After the big bang, where did pi, e and the rules originate?

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After the big bang, where did pi, e and the rules originate?

Postby 0.0 » Tue Jan 27, 2009 10:21 pm UTC

Don't know if this would be better under science or religion, but decided to put it here.

The question is pretty open and if you can come up with a decent theory, relay some known facts, or even a related question without calling on the omnipotent omniscient being, please reply. The reason for not wanting the God answer, is because I would like to start a discussion about what might cause all these rules without a catch all answer. If you do believe that God wrote all these laws, thats fine, but not for what I would like this discussion to be about. Heck, if you have an interesting reason to why a god made the universe this way, go ahead and add to the discussion.

So the question is: Whether the universe was here before, or appeared out of the big bang, why is e and pi so important? Why do they show up so much. Also there's the golden ratio in nature. Many of physics constants always made me wonder. I feel like the universe is laughing at us as we come up with so many complicated and brilliant formulas to explain the world around us, and yet they often rely upon an unexplainable number that must be included (the constant) if only because we discovered it through math. No other explanation for these numbers? Is there a theory out there I have not heard of?

Moving to Science.

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Re: After the big bang, where did pi, e and the rules originate?

Postby Klotz » Tue Jan 27, 2009 10:51 pm UTC

Well e and pi are mathematical constants, not physical ones. They exist outside of any physical framework. e describes an exponential function that is its own derivative, and pi describes a locus of points all equidistant from a single point. They would "exist" even if the universe didn't.

As for the universe, nobody knows why the laws worked out the way it did. The closest thing is the anthropic principle, which says that the laws of the universe are such that we exist in it.

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Re: After the big bang, where did pi, e and the rules originate?

Postby wisnij » Tue Jan 27, 2009 10:57 pm UTC

Pi shows up a lot in physical equations because spacetime is generally a good approximation to Euclidean space (i.e. flat). The golden ratio shows up because it's related to the logarithmic spiral and geometric progressions, so it tends to fall out of scaling laws; ditto for e.
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Re: After the big bang, where did pi, e and the rules originate?

Postby Klotz » Tue Jan 27, 2009 11:02 pm UTC

Oh yeah, as for why e and pi show up a lot....

Well things that oscillate harmonically (pretty much everything in physics if you delve deep enough) have a period of 2 pi. Also, anything that's round, like a star, has its shape described by pi.

e comes up in the solution to pretty much every differential equation in some form or another. For example, the radioactive decay relation that the rate of decay is proportional to the number of decayers. Also in a damped oscillator, if damping is related to speed.

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Re: After the big bang, where did pi, e and the rules originate?

Postby 0.0 » Tue Jan 27, 2009 11:03 pm UTC

the laws of the universe are such that we exist in it.

Is this really the best answer? This is more of a non answer. So I guess what you are saying is there is no answer, but thats really why I asked, to see if anybody had some cool or imaginative theory. I am betting this thread dies quickly because noone will have anything tangible or thought provoking, but I hope not.
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Re: After the big bang, where did pi, e and the rules originate?

Postby wisnij » Tue Jan 27, 2009 11:15 pm UTC

Can you state the question more precisely?
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Re: After the big bang, where did pi, e and the rules originate?

Postby Klotz » Tue Jan 27, 2009 11:34 pm UTC

Do you have a bone to pick or something?

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Re: After the big bang, where did pi, e and the rules originate?

Postby idobox » Tue Jan 27, 2009 11:45 pm UTC

The anthropic principle can summed up as "if the rules were different, we wouldn't be there, and couldn't ask the question" it is by no mean a physical or mathematical explanation.
Scientists have been looking for over 2 centuries for a great theory of theory of everything that would explain why things are the way they are, and not otherwise. But for now, no one has a convincing explanation.
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Re: After the big bang, where did pi, e and the rules originate?

Postby SmashtheVan » Wed Jan 28, 2009 12:12 am UTC

God created the heavens and the earth, man and beast, light and dark, and all the properties of matter and light that we see. Lastly, to reinforce these rules, he created geometry. His final creation was the circle, and decided he needed a way to relate the diameter and the circumference. He decided for fun, that since he had just about created everything else, he'd just start writing random numbers, infinitely. the result is pi, and god is still writing, which is why we dont know when it ends, and why there have no been any relevant creations since those first 6 days.

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Re: After the big bang, where did pi, e and the rules originate?

Postby gmalivuk » Wed Jan 28, 2009 12:15 am UTC

Mathematics is the study of self-consistent structures. Science is predicated on the universe being self-consistent. This, I believe, is why mathematics is so "uncannily" effective in the sciences.

As for these particular numbers, I guess I can only say vaguely that any interesting system of axioms is going to end up giving you some interesting elements, and so asking "why *these* ones" becomes rather meaningless. It's like asking, "How come Boston is so perfectly situated around these rivers to have its bridges where it does?" Because if the city were situated differently around those rivers, the bridges would obviously be in different places.
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Re: After the big bang, where did pi, e and the rules originate?

Postby Sir_Elderberry » Wed Jan 28, 2009 12:16 am UTC

Pi and e are, as it has been said, mathematical constants--they are inevitable. So the real question here is where "the rules" come from. I assume by this you mean physical constants like G, or the permittivity of free space, or what have you.

The way I see it, there are two possibilities. Actually, three.

-These constants are just as "inevitable" as mathematical constants, and when/if we learn more about the universe, we will find that they are the same in every conceivable universe, just as addition is always commutative, and 13 is always prime.

-These constants are really arbitrary, plucked from quantum uncertainty. This theory, to be viable, needs some kind of many-worlds theory or cyclic universe. In this model, our universe is very rare in being able to support life, but there have been lots and lots of failed attempts.

-The third possibility involves a religious explanation, although I myself do not subscribe to this view. It, after all, merely pushes the question back as to why whatever forces shaped the universe did so in this way, where they come from, what laws they are bound by, etc.
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Re: After the big bang, where did pi, e and the rules originate?

Postby Interactive Civilian » Wed Jan 28, 2009 12:31 am UTC

idobox wrote:The anthropic principle can summed up as "if the rules were different, we wouldn't be there, and couldn't ask the question" it is by no mean a physical or mathematical explanation.

It may not be, but it may be the correct answer. A lot of people don't like tautologies, because they don't really answer the question "why?" in a meaningful way that gives reason to everything. When getting to the big questions, my usual response is, "Why do you think there is a reason?" Asking "Why?" rather than "How?" suggests intent, which then opens a big, unanswerable (by science, anyway) can of worms. The answer may simply be, "It is because it is." It will always come down to that in the end anyway. There is either one "It is because it is" or it's "turtles all the way down." If it is the former, then there is no need to take the "it is because it is" any level higher than the observable universe WITHOUT evidence of something beyond.

Not to jump too far into flame war territory, but to put my last bit into the form of commonly spoken examples:
Person 1: "The universe just exists."
Person 2: "The universe exists because God made it. God just exists."
Person 3: "The universe exists because God made it. God was made by a super-God that just exists."
~~and so on...

Occam's razor suggests that, without any evidence otherwise, Person 1 is more likely to be correct.

For the record, I do subscribe to the "weak anthropic principle", which has been stated that the universe exists how it does because if it were different, we (in the specific sense, perhaps also in the general sense) wouldn't be here to ask the question. I do not subscribe to the strong anthropic priniciple, which suggests that the universe is how it is SO we can be here to question it. So, to the OP, my answer is that those rules are simply part of the universe (or, more accurately, mathematical approximations that we have come up with to help describe the universe that we observe) and originated with the universe. They simply are, because they are. Sometimes there are no better reasons.

Perhaps I am comfortable with this because I have a strong background in biology, and in the study of evolution (especially by natural selection), pretty much everything is a tautology. "Why does organism A have this trait?" "Because, it is either an advantageous trait or it is tagging along with an advantageous trait that allows it to survive and reproduce. Those without the advantageous trait did not survive to pass it on, so they are gone."
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[edit]
In suggesting that the answer may be tautological, I did not in any way mean to imply that we should stop looking for answers or wondering "why?" about the universe. Curiosity and imagination are keys to good science, and we should always be seeking to know more. If there is an answer to these big "Why?" questions beyond "Because it IS", then the only way to find those answers is continued investigation and furthering our understanding of the universe. However, even if that is the only answer, then we still will have striven for knowledge and furthered our understanding of the universe, and that is a good thing, IMHO.

Just wanted to clarify that, in case anyone decided to take it the wrong way. :)
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Re: After the big bang, where did pi, e and the rules originate?

Postby wisnij » Wed Jan 28, 2009 2:00 am UTC

Interactive Civilian wrote:For the record, I do subscribe to the "weak anthropic principle", which has been stated that the universe exists how it does because if it were different, we (in the specific sense, perhaps also in the general sense) wouldn't be here to ask the question. I do not subscribe to the strong anthropic priniciple, which suggests that the universe is how it is SO we can be here to question it. So, to the OP, my answer is that those rules are simply part of the universe (or, more accurately, mathematical approximations that we have come up with to help describe the universe that we observe) and originated with the universe. They simply are, because they are. Sometimes there are no better reasons.

The weak anthropic principle is also kind of funny in that, if the rules were different but still allowed life of some sort, that life would be asking the same questions. ;)

That said, an important part of cosmology is trying to figure out which properties of the universe are "necessary" in some more fundamental sense, and which are just incidental to its past evolution or current state. For instance, the current theory is that the four physical forces we see today (gravity, electromagnetism, weak nuclear and strong nuclear) were originally all combined in one unified "superforce" when the universe was much younger and hotter than it is now, and the forces we see today froze out of it as the universe cooled, like ice crystals freezing out of water. That was a symmetry-breaking event, which potentially could have happened in a myriad of different ways.
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Re: After the big bang, where did pi, e and the rules originate?

Postby frezik » Wed Jan 28, 2009 3:18 am UTC

0.0 wrote:the laws of the universe are such that we exist in it.

Is this really the best answer? This is more of a non answer. So I guess what you are saying is there is no answer, but thats really why I asked, to see if anybody had some cool or imaginative theory. I am betting this thread dies quickly because noone will have anything tangible or thought provoking, but I hope not.


Yeah, the anthropic principle does that to you. One can't really disagree with it, but it's somehow deeply unsatisfying. I generally take it at face value until a better explaination comes along.
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Re: After the big bang, where did pi, e and the rules originate?

Postby Interactive Civilian » Wed Jan 28, 2009 4:50 am UTC

frezik wrote:Yeah, the anthropic principle does that to you. One can't really disagree with it, but it's somehow deeply unsatisfying. I generally take it at face value until a better explaination comes along.

This is something I've never understood. Why is it deeply unsatisfying? For me, it doesn't make the universe an less fascinating. Whether or not there is some deeper reason for the universe's existence, whether or not there is some fundamental answer to "Why?", the universe IS still here and we are here to observe and explore it, and it is still mind-blowingly awesome.

In my humble opinion. ;)
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Re: After the big bang, where did pi, e and the rules originate?

Postby Bassoon » Wed Jan 28, 2009 6:09 am UTC

Correct me if I am wrong, but if the general shape of spacetime changes (from Euclidean to elliptical or hyperbolic, etc.) pi also changes to maintain a circle with a constant radius. So pi is pi because our universe has the shape that defines pi to be what pi is.

e, to me, seems more like a mathematical constant constructed from non-physical laws. Pi was first observed in circles and geometry and was later found to have applications in physics. e, on the other had, is more "abstract" in the sense that we can't measure e like we measure pi. I can't answer the question if math is different in another universe. Perhaps it is. But how it's different is more of the problem than if it is different. If it merely lacks certain axioms, we can simulate that here. But perhaps it lacks something we don't know about, or perhaps it adds properties we can't imagine (yet?), so I find math harder to find the origins of than physics. Physics, in a sense, are coded at the beginning of the universe. But when does math come along?

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Re: After the big bang, where did pi, e and the rules originate?

Postby Rentsy » Wed Jan 28, 2009 6:22 am UTC

A non-nutty look at the anthropic principle is that life like ourselves can only exist in this epoch of the universe. Too early, and conditions are, broadly, too "hot"; too late and things are too "cold".

7.62 MeV is the best though. 7.62 MeV was what Fred Hoyle (The H in [imath]B^2FH[/imath]) predicted as an excited state for carbon-12 with the anthropic principle - that if it wasn't, we as humans could not exist, because we are carbon-based lifeforms, and if carbon did not have an excited state at 7.62 MeV, not enough would be formed through stellar nucleosynthesis.

Hoyle later went on to believe that the laws of physics are NOT chance, and are somehow fine-tuned to allow for our existence.

As a scientist, I don't feel comfortable saying things like that. I can only say that they are what they are. Our existence is a special case of unrivaled complexity.

Traditionally, we human have ascribed to complex systems a certain specialness. We ourselves are fascinated by complex systems that display a sort of order.

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Re: After the big bang, where did pi, e and the rules originate?

Postby wisnij » Wed Jan 28, 2009 11:13 am UTC

Bassoon wrote:Correct me if I am wrong, but if the general shape of spacetime changes (from Euclidean to elliptical or hyperbolic, etc.) pi also changes to maintain a circle with a constant radius. So pi is pi because our universe has the shape that defines pi to be what pi is.

No. π is a mathematical constant defined as the the ratio of the circumference of any circle to its diameter in Euclidean space, and whose decimal expansion begins with 3.14159. If a given space happens to be non-Euclidean, the ratio measured within that space will be different than π (just as the internal angles of a triangle on a non-flat surface need not add up to π radians).

Because Euclidean space or a close approximation to it is often the type under discussion, the term "π" or "pi" is sometimes colloquially used to refer to the particular ratio measured on a specific circle, but strictly speaking this is not correct.
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Re: After the big bang, where did pi, e and the rules originate?

Postby BeerBottle » Wed Jan 28, 2009 11:20 am UTC

Interactive Civilian wrote:Occam's razor suggests that, without any evidence otherwise, Person 1 is more likely to be correct.
Genuine question - not flame war, not rethorical, I want to be educated - Can anyone cite a successful example of the use of Occam's Razor in physical science, i.e. an example of it giving the correct answer to a genuine scientific problem?

Olden days Person 1: Iron is hard and shiny. Water is soft and wet. That's just the way it is.
Olden Days Person 2: Actually matter is made of tiny particles which interact with each other in different ways by sharing little bits of themselves. In iron the little particles all share little bits of themselves together, so they all stick together and are very hard. In water, only small groups of three little particles are sharing little bits of themselves so it is soft and can easily pass through your clothes to make you wet.

Wouldn't Occam's razor say person 1 is more likely to be correct.

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Re: After the big bang, where did pi, e and the rules originate?

Postby wisnij » Wed Jan 28, 2009 11:23 am UTC

BeerBottle wrote:Olden days Person 1: Iron is hard and shiny. Water is soft and wet. That's just the way it is.
Olden Days Person 2: Actually matter is made of tiny particles which interact with each other in different ways by sharing little bits of themselves. In iron the little particles all share little bits of themselves together, so they all stick together and are very hard. In water, only small groups of three little particles are sharing little bits of themselves so it is soft and can easily pass through your clothes to make you wet.

Wouldn't Occam's razor say person 1 is more likely to be correct.

Occam's razor says "entities must not be multiplied beyond necessity", or put another way, "all other things being equal, the simplest solution is the best". Since ODP1's explanation has much less predictive power than ODP2's, all other things are not equal.

Specific scientific example: the luminiferous aether, once relativity was developed.
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Re: After the big bang, where did pi, e and the rules originate?

Postby Xanthir » Wed Jan 28, 2009 12:33 pm UTC

Bassoon wrote:Correct me if I am wrong, but if the general shape of spacetime changes (from Euclidean to elliptical or hyperbolic, etc.) pi also changes to maintain a circle with a constant radius. So pi is pi because our universe has the shape that defines pi to be what pi is.

Well, not quite. We all learn pi first as the ratio of a circles circumference to its diameter (or of its area to the square of its radius), but that's not really the fundamental definition of pi. Pi is just accidentally there as a result of the euclidean metric. As you note, if spacetime weren't flat (and it isn't), the ratios would be different. But pi would still appear in harmonic motion, in population statistics, in a multitude of simple infinite sums, and so on.
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Re: After the big bang, where did pi, e and the rules originate?

Postby Sir_Elderberry » Wed Jan 28, 2009 3:06 pm UTC

Spacetime, I thought, was flat except near gravity wells.
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Re: After the big bang, where did pi, e and the rules originate?

Postby Yakk » Wed Jan 28, 2009 6:30 pm UTC

BeerBottle wrote:Olden days Person 1: Iron is hard and shiny. Water is soft and wet. That's just the way it is.
Olden Days Person 2: Actually matter is made of tiny particles which interact with each other in different ways by sharing little bits of themselves. In iron the little particles all share little bits of themselves together, so they all stick together and are very hard. In water, only small groups of three little particles are sharing little bits of themselves so it is soft and can easily pass through your clothes to make you wet.

Wouldn't Occam's razor say person 1 is more likely to be correct.

So, Iron being Hard and Shiny can be viewed as a pair of axioms.
Water is Soft and Wet can be viewed as two more axioms.
Now keep going. Wood is Hard and has Splinters. 2 more axioms.
Gold is Soft and Shiny and Immune to Water. Copper is Soft and Shiny and Weak to Water.

Keep going. See how the axioms are being added to? There are lots of things that are as different as Iron and Water. Each of them needs a parcel of axioms to explain them.

Meanwhile, person 2. Happens to come up with modern physics. There are a bunch of axioms and parameters that have to be found experimentally -- call it 50 to 100. And from it, he explains Iron, Wood, Gold, Copper, Water -- all of it explained pretty darn well.

Person 2's model is simpler than person 1s, because there are more "kinds and properties of things" than there are "axioms of modern science". If you formulate the kinds/properties as emergent from (relatively) simple rules, you have a system that is simpler.

What is worse is that as you poke at things, properties that Person 1 didn't list pop up. Why does Water split into gasses that burn when you run electricity through it? Person 1 needs to add new properties left right and centre in response to each experiment. Person 2? Water is H2O, it has a binding energy, and when you shock it, naturally it falls apart. The bubbles are the elemental components of the water molecule, which happen to be gasses at reasonable tempuratures and pressures. And they are perfectly willing to remix and burn...

So yes, if the universe consisted of a chunk of iron, and all that iron was was shiny and hard (with no other properties), then modern physics wouldn't be the right answer. But that isn't the world.
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Re: After the big bang, where did pi, e and the rules originate?

Postby frezik » Wed Jan 28, 2009 7:26 pm UTC

Interactive Civilian wrote:
frezik wrote:Yeah, the anthropic principle does that to you. One can't really disagree with it, but it's somehow deeply unsatisfying. I generally take it at face value until a better explaination comes along.

This is something I've never understood. Why is it deeply unsatisfying? For me, it doesn't make the universe an less fascinating. Whether or not there is some deeper reason for the universe's existence, whether or not there is some fundamental answer to "Why?", the universe IS still here and we are here to observe and explore it, and it is still mind-blowingly awesome.


I suppose because it doesn't seem to get us anywhere, at least not in most of situations where it's used as an answer. It's not immediately obvious that it gives us any testable predictions.

Asking the question "why are we composed of carbon?", we may get answers like:

1) Because we wouldn't exist any other way
2) Because carbon is abundant and binds more easily in the same chemical formulas compared to silicon

#1 seems to have hit a brick wall in understanding. #2 opens up a lot of followup questions: why is carbon abundant? Why does it bind more easily than silicon? Why is this set of chemical formulas so important for life? Why silicon and not, say, boron?
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Re: After the big bang, where did pi, e and the rules originate?

Postby wisnij » Wed Jan 28, 2009 9:22 pm UTC

frezik wrote:#1 seems to have hit a brick wall in understanding. #2 opens up a lot of followup questions: why is carbon abundant? Why does it bind more easily than silicon? Why is this set of chemical formulas so important for life? Why silicon and not, say, boron?

Carbon is more abundant in the universe because it has a lower atomic number, so it shows up earlier in the stellar nucleosynthesis process. Silicon and carbon both can bond with a similar range of other elements, but carbon compounds have all sorts of varying characteristics, whereas silicon mostly just makes rocks.
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Re: After the big bang, where did pi, e and the rules originate?

Postby idobox » Wed Jan 28, 2009 9:42 pm UTC

Carbon, Silicon and Germanium make 4 stable bonds. All other elements have less stable bonds, and are not suited for building complex molecules.
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Re: After the big bang, where did pi, e and the rules originate?

Postby BlackSails » Wed Jan 28, 2009 9:54 pm UTC

idobox wrote:Carbon, Silicon and Germanium make 4 stable bonds. All other elements have less stable bonds, and are not suited for building complex molecules.


Silicon and Germanium have trouble forming double bonds.

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Re: After the big bang, where did pi, e and the rules originate?

Postby gmalivuk » Wed Jan 28, 2009 10:11 pm UTC

frezik wasn't, I believe, skeptically asking anything about carbon, but rather saying why the anthropic principle's answer to that question was unhelpful.

But that's why the weak anthropic principle isn't used to address questions like that. It's used to address questions that at present we have no way of testing scientifically. It gives an answer that is more scientifically satisfying than "god did it" to the sorts of questions that the religious like to use that answer for.
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Re: After the big bang, where did pi, e and the rules originate?

Postby frezik » Wed Jan 28, 2009 10:42 pm UTC

gmalivuk wrote:frezik wasn't, I believe, skeptically asking anything about carbon, but rather saying why the anthropic principle's answer to that question was unhelpful.


Right. I was also a little curious to see who would misinterpret things like that :)

But that's why the weak anthropic principle isn't used to address questions like that. It's used to address questions that at present we have no way of testing scientifically. It gives an answer that is more scientifically satisfying than "god did it" to the sorts of questions that the religious like to use that answer for.


That's kinda my point. The Anthropic Principle is like God in the Gaps for athiests.
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Re: After the big bang, where did pi, e and the rules originate?

Postby doogly » Wed Jan 28, 2009 10:55 pm UTC

frezik wrote:That's kinda my point. The Anthropic Principle is like God in the Gaps for athiests.


No, that is not how it works. Anthropic reasoning can, even in its weakest state, make predictions. See Weinberg and the cosmological constant. And if you have string theory and eternal inflation (not done deals but I'd put them at at least >30% odds) you can look at different models of the multiverse, and see how they deal with producing observers like us. I don't work in anthropics directly but it's very big at the department I am in now, at Tufts. Vilenkin even has a popular level book about how these things lead to actual science. The anthropic principle is not a "just so" story by any means.
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Re: After the big bang, where did pi, e and the rules originate?

Postby diotimajsh » Wed Jan 28, 2009 11:55 pm UTC

To expand on Yakk's reply to BeerBottle, science is valuable to us precisely because it allows the unification of diverse phenomena under general principles.

I believe that Person One's model, taken to an extreme, reduces to something like this: all things have the properties that they each have. (Or as a bard of our times put it, "Everything is everything.") A very simple theory, and completely true! Does it explain anything or help us in any way? Well... not really. The point for us humans is to see underlying similarities which bring together many different observations under a set of principles--principles which convey information and possess predictive power.

This is, incidentally, why deistic explanations are frequently unhelpful. "The world is as we see it now because God willed it thus." Well, okay, great. A simpler explanation than the Big Bang. But that doesn't help us understand anything more about the world unless we already completely understand the will of God. And how are we supposed to investigate that?

I think this is another way to put it: Occam's razor aims to give us the simplest explanations, yes; yet these explanations should be packed with as much explanatory and predictive information as possible. They should be as specific and comprehensive as possible, given their simplicity. "Things are as they are" covers the entirety of the universe, but it does not yield specific information about phenomena; using it, we can only learn what we already know. Using deistic explanations, we can only learn what we know about God's intentions. (Which is... not much, in my opinion.)
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Re: After the big bang, where did pi, e and the rules originate?

Postby Interactive Civilian » Thu Jan 29, 2009 1:21 am UTC

frezik wrote:That's kinda my point. The Anthropic Principle is like God in the Gaps for athiests.

With the very large exception that we (atheists) are not positing the existence of something supernatural to explain our gaps in knowledge about the natural. We merely state that the natural is there, so let's learn as much about it as we can.

It is only a useful answer so that we don't get bogged down in unanswerable philosophical or metaphysical questions. We simply accept that the universe is here and we try to learn about it.

So, no, it really isn't a "God in the Gaps" answer, because we aren't positing that there is anything supernatural or unexplainable in the gaps.
gmalivuk wrote:But that's why the weak anthropic principle isn't used to address questions like that. It's used to address questions that at present we have no way of testing scientifically. It gives an answer that is more scientifically satisfying than "god did it" to the sorts of questions that the religious like to use that answer for.
Well said. :)
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Re: After the big bang, where did pi, e and the rules originate?

Postby BeerBottle » Thu Jan 29, 2009 10:47 am UTC

diotimajsh, Yakk, thanks for your replies to my point. I'm afraid I'm still not quite sure of the relation of Occam's razor to scientific knowledge. diotimajsh, I appreciate your points about sciencetific knowledge, and how a theory can be correct but tell us nothing. But it still seems to me that Occam's razor favours empty yet true theories - let me try to explain why I think that. As history progresses, human understanding of nature has become more and more complex - a mere few centuries ago it would have been perfectly possible for one person to throughly understand all of human science, simply because there was so little of it about. Today, obviously that is no longer possible, because as we look deeper and deeper nature seems to be more and more complex. Take physics 1890 vs physics 1920. Before, "Oh yes we have a few particles and some forces and everything is pretty much solved." After, to paraphrase, "OMGWTF??!!??".

Now Yakk, you came up with the example of the Aether as an example of where Occams Razor succeeds. That's a good example; something (the Aether) was widely posited but it turned out to be an over-complication - unnecessary to explain the physical phenomina. But I think in the vast majority of cases, as science progresses we need to add new phenomina/entities/things, like all the particles currently flying around in the standard model vs the simpler classical picture, or the modern theories of the electronic structure of atoms compared with the plum-pudding model or the simple Bohr model with electrons in orbits like planets. The point I'm trying to make is that the universe is complicated, more complicated than we used to think, and I'll bet more complicated than we currently think.

So going back to Olden Days Persons 1 and 2, number 1 is technically correct yet his theory tells us virtually nothing, and without the light of evidence, Occam's Razor supports his position. Person 2 has randomly and extremely luckily guessed a better theory, but can't test it as it's the olden days and there's no scientific method yet. So perhaps a version of Occam's razor I'm more happy with is "Don't guess stuff". ODP2 did guess and my massive fluke got it right, but ODP3+ also guessed and they all got it totally wrong.

Onto a point made by Interactive Civilian earlier, Modern Day Persons might say the following:

MDP1: "The universe just exists"
MDP2: "The universe exists because God made it. God just exists."
MDP3: "The universe came from nothing without a rational designer. God does not exist"

Now both MDP2 and 3 make predictions, and in principle their theories are testable. But we have no evidence either way. Of course MDP1 is correct, as diotimajsh has already expounded, and Occam's razor must surely support him.

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Re: After the big bang, where did pi, e and the rules originate?

Postby Mr_Rose » Thu Jan 29, 2009 12:03 pm UTC

BeerBottle wrote:So going back to Olden Days Persons 1 and 2, number 1 is technically correct yet his theory tells us virtually nothing, and without the light of evidence, Occam's Razor supports his position. Person 2 has randomly and extremely luckily guessed a better theory, but can't test it as it's the olden days and there's no scientific method yet. So perhaps a version of Occam's razor I'm more happy with is "Don't guess stuff". ODP2 did guess and my massive fluke got it right, but ODP3+ also guessed and they all got it totally wrong.

Onto a point made by Interactive Civilian earlier, Modern Day Persons might say the following:

MDP1: "The universe just exists"
MDP2: "The universe exists because God made it. God just exists."
MDP3: "The universe came from nothing without a rational designer. God does not exist"

Now both MDP2 and 3 make predictions, and in principle their theories are testable. But we have no evidence either way. Of course MDP1 is correct, as diotimajsh has already expounded, and Occam's razor must surely support him.

Yes, so? Occam's razor is not an answer; it is a suggestion about the best way to find answers.
Suppose three random people come up with three explanations of a given situation, one of which is found to be the simplest without further evidence: Occam says that person is more likely to be correct. However, Occam does not say that they should stop looking for that further evidence now.
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Re: After the big bang, where did pi, e and the rules originate?

Postby Interactive Civilian » Thu Jan 29, 2009 1:28 pm UTC

Mr_Rose wrote:Yes, so? Occam's razor is not an answer; it is a suggestion about the best way to find answers.
Suppose three random people come up with three explanations of a given situation, one of which is found to be the simplest without further evidence: Occam says that person is more likely to be correct. However, Occam does not say that they should stop looking for that further evidence now.

Extremely well said. Occam's razor is not a law of the universe. It is a suggestion for determining which explanation is more likely to be correct. It seems to hold up pretty well under equal evidence, but sure, it can be shown to be wrong upon uncovering further evidence which may refute the original simpler theory -- not an actual historical example, but something to think about: Newton's Law of Universal Gravitation and Laws of Motion are much more simple than Einstein's Theory of General Relativity, especially when looking at easy to observe evidence like things falling on earth, the orbit of the moon around the earth, the orbit of the earth around the sun, and so on. WITHOUT having the evidence of Mercury, one would think that Occam's razor says Newton is correct. However, introduce that further bit of evidence, and now suddenly he is refuted, and the more complicated theory is now the correct one.

Remember: the continued observation of the universe and looking at how current theories stand up to new observations and evidence is essential to science. This is why the last step of the Scientific Method is "repeat". ;)
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Re: After the big bang, where did pi, e and the rules originate?

Postby Huitzilopochtli » Thu Jan 29, 2009 1:39 pm UTC

There are many versions of Occam's razor floating around today but, for scientists, the most useful one is
When you have two competing theories that make exactly the same predictions, the simpler one is the better.


It is clear that by that definiton Occam's razor cannot be applied to
1) Iron is hard and shiny. Water is soft and wet. That's just the way it is.
and
2) Actually matter is made of tiny particles which interact with each other in different ways by sharing little bits of themselves. In iron the little particles all share little bits of themselves together, so they all stick together and are very hard. In water, only small groups of three little particles are sharing little bits of themselves so it is soft and can easily pass through your clothes to make you wet.

because the two "theories" don't make same predictions. In fact, the first one isn't a theory at all, in the scientific sense.
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Re: After the big bang, where did pi, e and the rules originate?

Postby PM 2Ring » Thu Jan 29, 2009 6:29 pm UTC

Bassoon wrote: e, on the other had, is more "abstract" in the sense that we can't measure e like we measure pi.


We can easily give a geometric definition for e. Draw the hyperbola xy = 1. The area under the branch in the ++ quadrant between x=1 & x=e is exactly one. And so is the area between x=e & x=e². Etc.

The geometric definition of pi may be the most obvious, but is it truly the most "natural" one? IMHO, the fact that it arises in so many series that have little to do with circles in the Euclidean plane suggests that it is not.

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Re: After the big bang, where did pi, e and the rules originate?

Postby idobox » Thu Jan 29, 2009 6:52 pm UTC

As Euler once said to Diderot, ei.pi+1=0, hence god exists.
More seriously, there are a bunch of equations and definitions that use both e and pi, so I guess it's not that surprising this magical equation exists.
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Re: After the big bang, where did pi, e and the rules originate?

Postby 0.0 » Wed Feb 11, 2009 1:43 am UTC

I was just thinking that those variables exist the way that they do due to our base 10 system. Of course if we commonly used a different base they would still exist at the same value but just look different. What would math be like if we used base pi? Also reminded me of this little gem: http://cowbird.110mb.com/43.html
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Re: After the big bang, where did pi, e and the rules originate?

Postby Brooklynxman » Wed Feb 11, 2009 2:34 am UTC

Personally, I think God realized putting us in a space where physical rules/constants/laws are not set in stone would probably not be the best set up.
We figure out what all this means, then do something large and violent

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