When can true singularity take place? Was the big bang the only chance

[Pythagorean]

. . . I'd like to get mine in before the new rules apply:

Personally I believe this entire thread can be better approached from the perspective of Catastrophe Theory. This deals with "critical points" of phenomena when the dynamics changes qualitatively and often abruptly. Once these points are breached, descriptions describing the phenomena before the critical point are often insufficient to adequately explain the qualitatively new dynamics occurring beyond the critical point. I believe it is precisely these critical points that are being referred to as "singularities" in this thread. The Universe is filled with such dynamics at all scales from nuclear fission to collapsing stars. For example take dying. That is a critical point as the dynamics of life are suddenly replaced by qualitatively new dynamics of non-living. What happens to the concept of swimming in water at the critical point of freezing? Swimming reaches a singularity at that point as the phenomenon no longer applies to ice. Take conflicting nations. The peaceful conflict can escalates until the critical point of war is reached. Suddenly, a qualitatively new dynamics is reached at the nations reach this singular point in social contracts.

The dynamics of nature are not always smooth. There are points where it changes abruptly and qualitatively and often at these points new descriptions are needed to describe this new behavior. That is the case in my opinion to what we call the "singularity" at the Big Bang, and likewise, the singularity at the center of a black hole. Both of these represent a sudden and qualitative change in dynamics which renders our descriptions of the phenomena before the critical point, inadequate.

Good post =) (dynamical systems bias)

I'm curious though, have we ever actually observed a singularity in nature? Wouldn't that require measuring some value to be infinite?

 

[ZapperZ]

. . . I'd like to get mine in before the new rules apply:

Personally I believe this entire thread can be better approached from the perspective of Catastrophe Theory. This deals with "critical points" of phenomena when the dynamics changes qualitatively and often abruptly. Once these points are breached, descriptions describing the phenomena before the critical point are often insufficient to adequately explain the qualitatively new dynamics occurring beyond the critical point. I believe it is precisely these critical points that are being referred to as "singularities" in this thread. The Universe is filled with such dynamics at all scales from nuclear fission to collapsing stars. For example take dying. That is a critical point as the dynamics of life are suddenly replaced by qualitatively new dynamics of non-living. What happens to the concept of swimming in water at the critical point of freezing? Swimming reaches a singularity at that point as the phenomenon no longer applies to ice. Take conflicting nations. The peaceful conflict can escalates until the critical point of war is reached. Suddenly, a qualitatively new dynamics is reached at the nations reach this singular point in social contracts.

The dynamics of nature are not always smooth. There are points where it changes abruptly and qualitatively and often at these points new descriptions are needed to describe this new behavior. That is the case in my opinion to what we call the "singularity" at the Big Bang, and likewise, the singularity at the center of a black hole. Both of these represent a sudden and qualitative change in dynamics which renders our descriptions of the phenomena before the critical point, inadequate.

This is not new. What you're describing is a first-order phase transition, where certain state variables become discontinuous at the phase boundary.

But you will note that that is a GENERIC description of singularity, where you actually HAVE to know the quantitative aspect of the description, i.e. you have to know how the state variables evolve when you change certain parameters, and then realize that the discontinuity will result in a pole in, say, the first derivative of that state variable. In other words, you will NOT know that when water turns into ice, there are some singularities in some of the state variable simply by looking at it! You have to be able to know the mathematics and actually know the physics of what is being measured! This is what I meant earlier by what I was trying to say that people here talk about "singularity" as if it is something you could see, etc. That's bogus! Without the mathematics, you won't know it!

But if you notice, the earlier discussion on here were focusing really on the so-called "space-time singularity", while using the generic phrase "singularity". That is also another severe misinformation/misunderstanding.

Zz.

 

[Pythagorean]

Meaning what?

It's a loaded challenge. Many aspects of gravitational singularity are described mathematically (even the wiki authors know that). "There is no math describing a gravitational singularity" may be true if you spin it the right way, but then it would be a meaningless and irrelevant statement.

So there's really no defending it.

 

[jackmell]

\Without the mathematics, you won't know it!Zz.

Jesus dude, like I'm skiing. Suddenly and abruptly and I mean in a split second, the whole side of the mountain fractures into a very, very large avalanche. They ask about actually seeing a singularity in here. That's one in my opinion: the dynamics of the snow pack have suddenly and abruptly changed in a qualitative manner and I didn't have to know the mathematics to know it happened.

 

[Pythagorean]

Jesus dude, like I'm skiing. Suddenly and abruptly and I mean in a split second, the whole side of the mountain fractures into a very, very large avalanche. They ask about actually seeing a singularity in here. That's one in my opinion: the dynamics of the snow pack have suddenly and abruptly changed in a qualitative manner and I didn't have to know the mathematics to know it happened.

But don't you think deep philosophical conversation about singularities should be grounded in the mathematics? That the three of us (you, zapperz, and I) recognize the connection between singularities and bifurcation is probably deeply rooted in our mathematical understanding.

I think it makes definitions more lucid, personally. And it avoids wiggle room in ambiguous uses of the word that waste poster's time and PFs bandwidth.

edit: It's not that I don't think we can communicate in natural language once we've learned the math, you have perfectly demonstrated that in your big post. But I think it's the people that have had long-term exposure to mathematics that really understand your post.

 

[jackmell]

But don't you think deep philosophical conversation about singularities should be grounded in the mathematics? That the three of us (you, zapperz, and I) recognize the connection between singularities and bifurcation is probably deeply rooted in our mathematical understanding.

I'm afraid I can't be in the same category as Zapper. I know he's very knowledgeable in physics. Very much so I believe. I myself am not. See, I wouldn't say this stuff in a physics forum. I know better but philosophy, well ok but I was hesitant to post in here but I am interested in the subject of critical points, catastrophe, and bifurcation, nevertheless and view much of Nature from that perspective. I don't know your background though Pythagorean except that you are interested in brain science.

 

[Pythagorean]

I'm afraid I can't be in the same category as Zapper. I know he's very knowledgeable in physics. Very much so I believe. I myself am not and was hesitant to post in here because of that but I am interested in the subject of critical points, catastrophe, and bifurcation, nevertheless and view much of Nature from that perspective. I don't know your background though Pythagorean except that you are interested in brain science.

My undergraduate degree was in physics. I designed my current interdisciplinary degree. My advisor studies dynamical systems, and so there was mutual benefit for study neuron systems from the dynamical perspective. Once I was introduced to that perspective (in the context of transient chaos in nature) I became very interested in the general framework of dynamical systems and it's applications to biology in general (cell cycles, epigenetics and "junk" DNA) but continue to focus academically in dynamical systems and neuroscience.

I actually read about Lorenz's chaos before my physics education and was quite infatuated with it (always had chaos in my screen name). I had forgotten about that until I was reintroduced to it more formally (still currently learning a lot of the mathematics formally).

Anyway, I think the math is important. I think it has positively influenced the way I think about things I observe. I believe in the theory of linguistic relativity, that language influences how you think, and to some extent, who you are: and I believe mathematics is a language. So to my mind, it stands to reason that topics born in mathematics are elusive (even when using the proper english equivalents) to someone who doesn't have that innate, subconscious understanding that comes from years of exposure to mathematics.

Once you're five analogies into describing complex theory, each person is taking home their own story, over-applying the analogies that hit home with them the most.

 

[jackmell]

My undergraduate degree was in physics. I designed my current interdisciplinary degree. My advisor studies dynamical systems, and so there was mutual benefit for study neuron systems from the dynamical perspective. Once I was introduced to that perspective (in the context of transient chaos in nature) I became very interested in the general framework of dynamical systems and it's applications to biology in general (cell cycles, epigenetics and "junk" DNA) but continue to focus academically in dynamical systems and neuroscience.

I actually read about Lorenz's chaos before my physics education and was quite infatuated with it (always had chaos in my screen name). I had forgotten about that until I was reintroduced to it more formally (still currently learning a lot of the mathematics formally).

Anyway, I think the math is important. I think it has positively influenced the way I think about things I observe. I believe in the theory of linguistic relativity, that language influences how you think, and to some extent, who you are: and I believe mathematics is a language. So to my mind, it stands to reason that topics born in mathematics are elusive (even when using the proper english equivalents) to someone who doesn't have that innate, subconscious understanding that comes from years of exposure to mathematics.

Once you're five analogies into describing complex theory, each person is taking home their own story, over-applying the analogies that hit home with them the most.

Ok. Thanks for that. I'm interested in non-linear math too. You didn't see that brusselator thing we've been working on in the DE sub-forum huh? Anyway, I think it's fascinating that we can start with a purely random mixture of chemicals (like the primeval earth), and by the intrinsic dynamics alone, create ordered structures. And they wonder how complex life forms can emerge from scratch. What happens when we couple not two but two-hundred? :)

Anyway, it's singularities here. I think the "Big Bang singularity" gets a lot of people. They think linearly and then wonder what can exists before existence because they're thinking "more of the same". But that causes the problem I believe. Once jump-discontinuities, bifurcations, catastrophe, phase-transitions, and critical-points are added to the equation, then it's not too difficult to suppose maybe the reason we believe it's a "singular" point is because it's really a "critical point" and by virtue of the qualitative change that is often associated with critical points, our current (incomplete) laws of physics cannot apply. The same I believe can be said of black holes and other "singular" phenomena in nature: the singularity is a consequence of applying a (smooth) description of phenomenon across a critical point where the dynamics may not change smoothly but rather abruptly and discontinuously.

Just my opinion guys and again, it's philosophy and not the (empirical) physics sub-forums and I'm gettin' mine before the rules change. :)

 

[ZapperZ]

Jesus dude, like I'm skiing. Suddenly and abruptly and I mean in a split second, the whole side of the mountain fractures into a very, very large avalanche. They ask about actually seeing a singularity in here. That's one in my opinion: the dynamics of the snow pack have suddenly and abruptly changed in a qualitative manner and I didn't have to know the mathematics to know it happened.

So? You saw something. How does that relate to the fact that the description of it involves a singularity? I already gave you an example of water turning into ice. Would you have known that a mathematical description of that process has a singularity?

Just because you saw something doesn't mean you can recognize the mathematical description of it.

Zz.

 

[Pythagorean]

Ok. Thanks for that. I'm interested in non-linear math too. You didn't see that brusselator thing we've been working on in the DE sub-forum huh? Anyway, I think it's fascinating that we can start with a purely random mixture of chemicals (like the primeval earth), and by the intrinsic dynamics alone, create ordered structures. And they wonder how complex life forms can emerge from scratch. What happens when we couple not two but two-hundred? :)

I will occasionally wander to the DE forum, but I really prefer discussion to be motivated from science and observation. I checked out that thread though now that you mentioned it, and it looks like something I'll have to check out in-depth.

Anyway, it's singularities here. I think the "Big Bang singularity" gets a lot of people. They think linearly and then wonder what can exists before existence because they're thinking "more of the same". But that causes the problem I believe. Once jump-discontinuities, bifurcations, catastrophe, phase-transitions, and critical-points are added to the equation, then it's not too difficult to suppose maybe the reason we believe it's a "singular" point is because it's really a "critical point" and by virtue of the qualitative change that is often associated with critical points, our current (incomplete) laws of physics cannot apply. The same I believe can be said of black holes and other "singular" phenomena in nature: the singularity is a consequence of applying a (smooth) description of phenomenon across a critical point where the dynamics may not change smoothly but rather abruptly and discontinuously.

This is close to my opinion. To me, it seems several different behaviors can be represented by one system of equations if you construct the mathematics with nonlinearities in mind. So I guess the only difference really is that I speak of our models of reality only and their closeness to reality, but not reality itself.

Just my opinion guys and again, it's philosophy and not the (empirical) physics sub-forums and I'm gettin' mine before the rules change. :)

I don't know; to me, your posts don't seem like the target of the coming policy change. You may need to define things more carefully for non-dynamical peoples, but to me you are arguing from mathematics, even if you're not showing it mathematically.

 

[Maui]

It's a loaded challenge. Many aspects of gravitational singularity are described mathematically (even the wiki authors know that).

What aspects specifically are you referring to? I haven't read the wiki but my usual reference - Penrose's "the Road to reality" say no such thing.

"There is no math describing a gravitational singularity" may be true if you spin it the right way, but then it would be a meaningless and irrelevant statement.

No, i meant what i said. There is no math describing spacetime singularities.

So there's really no defending it.

I try to stay on the safe side, hence my statements are usually much stronger when I am perfectly aware that there is no empirical way to test the veracity of a theory that lies very very far in the future. Maybe you should explain in more detail what you meant so that i know what to reply to. I am completely in the dark as to what your above statements were supposed to mean.

 

[Pythagorean]

Maui:

http://en.wikipedia.org/wiki/Penrose-Hawking_singularity_theorems
http://en.wikipedia.org/wiki/Raychaudhuri_equation

 

[ZapperZ]

No, i meant what i said. There is no math describing spacetime singularities.

R. Geroch, Annals of Phys. v.48, p.526 (1968).
D. Christodoulou, Annals of Mathematics v.140, p.607 (1994).
etc...

Zz.

 

[Maui]

We won't know for quite sometime, if someone's arguing a certain point through proposed mathematical structures, depict spacetime singularities(or something quite fictitious) without some sort of empirical verification. Kind of leans towards the absurdly complex mathematics in ST that still has no empirical verification whatsoever. But there is nothing fundamenta lly wrong in being hopeful.

 

[ZapperZ]

We won't know for quite sometime, if someone's arguing a certain point through proposed mathematical structures, depict spacetime singularities(or something quite fictitious) without some sort of empirical verification. Kind of leans towards the absurdly complex mathematics in ST that still has no empirical verification whatsoever. But there is nothing fundamenta lly wrong in being hopeful.

But this is beside the point. You're arguing that there is NO gravitational/spacetime singularity of any kind. That in itself has no "empirical verification" either. I merely pointed out that there are plenty of theoretical papers that would counter your assertion.

Again, this is more suited to be done in the SR/GR forum where people who are more familiar with this area hang out. This is not a philosophy topic anymore.

Zz.

 

[Math Is Hard]

I agree with Zapper on this. Why speculate when there are experts in another part of Physics Forums.