That’s… interesting

But in our Physics Project we’ve developed a fundamentally different view of space—in which space is not just a background, but has its own elaborate composition and structure. And in fact, we posit that space is in a sense everything that exists, and that all “things” are ultimately just features of the structure of space. We imagine that at the lowest level, space consists of large numbers of abstract “atoms of space” connected in a hypergraph that’s continually getting updated according to definite rules and that’s a huge version of something like this…

~ Stephen Wolfram from, https://writings.stephenwolfram.com/2022/03/on-the-concept-of-motion/

I’m not sure what to say about this. I am certain that Wolfram is not crazy and that he is brilliant, but he’s pretty far beyond what I can understand. (Picture me doing that slightly askew, squinting thing.) On the other hand, if they really are making the progress they seem to be… it’s going to be a neat time to be alive, in another decade when they get things sorted out.

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Variance

However—fourth—over the last century there’s a huge relationship between how rich a country is and the variance in growth. The richest countries have low variance: They all stubbornly keep growing at around the same 1 or 2%. However, middle-income countries vary enormously.

~ “Dynomight” from, https://dynomight.net/gdp/

There’s several different interesting threads in this article. But this point about variance leapt out at me. I’m reminded of how just the other day, a piece about statistics that I mentioned was talking about variance (if you clicked through and read the article.) Variance feels like a sort of second-order thinking that I probably should be doing more often.

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Tasty numbers

For five years as a data analyst, I forecasted and analyzed Google’s revenue. For six years as a data visualization specialist, I’ve helped clients and colleagues discover new features of the data they know best. Time and time again, I’ve found that by being more specific about what’s important to us and embracing the complexity in our data, we can discover new features in that data. These features can lead us to ask better data-driven questions that change how we analyze our data, the parameters we choose for our models, our scientific processes, or our business strategies.

~ Zan Armstrong from, https://stackoverflow.blog/2022/03/03/stop-aggregating-away-the-signal-in-your-data/

This one just has neat graphs in it. And it has some interesting insights about what data analysts do. The phrase “big data” has been tossed around a lot in recent years—the way “quantum mechanics” gets tossed around by people who have no idea about that either. This article isn’t about truly big data sets, but it’s a neat dive into energy usage as an example of some spiffy data analysis.

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It’s subtle but critically important

It’s broadly agreed these days that consciousness poses a very serious challenge for contemporary science. What I’m trying to work out at the moment is why science has such difficulty with consciousness. We can trace this problem back to its root, at the start of the scientific revolution.

~ Philip Goff from, https://www.edge.org/conversation/philip_goff-a-post-galilean-paradigm

I once had a mathematics professor make a comment that it’s fascinating that mathematics is able to explain reality. I double-clutched at the time. And every single time I think about the point he was making, I still pause and my mind reels. If one is looking at—for example—classical mechanics, and one studies the ballistic equations, one can go along nicely using forces and trigonometry, and understand golf balls and baseballs in flight. Soon you realize your mathematics is only an approximation. So you dive into fluid mechanics, which requires serious calculus, and you then understand why golf balls have dimples and why the stitching on baseballs is strictly specified in the rules. All along the way, mathematics models reality perfectly!

But why? So you keep peeling. The math and physics gets more and more complicated—stochastic processes, randomness, quantum mechanics, wave-particle theory, etc.—as each layer answers another “why”… but it’s … is “cyclical” the right word? No matter how far you go, you can always ask “why” again, for the most complex and most accurate system you model and explain.

Down there at the bottom, that’s where Galileo declared there was a distinction between physical reality, and consciousness and the soul. We’ve had hundreds of years of progress via science on what Galileo divided off as “physical reality.” (And that progress is a Very Good Thing.) But as this article explores, is there actually a distinction? What if making that distinction is a mistake?

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Gömböc

So in a nutshell, Gömböc is cool, Hungarians are proud of it greatly. So naturally, they made a 4.5-ton statue replica of the shape.

~ Atlas Obscura from, https://www.atlasobscura.com/places/gomboc

I could probably write a blog post about other interesting math-related puzzles and shapes that come from Hungary… or about the number of Hungarian mathematicians… but instead, I’ll just point you towards this particularly interesting thing.

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Pasteur’s Quadrant

The core idea of Pasteur’s Quadrant is that basic and applied research are not opposed, but orthogonal. Instead of a one-dimensional spectrum, with motion towards “basic” taking you further away from “applied”, and vice versa, he proposes a two-dimensional classification, with one axis being “inspired by the quest for fundamental understanding” and the other being “inspired by considerations of use”

~ Jason Crawford from, https://rootsofprogress.org/pasteurs-quadrant

I’ve put a bit of thought into research. I’ve certainly considered the two properties of “research for understanding” and “research for application”. But I’ve never thought of them as two dimensions. Click through and check out the simple but illuminating quadrant graph.

And I’m immediately wondering: Can I think of a third dimension upon which to plot research? (Field-of-study comes to mind. Time; The thing being studied, is it something that happens in micro-time like particle physics, or macro-time like geology?) I’m also wondering: what other activities could be plotted in a quadrant? (Writing: insight versus length? Coaching: net change in performance versus time spent training?)

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Information loss

Our lack of perfect information about the world gives rise to all of probability theory, and its usefulness. We know now that the future is inherently unpredictable because not all variables can be known and even the smallest error imaginable in our data very quickly throws off our predictions. The best we can do is estimate the future by generating realistic, useful probabilities.

~ Shane Parrish from, https://fs.blog/2018/05/probabilistic-thinking/

It’s a good article—of course, why would I link you to something I think you should not read?

To be fair, I skimmed it. But all I could think about was this one graduate course I took on Chaos Theory. It sounds like it should be a Star Trek episode. (Star Trek: The Next Generation was in its initial airing at the time.) But it was really an eye-opening class. Here’s this simple idea, called Chaos. And it explains a whole lot of how the universe works. Over-simplified, Chaos is when it is not possible to predict the future state of a system beyond some short timeframe. Somehow, information about the system is lost as time moves forward. (For example, this physical system of a pendulum, hanging from a pendulum… how hard could that be?)

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That’s a moiré

“You don’t need [machine learning,]” Bryan said. “What you need is inverse Fast Fourier Transform.”

~ “Shift Happens” from, https://www.getrevue.co/profile/shift-happens/issues/moire-no-more-688319

I stumbled over a blog post, containing a pull-quote where someone mentioned inverse Fast Fourier Transform. (A mathematician named Fourier invented a fast way to do a certain sort of transformation that comes up a lot in science; It’s called a Fast Fourier Transform. There’s also a way to undo that transformation, called “the inverse”. Thus, Fast Fourier Transformations (FFT) and inverse FFT. Well, FFT/IFFT is the first thing I can recall that I could not understand. It was shocking. Every other thing I’d ever encountered was easy. But there I was, 20-some-years-old, in graduate school, and I encountered something that was beyond me. I think I had it sorted about 6 times and every time, the next morning, upon waking, it had fallen out of my head. Holy inappropriately long parentheticals, Batman!)

Anyway. Blog post. IFFTs. Time machine to the early 90s. Emotional vertigo.

…and then I clicked thru to the magnificent post which is brilliant. And then I realized the by-line was, “Shift Happens.” o_O This entire thing. I’m in nerd heaven.

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PS: Sorry, what? Oh, you read my title, heard the Italian word, “amore,” and wanted a, That’s Amore! pun? Okay, here: When an eel climbs a ramp to eat squid from a clamp… Yes. Really.

Why and how

Your ideas are worth less than you think—it’s all about how you execute upon them.

~ Chris Bailey from, https://alifeofproductivity.com/your-ideas-arent-that-unique/

The pull-quote says it all. I recently had a pleasant conversation, wherein the idea of the “why” and the “how” came up. Thanks to Simon Sinek, we all know to, “start with why,” (that is to say, start with the idea.) The idea is important, but it’s literally worthless without the execution. Because anything, multiplied by zero, is zero.

To my 20-something-year-old’s surprise, knowing Al Gebra turned out to actually be useful. Take, for example, evaluating some idea and its execution: The total value could be calculated by multiplying the value of the idea by the value of the execution. (Note my use of, “could be.”) Great ideas are represented by a large, positive value, and terrible ideas by a large, negative value; Similarly for the execution. Great idea multiplied by great execution? Huge total value.

This simple model also shows me how I regularly ruin my life: Terrible idea, (represented by a negative value,) with great execution… Or, great idea, with terrible execution, (represented by a negative value,)… either leads to a large negative total. Interestingly, the slightest negativity—in either of those cases—amplifies the magnitude of the other parameter’s greatness.

This leads to an algebra of idea-and-execution. If you’re going to half-ass the execution, (a negative value,) or you’re concerned that you cannot execute well, it’s better to do so with a “small” idea. Only if you’re sure you can do the execution passably well, (“positive”,) should you try a really great idea. If you work through the logic with the roles flipped, the same feels true. This leads to a question that can be used in the fuzzy, real world: Is this pairing of idea and execution in alignment? Am I pairing the risk of negative-execution align with a “small” idea, or pairing the risk of a bad idea with “small” execution. That to me is a very interesting “soft” analysis tool, which falls surprising out of some very simple algebra.

What I’m not sure about though is what to do with the double-negative scenarios. (Which I’ll leave as an exercise for you, Dear Reader.) Perhaps, I should be using a quadratic equation?

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Foucault’s Pendulum

Over on the Astronomy Stack Exchange site, (obviously I follow the “new questions” feed in my RSS reader,) someone asked if it was possible, without knowing the date, to determine one’s latitude only by observing the sun. These are the sorts of random questions that grab me by the lapels and shake me until an idea falls out.

So my first thought was: Well if you’re in the arctic or antarctic polar circles you could get a good idea… when you don’t see the sun for a few days. Also, COLD. But that feels like cheating and doesn’t give a specific value. Which left me with this vague feeling that it would take me several months of observations. I could measure the highest position of the sun over the passing days and months and figure out what season I was in…

…wait, actually, I should be able to use knowledge of the Coriolis Force—our old friend that makes water circle drains different in the northern and southern hemispheres, and is the reason that computers [people who compute] were first tasked with complex trigonometry problems when early artillery missed its targets because ballistics “appear” to curve to do this mysterious force because actually the ground rotates . . . where was I?

Coriolis Force, right. But wait! I don’t need the sun at all! All I need is a Foucault Pendulum and some trigonometry… Here I went to Wikipedia and looked it up—which saved me the I’m-afraid-to-actually-try-it hours of trying to derive it in spherical trig… anyway. A Foucault Pendulum exhibits rotation of the plane of the pendulum’s swing. Museums have these multi-story pendulums where the hanging weight knocks over little dominos as it rotates around. Cut to the chase: You only need to be able to estimate the sine function, and enough hours to measure the rotation rate of the swing-plane and you have it all; northern versus southern hemisphere and latitude.

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