Saturday, September 26, 2026

It’s been a while. Back to Topology

 Yes. In fact, mathematicians study non-orientable 3-dimensional manifolds, and they're a natural higher-dimensional analogue of the Möbius strip.

The key idea is the same:

  • An orientable space lets you consistently define "handedness" everywhere.
  • A non-orientable space does not.

From the Möbius strip to 3D

A Möbius strip is a 2D non-orientable surface. If you move a little 2D coordinate frame around it, it can come back mirrored.

Now imagine a fully 3D universe. At every point you define a little right-handed coordinate system ((x,y,z)). In an orientable 3D space, you can move that frame around any closed loop and it always returns with the same handedness.

In a non-orientable 3D space, there exist loops such that transporting the frame around them returns it as a left-handed frame.

So the notion of chirality reversal survives in 3D.

A simple example

One way to construct a non-orientable 3D space is analogous to how a Möbius strip is built.

For a Möbius strip, you take a rectangle and identify the ends with a flip.

For a 3D version, take a box and identify opposite faces, but make one identification include a reflection. Locally the space looks perfectly ordinary and three-dimensional, but globally an object traveling far enough can return to its starting point with reversed orientation.

You can think of it as a "Möbius universe."

What would happen to a person?

This is where things get philosophically interesting.

Suppose a right-handed astronaut travels around a loop that represents the orientation-reversing topology and comes back.

There are two ways to describe the result:

  1. Relative to the global topology, they have returned mirrored.
  2. Locally, they notice nothing unusual during the trip.

In fact, if the entire universe were non-orientable, distinguishing whether they had become a mirror image becomes subtle because there is no globally consistent definition of "right" and "left" to compare with.

Relation to parity

This touches an interesting point in physics.

For a purely geometric non-orientable 3-space, a loop can effectively implement a parity transformation (a mirror reflection). In particle physics, parity is not merely a coordinate convention; some processes genuinely distinguish left from right. If our universe had a non-orientable spatial topology, there could be deep consequences for the behavior of chiral particles.

A 4D perspective

Just as a Möbius strip can be viewed as a line whose local transverse direction flips after one circuit, a non-orientable 3-manifold can often be understood as a 3D space whose local frame flips after traversing certain loops. The analogy is almost exact:

Dimension

Orientable example

Non-orientable example

2D

Cylinder

Möbius strip

3D

3-torus

Various non-orientable 3-manifolds

The remarkable thing is that non-orientability is not tied to any particular dimension. It is a topological property that can occur in 2D, 3D, and higher dimensions.

So the answer is yes: there are non-orientable 3D spaces, and in such a space an object transported around certain closed paths can return with its handedness reversed in essentially the same way a 2D figure does on a Möbius strip. That idea has made non-orientable manifolds important in topology and has occasionally inspired speculative models of the large-scale structure of the universe.


Saturday, August 8, 2026

Common radioactive foods

 Pretty much all foods are slightly radioactive, because living things contain naturally occurring radioactive isotopes, especially potassium-40 (K-40) and tiny amounts of other radionuclides. 1 

Among common foods, the most radioactive tend to be: 

  1. Brazil nuts 🌰


    • Generally considered the most radioactive common food.


    • Their deep roots accumulate unusually high amounts of radium from the soil. 12


  1. Bananas 🍌


    • Famous for containing potassium, a tiny fraction of which is radioactive potassium-40.


    • The "banana equivalent dose" is often used as a lighthearted reference for very small radiation exposures. 13


  1. Potatoes 🥔


    • Rich in potassium and therefore contain naturally occurring K-40. 4


  1. Lima beans


    • Also relatively high in potassium and natural radioactivity. 4


  1. Carrots 🥕


    • Another potassium-containing food with measurable natural radioactivity. 4


  1. Shellfish and some seafood 🦪


    • Can accumulate small amounts of naturally occurring radioactive elements from the marine environment. 2


  1. Low-sodium salt


    • Often contains potassium chloride as a sodium substitute, increasing its K-40 content. 4


The important takeaway is that none of these foods are dangerous because of their radioactivity. The EPA notes that the levels are extremely low and do not pose a radiation risk as part of a normal diet. 1 

Fun fact: your own body is radioactive because it naturally contains potassium-40 and carbon-14. Every person experiences thousands of radioactive decays per second inside their body, and that's completely normal. 4


How to survive solar system vs. black hole…

 Yes. If humanity had advance warning, the challenge would become less "how do we stop the black hole?" and more "how do we remain a technological civilization while the Solar System becomes unstable?" 

A few possible survival paths: 

1. Earth survives, but its orbit changes


This is probably the best-case scenario. 

If Earth ended up in a stable orbit around the Sun, or around a Sun-black hole binary, humanity might simply adapt to different climate conditions with: 

  • Massive energy infrastructure


  • Climate engineering


  • Underground or enclosed cities


  • Space-based habitats supplementing Earth


Human civilization would be transformed, but not necessarily destroyed. 

2. Earth survives, but becomes too cold


If Earth's orbit moved outward, or if the Sun's energy reaching Earth changed substantially, the surface could become uninhabitable. 

In that case humanity might rely on: 

  • Fusion power


  • Geothermal energy


  • Underground habitats


  • Sealed biospheres


A sufficiently advanced civilization could survive even on a frozen Earth. 

3. Off-world habitats


Long before the situation became catastrophic, humans might move into: 

  • O'Neill cylinders


  • Large rotating space habitats


  • Artificial worlds built from asteroids


  • Habitats around Jupiter, Saturn, or other surviving bodies


Such habitats could be powered by fusion rather than sunlight. 

4. Living around the black hole


Surprisingly, a black hole could actually be an energy source. 

Matter falling into a black hole forms an accretion disk, and accretion can convert mass into energy very efficiently. In some circumstances it can be more efficient than nuclear fusion. 

An advanced civilization might build habitats: 

  • Orbiting far from the event horizon


  • Harvesting radiation from infalling matter


  • Using the black hole as a gravitational energy source


The major problem would be managing the intense radiation generated by the accretion process. 

5. Leaving the Solar System


This is probably the ultimate backup plan. 

If humanity had centuries or millennia of warning, it might build: 

  • Generation ships


  • Suspended-animation vessels (if that becomes possible)


  • Self-sustaining colony fleets


  • Interstellar probes carrying embryos or digital minds


Even modest fractions of the speed of light would allow migration to nearby star systems. 

The interesting part


A rogue black hole encounter would likely unfold over thousands to millions of years, not overnight. Planetary orbits are huge, and gravitational changes take time to propagate through the Solar System. 

That means the biggest advantage humanity would have is warning time. A civilization capable of building large-scale space infrastructure for even a few centuries before the worst effects arrived would have many plausible survival options. 

In a sense, this scenario is one of the more survivable cosmic disasters. A nearby supernova or gamma-ray burst could affect Earth with little opportunity for intervention, whereas a gravitational disruption of the Solar System would likely provide a long period during which an advanced civilization could prepare, relocate, or adapt.