Category: valentines day

The Universe Would Be Very Different Without Dark Matter

“Finally, the smallest galaxies of all — the ones that contain only hundreds or thousands of stars — wouldn’t be able to exist at all. In our Universe, they arose from a clump of normal-and-dark matter of approximately 100,000 solar masses, where an episode of star formation ejected the gas. Still, the dark matter persisted, and holds the stars together in their own bound structure even to the present day. In a Universe without dark matter, that same episode of star formation would blast the proto-galaxy apart entirely, leaving only a slew of individual, unbound stars behind.

There are many different lines of evidence that point towards dark matter’s existence, but it’s perhaps a little more interesting to consider all the ways our Universe would be different — and inconsistent with what we observe — if it had no dark matter at all. If you enjoy the fact that the Universe is held together as well as it is, you have dark matter to thank for it. Even if you don’t believe in it, it’s a key ingredient in the Universe that led to you.”

Happy Valentine’s Day, dark matter! I know you don’t get nearly enough love on even a normal day of the year, so on this special day, don’t forget to carve out a piece of your heart for the unseen-but-important “glue” that holds the Universe together.

Without dark matter, the Universe as we know it, containing humans, life, and even something as basic as rocky planets, might not be possible at all.

The Pale Blue Dot Celebrates Its 29th Anniversary, Reminding Us How Small And Fragile We Are

“But the most striking thing about these pictures is what Voyager 1 cannot see. In the single pixel that is Earth, all we can see is its average color and brightness. We cannot see its phase; we cannot see clouds, oceans, or continents; we cannot see our Moon. We cannot see the lights that illuminate our nighttime side. We cannot see our cities, monuments, or any signs of human activity. From 6 billion kilometers away, we are only a dot.

We have not even reached cosmic scales in this image. The Sun is still 8 million times brighter than the next brightest star, with the closest exoplanets approximately 1,000 times more distant than the ones in our Solar System. And still, even at such a close distance, there are no visible signs that anything of interest exists on planet Earth.”

Sometimes, I know, it seems like there is nothing out there that could possibly unite us all. Ideologies, politics, and our visions for the future divide us so thoroughly, that it’s easy to lose sight of what we all have in common: our place in the Universe. 29 years ago, today, an image was released that truly put it all into perspective: the Pale Blue Dot. From a distance of more than 6 billion kilometers, Earth was not even a single pixel, captured amidst the scattered light rays of the Sun. No sign of life, civilization, or even our oceans can be seen. Yet, from three times the distance to Pluto, that one dot contains us all.

Take a little bit of time today to gain a little perspective, and remember the most important lesson of all: in the human enterprise, we’re all in this together.

The Enduring Mystery Of Detecting The Universe’s Only Magnetic Monopole

“We may never know what went on inside that detector back on Valentine’s Day of 1982. Was there really a magnetic monopole that passed through it, where we were fortunate enough to find it but never saw another one? Was it an unprecedented glitch in the equipment? A most unusual cosmic ray with heretofore inexplicable properties? Or, perhaps, a prank played by a student, rival, or professional saboteur?

In experimental science, the most important thing is to be able to replicate your results, and a second monopole detection has never come to pass. As beautiful as a symmetric Universe might be, that simply doesn’t appear to be the Universe we have. Nobody knows what happened to fool us into thinking we’d detected a magnetic monopole, but without repeat confirmation, we have no choice but to conclude it wasn’t real. Magnetic monopoles, as far as we can tell, don’t appear to exist.”

37 years ago, an experiment was being performed that was searching for a very specific phenomenon that should exist in many scenarios of Grand Unified Theories: a magnetic monopole. These new particles, not a part of classical electromagnetism or the Standard Model, should be isolated north or south magnetic poles, without a matching dipole counterpart. If they were to pass through a specially-designed detector, an unambiguous signal should show up.

On February 14, 1982, that exact signal was observed. What happened? 37 years later, here’s the (unfortunately) very limited amount we know.

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There is no simple love story.

If it’s simple, its not love.

If it’s love, its complicated.

How complicated can it get? Well let’s find out!

Romeo and Juliet

Let’s consider a love affair between Romeo and Juliet.

We shall use functions R(t) and J(t) to quantify their love:

  R(t) –> Romeo’s love/hate for Juliet at time t

  J(t) –> Juliet’s love/hate for Romeo at time t

These quantities are positive for love and negative for hate.

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The simplest linear relationship that one can construct to describe their love affair is:

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These set of primitive equations*** can be used to predict how their relationship is going to evolve with time.

Now if you had taken a course in Linear Algebra then you might know how to solve these system of linear differential equations and obtain the solution. Here’s a quick review:

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INTERLUDE: What type of a person is Romeo ?

Remember that we said that Romeo’s love for Juliet evolves with the equation:

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Depending on the signs of the coefficients a and b , Romeo can exhibit one of four romantic styles:

1. Eager beaver: a > 0, b > 0 (Romeo is encouraged by his own
feelings as well as Juliet’s.)

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2. Narcissistic nerd: a > 0, b < 0 (Romeo wants more of what
he feels but retreats from Juliet’s feelings.)

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3. Cautious (or secure) lover: a < 0, b > 0 (Romeo retreats from
his own feelings but is encouraged by Juliet’s.) –>Most people

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4. Hermit: a < 0, b < 0 (Romeo retreats from his own feelings
as well as Juliet’s.)

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And based on the signs of the coefficients c and d Juliet can also exhibit one of four romantic styles as well.

If we know these coefficients for Romeo and Juliet, we can look compute the trace (a+d) and determinant (ad-bc), and look up the Poincaré diagram to predict the future of the Romeo-Juliet relationship:

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Example: A never-ending tale of love and hate

Let me illustrate with a special case where a = 0 , b = 1, c = (-1), d = 0:

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Trace = a + d = 0

Determinant = ad – bc = 1 

Looking up the Poincaré diagram we get a centered orbit:

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And we can verify this by using solving this system of linear equation numerically using applications such as pplane:

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              Plot of Romeo’s love for Juliet v/s Juliet’s love for Romeo

What this plot implies is that the couple is stuck for eternity in an orbit of love and hate. Wherever the initial point of starting might be on the plane, they always end up orbiting round the origin.

They spend three quadrants of their cycle in a turmoil of love and hate but spend one entire quadrant (R > 0 & J > 0) in true and unconditional love.


Happy Valentine’s day everybody!

* This post was Inspired by Strogatz’s Book on Nonlinear Dynamics and Sprott’s paper titled ‘Dynamics of Love affairs’.

** Previous giftboxes: 2016 , 2017

*** This is the simplest system that one can analyze