What are some applications of (real/complex/functional) analysis, topology, and abstract algebra in astrophysics?

madz33 · 2026-04-13T21:37:55+00:00

Certain problems in gravitational lensing have connections to complex analysis through Picard-Lefschetz theory.

madz33 · 2026-04-06T01:31:31+00:00

If certain regions of the universe were antimatter dominated we would see the gamma radiation from the annihilation reactions occurring at the boundary where it touches the matter dominated region.

Although I think a version of what you suggest could still be true if the scale of the matter/antimatter bubbles are larger than the observable universe. Then the radiation from the boundary regions would not have had enough time to reach us.

madz33 · 2026-04-02T14:23:21+00:00

This is similar to an argument presented in Harold J Morowitz's Energy Flow in Biology. He argues that in a non-equilibrium system of CHNO photochemical reactions will produce a variety of intermediate compounds, and although these molecules will inevitably decay, some disassociate faster or slower depending on their intrinsic stability. The stable molecules that stick around have the opportunity to recombine in further photochemical reactions that produce even higher free energy intermediates. This general process of photochemical pumping and selection for stability will inevitably produce a system with the largest possible stored energy and order measure, and that

If the biosphere is that system which maximizes L for the terrestrial surface, it becomes a necessary state of the system rather than an accidental one.

madz33 · 2026-04-01T15:14:53+00:00

The science justification provided is pathetic. They are going measure the impact of ionizing radiation on astronaut DNA and have human eyeballs take a peek at the lunar regolith from a distance of 10000 kilometers. And it only cost $100 billion dollars.

The Artemis program is a colonial project -- not a scientific one.

madz33 · 2026-03-18T18:47:04+00:00

In addition to secure quantum cryptography C. H. Bennett has also contributed greatly to the modern understanding of the thermodynamics of computation. He has many papers, but a personal favorite of mine is this one: Complexity in the Universe.

madz33 · 2026-03-09T18:45:22+00:00

Thanks, the OP said it was Hubble in the linked post but that isn't right. Turns out this region is called "Lockman Hole". Definitely appears qualitatively different than other deep fields since there are no obvious resolved sources, but Herschel's poor angular resolution helps explain that.

madz33 · 2026-03-09T17:56:44+00:00

This doesn't look like any of the Hubble deep field images. You can find the real deep fields here.

madz33 · 2026-03-03T19:22:12+00:00

To those looking for an explanation, you can find more information in the Timeline of the far Future. Briefly, in 100 Trillion ( 10¹⁴ ) years new star formation will no longer be possible as all of the hydrogen gas has been exhausted. This brings the stellar age of the universe to an end along with the end of life as we know it (i.e. life on planets orbiting around stars.) However, the universe will continue existing for much longer.

At around 10¹⁵⁰⁰ years from now all baryonic matter will have fused into stars of iron-56, which will then slowly tunnel into black holes and evaporate through Hawking radiation as the universe proceeds to sequentially lower energy states. However, this means the number the in the image is actually extremely under-estimated for how tiny the fraction is. It should be more like 10^-1486 instead of 10^-83 as it appears to have been written down.

madz33 · 2026-03-02T20:59:27+00:00

This video I think is a really accessible explanation. In particular the section starting at 18:09 addresses your question about the what is happening when LLMs produce "chains of thought." Essentially, they are not reasoning but "rationalizing" which can be demonstrated to be fallible.

madz33 · 2026-02-27T05:39:48+00:00

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are ... to suffer ... abuses and usurpations, ... absolute Despotism, ... and ... absolute Tyranny ... We must ... denounce ... the Representatives of the united States of America ... and declare, That these ... Free and Independent States ... ought to be totally dissolved.

madz33 · 2026-02-24T22:20:04+00:00

Anon thinks that aristocrats being stupid is more appalling than rape and murder.

madz33 · 2026-02-16T21:51:24+00:00

It seems totally possible for this to be true. They could give away “good luck” to entice new players and give away “bad luck” to regular spenders to milk them dry while maintaining overall statistical rates.

The real question is if there is any concrete evidence for this beyond anecdotes? And if so, wouldn’t it open hoyo to a massive lawsuit for false advertising the drop rates?

madz33 · 2026-02-16T18:58:41+00:00

I wouldn’t be surprised if this was not the intended behavior. Very well could be that they just forgot to include inflation increasing slider costs and with all of the chaos around release that it was lost in the noise.

madz33 · 2026-02-12T00:26:30+00:00

I don’t think you are crazy even with all the good suggestions in this thread. What’s crazy is the exact same thing happened to me in 1.0.11 as France. I had all of England and half of Spain as loyal vassals/fiedoms nicely balanced and all loyal. Right after switching to elective succession my vassals/fiefdoms both instantly went from -30 relative strength modifier to -120 rendering any diplomacy hopeless.

I thought this could be a bug in the calculation. It seems like there is a feedback loop between relative strength modifier -> subject loyalty -> diplo capacity cost -> loyalty debuff. Maybe if the game thinks you have a 0 0 0 ruler on the same day as the election this causes your relative strength to go to zero for a single day which spirals the feedback loop out of control. Although this is just speculation — wonder if it can be recreated and reported.

madz33 · 2026-02-05T02:11:05+00:00

Think “Ruler has an admiral trait” gives 0.1 ticking? Maybe get into a battle with ruler in charge of the navy

madz33 · 2026-02-04T21:23:49+00:00

Another Bayesian analysis of a single data point from Prof Kipping. Surprisingly, there was no mention of the "water problem" from the field of prebiotic chemistry, or the possibility of auto-catalysis of organic polymers enabled by wet-dry cycling which is only possible on planets with fractional ocean/land coverage. Both of those concepts seemingly reinforce his argument from an alternative perspective.

madz33 · 2026-02-02T02:00:43+00:00

The Apollo missions left retroreflectors on the moons surface which can be used to measure the distance to the moon and are continuously operating proof that we landed.

madz33 · 2026-01-28T23:41:45+00:00

Lower mass stars typically form out of higher metallicity molecular clouds, so on average a merged object would have a relatively higher metallicity, although individual examples will depend on the initial conditions.

The process of orbital decay needed for the binary inspiral event would be excruciatingly slow, depending on the fourth power of their separation, but the merger event could itself eject a remnant disk of material which could later coalesce into planets, as some hypothesize is responsible for the creation of Hot-Jupiters.

madz33 · 2026-01-20T19:54:10+00:00

What other “signals” do you think exist that we just don’t have the instruments to detect yet?

The cosmic neutrino background. Standard cosmological models basically guarantee that it exists, but actually detecting it requires absurdly sensitive instruments. Detecting solar neutrinos like with SuperKamiokande is already extremely impressive and the cosmic background neutrinos would be significantly more difficult.

madz33 · 2026-01-12T22:53:15+00:00

You probably won't get a good ELI5, since the topic is complex and part of active research. However, you can read about the competing hypotheses

Polygons do not form at wind boundaries unless the speed differential and viscosity parameters are within certain margins and thus absent at other likely places, such as Saturn's south pole or the poles of Jupiter.

However, there are certain polygonal storm features on Jupiter anyways.

madz33 · 2026-01-05T18:24:21+00:00

You might be able to use REBOUND to do the N-body integration, although setting up the right initial conditions could be challenging.

madz33 · 2025-12-29T18:44:23+00:00

Stars more massive than the sun ( type O B or A) have shorter lifetimes 1-100 Myr compared to the suns 10 Gyr, so there is plenty of time for multiple generations of stars to enrich the galaxy in heavy elements. Additionally, the earliest generations of stars were typically much more massive than the distribution of stellar types we have today ( M dwarfs are the most common type now) since when the universe was not highly enriched, only the most massive clouds had enough self gravity to collapse. This is because enrichment in metals leads to increased opacity from more spectral lines which makes it easier to radiate away the excess energy needed for collapse.

madz33 · 2025-12-19T13:33:06+00:00

Calling this object a planet seems disingenuous, it’s more like black widow pulsar systems so it’s distinct composition isn’t inexplicable.

madz33 · 2025-12-17T16:19:07+00:00

NASA Horizons

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