[alancalverd]

By memorizing mathematical operations like square root, exponentiation, integration, etc. Then apply them to some natural numbers to get those irrational number algorithmically.

I said "understand", not "calculate".

[alancalverd]

I mentioned speed instead of velocity.

And there's your misunderstanding. To go there at speed a and return at speed a, your velocity has changed by -2A
where A is a vector of magnitude a and direction "from here to there", so you have accelerated.

[Eternal Student]

Hi.

  Alancalverd said:    how do we "understand" 1.414213......, 3.141459..... 2.71828.....  or any other irrational number?
Hamdani replied:   By memorizing mathematical operations like square root, exponentiation, integration, etc....

    So just memorising some information is sometimes an acceptable way to understand? 
    Despite Gregory Chaitin's view of comprehension,  you don't always have to introduce concepts and some model to compress the information?

   It's hard to say what human understanding is.

   If you can predict something and also use it to acheive results you wanted, perhaps that's a demonstration of understanding.  So tennis players understand the motion of a ball.   A physicist using Newton's law also has some understanding of the motion of a ball.   However, the two ways of understanding probably weren't the same.  It's unlikely you could identify neurological processes occuring in the tennis player that correspond to performing some numerical calculation.

    There are other theories describing what understanding might, especially what "knowledge" might be.   In the theory of social constructivism, knowledge is not located in one individual.  Knowledge is located in society.  Language is important and there can be a specific set of vocabulary, a Lexicon, that accesses knowledge in society.   So you could trade an abstract object like irrational numbers for an object that, while equally abstract, society has made more tangible as a form of knowledge and understanding.   Some of the vocabulary you've used like "exponentiation" and "integration" has been key.   There's been a trade between some object you wished to understand (irrational numbers) and some knowledge and understanding of abstract objects that society has.   Although "exponentiation" and "integration" may seem like only two things, there's really no way to count how many things, ideas or concepts were involved and synthesised together when society came to an understanding of integration and exponentiation.   
   You may have taken a single abstract object (irrational numbers) and replaced it with more concepts than if you had just not tried to understand it in this way.   None the less, it seems more understood, it can be used etc.   This is quite different to Chaitin's view of understanding where he implies that if less concepts are involved, the better the understanding is likely to be.

Best Wishes.

[hamdani yusuf (OP)]

I'll let competing ideas compete, and let the best idea win. They don't have to be perfect, but I'll stick to the best one for the time being.

Great.  What is the best one?

The one which can give consistent answers for original twin paradox, the twins travelling in opposite direction, and also twin that changes frame of reference several times. It's yet to be demonstrated here.

[hamdani yusuf (OP)]

This guy here thinks he has resolved the twin's paradox with complete intuition.

The triplet paradox!

We will finally resolve the twin's paradox with complete intuition!

Chapter:
00:00 Intro
00:45 Why you don't understand Twin's paradox
1:28 Einstein's clock synchronisation
2:30 What do the brothers see?
3:14 What does the sister see?
4:46 The first half of twin's paradox
5:30 The relativity of simultaneity
7:53 Relativity of simultaneity equation
10:47 Resolving the first half of twin's paradox
12:20 It's NOT the acceleration!
14:24 Who is accelerating?
16:38 Resolving twin's paradox (What the brothers see)
17:12 Resolving twin's paradox (What the sister sees)
19:31 Summary

In the summary, he says that the key is the relativity of simultaneity.

[hamdani yusuf (OP)]

By memorizing mathematical operations like square root, exponentiation, integration, etc. Then apply them to some natural numbers to get those irrational number algorithmically.

I said "understand", not "calculate".

Understanding only needs you to know how to get the final result, without having to produce the exact final result. If you don't know ho to get it, it means you haven't understood it.

[hamdani yusuf (OP)]

I mentioned speed instead of velocity.

And there's your misunderstanding. To go there at speed a and return at speed a, your velocity has changed by -2A
where A is a vector of magnitude a and direction "from here to there", so you have accelerated.

Does time dilation depend on velocity?

[hamdani yusuf (OP)]

So just memorising some information is sometimes an acceptable way to understand? 

Without memory, you won't understand anything. It's necessary, but inadequate for understanding. You are missing the word "then" in my statement. That's why you sound surprised. I suppose it's unintentional.

[hamdani yusuf (OP)]

You may have taken a single abstract object (irrational numbers) and replaced it with more concepts than if you had just not tried to understand it in this way.

You would need infinite amount of information bits to express the exact value of irrational numbers in decimal. On the other hand, you can express it in finite amount of information bits to express them if you understand how to relate them to more familiar concepts.

[Halc]

Great.  What is the best one?

The one which can give consistent answers for original twin paradox, the twins travelling in opposite direction, and also twin that changes frame of reference several times.

All the valid explanations/techniques do that.

I mean, you're not going to find a you-tube video that gives the specific answer for the scenario you just made up, but using the methods as explained in the valid videos, you'll get the same answer in all cases.

It's yet to be demonstrated here.

Many valid explanations have been posted, and they all give the same results. Your claim here is not substantiated. You need to show that the method posted yields inconsistent results, and you've not done that. You don't even try.

Apparently no explanation, however correct, will satisfy you. You will continue to not learn it, and post all these denialist claims.

This guy here thinks he has resolved the twin's paradox with complete intuition.

I didn't see him use 'complete intuition' anywhere, but I didn't watch it all. He does leave out some critical frame references, especially when discussing the sync convention, so I find the video likely to confuse someone trying to learn.
If the video says that the key is relativity of simultaneity, that's often true, and is very much key in resolving the way he first describes the paradox. Almost all novices tend to discount RoS.  On the other hand, neither of two of the explanations I gave (the interval one that works in the most general case, and the single-frame one that is simplest) needed to reference relativity of simultaneity.

Understanding only needs you to know how to get the final result, without having to produce the exact final result. If you don't know ho to get it, it means you haven't understood it.

Agree. Apparently nothing we post can actually make you understand this simplest of relativity illustrations.

I mentioned speed instead of velocity.

And there's your misunderstanding. To go there at speed a and return at speed a, your velocity has changed by -2A where A is a vector of magnitude a and direction "from here to there", so you have accelerated.

Does time dilation depend on velocity?

In SR, it depends on speed. You're correct here. It's about speed, not velocity.
So in your twin going out halfway and back, twice, both travelers have the same speed relative to Earth at all times and thus arrive together back at Earth the same age as each other. All the velocity changes don't matter. What matters is that the speed in that frame is constant.
Note that this is using the 'easy method' I mentioned above.

[alancalverd]

What matters is that the speed in that frame is constant.

But it isn't. At some point you have to slow down, stop, turn round, and accelerate again.

[Origin]

I was going to respond to this:

The one which can give consistent answers for original twin paradox, the twins travelling in opposite direction, and also twin that changes frame of reference several times. It's yet to be demonstrated here.

However I see Halc already did and I have to agree with his reply:

Many valid explanations have been posted, and they all give the same results. Your claim here is not substantiated. You need to show that the method posted yields inconsistent results, and you've not done that. You don't even try.

Apparently no explanation, however correct, will satisfy you. You will continue to not learn it, and post all these denialist claims.

Especially the bolded part - you never accept any answer, it is very frustrating trying to have a conversation with someone like that.

[hamdani yusuf (OP)]

Many valid explanations have been posted, and they all give the same results. Your claim here is not substantiated. You need to show that the method posted yields inconsistent results, and you've not done that. You don't even try.

What I said was a plain fact.

The one which can give consistent answers for original twin paradox, the twins travelling in opposite direction, and also twin that changes frame of reference several times. It's yet to be demonstrated here.

[hamdani yusuf (OP)]

Apparently no explanation, however correct, will satisfy you. You will continue to not learn it, and post all these denialist claims.

How do you know? You haven't tried it yet.

[hamdani yusuf (OP)]

I didn't see him use 'complete intuition' anywhere, but I didn't watch it all. He does leave out some critical frame references, especially when discussing the sync convention, so I find the video likely to confuse someone trying to learn.
If the video says that the key is relativity of simultaneity, that's often true, and is very much key in resolving the way he first describes the paradox. Almost all novices tend to discount RoS.  On the other hand, neither of two of the explanations I gave (the interval one that works in the most general case, and the single-frame one that is simplest) needed to reference relativity of simultaneity.

IMO, the explanation in Mahesh' video there is the most general yet that I've seen. It explains the case for triple twin well. It takes into account the effects of acceleration on earth at the beginning and the end of the journey. It also breaks down the turning point into deceleration to stop and acceleration to move in the opposite direction.

But still, it hasn't explained the case where both twins changed their frame of reference. How their change of reference can cancel out the time difference?

[hamdani yusuf (OP)]

Agree. Apparently nothing we post can actually make you understand this simplest of relativity illustrations.

Appearance can be deceiving.

If the video says that the key is relativity of simultaneity, that's often true, and is very much key in resolving the way he first describes the paradox. Almost all novices tend to discount RoS.  On the other hand, neither of two of the explanations I gave (the interval one that works in the most general case, and the single-frame one that is simplest) needed to reference relativity of simultaneity.

Maybe you are among those novices?
Some of the authors that you disagree with are professional physicists.

[hamdani yusuf (OP)]

In SR, it depends on speed. You're correct here. It's about speed, not velocity.
So in your twin going out halfway and back, twice, both travelers have the same speed relative to Earth at all times and thus arrive together back at Earth the same age as each other. All the velocity changes don't matter. What matters is that the speed in that frame is constant.
Note that this is using the 'easy method' I mentioned above.

The easy method doesn't even address the core problem in twin paradox, which is the same events seen from the perspective of the travelling twin. Unlike in Lorentz' relativity, the travelling twin is also an equally valid observer in special theory of relativity.
It's not surprising if you don't find any problem there.

[hamdani yusuf (OP)]

What matters is that the speed in that frame is constant.

But it isn't. At some point you have to slow down, stop, turn round, and accelerate again.

How do they affect time dilation and the total time elapsed in both frame of references?

[hamdani yusuf (OP)]

However I see Halc already did

Can you point out which post?
How do change of reference frame cancel out time difference accumulated from time dilation during the journey?

[hamdani yusuf (OP)]

Especially the bolded part - you never accept any answer, it is very frustrating trying to have a conversation with someone like that.

It's the contrary. I accept every answer, including those which disagree with yours. I just want to go one step further, which is finding out the most effective and efficient one.