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Books

A universe without mathematics is beyond the scope of our imagination

Mathematics is the language of the universe. (Shutterstock)

Peter Watson, Carleton University

Almost 400 years ago, in The Assayer, Galileo wrote: “Philosophy is written in this grand book, the universe … [But the book] is written in the language of mathematics.” He was much more than an astronomer, and this can almost be thought of as the first writing on the scientific method.

We do not know who first started applying mathematics to scientific study, but it is plausible that it was the Babylonians, who used it to discover the pattern underlying eclipses, nearly 3,000 years ago. But it took 2,500 years and the invention of calculus and Newtonian physics to explain the patterns. https://www.youtube.com/embed/Rx-5dCXx1SI?wmode=transparent&start=0 Science Magazine looks at Babylonian clay tablets that contained mathematical formulas that are a precursor to calculus.

Since then, probably every single major scientific discovery has used mathematics in some form, simply because it is far more powerful than any other human language. It is not surprising that this has led many people to claim that mathematics is much more: that the universe is created by a mathematician.

So could we imagine a universe in which mathematics does not work?

The language of mathematics

The Sapir-Whorf hypothesis asserts that you cannot discuss a concept unless you have the language to describe it.

In any science, and physics in particular, we need to describe concepts that do not map well on to any human language. One can describe an electron, but the moment we start asking questions like “What colour is it?” we start to realize the inadequacies of English.

The colour of an object depends on the wavelengths of light reflected by it, so an electron has no colour, or more accurately, all colours. The question itself is meaningless. But ask “How does an electron behave?” and the answer is, in principle, simple. In 1928, Paul A.M. Dirac wrote down an equation that describes the behaviour of an electron almost perfectly under all circumstances. This does not mean it is simple when we look at the details.

For example, an electron behaves as a tiny magnet. The magnitude can be calculated, but the calculation is horrendously complicated. Explaining an aurora, for example, requires us to understand orbital mechanics, magnetic fields and atomic physics, but at heart, these are just more mathematics.

But it is when we think of the individual that we realize that a human commitment to logical, mathematical thinking goes much deeper. The decision to overtake a slow-moving car does not involve the explicit integration of the equations of motion, but we certainly do it implicitly. A Tesla on autopilot will actually solve them explicitly.

When overtaking a car, a Tesla will explicitly calculate what a human driver processes implicitly. (Shutterstock)

Predicting chaos

So we really should not be surprised that mathematics is not just a language for describing the external world, but in many ways the only one. But just because something can be described mathematically does not mean it can be predicted.

One of the more remarkable discoveries of the last 50 years has been the discovery of “chaotic systems.” These can be apparently simple mathematical systems that cannot be solved precisely. It turns out that many systems are chaotic in this sense. Hurricane tracks in the Caribbean are superficially similar to eclipse tracks, but we cannot predict them precisely with all the power of modern computers.

However, we understand why: the equations that describe weather are intrinsically chaotic, so we can make accurate predictions in the short term, (about 24 hours), but these become increasingly unreliable over days. Similarly, quantum mechanics provides a theory where we know precisely what predictions cannot be made precisely. One can calculate the properties of an electron very accurately, but we cannot predict what an individual one will do.

Hurricanes are obviously intermittent events, and we cannot predict when one will happen in advance. But the mere fact that we cannot predict an event precisely does not mean we cannot describe it when it happens. We can even handle one-off events: it is generally accepted that the universe was created in the Big Bang and we have a remarkably precise theory of that.

Designing social systems

A whole host of social phenomena, from the stock market to revolutions, lack good predictive mathematics, but we can describe what has happened and to some extent construct model systems.

So how about personal relationships? Love may be blind, but relationships are certainly predictable. The vast majority of us choose partners inside our social class and linguistic group, so there is absolutely no doubt that is true in the statistical sense.

But it is also true in the local sense. A host of dating sites make their money by algorithms that at least make some pretence at matching you to your ideal mate. In a TED talk, futurist Amy Webb shows that mathematics actually works in dating algorithms.

A universe that could not be described mathematically would need to be fundamentally irrational and not merely unpredictable. Just because a theory is implausible does not mean we could not describe it mathematically.

But I do not think we live in that universe, and I suspect we cannot imagine a non-mathematical universe.

Peter Watson, Emeritus professor, Physics, Carleton University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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Lifestyle

Why do cats’ eyes glow in the dark?

Curious Kids is a series for children of all ages. If you have a question you’d like an expert to answer, send it to curiouskidsus@theconversation.com.

Why do cats’ eyes glow in the dark? Chloe, age 10, Barkhamsted, Connecticut

Cats and many other animals, including most dogs, can reflect light from their eyes. That’s why cats’ eyes will usually shine brightly in photos taken in a dimly lit room or glow when illuminated in the dark by a flashlight or a car’s headlights.

Species whose eyes glow have evolved to see better in low light because they either forage or need to look out for predators throughout the night, or they do most of their hunting at dawn and dusk. In fact, domesticated cats can see in conditions that are only 16% as bright as what people require.

Above: Photo / Adobe Stock

Cats accomplish this because their pupils – the openings that appear black in the middle of their eyes that widen and narrow in response to light conditions – are special. Pupils operate like windows, with bigger ones letting more light into the eye. And a cat’s pupils can become up to 50% larger than human pupils in dim light. They also have a higher number of a specific type of light-sensing cell in the back of their eyes than we do. These cells, called rods, catch low-level light.

Humans do not have a tapetum lucidum but cats, including lynxes and pumas, do. The Open University, CC BY-SA

The tapetum lucidum

In addition to having large pupils and lots of rods, cats have something people don’t: a tapetum lucidum, a Latin medical term that translates to “bright or shining tapestry.” The tapetum lucidum is also known as “eyeshine.”

It’s located in the back of the eye behind the retina – a thin layer of tissue that receives light, converts the light to an electrical signal and sends this signal to the brain to interpret the image.

A cat’s tapetum lucidum is made up of cells with crystals that, like a mirror, reflect light back to the retina. This gives the retina a second chance to absorb more light.

The feline tapetum lucidum is special because its reflective compound is riboflavin, a type of vitamin B. Riboflavin has unique properties that amplify light to a specific wavelength that cats can see well, which greatly increases the sensitivity of the retina to low light.

In cats, the tapetum most often glows yellow-green or yellow-orange, but the color varies, just like their irises – the colorful part of their eye, which can be green, yellow, blue or golden. Variation in tapetum color is not unique to cats and can be found in lots of species.

Most dogs’ eyes will glow in dark spaces when a light shines on them. Tommy Greco, CC BY-SA

Other animals’ eyes glow too

Many other animals that need to see at night have a tapetum lucidum. That includes predators and prey alike, everything from wild foxes to farmed sheep and goats.

The tapetum lucidum is also useful to fish, dolphins and other aquatic animals, because it helps them see better in murky, dark water.

In land animals, the tapetum is found in the top half of the eye behind the retina, because they need to see what is on the ground best. But in aquatic animals the tapetum takes up most of the eye, because they need to see all around them in the dark.

Like cats, the lemur, a small primate, and its close relative, the bush baby – also known as a “night monkey” – also have a superreflective tapetum made with riboflavin.

Even though a lot of animals have eyeshine, some small domesticated dogs lack this trait. Most animals with blue eyes and white or light-colored coats have also lost this trait.

So don’t be alarmed if your dog’s or cat’s eyes don’t glow. The list of other species without a tapetum lucidum includes pigs, birds, reptiles and most rodents and primates – including humans.

Is there a downside?

Unfortunately, animals with a tapetum lucidum sacrifice some visual acuity for their ability to see in dim light.

That’s because all that light bouncing around as it reflects off the tapetum can make what they see a little fuzzier. So, a cat needs to be seven times closer to an object to see it as sharply as a person would in a brightly lit place.

But don’t worry, I’m sure your cat would rather see clearly at night than read a book.

Hello, curious kids! Do you have a question you’d like an expert to answer? Ask an adult to send your question to CuriousKidsUS@theconversation.com. Please tell us your name, age and the city where you live.

And since curiosity has no age limit – adults, let us know what you’re wondering, too. We won’t be able to answer every question, but we will do our best.

Braidee Foote, Clinical Assistant Professor of Veterinary Ophthalmology, University of Tennessee

This article is republished from The Conversation under a Creative Commons license. Read the original article.

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Apps, D.I.Y., Lifestyle, Observation, Social Media, TikTok

The Whole “be real” thing is Hard if you spent years learning to be Professional First

Video

Above: Photo Collage / Lynxotic

Who am I? I’m the person writing this.

But is it really necessary for you to know that I am female, love only cats (no dogs) and just got engaged?

No? Good, cause none of that is true. (Except the female part) That’s only one example of the odd twists that can come with the current trend of people going viral when they show “realness” and vulnerability.

Heard of acting? That’s what Meryl Streep does when she plays a person that never went to Yale and is not a rich famous actor, wink wink.

I suppose, as with so many online phenomena these days, it’s TikTok leading the way. No longer a place for young girls to dominate using only dancing, beauty and feminine wiles, it’s now a place where less objectively attractive people can blow up by showing, ostensibly, who they are.

Or by wearing a bear head as a hat.

https://www.tiktok.com/@madelin._.crochets/video/6983841654092352773

This trend towards realness has, based on informal research, also spilled over into places like LinkedIn, Medium and even Twitter.

On the whole, I think it’s a great thing. If Meryl Streep was only able to play herself, movies would be much less interesting, no doubt!

And maybe at least half of all the realness really is real. Just take it with a grain of salt if you see posts of someone getting engaged 3 times. In the same week.

All kidding aside this trend is part of a bigger, important evolution in digital communication

The evolution from journalistic norms, such as never referring to yourself directly but only as “your scribe”, “the writer”, “your correspondent” or just “one”, as in “one can only wonder…” to today’s norm of writing like the whole world wants to read your diary….

These journalistic conventions seem archaic and even ridiculous when the formerly forbidden “I” is commonplace and the authenticity of direct TikTok style casual presentation is already dominant and growing as a trend.

But the overall shift has more than just a style preference behind it, if you ask this writer (me).

It’s also far more than just the outgrowth of armies of non-journalists communicating spontaneously in every format and on every platform.

It’s really the early beginnings of what has become a common topic of late: the transition to the so-called Metaverse.

Not the Zuckerbergian Metaverse where people run around without legs and have joyless celebrations of themselves.

But rather, the real life cyber world where billions are on their phones communicating in various ways basically all the time. Even while jaywalking.

And as we do this more in every imaginable format, the desire to see “beautiful” landscape photos that have been photoshopped to death, instagram style, is eventually diminished to zero.

And what follows in a new hunger for the “real” or at least the honest seeming portrayal of the real (hi there Meryl!) and content that pushes an entirely different layer of psychological buttons.

As I mentioned above, dear reader, I love this! In spite of the fact that it leads to really scary TikToks (just check out the posts of some of the people that follow you on Tiktok (to see what I mean, the ones that follow 8753 people and get followed by like, 23 have nice videos…) where the frightening reality that’s out there (the banality of empirical unattractiveness you might call it) is already on full display, and how.

But that’s just the price to pay for a deeper and more authentic experience. And for the benefit of the real and valuable advice and knowledge you can get directly from “non-professional” actors who are not acting (presumably). We are reaping the profits of real life experiences, in exchange for nothing more than our attention, and clicks, likes and follows. And I say, Amen to that, bro.

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D.I.Y., Health and Diet, Lifestyle

New Years Challenge: How to Find Your Triumph of Meaning

Above: Photo Collage / Lynxotic / Adobe Stock

For a lot of us, the New Year kicks off by creating resolutions of things we hope to change

In the past, I have unconsciously set myself up for failure whenever forming resolutions. The unrealistic rhetoric of “New Year, New Me”, got me thinking that the way I was setting my resolutions, was almost automatically leading me down the same path, one that would be extremely short lived and make me feel bad that I couldn’t “change” and ultimately fail.

This year instead of trying to give myself over-reaching and vague goals like “lose weight”, or “try a diet plan” or “join a gym” ( which is a precarious decision right now anyways) I decided to do it differently.

Again, for me, in the many years I’ve pledged in the past, to aim for these types of resolutions, I’ve have almost always petered out. The focus and effort only lasted for a very short period, sometimes less than a month.

Setting up these absurdly, overly ambitious and wholly unrealistic goals, it’s no wonder that almost no kind of transformation or shift in my behavior ever actually happened.

With all the craziness of 2020, and the continuing rocky start in 2021, I wanted to do something a little different. Instead of a resolution or straight-up decision to change, I decided to instead focus on creating healthy and positive intentions and goals.

How to narrow focus, yet open up to the idea of what success actually looks like

After the pandemic and all the stressors that came alongside it (physical, emotional, financial) putting another unnecessary stressor, such as desperately wanting to get down to my high school weight seemed wrong.

I consider myself a generally healthy person that “sometimes” works out, though with covid-19, the workouts have been more sporadic and inconsistent. This year, I wanted to make healthy goals, in the form of a realistic resolution, while also holding myself accountable in ways I could actually attain.

I wanted my resolution to encompass something physical while also trying to get better with my followthrough ( I’m very much a “phase” person).

I decided I wanted to have run 1,000 miles by the end 2021.

Having a specific number, like 1,000, I would be able to better breakdown and track myself and monitor my progress. I also by thinking number itself as a concrete thought, or writing it out to solidify the idea, can help to engender a stronger commitment.

Looking at that number, 1,000, I knew it was a high number, but when broken down, I knew it could easily be achieved. I just did some simple math. There are 365 days in a year if you divide that by my goal of 1000 miles that’s only a little bit less than 3 miles a day (2.73).

While 3 miles is not a lot for a “runner”, it certainly is do-able for me and would not take more than an hour a day. On days where I have full energy, I am able to run a mile in about 10 minutes, although sometimes I’m not in the mood to run and I walk which then takes double that. Still either method would count toward the distance goal and is definitely possible to achieve.

It’s both the challenge to improve and the satisfaction of meeting a goal of my very own that drives me forward

With this concept in mind, the design of my resolution, and how to reach it, gives a little more flexibility. If I don’t feel good for example or have a crazy busy day, and take a day off, there might be “make-up-days” where I’m going to run 6 miles. I think having more than 2 off days (meaning I would have to be responsible for 9 miles) would put me on check not to get too far behind.

I think it’s important to be gentle with yourself when putting forth energy into something new and positive for yourself. There are always and understandably going to be “fails” and bumps that get in the way. Yet if you are able to not get down on yourself, these fails can be opportunities to learn about yourself and even turn into internal motivators to keep going.

My hope in that I can achieve my goal. I’m optimistic because I’ve purposely made the resolution (intention, goal, etc) based on something that I already do (exercise). Instead of trying to achieve something that is not even in my wheel-house, like win first place in a triathlon.

Why? Because I think it’s important to find reasons to be proud of yourself. Last year was really rough, yet many of us have survived, so while this year is starting out rough for many, I feel that, for me, a resolution focusing on something under my personal control is a way to start 2021 to be better. In short it’s privately optimistic beginning that hopefully leads to a much better outcome as the new year unfolds.

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