Why 'Change without Change' Is One of the Fundamental Principles of the Universe
Symmetry is about way more than splitting circles: It's change without change, and it has applications throughout mathematics, physics, and nature.
Frank Wilczek is an American theoretical physicist, mathematician and a Nobel laureate. He is currently the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology (MIT). Wilczek, along with David Gross and H. David Politzer, was awarded the Nobel Prize in Physics in 2004 for their discovery of asymptotic freedom in the theory of the strong interaction. He is on the Scientific Advisory Board for the Future of Life Institute. His new book is titled A Beautiful Question: Finding Nature's Deep Design.
Frank Wilczek: Symmetry in common usage is a kind of vague term like most terms in common usage. We use it flexibly. The idea of symmetry that has turned out to be extremely fruitful in mathematics and physics and in the fundamental description of nature is a precise distillation of some aspects of the common usage. So it’s not unnatural to call it symmetry, but it’s something very precise that we can describe.
When I say what it is it’ll sound kind of mystical, but it’s actually — I’ll spell it out and you’ll see what I mean. So symmetry in the sense that’s turned out to be fruitful in mathematics and physics and fundamental investigations is change without change. Now you might be puzzled. What does that have to do with symmetry? Well consider a circle. A circle is a very symmetric object. You can rotate it around its center by any angle and although every point on the circle may move, the circle as a whole doesn’t change. And that’s what makes it symmetric in the intuitive sense. You can change it. You can make changes on it which might have changed it, but although they transformed each part of it, don’t transform the thing as a whole. So that’s what makes a circle a symmetric object.
An equilateral triangle, for instance, you can’t rotate through any angle and get the same thing. It’ll change. If you rotate it one-third of the way around though by 120 degrees, it goes over into itself. If you rotate around the center by 120 degrees, it’s the same equilateral triangle. Whereas if you take some lopsided triangle, it’ll never go back to itself until you come all the way back to a trivial transformation. That doesn’t change anything. So change — so a triangle has less symmetry than a circle according to this concept, but some symmetry.
And so you start to see how this concept of change without change matches the intuitive notion of symmetry. The great advantage of that definition is that you can apply it in very broad context not only to describing the symmetry of objects, but to describing the symmetry of physical laws or the symmetry of equations. So, for instance, the theory of relativity is a statement of symmetry that if you change the way the world looks by moving past it at a constant velocity, you change the appearance of everything that’s happening. But the underlying laws are still valid. That’s the assumption of the theory of relativity that drives it and makes it powerful.
The idea that the laws of physics don’t change as a function of time is also a symmetry because it means you can change when you start your clocks and although the time stamps you’ll give to each event look different, the underlying equations will be the same. That’s the way of staying, that the laws of physics don’t change. And similarly with that the fact that the same physical laws apply at different places is a symmetry because you can change your position without changing the way the laws work. So symmetry is a very powerful constraint on our description of the world that nature seems to respect in many ways. Now the kind of symmetry that leads to quantum chromodynamics or general relativity or quantum electrodynamics is, mathematically, considerably more complex but it’s the same idea.
So there are transformations of the equations that change the different terms in them. So they might change an electric field into a magnetic field or a magnetic field into a combination of electric and magnetic that change the way the equations look, but don’t change their consequences. So the equations look quite different — some parts have moved over to the left and some parts have moved over to the right and some things have been multiplied in funny ways. But their consequences, their content is exactly the same. That’s the kind of equations that are like the circles among equations — are ones that have this symmetry property and those are the kinds of equations that turn out to be the ones that appear most prominently in our fundamental description of nature. It’s an extraordinary thing — but that’s not only true, but that’s how we got to the equations in the first place.
In his new book A Beautiful Question, theoretical physicist and Nobel laureate Frank Wilczek marries the age-old human quest for beauty and the age-old human quest for truth into a thrilling synthesis: The universe wants to be beautiful. In this video interview, Wilczek delves deep into the fundamental idea of symmetry. Did you know symmetry is much more complex than what we were taught in school? The possible and plausible abstractions of symmetry throughout physics and nature are plenty. The world is full of instances of change without changing.
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- The scientists show that tides created tidal pools, stranding fish and forcing them to get out of the water.
- The researchers ran computer simulations to get their results.
Neil deGrasse Tyson Explains the Tides<span style="display:block;position:relative;padding-top:56.25%;" class="rm-shortcode" data-rm-shortcode-id="9913a65f847775722d7c23d40d78938b"><iframe type="lazy-iframe" data-runner-src="https://www.youtube.com/embed/dBwNadry-TU?rel=0" width="100%" height="auto" frameborder="0" scrolling="no" style="position:absolute;top:0;left:0;width:100%;height:100%;"></iframe></span>
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- AI analysis of satellite images sees trees and shrubs where human eyes can't.
- At the western edge of the Sahara is more significant vegetation than previously suspected.
- Machine learning trained to recognize trees completed the detailed study in hours.
Why this matters<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDU2MDQ1OC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYzOTkyODg5NX0.O3S2DRTyAxh-JZqxGKj9KkC6ndZAloEh4hKhpcyeFDQ/img.jpg?width=980" id="3770d" class="rm-shortcode" data-rm-shortcode-id="3c27b79d4c0600fb6ebb82e650cabec0" data-rm-shortcode-name="rebelmouse-image" />
Area in which trees were located
Credit: University of Copenhagen<p>As important as trees are in fighting climate change, scientists need to know what trees there are, and where, and the study's finding represents a significant addition to the global tree inventory.</p><p>The vegetation Brandt and his colleagues have identified is in the Western Sahara, a region of about 1.3 million square kilometers that includes the desert, <a href="https://en.wikipedia.org/wiki/Sahel" target="_blank">the Sahel</a>, and the <a href="https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/subhumid-zones" target="_blank" rel="noopener noreferrer">sub-humid zones</a> of West Africa.</p><p>These trees and shrubs have been left out of previous tabulations of carbon-processing worldwide forests. Says Brandt, "Trees outside of forested areas are usually not included in climate models, and we know very little about their carbon stocks. They are basically a white spot on maps and an unknown component in the global carbon cycle."</p><p>In addition to being valuable climate-change information, the research can help facilitate strategic development of the region in which the vegetation grows due to a greater understanding of local ecosystems.</p>
Trained for trees<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDU2MDQ3MC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYzNTk5NTI3NH0.fR-n1I2DHBIRPLvXv4g0PVM8ciZwSLWorBUUw2wc-Vk/img.jpg?width=980" id="e02c0" class="rm-shortcode" data-rm-shortcode-id="79955b13661dca8b6e19007935129af1" data-rm-shortcode-name="rebelmouse-image" />
Credit: Martin Brandt/University of Copenhagen<p>There's been an assumption that there's hardly enough vegetation outside of forested areas to be worth counting in areas such as this one. As a result the study represents the first time a significant number of trees — likely in the hundreds of millions when shrubs are subtracted from the overall figure — have been catalogued in the drylands region.</p><p>Members of the university's Department of Computer Science trained a machine-learning module to recognize trees by feeding it thousands of pictures of them. This training left the AI be capable of spotting trees in the tiny details of satellite images supplied by NASA. The task took the AI just hours — it would take a human years to perform an equivalent analysis.</p><p>"This technology has enormous potential when it comes to documenting changes on a global scale and ultimately, in contributing towards global climate goals," says co-author Christian Igel. "It is a motivation for us to develop this type of beneficial artificial intelligence."</p><p>"Indeed," says Brandt says, "I think it marks the beginning of a new scientific era."</p>
Looking ahead and beyond<p>The researchers hope to further refine their AI to provide a more detailed accounting of the trees it identifies in satellite photos.</p><p>The study's senior author, Rasmus Fensholt, says, "we are also interested in using satellites to determine tree species, as tree types are significant in relation to their value to local populations who use wood resources as part of their livelihoods. Trees and their fruit are consumed by both livestock and humans, and when preserved in the fields, trees have a positive effect on crop yields because they improve the balance of water and nutrients."</p><p>Ahead is an expansion of the team's tree hunt to a larger area of Africa, with the long-term goal being the creation of a more comprehensive and accurate global database of trees that grow beyond the boundaries of forests.</p>
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- A study surveying 1,145 people in the U.S. found that the majority of people believed that they were less likely to catch the virus than the average person, regardless of the person's age or gender.
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Optimism bias<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDU5OTg2OS9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTYzMTAzNDM0Mn0.vRtlUDOpCnC_ZOdjxZUpRL5J9fnBeITmXXIPOMXOzhg/img.jpg?width=1245&coordinates=0%2C2291%2C0%2C1908&height=700" id="abbcf" class="rm-shortcode" data-rm-shortcode-id="ff0569ffedf799d7a1237068dc1ee72f" data-rm-shortcode-name="rebelmouse-image" alt="smiley paint on gray ground in front of people" />Photo by Nathan Dumlao on Unsplash<p>Most people have a tendency to overestimate the chances of experiencing a positive (like getting a promotion), and underestimate the likelihood of experiencing a negative event (like getting robbed or sick). Typically a benign — even beneficial — human quirk, the "optimism bias" could be contributing to the spread of coronavirus according to behavioral psychologists.</p><p>Experts argue that it has caused people to discount their individual chances of contracting COVID-19, despite being aware of its risk to the rest of the population. A study that was conducted over three phases this year surveying 1,145 people in the U.S. found that the majority of people believed that they were less likely to catch the virus than the average person is, regardless of the person's age or gender. </p><p>"This is very typical of what optimism bias is," Tali Sharot, a cognitive neuroscientist at University College London and lead author of the study, <a href="https://www.cnbc.com/2020/10/22/why-optimism-bias-could-be-unhelpful-in-a-pandemic-say-psychologists.html" target="_blank" rel="noopener noreferrer">told CNBC Make It</a>. "You usually believe that your likelihood of experiencing negative events is lower than people like you, and the likelihood of you experiencing positive events is higher than other people like you."</p><p>According to Sharot, optimism bias is a product of our tendency to vividly imagine positive future events and attribute more probability to them happening. </p><p>In certain circumstances, such as in our jobs and relationships, this can be beneficial by encouraging us to behave in ways that may contribute to positive outcomes, thus becoming a self-fulfilling prophecy. But we're in a pandemic, and it's having a concerning impact on our ability to assess risk and react appropriately. As time goes on and COVID-19 cases <a href="https://www.cnn.com/2020/10/26/health/us-coronavirus-monday/index.html" target="_blank" rel="noopener noreferrer">continue to rise and spread</a> the threat of the virus is becoming a background hum to everyday life making this bias worse. </p><p>"I think now the risk is greater because we have gotten used to this threat. And when you get used to a threat you underestimate it even more," said Sharot.</p><p>The United States is now reporting the greatest number of cases it's seen to date, with a seven-day average of daily new cases reaching 68,767 on Sunday, according to data from Johns Hopkins University. </p>
Other menacing biases<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yNDU5OTg3Mi9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY2MzA1OTMwOX0.f68UAZY--fN5yJ_26v7OjhQG5Ieda_HQx_iDF5NKHJI/img.jpg?width=1245&coordinates=0%2C30%2C0%2C31&height=700" id="79c78" class="rm-shortcode" data-rm-shortcode-id="8b155c7f4503e53d756c1451be9874c8" data-rm-shortcode-name="rebelmouse-image" />
Credit: Michael Siluk/Education Images/Universal Images Group via Getty Images<p>Optimism bias may be compounded by <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7144592/" target="_blank">confirmation bias</a>, or the tendency to interpret new information as confirmation of one's existing beliefs or theories while disregarding information that contradicts one's preferred narrative of reality. Salience bias is also at play, leading people to underplay or discount the threat of something they cannot see such as a microscopic virus or sick people in the hospital.</p><p>Additionally, internet echo chambers exacerbate these cognitive biases. When others share our viewpoints, our biases are typically inflated, and it's never been easier to curate our social circles with networks of people who do exactly that. This feeds into the tribalism and polarization that has added to the challenges of getting a majority of the U.S. population to comply with virus safety measures. Think, for example, how the act of <a href="https://bigthink.com/coronavirus/face-masks-transmission" target="_blank">wearing a mask has become politicized</a> in the U.S. as a perceived badge as to which group one belongs to, masks often being associated with liberal-leaning people and no masks (<a href="https://bigthink.com/coronavirus/christian-nationalism" target="_blank">anti-maskers</a>) being associated with the far-right. </p>