The Nature of reality - revisited

[Naina_Marbus]

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I am returning to the forum after a long hiatus. When I logged in, the first thread that
caught my attention was that of Shri TKS on the nature of reality. However, I found
that the thread has been closed. I therefore started this just to get clarification on
something from anyone who can offer enlightening perspectives. Here is my query.

Most of us are familiar with Euler's equation: e[SUP]iπ [/SUP]+ 1 = 0
What does this equation represent?
Does it say anything about the nature of reality?

The letter "e" represents an irrational number 2.71828...(with unending digits).
Next, "i" represents an "imaginary number": the square root of -1. It is called “imaginary”
because there is no number which can be multiplied by itself to produce a negative number
( i.e. negative numbers do not have square roots).

π is the ratio of a circle's circumference to its diameter. Like "e," it represents an irrational
number 3.1415926535897932…. ...(with unending digits).

Putting it all together, "e" raised to the power of the imaginary "i" multiplied by pi equals -1.

As per Euler's equation, adding 1 to the above product gives a value of 0.

Incredibly, all these strange numbers — real and imaginary, rational and irrational — combine
in such a simple manner, and yield sunyam!

 

[yesmohan]

Sir,

Anything irrational ....if it would be raised with the power of imagination of irrationals proves out even after added with one concrete rational (1) could all be " Soonyam".

I presume but could not confirm ............... is this the truth we ought to learn from Euler's Equation.

But I could not understand why you would like to impress upon this in a subtle way to the forum.

 

[sravna]

Good useful thread. It is necessary to understand the rationale behind physical laws and the equations because they always tell something deeper about reality than the just the relationship between the physical variables and constants.

 

[auh]

I gave that example to show that basic quantities such as Time are not absolute though in our day today life we take then as such (and it is valid). Time itself slows down and the experience of a person traveling fast is that only few minutes have elapsed for them and in other place elapsed time is of the order of years.

This is counter intuitive and challenged the scientists about basic notions of space/time/mass etc but measurements at atomic levels confirm the accuracy of this theory. In fact there was even an experiment to directly verify time dilation in the 1970s. If one is not baffled by this theory or of quantum mechanics it means they do not understand ( a modified quote of Bohr )

https://en.wikipedia.org/wiki/Time_dilation

https://www.youtube.com/watch?v=yirQ4YXZZVk

The above is taken from the original thread and is Shri tks' response to my post.

When I wanted to reply the thread was already closed, and hence here

I want to comment on the words in bold:

We observe that things have a life span during which they exhibit certain characteristics, i.e., of growth, maturity, and death. These are obviously different for different types of beings, and a common base is the unit of time - the second.

[TABLE="width: 100%"]
[TR]
[TD][FONT=Myriad Roman,Syntax,Arial,Helvetica]Unit of time (second)[/FONT] [/TD]
[TD][FONT=Myriad Roman,Syntax,Arial,Helvetica]Abbreviations: CGPM, CIPM, BIPM[/FONT][/TD]
[/TR]
[/TABLE]
[FONT=Myriad Roman,Syntax,Arial,Helvetica] [/FONT] [FONT=Myriad Roman,Syntax,Arial,Helvetica] The unit of time, the second, was defined originally as the fraction 1/86 400 of the mean solar day. The exact definition of "mean solar day" was left to astronomical theories. However, measurement showed that irregularities in the rotation of the Earth could not be taken into account by the theory and have the effect that this definition does not allow the required accuracy to be achieved. In order to define the unit of time more precisely, the 11th CGPM (1960) adopted a definition given by the International Astronomical Union which was based on the tropical year. Experimental work had, however, already shown that an atomic standard of time-interval, based on a transition between two energy levels of an atom or a molecule, could be realized and reproduced much more precisely. Considering that a very precise definition of the unit of time is indispensable for the International System, the 13th CGPM (1967) decided to replace the definition of the second by the following (affirmed by the CIPM in 1997 that this definition refers to a cesium atom in its ground state at a temperature of 0 K): [/FONT]

• [FONT=Myriad Roman,Syntax,Arial,Helvetica]The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.[/FONT]
  

I do not know as to how they say that time slows down in space. Perhaps it may be that the "duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom" is longer than what it is on earth. But would such a delay or slowness of time cause an equivalent "delay in depreciation (or aging)" of the body that is in space (relative to earth)? Only then can we say that time slows and with it an entity also ages less.

 

[tks]

I am returning to the forum after a long hiatus. When I logged in, the first thread that
caught my attention was that of Shri TKS on the nature of reality. However, I found
that the thread has been closed. I therefore started this just to get clarification on
something from anyone who can offer enlightening perspectives. Here is my query.

Most of us are familiar with Euler's equation: e[SUP]iπ [/SUP]+ 1 = 0
What does this equation represent?
Does it say anything about the nature of reality?

The letter "e" represents an irrational number 2.71828...(with unending digits).
Next, "i" represents an "imaginary number": the square root of -1. It is called “imaginary”
because there is no number which can be multiplied by itself to produce a negative number
( i.e. negative numbers do not have square roots).

π is the ratio of a circle's circumference to its diameter. Like "e," it represents an irrational
number 3.1415926535897932…. ...(with unending digits).

Putting it all together, "e" raised to the power of the imaginary "i" multiplied by pi equals -1.

As per Euler's equation, adding 1 to the above product gives a value of 0.

Incredibly, all these strange numbers — real and imaginary, rational and irrational — combine
in such a simple manner, and yield sunyam!

Sri NM,

Not sure if I have an enlightening perspective but let me share my comments.

This is a beautiful theorem and fascinating from many perspectives within mathematics.

However it is not all that mysterious to me and the usage of term Shunyam for the number zero will not apply here in my understanding. Let me elaborate.

Zero is a number and all its usage arises within a given context. For example I may have an apple and then eat the apple. Then I have zero apple left. Here the number zero is in the context of something that is missing. In that sense it can be called a relative number like any other number.
All equations like

25 - (5*5) = 0

deal with number zero in a relative sense. The word Shunyam is referred to an absolute non-existence without any context whatsoever.

It is another topic to talk about why Shunyam cannot exist though the Buddhist 'believe' that everything in this world appeared to come out of Shunyam. There are also many misconceptions about this concept.

The Rishis of India studied how we acquire knowledge such as direct perception (of our sense organs) and by deduction of our mind. The deduction itself has been categorized into many aspects one of which is called Anupalabdhi which is ability to know absence of an item. Such a means of knowing is always with respect to a context. Zero occurring in mathematics is similar to the means of knowledge termed Anupalabdhi.

Now looking at Euler's identity namely
e[SUP]iπ[/SUP] + 1 = 0

1. It is just an identity. An assertion of the truth of some items
2. Human mind understands of entities of the world by having a form (based on some sensory input or imagination) with a key word of a name. This ability of storage and recall is popularly referred to as follows. Jagat is characterized by human mind in terms of Nama-Rupa.
Now entities like complex numbers (square root of -1) or infinity cannot be imagined or perceived by our mind. But it need not stop our ability to name them with symbol(s)
3. This has afforded us to 'sum' up infinite series of numbers (like Geometric series in middle school mathematics) or more sophisticated formulas. In Physics there is this usage of Hilbert Space, which is an infinite dimensional space imagined to solve real world problems. Most second or third year undergraduate physics student may not comprehend a Hilbert space and yet be able to manipulate algebra and calculus to solve real world problems.
4. The Euler's constant e raised to any complex entity has an infinite series expansion which can be broken up into sum of two infinite series - one being all real numbers and another sum of all imaginary infinite series numbers. It turns out that the real infinite series adds to nothing but Cosine function and imaginary part adds to sine function. Both these cosine and sine are functions studied in high school trigonometry.
5. There are physical way to understand this identity using circles and right angled triangles and the identity itself is therefore not a mystery any more than the mystery of the identity 25 - (5*5) = 0 for example.

It is a beautiful theorem and its generalization has great many applications in many engineering disciplines.

 

[tks]

The above is taken from the original thread and is Shri tks' response to my post.

When I wanted to reply the thread was already closed, and hence here

I want to comment on the words in bold:

We observe that things have a life span during which they exhibit certain characteristics, i.e., of growth, maturity, and death. These are obviously different for different types of beings, and a common base is the unit of time - the second.



I do not know as to how they say that time slows down in space. Perhaps it may be that the "duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom" is longer than what it is on earth. But would such a delay or slowness of time cause an equivalent "delay in depreciation (or aging)" of the body that is in space (relative to earth)? Only then can we say that time slows and with it an entity also ages less.

Sri auh,

The topic area has nothing to do with aging or space or how clocks work. Space is everywhere by the way

Clocks even mechanical or atomic clocks functions the same everywhere except that atomic clocks are more precise.

I did not specifically say time slows down in space Time itself 'slows down' in a fast moving object relative
to experience of time in a stationary place relative to the fast moving object. I also mentioned that this has been verified directly. A group of scientists took atomic clocks and flew around the world in a plane and compared the clocks in a stationary place in their lab. The slower time measured is in general agreement with the theory,

Here is a reference
https://en.wikipedia.org/wiki/Hafele–Keating_experiment


"The Hafele–Keating experiment was a test of the theory of relativity. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks against others that remained at the United States Naval Observatory. When reunited, the three sets of clocks were found to disagree with one another, and their differences were consistent with the predictions of special and general relativity."

So the thing to understand is that time itself is not an absolute quantity and is not same everywhere.


All-
In the other thread in brief history of time in the scholarly section I had a simple proof why time itself is unreal and that the truth of time is timelessness.

Space can also be shown to be similarly unreal.

Objects in time space fabric itself do not have reality the way we imagine them to be.

For metaphysical understanding Physics cannot help. Our scriptures like Madukya Upanishad, Ashtavakra Samhita, Yoga Vasishtam (Utpatti Prakaranam) , Sri Sankara's writings, Upadesha Sahra etc all have gotten the nature of space and time understanding correct. I do not plan to engage in further discussion on these items but mentioned the references for interested readers to follow up on their own.

 

[auh]

Sri auh,

The topic area has nothing to do with aging or space or how clocks work. Space is everywhere by the way

Clocks even mechanical or atomic clocks functions the same everywhere except that atomic clocks are more precise.

I did not specifically say time slows down in space Time itself 'slows down' in a fast moving object relative
to experience of time in a stationary place relative to the fast moving object. I also mentioned that this has been verified directly. A group of scientists took atomic clocks and flew around the world in a plane and compared the clocks in a stationary place in their lab. The slower time measured is in general agreement with the theory,

Here is a reference
https://en.wikipedia.org/wiki/Hafele–Keating_experiment


"The Hafele–Keating experiment was a test of the theory of relativity. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks against others that remained at the United States Naval Observatory. When reunited, the three sets of clocks were found to disagree with one another, and their differences were consistent with the predictions of special and general relativity."

So the thing to understand is that time itself is not an absolute quantity and is not same everywhere.

Yes, I understand that I am taking out a sentence from your OP and elaborating on it but that was precisely to show that we do not have any consistent way to measure the absoluteness of "time". In fact this is evident from the very nature of what we call "time".

 

[auh]

Reply to Shri Sravna's post:

The idea is time perceptibly slows down when you are travelling at high speed. That is, an event which would take a certain duration of time now takes longer to complete. That would explain why the body ages slower.

But that is only in thought. I have a problem with that. At very high speed, I think matter would begin to disintegrate and when one is travelling at a speed approaching that of light, he would be shred to pieces . Definitely not look younger I suppose.

Any thoughts on the above?

I will try to give an analogy to what I am trying to say.

We will assume that 840,960,000 breathes constitutes the lifespan of a human and no other diseases or accidents or events occur that would hamper this span.

We will also assume that each breath is of a same duration "x".

The question is would a person (A) be able to take 840,960,000 breathes at a duration "y" (each) that is slightly longer than "x", and thus outlive the person (B) who takes 840,960,000 breathes at duration x? Or would person A take lesser breathes of duration "y" thus equating his lifespan to that of B?

 

[sravna]

Reply to Shri Sravna's post:

I will try to give an analogy to what I am trying to say.

We will assume that 840,960,000 breathes constitutes the lifespan of a human and no other diseases or accidents or events occur that would hamper this span.

We will also assume that each breath is of a same duration "x".

The question is would a person (A) be able to take 840,960,000 breathes at a duration "y" (each) that is slightly longer than "x", and thus outlive the person (B) who takes 840,960,000 breathes at duration x? Or would person A take lesser breathes of duration "y" thus equating his lifespan to that of B?

Dear auh,

All the talk about slower ageing surrounding time travel is only in imagination, not even backed by solid theory. In my view if time slows down disintegration of physical things begin to happen. This I surmise from my understanding of timelessness where reality is a whole. If you want me to give the rationale I would say that the energy barrier between two points of time for that person has increased. So the points are more in isolation and paves the way for disintegration.

On the basis of the theory of relativity alone we may think as time slows down, ageing also slows down. It seems to me that this is facile reasoning and has no logical basis.

 

[tks]

Yes, I understand that I am taking out a sentence from your OP and elaborating on it but that was precisely to show that we do not have any consistent way to measure the absoluteness of "time". In fact this is evident from the very nature of what we call "time".

In restatement when context is lost meaning is also lost.

The talk of measuring or 'consistently measuring' itself has no applicability because there is no entity called absolute "time"

I will not be commenting further - you are welcome to have the last word!

 

[Naina_Marbus]

Sir,

Anything irrational ....if it would be raised with the power of imagination of irrationals proves out even after added with one concrete rational (1) could all be " Soonyam".

I presume but could not confirm ............... is this the truth we ought to learn from Euler's Equation.

But I could not understand why you would like to impress upon this in a subtle way to the forum.

Interesting interpretation!

 

[Naina_Marbus]

Sri NM,

Not sure if I have an enlightening perspective but let me share my comments.

This is a beautiful theorem and fascinating from many perspectives within mathematics.

However it is not all that mysterious to me and the usage of term Shunyam for the number zero will not apply here in my understanding. Let me elaborate.

Zero is a number and all its usage arises within a given context. For example I may have an apple and then eat the apple. Then I have zero apple left. Here the number zero is in the context of something that is missing. In that sense it can be called a relative number like any other number.
All equations like

25 - (5*5) = 0

deal with number zero in a relative sense. The word Shunyam is referred to an absolute non-existence without any context whatsoever.

It is another topic to talk about why Shunyam cannot exist though the Buddhist 'believe' that everything in this world appeared to come out of Shunyam. There are also many misconceptions about this concept.

The Rishis of India studied how we acquire knowledge such as direct perception (of our sense organs) and by deduction of our mind. The deduction itself has been categorized into many aspects one of which is called Anupalabdhi which is ability to know absence of an item. Such a means of knowing is always with respect to a context. Zero occurring in mathematics is similar to the means of knowledge termed Anupalabdhi.

Now looking at Euler's identity namely
e[SUP]iπ[/SUP] + 1 = 0

1. It is just an identity. An assertion of the truth of some items
2. Human mind understands of entities of the world by having a form (based on some sensory input or imagination) with a key word of a name. This ability of storage and recall is popularly referred to as follows. Jagat is characterized by human mind in terms of Nama-Rupa.
Now entities like complex numbers (square root of -1) or infinity cannot be imagined or perceived by our mind. But it need not stop our ability to name them with symbol(s)
3. This has afforded us to 'sum' up infinite series of numbers (like Geometric series in middle school mathematics) or more sophisticated formulas. In Physics there is this usage of Hilbert Space, which is an infinite dimensional space imagined to solve real world problems. Most second or third year undergraduate physics student may not comprehend a Hilbert space and yet be able to manipulate algebra and calculus to solve real world problems.
4. The Euler's constant e raised to any complex entity has an infinite series expansion which can be broken up into sum of two infinite series - one being all real numbers and another sum of all imaginary infinite series numbers. It turns out that the real infinite series adds to nothing but Cosine function and imaginary part adds to sine function. Both these cosine and sine are functions studied in high school trigonometry.
5. There are physical way to understand this identity using circles and right angled triangles and the identity itself is therefore not a mystery any more than the mystery of the identity 25 - (5*5) = 0 for example.

It is a beautiful theorem and its generalization has great many applications in many engineering disciplines.

Shri TKS: you have given an interesting, albeit tortuous, discussion on the significance of Euler's equation. However,
I am curious if one can come up with a simple interpretation in which the equation would serve as a metaphor for
some event - real or mythological. For instance, a friend of mine took a quick look at the equation and made a 'queer'
remark that it is a metaphor for how kaliyugam will end!

 

[sravna]

Shri TKS: you have given an interesting, albeit tortuous, discussion on the significance of Euler's equation. However,
I am curious if one can come up with a simple interpretation in which the equation would serve as a metaphor for
some event - real or mythological. For instance, a friend of mine took a quick look at the equation and made a 'queer'
remark that it is a metaphor for how kaliyugam will end!

Dear Shri Naina_Marbus,

Here's my try:

e^(in)= e^i * e^n

e and n are transcendental numbers.Something to do with beyond physical reality as they cannot be calculated precisely

The base e represents our nature and n being a transcendental number, e^n implies empowered in the natural way

We know that i is an imaginary number and so may be connected to illusory reality.

We know e^n * e^i=-1

So if e^n = 100, e^i = -(1/100)

It is both a reciprocal and opposite sign. meaning the empowerment of e^i works in a negative way compared to that of e^n and the actual power is also only a reciprocal of that of e^n

So e^n and e^i may represent the spiritual and physical empowerment resp at a particular level.

 

[mskmoorthy]

Not necessarily ofr this equation, there has been strange coincidences (deep relationships ) In mathematics they have a term called moonshine theory https://en.wikipedia.org/wiki/Monstrous_moonshine
The term "monstrous moonshine" was coined by Conway, who, when told by John McKay in the late 1970s that the coefficient of

(namely 196884) was precisely the dimension of the Griess algebra (and thus exactly one more than the degree of the smallest faithful complex representation of the monster group), replied that this was "moonshine" (in the sense of being a crazy or foolish idea).[SUP][3][/SUP] Thus, the term not only refers to the monster group M; it also refers to the perceived craziness of the intricate relationship between M and the theory of modular functions.
The most famous being Conway-Simon moonshine conjecture which was settled by Richard Borcherds (for which he won the Fields Medal in 1998)

 

[mskmoorthy]

Since I am unable to edit my posts, I will like to add an article that was recently published in the quanta magazine about moonshine theories
(March 2016)
https://www.quantamagazine.org/20150312-mathematicians-chase-moonshines-shadow/

 

[tks]

Shri TKS: you have given an interesting, albeit tortuous, discussion on the significance of Euler's equation. However,
I am curious if one can come up with a simple interpretation in which the equation would serve as a metaphor for
some event - real or mythological. For instance, a friend of mine took a quick look at the equation and made a 'queer'
remark that it is a metaphor for how kaliyugam will end!

Actually I had not given any interpretation other than to say that

• The idea of shunyam is inapplicable to number zero
• This equation though beautiful mathematically is no more significant than even a simple equation like 8+2=10
• Human mind can deal with items it cannot imagine with senses (like visualization) by using symbols for imaginary number etc

I just want to add that mathematics and Physics are very precise in dealing with descriptions of the phenomenological reality we observe using constructs that may not be understandable by our senses but can be processed by our mind.

Vedanta as properly interpreted by people such as Sri Sankara is just as precise and rigorous in describing the metaphysical reality that is subject to teaching and understanding without imagination and unwarranted beliefs.


In describing reality at various levels there are no rooms for imagination and beliefs in any case.



Human beings are endowed with the capacity to imagine and the multitudes of religions in the world are proofs of human capacity to imagine. So one can take an equation and imagine. One can imagine about ideas like Yuga and Kali Yuga etc. One can imagine about predicting the future (which is very different from predictions of science and statistics with associated probabilities). One can imagine about extraordinary powers one may attribute to a person like a god man.

Creative capacity of human beings have nothing to do with these imaginations and have nothing to do with reality at any levels.


Let the discussion continue with others since I do not have anything more to say.

 

[tks]

Not necessarily ofr this equation, there has been strange coincidences (deep relationships ) In mathematics they have a term called moonshine theory https://en.wikipedia.org/wiki/Monstrous_moonshine
The term "monstrous moonshine" was coined by Conway, who, when told by John McKay in the late 1970s that the coefficient of

(namely 196884) was precisely the dimension of the Griess algebra (and thus exactly one more than the degree of the smallest faithful complex representation of the monster group), replied that this was "moonshine" (in the sense of being a crazy or foolish idea).[SUP][3][/SUP] Thus, the term not only refers to the monster group M; it also refers to the perceived craziness of the intricate relationship between M and the theory of modular functions.
The most famous being Conway-Simon moonshine conjecture which was settled by Richard Borcherds (for which he won the Fields Medal in 1998)

Interesting post, great references indeed!

 

[yesmohan]

It appears that the matter that are all beyond the "perception of mind and imagination" are all termed as "shunyam".

 

[Jaykay767]

Religions are not founded on imagination of people, there is a vast knowledge for those who seek it with an open mind, none for those who come with closed minds.

Shankara’s Advaita does not originate in a vacuum; it is a culmination of millennia of enquiry by our ancient Rishis. Shankara himself credits his Guru for his vast knowledge.

That 1 day in Brahma lokam translates to 1000s of years in the Bhulokam is not some timepass imagination. This is the core of Einstein’s nobel winning relativity – that time slows down on objects moving at higher speed than earth. so to explain in lay men terms, planets/worlds transiting at higher speeds than earth will have slower time. So this means, that for any planet travelling at speed of light, the time will standstill – in here, people will never age - eternal youth.

So when Einstein/scientist talks about eternal youth, it is great. But if our ancient rishis talk about eternal youth in Kailasam & Vaikuntam, it is funny?

So just coz Einstein’s theory sounds very modern it is okay, but brahma lokam, Bhulokam, Kailasam, Vaikuntam sounds very ancient, funny, these are wrong.

Similarly Gandhari giving births to 100s of sons by splitting the prasadam into 100 pots, is not imagination. How can our ancients even think that they can conceive a child outside of the human body, like we do today via test tube babies?

Similarly the many stories on flying across the world via many machines, etc.. are not imagination.

It is amusing to see how some people continue to be enamored by Eulers’ identity, Einstien’s relativity, etc.. at the same time make fun of our scriptures. And they blame Bobby Jindal.. LOL !!

LOL !