Some Fun Science Trivia

[SelfSim]

I'm confused.

Yep.

You think humans may have invented apples? I don't have an actual test, other than some poetry:

Poems are made by fools like me,
But only God can make a tree.

.. (which is untestable in science).

Okay I agree with that, when it comes to really small things and really big things and really old things. But not apples or 2+2.

Size makes no difference to the principle I've outlined.

Well you have to observe something before you can speculate about it.

Nope .. speculation isn't an observation. Its an idea.

I mean sure, you can speculate about unicorns or space aliens, but not when you're doing serious science.

Science starts with a tentative, (speculative) statement about such things as maybe being part of objective reality. Once 'unicorns or space aliens' is defined (somehow), a scientific thinker would attempt to test those definitions. Clearly those definitions would fail and therefore would not proceed further in rising to being considered as being part of science's objective reality.
Those steps I just described, is what demonstrates the scientific method in action .. and therefore, that is doing serious science.

But wait isn't this thread about science trivia??

I don't know what you mean by "fingerprints".

Persisting, consistent evidence that only an active human mind can generate.

When I said you sounded post-modern, I wasn't kidding.

I'm sure you weren't. But I assert your claim arises only because you apparently haven't taken off your 'Post Modernist' philosophical detecting sunglasses! So take 'em off pplease .. its your choice because I didn't ask you to put 'em on in the first place because they are irrelevant in scientific thinking!

There's this self-proclaimed post-modernist professor named Thadeus Russell who claims the Pythagorean Theorem isn't true, because it's just "something some guy made up".

Yep .. he certainly sounds to be a trivial player!

 

[sjastro]

Whether mathematics is invented or discovered ultimately depends on who you ask.
Pure mathematicians will tell you mathematics is invented as it is a product of their creative minds, (most) applied mathematicians think mathematics is discovered.
Mathematics as a discovery is probably demeaning to many pure mathematicians, the prominent pure mathematician of the 20th century GH Hardy referred to a pure mathematician as “like a painter or poet, is a maker of patterns.... The mathematician’s patterns... must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way." and described applied mathematics as dull and trivial.

Having done both pure and applied mathematics I sit on the fence and claim mathematics can be both invented and discovered.
I have used the example of Laguerre polynomials in the past which where invented in the 19th century as a solution to a particular type of differential equation.
When the quantum mechanical model of the hydrogen atom was devised in the early 20th century, Laguerre polynomials emerged from the equations which constituted a discovery despite the polynomials being invented decades earlier; the invention of the polynomials played no role in its discovery.

This is what AI has to say on the subject with more detail.

 

[SelfSim]

Whether mathematics is invented or discovered ultimately depends on who you ask.
Pure mathematicians will tell you mathematics is invented as it is a product of their creative minds, (most) applied mathematicians think mathematics is discovered.
Mathematics as a discovery is probably demeaning to many pure mathematicians, the prominent pure mathematician of the 20th century GH Hardy referred to a pure mathematician as “like a painter or poet, is a maker of patterns.... The mathematician’s patterns... must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way." and described applied mathematics as dull and trivial.

Having done both pure and applied mathematics I sit on the fence and claim mathematics can be both invented and discovered.
I have used the example of Laguerre polynomials in the past which where invented in the 19th century as a solution to a particular type of differential equation.
When the quantum mechanical model of the hydrogen atom was devised in the early 20th century, Laguerre polynomials emerged from the equations which constituted a discovery despite the polynomials being invented decades earlier; the invention of the polynomials played no role in its discovery.

This is what AI has to say on the subject with more detail.

View attachment 359907

So let's take a close look at this:
i) Laguerre invented his polynomials as part of his work on mathematical analysis and differential equations.
ii) They then re-emerged in QM, specifically in the solution to the radial part of the Schrodinger Equation for the Hydrogen atom.

All of: 'mathematical analysis, differential equations' and 'the QM solutions pertaining to the Schrodinger equation' are mathematical topics and constructs, yes? All of these came from the minds of humans thinking in very specific ways too, yes?
So an easy observation there, is that both Laguerre Polynomials and the Schrodinger equation, bear the names of the very minds that devised them. We can find no evidence that any of that existed independently of those human minds.

The same can be said about the history behind the various models of 'what hydrogen is' by Bohr, Rutherford and Sommerfeld. Yet more human names appear there, demonstrating that human minds produced those models, with nothing there suggesting anything existing independently from those human minds.

Even the name 'hydrogen' derives from the Greek hydro for 'water' and 'genes' for 'forming', when a type of air apparently combusted and then formed water. The words there, is how humans summarised their observations, (Lavoisier in 1783 and, then the English physicist Henry Cavendish in 1766, who actually called the observation 'inflammable air').

Everything mentioned above, commenced with descriptions of observations, or perceptional models of one kind or another and there is no evidence of anything existing independently from those models, nor has the science depended, in any way, on that notion.
The only observation to make there, is of human scientists and mathematicians 'discovering' or 'inventing' new ways to carefully describe their perceptions/observations under certain specified conditions, using their language of choice, yes(?)

Its certainly all a trivial observation to make after looking at the historical record behind the development of the models called 'the hydrogen atom' or 'the element - hydrogen'.

 

[AV1611VET]

Trivia question:

What is the largest desert on Earth?

 

[SelfSim]

Trivia question:

What is the largest desert on Earth?

Go look it up!

 

[AV1611VET]

Go look it up!

Why don't Weebles fall over?

 

[SelfSim]

Why don't Weebles fall over?

Go ask an AI/chatbot.

 

[Chesterton]

Trivia question:

What is the largest desert on Earth?

Earth's largest pumpkin pie.

Oh sorry, I thought you said dessert.

Why don't Weebles fall over?

They do fall over.

 

[sjastro]

So let's take a close look at this:
i) Laguerre invented his polynomials as part of his work on mathematical analysis and differential equations.
ii) They then re-emerged in QM, specifically in the solution to the radial part of the Schrodinger Equation for the Hydrogen atom.

All of: 'mathematical analysis, differential equations' and 'the QM solutions pertaining to the Schrodinger equation' are mathematical topics and constructs, yes? All of these came from the minds of humans thinking in very specific ways too, yes?
So an easy observation there, is that both Laguerre Polynomials and the Schrodinger equation, bear the names of the very minds that devised them. We can find no evidence that any of that existed independently of those human minds.

The same can be said about the history behind the various models of 'what hydrogen is' by Bohr, Rutherford and Sommerfeld. Yet more human names appear there, demonstrating that human minds produced those models, with nothing there suggesting anything existing independently from those human minds.

Even the name 'hydrogen' derives from the Greek hydro for 'water' and 'genes' for 'forming', when a type of air apparently combusted and then formed water. The words there, is how humans summarised their observations, (Lavoisier in 1783 and, then the English physicist Henry Cavendish in 1766, who actually called the observation 'inflammable air').

Everything mentioned above, commenced with descriptions of observations, or perceptional models of one kind or another and there is no evidence of anything existing independently from those models, nor has the science depended, in any way, on that notion.
The only observation to make there, is of human scientists and mathematicians 'discovering' or 'inventing' new ways to carefully describe their perceptions/observations under certain specified conditions, using their language of choice, yes(?)

Its certainly all a trivial observation to make after looking at the historical record behind the development of the models called 'the hydrogen atom' or 'the element - hydrogen'.

Generally one thinks of mathematics in explaining or describing an observation, Kepler’s laws of planetary motion are an empirical explanation of Tycho Brahe’s meticulous records as are Newton’s laws of motion based on experiment and observation.
In these cases, experiments and observations are followed by the mathematics which is an invention.

Mathematics however has revealed deeper insights that the human mind had never considered, one example was the Brachistochrone problem of the early 18th century which was a thought experiment which described the shape of a frictionless wire where a bead would slide under gravity in the shortest period of time.

Intuitively one would expect the wire to be in the shape of a straight line but the shape is a cycloid in red.

While gravity is considered to be a fundamental force, there is a deeper underlying principle in nature which was developed as Lagrangian mechanics decades after Newton which could explain why the shape is cycloid.
Here the underlying principle revealed by the mathematics was the principle of least action where Newton’s laws of motion could be derived mathematically without any experiments or observations.

Much of modern day theoretical physics is based on Lagrangian and the related Hamiltonian physics such as quantum mechanics and quantum field theories.
Here the mathematics is discovered rather than invented and has led to criticisms by some in the science community that physics in particular is becoming less empirical as a result.

Getting back to the main point about Laguerre polynomials, Schrodinger’s equation for the hydrogen atom is a mathematical invention but the wavefunction ψ of the equation is open to various QM interpretations such as whether it is real or a mathematical object.
While the time evolution of ψ is deterministic the solutions to the equations which are the observables are not.
These are seen in the radial solution of the equation which are found to be Laguerre polynomials where the probability density of the electron cloud is a function of the radial distance from the nucleus.
The mathematics through Laguerre polynomials reveals at quantum scales nature is not deterministic.

 

[SelfSim]

Generally one thinks of mathematics in explaining or describing an observation, Kepler’s laws of planetary motion are an empirical explanation of Tycho Brahe’s meticulous records as are Newton’s laws of motion based on experiment and observation.
In these cases, experiments and observations are followed by the mathematics which is an invention.

Mathematics however has revealed deeper insights that the human mind had never considered, one example was the Brachistochrone problem of the early 18th century which was a thought experiment which described the shape of a frictionless wire where a bead would slide under gravity in the shortest period of time.

View attachment 359940​

Intuitively one would expect the wire to be in the shape of a straight line but the shape is a cycloid in red.

While gravity is considered to be a fundamental force, there is a deeper underlying principle in nature which was developed as Lagrangian mechanics decades after Newton which could explain why the shape is cycloid.
Here the underlying principle revealed by the mathematics was the principle of least action where Newton’s laws of motion could be derived mathematically without any experiments or observations.

Much of modern day theoretical physics is based on Lagrangian and the related Hamiltonian physics such as quantum mechanics and quantum field theories.
Here the mathematics is discovered rather than invented and has led to criticisms by some in the science community that physics in particular is becoming less empirical as a result.

Getting back to the main point about Laguerre polynomials, Schrodinger’s equation for the hydrogen atom is a mathematical invention but the wavefunction ψ of the equation is open to various QM interpretations such as whether it is real or a mathematical object.
While the time evolution of ψ is deterministic the solutions to the equations which are the observables are not.
These are seen in the radial solution of the equation which are found to be Laguerre polynomials where the probability density of the electron cloud is a function of the radial distance from the nucleus.
The mathematics through Laguerre polynomials reveals at quantum scales nature is not deterministic.

As usual, I have no probs with anything there.

I'm pretty sure that when you speak about mathematics being 'discovered or invented', and I speak about whether or not mathematics is 'truly mind independent' or 'mind dependent', we're talking about different aspects there(?) I'm hoping you agree :fingerscrossed(?)

I've noticed from my ongoing reading about the history of mathematics, the story about polynomials goes way back to the ancient greek philosopher/astronomer times, when they were contemplating conic sections, (Apollonius of Perga c: 240-190BC, with Euclid and Archimedes also playing important roles). If so, the well known basis of maths/geometry, the Euclidean axioms, would seem to be likely at the grass roots origins of polynomials(?)

 

[sjastro]

As usual, I have no probs with anything there.

I'm pretty sure that when you speak about mathematics being 'discovered or invented', and I speak about whether or not mathematics is 'truly mind independent' or 'mind dependent', we're talking about different aspects there(?) I'm hoping you agree :fingerscrossed(?)

There is no clear distinction pure mathematicians will tell you maths is mind dependent as their work is an invention, but the maths that is "out there in the real world" is mind independent and exists irrespective of whether we understand it or not.
There are many examples of mathematics which started off as an intellectual exercise such as non Euclidean (Riemannian) geometry where the geometry of space is defined by its geodesic or the shortest distance between two points, and used by Einstein to develop general relativity where it is found that light travels along geodesic paths.
Is this a coincidence or is it part of the real world, Einstein's field equations like Newton's laws of motion can be derived using the principle of least action which is why light travels along geodesic paths suggesting non Euclidean geometry is as much part of the real world and mind independent as it is an invention.

 

[SelfSim]

There is no clear distinction pure mathematicians will tell you maths is mind dependent as their work is an invention, but the maths that is "out there in the real world" is mind independent and exists irrespective of whether we understand it or not.
There are many examples of mathematics which started off as an intellectual exercise such as non Euclidean (Riemannian) geometry where the geometry of space is defined by its geodesic or the shortest distance between two points, and used by Einstein to develop general relativity where it is found that light travels along geodesic paths.
Is this a coincidence or is it part of the real world, Einstein's field equations like Newton's laws of motion can be derived using the principle of least action which is why light travels along geodesic paths suggesting non Euclidean geometry is as much part of the real world and mind independent as it is an invention.

Again .. I, personally, have no problems in understanding and accepting everything you're saying there, because I know when I delve into topics like Riemannian geometry, (as far as I may dare), I can see lots of evidence of it having been, (at least, originally), a product of Riemann's imagination (aka mind dependence ... aka his .. and likely others' before him). I can also see/find out (for myself) Newton's laws of motion and Einstein's GR derivations, from the idea of the principle of least action, (and all that's very cool).

So when it gets to the tricky part, (underlined above), I can also visualise all of that as being a conceptual model for 'what the universe, (real world, nature, etc), is'.
I can also observe that I did that visualisation using my (obviously, human) mind. What's more important there however is, I find lots of observational evidence I can come up with for supporting that the kind of 'mind independence' there, is actually a well-tested model used in Cosmology/Physics .. and is ingrained in many of us, as being the way we separate our own wild imaginings, beliefs, intellectual inventions and discoveries, from what our physical senses detect and how our minds make sense of those.

I just can't say this in a better way and I hope it doesn't sound patronising, (that, most assuredly, isn't my intention), but I just know from experience that the way you use this demonstrably mind dependent model of 'mind independence', never impacts the science content or its supporting evidence which you frequently share with others, (myself included). Not many people leave me with that impression.
Rgds.

 

[sjastro]

Again .. I, personally, have no problems in understanding and accepting everything you're saying there, because I know when I delve into topics like Riemannian geometry, (as far as I may dare), I can see lots of evidence of it having been, (at least, originally), a product of Riemann's imagination (aka mind dependence ... aka his .. and likely others' before him). I can also see/find out (for myself) Newton's laws of motion and Einstein's GR derivations, from the idea of the principle of least action, (and all that's very cool).

So when it gets to the tricky part, (underlined above), I can also visualise all of that as being a conceptual model for 'what the universe, (real world, nature, etc), is'.
I can also observe that I did that visualisation using my (obviously, human) mind. What's more important there however is, I find lots of observational evidence I can come up with for supporting that the kind of 'mind independence' there, is actually a well-tested model used in Cosmology/Physics .. and is ingrained in many of us, as being the way we separate our own wild imaginings, beliefs, intellectual inventions and discoveries, from what our physical senses detect and how our minds make sense of those.

I just can't say this in a better way and I hope it doesn't sound patronising, (that, most assuredly, isn't my intention), but I just know from experience that the way you use this demonstrably mind dependent model of 'mind independence', never impacts the science content or its supporting evidence which you frequently share with others, (myself included). Not many people leave me with that impression.
Rgds.

Let’s continue with the general relativity theme.

The conservation of energy is clearly a mind dependant model based on observations and experiments but general relativity almost never got off the ground as a “fatal flaw” was revealed, the conservation of energy is ambiguous and need not apply in certain frames of references.
This led to two possibilities general relativity is wrong or within the mind dependant mathematics of general relativity there was something the human mind had never perceived.
As history shows it was the latter when it was discovered by the mathematician Emmy Noether, the mathematical relationship between the symmetry of a system being invariant and the corresponding conservation law.

For energy to be conserved, the system remains time invariant or unchanged.
As a practical example consider the cosmological redshift of light; when light is redshifted energy is lost and question is where does it go if the conservation of energy exists?
The answer is nowhere, the energy disappears and the conservation law does not apply since the universe is expanding and the symmetry, in this case the geometry of spacetime, is not invariant but changes with time.

 

[SelfSim]

Let’s continue with the general relativity theme.

The conservation of energy is clearly a mind dependant model based on observations and experiments but general relativity almost never got off the ground as a “fatal flaw” was revealed, the conservation of energy is ambiguous and need not apply in certain frames of references.
This led to two possibilities general relativity is wrong or within the mind dependant mathematics of general relativity there was something the human mind had never perceived.
As history shows it was the latter when it was discovered by the mathematician Emmy Noether, the mathematical relationship between the symmetry of a system being invariant and the corresponding conservation law.

For energy to be conserved, the system remains time invariant or unchanged.
As a practical example consider the cosmological redshift of light; when light is redshifted energy is lost and question is where does it go if the conservation of energy exists?
The answer is nowhere, the energy disappears and the conservation law does not apply since the universe is expanding and the symmetry, in this case the geometry of spacetime, is not invariant but changes with time.

If I recall correctly, this was the key debunking evidence against the EU static universe/tired light gobbledegook(?)

 

[sjastro]

If I recall correctly, this was the key debunking evidence against the EU static universe/tired light gobbledegook(?)

The resident EU acolyte of the time was insistent that cosmologists, astronomers, astrophysicists or any physicist for that matter were stupid because they failed to understand cosmological redshift 'violated' the conservation of energy.

Pointing out to him Noether's theorem was like a ball bouncing off a brick wall as was the history that luminaries such as Einstein and the mathematical genius David Hilbert (who recruited Emmy Noether to investigate the issue) came to accept the idea that conservation laws in GR were not as inviolate as in classical Newtonian physics.

I got a similar reaction that tired light is completely refuted by the evidence that a percentage of microwave photons reaching us from the CMB are polarized indicating Thomson scattering which is an elastic process involving no energy loss and therefore redshift is cosmological.

Here is a video of Noether's theorem in a nutshell.

 

[SelfSim]

The resident EU acolyte of the time was insistent that cosmologists, astronomers, astrophysicists or any physicist for that matter were stupid because they failed to understand cosmological redshift 'violated' the conservation of energy.

Pointing out to him Noether's theorem was like a ball bouncing off a brick wall as was the history that luminaries such as Einstein and the mathematical genius David Hilbert (who recruited Emmy Noether to investigate the issue) came to accept the idea that conservation laws in GR were not as inviolate as in classical Newtonian physics.

I got a similar reaction that tired light is completely refuted by the evidence that a percentage of microwave photons reaching us from the CMB are polarized indicating Thomson scattering which is an elastic process involving no energy loss and therefore redshift is cosmological.

Here is a video of Noether's theorem in a nutshell.

Ha! That is the exact same video I watched earlier on, following your previous post, to remind myself of how it all comes together!
Nice accent that girl has too!

 

[sjastro]

Ha! That is the exact same video I watched earlier on, following your previous post, to remind myself of how it all comes together!
Nice accent that girl has too!

A nice Aussie girl doing her PhD at Cambridge.

 

[AV1611VET]

If you fire a bullet from a .44 magnum in a vacuum, and drop a penny at the same time, both the bullet and the penny will hit the ground at the same time.

 

[SelfSim]

If you fire a bullet from a .44 magnum in a vacuum, and drop a penny at the same time, both the bullet and the penny will hit the ground at the same time.

Not so:

i) whenever the gun is not aimed perpendicularly, relative to the unobstructed, projected descent path of the penny .. (which would be just about all of the time) and;
ii) the starting height of the bullet to be fired, is not identical to the starting height of the penny to be dropped .. (which would be just about all of the time).;
iii) the release of the bullet and the penny is not perfectly synchronised .. (which would be just about all of the time).

 

[AV1611VET]

Not so:

So.

i) whenever the gun is not aimed perpendicularly, relative to the unobstructed, projected descent path of the penny .. (which would be just about all of the time) and;
ii) the starting height of the bullet to be fired, is not identical to the starting height of the penny to be dropped .. (which would be just about all of the time).;
iii) the release of the bullet and the penny is not perfectly synchronised .. (which would be just about all of the time).

I left out the variables for obvious reasons.