Should I be amazed?

[Agent Smith]

Imagine there's a mathematical constant $k_1$ and that your mathematical study of the natural world shows that $k_1$ is "everywhere". You are very happy at having made such a profound mathematical discovery. But ... along comes someone else and in the same things you found $k_1$, he finds another mathematical constant $k_2$. A third person then finds $k_3$ (a third mathematical constant) exactly in the same places you and the other guy found $k_1$ and $k_2$.

I mean $36 = 2 \times 18$, but $36 = 4 \times 9$, just as $5 = 2 + 3$ and also $5 = 1 + 4$.

 

[topsquark]

Imagine there's a mathematical constant $k_1$ and that your mathematical study of the natural world shows that $k_1$ is "everywhere". You are very happy at having made such a profound mathematical discovery. But ... along comes someone else and in the same things you found $k_1$, he finds another mathematical constant $k_2$. A third person then finds $k_3$ (a third mathematical constant) exactly in the same places you and the other guy found $k_1$ and $k_2$.

I mean $36 = 2 \times 18$, but $36 = 4 \times 9$, just as $5 = 2 + 3$ and also $5 = 1 + 4$.

And?

-Dan

 

[Agent Smith]

And?

-Dan

None of the 3 should be amazed at what they found, but ... there are some who are amazed (possibly me).

 

[Agent Smith]

It all depends on (I think): $R = a_1 k_1 ^{n_1} = a_2 k_2 ^{n_2} = \dots$, where R is a natural world number (ratio?) and the a's and n's are integers and the k's are different mathematical constants.

I think a better way to state the above is $R = f_1\left(k_1\right) = f_2\left(k_2\right) = \dots = f_n\left(k_n\right)$

 

[topsquark]

It all depends on (I think): $R = a_1 k_1 ^{n_1} = a_2 k_2 ^{n_2} = \dots$, where R is a natural world number (ratio?) and the a's and n's are integers and the k's are different mathematical constants.

I think a better way to state the above is $R = f_1\left(k_1\right) = f_2\left(k_2\right) = \dots = f_n\left(k_n\right)$

And?

-Dan

 

[Agent Smith]

And?

-Dan

And ... we should not be amazed, but we are: Sunflower seeds, nautilus shells, phyllotaxy, etc. (for $\varphi$)???

 

[topsquark]

And ... we should not be amazed, but we are: Sunflower seeds, nautilus shells, phyllotaxy, etc. (for $\varphi$)???

What does any of this have to do with the OP?

-Dan

 

[Agent Smith]

What does any of this have to do with the OP?

-Dan

I should think the comment is apropos. There are mathematical relationships in nature, but there are as many other mathematical relationships too. I'm not denying the existence of such relationships. I just want to know if they're special.

 

[topsquark]

I should think the comment is apropos. There are mathematical relationships in nature, but there are as many other mathematical relationships too. I'm not denying the existence of such relationships. I just want to know if they're special.

Define "special." You seem uncommonly interested in the constants of Mathematics and Nature as if they have any specific meaning as to their values. So far as we know, they do not.

-Dan

 

[Agent Smith]

Define "special." You seem uncommonly interested in the constants of Mathematics and Nature as if they have any specific meaning as to their values. So far as we know, they do not.

-Dan

Google should show interesting results (much better than I can). By "special" I mean unique/different/special/extraordinary/worthy-of-note/etc. If I find $\varphi$ in a sun flower's inflorescence, is that special? If I find $\varphi$ in rabbit populations, does this specialness increase?

 

[topsquark]

Google should show interesting results (much better than I can). By "special" I mean unique/different/special/extraordinary/worthy-of-note/etc. If I find $\varphi$ in a sun flower's inflorescence, is that special? If I find $\varphi$ in rabbit populations, does this specialness increase?

I have no idea why $\phi$ shows up in so many places. If you want to feel that's special, then fine.

But it is not special in the context of the OP.

-Dan

 

[Agent Smith]

I have no idea why $\phi$ shows up in so many places. If you want to feel that's special, then fine.

But it is not special in the context of the OP.

-Dan

That's correct I feel. So it's special in some other context. I don't know which one.