Mindfulness is calculus made spiritual

OK, I'm wading into some deep philosophical waters here, given the title of this blog post, because I only took one semester of calculus in graduate school, and then only because I was forced to by the powers-that-be in control of the Portland State University Systems Science Ph.D program.

I found calculus to be difficult. By contrast, I've gotten back to reading an engaging book by Stephen Strogatz about calculus, Infinite Powers, which I blogged about back in August, noting that it had some spiritual aspects.

This morning, reading a chapter on "The Vocabulary of Change" before I meditated, I was struck by how mindfulness practice -- which basically involves focusing on what's going on here-and-now versus there-and-then -- resembles what Strogatz calls the Infinity Principle. 

Here's how Strogatz described this in the chapter I read today. 

Notice that we are using the Infinity Principle here -- we are trying to make a complicated curve simpler by chopping it into infinitesimal straight pieces. This is what we always do in calculus. Curved shapes are hard; straight shapes are easy, even if there are infinitely many of them and even if they are infinitesimally small. Calculating a derivative in this way is a quintessential calculus move and one of the most fundamental applications of the Infinity Principle.

In his book, Strogatz uses a graph of the length of days to talk about how an underlying mathematical function, in this case the complex motions of the Earth as it revolves around the sun, is used to produce a graph such as the one below that I found via some Googling.

What struck me is that while it's impossible to derive a mathematical function of life, we all have the feeling that our life consists of ups and downs. 

Our most significant "up," of course, is the moment of our birth. And our most significant "down" is the moment of our death. But in-between those moments we experience a wide variety of joys and sorrows, triumphs and disappointments, pleasures and pains.

It's natural to view the present moment in the context of both remembered previous ups and downs, and of imagined future ups and downs. However, this makes more sense when something is genuinely cyclical, as is the case with the amount of daylight (vertical axis in image above).

In our own life, it's often difficult to predict what is going to happen next. And our memory of what's happened in the past is prone to errors, since we tend to remember most clearly the Big Moments in life, not the Ordinary Moments -- even though the latter are much more common than the former.

So there's a lot to like about mindfulness, which I've noted is my current approach to meditation. 

Calculus can deal with curves such as those in the image above because it divides them into an infinity of straight lines. Similarly, mindfulness helps us to deal with the ever-changing circumstances of our life by guiding us to focus on the small things that are happening at this very moment, rather than the largeness of our actual past and potential future.

I'm not saying that mindfulness in any way takes away ups and downs, or pleasures and pains. But just as a portion of a curved line looks almost exactly straight if it is zoomed in enough, so are we able to look upon our life with more equanimity if we're able to be mindful of what is actually occurring to us -- versus what we hope will occur, or are worried will occur.

As a final observation, Strogatz uses Usain Bolt's record-breaking 100 meter dash performance in the 2009 World Championships as an example of how small ups and downs are largely meaningless when looking at a curve that is smooth at a larger scale. He shares a graph based on laser guns that tracked Bolt's speed hundreds of times a second.

The little wiggles on the overall trend represent the ups and downs in speed that inevitably occur during strides. Running, after all, is a series of leapings and landings. Bolt's speed changed a little whenever he landed a foot on the ground and momentarily braked, then propelled himself forward and launched himself airborne again.

...To me, these wiggles hold a larger lesson. i see them as a metaphor, a kind of instructional fable about the nature of modeling real phenomena with calculus. If we try to push the resolution of our measurements too far, if we look at any phenomenon in excruciatingly fine detail in time or space, we will start to see a breakdown of smoothness. 

...Yet if what we care about are the overall trends, smoothing out the jitters may be good enough. The enormous insight that calculus has given us into the nature of motion and change in this universe is a testament to the power of smoothness, approximate though it may be.

in the same way, mindfulness requires an appropriate level of resolution. Our life shouldn't be viewed in such excruciating detail as to miss the big picture, nor in such a broad scope as to miss the reality of what is actually happening at any given moment.

Comments

[Vinny]

Mindfulness is awareness of fastidious people. Atomic energy realm is beyond mindfulness because when this energy was present there was no mind then, no creation and only energy.

[Spence Tepper]

Calculus is used to describe motion, volume and time. Consider that Calculus not only divides continuous functions into discrete series, but in doing so, time as well.

From the perspective of Calculus, and indeed all equations involving change and time, time is considered an infinite series of static, discrete points. Points of time that themselves do not move.

Movement is nothing more than an infinite set of immovable and unchanging points. We move through a static series of infinite realities, each entirely unmoving.

Motion pictures, and even the brain, works in the same way.

What we perceive as continuous motion are the many fixed snapshots our brain captures of a reality Newton (and Liebnitz) described as a series of static unmoving events.

From this perspective movement doesn't actually exist, just as in a motion picture, no movement exists. We perceive movement in the thousands of static images flashed before our consciousness.

Time is at best, using Newton's model, an arrangement of a series of fixed and unmoving elements perfectly arranged.

It's like traveling on a train through scenery. It seems all the scenery is moving. But only we are moving through it.

Newton perfectly depicted this analogue world in a discrete digital model that has since moved technology forward in wonderful ways. But within it remains the secret of this reality.

Because the rate at which our brain takes snapshots is not the same as the rate at which we can perceive.

The hidden secret of Mindfulness is to see apart from our brain's movie projector. To see the static snapshots directly, to examine one or two. And in doing so, for that instant moment, Step outside of time.

[Sonia]

I used to have Namaste in big letters on a wall in my my room. When my brother (who excelled and math—breezed through calculus) saw it he said, “What did the mathematician say? Numbers stay 🙏”.

I know it’s an old joke but I hadn’t heard before and I thought it was so funny at the time (not sure what state my mind was in) that I bought the domain name. 😂

More on this later! I love this topic!!

[Meditator]

Whatever has been in the physical realm is definable by some law, theory, system, science etc but not a non-entity as the conscious 'observers' - the real we, wherein lie the surprise of surprises.

[Sukh Thandi]

Badal and RSSB relationship is so strong though Badal group claimed to believe in only SGGS .... not any living human guru but involved with GSD to deep .. who tell others that SGGS can't be guru...

https://www.google.com/amp/s/www.outlookindia.com/newsscroll/amp/mortal-remains-of-radha-soami-sect-chiefs-wife-consigned-to-flames/1679662

Mortal remains of Radha Soami sect chief''s wife consigned to flames
PB-RADHA SOAMI
Amritsar, Dec 6 Mortal remains of Radha Soami Satsang Beas chief Gurinder Singh Dhillon''s wife Shabnam Dhillon were consigned to flames on Friday. Â Â Â Â Â Â Â Â Â

She had passed away in a hospital in England on November 27. Â Â Â Â Â Â Â Â Â

Her last rites were performed at the dera headquarter, also known as Dera Baba Jaimal Singh, nearly 45 km away from the city of Amritsar.

She is survived by her husband Gurinder Singh Dhillon and two sons-- Gurpreet Singh Dhillon and Gurkirat Singh Dhillon.

The pyre was lit by her elder son Gurpreet Singh in the presence of family members and relatives.

Shabnam Dhillon had developed some complications after undergoing a stomach surgery.

She went to England on November 12, where she was operated upon on November 20.

Shabnam had undergone a surgery earlier at a Gurgaon hospital.

Prominent among those who attended the cremation were SAD chief Sukhbir Badal, his wife and Union minister Harsimart Kaur Badal, Akali leader Bikram Singh Majithia, Punjab ministers O P Soni and Vijay Inder Singla. JMS CHS RDK RDK

[Jen]

Hi Spence, sorry for my previous knee jerk reaction to your comment on Open Thread. Hope you can forgive me. I need to have more patience. We all have different mindsets.

Now this comment of yours on this thread I find very interesting:

"The hidden secret of Mindfulness is to see apart from our brain's movie projector. To see the static snapshots directly, to examine one or two. And in doing so, for that instant moment, Step outside of time."

Spence, every now and then I have something like a photo flash in my mind which surprises me and its a picture of something that happened in the past. Its quite strange at the time but I find it interesting. Wondering how long memories are stored in the brain and why sometimes a random memory will suddenly appear?

[Sonia]

Brian,

I read this post several times for some reason. It was as if my mind was telling me there’s something very important in this.

Turns out the “very important thing” was simple: when we’re truly in the moment we don’t feel the ups and downs. At least, that’s how my brain interpreted it.

We hear this sort of thing over and over again. The way we frame concepts gets to be like buzz words. Over time they carry less and less weight.

Water actually tastes different in different types of material—plastic, paper, glass, etc... Concepts are like water. Sometimes you have to put them in a different container to make them more palatable. And by palatable I mean understandable.

Thanks for putting this beautiful concept in a new container!!