:

If your data has class imbalance (which it will since you're doing 1 v. all classification), your validation and training sets must be selected in a way which preserves something like the desired class balances - if you put all the minority class exemplars in one of the two sets, things aren't going to work.
If data limitations are an issue, and you are considering up/down sampling the classes, then make sure you partition off the validation set before doing so.
Comment: that's a good idea, however i am worried that it will also decrease its performance since we would be using half of the training set provided.. I'll try a smaller validation set...
Comment: That's a good point. I will update the answer to reflect it.
Comment: Also worth considering: cross-validation.


At what point do I start to burn muscle on a calorie deficit diet?

Question: If I'm on a calorie deficit and trying to burn fat, at what point do I start burning muscle instead of fat?  How can I be sure that I'm eating enough to minimize muscle loss, but remain on a calorie deficit so that I can burn fat?
Comment: We don't know your weight/length/BMI or your exercise level, so answering this is really just a shot in the dark. I would tell you to start working out (more), rather than crash yourself. But that entirely depends on your current conditions
Answer: If you are "actually" overweight, meaning that your body considers itself to have excess fat, then you can restrict calories significantly as long as you maintain a healthy lifestyle of exercise and can do so without becoming exhausted or excessively hungry. Some people can reduce intake into the low hundreds (300-500) or even stop eating completely for a period of time and stay active and are healthy, while others have to stay above 1000-1200 to maintain an active lifestyle.
Personally, when I was on a weight loss plan, I was able to go for a period of time eating 3-4 small meals (~500 calories per meal) each week. This only lasted for a few weeks, and during that time I lost an average of a pound each day. During that time, I walked 4-5 miles every day and remained almost as active as normal, with only very slight changes.
Your body is intelligent enough to start burning the stuff it needs least first, and will not start to burn needed/used muscle until you are down to your lowest healthy body fat percentage. If you sit on the couch and don't eat, your body will consider muscle fair game since it isn't being used.
Calorie reduction will also cause dehydration, and the further you reduce, the more severe the dehydration becomes. Be certain to drink all the pure, plain, unaltered water (I stress pure water) that you need. Drink water any time you feel thirsty.
Talk to your doctor before you decide to do any diet, especially any form of extreme calorie reduction. Some doctors refuse to recommend extreme calorie reduction for patients, while others are fine with it, but at least ask about the risk specifically presented to your health, as your doctor will know your health history best.
Be absolutely certain that you do not continue a calorie restrictive diet past the point of reaching your minimum healthy weight, or you will begin burning muscle. The muscle you will burn includes your internal organs such as your heart. Taking muscle from your organs is extremely hazardous to your health and can lead to long term or permanent damage.
Comment: Doesn't this type of strict diat with very low calorie intake bring the metabolism into starvation mode including the following dreaded yoyo effect?


How do you tell whether fluorine goes to axial or equatorial position in iodine dioxide difluoride?

Question: I need to find the $\ce{F-I-F}$ bond angle of $\ce{[IO2F2]^-}$. But the thing is I can put 2 fluorines in the equatorial  or axial positions so I get 3 different answers. I'm guessing they're all three different molecules with slightly different properties and I have to pick out the most stable one. Looking it up on the internet I find the two in axial position which I guess is because the two fluorines pull charge towards themselves and repel the other fluorine so they want to stay far away from each other, am it right?
Comment: Related: [Why does F replace the axial bond in PCl5?](https://chemistry.stackexchange.com/q/18427/16683) (please note also Martin's comments on the question.)
Answer: First, you would need to find out what the bonding situation is at all; i.e. how many bonds of which type will be formed. You can use a scheme like the one I outlined in this answer. This should give you three bonding electron pairs and 14 lone pairs. Since we have more atom connections to make than we have bonding electron pairs, we cannot consider only 2-electron-2-centre bonds as would be the case e.g. in iodate. We must utilise one 4-electron-3-centre bond to be formed from one of the lone pairs and one of the bonding electron pairs. Read more about this type of bond for example in this well-written answer by Ron.
As we are deaing with a single 4e3c bond, iodine will need to be hybridised as $\mathrm{sp^2}$ or less. This means we have one direction (axial) with a $\mathrm p$ type bonding orbital and one (equatorial) with something like $\mathrm{sp^2}$ or similar. We can now use Bent's rule to deduce that fluorine should occupy the axial positions as it is the more electronegative substituent.
We could also have arrived there by realising that oxygen hardly ever takes part in 4e3c bonds. These bonds are basically the incorporation of a central atom into an existing $\ce{X-X}$ bond on a formal basis. Oxygen, however, needs two electrons per atom to reach an octet meaning that there needs to  be another additional bond. This cannot be the case in simple compounds such as $\ce{IO2F2-}$.
Comment: @Vrisk The three atoms (in Ron's case chlorine, phosphorus and chlorine or in this case fluorine, iodine and fluorine) align in a linear fashion. Each contributes a p-type orbital to the bonding situation. Since we have three (atomic) orbitals we are mixing, we must end up with three (molecular) at the end. It is obvious that the highest and lowest must be fully antibonding and fully bonding, respectively. The central orbital must be something different so one in which the two outer orbitals point the same phase to the central atom.
Comment: Since there is no way a p-type orbital can interact in a symmetry-allowed manner towards both sides, there is no contribution by the central atom to the orbital in the middle. However, due to the (weak) bonding interaction of the two terminal aoms, this is a (weakly) bonding orbital. Therefore, we have more bonding electrons than antibonding ones and thus bond formation is favourable.
Comment: Im sorry but I didn't quite get what 4ec3 is, I didn't find the Wikipedia link helpful and I'm not able to find anything much on google. I read somewhere that it's 4 electrons shared by 3 atoms which I don't understand how it's applied here
Comment: @Vrisk Did you also read ron's answer linked in mine? I think he explains it rather well.
Comment: okay I read it again -  P has 5 valence electrons 2 in s and 3 in p, you form 3 sp2 orbitals and you'll have 2 electrons filling that one p orbital then what? How do two chlorines combine with 1 p orbital? How did he get that MO diagram?


I need a poison that in low dose will paralyze temporarily, in high dose will kill

Question: I'm writing a (fictional) story, and at one point the main character is temporarily paralyzed due to poison. Does anyone know of a poison that would, if taken in a very small amount or if it just touched one's lips would paralyze you for a period of time, but if ingested in higher amounts (say, a swallow or two) would kill you? I've considered aconite, but can't find any good sources on if that would actually work for the purpose described above.
Comment: Nice try, Vlad Putin, but it will not work here
Comment: that will be true of most paralytics,  once they paralyze the diaphragm your done.
Comment: Good to have these things clarified at the start
Answer: Botulinum toxin

It prevents the release of the neurotransmitter acetylcholine from axon endings at the neuromuscular junction and thus causes flaccid paralysis.
The toxin is also used commercially in medicine, cosmetics and research.

You have an example of this with all those celebrities who use "botox" to flatten their wrinkles (at the cost of losing facial expressivity due to the paralized muscles)

Botulinum is the most acutely lethal toxin known, with an estimated human median lethal dose (LD50) of 1.3–2.1 ng/kg intravenously or intramuscularly and 10–13 ng/kg when inhaled.

It can be easily found in non properly prepared canned food

as food canning was approaching a billion-dollar-a-year industry, botulism was becoming a public health hazard.

Since preparing a proper dose of botulin can be difficult, you can also use
Fugu:

Fugu can be lethally poisonous due to its tetrodotoxin; therefore, it must be carefully prepared to remove toxic parts and to avoid contaminating the meat.
Fugu contains lethal amounts of the poison tetrodotoxin in its inner organs, especially the liver, the ovaries, eyes, and skin. The poison, a sodium channel blocker, paralyzes the muscles while the victim stays fully conscious. The standard treatment is to support the respiratory and circulatory systems until the poison is metabolized and excreted by the victim's body.
Comment: @a4android, many celebs use botulin, or botox, to paralize facial muscles and flatten wrinkles. About fugu, I have read somewhere that the skill of the cook is in leaving enough toxin in the prepared fish to "tingle" one's mouth but not paralyze them. The same source said there are people actually using self prepared fugu to fall into a self induced paralysis, which they apparently enjoy. Considered the topic I don't feel comfortable in indicating dosage (IANAD).
Comment: I can't work out if botulin causes non-lethal paralysis from your answer. If the respiratory & circulatory systems need supporting to survive tetrodotoxin, this suggest the paralysis it causes may be lethal. Both examples could be improved with more information about their non-lethal and lethal dosages. Otherwise, very good. Nice choices.
Answer: Most neurotoxins will produce results like this, but you would have to be very careful because the difference between a lethal dose and a non-lethal one is generally very small.  They also have a reasonably high risk of causing lasting damage if not used carefully.
Examples of easily available neurotoxins that would probably work include:

Botulinum toxin. Already mentioned in one of the other answers, so I wont' cover the specifics here.  This is a really risky one though, as the median lethal dose is about 2 thousandths of a microgram per kilogram of body weight.
Tetanospasmin.  A toxin produced by the vegetative cells of Clostridium Tetani, the bacteria that causes tetanus.  There's a slightly bigger margin of safety here than with botulinum toxin (the difference in LD50 is about 0.5 thousandths of a microgram).
Saxitoxin. This is the primary toxin responsible for the toxicity of red tides.  It has well characterized behavior in living things, is pretty easy to harvest, and can easily be added to a dish of food (it can often survive cooking), so it's probably your best bet.  Median lethal dose for adult humans is about 5.7 micrograms per kilogram (roughly a single grain of sand for a normal adult male), so you've got a much wider margin of safety here than for the first two.
Tetrodotoxin.  This was also mentioned in one of the other answers, though by reference to one of it's sources (fugu).  It can be found in a wide variety of marine life, so it's pretty easy to find.  It's not quite as dangerous as the first two, and pretty reliably produces paralysis (most marine life that produces it relies on this fact for defense or to hunt).  Median lethal dose for humans is similar to but higher than saxitoxin (I couldn't find conclusive information on an exact value).


Rotate coordinate frame using 2-axis inclinometer angles

Question: How to rotate coordinate frame (transform point or vector coordinates) using angles from 2-axis inclination sensor if both X and Y angles are non-zero?
Comment: What format is the inclinometer output?  Euler angles or Tait–Bryan angles?  And which axis comes first?  And for only 2 axes, if both axes are not 90 degrees, does it even  matter?  I would need these questions answered before attempting your 3(!) questions on this topic.  If you don't know the answer, perhaps this would be a good separate question.
Comment: The inclinometer is GEMAC IS2TK090-C-RL (2 axis XY, 90 degrees). Docs don't mention neither angle types, nor which axis comes first. As I understand it, those angles indicate _simultaneous_ rotation with respect to XY plane. What I can't get is what **projection of a gravitational vector on X/Y axis** means: is it the angle 0) between inertial & inclined Z axis or 1) XY plane and respective X'/Y' axis.
Answer: The output angle of an inclinometer is generally the angle between the axes of the sensor frame and the horizontal plane instead of the Euler angles. You can refer to the following article about how to use these two angles to get the rotation matrix:
Integrated calibration of a 3D attitude sensor in large-scale metrology
It is worth noting that the inclinometer cannot obtain a complete rotation matrix, and may need to cooperate with other sensors


Which enzymes degrade dynorphins and what drugs inhibit these enzymes?

Question: Which enzymes degrade dynorphins and what drugs are there available to inhibit said enzymes?
Answer: This paper was looking at inhibition of dynorphin converting enzymes and their importance. Although they don't seem to know if it is a single enzyme, or if it is multiple enzymes.
This paper looked at bikunin as an endogenous inhibitor of dynorphin convertase in human cerebrospinal fluid.
This paper looked at several inhibitors (some of which are known to irreversibly inhibit other enzymes), like N-peptidyl-O-acyl hydroxylamines and their effects on hCSF-DCE, the enzyme that cleaves dynorphin A, dynorphin B and alpha-neoendorphin to release Leu-enkephalin-Arg6. However, it is known to inhibit serine and cysteine proteinases.
However, I don't see any actual medications that are meant to inhibit Dynorphin enzymes. Instead I found Al-Fayoumi et. al were actually looking to identify stabilized dynorphin A derivatives instead of just inhibition of enzymes.
Comment: Although nicely referenced, a list of articles touching on OP's question is not a suitable answer. The answer should be *supported* by references, a reference list in itself is not an answer.
Comment: I did say at the end of my answer that I hadn't come across any medications that specifically inhibited Dynorphin enzymes @AliceD and pulled from those articles what they had used to inhibit the enzymes. I also noted that hCSF-DCE is the enzyme responsible for cleaving dynorphins.
Comment: Yes I agree that your answer is quite complete and I removed my downvote. I do still believe it is not a well-formulated answer, so I will not upvote.


Why don't ions have one equilibrium potential? (Nernst equation)

Question: I know that equilibrium potentials are dependent on the ratio of ion concentrations inside and outside of the cell and temperature. I also know that the equilibrium potential is reached when there is no net movement of ions across the membrane, i.e. the chemical and electrical gradients are equal. Why don't the ions move until they reach the same ratio of inside and outside concentration every time? For example, why doesn't ion "x" always diffuse until the ratio of inside to outside concentration is 15 to 1? Thanks in advance!
Answer: Good question.  The answer (as I understand it) is that if there were only a single type of permeable ion, then there would be only one equilibrium ratio, and it would depend on the transmembrane potential.
However, in real life, there (a) is usually more than one membrane permeable ion, and more importantly (b) the transmembrane potential is not a fully independent variable but is affected by the transmembrane permeation of all those ions.
Imagine sovling a single instance of the Nernst equation when you know the electrical potential $\Delta \psi$:

$\frac{\Delta G}{F}=\text{ion motive force}=0=-m \Delta \psi+ RT\ln{\frac{[X_{out}]}{[X_{in}]}}$

If you know $\Delta \psi$ (and $R$ and $T$) and you are at equilibrium (so $\Delta G$ is 0), then the ion concentration ratio will always go to the same value, as you suggested in your question.
But now suppose there are many equilibrating ions, say sodium, potassium, protons, and chloride.  And suppose you don't know $\Delta \psi$.  Now, there is a Nernst equation for each species, as well as Gauss's law that $\nabla \centerdot \bf{E} = \frac{\rho}{\epsilon}$.  And probably also total material balances like $V_{out}[X_{out}] + V_{in}[X_{in}] = N_{tot}$ for each ion.   To fully solve the system to determine equilibrium, all equations have to be solved at once!  I hope you can see that (a) doing this is complicated and (b) if parameters like the volume of the cell $V_{in}$ or even more likely the total amount $N_{tot}$ of ions in the system changes for one ion, it could completely change the ratio $\frac{[X_{out}]}{[X_{in}]}$ for other ions.  That's why in general, the ratio is not the same every time.
Comment: Even when there is only one permeable ion, my professors have led me to believe that the equilibrium potential for that one ion is not a constant. Also, the Goldman equation is used when there are multiple ions that are permeable.
Comment: The Goldman equation is a more general case that can be used when ion fluxes are not zero, i.e. the membrane is not at equilibrium.  For equilibrium calculations, the Nernst equation applies.
Comment: Looking at the wiki page for the Goldman equation, I now see that the membrane reaches its reversal potential (net current from all ions is 0) but doesn't necessarily mean that the ions themselves are at equilibrium. Can you see any way for there to be multiple equilibrium potentials for a specific ion when only that ion is permeable?


What is the minimum number of time points recommended for accurate instantaneous phase estimates using the Hilbert transform

Question: I have two time series.  The two series look like they follow the same function, but one appears to lag slightly behind the other.  I would like to determine if there are phase differences between the points in these time series, but each time series is only 4 points long.  Is this enough data to get accurate phase differences using the Hilbert transform?
Comment: Can you elaborate or link to a picture? What properties suggest to you they follow the same function or lag slightly, 4 points seems to small to say this.
Comment: Define "accurate" quantitatively.  Also if you know whether the signals are bandlimited or not?  And within what band?
Answer: Forgive me for not having a numerical answer to the question. But here are a few things to think about. The answer depends on how the Hilbert transform (HT) is implemented. If the HT is implemented using an $N$-point tapped-delay line filter-like block diagram the first and last $N$-1 output samples are incorrect. So in this situation four input times samples is definitely not enough samples to produce useful results.
If HT is implemented by way of a forward FFT, zero the neg-frequency spectral components, and inverse FFT (as is done in Matlab) you have a better chance of computing meaning results. However, in this second implementation the input time sequence must be long enough to contain at least one cycle of all the spectral components of your input signal in order to compute somewhat meaningful results. It seems to me that four times samples is too short to reliably estimate any signal parameters of most real-world (information-carrying) signals.
Comment: Setting one side to zero and leaving the other side is the  same as multiplying it by a filter that has zeros in the negative frequency portion and is unity in the positive frequency -  the impulse response that corresponds to this filter is infinite - therefore time domain wrap around will occur. The advantage in the frequency domain is you don't have to deal with the group delay.
Comment: Because the Hilbert transform has an infinite impulse response, If you implement the Hilbert transform using the FFT you will introduce time-domain wrap around effects, so in essence all your time domain samples will be corrupted due to the periodic wrapping of the infinite impulse response. Essentially it's the same reason you don't implement a brickwall filter in the frequency domain.
Comment: The Sinc function impulse response is sampled as zero in the time domain wrap around distortion only for exactly integer periodic in aperture waveforms. Otherwise, the Sinc is offset, and thus samples as non-zero, wrapping around.  So an exactly 2 cycle sinusoid is a special case.  Zeroing bins in an FFT produces the exact same problems/artifacts for both attempted brick-wall filtering and for trying to create a Hilbert transform. See: http://dsp.stackexchange.com/questions/6220/why-is-it-a-bad-idea-to-filter-by-zeroing-out-fft-bins/6224#6224
Comment: Implementing an HT in the freq domain does not involve any kind of freq-domain multiplication to implement time-domain convolution. Implementing an HT in the freq domain is performed as follows: (1) perform an FFT on a real-valued input sequence; (2) setting the negative-frequency spectral magnitude and phase samples to zero; (3) performing an inverse FFT on the modified spectral samples to produce the desired analytic signal in time domain. No "time-domain wraparound" problems  occur in this case.
Comment: David: I'm thinking of the scenario where in software, for example, we generate a 32-sample cosine sequence containing exactly two sinusoidal cycles. Then we perform a 32-FFT on that sequence and set the 31st spectral sample to zero. Finally, we perform a 32-point inverse FFT on the modified spectral samples. That will produce a complex (analytic) 32-sample time-domain sequence whose real part is a two-cycle cosine sequence and whose imaginary part, a two-cycle sine wave, is the HT of the real part. The final time sequence is not infinite in length and no wrap-around error occurs.
Comment: Richard, I'd have to look at that more carefully.
Answer: The answer depends on the signal to noise ratio and whether the signal is a single sinusoid that is integer periodic in a window that number of samples in length.  Or perhaps a number of pure integer periodic sinusoids that is low enough compared to N/2.
The a-priori bandwidth of the signal would also need to be small enough with respect to the number of samples, otherwise aliasing ambiguity leads to phase ambiguity.
A Hilbert transform doesn't magically add information to frequency estimation methods.  And frequency estimation errors lead to phase estimation errors.
Answer: I would not recommend that, because, 4 points may not describe your signal really well. These 4 points can be coming from anywhere. To experiment with that I wrote the following extremely simple code:
<code>% generate a signal
x = cos(pi/4*(0:99));
y = hilbert(x);
sigphase = (unwrap(angle(y)))';
X = ones(length(sigphase),2);
X(:,2) = (1:length(sigphase))';
beta = X\sigphase;
beta(2)
</code>
beta(2) will be very close to the frequency. If you generate x using:
<code>x = cos(pi/4*(0:3));
</code>
you will immediately see that the frequencies do not match. This is of course a tough one due to the cosine signal, but there might be ambiguous cases, similar to that one.
Why don't you use a running correlation analysis instead?


If an event has a statistical probability of only 50%, is it possible to use a neural network to predict it with more than 50% accuracy?

Question: For example using a neural network to predict a coin toss. Can a trained neural network to predict it with more than 50% accuracy?
Comment: The short answer is "No." :)
Comment: Could you give more details? Do you have any information about the process of the event before it starts that could feasibly be used to make a prediction, as opposed to simply knowing that the event has been observed in the past (or is expected due to its nature) to occur with $p=0.5$? For instance, are sequential events *not* independent (a theoretical coin toss is independent of previous coin tosses)?
Comment: @clementzach True randomness may be a false proposition, since we can't find features that accurately predict it, it's true randomness, and once we find features that accurately predict it, it's no longer true randomness.
Comment: @NeilSlater Knowing more information also does not prove that the additional information is related to the probability of the event occurring, as I know the quality of the dice, the material from which it is made, etc. I put this information into the neural network and it doesn't increase the accuracy either.
Comment: If you're evaluating your neural network on the same set of data used to train the model, you could definitely get higher than 50% "accuracy". But, the accuracy would go down to 50% once evaluated on unseen data if the event is truly random (i.e. truly unrelated to any features fed into the neural network).
Comment: @JoeHuang Yes, I agree. The extent to which an event is "truly random" to an observer doesn't have anything to do with the type of event itself, but it does have to do with the other information an observer has.
Comment: When does the NN predicts the outcome? 1 ms before the coin stops moving? When the coin is in the air? In my hand? in my pocket? These are different levels of uncertainty.
Comment: Using the result of a coin flip as a feature to predict the result the person calling it will say, leads to an event with about 50% probability that you can predict with about 100% probability. It's a trivial example, but it should demonstrate the point.
Answer: This is a question of marginal vs. conditional distribution
The marginal distribution of the coin may be a Bernoulli random variable with 50% probability for either outcome.
However, the conditional distribution of the outcome given information about other factors (e.g. the angle, throw height, ... see other answers) may look entirely different. Provided these features determine the outcome in some way, a neural network can absolutely predict the outcome with more than 50% accuracy.
A neural network could not exceed 50% accuracy, if

The information determining the throw outcome is not available
The function is of a nature that can not be learnt by the neural network
The coin toss is truly random

A coin toss is often used as a casual example of a "truly random" event, so in this sense the answer to your question is "No". In reality however, it is very hard to find any truly random events (at least outside quantum mechanics), which is why random number generation is a big challange and neural networks can predict a lot of things.
Comment: @JoeHuang, another example is the sorts of functions you'd find in modern cryptography. Although they can support some non-linearities, a neural network still relies on at least local smoothness for gradient descent and generalization. Hash or encryption functions, by design, do not have that. (In principle a sufficiently large neural network could encode such a function, just by memorising the mapping, but it wouldn't do any better than a lookup table.)
Comment: This is the best answer, hands down. The question cannot be answered with "Yes" or "No" without knowing the nature of randomness.

I find it misleading to even begin or end any answer with such a definitive summarization, even if it is clarified in the details (which not everybody reads carefully after seeing a simple, bold answer).
Comment: @JoeHuang For example, a neural network with only linear layers can only predict linear functions. (Nobody uses this type of neural network). Or the neural network could be too small for the complexity of the prediction.
Comment: What nature of function  can prevent neural networks from learning?
Comment: What's the logical nature of your bulleted list? Do all these conditions need to be satisfied, or any of them?
Comment: Good point - any of the criteria listed will suffice to prevent the network from learning.
Answer: No.
If there are no patterns, relations or correlations in your data, AI can do nothing to improve what essentially is just guessing.
My last 5 tosses were Heads, Tails, Tails, Heads, Tails. Can you predict the next toss outcome? How would you explain your guess? If you give AI this same data, it cannot do better than just guessing.
The question changes if you have data that is related to the outcome of the coin toss, such as the direction and force the coin was tossed before it lands. In this case, it isn't "an event with a statistical probability of 50%" anymore. If you measured everything perfectly, you could have 99.9% accuracy on what the outcome of the coin toss would be.
AI can only produce accurate results if a super smart human could theoretically also produce accurate results.
Comment: I do agree with the first part (no patterns = guessing), but I don't think the second part is strictly speaking correct. You don't _need_ more types of data (like force or direction), you just _need_ any patterns at all. While I can't say much from your dataset of five throws (neither can AI), if you gave me results of _many_ more of _your_ throw, it might show that you have a slight tendency for heads. Maybe that's the side you intuitively put the coin on your hand and you don't throw with many rotations. Maybe the coin is not perfectly balanced.
Comment: I'm not saying that the probability of a right prediction will be 90% in such case, but it still might be some number above like 50,01% (which is > 50%)
Answer: YES
If you obtain information about the force and angle of the throwers thumb striking the coin at release, that would give insight into how many times the coin would be expected to rotate. Combine this with what faces up when the coin releases, and you should be able to do better than 50/50.
I don't have a firm source (perhaps there is something on Skeptics), but it seems that people have trained themselves to flip coins to reliably land on one of the sides, so there are some features that dictate how the coin rotates.
Really, this is kind of the point of regression. You think some process has a 50/50 chance of the two outcomes, but once you know a bit more (features), you can sharpen that estimate. Formalizing this mathematically involves the conditional vs marginal distribution discussed in the answer by Scriddie.
Comment: this is cherry picking an example. To be more precise, I think OP's example relates more to e.g. a Random Variable $X \sim \mbox{Bernoulli}(0.5)$, in which case a NN _cannot_ predict $x \sim X$ with accuracy (significantly) different to 50%.
Comment: @Dave As you say Dave, this is an issue of statistics. You are assuming the existence of the extra information that you can _condition_ on knowing. Assume this extra information is denoted by $Z$, then you're actually proposing to learn approximate the distribution of $X | Z$, which is a totally different random variable to simply $X$. So, again, referring to my original comment, it depends on what exactly OP is asking. (If this is confusing, perhaps you can ask on the CVSE that you linked to earlier).
Comment: @DavidIreland Maybe, but the whole point of doing a regression model like a neural network is to take a process that seems unpredictable (e.g., flipping a coin) and use related information (e.g., force of the flip) to reliably make better predictions.
Comment: This does not predict **statistical** probability. AI may highlight patterns that imply deviation from pure luck, e.g. a roulette wheel being imbalanced or a person being more likely to spin full circles with the coin, but this is not of statistical significance, rather priorly unknown factors that cause deviations from expected probability.
Comment: @user3819867 That's what regression is: using outside factors to predict something better than you could without that outside factor. If you're unclear about this, you might consider asking for clarification on a statistics website like [Cross Validated Stack Exchange](https://stats.stackexchange.com).
Comment: It seems like your answer to "can a neural network predict a 50/50 outcome with more than 50/50 accuracy?" is "yes, as long as the outcome isn't 50/50"...?
Comment: @Daevin The whole point of using features in a regression is to expose the fact that what appears to be 50/50 is not 50/50 once those features are considered, so there is a sense in which your comment is correct, yes. // This is really a statistics issue, and if it is confusing, I recommend asking about it on the Cross Validated Stack Exchange I linked earlier. It might be worth linking that question in the comments here.
Answer: You need to ask yourself, what is the limiting factor in the accuracy for whatever you are trying to predict.

If the limiting factor is in the quality of the algorithm being
used to calculate the prediction, then perhaps you could find a
better algorithm that would improve the accuracy.
If the limiting factor is in the very nature of the problem itself,
such as a coin flip, then there is no method of calculation that
could improve the accuracy.
Comment: Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer).
Answer: Although the question is a little vague, I'll treat it as a statement about the mapping of inputs and outputs in the underlying random process - no matter what conditions/inputs/features we observe, there is not a consistent mapping from input to output. A statistical probability of 50% suggests in two cases with identical inputs, we may find different outputs. A traditional deterministic neural network cannot do this, as it is really just a mathematical function, which by definition maps every possible input to exactly one output - it is not possible to use the same inputs and get different outputs. Because of this, a deterministic neural network can't achieve more than 50% accuracy in the long run in this case. No matter what set of features is input, there are in reality two possible outcomes, but the neural network can only return one outcome for any particular input. On average, the neural network will return the correct output only half the time - it can't achieve more than 50% accuracy.
Answer: If a neural network was only able to be as reliable as random guessing, they wouldn't be much use!
Let's suppose there's an election on, and the result is finely balanced between the yellow party and the purple party. At a top level, 50% of people will vote for each colour. If you know nothing else about the people, "Who will the next person in the polling station vote for?" is intrinsically an even guess.
It would still be possible to use a neural network (or a decision tree, or a human!) to predict at much better than 50% if you have additional input. For example, if you look at them and can read their apparent wealth, race, gender presentation, or whether they come accompanied or alone, it may then be possible to identify membership of a sub-population which is more likely to vote yellow.
The fundamental limit on performance isn't the baseline 50:50 probability. Instead it is the component which is caused by some inputs (which may but doesn't have to be true randomness) that are simply not available to the network. Suppose for example that there's a 5% chance that someone has been bribed to flip their vote and the network can't know that. In this case it won't get to more than 95% reliable predictions, but can still do much better than 50% with demographic data.