Exploring Nature's Number Three - ln & e

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In summary, my teacher showed the class how many things in nature are related to the number three.. One interesting one that the class seemed to enjoy was how Bubbles, yes, bubbles, all seem to connect to one another in threes. Is there a scientific reason to why a bubble connects to another bubble in threes? He also explained how the value of ln is found in a nautilus, which is indeed correct.. He also said something about the value of e (2.71) is found in nature, and in the human body.. Does anyone know what he is talking about?Does he have a point about the number 3? the value of ln and
  • #1
gr3g1
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Hey guys, I have a question..

In my humanities class, my teacher asked us to write an essay on 'How can we prove if god exists or not'. Dont worry, my question doesn't reflect my essay..

He showed the class how many things in nature are related to the number three.. One interesting one that the class seemed to enjoy was how Bubbles, yes, bubbles, all seem to connect to one another in threes. Is there a scientific reason to why a bubble connects to another bubble in threes?

He also explained how the value of ln is found in a nautilus, which is indeed correct.. He also said something about the value of e (2.71) is found in nature, and in the human body.. Does anyone know what he is talking about?


Does he have a point about the number 3? the value of ln and e?
Thanks a lot


Here are some images of what I am talking about:

http://pharyngula.org/images/bubbles-ommatidia.jpg [Broken]
http://www.susqu.edu/facstaff/b/brakke/evolver/examples/3/3-inner8.gif
 
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  • #2
Three spheres are the most that can be in simultaneous contact. I assume that this holds for the 'blended' spheres that bubbles become when joined. The sphere is the most space-effective shape, so the bubbles aren't likely to expend the energy necessary to take on a topography that would allow for more in the bunch.
 
  • #3
Of course he has a point about the number 3. you'll find that number a lot in nature. Nature really loves 2s also day and night, two eyes, two legs, an egg has two sides. Oh and nature loves 4s there are 4 seasons, 4 states of matter, 4 paws on a dog, 4 pts of the compass Oh and nature loves 1s one mouth, one moon, one direction of time. Oh and nature loves 4098 4098 species of biting insects, 4098 needles on a christmas tree's top branch oh and nature loves...
there are plenty of examples for any number you can think of, actually I think nature hates the number 3. There are only 2 sexes not 3, No species of animal has 3 arms, there are more than 3 elements on the periodic table, Even numbers are never 3.
 
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  • #4
Danger said:
Three spheres are the most that can be in simultaneous contact. I assume that this holds for the 'blended' spheres that bubbles become when joined. The sphere is the most space-effective shape, so the bubbles aren't likely to expend the energy necessary to take on a topography that would allow for more in the bunch.

Really? I find that hard to believe.

For example, let's see we have three spheres in contact. They form a triangle of sorts, and each sphere has it's center on a plane. Knowing this, I take a sphere placed directly in the center and above the three and lower it down until it just touches one of them: and therefore all of them since it's equidistant from each.

What's wrong with that?
 
  • #5
tribdog said:
Of course he has a point about the number 3. you'll find that number a lot in nature. Nature really loves 2s also day and night, two eyes, two legs, an egg has two sides. Oh and nature loves 4s there are 4 seasons, 4 states of matter, 4 paws on a dog, 4 pts of the compass Oh and nature loves 1s one mouth, one moon, one direction of time. Oh and nature loves 4098 4098 species of biting insects, 4098 needles on a christmas tree's top branch oh and nature loves...
there are plenty of examples for any number you can think of, actually I think nature hates the number 3. There are only 2 sexes not 3, No species of animal has 3 arms, there are more than 3 elements on the periodic table, Even numbers are never 3.
NASA hates ants so they gave them three eyes.
It's the truth.
They also hate people who make odd claims about the pineal gland.
 
  • #6
gr3g1 said:
Bubbles, yes, bubbles, all seem to connect to one another in threes.
http://pharyngula.org/images/bubbles-ommatidia.jpg [Broken]
The image in panel g would appear to refute the point very clearly. There are 4 bubbles connected there. That's also only a 2-dimensional cluster of bubbles. If you imagined some in front of and behind it, you'd have a much larger cluster. Dump some dish detergent into a dishpan and fill it up with the water turned on to maximum flow...see all those suds? Those are bubbles. And there are more than 3 all stuck together.

Also, when it comes to things like the Nautilus and those claims of finding whatever number someone fancies in the human body, you should insert the word "approximately" in front of it. http://www.nexusjournal.com/Sharp_v4n1-pt04.html [Broken]
 
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  • #7
I've never noticed anything unusual about bubbles, I've seen them in threes and fours and twos and ones. Same with the number of chambers in a peanut...thing.

I'm probably the only one here who cares enough to really push for this reasearch. I've been researching for the past three hours, the only way a good scientist can: I called a psychic hotline.

But seriously, if there's one thing here that does seem to hold some water, it's that people who want to philosophize about science and god almost always take scientific principles out of context, or just plain accept any cliam they hear.

Yes e is found in nature. Every number is found in nature, it's simply a matter of how to observe nature itself.
 
  • #8
Alkatran said:
Really? I find that hard to believe.
For example, let's see we have three spheres in contact. They form a triangle of sorts, and each sphere has it's center on a plane. Knowing this, I take a sphere placed directly in the center and above the three and lower it down until it just touches one of them: and therefore all of them since it's equidistant from each.
What's wrong with that?

3 is the most you can have with every sphere touching all the other spheres.
 
  • #9
franznietzsche said:
3 is the most you can have with every sphere touching all the other spheres.

No. Imagine forming a triangle with three billiards balls, then balancing a ball on top smack dab in the middle.
 
  • #10
KingNothing said:
Yes e is found in nature. Every number is found in nature, it's simply a matter of how to observe nature itself.


The thing about e, its just a convenient number. You could use any positive number except for one for the basis of exponential decay or growth (using different formulas for the power,). But e is mathematically significant in a number of ways, so it makes more sense to use e rather than say 1.5 or 3.
 
  • #11
I thought e was significant because it had something to do with it being its own derivative in a sense...
 
  • #12
Pengwuino said:
I thought e was significant because it had something to do with it being its own derivative in a sense...

Yes, it is it's own nth derivative and nth anti-derivative, if I remember correctly.
 
  • #13
Yah so it seems like you couldn't use 1.5 or 2 or anything like that...
 
  • #14
Pengwuino said:
I thought e was significant because it had something to do with it being its own derivative in a sense...


Exactly, it has huge mathematical significance, and shows up repeatedly in a variety of places. But physically speaking, its not all that special, just another number. Its the mathematical significance that makes it so useful for describing nature. But other numbers could be used in its place, just with more mathematical difficulty.
 
  • #15
KingNothing said:
No. Imagine forming a triangle with three billiards balls, then balancing a ball on top smack dab in the middle.
Yep, just look at the top two layers in this illustration:
http://www.math.pitt.edu/articles/cannonOverview.html

(This is an interesting page for it's own sake too...a mathematician has solved the problem of the most efficient way to stack oranges...:rofl:...or at least that's how it's been publicized.)
 
  • #16
franznietzsche said:
3 is the most you can have with every sphere touching all the other spheres.

I asked what was wrong with it, not for are bold assertion.

Here, I even have 4 unit spheres that all touch, with centers:
{ (0, 0, 0), (2, 0, 0), (1, sqr(3), 0), (1, sqr(1/3), sqr(8/3)) }
 
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  • #17
KingNothing said:
No. Imagine forming a triangle with three billiards balls, then balancing a ball on top smack dab in the middle.
Cripes! I was thinking in 2D! :redface:
 
  • #18
Danger said:
Cripes! I was thinking in 2D! :redface:

Actually, I think if you allow differing sizes you can get 4 circles to touch in 2-d (I just did it in paint, three identical circles touching and one smaller one in the middle), maybe you meant identical circles. Is four the limit? This is quite interesting, reminds me of the four colors problem.
 
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  • #19
If the circles can be any size, you can have an infinite amount touching. I'm hoping the original poster pops in and gives us an update on how his class turned out when they went over this.
 
  • #20
KingNothing said:
If the circles can be any size, you can have an infinite amount touching. I'm hoping the original poster pops in and gives us an update on how his class turned out when they went over this.

Can you give an example of 5 touching?

I think the maximum is 4. Given four circles touching (in a triangle with one on the inside) you can't even draw continuous line that touches all of them without passing through the intersection points of the circle, which would imply the circle would have to be on top of the other circles.
 
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  • #21
Also, any bounded region can be bounded by no more than 3 circles for the condition of simultaneous contact and no overlap to be met. If the most circles any new circle to be drawn can contact is three, four is the maximum number of circles total.
 
  • #22
Danger said:
Cripes! I was thinking in 2D! :redface:
I think there is another word for a sphere in 2d.
 

1. What is the number "e" in nature?

The number "e" is a mathematical constant that is approximately equal to 2.71828. It is a unique number that appears in many different natural phenomena, such as population growth, radioactive decay, and compound interest.

2. How is "e" related to the natural logarithm, or "ln"?

The natural logarithm, or "ln", is the logarithm with base "e". This means that ln(x) is the power to which "e" must be raised to equal x. The natural logarithm is useful for solving exponential growth and decay problems, as well as for finding the rate of change in a variety of natural phenomena.

3. Can you provide an example of "e" in nature?

One example of "e" in nature is the growth of populations. When studying populations, you may notice that the rate of growth is proportional to the current size of the population. This is described by the exponential function, and the base of this function is "e". This can be seen in the growth of bacteria, plants, and animal populations.

4. How can "e" be used to calculate compound interest?

In finance, compound interest is interest that is calculated not only on the initial amount of money, but also on the accumulated interest from previous periods. The formula for compound interest is A = Pe^(rt), where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the number of years. The constant "e" is used in this formula to represent continuous compounding.

5. Is "e" the only number that appears in nature?

No, "e" is not the only number that appears in nature. There are many other mathematical constants that have been observed in natural phenomena, such as pi (π), the golden ratio (φ), and the square root of 2 (√2). These constants often appear in patterns and relationships found in the natural world, and they are essential for understanding and describing these phenomena mathematically.

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