“42” as an answer to five fundamental questions of science

While we still don't know the question itself, we do know that the answer to life, the universe, and everything else is “42.” And here are 5 possible questions.

One of the funniest stories in all of science fiction is Douglas Adams's The Hitchhiker's Guide to the Galaxy, in which a supercomputer is tasked with finding “the answer.” Ostensibly designed to answer “the ultimate question about life, the universe, and everything,” the computer spends 7.5 million years calculating the answer and finally spits out the answer: 42. Only when the answer is finally revealed, no one can remember what, in fact, the “main question” was. This is another example of the fact that you should not be so obsessed with the idea of getting to your goal that you initially lose sight of the whole point of the journey – then achieving it will no longer matter,

Fortunately for us, there are a number of possible candidate questions that we can use in hindsight, since they may indeed be the ultimate question – because we know that the answer to these questions is indeed “42”. Could any of these options be what the supercomputer was asking when it came to uncovering the answer to “the ultimate question about life, the universe and everything”? While no one can be sure, even in the fictional world of Douglas Adams, here are five possible questions that are among the most fascinating. The answer to each of them is indeed “42”, and perhaps one of them will seem really exciting to you.

When photographed from an airplane, direct sunlight falling on a “wall of water droplets” formed by rain clouds can cause not only a primary rainbow, but also a secondary one, forming a circular double rainbow. A primary rainbow, which occurs when a light source shines on drops of water, always forms an arc of 42 degrees, offset from the light source that creates it. The secondary rainbow is visible above it, offset to a larger angle. An angle of 42 degrees is the universal angle for a rainbow created in the air by droplets of fresh water.

How many degrees from the Sun (or any light source) is the rainbow displaced?

There are many ways to create a rainbow: it is generated by raindrops, waterfalls, garden hoses, fog and splashes from reservoirs. However, they all have several common features. All of them are associated with light reflected from water droplets. They all appear in the opposite direction to the light source. And all of them – unless they are created from drops of fresh water – have a peak intensity distributed in an arc that is actually part of a full circle, offset 42° from the direction of the light source.

All primary rainbows you've ever seen have the same arc angle. If a rainbow is created by the Sun, then by looking in the direction opposite to the direction of the Sun's movement and finding a circle (or part of a circle) offset from this direction by 42°, you will be able to see it. The reason is simple physics: light behaves like a beam, the speed of light in water is different from the speed of light in air, and when light enters or exits a medium, it always refracts in a predictable way, determined by the angle of incidence at the interface between water and air.

When light passes from a vacuum (or air) into a drop of water, it is first refracted, then reflected from the inside of it, and finally refracted as it exits back into the vacuum (or air). The angle that incoming light makes with outgoing light is always 42 degrees, which explains why a rainbow always bends at the same angle from the sun's rays.

When light passes from air to water, different waves are refracted at different angles, causing colors to scatter. When light hits the inside of a water drop (we're fairly confident that all drops are perfectly spherical), it bounces off at a known, predictable angle. And when it exits back into the air, each wavelength leaves at a specific angle offset from the original: from just under 41° to just under 43° in the visible light spectrum, with peak intensity at 42°.

Any planet that has a thin atmosphere transparent to visible light, in which the speed of light is close to the speed of light in a vacuum, and in which drops of pure water are present, will produce the same rainbow, deflected at an angle of 42°. However
this angle will not be truly universal: if the atmosphere has a negligible index of refraction, if the drops are not spherical but elliptical, if they are made of salt water rather than fresh, if they are made of a different substance, or if the species of creatures observing a rainbow , does not see the same wavelengths of light as we do, then the rainbow may appear from a completely different angle.

Perhaps these limitations mean we should consider another candidate for the top question.

These diagrams, known as Young diagrams, show how different numbers can be divided mathematically. (Partitions for numbers 1 through 8 are shown here.) For the number 1, there is 1 way to partition (1); for 2 - 2 (2, 1+1); for 3 there is 3 (1+1+1, 1+2, 3), but for 4 there is 5, for 5 there is 7, etc. Going further down the ladder, there are exactly 42 unique ways to divide the number 10. — These diagrams, known as Young diagrams, show how different numbers can be divided mathematically. (Partitions for numbers 1 through 8 are shown here.) For the number 1, there is 1 way to partition (1); for 2 – 2 (2, 1+1); for 3 there is 3 (1+1+1, 1+2, 3), but for 4 there is 5, for 5 there is 7, etc. Going further down the ladder, there are exactly 42 unique ways to divide the number 10.

How many ways can you divide the number 10?

It's easy to come up with different ways to divide any number. For example, if you have three oranges and two people, you could give all three to person 1, all three to person 2, one to person 1 and two to person 2, or 1.5 to each of the two people. However, in mathematics, partitioning has a very special meaning: how many unique ways can you add positive integers to get a certain number? Positive integers mean that no one can get a zero or a fractional number; unique means that the option “2 and 1” is the same as the option “1 and 2”.

As an example of partitioning, there are 7 ways to divide the number 5:

1 + 1 + 1 + 1 + 1,
1 + 1 + 1 + 2,
1 + 1 + 3,
1 + 2 + 2,
1 + 4,
2 + 3,
5.

For the number 10, with all the variety of ways to perform it, there are a total of 42 unique ways. Surprisingly, this is not the only connection between 10 and 42, since 10 can be written as 2¹ + 2³, and 42 can be written as 2¹ + 2³ + 2⁵. If we were to write these numbers in binary, then “10” would become 1010, and “42” would become 101010. These numbers and these relationships play an important role in both mathematics and physics (in particular, group theory), Moreover, 42 has some amazing properties that are completely independent of any measurable physical phenomena.

Equation 1 = 1/a + 1/b + 1/c + 1/d has only a few unique solutions if a, b, c, and d are different positive integers. The largest number for which there is a solution to this equation, surprisingly, is the number 42.

What is the largest integer whose reciprocal coefficient, together with three other unique inverse coefficients of integers, adds up to 1?

Perhaps the universe, as some have suggested, is indeed governed by mathematical relationships at a basic level, and these relationships underlie the physical laws of reality. For those who think this might be the case, here is a mathematical puzzle:

Can you find four positive integers, a, b, c and d, where (1/a) + (1/b) + (1/c) + (1/d) = 1?

Under some assumptions this is easy to do. For example, if a, b, c and d are equal to 4, then this is very simple, since ¼ + ¼ + ¼ + ¼ = 1. If we assume that at least some of the numbers (a, b, c, d) can be are equal to each other, then there are many possible solutions:

a=2, b=4, c=d=8;
a=b=3, c=4, d=12;
a=2, b=c=d=6;

and so on.

But if you insist that all four of these numbers must be different from each other, then there are very few unique solutions. You can even find the largest number that will fit the given equation.

And what is this number? 42.

If we take a=2, b=3, c=7 and d=42, then the equation will be obtained. Interestingly, this is not the only connection between these four numbers, since 2, 3 and 7 are simple coefficients of 42: 42 = 2 × 3 × 7. Even in a purely mathematical sense, 42 has truly amazing properties.

The European Southern Observatory tracked the positions and orbits of 14,000 stars near the Sun for 15 years, reconstructing their orbital movements with the Sun over the past 250,000,000 years—the time required to complete approximately 1 galactic year. The position of the galactic center does not change relative to the movement of the stars around it, and the orbit of our Sun is elliptical rather than perfectly circular.

How many times will the Sun pass through the orbit of the Milky Way before, as a result of catastrophic transformations, it turns into a red giant?

This is one of the funniest facts about our solar system, where the planets revolve around the Sun, and the Sun, like all stars, revolves around the center of the Milky Way. Like all stars, the Sun has a limited amount of time during which it will live, and various milestones mark its critical transitions. It took tens of millions of years for the protostellar nebula from which our solar system emerged to form the Sun, which officially became a star when nuclear fusion of hydrogen into helium began at its core.

The Sun will then move forward for billions of years until its core runs out of hydrogen fuel, at which point it will begin to swell into a red giant, burning hydrogen in its shell until the helium core ignites. During this transformation phase, the star will undoubtedly engulf Mercury and Venus, and it is likely (but not certain) that the Earth will too. Icy worlds such as Triton, Pluto and most Kuiper Belt objects sublimate almost completely. This red giant phase will last hundreds of millions of years while the helium burns out completely. At this point, the Sun will blow off its outer layers and die, giving birth to a planetary nebula and a white dwarf.

When the Sun becomes a true red giant, it will probably swallow or consume the Earth, and will certainly fry it greatly. The outer layers of the Sun will increase in diameter by more than 100 times, but the exact details of its evolution and how these changes will affect the orbits of the planets are still uncertain. Mercury and Venus will definitely be consumed by the Sun, but the Earth will be very close to the border between survival and absorption.

However, despite all these changes, the Sun and our solar system will continue to orbit the center of the Milky Way, completing a full rotation every ~250 million years or so. The time to return to the starting point is called a galactic year and has an error of ~10% relative to how long it will actually take. Meanwhile, if we talk about stellar evolution, we are quite confident that the Sun will exist for approximately 10-12 billion years from the moment nuclear fusion begins in its core until the beginning of the red giant phase, towards which we are now a little over 4.5 billion years.

So, how many galactic years will it take for the Sun (and Earth) before the Sun turns into a red giant and planet Earth is (most likely) completely destroyed?

Although reasonable estimates typically range from 40 to 45—largely due to the ~10% uncertainty about the Sun's orbital speed around the center of the Milky Way—42 is an answer that agrees extremely well with the best data we have. It may yet prove to be an accurate answer to this question, although more precise data will be needed to know for sure.

However, this is an earthly point of view, and perhaps we should look to the larger Universe to consider an even grander question.

The European Space Agency's Gaia spacecraft has mapped the three-dimensional positions and positions of more than a billion stars in our Milky Way galaxy - the most ever. The ability to measure stellar parallax, or how the actual (as opposed to apparent) position of a star changes over the course of a calendar year, is greatly aided by superior instrumentation, a large aperture size, Gaia's location in space, and the development of photography and computer determination of the relative displacement of stars. — The European Space Agency's Gaia spacecraft has mapped the three-dimensional positions and positions of more than a billion stars in our Milky Way galaxy – the most ever. The ability to measure stellar parallax, or how the actual (as opposed to apparent) position of a star changes over the course of a calendar year, is greatly aided by superior instrumentation, a large aperture size, Gaia's location in space, and the development of photography and computer determination of the relative displacement of stars.

How fast is the Universe expanding today?

We exist in the Universe exactly 13.8 billion years after the earliest stages of the hot Big Bang began. Throughout cosmic time, the Universe expanded and cooled, and therefore became less dense. In an expanding Universe, the rate of expansion is determined by the density of all the different forms of energy combined, so in an expanding Universe filled with matter and radiation, the expansion inevitably slows down over time.

The rate of expansion today is slower than at any time in the past and continues to slow gradually. If we wait long enough, the density of matter and radiation will drop to zero, leaving only dark energy—the energy inherent in space itself. By tradition (and for no other reason) we usually report the rate of expansion as the speed (how fast something is moving) per unit distance (depending on how far it is from us): in units of kilometers per second, in megaparsecs.

This graph shows the 1550 supernovae included in the Pantheon+ analysis, plotted as a function of their magnitude relative to redshift. Supernova data for many decades (since 1998) has indicated that the Universe is expanding in a special way that requires something beyond matter, radiation, and/or spatial curvature: a new form of energy that drives the expansion, known as dark energy. All supernovae lie along the line predicted by our standard model of cosmology, with even the highest frequency and most distant Type Ia supernovae following this simple relationship.

In these units, we have two classes of measurements that give conflicting values: measurements based on relics imprinted from early times, such as CMB fluctuations or clustering of galaxies in large-scale structure, and measurements obtained from individual sources in late cosmic times. such as supernovae or gravitational lenses. The first set of measurements gives a value of 67-68 km/s/Mpc, and the second – 73-74 km/s/Mpc. Finding a solution to this puzzle—that is, which group of measurements is actually correct and why—is one of the biggest challenges in modern cosmology.

But if the first group is right, then perhaps the answer to the question of how fast the Universe is expanding is indeed 42.

This is because we must remember this fact: Douglas Adams was writing in 20th century England, where distances are measured in miles, not kilometers! If we convert kilometers to miles, then the first value of the expansion rate, which was 67-68 km/s/Mpc, becomes 42 miles/s/Mpc, which can easily be considered the answer to the biggest question in all of space: how fast does it expand? Universe right now? Although more scientific research will be needed to truly solve this cosmic mystery, “42” is a very possible and even most likely answer.

A number of different studies that have attempted to measure the expansion rate of the Universe, and their results, highlighted in color. Note the significant discrepancy between the results obtained for the early (top two) and late (other) times, with the error bars being significantly larger for each of the late times. Although these two classes of measurements produce inconsistent results, no one knows why the Universe appears to be expanding differently depending on the method used to measure expansion.

In general, there are many questions to which the answer is clearly “42”, but only a few of them are of fundamental, universal or cosmic significance. If this is truly the answer to the ultimate question about life, the universe, and everything else, we have a responsibility to try to understand what that question might be. From mathematics to physics, five vital questions arise, the answer to which can rightfully be 42.

A rainbow always appears offset at an angle of 42° relative to the light source that creates it.
The number 10 can be divided mathematically in exactly 42 different ways.
42 is the largest number whose reciprocal, when added to three other unique positive integers, equals exactly 1.
42 is the number of galactic years that the Sun-Earth system will live before its destruction.
42 is the rate of expansion of the entire Universe in miles per second per megaparsec.

It turns out that “42” may actually be the answer to the biggest question about life, the universe and everything. Now we have to find out what this annoying main question is!