Very large numbers are not numbers: Infinity does not exist

(this blog post was originally published in https://eyemath.wordpress.com/ . It has been moved to this blog – with slight changes.)

Remember Nietzsche’s famous announcement, “God is dead“? In the domain of mathematics, Nietzsche’s announcement could just as well refer to infinity.

There are some philosophers who are putting up a major challenge to the Platonic stronghold on math: Brian Rotman, author of Ad Infinitum, is one of them. I am currently reading his book. I thought of waiting until I was finished with the book before writing this blog post, but I decided to go ahead and splurt out my thoughts.

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Charles Petzold gives a good review of Rotman’s book here.

Petzold says:

“We begin counting 1, 2, 3, and we can go on as long as we want.

That’s not true, of course. “We” simply cannot continue counting “as long as we want” because “We” (meaning “I” the author and “you” the reader) will someday die — probably in the middle of reciting a very long (but undoubtedly finite) number.

What the sentence really means is that some abstract ideal “somebody” can continue counting, but that’s not true either: Counting is a temporal process, and at some point everybody will be gone in a heat-dead universe. There will be no one left to count. Even long before that time, counting will be limited by the resources of the universe, which contains only a finite number of elementary particles and a finite amount of energy to increment from one integer to the next.”

Is Math a Human Activity or Eternal Truth?

Before continuing on to infinity (which is impossible of course), I want bring up a related topic that Rotman addresses: the nature of math itself. My thoughts at the moment are this:

You (reader) and I (writer) have brains that are almost identical as far as objects in the universe. We share common genes, language, and we are vehicles that carry human culture. We cannot think without language. “Language speaks man” – Heidegger.

Since we have not encountered any aliens, it is not possible for us to have an alien’s brain planted into our skulls so that we can experience what “logic”, “reality” or “mathematical truth” feels like to that alien (yes, I used the word, “feel”). Indeed, that alien brain might harbor the same concept as our brains do that 2+2=4….but it might not. In fact, who is to say that the notion of “adding” means anything to the alien? Or the concepts of “equality”? And who is to say that the alien uses language by putting symbols together into a one-dimensional string?

More to the point: would that alien brain have the same concept of infinity as our brains?

It is quite possible that we can never know the answers to these questions because we cannot leave our brains, we can not escape the structure of our langage, which defines our process of thinking. We cannot see “our” math from outside the box. That is why we cannot believe in any other math.

So, to answer the question: “Is math a human activity or eternal truth?” – I don’t know. Neither do you. No one can know the answer, unless or until we encounter a non-human intelligence that either speaks an identical mathematical truth – or doesn’t.

Big Numbers are Patterns

My book, Divisor Drips and Square Root Waves, explores the notion of really large numbers as characterized by pattern rather than size (the size of the number referring to where it sits in the countable ordering of other numbers on the 1D number line). In this book, I explore the patterns of the neighborhoods of large numbers in terms of their divisors.

This is a decidedly visual/spatial attitude of number, whereby number-theoretical ideas emerge from the contemplation of the spatial patterning.

The number:

80658175170943878571660636856403766975289505440883277824000000000000

doesn’t seem to have much meaning. But when you consider that it is the number of ways in which you can arrange a single deck of cards, it suddenly has a short expression. In fact it can be expressed simply as 52 factorial, or “52!”.

So, by expressing this number with only three symbols: “5”, “2”, and “!”, we have a way to think about this really big-ass number in an elegant, meaningful way.

We are still a LONG way from infinity.

Now, one argument in favor of infinity goes like this: you can always add 1 to any number. So, you could add 1 to 52! making it 80658175170943878571660636856403766975289505440883277824000000000001.

Indeed, you can add 1 to the estimated number of atoms in the universe to generate the number 10⁸⁰ + 1. But the countability of that number is still in question. Sure you can always add 1 to a number, but can you add enough 1’s to 10⁸⁰to each 10⁸⁰⁰?

Are we getting closer to infinity? No my dear. Long way to go.

Long way to “go”? What does “go” mean?

Bigger numbers require more exponents (or whatever notational schemes are used to express bigness with few symbols – Rotman refers to hyper-exponents, and hyper-hyper-exponents, and further symbolic manipulations that become increasingly hard to think about or use).

These contraptions are looking less and less like everyday numbers. In building such contraptions in hopes to approach some vantage point to sniff infinity, one finds a dissipative effect – the landscape becomes ever more choppy.

No surprise: infinity is not a number.

Infinity is an idea. Really really big numbers – beyond Rotman’s “realizable” limit – are not countable or cognizable. The bigger the number, the less number-like it is. There’s no absolute cut-off point. There is just a gradual dissipation of realizability, countability, and utility.

Where Mathematics Comes From

Rotman suggests taking God out out mathematics and putting the body back in. The body (and the brain and mind that emerged from it) constitute the origins of math. While math requires abstractions, there can be no abstraction without some concrete embodiment that provides the origin of that abstraction. Math did not come from “out there”.

That is the challenge that some thinkers, such as Rotman, are proposing. People trained in mathematics, and especially people who do a lot of math, are guaranteed to have a hard time with this. Platonic truth is built in to their belief structure. The more math they do, the more they believe that mathematical truth is discovered, not generated.

I am sympathetic to this mindset. The more relationships that I find in mathematics, the harder it is to believe that I am just making it up. And for that reason, I personally have a softer version of this belief: Math did not emerge from human brains only. Human brains evolved in Earth’s biosphere – which is already an information-dense ecosystem, where the concept of number – and some fundamental primitive math concepts – had already emerged. This is explained in my article:

The Evolution of Mathematics on Planet Earth

I have some sympathy with Roger Penrose: when I explore the Mandelbrot Set, I have to ask myself, “who the hell made this thing!” Certainly no mathematician!

After all, the Mandelbrot Set has an infinite amount of fractal detail.

But then again, no human (or alien) will ever experience this infinity.

Number Portraits

I designed a set of number portraits for the integers from 1 to 36.

Each number is either a prime or a composite. If it is a prime number, then it has two divisors: 1 and itself. This is visualized as the gray-colored half circle, where the top represents 1 and the bottom represents the number itself. Composite numbers have other pairs of divisors, and these are visualized as the smaller, colored arcs.

The perfect squares (4, 9, 16, 25, and 36) each have a line segment located at the square root.

The numbers 6 and 8 each have one pair of divisors (besides 1 and themselves); they are (2,3) and (2,4), respectfully. Since the first number in each pair is 2, these arcs are colored green. Divisor pairs in which the first divisor is 3 are colored blue; divisor pairs in which the first divisor is 4 are colored red. And divisor pairs in which the first divisor is 5 are colored yellow. These colors visualize divisibility by these first 5 positive integers.

The highly-composite numbers 12, 24, and 36 are shown enlarged below.

The number 36 has the most divisors in this set. It’s divisor pairs are

(1, 36) (2, 18) (3, 12) (4, 9) (6, 6).

These are in a similar spirit to the Divisor Plot images I created in 2010:

http://www.divisorplot.com/index.html

Thelonius Monk’s Shapeshifting Chord

monk-chord

One of my part-time hobbies is being a Monk interpreter. A Monk interpreter not only learns how to play Monk’s compositions, but also makes a point of getting into the head of this eccentric man. The reason to do this is that Monk was an improvisor – and he was driven by an inner vision. If you can tap that inner vision, then you can generate Monk-like music – and improvise on it…even while playing Beatles songs.

I wrote a piece in 2013 about Monk as a mathematician.

Math can be about patterns (visual or sonic). Math does not always have to be expressed in numbers. Monk once said,“All musicians are subconsciously mathematicians”.

A Symmetrical Chord

The chord I’m talking about has four notes. It is typically used as a dominant chord – which naturally resolves to the tonic. Unlike the classical dominant-seventh, this chord has a flatted fifth – which makes it slip into a symmetrical regime – as shown in the picture above – inscribed in the circle of fifths.

According to Wikipedia, this chord is called the “Dominant Seventh Flat-Five Chord“. The cool trick about this chord is that it can resolve to either of two different tonics – each being a tri-tone apart.

So for instance, a chord with these notes: Eb F A B can resolve to either Bb or E as the home key.

This chord also happens to contain 4 of the 6 tones in a whole tone scale, which Monk famously used (often as a dominant arpeggio).

If you are not familiar with music theory, you may still appreciate the beauty of sonic geometry and how it can generate such variety. If you apply similar concepts to rhythm as to harmony then you have a wonderfully rich canvas for endless musical expression. I like the way Monk wove these geometries together in a way that makes the foot tap and the ear twinge – and the brain tweak.

Monk was of course not the only one to apply these ideas – but he did accomplish something remarkable: the application of embodied math. If you have spent as much time as I have learning his language, listening to him improvise can cause a smile – or the occasional giggle – to pop out. Like an inside joke.

There is plenty of material on the internet about Monk. Here’s one voice among the many who have acquired an appreciation for Monk: How to Listen to Thelonius Monk – by George H. Jensen, Jr.

Why is it a Color “Wheel” and Not a Color “Line”?

This blog post was published in May of 2012 on EyeMath. It is being migrated to this blog, with a few minor changes.

I’ve been discussing color algorithms recently with a colleague at Visual Music Systems.

We’ve been talking about the hue-saturation-value model, which represents color in a more intuitive way for artists and designers than the red-green-blue model. The “hue” component is easily explained in terms of a color wheel.

Ever since I learned about the color wheel in art class as a young boy, I had been under the impression that the colors are cyclical; periodic. In other words, as you move through the color series, it repeats itself: red, orange, yellow, green, blue, violet…and then back to red. You may be thinking, yes of course…that’s how colors work. But now I have a question…

Why?

Consider five domains that can be used as the basis for inventing a color theory:

(1) the physics of light, (2) the human retina, (3) the human brain, (4) the nature of pigment and paint, and (5) visual communication and cultural conventions.

(1) In terms of light physics, the electromagnetic spectrum has a band visible to the human eye with violet at one end and red at the other. Beyond violet is ultraviolet, and beyond red is infrared. Once you pass out of the visible spectrum, there aint no comin’ back. There are no wheels in the electromagnetic spectrum.

(2) In terms of the human retina, our eyes can detect various wavelengths of light. It appears that our color vision system incorporates two schemes: (1) trichromatic (red-green-blue), and (2) the opponent process (red vs. green, blue vs. yellow, black vs. white). I don’t see anything that would lead me to believe that the retina “understands” colors in a periodic fashion, as represented in a color wheel. However, it may be that the retina “encourages” this model to be invented in the human brain…

(3) In terms of the brain, our internal representations of color don’t appear to be based on the one-dimensional electromagnetic spectrum. Other factors are more likely to have influence, such as the physiology of the retina, and the way pigments can be physically mixed together (a human activity dating back thousands of years).

(4) Pigment and paint are very physical materials that we manipulate (using subtractive color), thereby constituting a strong influence on how we think about and categorize color.

(5) Finally: visual communication and culture. This is the domain in which the color wheel was invented, with encouragement from the mixing properties of pigment, the physiology of the retina, and the mathematical processes that are formulated in our brains. (I should mention another influence: technology…such as computergraphical displays).

Red-Green-Blue

Consider the red-green-blue model, which defines a 3D color space – often represented as a cube. This is a common form of the additive color model. Within the volume of the cube, one can trace a circle, or a hexagon, or any other cyclical path one wishes to draw. This cyclical path defines a periodic color representation (a color wheel). A volume yields 2D shapes, traced onto planes that slice through the volume. It’s a process of reducing dimensions.

But the electromagnet spectrum is ONE-DIMENSIONAL. The physical basis for colored light cannot yield a higher-dimensional color space. The red-green-blue model (or any multi-dimensional space) therefore could not originate from the physics of light.

DID HUMANS INVENT PURPLE IN ORDER TO GLUE RED AND VIOLET TOGETHER?

An alternate theory as to the origin of the color wheel is this: the color wheel was created by taking the two ends of the visible spectrum and connecting them to form a loop (and adding some purple to form a connective link). I just learned that Purple is NOT a spectral color (although “violet” is :) Purple can only be made by combining red and blue. Here’s an explanation by Deron Meranda, in a piece called…

“PURPLE: THE FAKE COLOR – OR, WHAT REALLY LIES AT THE END OF A RAINBOW?“

And here’s a page about how purple is constructed in the retina: HOW CAN PURPLE EXIST?

Did the human mind and human society impose circularity onto the color spectrum in order to contain it? Was this encouraged by the physiology of our eyes, in which various wavelengths are perceived, and mixed (mapping from a one-dimensional color space to a higher-dimensional color space)? Or might it be more a matter of the influence of pigments, and the age-old technology of mixing paints?

Might the color wheel be a metaphorical blend between the color spectrum and the mixing behavior of pigment?

Similar questions can be applied to many mathematical concepts that we take for granted. We understand number and dimensionality because of the ways our bodies, and their senses, map reality to internal representations. And this ultimately influences culture and language, and the ways we discuss things…like color…which influences the algorithms we design.

Enough with this Square Root of -1 Business!

Like so many other people, I was kept from appreciating the beauty and utility of mathematics because of the way it was taught to me.

The majority of introductions to complex numbers start with the elusive and mysterious square root of -1, denoted by i.

A number that has an i stuck on to it is called “imaginary” (a convenient differentiator to “real”). Being asked to learn something that is called “imaginary” is not very motivating to young learners who work best starting with concrete metaphors.

51tPEpSto+L._SX322_BO1,204,203,200_

The imaginary number i is counterintuitive and confusing. And it’s not the coolest part. Sure, i was an important invention at a critical stage in the history of math when there was no good way to express z² = -1. And yes, it makes a good ending to a long story (which happens to be true): math has advanced through several expansions of the concept of “number” … from the counting numbers to the wholes – to the negatives – to the fractions – to the irrationals – and finally to complex numbers – where i came along and saved the day.

But…does this mean that invoking i is the best way to explain complex numbers to novices – to everyday people? I join many others in saying that there is a better way to learn about the wonderful world of two-dimensional numbers. One voice among those is Kalid Azad.

He speaks in metaphors and freely engages the visual mind to help us grasp math concepts using our whole brain. In his explanation on complex numbers, Azad says this about i: “It doesn’t make sense yet, but hang in there. By the end we’ll hunt down i and put it in a headlock, instead of the reverse.”

…..

When you get an intuitive, aesthetic feeling for why certain mathematical ideas are being taught, you become more motivated to learn the notation. The corollary: learning math notation without understanding why is like learning musical notation before ever being allowed to listen to or play music.

Paul Lockhart, in A Mathematician’s Lament, compares the way math is taught to a nightmare scenario in which music is taught to students using sheet music notation only (no actual music is played or heard) – until the student is advanced enough to start “using” it.

What is a Two-Dimensional Number?

When I read that complex numbers are really no more “imaginary” than real numbers, I decided that I would start dismantling my old worldview. Why should I assume that numbers have to be one-dimensional? Over time, I became more accustomed to the notion that a number can occupy a plane (the complex plane) and not just a line (the number line). Learning how to make images of the Mandelbrot Set helped a lot.

Think of Multiplication as Rotation

Instead of trying to wrap your mind around i, and how it magically makes equations come out right, let’s start with geometry. Think of multiplication as rotation and expansion. In the blog Girls Angle, Ken Fan introduces complex number multiplication in a nice visual way… here.

Here’s a video explaining complex numbers in terms of physical metaphors, and eventually explaining why the square root of -1 becomes a necessary part of the notation.

Squaring

Consider the following diagram showing what happens when you square certain complex numbers that lie on the unit circle:

complex plane gravitation

The dot on the right represents the complex number (1+0i). When you square it, it stays the same (no surprise: 1×1=1). The number at the left is (-1+0i). When you square that, it becomes (1+0i). But when you square the number at top (0+1i) it “rotates” by 90 degrees to (-1+0i). Finally, at the bottom, the number (0-1i) rotates…but would it be correct to say that it rotates by 90 degrees clockwise to (-1,0i)? Depends on how you look at it. Rotating by 270 degrees counter-clockwise has the same result. This is the nature of rotation and angular reality: it is periodic – it cycles…it repeats.

What an awesome idea. Multiplication is like doing a whirling dervish jig.

Animated Squaring

Here’s an interactive tool I made that allows you to play with 200 dots (complex numbers) randomly scattered on the complex plane. You can experience what happens when complex numbers are squared. It also allows you to multiply the dots (using a complex number dot that you can drag along the screen).

http://ventrella.com/ComplexSquaring/

This interactive tool might make you feel as if the dots on the screen are obeying some sort of gravitational law of physics. Well, in a way, yes, that’s what’s happening. When you add, multiply, or exponentiate numbers, you get a new number. In the complex plane, the space where that change takes place is two-dimensional. That’s cool! We like images.

Here’s another visual tool: when we multiply two complex numbers, such as (a+bi) and (c+di), we can visualize the operation in this way:

In pseudocode:
realPart = (a*c) - (b*d); imaginaryPart = (a*d) + (b*c);

This explanation of multiplication does not require i.

To this day, I STILL do not feel very much music when I think about the square root of -1.

On the other hand, the more I play around with visualizing and animating complex numbers, the more intuitive they become, and the deeper my sense that these numbers are as real as any old one-dimensional number.

They are not imaginary at all.

Math Word Problems are Problematic

Mark Twain said: “Never let school interfere with your education.“

Here’s a math riddle:

“Peter has 21 fewer marbles than Nancy. If Peter has 43 marbles, how many marbles does Nancy have?”

The first sentence requires me to do some linguistic fiddling. There is an implication that both Peter and Nancy possess marbles – but it is not directly stated. The second sentence begins with “If”, which means the primary grammatical elements in the question are postponed until the end. Let’s re-phrase this riddle to say:

“Peter and Nancy each have a bag of marbles. Peter has 43 marbles in his bag. Peter has 21 fewer marbles than Nancy has. How many marbles does Nancy have in her bag?”

….

This might make the riddle easier to solve. Or it might not. Either way, I can say for sure that all this wordy bullshit is irrelevant to the actual math.

Math, like Music, is a Universal Language

Now consider what it would be like if you were naturally talented in math, and you were faced with a math riddle expressed in English…but English were not your first language. You may have to spend more time on the question, and you may make some critical mistakes. The subtleties of one language may not translate to another language, causing you to trip up.

We are playing with words here. Now, playing with words is fine; it’s part of how we learn to speak, listen, read, and write. In fact, playing with words that have mathematical content is a good exercise. But this should not come into play for testing students on math skills. The problem (as always) is in the testing.

Here’s another one:

“Sue has two pencils. She spends one hour at the store and buys three more pencils. How many pencils does Sue have in all”.

bivdg4wrggssxq8akk2r

WTF does “spends one hour in the store” mean? Is this just narrative fluff, or is there some clever hint in there?

If I had been presented with this problem as a young student, I would have spent some time mulling over “spends one hour at the store”. However, this is irrelevant and unrelated to the answer.

How to Obfuscate Mathematical Thinking With Clever Language

For dyslexic students, students who learn through action (kinesthetic learners), students who are visual thinkers, and students who learn best by building things, this wordsmithing can be a recipe for failure.

In the real world of adults getting things done and making a living, math is rarely experienced in the form of clever riddles. Math – at its best – is manifested deep within the texture of our daily actions.

Here’s another one:

“You have 24 cookies and want to share them equally with 6 people. How many cookies would each person get?”

Let’s think about this. I “have” 24 cookies. (That’s a lot of cookies – why would I have so many cookies?) I “want” to share them with 6 people. Okay. I have a desire to share cookies. So far so good. I’m a generous guy! But then the second sentence appears unrelated: “How many cookies would each person get?” Wait a minute: am I about to give these cookies to these people? And what exactly does “equally” mean?

I know it may seem trivial for me to analyze these details. As an adult I know what this sentence means. But as a young student, I may not have had the full vocabulary or grammatical wherewithal to jump right to an answer. Also, as a “narrative learner”, I would have really wanted to make sure I understood the characters involved, their motivations, etc. I could imagine getting easily get swept up by the storyline (simple as it is).

In short, by working out the characters of this story and their motivations, I may not actually be doing math: I might be engaging in language craft and storytelling. Which is great! But this should not interfere with my being tested on my innate math skills.

Here’s another:

“Kennedy had 10 apples. She gave some to John. Now she has 2 apples left. How many apples did she give to John?”

The tense of this little story jumps back and forth between past and present. At age 55, I am now quite facile with language, but when I was 10, I would have had to put in some effort into parsing these shifts in tense.

tumblr_ma5ndonxYD1rgqecyo1_500

In fact, my language skills were quite poor when I was 10, and this had an impact on all my school subjects (not just math). Later in life, after I had escaped school and actually started to gain some relevant skills, MIT offered me an opportunity to earn a Master’s degree. They did not ask me any math riddles. MIT knows better than that.

Language

One might argue that language skills are fundamental and important for learning most anything. That’s accurate. Reading, writing, speaking, and listening are fundamentally useful, and the better you are at language, the better you are likely to become at most other skills.

If this is the case, we might conclude that mixing grammatical sentence structure with mathematical logic is a valuable skill.

Indeed.

But school curriculum designers should not confuse the ability to parse a cleverly-crafted sentence with one’s innate mathematical abilities.

The problem, as always, is with TESTING.

I’ll close with this:

An Open Letter to the Education System: Please Stop Destroying Students

The Evolution of Mathematics on Planet Earth

$math-heart$ Many people couldn’t imagine Math and Biology going out on a date. Flirting with each other from time to time…maybe. But a date? Never! Math is precise, abstract, cool, and distant. Biology is messy, unpredictable, prone to mood swings, and chemically dependent…as it were.

But this may be changing.

“The conversion of biology into a more quantifiable science will continue to the extent that it might even become the main driving force behind innovation and development in mathematics”

— Philip Hunter

Let me explain why I think Math and Biology are ultimately compatible, and in fact, part of a Single Reality.

tumblr_my165xRv5f1swaxzgo1_250

I have written a few articles on the subject of math, and raised questions as to the universality, truth-status, and God-givenness of Math. Here is something to consider about Math and Biology:

Math Evolved in the Biosphere

Let’s start with numbers. Imagine a mother crow busily feeding her three chicks. She would become worried if she came back to her nest to suddenly find two chicks instead of three.

She would know there something is wrong with this picture…because crows can count (they can subitize small numbers, like about 2 or 3).

How did it come about that some animals, like crows and humans, can count? First of all, in order for intelligent beings to be able to count, they have to live in an environment where countable objects are found, and where counting has some evolutionary benefit. Consider a gaseous planet where fluids intermix and there is no way to detect a “thing” or “event” and to compare that with another “thing” or “event”. In this kind of world, there is nothing to count.

For that matter, it is unlikely that an intelligent entity that can count could ever evolve on such a planet in the first place, because structure and differentiation at some physical level are required for living things to bootstrap themselves into existence.

Theories of autopoiesis, negentropy, and the emergence of mind from matter rely on the existence of a prior structure to the universe where it is possible for self-regulation, and self-creation to arise. One might say that the origins of life had a head start long before those first molecules started dancing together and accidentally reproducing. Maybe it wasn’t such an accident after all.

…which brings me to a core concept: since Earth’s biosphere gave rise to animals that can count, as well as those things that can be counted – at the same time, we must understand ourselves as in and of the biosphere – we and it all evolved together: one did not come before the other.

Which came first: the chicken or the egg? Neither. They have both been in a continual state of becoming since egg-like things and chicken-like things have existed. And if you go back in time far enough, these things look less and less like chickens and eggs.

We animals have evolved to understand containment, and that is partly because hierarchy evolved within the fabric of physical biology. We know what it means for something to be “inside” or “outside” of something else. We clumpify, categorize, differentiate, compare, and identify. All animals need some degree of this compartmentalization of nature in order to operate within it.

We cannot separate our math from the environment from which it evolved. The very foundations of math evolved within the bodies and minds of animals as a part of evolution. At least this is what several recent scientists and philosophers are suggesting. (Mathematicians are more likely to claim that math is universal, constant, and unchanged by biology.)

OctoMath

In a previous article I consider what kind of math would have emerged if octopuses has evolved to become the complex and dominant species on earth, instead of humans. This is not so hard to imagine, considering how intelligent they are.

Would an advanced octopus race have stumbled upon complex numbers? Would they have become as obsessed with the Cartesian coordinate system as we are? Since they have no skeletons, would they have formulated a geometry based on angles and lengths? Of course we can’t know, but it is likely that they would have created some math concepts that we may never achieve. And that would be because the long history of math that we have built and that we rely on to create new math has taken our brains and societies too far away from the place where an octopus-like math would naturally arise.

Now consider aliens from a completely different kind of planet than Earth. What kind of math would originate in that world? Many people would argue that math is math and it doesn’t matter who or what discovers or articulates it. And there may be some truth to this. But we can only hope and imagine that this is the case.

Until we meet aliens from another planet and ask them if they understand and appreciate the fibonacci sequence, I have to assume that their math is different than ours.

What do you think?

(I would have consulted one of my octopus friends on the subject…but I don’t speak their language).

Quantum Physics Has a Language Problem

I have become interested in theories of mind and all the new thinking at the intersection of physics and consciousness. So when I set out to read The Self-Aware Universe by Amit Goswami, I hoped to get a better sense of how quantum physics relates to mind.

Didn’t happen.

I also didn’t get any major insights about “action at a distance“. And most of all, I did not get any deeper insights on the idea that the act of observation can change the physical world. I’ve known about quantum mechanics for a while – enough to have a casual conversation over beer – or more likely – over a joint. But I expected that Goswami would help me get to the next level of understanding. I read the words, I followed the logic…

…but nothing ever got much farther than a few centimeters into my brain. There was no gut feeling – no somatic resolution.

Now, to be sure, I wasn’t expecting epiphanies to come tumbling out. After all, Richard Feynman famously said, “If you think you understand quantum mechanics, you don’t understand quantum mechanics.”

So, I was appropriately prepared for the difficulty of the subject matter.

What the Hell is a “Quantum Object” Anyway?

Sean Carroll says that physical theories:

“…aren’t supposed to have ambiguities … the very first thing we ask about them is that they be clearly defined. Quantum mechanics, despite all its undeniable successes, isn’t there yet.”

The main problem with explanations of quantum physics is the choice of words.

The terms “observation”, and “measurement” have particular meanings in the physicist’s lab, where a scientist might be trying to gather data on the behavior of a single photon.

Truly not something that most of us experience in daily life. Even the sight of a faint star in the night sky involves a hell of a lot of photons. And one second of this experience is actually a really long time.

But…a single photon?

I wonder if the scientist in the lab actually “experiences” a photon anyway. How does one “experience” a photon? And what does it mean to “measure” or “observe” something as fleeting and tiny as a subatomic particle?

Sean Carroll again:

“There is no consensus within the physics community about what really constitutes an observation (or “measurement”) in quantum mechanics, nor on what happens when an observation occurs.”

Another problematic term is “quantum object”. The word “object” is very familiar in classical physics. But it invites contradiction and cognitive dissonance when applied to phenomena on the quantum level.

Niels Bohr said: “We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections.”

While reading explanations on quantum physics, I become optimistic: I feel as if I am about to get a picture of why certain puzzling phenomena are true. Authors use familiar narratives and metaphors that I have direct experience with, but what they are illustrating are observations in a physics lab where fleeting subatomic particles exhibit paradoxical behaviors. These carefully-orchestrated observations that only happen in expensive laboratories are hardly the stuff of everyday experience.

And then they start talking about cats in boxes – right after telling us that cats and boxes are VERY DIFFERENT than subatomic particles.

Thanks!

By the way…apparently, it IS possible to experience the effects of quantum physics in your own home:

I just love the fact that styrofoam cups were used in this experiment.

Can Quantum Physics Ever Really Be “Explained?”

Because our sense organs and brains are optimized to deal with things on a human scale, it’s difficult for us to think about things as small as atoms (where quantum physics really matters) or as big as galaxies (where relativity really matters).

As I set out to write this article, I did some searching and noticed right away that a lot of people have pointed out that quantum physics has a language problem. And so here is where I bow out, and let the real experts speak…

Is there a Language Problem with Quantum Physics?

The Copenhagen Interpretation

So, You’re Not a Physicist…

Quantum Physics and Human Language

What If There’s a Way to Explain Quantum Physics Without the Probabilistic Weirdness?

Quantum Mechanics Made Easy

Maybe classical clockwork can explain quantum weirdness