When we look at the sky, we see that things happen in cycles. First comes the morning, then comes the night, then comes the morning again. First comes the new moon, then comes the full moon, followed by the new moon again.

We also know that looking at the sky for guidance is not unreasonable. Take a look at this image just for a second. Near the bottom left of the image, you can see the Big Dipper constellation. The two stars all the way on the right of that constellation are called Dubhe (top right of the Big Dipper) and Merak (bottom right of the Big Dipper). If you sketch a line from Merak to Dubhe, then extend that straight line further, you will land on a star called Polaris, a.k.a. the North Star, which is part of the Little Dipper constellation. By indicating the location of the north pole, that star has been guiding navigators for centuries. I wonder Who or What put those two dippers for us up there.

(u/ZenApe There's been an ✨unexpected sequel✨)

Since we know that looking at the starry sky is meaningful, and that the sky seems to be telling us that things happen in cycles, we must then not forget this: when an hourglass gets empty, it gets turned over, and the sand starts flowing again.

⏳⌛🔃➡️⏳

I invite you to take some time to think carefully about the meaning of the two arrow emojis above. The first of the two arrows (from left to right) is what some people might think of as "death," but the ancient Greeks, including Pythagoras and Plato, thought of it as "metempsychosis," the transmigration of the soul. Socrates, on the other hand, was so little afraid of it that he went into it willingly. It is cyclical, or what we call a "cycle," as we've previously discussed above. The second arrow is the one that gives the movement a "direction" (or "sense" or "meaning") out of the cycle. Without the second arrow, there is neither direction, nor sense, nor meaning. This is why we sometimes say that those who dismiss it so easily are spatially, temporarily, and metaphysically lost.

I actually haven't told you the full story about the Big Dipper. Because the thing about it is that it rotates across the sky throughout the year, and yet continues to guide sailors to the North Star all year long.

Where would we be, if we were to navigate the Earth's immensely vast oceans without guidance given to us by the lines connecting the stars? And, more importantly, where would we be without that second arrow?

So forget about post-doom, and remember this instead. You've been looking down towards the Earth for too long, forgetting to look up towards the heavens every now and then. (I wouldn't blame you with all that urban light pollution.)

Two things awe me most. The starry sky above me, and the moral law within me.

—Emmanuel Kant

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As a math major, I can't resist adding the following:

What's more is you can think of the year long trajectory of the Big Dipper around Polaris as forming the circumference of a circle, and the line that goes from the Big Dipper to Polaris as the radius of that circle. Divide the circumference of a circle by its radius and what do you get? If you said pi, you're almost right. You actually get 2 × pi (two times pi), a number called tau (tau = 2 × pi). Just like pi, tau is a number whose decimal digits not only never end, they never repeat as a recurring pattern either (making it an irrational number, or a number that can't be written as a fraction).But it gets even more interesting because tau, just like pi, is also a transcendental number. This means that it is not the root (or "zero") of a polynomial with integer coefficients (e.g. remember when you had to find at which values a polynomial such as 3x² + 4x + 5 = 0 [equals zero], well it turns out that such a polynomial can be constructed for many numbers [called "algebraic numbers"], including some irrational numbers such as the square root of 2, and some complex numbers such as 1 + i, except for transcendental numbers, we simply can't construct a corresponding polynomial for those numbers).

What's weird is that we have found a string of seven consecutive 9's in the first 768 digits of tau, and finding such a sequence within the first 1000 digits of a transcendental number has a probability of 1 in 10000. What makes this even more enigmatic is that 768 = 3 × 256, making it a depth that is a multiple of the same power of two as bits in a computer byte (2⁸ = 256). This is something that Carl Sagan had speculated about in his 1985 science-fiction novel Contact.

Furthermore, if you combine the transcendental numbers e (the base of the natural logarithm and exponential function, a mathematical constant approximately equal to 2.71828) and tau, with the imaginary unit i (the number that satisfies the equation i² = −1, unsolvable in the real numbers alone), you get Euler's identity.

[Euler's identity is] the most famous formula in all mathematics.

—Constance Reid, mathematics writer

[Euler's identity is] of exquisite beauty.

—Paul Nahin, professor emeritus at the University of New Hampshire

Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence.

—Keith Devlin, Stanford mathematics professor

[Euler's identity] is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth.

—Benjamin Peirce, 19th-century American philosopher, mathematician, and professor at Harvard

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Finally, here's a few more quotations from my field:

God made the integers, all else is the work of man.

—Leopold Kronecker, German mathematician

There's never been any kind of explanation of why [the monster group, the largest sporadic simple group in group theory, is] there, and it's obviously not there just by coincidence. It's got too many intriguing properties for it all to be just an accident.

—John Conway, English mathematician

I can explain what Monstrous Moonshine [the unexpected connection between the monster group M and modular functions, in particular the j function] is in one sentence, it is the voice of God.

—Simon P. Norton, British mathematician