Search for an agreeable definition of fractals in nature

[billtavis]

Let me just start by saying thanks for the wonderful, thought provoking discussion we are having! I was nervous, being new to the forum and finding myself trying to defend an unpopular viewpoint, but I must say this is a great group! 

I think, when eiffie said oil on water, he didn't mean a thin film of oil which would indeed cause pretty rainbow effects, nor did he mean huge oil spills which are not contained in any form and thus are more like clouds in the sky which also are decidedly fractal.
Rather, he refered to a situation like this one:

Well that line between the red and blue certainly looks straight! It's a great illustration of the counter-example, but unfortunately I do have a couple issues with it.
First, OP asked about nature but this situation would not occur in nature. Natural interactions of oil and water do not occur inside circular containers, they occur inside fractal containers. Trying to separate the interaction from the container is missing the point, because everything in nature is a fractal pushing up against another fractal!
Second, I think that fractals are present even in this particular situation, they are just hard to see. At room temperature, water molecules travel along fractal trajectories at ~1400 miles per hour in constant collision      <a href="https://www.youtube.com/v/w1aVqKDAx6o&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/w1aVqKDAx6o&rel=1&fs=1&hd=1</a>

Thank you for explaining more thoroughly why the surface of a boulder is fractal, scalefreeness is an interesting way to think about self-similarity.

I'd argue that a tree isn't a boundary fractal.+
I suppose the boundary can be fractal too - bark typically has rather self-similar or scale-free patterns and textures in it - but that's not related to the fractalness you typically consider when talking about a plant: The branching pattern. That pattern can be described as a Lindenmayer-System and it's not a 2D situation but rather a 1D one.

An L-system is an abstract mathematical model and a 1D tree is not found in nature. Hele-shaw experiments are a good way to understand branching as a boundary phenomenon. But lets consider a real tree. At a distant scale, the shape of the boundary(silhouette) is a trunk with branches. Walking up to the tree, the individual branches of the boundary also have their own branches, and on for a couple more generations. At closer scales, other fractals take over, like the bark you mentioned, or a leaf. Looking even closer through a microscope, cellular and eventually molecular fractals would be seen.  Notice that self-similarity does not succeed in capturing all of this at once but must be redefined at various levels of zoom and for different botanical features. However, I point out that the entire time we were talking about the same boundary. The boundary-based viewpoint continues to serve us well when we look at the spaces between trees in a forest, which form yet another fractal:

Note, though, that some pretty darn smooth things are fractals by this definition. For instance, a logarithmic spiral, a straight line, a plane... Anything of which a piece can be matched up with a bigger part, and where that can be done multiple times, qualifies.

Wait, you're saying that a perfectly smooth plane is self-similar so it counts as a fractal? Then by your own terms, even if we consider the oil-water interface to be perfectly flat it would still be fractal anyways, and not a counter-example to my boundary definition.
I tend to think, though, that perfectly flat planes are not fractal. Let's say you can see the whole plane on a certain scale.  You can identify all four corners and all four edges, and that is a certain amount of detail. You can zoom in forever and not find any more detail. You can zoom out forever and not find any more detail. Thus it is not a fractal (thinking of the scalefreeness of the boulder right now).

[kram1032]

I noticed that problem too, already while writing about it.
There are precisely two ways I could see people define a fractal in a sensible manner:

1) You can identify some kind of scale-invariance be it discrete (you zoom in a fixed amount to find the same thing or, in case of quasi-selfsimilarity, almost the same thing) or continuous (no matter how much you zoom in, you find the same things over and over)

2) The object you are looking at can be assigned at least one non-integer Hausdorff-Dimension

Definition 1 is very inclusive. By that definition, pretty much anything is fractal. Smooth surfaces can be self-similar and thus fractal.

Definition 2 is very exclusive. The beautiful, intricate boundary of the Mandelbrot Set, for instance, has Hausdorff Dimension == 2, so it would not be a fractal in that case.

I haven't seen any other sensible definition. I don't feel like your particular definition that fractals always occur at boundaries and boundaries always cause fractals (e.g. there is no natural fractal that isn't a boundary process and there is no boundary which doesn't create a fractal) is satisfying, however a wide array of examples for this coincide with definition 1) above.

I also prefer definition 1) simply because I don't think having the Mandelbrot Set not be classified as fractal would make any sense at all.

Although thinking about it right now, perhaps one could slightly refine definition 2:

The Mandelbrot Set itself is a 2-Dimensional set. The boundary of the M-Set thus is a 1D-line, which corresponds to the topological dimension of the M-Set.
Perhaps, if the Hausdorff-Dimension of the topology is greater than the topological dimension, you are looking at a fractal? - Since that definition is about the boundary, it would fit nicely with your model while still excluding lines, circles, spheres or planes.
Not quite sure whether that works though. The Hausdorff-Dimension is always set between the topological dimension (dimension of the hyper-surface) and the geometric dimension (dimension of the hyper-volume) which always differ by 1. - However, if you talk about the dimension of the boundary, you are technically calculating the topological dimension, right? I should read up on that to make sure. But if that's the case, the M-Set has that weird case where the Hausdorff-Dimension of the surface is equal to the geometric dimension of the volume. Not quite sure how that works... I have never actually read a proof on the fact that the M-Set's boundary has Hausdorff-Dimension 2 though. Perhaps that would clarify.

Though I think you gave a good counter example in your last post: fractal trajectories of individual particles in a fluid.
A fluid does not have a boundary within itself. Only as it touches a different fluid and the two fluids are not nicely soluble in each other, you get a boundary.
However, even without that boundary, the particles move in brownian motion.

Furthermore, once you get down to the molecular level, speaking of boundaries starts become a little fishy. At that scale, everything would just look like fuzzy balls with vacuous gaps in between. You wouldn't actually see a boundary. Instead of seeing a wall you bounce off of, you see similar-sized individuals you bounce off of.

And even a single free particle in vacuum, where you most definitely do not have a boundary: A quantum physical trajectory effectively acts like brownian motion due to the uncertainty in both velocity and position. That very natural phenomenon most certainly does not stem from some boundary.

[billtavis]

Well I do grant you that the boundary definition does not directly capture the idea of "complexity at varying scales" which is an important feature of fractals, and I realized that this is what I relied upon when making my case against a simple plane being fractal.
While researching this topic some more I found this quote from a professor who said "Fractals have two related characteristics: they show complexity at every magnification; and their edges and interfaces are not smooth, but are either perforated or crinkled." This satisfied me because it relates self-similarity with boundaries. And I think 'complexity at every magnification' is much easier for me to swallow than 'statistical self-similarity' even if they are referring to the same thing, because thinking of it as complexity takes all the pressure off of trying to identify a matching pattern.

Though I think you gave a good counter example in your last post: fractal trajectories of individual particles in a fluid.
A fluid does not have a boundary within itself.

I disagree. The Brownian motion of a molecule is a direct result of the constant interactions that occur at the boundaries between that molecule and it's neighbors. All the molecules in water are moving in their own individual fractal paths, constantly bumping into eachother, and as a result they cause eachother to continue moving in fractal paths. Like I said before, everywhere in nature we see fractals pushing up against other fractals.
And I think that even on the macro scale, the water exhibits fractal boundaries within itself: imagine separating the water into two groups: one group with all the water hotter than the average temp, and one group with all the water cooler than the average temp. The boundary between these two groups, if it could somehow be made visible, would be fractal.

I don't comprehend much about quantum mechanics... so I can't say whether or not a boundary of some sort is involved in your example. But I do know that the conditions you described don't arise in nature, only in carefully controlled labs - again to find a counter example you resorted to isolating an element from its environment, which IMHO is missing the point.

And yeah I don't understand how the Mandelbrot set has an integer dimension either. Sometimes I think maybe it's such a perfect fractal that it transcended all the way to the next higher integer, as if it is infinitely "rough"?  But with much certainty, I can use the professor's two-pronged definition above and state that the Mandelbrot set is a fractal because its boundary is not smooth and it has complexity at all scales.

[youhn]

It's just roughness (with self-similarity on a multitude of scales).

- Roughness excludes all things smooth (flat plates, circles, spheres, emptyness, lines, points, solids, etc)
- Self-similarity includes the iterative/recursive property of fractals
- A multitude of scale, to wider the definition to include natural things like trees, lungs, (natural) surface roughness, clouds, rivers, etc.

[kram1032]

The conditions I described happen pretty much all the time in nature. In space.
And once again, once you go down to single atoms and molecules, there isn't really a boundary to speak of. There is no hard limit those particles can't pass through. No sharply defined wall.
Particles are not like billiard balls. - Natural particles, that is. It's artificial, newtonian, simplified mathematical particles that might act exactly like billiard balls.

Though I guess you could just add roughness/detail at all scales to the definition to avoid flat, smooth things like lines or planes to be fractal.
The question then arises, what exactly is meant by that. It's an intuitive idea but it might be hard to, like, find an algorithm that can decide that, yes, this has details on all scales so yes, this is a fractal.

[Chillheimer]

ah, this finally gets really interesting
I have to admit that I'm relieved that I'm not the only one bothered with a real lack of definition and you guys seem to be struggling with it as well..

welcome billtavis - very nice discussion indeed!  

phew, there is so much to reply to, I need to check the forum more frequently.

first: I like the idea of boundaries as a "main-feature" of fractals.
it might not be the one feature, but you can't have a fractal without a boundary - right?
-then again, if you had no boundary, you'd have just 'one thing' and if there is no other thing that one thing might as well be no-thing -
is there any non-theoretical thing that has no boundary?
I can't think of one. (this would fit well with the "everything is fractal" thought.)

Trying to separate the interaction from the container is missing the point, because everything in nature is a fractal pushing up against another fractal!
Second, I think that fractals are present even in this particular situation, they are just hard to see.

Ah, I love it to meet likeminded people! I keep wondering where they all are, as this topic seems so incredibly important, yet no one in my real life surrounding cares a bit.. cheers bill!
I actually think that fractals don't just appear in nature but also in man-made objects. if you e.g. see the tree of evolution as a fractal, you can also see the evolution of man-made design as a fractal.
you probably enjoy this 'little collection' I'm working on: http://www.pinterest.com/chillheimer/life-is-fractal/

I tend to think, though, that perfectly flat planes are not fractal. Let's say you can see the whole plane on a certain scale.

But a perfectly flat plane probably doesn't exist in the universe. If you zoom deep enough, the single atoms will 'bump out of the plane. So I think this only is a theoretical thought and thus not so relevant.

Liquids can stay atop each other in a very clearly separated manner and the boundary can be incredibly smooth.

and yet, if you zoom in close enough the boundary probably becomes fractal, even if it's the 'boundary of the forces active between the atoms'  (sorry for repeating myself, this post hat become too long...)

Though (quasi-)self-similarity and scalefreeness are basically the same concept. The difference is just that one is discrete while the other is continuous. So both are important and both describe fractals.

thank you kram for pointing out the difference between self similarity and scalefree-ness. I hadn't really considered this.

I'd argue that a tree isn't a boundary fractal.
I suppose the boundary can be fractal too - bark typically has rather self-similar or scale-free patterns and textures in it - but that's not related to the fractalness you typically consider when talking about a plant: The branching pattern. That pattern can be described as a Lindenmayer-System and it's not a 2D situation but rather a 1D one.

I'd counter that a tree is a boundary fractal, as it extends the boundary of a solid (earth) into a gas(sky) through self similar branching (as a nice addon)..
[/quote]

And the only reason we don't see any higher-dimensional fractals, in the literal sense of "see", is because we are limited to 3 dimensions in space.....
..The 4D ones would have to incorporate time, so you'd have to watch time in timelapse while being able to slice through the 3D structure to potentially be able to actually "see" the fractalness inherent in this.´

I personally believe that time is fractal. It's only a matter of perspective. There are so many time scales and different speeds happening, comparing femto-seconds to the age of the universe, in a tiny moment countless things can happen, like reactions single atoms. compared to thousands of years, were countless reactions between humans happen. or billions of years where countless interactions between stars happen..
--edt: of course it is, and it's been proven. I keep forgetting important stuff, this topic is so huge..
the heartbeat rate is proven to follow fractal variations in time, as well as the stock market, the frequency and strenght of earthquakes.......
a quote from this interesting article: http://www.psychologytoday.com/blog/the-chaotic-life/200909/fractal-brains-fractal-thoughts
Other examples include the size of extinction events in animal species, numbers of academic publications (a few researchers do huge amounts of work and the rest of us do just a little), numbers of hits to web-sites, wait times in stop-and-go traffic, and word usage in literature (i.e., zipf's law).

As for how exact a match you need: Usually, if it visually seems like a fractal, which a stone surface does, it'll be close enough.

the amount of roughness can be extremely high, try fiddling around in mandelbulb3d with extreme values. you'll see just noise or stuff that doesn't look like fractals at all. and yet it comes from a fractal formula.
I believe that this happens in nature a lot, which is why we don't see directly that absolutely everything is fractal (yes, there I go again )

Reality is further complicated by the existence of Multifractals which describe most natural, typically considered fractal phenomena better than single-dimension-fractals.

exactly. as reality is a multifractal system of multifractals    
there's no way we can easily see the overall connection. that everything is connected. scientifically speaking, like in the m-set.. and as a nice side-effect this fits to what most religions and esoterics say.
for me this 'scientific base' has huge implications. absolutely ground shaking, a different paradigm..
that deserves huge attention!

All physical laws also are scale invariant. That basically means that physics don't care how big you are, they always work the same way.
http://en.wikipedia.org/wiki/Scale_invariance

Is that truly so? Would be nice, but what about the quantum world?

Furthermore, once you get down to the molecular level, speaking of boundaries starts become a little fishy. At that scale, everything would just look like fuzzy balls with vacuous gaps in between. You wouldn't actually see a boundary. Instead of seeing a wall you bounce off of, you see similar-sized individuals you bounce off of.
And even a single free particle in vacuum, where you most definitely do not have a boundary: A quantum physical trajectory effectively acts like brownian motion due to the uncertainty in both velocity and position. That very natural phenomenon most certainly does not stem from some boundary.

If I understand the brownian motion correctly it doesn't happen for one particle in the vacuum and there is no uncertainity, as the one particle will keep flying in the same direction with a constant speed.
Ah, now I get what you mean - heisenbergs uncertainity principle and us not being able to measure where in time and place a particle is. I'm not sure if you can say with certainty that this is the same thing as brownian motion.
maybe we are just not yet able to measure position/time as we're technologically not advanced enough at this point in time.

It's just roughness (with self-similarity on a multitude of scales).
- Roughness excludes all things smooth (flat plates, circles, spheres, emptyness, lines, points, solids, etc)

which all seem to be theoretical things that only exist in the mathematic realm.
and maybe even these smooth things like lines, spheres, planes are just very special cases of fractals with very special properties.
just like a perfect square always is a square, but not the other way round.
Afterall, I think we've seen 'perfect spheres' in mandelbulb3d.. but maybe we haven't zoomed close enough

- Self-similarity includes the iterative/recursive property of fractals

I tend to think that the iterative-part could be the one main feature. self-similarity comes naturally with it - not so vice-versa..

- A multitude of scale, to wider the definition to include natural things like trees, lungs, (natural) surface roughness, clouds, rivers, etc.

hm.. should it be 'so easy' ?

• recursion
• multitude of scale

and the only necessary 'adjustment screw' is the variable of roughness


seems plausible. and as I think of it, it's exactly what mandelbrot says.
probably my brain needed 9 months to really understand what he meant.
thanks for naming this here youhn!

hm. maybe the only absolutely basic thing needed for fractals is recursion and everything else results from it automatically (if the conditions are right)

I need to think more about this..


phew.. 1 hour later... why do discussions about fractals tend to branch out into so many sub-branches that it gets complex close to chaos?!
pun intended?

[kram1032]

Brownian Motion corresponds to a gaussian uncertainty in every single step of a path. And if you look at a free particle in space, you also have precisely this gaussian uncertainty in both impulse (impulse = velocity * mass, so you could have uncertainties in the mass of your particle, the speed of your particle and the direction of your particle) and position, so the end result is that such particles behave like a particle in Brownian motion would.
There are some caveats to this, but it's pretty much correct.

And yes, scale-invariance of physical laws actually is an important property of them. There is an axiom which states that even new laws we might discover (for instance what ever exactly dark matter and dark energy are) should be scale invariant.
Of course, this invariance does break down at some scale: Nothing can be smaller than the Planck Volume. Or, more accurately, while you can think of scales smaller than that, physics (actual, real life physics, at least as they are found to be today) cannot distinguish between two things that are closer to each other than this quantity.

Btw, you shouldn't imagine this to be like pixels or voxels or something like that: There is, to our knowledge, no grid to the structure of the universe. It's all about the difference. If two precise positions happen to be closer to each other than a Planck length, no physical process exists - none even could exist in principle - that could differentiate the two locations.

But above that scale, all the way, in principle, to infinitely many Planck lengths, all scales are treated the same.

Btw, I think the reason we find so little research into fractals actually is the same as the reason this topic came to be:
People are unsure what a fractal even is or, more importantly, what isn't a fractal. Thus, as far as research goes, it's kind of a vague, useless term.
If you want to look for research about fractals, you'll probably rather need to look into "complex systems" or "emergent properties" or "non-equilibrium thermodynamics" or "strange attractors" all of which often have fractal properties. It is only when people directly do research on already well known fractals like variations of the M-Set, L-systems and other geometric substitution fractals, Indra's Perls style fractals or cantor dust style fractals (I guess those all are either geometric substitution or functional iteration which in turn also usually have geometric concepts attached to them), only when those are directly researched you'll find a new paper on fractals pop up.
When you guys say you thought you are alone, the research landscape on all those topics really does proof that you are very clearly not.

[Sockratease]

Brownian Motion corresponds to a gaussian uncertainty in every single step of a path. AndBtw, I think the reason we find so little research into fractals actually is the same as the reason this topic came to be:
People are unsure what a fractal even is or, more importantly, what isn't a fractal. Thus, as far as research goes, it's kind of a vague, useless term.

I was keeping out of this discussion because I didn't want to spoil the fun   

But I do believe the reason we can not agree upon a definition of fractals in nature is because there are none.

Just things that resemble fractals and stuff made by some sort of iterative process.

But I doubt we will ever find anything fractal outside of mathematical constructs, and from that point of view the difficulty of reaching a definition becomes clear : One cannot define something that does not exist!

We can get clear images of Mandelbrot Zooms much smaller than the Planck Length - until we can do that in Nature...  we'll never have "True" fractals outside of mathematical constructs.

Sorry to raise my unpopular views again, but it's a possibility that should not be left out when discussing the problems of reaching an agreeable definition of fractals in nature.

[youhn]

Who or what has made the definition for fractal infinite and therefore stricly mathematical?!

I think this was plain stupidity.

[Sockratease]

Who or what has made the definition for fractal infinite and therefore stricly mathematical?!

I think this was plain stupidity.

That would be the same person who included "scale invariant" in the definition   

And I agree - it is - as you say - "plain stupidity" to expect anything infinite to appear in reality, but we try not to call it that because plain stupid people take offense to such words.

Let's just call it "futile" to avoid offending anybody.

[Chillheimer]

thank you kram for taking the time to explain in detail.

I was keeping out of this discussion because I didn't want to spoil the fun  

hihi, nope, it would take much more to spoil the fun.
first of all, I started the thread deliberatly asking for a definition for fractals in nature. not for the pure mathematical ones.

But I do believe the reason we can not agree upon a definition of fractals in nature is because there are none.
Just things that resemble fractals and stuff made by some sort of iterative process.
But I doubt we will ever find anything fractal outside of mathematical constructs, and from that point of view the difficulty of reaching a definition becomes clear : One cannot define something that does not exist!

I couldn't agree less.
And the 'inventor' of fractals, Benoit Mandelbrot himself would disagree as well. And all those countless studies that proved fractals..
I don't even see a point in explaining why, isn't it obvious?
Please take a look at romanesco broccoli again:

and then tell me again that the base for the construction plan of it is not fractal.
or, as an alternative, tell us what word you would use to describe this.
you probably just use the word fractal differently than 'we' do. (even different to the man who came up with the word fractal)

We can get clear images of Mandelbrot Zooms much smaller than the Planck Length - until we can do that in Nature...  we'll never have "True" fractals outside of mathematical constructs.

only because you can't see it or don't have the means yet to examine it doesn't mean it isn't there.
500 years ago people couldn't see the earth is round. so it actually was a flat plate and suddenly turned into a sphere?

the question is who gets to decide what "true" is?
in a way you are turning around my point from the last post, that all perfect squares(not sure if i translate this correctly, "quadrat" in german) are always squares but not vice versa.  
when you say only 'true fractals are fractals', you could also say only a quadrat is a square. if it hasn't 90° in all corners and the same lenght for each side it can't be a square.

Sorry to raise my unpopular views again, but it's a possibility that should not be left out when discussing the problems of reaching an agreeable definition of fractals in nature.

that's perfectly fine and welcome! I guess we need this sort of input (even if it's clearly wrong   ) to improve our reasoning, to question the own beliefs..

Who or what has made the definition for fractal infinite and therefore stricly mathematical?!

I'm not sure if anybody really has.
And if someone (preferrably the inventor of the word fractal, Mandelbrot himself) has, I'd love to see a quote including the source.
(And if that exists, I'd disagree and say that this is a mistake we have to correct.)

If you watch this from a purely mathematical standpoint, Sockratease is right.
But without the intend to insult, to say that all those smart guys like Mandelbrot and other scientists that prove fractal structures in nature are simply wrong - that seems to be very arrogant..

I for myself believe that math isn't at the root of fractals but that (as everything is fractal) they also can be seen in a mathematical way.
for me, at the moment, math is probably just another language that speaks/describes fractals.

[kram1032]

- Infinite isn't technically part of the definition
- The M-Set is not embedded in a physical space but rather in the space of Complex numbers which is isomorphic to R² which does not feature a minimal length scale and thus has no limit in detail scale. Pictures of the M-Set do not have an inherently minimal scale and thus you can't say that any particular resolution goes beyond the Planck Scale.
- All the definitions of scalefreeness and selfsimilarity can easily be altered to not go over all scales (from infinitely small to infinitely large) but only over all scales (from planck scale to infinitely large) or over a (wide) range of scales (from minimal_scale to maximal_scale with min << max) without altering them in any substantial way.

That's exactly how natural fractals are handled. If you look at a river or the shoreline of an island or a mountain or something, the things you can say about it will be limited between two scales after which the whole definition won't make any sense anymore. That'll typically be from the scale of the whole object - say, measuring the "height" of Great Britain with a ruler, to the molecular scale, realistically earlier than that because individual molecules - even individuals pebbles and grains of sand and what not - move way too quickly for this amount of detail to be of any use.
And for a fundamental law of physics, it'll be from Planck-scale to infinity.
This still spans several orders of magnitude and that's already truly mind-bending scales our minds can't really handle anyway.

Also, infinity, for the most part, unless you are trying to talk about the entirety of the universe beyond the observable parts, is just a convenient mathematical approximation to the truth.
And in case of the entire universe, we simply do not know yet. We could live in a spherical universe which is finite in total volume, or in a flat or hyperbolic universe in case of both of which our universe would be infinite. Evidence currently supports a flat universe best, but the other possibilities are not yet ruled out.

In any case, whether it's infinite scales both ways or it's a finite but wide number of ranges, it doesn't really matter. Both are valid descriptions of a fractal.
If you prefer, and I really think this is nitpicky at best, you could call what we find in nature "approximate fractals".

[kram1032]

If you watch this from a purely mathematical standpoint, Sockratease is right.

Not even then, for you could actually define spaces in which a minimal scale does exist and in doing so, you would basically get much more natural fractals which feature a minimal scale equal to the scale you choose for your space.
The real numbers can be extended to so-called real closed fields which behave just like real numbers in all the important ways (they are dense, ordered and closed under subtraction and division) but they can have differing properties. One of which, in principle, could be such a minimal length scale.

[Chillheimer]

-----kidnapping 'my own' thread-----

I believe that one area of study that is largely ignored, but should not be, is related to the fact that atoms are mostly empty space.  We focus on the "matter" and try to understand it - but it's only 0.000001% or so of what makes up stuff.  Stuff is 99.99999% "Empty" Space.

That space is said to have an enormous energy, so much so that Physics had to correct for it when defining things mathematically or else it would overwhelm everything else.

We should ignore the statistically insignificant matter and focus much more study on that so-called "Empty" Space!

I think that's where the next big breakthroughs will be made in out understanding of The Universe.

I just read this again after recently watching a video by Nassim Haramein, a strange guy, not accepted in the scientific world who has a nice theory regarding this issue, resolving the problem without this 'fake-correction'
<a href="http://www.youtube.com/v/TW1gl6_QK-M&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/TW1gl6_QK-M&rel=1&fs=1&hd=1</a>
The essence is that empty space/vacuum has "incredible density", which can only mean that we live inside a black hole. (he goes on that in each proton(?) there's also a miniblackhole)...

Too bad he also has to talk about ancient egyptians being helped by extraterrestrials to build the pyramids, which makes taking this guy serious even harder.

But besides that, my problem is that my math-&physicsknowledge by far isn't enough to dis-/prove him.   And googling finds esoteric pro guys and no real scientists backing the theory, but also none that disprove him, only comments like  "this is such nonsense, not even worth of disproving" -which reminds me of the reaction of people when galileo wanted to prove and show the disbelievers by a look at saturn through his telescope: "this is so stupid, we won't even look through your telescope"
I'm unsure what to think of this whole thing, although it sounds so logically.

Maybe one of the math-heads here takes  a little time to look through his telescope and tell me what he sees?
------threadnappig*off-----------

[kram1032]

I can't recall where exactly I found it but I think I saw somebody actually debunking that guy.
He's been around for years with his pretty ridiculous claims.
What he does sounds nice but it comes out of nowhere. He pretty much sells pretty pictures with no true background.

And people very much study empty space. It's an important topic. Just look at all the research, calculations and thought experiments that happen around the topic of vacuum. There are tons each year.