Should I be amazed?

[Agent Smith]

Suppose in a hypothetical universe consisting of 2 objects, A and B, I discover the ratio $\text{Mass(A) : Mass(B)} \approx n\phi$, where $\phi$ is our Divina proportione or golden ratio and n is a whole number > 0.

Should I consider this "discovery" some kinda hidden mathematical truth ... do I have warrant to believe that a great secret has been revealed to me?

I ask because there are other constants too e.g. Pythagoras' constant ($p = \sqrt 2$) and we also have $\pi$.

Say the ratio I calculated above = $94$ = $\text{Mass(A) : Mass(B)}$. But $2\phi^8 \approx 30\pi \approx 47p^2 = 94$

From my preliminary investigations, given $M$ is some physical measurement and $K$ is any math/physical constant, and $p$ is some exponent and $n$ is some integer ($n \ne 0$) and we have the expression $M \approx nK^p$, there's always some integer $n$ and some integer $p$, for any and every constant $K$ that satisfies the equation $M \approx nK^p$. And just like that the finding that $\text{Mass(A) : Mass(B)} = 94 \approx 2\phi^8$ is trivialized (it carries no special meaning).

 

[Otis]

Suppose in a hypothetical universe consisting of 2 objects, A and B, I discover the ratio Mass(A) : Mass(B)

Are you hypothetically outside of this universe, or are you one of the objects?

 

[Agent Smith]

Are you hypothetically outside of this universe, or are you one of the objects?

A detail that turns out is inconsequential. I'd first written "[...]2 objects, A and B, and me[...]"

 

[Agent Smith]

Corrigendum: $M$ is some ratio of physical measurements ()

 

[Agent Smith]

So I should NOT be amazed?

 

[topsquark]

So I should NOT be amazed?

If you have some reason to predict that the ratio should be $\phi$, then yes, be amazed. Otherwise the ratio has to be some number. It's a coincidence. If you want to be amazed by that then go ahead.

-Dan

 

[Agent Smith]

So sad, but gracias. What explains the golden ratio found in the Parthenon and the nautilus shell?

 

[topsquark]

So sad, but gracias. What explains the golden ratio found in the Parthenon and the nautilus shell?

Is this a new question? Then it belongs in a new thread.

The Greeks designed the Parthenon and the nautilus creates the shell via a Mathematical process. It is completely different than two masses in their own Universe having a specific ratio.

-Dan

 

[Agent Smith]

@topsquark but what if someone found the golden ratio in other objects in the universe? I could always find some relationship $r \approx ak^n$ for any natural ratio $r$, where $k$ is some mathematical constant (like the golden ratio) and $a, n \in \mathbb{Z}$

 

[topsquark]

@topsquark but what if someone found the golden ratio in other objects in the universe? I could always find some relationship $r \approx ak^n$ for any natural ratio $r$, where $k$ is some mathematical constant (like the golden ratio) and $a, n \in \mathbb{Z}$

Then you have an hypothesis and you need to find a theory to fit it.

-Dan

 

[Agent Smith]

The OP has some evidence.

 

[topsquark]

The OP has some evidence.

For two particles. A coincidence.

-Dan

 

[Agent Smith]

@topsquark you mean to say that for > 2 particles, it isn't a coincidence? So far I've read a whole lot of recreational math and very little formal math. Of what I've seen the golden ratio tops the list of favorite number to find in nature, but from the OP I can, it seems, find another irrational constant with similar "mind-blowing" relationships. So doesn't that trivialize the golden ratio's alleged presence in the natural world? Thank you. What am I missing here?

 

[topsquark]

@topsquark you mean to say that for > 2 particles, it isn't a coincidence? So far I've read a whole lot of recreational math and very little formal math. Of what I've seen the golden ratio tops the list of favorite number to find in nature, but from the OP I can, it seems, find another irrational constant with similar "mind-blowing" relationships. So doesn't that trivialize the golden ratio's alleged presence in the natural world? Thank you. What am I missing here?

A relationship between a small number of data points is a coincidence. A relationship between a large number of data points is a correlation.

Find an Introductory Probability text and review it.

-Dan

 

[Agent Smith]

@topsquark thanks, that makes sense.

 

[Agent Smith]

Any other reasons I should ignore the results?

 

[topsquark]

Any other reasons I should ignore the results?

No, that covers it.

-Dan

 

[Agent Smith]

A relationship between a small number of data points is a coincidence. A relationship between a large number of data points is a correlation.

Find an Introductory Probability text and review it.

Sorry, but it's not quite clear to me why you say this. If I find a natural world mathematical relationship with $\varphi$ in it, I should ignore it? What about sunflower seeds, nautilus shells, phyllotaxy, etc.?

 

[topsquark]

Sorry, but it's not quite clear to me why you say this. If I find a natural world mathematical relationship with $\varphi$ in it, I should ignore it? What about sunflower seeds, nautilus shells, phyllotaxy, etc.?

Is there a mechanism that is creating all these $\phi$s? Then, yes, it's special. But that isn't what your OP was about.

-Dan

 

[Agent Smith]

@topsquark there may be a logic to it, yes but I can't quite put me finger on why