Yep! agree with you ✌(......🤔)

Even if you can't calculate it all it does help to follow along

Absolutely!! He explains them beautifully, and they really help.

You can really understand why they say what they say when you have equations as opposed to when they go “so we crunched the numbers”

That made me laugh so much :D

Beyork.

If ANYTHING could persuade the universe to bring Einstein back, surely it would be Professor Copeland's soft, hear felt "Yes, please."

You may mock my equations, mortal, but I shall rule the world with the power to create atom bombs........ wait. That was a bit too real..

Lol yeah, also every supervillan has a PhD, "Dr.this", "Dr.that" you may be onto something!

+Elliott Collins Yes, he's adorable.

+Anders23 was gonna say the same thing. its funny that this player can actually wrap 85 secs in min

did it stop being able to now?

16:44

Such a pure, innocent response! His eyes looks like that of a child who has just been offered ice cream haha

Sadly, we will never have another person quite like Albert Einstein. His intuition with regard to the universe was wholly unique, and is very missed to this day.

Jovetj we will.

@@jovetj i am sure people said the same thing after Newton

+Ben F The math is the most interesting part.

+Oliver Ocean Agreed.

+Oliver Ocean it's very basic math too. And it's seeing the scientists' interpretations of the equations that is the most intriguing part for me.

I know, I think the same. Sadly he hadn't follow the trend :(

Believe me - regarding maths in relativity you only see the tip of the iceberg in this vid. He showed the main result of the Einstein equations for an isotropic and honogeneous universe. He skipped how to derive the basic form of the metric by evaluating the cosmological principal, he skipped to derive the energy momentum tensor of a radiation dominated universe and he skipped evaluating the field equations for the Robertson Walker metric - all this taken together yields the equations you've just seen. Great Video though and straight to the point.

I would ask him to critique Bell's 1964 paper. What I think would happen is that Einstein would say that since clocks are affected by gravity, the twin particles would not age in phase locked synchrony, so that the presumptive hidden variable would not vanish, but would result in a residual non-zero "beat frequency." And then, Einstein would dub that "spooky timekeeping at a distance."

Hah, yeah, Professor Copeland was quick with the "yes please", like a kid being asked if they want candy.

+RimstarOrg ^This :D

+RimstarOrg Absolutely. Pr. Copeland is one my favorites of the show :) His very smooth voice giving clear explanations, with the twinkle of passion always in his eyes...

he's strangely comforting

Lost track of the maths about halfway through but kept listening :)

I lost track of it too. It reminded me of Uni - a professor writing equations all over the board that took top scientists 10 years work to figure out & I was supposed to absorb it in a few minutes.

+Cr42yguy he was! :)

i know, it's just nice to be able to participate :)

+Cr42yguy Exactly the reason why i love Sixty Symbols. :)

+Cr42yguy I wish I could understand

He is one of my favorites!

+Ansh Shah no, go to numberphile for that

Kobil Shakur most of physics is based on math , I don't see why they don't include Math in their videos. P.s - I know what numberphile is.

Ansh Shah look it up, you're def going to enjoy it

+Kobil Shakur Thing is, even Numberphile is not very ''math'' heavy... It's often a lot of playing with numbers or math explained, but purely logically. I agree with what I've seen here; it's very refreshing to see something that isn't dumbed much down, unlike the usual content on Brady's channels (No offense by it, but yeah :P)

+justarandompally true story.

+00Billy that's Numberphile only! :)

Sixty Symbols hehe..only watched EVERY video...and never noticed that...lol Thanks.. Still, the brown paper is better !

+00Billy ow silly billy

+Sixty Symbols maybe do a 2 hour Numberphile + Sixty Symols GR math video with Prof. Copeland?

+Elios0000 now this is what I want to see. Although PBS spacetime have a great GR playlist

+Richard Melcher Could be even more for me. Maybe in a bonus video for those who want it :)

I agree, more maths in Physics videos! It does not need to be long derivations of formulas, just equations like this where you can say: look, this here is the term related to the mass of the universe, this is the pressure, this is the cosmological constant. It IS called Sixty Symbols after all, show us the symbols! :-)

+Richard Melcher Really heavy? This is only algebra.

+Senrade2 really heavy compared to usual.

Senrade2 It is undeniably heavy on the maths for a Sixty Symbols video. That's in no way to say that it is objectively heavy. So while you are correct that the only maths actually shown in the video is algebra (with the actual solving of all involved differential equations left out for obvious reasons), that's kind of irrelevant.

+poseidon In my opinion, including the equations made the whole thing a lot easier to follow. I hope other physics topics get the same treatment.

+poseidon Agreed. I think most of us who would watch videos like this have already some basic understanding of the math involved.

Niven42 actually my knowledge of the math involved is roughly equivalent to that of a brick. However after each set of equations the prof takes a few seconds to make an easy explanation for us lesser beings that makes it possible for us to keep up with the narrative. So for me it goes.... blah blah equations blah.. what this means is that for this to work this funny squiggle must be zero.... because Maths. Which is fine for me.

+Niven42 I don't have any understanding of the math involved. But explained like this, it was very easy to follow along and get the 'gist' of what he means. Prof Copeland is the best

I totally agree . This video is useful. I’m tired of dummed down fluffy arguments.

I would ask him to critique Bell's 1964 paper. What I think would happen is that Einstein would say that since clocks are affected by gravity, the twin particles would not age in phase locked synchrony, so that the presumptive hidden variable would not vanish, but would result in a residual non-zero "beat frequency." And then, Einstein would dub that "spooky timekeeping at a distance."

Plug and chug or You shall not pass.

You merely adopted the field equations.

In Soviet Russia, _equations_ fear *you*

@@avinotion Because all you're going to do is manipulate the poor bastards.

"I'm not afraid" "You will be, _you will be._ "

Albert Einstein new about "Mass-SPACE relation", however he applied "Static" = "Infinite sponge" = "Non-Space-Expandable Universe" (just added to Newton "Sponge Structural-Geometrical Deformation Ability") (logic - if space is infinite= can't further to expand) into General Relativity model and than Edington "proved it" (he "measured" light bend - 0,00000000000000000000000000000001% of a single radius degree, as a "Flag Evidence".. hmm "how u can measure if its a wave" so precisely anyway, by tracking single photons?) in 1925 or 1919? ...but then Mr Edwin Hubble in 1929 completely demolished Einstein's "Static Universe" by discovering that "Universe is expanding" (they just didn't realise that it was "Space Expansion"), but false statements never been dismissed. They were "updated" - new solutions/transformations added to the equations, but "main conclusion" that "mass not curves, but expands space=distance effectively", never been noticed ("Cosmological Constant" MIA) and this is the reason why Invisible Ghosts of Dark Energies" overtaken XX century physics.

What, exactly, does this have to do with Maths helping me understand Physics?

"This" is a "Real Physics" = description of the energy transformation mechanism. What u "practicing" with "math calculations" (can u explain what "physical truths" you reveal with your mathematics?) got nothing to do with the real physical model.

I do a Physics degree. Everything I do is explaining the physical significance of the maths.

You can even do and call it "Master degree of the Universe Math Champions", but that has nothing to do with a real physics which is description of energy transformations. As a pupil or scientists you got no idea even about ATOM EXPANSION POSSIBILITY (and that's BASICS OF THE THERMODYNAMICS) , you got no idea either about MACROSCOPIC UNIVERSE where mass cumulating in nucleuses of stars and galaxies expands space . So honestly i got no clue what is all about... when you claim : "math helped me to understand physics" (how that could happen).

+Palvindar Chhokar you're welcome

Einstein himself called it a blunder.

The blunder is he already had the solution in some of his equations but removed it because he was too stubborn to accept the universe was expanding .

@@brainimp His "blunder" was his failure to make yet another brilliant conjecture to stun the world of science.

@@brainimp It wasn't even known then if the universe included objects beyond the Milky Way. Give them some space.

That's great!

Francis Galiegue Except he did an awful job at actually explaining any of them. Equations are fine, but meaningless and even obfuscating if you're just going to carelessly skim over the terms and relationships.

***** awful job?? That is your opinion; my opinion is quite the opposite, his explanation was spot on

Francis Galiegue "Spot on" is irrelevant in a discussion concerning effective communication.

***** if _this_ communication was not effective to you, I don't know what communication will ever be, to be honest.

Francis Galiegue My bet is you're either afflicted by an inflationary sense of comprehension, or have some background in physics and are simply as poor a communicator as buddy in the video.

+spinvalve - He did have a pretty high pitched voice, but that clip sounds _too_ high. It may have been filmed at 18 fps and played back at 24. Or it may have been filmed from the top of a train going at 99.8% of the speed of light, of course.

+RFC3514 But i thought the human eye cant see above 1 fps :/

***** - While old microphones weren't very sensitive to low frequencies (leading to a kind of unbalanced "tinny" tone), they couldn't really _shift_ the frequency. Doing that requires either a lot of complex spectral processing or (in 99% of cases) playing the sound back at a different speed (play it faster and the pitch goes up, play it slower and it goes down). Between the 1920s and 1950s it was common to shoot film at 18 fps or less (sometimes the speed even varied _during_ the clip, because the camera was cranked by hand - though that was mostly in the silent era), and there were no embedded timecodes or sync signals (or, in many cases, even a label on the reel saying what speed it had been recorded at). When those films get played back at the "modern" standard of 24 fps (or sometimes even directly at 30 fps for TV, if the telecine operator is _really_ incompetent), the result is that everyone moves very fast and talks with a high-pitched voice. Even a small difference (ex., assuming the film was shot at 18 fps when in fact it was shot at 16 fps) can lead to a noticeable shift in audio pitch.

RFC3514 Figures then. But what has always intrigued me is how Google managed to keep videos from sounding chipmunky even when we speed them up on KZfaq.

+spinvalve That isn't really that new of a concept. Most decent pieces of audio software have it built in. Google might be your friend (if you are nice).