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Physicists puzzled by strange numbers that could explain reality
Eight-dimensional octonions may hold the clues to solve fundamental mysteries.
- Physicists discover complex numbers called octonions that work in 8 dimensions.
- The numbers have been found linked to fundamental forces of reality.
- Understanding octonions can lead to a new model of physics.
Is our reality, including its forces and particles, based on the strange properties of numbers with eight dimensions called "octonions"? A physicist thinks so, having found a way to expand 40-year-old research to reach surprising new directions.
First, a brief history of numbers.
Regular numbers that we are familiar with in our everyday life can be paired up in a special way to create "complex numbers," which act like coordinates on a two-dimensional plane. This was discovered in 16h-century Italy by the mathematician Gerolamo Cardano. As explains Natalie Wolchover of Quanta Magazine, you can perform operations on complex numbers like adding, subtracting, multiplying and dividing by "translating and rotating positions around the plane."
An Irish mathematician by the name of William Rowan Hamilton discovered in 1843 that if you pair the complex numbers in a certain way, they can form 4-D "quaternions." He was apparently so excited about figuring out that formula, that he immediately carved it into the Broome Bridge in Dublin. Not to be outdone, John Graves, a friend of Hamilton's who was a lawyer and math whiz, showed that quarternions can be paired up to become "octonions" – numbers that can assume coordinates in an abstract 8-dimensional (8-D) space.
Each type of numbers has been utilized extensively in the development of modern physics, with complex numbers used in quantum mechanics and even the quaternions employed in Albert's Einstein's special theory of relativity.
What hasn't been completely understood and put to work – the octonions, usually represented by the capital letter O and whose multiplication rules are encoded in a triangular diagram called the Fano plane (that looks like something the Freemasons would devise).
A mnemonic for the products of the unit octonions using the Fano plane.
The mystery of these numbers has led to speculation among researchers that they have a special purpose and can eventually explain the deeper secrets of the universe. In an email interview with Quanta Magazine, the particle physicist Pierre Ramond from the University of Florida explained that "Octonions are to physics what the Sirens were to Ulysses."
In 1973, Murat Günaydin, the then-Yale-graduate student (now professor at Penn State) and his advisor Feza Gürsey, discovered that there is an unexpected link between octonions and the strong force that keeps quarks together in an atomic nucleus. Günaydin continued his research quite outside the mainstream, looking at connecting the numbers to such ideas as string theory and M-theory.
In 2014, Cohl Furey, a graduate student at the University of Waterloo, Canada, built on Günaydin's work by finding a new use for the hard-to-imagine numbers. She devised an octonionic model that includes both the strong and electromagnetic forces. Now a postdoc in UK's University of Cambridge, Furey generated a series of results that link the octonions to the Standard Model of particle physics, in work that has been praised by other scientists. She has "taken significant steps toward solving some really deep physical puzzles," said Shadi Tahvildar-Zadeh, a mathematical physicist at Rutgers University.
Others, like the noted string theorist and Imperial College London professor Michael Duff, are more reserved, excited about her work but saying it's "hard to say" yet if it will become "revolutionary."
Furey is undeterred by working in a currently obscure field, thinking of her research as a "process of collecting clues," as she explained in an interview.
She published a paper in May 2018's The European Physical Journal C, where she consolidated several of her findings, looking to complete the standard model of particle physics and find the rightful place in our understanding of the world for the octonions.
To learn more, watch Furey explain the octonions here:
For those inclined to delve deeper into the math, check out this fascinating graphic:
Lucy Reading-Ikkanda/Quanta Magazine
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From "if-by-whiskey" to the McNamara fallacy, being able to spot logical missteps is an invaluable skill.
- A fallacy is the use of invalid or faulty reasoning in an argument.
- There are two broad types of logical fallacies: formal and informal.
- A formal fallacy describes a flaw in the construction of a deductive argument, while an informal fallacy describes an error in reasoning.
Appeal to privacy<p>When someone behaves in a way that negatively affects (or could affect) others, but then gets upset when others criticize their behavior, they're likely engaging in the appeal to privacy — or "mind your own business" — fallacy. Examples:<br></p><ul><li>Someone who speeds excessively on the highway, considering his driving to be his own business.</li><li>Someone who doesn't see a reason to bathe or wear deodorant, but then boards a packed 10-hour flight.</li></ul><p>Language to watch out for: "You're not the boss of me." "Worry about yourself."</p>
Sunk cost fallacy<p>When someone argues for continuing a course of action despite evidence showing it's a mistake, it's often a sunk cost fallacy. The flawed logic here is something like: "We've already invested so much in this plan, we can't give up now." Examples:<br></p><ul><li>Someone who intentionally overeats at an all-you-can-eat buffet just to get their "money's worth"</li><li>A scientist who won't admit his theory is incorrect because it would be too painful or costly</li></ul><p>Language to watch out for: "We must stay the course." "I've already invested so much...." "We've always done it this way, so we'll keep doing it this way."</p>
If-by-whiskey<p>This fallacy is named after a speech given in 1952 by <a href="https://en.wikipedia.org/wiki/Noah_S._Sweat" target="_blank">Noah S. "Soggy" Sweat, Jr.</a>, a state representative for <a href="https://en.wikipedia.org/wiki/Mississippi" target="_blank">Mississippi</a>, on the subject of whether the state should legalize alcohol. Sweat's argument on prohibition was (to paraphrase):<br></p><p><em>If, by whiskey, you mean the devil's brew that causes so many problems in society, then I'm against it. But if whiskey means the oil of conversation, the philosopher's wine, "</em><em>the stimulating drink that puts the spring in the old gentleman's step on a frosty, crispy morning;" then I am certainly for it.</em></p>
Slippery slope<p>This fallacy involves arguing against a position because you think choosing it would start a chain reaction of bad things, even though there's little evidence to support your claim. Example:<br></p><ul><li>"We can't allow abortion because then society will lose its general respect for life, and it'll become harder to punish people for committing violent acts like murder."</li><li>"We can't legalize gay marriage. If we do, what's next? Allowing people to marry cats and dogs?" (Some people actually made this <a href="https://www.daytondailynews.com/news/national/cats-marrying-dogs-and-five-other-things-same-sex-marriage-won-mean/dLV9jKqkJOWUFZrSBETWkK/" target="_blank">argument</a> before same-sex marriage was legalized in the U.S.)</li></ul><p>Of course, sometimes decisions <em>do </em>start a chain reaction, which could be bad. The slippery slope device only becomes a fallacy when there's no evidence to suggest that chain reaction would actually occur.</p><p>Language to watch out for: "If we do that, then what's next?"</p>
"There is no alternative"<p><span style="background-color: initial;">A modification of the </span><a href="https://en.wikipedia.org/wiki/False_dilemma" target="_blank" style="background-color: initial;">false dilemma</a><span style="background-color: initial;">, this fallacy (often abbreviated to TINA) argues for a specific position because there are no realistic alternatives. Former British Prime Minister Margaret Thatcher used this exact line as a slogan to defend capitalism, and it's still used today to that same end: Sure, capitalism has its problems, but we've seen the horrors that occur when we try anything else, so there is no alternative.</span><br></p><p>Language to watch out for: "If I had a magic wand…" "What <em>else</em> are we going to do?!"</p>
Ad hoc arguments<p>An ad hoc argument isn't really a logical fallacy, but it is a fallacious rhetorical strategy that's common and often hard to spot. It occurs when someone's claim is threatened with counterevidence, so they come up with a rationale to dismiss the counterevidence, hoping to protect their original claim. Ad hoc claims aren't designed to be generalizable. Instead, they're typically invented in the moment. <a href="https://rationalwiki.org/wiki/Ad_hoc" target="_blank">RationalWiki</a> provides an example:<br></p><p style="margin-left: 20px;">Alice: "It is clearly said in the Bible that the Ark was 450 feet long, 75 feet wide and 45 feet high."</p><p style="margin-left: 20px;">Bob: "A purely wooden vessel of that size could not be constructed; the largest real wooden vessels were Chinese treasure ships which required iron hoops to build their keels. Even the <em>Wyoming</em> which was built in 1909 and had iron braces had problems with her hull flexing and opening up and needed constant mechanical pumping to stop her hold flooding."</p><p style="margin-left: 20px;">Alice: "It's possible that God intervened and allowed the Ark to float, and since we don't know what gopher wood is, it is possible that it is a much stronger form of wood than any that comes from a modern tree."</p>
Snow job<p><span style="background-color: initial;">This fallacy occurs when someone doesn't really have a strong argument, so they just throw a bunch of irrelevant facts, numbers, anecdotes and other information at the audience to confuse the issue, making it harder to refute the original claim. Example:</span><br></p><ul><li>A tobacco company spokesperson who is confronted about the health risks of smoking, but then proceeds to show graph after graph depicting many of the other ways people develop cancer, and how cancer metastasizes in the body, etc.</li></ul><p>Watch out for long-winded, data-heavy arguments that seem confusing by design.</p>
McNamara fallacy<p>Named after <a href="https://en.wikipedia.org/wiki/Robert_McNamara" target="_blank">Robert McNamara</a>, the <a href="https://en.wikipedia.org/wiki/United_States_Secretary_of_Defense" target="_blank">U.S. secretary of defense</a> from 1961 to 1968, this fallacy occurs when decisions are made based solely on <em>quantitative metrics or observations,</em> ignoring other factors. It stems from the Vietnam War, in which McNamara sought to develop a formula to measure progress in the war. He decided on bodycount. But this "objective" formula didn't account for other important factors, such as the possibility that the Vietnamese people would never surrender.<br></p><p>You could also imagine this fallacy playing out in a medical situation. Imagine a terminal cancer patient has a tumor, and a certain procedure helps to reduce the size of the tumor, but also causes a lot of pain. Ignoring quality of life would be an example of the McNamara fallacy.</p><p>Language to watch out for: "You can't measure that, so it's not important."</p>
A new study looks at what would happen to human language on a long journey to other star systems.
- A new study proposes that language could change dramatically on long space voyages.
- Spacefaring people might lose the ability to understand the people of Earth.
- This scenario is of particular concern for potential "generation ships".
Generation Ships<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="a1e6445c7168d293a6da3f9600f534a2"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/H2f0Wd3zNj0?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span>
Many of the most popular apps are about self-improvement.
Emotions are the newest hot commodity, and we can't get enough.