### The Earth isn't Flat, but the Universe is?

#### TL;DR

1. The Earth isn't flat, but the Universe is?
2. A galactic merger of equals, Part 2

#### Today I learned / This week in space history

We can all agree the Earth isn't flat (I hope!), but the shape of the Universe is an important question in modern cosmology. The origins of that debate owe greatly to one man - Bernhard Riemann. On June 10, 1854, Riemann gave a groundbreaking lecture on curved space and multidimensional geometry, laying out what would become the mathematical foundation of Einstein's General Relativity over 60 years later!

 Remember Riemann sums for calculating integrals in AP Calculus? Same guy!

Some background: since time of the Ancient Greeks, Euclidean geometry (the classic geometry from school) reigned supreme, but by the 1800s advanced branches of non-Euclidean geometry were developed to solve modern problems, similar to how quantum physics superseded Newtonian physics in the early 20th century. Riemann's lecture proposed the question, "how do we define an n-dimensional space, and what sort of geometry describes the space we actually live in?"

Fast forward to our modern cosmological problem. Einstein proved the 3D space we observe is more than just emptiness - space itself bends depending on the amount of mass present. So if we calculate the average mass-energy density of the cosmos, can we determine the curvature of the whole Universe? What possible shapes exist? To visualize, let's take a simpler example - we know the angles of a triangle on a flat piece of paper sum up to 180$^\circ$. But if we draw the triangle on sphere like the Earth (i.e. positive curvature), the angles of the triangle will exceed 180$^\circ$!

 Don't believe me? Here's a triple right triangle on the surface of a sphere: 270$^\circ$! Mind = blown

Below you'll find illustrations of the three possible curvatures of the Universe: flat, spherical, and hyperbolic, all of which depend on how much mass exists in the Universe. One important note though: notice how these are 2D projections onto 3D objects. Since we live in a 3D Universe projected onto 4 dimensions, to truly picture the Universe you'd need to step all these diagrams up by one dimension. The problem - our feeble minds can't visualize 4 dimensions! But hopefully you get the point.

 The shape of the Universe has critical implications to the fate of the Universe as well! Learn more here

So what's the answer? Our best experimental value calculated by the Lambda-CDM model demonstrates the Universe is flat, to within a 0.4% margin of error. Confused by any of this?? Never fear - the below video is a great resource. And if you think a flat Universe is a let down, there's actually a very interesting unsolved cosmological question embedded in our flat Universe, also well explained in this video

WATCH THIS VIDEO!! :D

#### Current events

While this merger isn't quite as large as the Milky Way-Andromeda collision I described back in March, it's relevant to my investment banking day job! Raytheon and United Technologies just announced a ~$166 billion merger of equals, catapulting them to be the world's second largest aerospace company (behind Boeing). The two businesses actually have little overlap: UTX is strongest in commercial aviation (think jet engines) while Raytheon boasts a vast arsenal of missile defense systems (like the Tomahawk), so the banker in me is curious where the synergies will come from. At least the deal probably won't fall through due to anti-trust!  Somewhere out there on Wall Street, there's a managing director who's just earned himself a FAT bonus$

Two reasons why I care about this: first, NASA awards lucrative contracts to both companies for everything ranging from our current spacesuit to scientific instruments on deep space probes, so I worry the combined company will have more bargaining power to push for better pricing. And second, my company Evercore was involved in the deal, advising UTX! But don't ask me for stock tips or other insider information. I cover the healthcare space, so I found out about this the same time as everybody else! But one of my classmates from the UT Austin Business Program was on the deal! He works for Goldman Sachs, and I don't think he's known sleep in over a month...