Shulou(Shulou.com)11/24 Report--

Stone scissors and paper is a must-have game at home, but does this seemingly fair probability game have a secret skill to improve the winning rate? Q1. Since we can change the frame of reference, why can't we take the earth as the center of the universe? By dyx

A:

First of all, the earth is the center of the observable universe (correct nonsense). In other words, where you are, the center of the observable universe for you is.

Second, current observations do not support the center of existence of the universe. One view is that the universe is a hyperspherical surface. In three-dimensional space, the universe has no boundaries, but its volume is limited. Analogically to a dimension that is easy for human beings to understand, suppose a two-dimensional creature lives on a sphere, and the sphere we see is their "universe". They will find that their universe is boundless, but its area is limited. They can even observe the expansion of the universe as we do-imagine a balloon that is gradually blown up and the distance between any two points on the sphere is getting larger. In addition, the center of the spherical universe is at the center of the sphere, not on the sphere-there is no center of the universe. Of course, this example is only a superficial schematic analogy and simplification of our real cosmology.

Finally, the arbitrariness of the selection of the frame of reference has nothing to do with "a certain point can be the center of an object". For example, the following disk, assuming that its rotation axis is the center O, through the transformation of the frame of reference, we can think that each point on the disk moves in a circle relative to point A, but the center of the disk is still point O.

By is a Tibetan fanatic.

Q.E.D.

Q2. How to improve the winning rate of stone scissors paper? By Personna

A:

We often disagree about some things, such as who will take out the garbage and pick up the water with takeout, so we often solve it by guessing fists. So let's talk about ways to improve the winning rate this time.

If two people punch at random, then the winning rate on both sides is 1 beat 3, which is a completely fair game. But people's mind is easily swayed by other factors, not completely random punches, so this is actually transformed into a psychological problem.

Researchers at Zhejiang University have recruited 360 students to carry out the experiment of rock scissors and paper. The results show that people have about 36% probability to produce rock, 32% probability to produce scissors, and 33% probability to produce paper. The winner is more likely to use the last action, while the loser is more likely to use the action to restrain the winner's last result. [1]

Therefore, according to the conclusion of the paper, we can draw two strategies.

Playing first in the opening game will increase the winning rate.

If you win, you will lose the action of the opponent in the last game, and if you lose, the action of the other side will be restrained in the next game.

Furthermore, we can also use words to control our minds, such as announcing in advance what the other person is going to do. If it is announced that the other party is about to produce a rock, then if the other party does not believe it, they will think that we will produce scissors or paper, then we will choose the safe scissors (draw or win). At this time, we will win if the other party really believes that we are going to produce stone and choose paper, then we can continue the game in accordance with the second strategy above.

You can even analyze his boxing habits and find countermeasures by collecting a large number of stone scissors and paper games between friends and others. (what is big data's game, tactical leaning back)

Director Bi also made an interesting video in which he discussed the issue in more detail [2].

[1] Wang, Z., Xu, B. & Zhou, HJ. Social cycling and conditional responses in the Rock-Paper-Scissors game. Sci Rep 4, 5830 (2014). Https://doi.org/10.1038/srep05830

[2] remember two simple tips to ensure that your winning rate of rock scissors is more than 80%! -Director Bi

By Minke

Q.E.D.

Q3. Why is the sunrise and sunset of a day not symmetrical about 12:00? By preserved egg porridge

A:

There are three main reasons. First, because the time zone you use is not strictly set according to your longitude. For example, Beijing is in longitude 116 °east, but the east eight districts adopted are based on longitude 120 °east. The difference of 4 °between them will produce a deviation of 16 minutes. This effect is very simple, purely man-made, but the latter two reasons are complicated.

Second, because the earth's orbit is elliptical, the distribution of rotation speed in the whole year is not uniform. For example, at aphelion in early July, the revolution is slow, and at perihelion in early January, the revolution is fast. As a result, the time of each true solar day (that is, the interval at which the sun moves to the same longitude relative to the earth) is different, with longer than 24 hours at the beginning of July and less than 24 hours at the beginning of January, but the average solar day for the year is still 24 hours.

Because of the revolution, the earth actually rotates more than one circle in a day because the direction of the earth's axis tilting relative to the sun is changing. In order to make it easier to understand, we first think that the orbit of the earth around the sun is a positive circle, without considering the earth's rotation, so that the direct point of the sun will leave a circular track from west to east on the earth's surface. When the Summer Solstice or the Winter Solstice, the tilt direction of the earth's axis is parallel to the sun-earth line, and the projection sweeps across the earth's surface in the east-west direction, which increases the equivalent rotation velocity of the sun; in the Spring Equinox or the Autumn Equinox, the tilt direction of the earth axis is perpendicular to the sun-earth line. the north-south component of the velocity projected across the earth's surface reaches the maximum, which reduces the equivalent rotation speed of the sun.

The latter two reasons are reflected in the direct solar point, and you will find that when you fix a certain solar time (such as 4:44 Universal Standard time), the direct point will move not only north-south, but also east-west.

Left: look at the direct point from the perspective of the sun; right: fixed the earth's perspective at the direct point of view | Image source [1] from another angle, if you take a picture of the sky at 12:00 at noon somewhere on the earth every day, a year later, you will get a map of the noon trajectory of the sun for the whole year. From the picture, we can see that the sun changes not only in height, but also in azimuth, which is combined into a "figure 8" track, which has a special name-analemma.

Note that this is looking toward the sky, so left east, right west | the difference between true solar time and mean solar time in Stellarium simulation is astronomically called "mean time difference". After quantitative calculation [2], the following figure can be drawn. On the upper left is the time difference caused by the elliptical orbit. From early October (about 275 days) to early April next year (about 93 days), the speed is faster than the average, so the sun is gradually eastward, and the mean time difference is gradually negative. The upper right is the time difference caused by the inclined earth axis. in spring and autumn, the speed of the direct point in the east-west direction is slower than the average speed, the solar direct point gradually deviates to the west, and the mean time difference becomes positive gradually; in summer and winter, the speed of the direct point in the east-west direction is faster than the average speed, and the solar direct point gradually tends to the east, and the mean time difference gradually becomes negative. The lower left is a combination of the two effects. The lower right is to consider the north-south movement of the direct point to get the daily trail.

Mean time difference and daily trail | the image point of the image source [3]. If only the elliptical orbit is considered, the direct point trajectory will be an ellipse, and if only the rotation of the inclined axis is taken into account, the direct point trajectory will be an equal size figure 8. The combination of the two is the figure 8 we see on earth.

The two effects are combined into an unequal figure of 8. [4] there is a similar phenomenon on other planets in the solar system, such as ellipses on Jupiter and Venus, and water droplets on Saturn and Mars.

Daily movements on Mars [5] now you can see why a true solar day is not symmetrical about 12:00 in the mean time, in addition to the difference between the local time and the time zone used, but also because the sun dances in the sky every year.

Reference:

[1] Earth and Sun-Bartosz Ciechanowski

[2] Why does the sun dance "figure 8"? -Wang Yun Maigo

[3] Equation of time

[4] The solar analemma-Luxorion

[5] Japanese travel book-encyclopedia knowledge of Chinese

By sheep herding

Q.E.D.

Q4. What is the principle of car seat belt? Why does the pulling speed get stuck if it is too fast? By, come and blow the pot.

A:

In the car seat belt structure, the seat belt is connected to the retractor, which allows the passenger's upper body to move freely, while the passenger's upper body movement can be restricted in the event of a collision. In the winder, the spool wraps the ribbon, the spiral spring provides the rotating force or torque for the reel, pulls the ribbon outward, the spool rotates counterclockwise, and the spring recovers the deformation, producing a reverse force, and after loosening the ribbon, the ribbon is re-involved in the spool, so that the upper body of the passenger can move freely with the full belt.

Figure 1 shows the winder mechanism on the right and the locking scheme triggered when the car suddenly slows down on the left. Image source: reference 1 and the winder has a locking device, which can provide locking protection in the event of a car collision and prevent the passenger from moving. There are generally two kinds of locking devices: the locking triggered by the motion of the car, and the core component is the weighted pendulum. When the car stops suddenly, the inertia makes the pendulum swing forward, the pawl at the other end of the pendulum moves, and the toothed ratchet of the spool is stuck. Prevent the spool from continuing to rotate counterclockwise, only after the end of the collision clockwise rotation can be separated. The second scheme is locked after jerking the ribbon mentioned in the title. The activation of the locking depends on the speed at which the spool rotates when pulling the belt. The core element is a weighting lever installed on the spool. When the spool rotates slowly, the force of the spring will fix it, while when the ribbon rotates quickly, the centrifugal force will move the weighted end of the lever outward, while the elongated lever will push the cam on the retractor shell. The cam is connected to the rotating ratchet by a sliding pin, and when the cam moves to the left, the pin moves along the groove in the pawl, and the pawl is pulled into the rotating ratchet gear connected to the spool, so that the pawl is stuck in the tooth, thereby preventing the counterclockwise rotation of the spool.

Figure 2 depends on the locking scheme excited by the rotation speed of the spool. The first picture shows that when the spool rotates slowly, the spring presses the weight lever, the second picture shows the lever protruding outward when it rotates rapidly, and the third picture shows the extended lever pushing the black-gray cam to move. Picture source: ref. 1 Ref.

[1] How seatbelts work

[2] Seat belt

By jita

Q.E.D.

Why can't sodium hydroxide be obtained by Q5 evaporating sodium carbonate solution? By NADH

A:

We solve this problem within the scope of our high school knowledge.

There is such an equilibrium in sodium carbonate solution, and the equilibrium constant is about. When the solution is gradually evaporated, the solution is slightly alkaline, and the concentrations of bicarbonate and hydroxide are basically the same. according to the equilibrium constant of equilibrium constant, it can be obtained that for any concentration of sodium carbonate solution, the concentration of carbonic acid is basically fixed, about. According to the equilibrium constant of the conversion between carbon dioxide and carbonic acid, the concentration of dissolved carbon dioxide is about 600 times that of carbonic acid. The solubility of carbon dioxide at atmospheric pressure 25 ℃ is about 2.6 g / L. So carbon dioxide doesn't escape. Since there is no loss of carbon, if you push it back, the first-order hydrolysis equilibrium of the carbonate ion (the top equation) will move toward the carbonate, so the product will eventually be sodium carbonate rather than sodium hydroxide.

By is a Tibetan fanatic.

Q.E.D.

Q6. Why doesn't the moon have an atmosphere? by a star

A:

First of all, the moon's gravity is so weak that it is easy for the gas to escape. We know that there is a corresponding escape velocity for each particular celestial body, which refers to the minimum velocity that a non-powered object needs to escape from the gravitational potential field of a massive celestial body (that is, reaching infinity). According to the conservation of mechanical energy, we have, we can get the escape velocity. For the earth, the escape velocity is about 11.2km / s. For the moon, the escape velocity is about 2.37km / s. On the other hand, air molecules are in constant thermal motion, and their velocity distribution accords with Maxwell's velocity distribution law.

At 300K, the average velocity of air molecules is 461m / s. On Earth, the probability of its rate exceeding the escape velocity is extremely small, so the earth can retain its atmosphere without escaping. But on the moon, the rate of gas molecules is likely to exceed its escape velocity, so it is difficult for the moon to retain its atmosphere. Here we take the nitrogen and helium that may exist on the earth and the moon as examples.

Probability density diagram of molecular velocity distribution of helium gas at 300K

The probability density diagram of nitrogen molecular velocity distribution at 300K shows that for helium molecules, the probability that the velocity is less than the lunar escape velocity is 0.971, and the probability of more than 2370m / s is 0.029. This means that 2.9% of helium molecules escape from the moon all the time. For nitrogen molecules, the velocity is mostly in the range of 0-2000m / s, which is close to the lunar escape velocity of 2370m / s. Considering the randomness of thermal motion, nitrogen molecules have a considerable probability of escaping from the moon over the escape velocity under long-term thermal motion. However, the escape velocity 11.2km / s of the earth is much larger than that of nitrogen, and the possibility of escape is very low even on the time scale of 100 million years. Second, the moon has no magnetic field to protect the atmosphere from damage by high-energy particles such as the solar wind.

In addition, whether there is an atmosphere on the moon remains to be studied. The European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA) solar and heliospheric probe program discovered in 2019 that the Earth's corona extends to 630,000 kilometers away [1], so the moon is also included in such an atmospheric spill layer of thin hydrogen atoms. Due to the presence of the corona, there are still some gas molecules on the surface of the moon, but its density is extremely thin, about one-third of the earth's atmosphere. In addition, the bombardment of lunar soil by high-energy ions such as the solar wind and the moon's geological activities will also release gas molecules into the outer space of the moon. From the above calculation of the velocity distribution law, we can also see that the heavier the gas molecule, the lower the thermal motion rate, so it is more likely that it cannot escape, and it is possible to retain the rarefied atmosphere on the moon. Therefore, it does not seem to be quite right to say that the lunar surface is a complete vacuum.

References:

[1] Baliukin I ·Bertaux J L, Q é merais E ·et al. SWAN/SOHO Lyman- α mapping: the Hydrogen Geocorona Extends Well Beyond TheMoon [J]. Journal of Geophysical Research: Space Physics, 2019.

By single male youth

Q.E.D.

Q7. Why do you ride faster with narrower tires? By Anonymous

A:

There is no point in answering this question and putting aside the conditions to discuss it. Different cycling roads and different types of bicycles all have an impact on the conclusion of this problem. On rough roads, people usually ride mountain bikes rather than road bikes; on highways, many cyclists ride road bikes so fast that they can easily get rid of mountain bikes. Mountain bikes and road bikes are not the same type of bicycles, and it is meaningless to compare them in terms of tire width. Therefore, under the same bicycle frame and the same road condition, change the tires of different widths to test.

In this case, the problem of wide and narrow tires has puzzled people for a long time, in fact, wide tires are not slow. On the smooth surface, the tire deformation decreases with the increase of air pressure, thus the resistance decreases; on the rough real road, the narrow tire with higher air pressure will bring stronger vibration, produce greater deformation and absorb more energy. Often faster cars produce more vibration, while narrower tires give people the illusion that they are faster, but there is no obvious difference in speed, just a sensory illusion. The increase of tire width will increase some wind resistance, but in the process of riding, most of the wind resistance comes from the contact between the human body and the wind, and the increased area of the tire can be ignored. The increase of tire width increases the weight of tire material, and the difference may be smaller than expected. The softness of the tires is also a factor affecting speed. Soft tires can reduce vibration and consume less energy.

Therefore, it is not that the narrower the tire, the faster the ride, the tire will only affect the feeling of cycling, the narrower tire can achieve better flexibility and acceleration, while the wider tire has excellent turning and gripping ability, it can also drive fast when the road is rough.

Reference:

[1] Myths Debunked: Wide Tires Are NOT Slower

[2] Why narrow tires FEEL faster

By jita

Q.E.D.

Q8. Why can't you help but shake when you hear the music with emotion? By Anonymous

A:

This question may more belong to the category of psychology, although many articles have done related research, but the results are still conjecture.

First of all, we need to understand that listening to music increases the flow of blood to the areas of the brain that generate and control emotions, and then the areas of the brain that are specifically responsible for processing emotions and controlling memory begin to work. We call it the limbic system (limbic system), which works by affecting the endocrine system and the autonomic nervous system. Its structure and interaction areas are involved in motivation, emotion, learning and memory.

The red part is the limbic system of the brain (including the limbic lobe). [1] the response we make when we hear a particular piece of music is strongly regulated by dopamine from the limbic system. When the brain is familiar with a particular song, the body may release dopamine when it hears the first few notes of the song.

I believe that in the traditional impression, dopamine is usually described as the main chemical of happiness. But the current scientific view is that dopamine has a function called motivational saliency (motivational salience), which means that it senses the motivation that the organism has already produced, determines whether it is desirable or disgusted, and then sends a regulatory signal, which in turn feeds back and regulates the body's behavior in a direction that is close to or away from the result. That's why we get more and more upbeat when we hear cheerful songs, and get more and more sad when the midnight net suppresses the clouds.

In addition, related studies have also explored the relationship between music characteristics such as rhythm and timbre (pulse clarity and spectrum flux) and the movement characteristics of different body parts when listening to music. The conclusions of the experiment are as follows: when music contains rhythms that are easy to perceive clearly, listeners will use more different types of body motion to participate in feedback, while low-frequency (50-100Hz) spectrum flux is positively correlated with head speed; high-frequency (6400-12800Hz) flux is related to head and hand speed and hand distance movement; percussion music is related to shoulder swing.

After understanding the above, I believe readers will understand why most people, like the respondents, unconsciously swing to the rhythm in live or music festivals, because the songs they listen to cover elements such as low-frequency spectrum flux (bass guitar), high-frequency spectrum flux (tread and cymbals), percussion (drums) and so on, and the music beat is mostly strong and obvious.

Finally, a song "do you want to dance" starts a happy weekend with the sun of Q3.

Reference:

[1] Limbic system

[2] Dopamine

[3] Burger B, Thompson MR, Luck G, Saarikallio S, Toiviainen P. Influences of rhythm- and timbre-related musical features on characteristics of music-induced movement. Front Psychol. 2013 Apr 1210 418.

By 17

Q.E.D.

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: Frions

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