Better break the news gently to Mo: Y-chromosome Adam and mitochondrial Eve did exist, but thousands of years apart in time. And they were not alone, each was part of a wider population.
Nassar – that last line is worthy of a haiku translated by google from japanese to English via sumerian and navajo, Sir I congatulare you on your skillz. Please accept my hubble verse in your prayese.
” On J&M Nasser writes prose
Or poetry – nobody knows.
His skills are unique
I’d love to hear him speak
But then again I’d possibly doze”
Nothing funnier than a young earth creationist laughing at a flat earther. Thanks for this one, Author.
Oops. Wrong email address to have my avatar appear. I never know which one to choose. Can I correct this?
Nothing funnier than a young earth creationist laughing at a flat earther. Thanks for this one, Author.
Apparently I could. Sorry about the double post.
Re SoG:
Archeogenealogically “Adam” is defined is the oldest male that had 2 or more sons that had male-line descendants still alive today.
Equally, “Eve” is the woman that had at least 2 daugthers that had female-line descendants still alive today.
Neighther has as yet been positively identified, but the chance they ever met is absolutely zero.
They might be from opposite places on earth, and from millennia apart.
Those definitions imply, that if from eighther one line dies out, the title automatically shifts down to where the definition still applies.
Alternatively; if a woman is found whose mitochondrial DNA is incompatible with the evolution of current females, “Eve” moves up to where it is plausible again.
Same goes for Y-chromosomal makeup for “Adam”.
Isn’t every place the center of the universe and no place is the center of the universe?….there is no center as we understand it. And can’t you, y’know, move all parts of the equation from one side of the = to the other? So the Earth can turn on its axis, or the Earth can be still, and the entire universe turn around it. I don’t know how the Earth orbiting the sun effects this notion. And the sun going around the center of the galaxy…. and the galaxy being pulled by whatever (dark matter?) is tugging on the Local Group….and….and….and Relativity, man…
Nice one, Author, and timely to boot. My son-in-law told me just yesterday that a work colleague had become convinced of the flat earth nonsense after watching some youtube videos, and was busily trying to convince everybody at work that it’s true. My son-in-law is not particularly science-minded so he asked me for a good rebuttal.
‘Easy,’ said I, ‘when he starts explaining it, listen carefully for a minute or two, then point and laugh’.
I also gave him several reasons we know the earth is a sphere (ever-so slightly oblate), but in the certain knowledge that Mr. Flat-Earther will dismiss any evidence as being part of a conspiracy ‘That’s what THEY want you to believe’).
Years ago I used to teach celestial navigation. One of the first things I’d tell my students was “Forget Copernicus, for the purposes of navigation we will assume the Earth is fixed in the center of the universe and the sky rotates around it.” That makes the math a lot easier.
Incidentally the thing that takes longest when learning navigation is star recognition. There are 58 navigational stars (including Polaris) and I expected my students to know at least 25 of them. A second group of 115 “tabulated stars” can also be used for navigation, but are less familiar to the average navigator and require extra calculations.
Morgul, the problem with the universe rotating around a stationary earth is that the outer galaxies would have to move at a speed many times that of light, which should exclude Joshua 10:12 as a useable frame of reference (not that I am an astrophysicist at all…)
The point of the theory of relativity is that there is no unique reference frame and you can choose any you like, including the earth, and have the Sun and the universe rotate about it. That makes the prediction of the orbits of planets complicated and I wouldn’t like to have the to write the transformation equations. The T of R doesn’t preclude an apparent movement exceeding the speed of light; it precludes information from being sent at speeds greater that light.
Michael–don’t just leave your fascinating career at that! Havent you got a link? Seriously–I’ll always regret not learning more of this from my dad (with whom I built a telescope including grinding the lenses) as a kid. What a great skill to have. Say more things.
The earth is flat?
I don’t care about that,
if that’s what someone believes.
I’m much more perturbed,
in fact somewhat disturbed
by the dumb myth of Adam and Eve.
Belief in creation
won’t screw up navigation
but interferes with teaching biology.
Science is demanding.
It demands understanding,
Not an ancient simplistic ontology.
There actually is a solution to Einstein’s field equations that describes a universe where every observer sees the entire universe rotating around himself. Make of that what you will.
(It also has the interesting property that time travel is allowed).
Mahatma coat, I don’t think your comments on relativity theory are quite correct. Or rather, I think they’re quite wrong 🙂
It can be quite tricky (and tedious) to make perfectly correct statements so a certain amount of handwaving and simplification is often ok when trying to explain tricky concepts.
I’m just mentioning this so that anyone interested may read the Wikipedia articles on Special Relativity, Inertial Reference Frames, General Relativity and Metric Expansion of Space…
Anonymous, in that I made specific claims about ToR, I wonder if you’ll explain specifically which and how my claims are “quite wrong”? I didn’t attempt to try to “explain tricky concepts” but simply to state what ToR says.
Are you talking about Newton’s theory of relativity, or the special theory of relativity, or general relativity?
Rotating systems aren’t inertial reference Frames. The physics of having the universe rotating around the earth are not the same as those of having a spinning earth. Take the proverbial ice-skater, with the universe spinning around her. When she puts her arms out, the entire universe suddenly spins more slowly?
What do you mean by “apparent” movement exceeding the speed of light? Light always appears to (and actually does) move at the speed of light (and nothing else can move faster). *That* is (one of) the points of special relativity.
But also the distance between us and far away galaxies is increasing at a rate greater than that of the speed of light. That’s also an actual, and not just apparent, increase.
Sorry to intrude on a private conversation between Anonymous & mahatmacoat, but I don’t think there is a theory of relativity named after Newton. As I understand it, Newtonian mechanics works very well in practice, but with certain inaccuracies. Einstein’s theories of relativity can be thought of as fine tuning of Newtonian ideas, but are hard to understand, as they are contra-intuitive, whereas Newton’s ideas make sense intuitively.
Sorry if I’ve got the wrong end of some stick or other!
…general relativity exhibits general covariance: its laws—and further laws formulated within the general relativistic framework—take on the same form in all coordinate systems.
This includes rotating coordinate systems. So Mahatmacoat’s statement looks basically correct to me.
jb’s quotation from Wikipedia confirms what I said about there being no unique (or favoured) reference frame and this was Einstein’s jumping off point, initially for inertial reference frames and later for accelerated frames (in theory of general relativity). To appeal to authority in support of my claim re apparent speed, see Cox & Forshaw’s “The Quantum Universe”, Penguin Books 2012, p47. Newton’s laws work extremely well in practice and are what’s used for sending people off to the moon, etc. but are deficient because they rely on instantaneous action at a distant, as well as not dealing accurately with the precession of the perihelion of Mercury and other observed phenomena. Thanks to Anonymous, Son of Glenner and jb for their contributions and the opportunity to display my erudition.
I think that the important part of Mahatma’s original comment is “The T of R doesn’t preclude an apparent movement exceeding the speed of light (emph. mine).
Technically the statement is correct. If we take a stationary Earth to be our reference point, then our calculations of the speed of even the nearest stars would appear to be many times the speed of light, therefore allowing us to observe movement which apparently violates the Universal speed limit.
However, although the Earth appears to us to be static with the entire Universe revolving around us, we know that it isn’t, so the apparent movement of objects exceeding the speed of light is an illusion caused by the faulty starting premise of a static Earth.
All of the above, though, has less to do with the relativity theories and more with basic maths.
If you flicked a laser pointer from Earth across the face of the Moon, the spot could conceivably travel much faster than the speed of light! But nothing is physically traveling faster than light (i.e., no physical object ever moves along a space-like path), and the people on the East side of the Moon can’t use the phenomenon to send messages to those on the West, because they don’t control the spot. I think that’s what “apparent movement” refers to in this context.
Similarly, if I focus in on a distant star and fix it on the very left of my telescope’s eyepiece, then quuckly move the ‘scope to re-position the star to the very right, then although the star only moved 10mm iin the eyepiece and 150mm across the end of the scope,, the apparent movement of the star in space would be tens or even hundreds of light years in a fraction of a second.
Even if I didn’t move the telescope after the initial fixing of the star, it would still move across the eyepiece at an apparently impossible speed.
As I said earlier, this illusion of speed is only possible because the actual movement is at our end owing to the rotation of earth or by me changing the position of my telescope.
If I’ve got this right, speed is relative to the observer; if I am driving at 60moh, an observer stood by the road would see my speed as 60mph. The driver of a car travelling in the opposite direction at 60mph would see our closing speed as 120mph. If we could see a galaxy moving east at 3/4 the speed of light and another moving exactly opposite at the same rate, then we in the middle would see the distance between them increase at 1.5 times the speed of light, and an observer on either galaxy would see the other galaxy moving at 1.5 x c.
‘S’all relative, innit!
Another example of relative speed; if I were driving at 60mph and was overtaken by a car travelling at 80mph, the driver of the other car would see herself moving at 80mph, but relative to my 60mph, I would see her moving away at only 20mph.
AOS… your example with the galaxies is not quite correct. If you changed to the frame of reference of one of the galaxies it would not observe the other one moving away at faster than the speed of light. Such addition (or subtraction) of velocities is also modified slightly by Spec Rel. not noticeable for speeds small compared to c, but it means you don’t have objects with relative speeds above c (ignoring, “unphysical” apparrent speeds such as the example of the speed of the dot of the laser pointer traversing the face of the moon).
Thanks, Theo. I was aware that the speed of light itself isn’t added to the speed of the object emitting it (so the light from the headlights of a speeding car isn’t c+100mph, for example) but didn’t know that it applied to two or more objects travelling at speeds relative to c.
I am correct in saying that the relative speed of seperation of the two galaxies in my original example would be cx1.5, aren’t I? Otherwise, I give up on logic 🙂
AoS:
Don’t give up on logic, but DO modify it to replace Newtonian logic by Einsteinian.
At speeds “small” compared to c the results are the same (within the accurasy with which you define “small”).
At relativity speeds, “addition” just is modified.
(The fact that the speed of light is the same in all direction, mathematically described by c + v = c, led Albert to design a relationship that accounted for the physical findings; and he worked it out to become Relativity Theory. Rigorous calculations from it surprisingly reduced to E = mc^2).
AOS… you are correct. From a third party point of view, the speed of separation of the two galaxies is 1.5c. That is similar to the moon and laser pointer example. It’s only the relative velocity of any object compared to us (or whichever frame of reference you are taking) that will be less than c. Two “third party objects” can have relative speeds above c.
e.g. if someone fires a rocket in the “forward” direction from one of the galaxies at a speed of 3/4 c (relative to them) then, while by “Galilean/Newtonian thinking” the rocket’s speed relative to us should be 1.5c… it would actually be less than c relative to us (the speed relative to us being (u + v) / (1 + uv/c^2) where both u and v are 3/4 c in this case).
dr John de Wipper importantly points out that this makes little difference at “everyday” speeds – c being so large that uv / c^2 is about zero and so the formula just becomes approximately u + v, as we commonly experience.
Prof. Einstein did not make Sir Isaac “wrong”, all he did was to fill in a few blanks that Prof. Newton never mentioned and to make Newtonian Mechanics slightly more accurately representative of Observed Reality.
He extended Newton’s work.
Cassini, Huygens, Galileo, the Pioneers, the Voyagers and Pluto’s flyer-by all show that Newton works just fine most of the time.
The G.P.S. system tells us that it is a little imprecise in the edge cases.
And that is how Science works so very well.
Doctor Einstein was not the very last word. He, too, has been and is being improved upon.
Science in action, even today.
It’s magical, but magic that works! 🙂
Merry Christmas, or whatever it is when you read this.
Jesus & Mo (the characters) are absurd, blinkered, and oddly very sweet. J&M (the cartoon) is brilliant: sharp, delicious, irresistible. Salman Rushdie
Jesus and Mo cartoons are wonderfully funny and true. Richard Dawkins
Jesus and Mo make the world a better place, bless their little hearts. Ophelia Benson
In a world defined by outrage and offence and liberal spinelessness, Jesus and Mo is a treasure, whose value we should never fail to recognize. Read them. Laugh. And think. Kenan Malik
The brilliant, celebrated, freaking hilarious atheist comic strip ... Greta Christina
...rays of sanity in a befuddled world. Keri Hulme
The liveliest depictions of Muhammad currently available... Malise Ruthven
J & Mo is the funniest and most consistently thought-provoking cartoon strip on the Net. In a saner world, it would run in a major newspaper. Nelson Jones, Heresy Corner
Consistently amusing, frequently thought-provoking and often heart-warming. New Humanist
Jesus & Mo is one of the most wonderful things on the internet.. JT Eberhard
Wittily captures much of the absurdity of religious apologetics. Mano Singham
I love jesusandmo.net cartoons - witty and sharp! Katha Pollitt
Often hilarious, frequently wry, these cartoons do what all the best cartoons do: they tell the truth through humour. Terry Sanderson, NSS President
...a wonderfully acid British cartoonist... Nick Cohen
I love the scrappy mockery of Jesus and Mo. Freedom of speech
includes the freedom to mock any person, any thing, any activity, and
any belief -- and J&M stands up for this unflinchingly Richard Stallman
...empowering, important and deeply progressive, not to mention hilarious... Council of Ex-Muslims
August 12, 2020
Autor,
the word “is”is missing in the 3rd pane,
Thanks, John! Fixed now.
Better break the news gently to Mo: Y-chromosome Adam and mitochondrial Eve did exist, but thousands of years apart in time. And they were not alone, each was part of a wider population.
It is written “The world is flat”
In the qur’an, that is a fact
It is also said
Apostates to lose their head
With a sword of it is to get a whack
What happened, Nassar? That one was almost good!
Nassar – that last line is worthy of a haiku translated by google from japanese to English via sumerian and navajo, Sir I congatulare you on your skillz. Please accept my hubble verse in your prayese.
” On J&M Nasser writes prose
Or poetry – nobody knows.
His skills are unique
I’d love to hear him speak
But then again I’d possibly doze”
Nothing funnier than a young earth creationist laughing at a flat earther. Thanks for this one, Author.
Oops. Wrong email address to have my avatar appear. I never know which one to choose. Can I correct this?
Nothing funnier than a young earth creationist laughing at a flat earther. Thanks for this one, Author.
Apparently I could. Sorry about the double post.
Re SoG:
Archeogenealogically “Adam” is defined is the oldest male that had 2 or more sons that had male-line descendants still alive today.
Equally, “Eve” is the woman that had at least 2 daugthers that had female-line descendants still alive today.
Neighther has as yet been positively identified, but the chance they ever met is absolutely zero.
They might be from opposite places on earth, and from millennia apart.
Those definitions imply, that if from eighther one line dies out, the title automatically shifts down to where the definition still applies.
Alternatively; if a woman is found whose mitochondrial DNA is incompatible with the evolution of current females, “Eve” moves up to where it is plausible again.
Same goes for Y-chromosomal makeup for “Adam”.
Isn’t every place the center of the universe and no place is the center of the universe?….there is no center as we understand it. And can’t you, y’know, move all parts of the equation from one side of the = to the other? So the Earth can turn on its axis, or the Earth can be still, and the entire universe turn around it. I don’t know how the Earth orbiting the sun effects this notion. And the sun going around the center of the galaxy…. and the galaxy being pulled by whatever (dark matter?) is tugging on the Local Group….and….and….and Relativity, man…
Nice one, Author, and timely to boot. My son-in-law told me just yesterday that a work colleague had become convinced of the flat earth nonsense after watching some youtube videos, and was busily trying to convince everybody at work that it’s true. My son-in-law is not particularly science-minded so he asked me for a good rebuttal.
‘Easy,’ said I, ‘when he starts explaining it, listen carefully for a minute or two, then point and laugh’.
I also gave him several reasons we know the earth is a sphere (ever-so slightly oblate), but in the certain knowledge that Mr. Flat-Earther will dismiss any evidence as being part of a conspiracy ‘That’s what THEY want you to believe’).
Years ago I used to teach celestial navigation. One of the first things I’d tell my students was “Forget Copernicus, for the purposes of navigation we will assume the Earth is fixed in the center of the universe and the sky rotates around it.” That makes the math a lot easier.
Incidentally the thing that takes longest when learning navigation is star recognition. There are 58 navigational stars (including Polaris) and I expected my students to know at least 25 of them. A second group of 115 “tabulated stars” can also be used for navigation, but are less familiar to the average navigator and require extra calculations.
Morgul, the problem with the universe rotating around a stationary earth is that the outer galaxies would have to move at a speed many times that of light, which should exclude Joshua 10:12 as a useable frame of reference (not that I am an astrophysicist at all…)
It makes perfect sense for one to believe the universe revolves around the Earth, when the Earth itself clearly revolves around them.
The point of the theory of relativity is that there is no unique reference frame and you can choose any you like, including the earth, and have the Sun and the universe rotate about it. That makes the prediction of the orbits of planets complicated and I wouldn’t like to have the to write the transformation equations. The T of R doesn’t preclude an apparent movement exceeding the speed of light; it precludes information from being sent at speeds greater that light.
Michael–don’t just leave your fascinating career at that! Havent you got a link? Seriously–I’ll always regret not learning more of this from my dad (with whom I built a telescope including grinding the lenses) as a kid. What a great skill to have. Say more things.
The earth is flat?
I don’t care about that,
if that’s what someone believes.
I’m much more perturbed,
in fact somewhat disturbed
by the dumb myth of Adam and Eve.
Belief in creation
won’t screw up navigation
but interferes with teaching biology.
Science is demanding.
It demands understanding,
Not an ancient simplistic ontology.
There actually is a solution to Einstein’s field equations that describes a universe where every observer sees the entire universe rotating around himself. Make of that what you will.
(It also has the interesting property that time travel is allowed).
jb. But can that solution explain its own existence?
We are all time travellers, moving through time at 1 second per second at sea level, and slightly less than that for the lucky sods on the ISS.
Mahatma coat, I don’t think your comments on relativity theory are quite correct. Or rather, I think they’re quite wrong 🙂
It can be quite tricky (and tedious) to make perfectly correct statements so a certain amount of handwaving and simplification is often ok when trying to explain tricky concepts.
I’m just mentioning this so that anyone interested may read the Wikipedia articles on Special Relativity, Inertial Reference Frames, General Relativity and Metric Expansion of Space…
Anonymous, in that I made specific claims about ToR, I wonder if you’ll explain specifically which and how my claims are “quite wrong”? I didn’t attempt to try to “explain tricky concepts” but simply to state what ToR says.
Are you talking about Newton’s theory of relativity, or the special theory of relativity, or general relativity?
Rotating systems aren’t inertial reference Frames. The physics of having the universe rotating around the earth are not the same as those of having a spinning earth. Take the proverbial ice-skater, with the universe spinning around her. When she puts her arms out, the entire universe suddenly spins more slowly?
What do you mean by “apparent” movement exceeding the speed of light? Light always appears to (and actually does) move at the speed of light (and nothing else can move faster). *That* is (one of) the points of special relativity.
But also the distance between us and far away galaxies is increasing at a rate greater than that of the speed of light. That’s also an actual, and not just apparent, increase.
Sorry to intrude on a private conversation between Anonymous & mahatmacoat, but I don’t think there is a theory of relativity named after Newton. As I understand it, Newtonian mechanics works very well in practice, but with certain inaccuracies. Einstein’s theories of relativity can be thought of as fine tuning of Newtonian ideas, but are hard to understand, as they are contra-intuitive, whereas Newton’s ideas make sense intuitively.
Sorry if I’ve got the wrong end of some stick or other!
From Wikipedia:
This includes rotating coordinate systems. So Mahatmacoat’s statement looks basically correct to me.
jb’s quotation from Wikipedia confirms what I said about there being no unique (or favoured) reference frame and this was Einstein’s jumping off point, initially for inertial reference frames and later for accelerated frames (in theory of general relativity). To appeal to authority in support of my claim re apparent speed, see Cox & Forshaw’s “The Quantum Universe”, Penguin Books 2012, p47. Newton’s laws work extremely well in practice and are what’s used for sending people off to the moon, etc. but are deficient because they rely on instantaneous action at a distant, as well as not dealing accurately with the precession of the perihelion of Mercury and other observed phenomena. Thanks to Anonymous, Son of Glenner and jb for their contributions and the opportunity to display my erudition.
I think that the important part of Mahatma’s original comment is “The T of R doesn’t preclude an apparent movement exceeding the speed of light (emph. mine).
Technically the statement is correct. If we take a stationary Earth to be our reference point, then our calculations of the speed of even the nearest stars would appear to be many times the speed of light, therefore allowing us to observe movement which apparently violates the Universal speed limit.
However, although the Earth appears to us to be static with the entire Universe revolving around us, we know that it isn’t, so the apparent movement of objects exceeding the speed of light is an illusion caused by the faulty starting premise of a static Earth.
All of the above, though, has less to do with the relativity theories and more with basic maths.
If you flicked a laser pointer from Earth across the face of the Moon, the spot could conceivably travel much faster than the speed of light! But nothing is physically traveling faster than light (i.e., no physical object ever moves along a space-like path), and the people on the East side of the Moon can’t use the phenomenon to send messages to those on the West, because they don’t control the spot. I think that’s what “apparent movement” refers to in this context.
Similarly, if I focus in on a distant star and fix it on the very left of my telescope’s eyepiece, then quuckly move the ‘scope to re-position the star to the very right, then although the star only moved 10mm iin the eyepiece and 150mm across the end of the scope,, the apparent movement of the star in space would be tens or even hundreds of light years in a fraction of a second.
Even if I didn’t move the telescope after the initial fixing of the star, it would still move across the eyepiece at an apparently impossible speed.
As I said earlier, this illusion of speed is only possible because the actual movement is at our end owing to the rotation of earth or by me changing the position of my telescope.
If I’ve got this right, speed is relative to the observer; if I am driving at 60moh, an observer stood by the road would see my speed as 60mph. The driver of a car travelling in the opposite direction at 60mph would see our closing speed as 120mph. If we could see a galaxy moving east at 3/4 the speed of light and another moving exactly opposite at the same rate, then we in the middle would see the distance between them increase at 1.5 times the speed of light, and an observer on either galaxy would see the other galaxy moving at 1.5 x c.
‘S’all relative, innit!
Another example of relative speed; if I were driving at 60mph and was overtaken by a car travelling at 80mph, the driver of the other car would see herself moving at 80mph, but relative to my 60mph, I would see her moving away at only 20mph.
AOS… your example with the galaxies is not quite correct. If you changed to the frame of reference of one of the galaxies it would not observe the other one moving away at faster than the speed of light. Such addition (or subtraction) of velocities is also modified slightly by Spec Rel. not noticeable for speeds small compared to c, but it means you don’t have objects with relative speeds above c (ignoring, “unphysical” apparrent speeds such as the example of the speed of the dot of the laser pointer traversing the face of the moon).
Thanks, Theo. I was aware that the speed of light itself isn’t added to the speed of the object emitting it (so the light from the headlights of a speeding car isn’t c+100mph, for example) but didn’t know that it applied to two or more objects travelling at speeds relative to c.
I am correct in saying that the relative speed of seperation of the two galaxies in my original example would be cx1.5, aren’t I? Otherwise, I give up on logic 🙂
AoS:
Don’t give up on logic, but DO modify it to replace Newtonian logic by Einsteinian.
At speeds “small” compared to c the results are the same (within the accurasy with which you define “small”).
At relativity speeds, “addition” just is modified.
(The fact that the speed of light is the same in all direction, mathematically described by c + v = c, led Albert to design a relationship that accounted for the physical findings; and he worked it out to become Relativity Theory. Rigorous calculations from it surprisingly reduced to E = mc^2).
AOS… you are correct. From a third party point of view, the speed of separation of the two galaxies is 1.5c. That is similar to the moon and laser pointer example. It’s only the relative velocity of any object compared to us (or whichever frame of reference you are taking) that will be less than c. Two “third party objects” can have relative speeds above c.
e.g. if someone fires a rocket in the “forward” direction from one of the galaxies at a speed of 3/4 c (relative to them) then, while by “Galilean/Newtonian thinking” the rocket’s speed relative to us should be 1.5c… it would actually be less than c relative to us (the speed relative to us being (u + v) / (1 + uv/c^2) where both u and v are 3/4 c in this case).
dr John de Wipper importantly points out that this makes little difference at “everyday” speeds – c being so large that uv / c^2 is about zero and so the formula just becomes approximately u + v, as we commonly experience.
“Mitochondrial Eve”? “Y-chromosome Adam”?
All humans are related to the recently deposed Trumpet?
Twice?
I think I need a bucket then a strong cup of tea.
Prof. Einstein did not make Sir Isaac “wrong”, all he did was to fill in a few blanks that Prof. Newton never mentioned and to make Newtonian Mechanics slightly more accurately representative of Observed Reality.
He extended Newton’s work.
Cassini, Huygens, Galileo, the Pioneers, the Voyagers and Pluto’s flyer-by all show that Newton works just fine most of the time.
The G.P.S. system tells us that it is a little imprecise in the edge cases.
And that is how Science works so very well.
Doctor Einstein was not the very last word. He, too, has been and is being improved upon.
Science in action, even today.
It’s magical, but magic that works! 🙂
Merry Christmas, or whatever it is when you read this.