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by
Max Tegmark
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May 29, 2014 - October 24, 2015
explore a crazy-sounding belief of mine that our physical world not only is described by mathematics, but that it is mathematics, making us self-aware parts of a giant mathematical object.
“If you have a tough question that you can’t answer, first tackle a simpler question that you can’t answer.”
the Sun is almost 20 times farther away than Aristarchos estimated, and about 109 times larger than Earth in diameter—so you could fit over a million Earths inside the volume of the Sun.
In astronomy, we can use this same parallax trick and pretend that we’re giants with eyes 300 billion meters apart, which is the diameter of Earth’s orbit around the Sun.
major break in the case using a totally different approach. In 1814, the German optician Joseph von Fraunhofer invented a device called a spectrograph, which let him separate white light into the rainbow of colors from which it’s made up, and measure them in exquisite detail.
a 1925 conference, jaws dropped: he argued that Andromeda was a galaxy about a million light-years away, a thousandfold farther than most stars my grandma saw in her night sky! We now know that the Andromeda galaxy is even more distant than Hubble estimated, about three million light-years from us,
topology. They’ve defined flat spaces that connect back on themselves in all their dimensions, and call such a space a torus.
In summary, the space we live in might go on forever and it might not—both possibilities are perfectly reasonable according the best theory we have for the nature of space, Einstein’s general relativity.
Isaac Newton finally answered this question by exploring an idea that was as simple as it was radical: that heavenly objects obey the same laws as objects here on Earth.
A cannon ball (D) fired faster than 11.2 kilometers per second escapes from Earth never to return (ignoring air resistance). If fired slightly more slowly (C), it instead enters an elliptical orbit around Earth. If fired horizontally at 7.9 kilometers per second (B), its orbit will be perfectly circular, and if fired at lower speeds (A), it eventually crashes into the ground.
Earth’s rotation, which is slowed down by tidal friction: if you ever feel that there aren’t enough hours in a day, just wait 200 million years, and days will be twenty-five hours long!
Often we wish to use knowledge of the present to predict the future, as with weather forecasts. However, the equations can be solved equally well in reverse, using knowledge of the present to reveal the past—such as reconstructing the exact details of the eclipse Columbus witnessed on Jamaica.
Since all the spin (or angular momentum, as we physicists call it) comes from the rotation of the original cloud, it’s no surprise that all planets in our Solar System are orbiting around the Sun in the same direction (counterclockwise if you’re looking down at the North Pole), which is also the same direction that the Sun itself rotates roughly once per month.
some rocks from the Jack Hills of western Australia have been found to be over 4.404 billion years old. The record age for meteorites is 4.56 billion years, suggesting that both our planet and the rest of our Solar System formed in the ballpark of 4.5 billion years ago—in
a key lesson from both Newton and Friedmann is this simple mantra: “Dare to extrapolate!” Specifically, take your current understanding of the laws of physics, apply them in a new uncharted situation, and ask whether they predict something interesting that we can observe.
The most ambitious 3-D mapping project to date is called the Sloan Digital Sky Survey,
We’ve measured the density of atoms (there’s about one atom for every two billion photons)—but what process produced that amount?
For example, waves that arrive with a wavelength of 210 centimeters have been stretched to 10 times their original length, so they were emitted when our Universe was 10 times smaller than it is now. This technique has become known as 21-centimeter tomography,
In mathematics, we have a fancy and intimidating name for wave sorting: Fourier transforming.
• Einstein’s gravity theory arguably broke the record as the most mathematically beautiful theory, explaining gravity as a manifestation of geometry. It shows that the more mass space contains, the more curved space gets. This curvature of space causes things to move not in straight lines, but in a motion that curves toward massive objects.
Q: What caused our Big Bang? A: There’s no explanation—the equations simply assume it happened.
