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Carl Sagan Explains the Fourth Dimension

We're all pretty familiar with the first three dimensions -- after all, we experience those dimensions daily as we move about our world. But scientists and mathematicians have long gone three dimensions using thought experiments, conceptualizing a fourth dimension -- and of course, to many more dimensions beyond. You may have heard of the fourth dimension via Madeleine L'Engle's A Wrinkle in Time, which mentioned the tesseract, a four-dimensional "hypercube." In L'Engle's work, the tesseract had properties that could bend space-time, though a real tesseract would simply be an object in four-dimensional space. Anyway, let's not get carried away with tesseracts just yet. I stumbled across a wonderful video of Carl Sagan explaining the fourth dimension in a way that anyone can understand. He explains dimensionality as a notion, expanding from a two-dimensional "flatland" to our three-dimensional world, and onward to the fourth dimension. The video is only seven minutes long -- have a look:

Neat, huh? See also: Flatland: A Romance of Many Dimensions, a sci-fi story from 1884.

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science
What Pop Culture Gets Wrong About Dissociative Identity Disorder
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From the characters in Fight Club to Dr. Jekyll and Mr. Hyde, popular culture is filled with "split" personalities. These dramatic figures might be entertaining, but they're rarely (if ever) scientifically accurate, SciShow Psych's Hank Green explains in the channel's latest video. Most representations contribute to a collective misunderstanding of dissociative identity disorder, or DID, which was once known as multiple personality disorder.

Experts often disagree about DID's diagnostic criteria, what causes it, and in some cases, whether it exists at all. Many, however, agree that people with DID don't have multiple figures living inside their heads, all clamoring to take over their body at a moment's notice. Those with DID do have fragmented personalities, which can cause lapses of memory, psychological distress, and impaired daily function, among other side effects.

Learn more about DID (and what the media gets wrong about mental illness) by watching the video below.

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History
Scientists Reveal Long-Hidden Text in Alexander Hamilton Letter
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Age, deterioration, and water damage are just a few of the reasons historians can be short on information that was once readily available on paper. Sometimes, it’s simply a case of missing pages. Other times, researchers can see “lost” text right under their noses.

One example: a letter written by Alexander Hamilton to his future wife, Elizabeth Schuyler, on September 6, 1780. On the surface, it looked very much like a rant about a Revolutionary War skirmish in Camden, South Carolina. But Hamilton scholars were excited by the 14 lines of writing in the first paragraph that had been crossed out. If they could be read, they might reveal some new dimension to one of the better-known Founding Fathers.

Using the practice of multispectral imaging—sometimes called hyperspectral imaging—conservationists at the Library of Congress were recently able to shine a new light on what someone had attempted to scrub out. In multispectral imaging, different wavelengths of light are “bounced” off the paper to reveal (or hide) different ink pigments. By examining a document through these different wavelengths, investigators can tune in to faded or obscured handwriting and make it visible to the naked eye.

A hyperspectral image of Alexander Hamilton's handwriting
Hyperspectral imaging of Hamilton's handwriting, from being obscured (top) to isolated and revealed (bottom).
Library of Congress

The text revealed a more emotional and romantic side to Hamilton, who had used the lines to woo Elizabeth. Technicians uncovered most of what he had written, with words in brackets still obscured and inferred:

Do you know my sensations when I see the
sweet characters from your hand? Yes you do,
by comparing [them] with your [own]
for my Betsey [loves] me and is [acquainted]
with all the joys of fondness. [Would] you
[exchange] them my dear for any other worthy
blessings? Is there any thing you would put
in competition[,] with one glowing [kiss] of
[unreadable], anticipate the delights we [unreadable]
in the unrestrained intercourses of wedded love,
and bet your heart joins mine in [fervent]
[wishes] to heaven that [all obstacles] and [interruptions]
May [be] speedily [removed].

Hamilton and Elizabeth Schuyler married on December 14, 1780. So why did Hamilton try and hide such romantic words during or after their courtship? He probably didn’t. Historians believe that his son, John Church Hamilton, crossed them out before publishing the letter as a part of a book of his father’s correspondence. He may have considered the passage a little too sexy for mass consumption.

[h/t Library of Congress]

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