# Category Archives: Brain Bubble

## BB #85: More Fraction Fun

I don’t know why I’m so fascinated that the rational numbers are countable even though they’re a dense subset of the uncountable real numbers. A rational number can be arbitrarily close to any real number, making you think they’d be infinite like the reals, but in fact, nearly all numbers are irrational (and an uncountable subset of the reals).

So, the rational numbers — good old p/q fractions — though still infinite are countably infinite (see this post for details).

More to the point here, a common way of enumerating the rational numbers, when graphed results in some pretty curves and illustrates some fun facts about the rational numbers.

## BB #84: Zeno Was Right!

Zeno’s famous Paradoxes involve the impossibility of arriving somewhere as well as the impossibility of even starting to go somewhere. And that flying arrows have to be an illusion. [Time flies like an arrow, but fruit flies like a banana.]

If Zeno were alive today, he’d be over 2500 years old and would have seen his paradoxes explained in a variety of ways by a lot of very smart people. Yet at heart they still have some metaphysical oomph. And the thing is, at least in some contexts, Zeno was (sort of) right. There is something of a paradox here involving space and time.

Or at least something interesting to think about.

## BB #83: The Born Rule is Pythagorean

It’s actually obvious and might fall under the “Duh!” heading for some, but it only recently sunk in on me that the Born Rule is really just another case of the Pythagorean theorem. The connection is in the way the coefficients of a quantum superposition, when squared, must sum to unity (one).

For that matter, Special Relativity, which is entirely geometric, is yet another example of the Pythagorean theorem, but that’s another story. (One I’ve already told. See: SR #X6: Moving at Light Speed)

The obvious connection is the geometry behind how a quantum state projects onto the basis eigenvectors axes.

## BB #82: Symmetry Breaking

In The Road to Reality (2004), Roger Penrose writes about a great analogy for symmetry breaking. Apparently, this analogy is rather common in the literature. (No, it’s not the thing about the pencil — this one involves an iron ball.) Once again, I find myself agreeing with Penrose about something; it is a great analogy.

Symmetry breaking (which can be explicit or spontaneous) is critical in many areas of physics. For instance, it’s instrumental in the Higgs mechanism that’s responsible for the mass of some particles.

The short post is for those interested in physics who (like I) have struggled to understand exactly what symmetry breaking is and why it matters.

## BB #81: Animal Gods

I’ve lived with a Beagle, a Keeshond, a Belgian Shepard, a Great Dane, and a Black Labrador. I’ve dog-sat a German Shepard, two Black Labs, and the delightful Bentley, an American Bully.

I’m not bragging or claiming expertise (many have much more and far broader experience living with dogs). Just saying I’ve spent some solid hours with dogs pondering what the world looks like to them, how they perceive things.

It’s often struck me that, while humans may imagine and believe in gods (or not), animals live in a world where apparent gods walk among them. Dogs, and some other animals, live with their god(s) — depend on them and are subject to their every whim.

## BB #80: Gravity Waves

Being retired, along with doing all my TV watching via streaming services, has the consequence of almost completely disconnecting me from the weekly rhythm. Weekends mean nothing when every day is Saturday. To create some structure, I follow a simple schedule. For instance, Mondays I do laundry and Thursdays I buy groceries.

More to the point here, Monday (and sometimes Tuesday) evenings are for YouTube videos, many of which are science related. Last night I watched Jim Baggott give two talks at the Royal Institution, one about mass, the other about loop quantum gravity (LQG).

In the latter, Baggott mentioned gravity waves and that generated a Brain Bubble.

## BB #79: Near Zero

If you know me, or if you’ve followed this blog a while, you know I honor Solar holidays more than human ones. The former are directly linked with the seasons, obviously (and who doesn’t love seasons), but to me they’re about how much (or how little) sunlight we get.

If you know me, or if you’ve followed this blog a while, you know sunlight really matters to me. The skylight in my living room was a key buying point for my condo, and enough south-facing windows was always a requirement.

I may love the night and the lights, but I thrive on sunlight.

## BB #78: Relational Theories

I read Three Roads to Quantum Gravity (2001), by Lee Smolin, a theoretical physicist whose thoughtful style I’ve always appreciated. I don’t always agree with his ideas, though. This book is about Loop Quantum Gravity, in which Smolin has invested considerable effort, and that idea I’m utterly neutral on. It does seem to make more sense than string theory.

One notion I have a lot of trouble swallowing (like a cup of coffee with eight lumps of sugar) is the relational view. (As a philosophy, relationism. Al stayed home.) It’s a fundamental aspect of LQG.

But I (and apparently Kant agrees) think Leibniz was wrong.

## BB #77: Smooth Spacetime

I read Three Roads to Quantum Gravity (2001), by Lee Smolin, a theoretical physicist whose thinking I’ve appreciated since I read his 2006 book, The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next.

Three Roads, as the title suggests, is about the efforts to reconcile quantum mechanics and General Relativity, our two best physical theories. String theory is one road, Loop Quantum Gravity (Smolin’s preferred approach) is another. The third road is complete theory reconstruction (such as discussed by Philip Ball in his book Beyond Weird).

None of that is the subject of this post.

## BB #76: The Holographic Theory

I finished reading Three Roads to Quantum Gravity (2001), by Lee Smolin, a theoretical physicist whose general sensibility I’ve always appreciated. I don’t always agree with his ideas, but I like the thoughtful way he expresses them. Smolin brings some philosophical thinking to his physics.

While he added a lengthy Postscript to the 2017 edition, the book is outdated both by time and by Smolin. In 2006 he published The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next, which explored issues in the practice of theoretical physics. But in 2001 he still thought string theory was (at least part of) The Answer.

Almost none of which is the subject of this post.