[alancalverd]

Traditional search engines like Google prioritize most referred sources.

...like The Bible, Koran, Little Red Book, Shakespeare, Alice in Wonderland, and other frequently-cited sources of utter nonsense.

At best, consensus represents the opinion of the average man. Advances in understanding are made by exceptional people questioning the consensus. Out of 8,000,000,000 people, no more than 18 are deemed worthy of Nobel prizes each year, and if we discount those that don't involve increasing knowledge, we are down to 9. 

[hamdani yusuf (OP)]

At best, consensus represents the opinion of the average man.

That's what democracies depend on. Democratic societies whose constituents are mostly incompetent are less likely to survive. Usually, least competent members of the societies would die out earlier. It would tip the average value upward.

[hamdani yusuf (OP)]

Advances in understanding are made by exceptional people questioning the consensus.

There are some types of research gaps.

In this video, I dive deep into the landscape of academic research. I share insights from my own journey, focusing on the discovery and exploration of research gaps. These gaps, often seen as voids in our understanding, are in fact golden opportunities for innovation and progress. I discuss four distinct types of research gaps that I've encountered, including the personal challenges and triumphs I've experienced in bridging them.

[hamdani yusuf (OP)]

At best, consensus represents the opinion of the average man.

Or average researchers.

How To Use Consensus AI - Don?t Get Left Behind

Embark on a journey to redefine your academic search with Consensus AI, the cutting-edge tool transforming the landscape of research.
TIMESTAMPS
00:00 How to use Consensus
00:48 How to Use AI Summary
02:43 How to use Consensus Meter
03:23 How to use Consensus Co Pilot
04:47 How to Filter with Consensus
06:40 Digging Deeper into Consensus
08:41 Consensus on the GPT Store
09:38 Wrapping Up

[alancalverd]

Democratic societies whose constituents are mostly incompetent are less likely to survive.

It is a characteristic of most human societies that we protect and nurture the incompetent and superstitious, and even insist that they have a right to breed and/or disseminate their superstitions. Hence

Usually, least competent members of the societies would die out earlier.

is no longer a "given"
and

It would tip the average value upward.

is clearly not the case in, for example, the USA or anywhere that religion or party/tribal loyalty influences the democratic process.

[hamdani yusuf (OP)]

is clearly not the case in, for example, the USA or anywhere that religion or party/tribal loyalty influences the democratic process.

There might be some exceptions in short terms, for whatever reason. But in the long term the trend is usually maintained.

[hamdani yusuf (OP)]

In atoms, only certain orbitals are permitted (quantization)
- To calculate these orbitals, you need to solve the wave equation for the electron.
- Some of these orbitals are spherical, but others look like a cluster of balloons assembled by a clown. How do you calculate the radius and centripetal motion for these?

The shapes of the first five atomic orbitals are: 1s, 2s, 2px, 2py, and 2pz. The two colors show the phase or sign of the wave function in each region. Each picture is domain coloring of a ψ(x, y, z) function which depends on the coordinates of one electron.


Atomic orbitals of the electron in a hydrogen atom at different energy levels. The probability of finding the electron is given by the color, as shown in the key at upper right.

https://en.m.wikipedia.org/wiki/Atomic_orbital


These atomic orbitals may not represent position of electrons around the nucleus. For me, it looks more like radiation patterns around antenna.

Figure 4. Normalized 3d radiation pattern for the 1-wavelength dipole antenna.


Figure 5. Normalized 3d radiation pattern for the 1.5-wavelength dipole antenna.
https://www.antenna-theory.com/antennas/dipole.php



From chegg.com

Spatially, the patterns extend to infinity, although with quickly dropped magnitude for further distances. While dark regions within finite distances might be interpreted as products of destructive interference.

Unlike in a dipole antenna where the movement of electrons is confined in one dimension, the electrons around atomic nucleus can move in three dimensions.

[hamdani yusuf (OP)]

Spherical Harmonics

We describe the possible fundamental vibrations on a sphere in three dimensions by counting, mirroring and rotating nodal lines.
This video ist part of the online course www.quantumreflections.net dealing with quantum physics, produced by the institute for physics education research, M?nster university (Germany)

[hamdani yusuf (OP)]

Spatially, the patterns extend to infinity, although with quickly dropped magnitude for further distances. While dark regions within finite distances might be interpreted as products of destructive interference.

Unlike in a dipole antenna where the movement of electrons is confined in one dimension, the electrons around atomic nucleus can move in three dimensions.

Based on the radiation patterns that we can measure for various shapes of antenna where we can control the motion of the electrons, we can calculate backwards to infer how electrons should move around the nucleus to produce radiation patterns resembling known atomic orbitals. It will require adequately accurate and precise electrodynamic model.

[hamdani yusuf (OP)]

It's worth noting that Schrodinger himself didn't like Max Born's interpretation of his wave equation for atomic orbitals (after being squared) as probability density of finding electrons in particular region.  One of the objections to the implications of that interpretation is the formation of two or more separated regions in space where electrons can be found, but not between them. It's as if electrons can magically jump from one region with high probability to another regions without having to travel the space between them.

[alancalverd]

Based on the radiation patterns that we can measure for various shapes of antenna where we can control the motion of the electrons, we can calculate backwards to infer how electrons should move around the nucleus to produce radiation patterns resembling known atomic orbitals. It will require adequately accurate and precise electrodynamic model.

It is precisely the absence of electromagnetic emission from atoms in equilibrium that put an end to the Bohr atom.

It's as if electrons can magically jump from one region with high probability to another regions without having to travel the space between them.

There's no implication that they magically jump. If you start with a classical model, you probably won't derive a quantum result, but if you start with a quantum and probabilistic model, you can usefully predict molecular orbitals that correspond with ball-and-stick models, crystallographic measurements, and observed spectra.

[hamdani yusuf (OP)]

It is precisely the absence of electromagnetic emission from atoms in equilibrium that put an end to the Bohr atom.

No. It's why Bohr proposed his model, against Rutherford's planetary model.

[hamdani yusuf (OP)]

There's no implication that they magically jump.

You can say that they casually leap or tunnel. But what matters is what it means. It suggests that electrons can disappear from their previous positions and reappear in new position without traveling through the space in between.

[alancalverd]

You can say that they casually leap or tunnel.

No. Tunneling is an entirely different phenomenon.

It suggests that electrons can disappear from their previous positions and reappear in new position without traveling through the space in between.

No. Probability does not imply that anything moves. The probability of encountering a person with a black face in the street in Kinshasa is close to 100%, in Manchester, about 5%. There is no implication of instantaneous transport between the two cities.

[alancalverd]

No. It's why Bohr proposed his model, against Rutherford's planetary model.

Bohr's electrons orbit, That's the problem.

[hamdani yusuf (OP)]

No. It's why Bohr proposed his model, against Rutherford's planetary model.

Bohr's electrons orbit, That's the problem.

He postulated that some orbits are stable, hence electrons occupying them don't radiate energy.

[hamdani yusuf (OP)]

No. Probability does not imply that anything moves.

How can electrons have momentum if they don't move?

[hamdani yusuf (OP)]

No. Tunneling is an entirely different phenomenon.

Are you fine with the word leap?

[alancalverd]

He postulated that some orbits are stable, hence electrons occupying them don't radiate energy.

Orbiting equals acceleration. Accelerating charges emit electromagnetic radiation. So the classical model is wrong.

[alancalverd]

No. Tunneling is an entirely different phenomenon.

Are you fine with the word leap?

Different phenomena.