# The Naked Scientists Forum

### Author Topic: Does the Universe have a 3D shape? If so, where is the centre?  (Read 21628 times)

#### JohnDuffield

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« Reply #50 on: 15/01/2015 13:43:46 »
There's no evidence of any unbounded topology or any higher dimensions. People wax lyrical about the three-dimensional space of the universe being like a spherical surface, but there's simply no evidence of anything like that. None whatsoever. From the evidence we have, the universe started off small circa 13.8 billion years ago, it's been expanding ever since, and it's "flat". That suggests to me that space is an ordinary 3D shape such as a ball, with an edge and a centre.

Quote from: jeffreyh
Well John I would like to know the path you took in deriving your equations. What steps did you go through?
I didn't. It's a well-known Schwarzschild-metric equation.

Quote from: PmbPhy
What in the name of God do you mean by this? What justification do you have that the pressure is always balanced and that because of this the universe can't expand? The equations of motion for an expanding universe certainly does hold true for our universe, that's for sure.
Yes, our universe is expanding. I'm saying the pressure isn't counterbalanced and that's why it expands. If the universe was infinite, space couldn't expand because the pressure is counterbalanced at all locations. See the stress-energy-momentum tensor, note the energy-pressure diagonal. There's a "spatial pressure gradient" around the Earth. In the universe overall there's no pressure gradient, just pressure. Space has this innate pressure. It expands. Provided it isn't infinite.

#### jeffreyH

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« Reply #51 on: 15/01/2015 20:36:42 »

Quote from: jeffreyh
Well John I would like to know the path you took in deriving your equations. What steps did you go through?
I didn't. It's a well-known Schwarzschild-metric equation.

[/quote]

You do realize of course that the equation is for a special situation involving a non-rotation body. This is one of the solutions for a black hole and not very realistic. The other is the Kerr solution for a rotating mass.

http://en.wikipedia.org/wiki/Kerr_metric

You have 4 solutions listed, all of which involve perfect spheres as far as I can remember.

Now this shows you how difficult your position is in this argument.

Note that the ergosphere is the real danger point. What this shows is you can't make glib statements without reviewing all the maths. You may think physicists get 'lost in the maths' but without the maths there is no physics.

#### PmbPhy

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« Reply #52 on: 16/01/2015 07:12:10 »
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Ooh-er, I don't think I can visualise a flat cone...
We're talking about the intrinsic curvature, not the extrinsic curvature here. See:
http://mathworld.wolfram.com/IntrinsicCurvature.html
Quote
A curvature such as Gaussian curvature which is detectable to the "inhabitants" of a surface and not just outside observers. An extrinsic curvature, on the other hand, is not detectable to someone who can't study the three-dimensional space surrounding the surface on which he resides.

#### PmbPhy

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« Reply #53 on: 16/01/2015 07:34:06 »
Quote from: JohnDuffield
There's no evidence of any unbounded topology or any higher dimensions.
The term scientific evidence is defined as http://en.wikipedia.org/wiki/Scientific_evidence
Quote
Scientific evidence is evidence which serves to either support or counter a scientific theory or hypothesis. Such evidence is expected to be empirical evidence and in accordance with scientific method. Standards for scientific evidence vary according to the field of inquiry, but the strength of scientific evidence is generally based on the results of statistical analysis and the strength of scientific controls.
As such there is plenty of evidence that the universe might be infinite. But we're talking about the various models of the universe and the ramifications of what is implied when one of the models is true. My comments applied to the situation where we assumed that the universe is spatially infinite. It didn't apply to what it "really" is since that can't be known.
« Last Edit: 16/01/2015 09:58:43 by evan_au »

#### JohnDuffield

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« Reply #54 on: 17/01/2015 14:02:03 »
As such there is plenty of evidence that the universe might be infinite.
No there isn't. None whatsoever. If you beg to differ, show me some.

But we're talking about the various models of the universe and the ramifications of what is implied when one of the models is true. My comments applied to the situation where we assumed that the universe is spatially infinite. It didn't apply to what it "really" is since that can't be known.
Don't assume what you don't know. Instead, be scientific. Think about the alternatives.

#### JohnDuffield

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« Reply #55 on: 17/01/2015 14:28:54 »
You do realize of course that the equation is for a special situation involving a non-rotation body. This is one of the solutions for a black hole and not very realistic. The other is the Kerr solution for a rotating mass.
At the event horizon the coordinate speed of light is zero. So the Kerr black hole is spinning faster than the local speed of light. That doesn't seem too realistic to me.

Now this shows you how difficult your position is in this argument.

Note that the ergosphere is the real danger point. What this shows is you can't make glib statements without reviewing all the maths. You may think physicists get 'lost in the maths' but without the maths there is no physics.
Oh dear, it starts with the science of Interstellar. This movie features time travel. I'm afraid it's science fiction masquerading as serious science. Because yes, physicists do get "lost in maths". See where Jesse says the time dilation goes to infinity as you approach the Schwarzschild radius. Think of a light clock. When it goes slower, it isn't because "time goes slower". It's because "light goes slower". And when time dilation goes to infinity, it's because light stops. This is what I was referring to when I said the coordinate speed of light is zero. And for a Kerr black hole to exist, the black hole has to be spinning faster than light. That can't happen, but Jesse and the guys he's talking to have missed this. See in post #23 where he refers to a non-rotating black hole? You think Ahah! Now we're talking! But then he brings in Kruskal-Szekeres coordinates. These involves a cringeworthy schoolboy error, wherein you put a stopped observer in front of a stopped light-clock and claim he sees it ticking normally. Even though light is stopped. Then in post #24 Smithers refers to the "river model" (aka waterfall analogy) in which space is thought of as being like flowing water that "drains" through black holes. This is just junk. A gravitational field alters the motion of light and matter through space. It doesn't suck space in. It just goes from bad to worse.

#### yor_on

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« Reply #56 on: 24/01/2015 21:02:02 »
An interesting argument Ron "Only it can't be infinite if it's expanding. If it was infinite the energy-pressure* would be counterbalanced at all locations. It couldn't expand. "

You could simplify it to asking how something already infinite can be allowed to become more 'infinite' in a expanding acceleration. Then again, that depends on your definitions of what infinite should be. You can turn that around, ignoring 'dimensions' for now, asking yourself if it all is about 'communication', then what defines a universe. Its ability to communicate between 'points'? And those points, do they have a 'background', or do they create it?

#### yor_on

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« Reply #57 on: 24/01/2015 21:13:55 »
Thinking of it that way a singularity as a black hole indeed could be defined as a 'cosmic censorship', because that area is one where points do not communicate, even though you can find a Hawking radiation, possibly. And then you can, if you like, think of those points able to communicate as also defining, and possibly creating, our 'dimensions'. That puts any definition of a 'infinite universe' into another light for me. As long as there is communication the universe exist.

#### yor_on

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« Reply #58 on: 24/01/2015 23:51:47 »
And Pete, any way one can explain, in simple terms please :) " For example, a circle in the plane is obviously curved, but you wouldn't notice when moving inside the circle. All one-dimensional manifolds have zero intrinsic curvature. " And what about a extrinsic curvature in this case? As defined as from where? I keep getting stuck on this one.
=

From https://math.stackexchange.com/questions/345297/why-is-mean-curvature-extrinsic

#### jeffreyH

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« Reply #59 on: 25/01/2015 02:29:22 »
See where Jesse says the time dilation goes to infinity as you approach the Schwarzschild radius. Think of a light clock. When it goes slower, it isn't because "time goes slower". It's because "light goes slower". And when time dilation goes to infinity, it's because light stops.

Your reference to light is a total red herring. Everything slows down, not just light. Rates of change slow down and what do we use to measure rates of change? Come on John you know the answer to this one. You can see this in the shifting wavelengths. How do you measure a frequency? You'll have to remind me it has slipped my memory.... Begins with a T I think.

#### Atomic-S

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« Reply #60 on: 25/01/2015 05:38:47 »
Quote
More of a sphere - top and bottom were also contiguous; perhaps I should have said 'edge' rather than 'side'...
No, a torus (doughnut).

#### JohnDuffield

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« Reply #61 on: 25/01/2015 13:22:40 »
Your reference to light is a total red herring.
It isn't. It gets to the heart of the matter.

Everything slows down, not just light.
Because everything has an electromagnetic nature. We make electrons (and positrons) out of light in pair production.

Rates of change slow down and what do we use to measure rates of change? Come on John you know the answer to this one. You can see this in the shifting wavelengths. How do you measure a frequency? You'll have to remind me it has slipped my memory.... Begins with a T I think.
You measure it with a clock. The most precise clocks are optical clocks.

#### jeffreyH

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« Reply #62 on: 25/01/2015 17:15:04 »
Your reference to light is a total red herring.
It isn't. It gets to the heart of the matter.

Everything slows down, not just light.
Because everything has an electromagnetic nature. We make electrons (and positrons) out of light in pair production.

Rates of change slow down and what do we use to measure rates of change? Come on John you know the answer to this one. You can see this in the shifting wavelengths. How do you measure a frequency? You'll have to remind me it has slipped my memory.... Begins with a T I think.
You measure it with a clock. The most precise clocks are optical clocks.

You are dancing around here. You mention a clock. What do clocks measure?

#### jeffreyH

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« Reply #63 on: 25/01/2015 17:33:16 »
John you said, "Because everything has an electromagnetic nature. We make electrons (and positrons) out of light in pair production." There is an electromagnetic field which arises because of mass. The problem you have is that you first need to determine what is slowing down and exactly why. This may sound like a bizarre statement at first read but it cuts to the heart of the matter. Does the intrinsic spin slow down. Does that imply that the intrinsic energy of the electromagnetic field decreases. Is it still the same amount of energy distributed over a longer time period. All sorts of questions arise. Does energy itself depend upon time.

#### JohnDuffield

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« Reply #64 on: 25/01/2015 22:31:30 »
You are dancing around here. You mention a clock. What do clocks measure?
A clock "clocks up" some kind of regular cyclical local motion and displays a cumulative result that we call the time. If it's a grandfather clock the regular cyclical local motion is a swinging pendulum. If it's a mechanical watch it's the motion of a sprung rocker. If it's a quartz watch it's the vibration of a piezo-electric crystal. If it's an atomic clock it's the motion of the microwaves emitted by a hyperfine spin-flip. A clock doesn't actually measure the flow of time. It isn't some kind of cosmic gas meter with time flowing through it instead of odorized methane. Time doesn't literally flow or pass, that's just a figure of speech. Things move, including things in clocks.

John you said, "Because everything has an electromagnetic nature. We make electrons (and positrons) out of light in pair production." There is an electromagnetic field which arises because of mass. The problem you have is that you first need to determine what is slowing down and exactly why. This may sound like a bizarre statement at first read but it cuts to the heart of the matter. Does the intrinsic spin slow down.
Yes. But note that conservation of energy applies. The internal kinetic energy of a falling electron is converted into its macroscopic kinetic energy. When you get rid of this you're left with a mass deficit.

#### yor_on

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« Reply #65 on: 26/01/2015 17:20:26 »
No John. Light is defined as a constant, you can't have a constant of varying 'time'. Meaning that a observer observing a event horizon can't use some 'light clock' observed over there (and as compared to his own local 'light clock' sitting on the desk) as being 'stopped'. If you do you now have defined a variable light speed as well as a variable time. Unless you assume that there to be a balance of sorts to it, slower light in slower 'time', and then treat it as some 'time molasses' clinging to certain areas due to for example gravity. That one can easily be shoot down though by using moving observers instead, each one defining a unique result to that event horizons 'ticks', as you with different motions also will observe the far away clock (event horizon) to 'tick' differently slow.

So light speed is a constant, defined locally and true everywhere, even at a event horizon. The best clock would be one able to measure lights speed at Planck scale, 'one Planck step at one Planck time'. You can get one theoretically by splitting 'c'  to that scale, doing so you will notice that your measurement of local time and lights 'propagation' fits perfectly. So 'c' is the ultimate clock, and depending on whether you want to stop there also a limit for our universe.

#### JohnDuffield

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« Reply #66 on: 26/01/2015 17:50:11 »
Go and look up what Einstein said:

"Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable".

This Baez article is pretty good too. The locally measured speed of light is always 299,792,458 m/s because we use the local motion of light to define our second and our metre. However the "coordinate" speed of light varies with gravitational potential. At the event horizon, it's zero. The observer at the event horizon is said to observe everything happening normally, but the infinite time dilation means it hasn't happened yet. See the formation and growth of black holes where Kevin brown says this:

"Historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock asymptotically approaches "full stop" (i.e., running at a rate of zero). It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. In contrast, according to the geometric interpretation, all clocks run at the same rate, measuring out real distances along worldlines in curved spacetime. This leads us to think that, rather than slowing down as it approaches the event horizon, the clock is following a shorter and shorter path to the future time coordinates. In fact, the path gets shorter at such a rate that it actually reaches the future infinity of Schwarzschild coordinate time in finite proper time."

Note that where he mentions Einstein he used to mention Wheeler, and still should IMHO. Einstein would have had no truck with a clock reaching future infinity. That's the end of time. It hasn't got there yet, and never ever will.
« Last Edit: 26/01/2015 17:52:03 by JohnDuffield »

#### yor_on

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« Reply #67 on: 26/01/2015 22:40:59 »
Doesn't matter John, seen that argument(s) before but light is still defined as a constant. And it's one of the most tested facts existing as I know, as SR builds on it.
=

Where it gets questioned is mostly from the aspect of assuming some sort of 'container universe', containing us all. Naively also assumed to be both 'infinite', as well as having some sort of boundaries, as in examples where you can walk out of a universe to the right, just to find yourself to appear at the left. Myself I'm not happy about those ones, I like the universe to be infinite and 'bound less' in all ways you can define it, assuming it to build itself up through the 'protocols' used, laws, constants, etc, defining it. That means that you won't find that sort of situation in 'my' idea of a :) isotropic and homogeneous universe. Instead every other place you look out from, at the universe, it will look the same, no boundaries and no 'seams'. And it treats a inflation the same way as a expansion. Happening in 'all points'. In short, the 'protocol' (heh, some sf writer that likes that one? Feel free to use it) is the universe, and there is no way for me to step outside it, as the universe should be what communicate.

The difference is subtle, but there are no 'seams' in my sort of universe. Instead communication defines its limits. Which can be interpreted as where there is no communication my universe 'ends'. But on the other tentacle also should be understood as 'limits' doesn't exist, not for us at least inside it, if we by that means something defining 'seams' or the universes possible 'size', etc. With such a universe any definitions of a 'size' becomes questionable. A little like wanting to prove a universe to 'rotate', relative what?

But there are 'limits' if we by it mean constants, laws, rules, statistics etc. And 'c' is one of them. And another thing, the size of such a universe may be questionable, but scales, as QM use, is not, as far as I know. And that sort of scaling should hold true wherever you go, just as I would expect conservation laws to do. You can translate that one (scaling) into the one defining your local measurement of a length as belonging to a constant too. Your ruler never change its length, and the measurements (experiments) you make on a microscopic scale should be repeatable, as well as using a 'same scale', throughout a universe. Those are all ideal definitions naturally, as we consist of constituents of mass, acting and being acted on by mass. But Einstein has already defined the clock and the ruler ideally so I hope we can jump that one here.

also, as I use a strict local definition a black hole is communicative locally defined, in the sense that you can join it, on your own peril naturally, and so locally defined describe it (communicate with it). If we instead define communication as in the constant sending and receiving of information throughout a 'whole universe', a black hole may as per Hawking radiation, or may not, be 'communicative'. In the last definition where it is not it becomes a cosmic censorship, but it doesn't define a outside. Possibly one could look at it as another 'inside' though :) if we look at how I defined it here, two out of three possibilities define it as communicative, so maybe it is? I don't know :)

Well, actually I think I do know, if I stay with strict locality you can go into a black hole and communicate with it. That the local definition I like, avoiding ideas of a universe as described through 'container models' needing higher dimensions.
====

And yes, I think Einstein wanted a 'container universe'. He used 'dimensions' and as I understand kept searching for a way to define a fifth that would join observer dependencies into one perfect description of the 'real universe'. He also had a faith of sorts it seems, not in a 'God' creating men into his image, but of something more than just the universe, unless, maybe he thought of the universe as being just that? I don't know there but I wish I did.
==

btw: I don't think Einstein used a geometric definition originally, he adopted it after some initial irritation from Minkowski

"By 1907 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are not separated entities but intermingled in a four dimensional space–time, and in which the Lorentz geometry of special relativity can be effectively represented. The beginning part of his address delivered at the 80th Assembly of German Natural Scientists and Physicians (21 September 1908) is now famous:

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

Einstein himself at first viewed Minkowski's treatment as a mere mathematical trick, before eventually realizing that a geometrical view of space–time would be necessary in order to complete his own later work in general relativity"

And that geometrical way gives different 'paths of propagation' to a ray, depending on mass, acting and being acted on, as I understands it. Einstein used Algebra for SR, and I suspect he trusted more to that than the geometrical definition in his later works too, which may bring some light to him saying as he did in your citation. That is unless you can prove that a 'curved path' (geometrically defined), due to mass, can't be translatable into a longer path, equivalent to a longer time for the ray to reach the observer.
« Last Edit: 27/01/2015 01:10:35 by yor_on »

#### Ron Maxwell

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« Reply #68 on: 24/12/2015 12:26:13 »
I don't know what distortion of the usual meaning of 'centre' would allow an unbounded topology to have one; does a loop or circle have a centre? or the surface of a sphere? or an unbounded volume? if so, how does one calculate it?
We are considering three dimensions of space so yes, they all have a centre.

#### puppypower

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« Reply #69 on: 24/12/2015 13:53:21 »
If we reverse the expansion of the universe and space-time; play it backwards, this leads us to the singularity of the BB. If we could see energy burst, from that original event, shouldn't that event appear as a single point in space; center of the universe?

In other words, if all the matter/energy of the early universe was contained in a volume of say one light year in diameter, something that small, in the context of the entire modern universe; billions of light years in diameter, would occupy a very tiny angle of view from the earth. Such a tiny angle of view can't be both behind us and in front of us or all around us, since the angle of view; due to size, is less than 1 second arc, and not more than 180 degrees.

If the argument is light bends due to relativity and expanding space-time, so there is no center, then do we the oldest ancient quasar, both behind and in front of us, due to the same light bending affect? Would the light bending affect make one ancient star look like millions of ancients stars all around us, just like we assume of the BB event is all around us?

Have we found the center point; observation of the 1 light year universe. I assume a center since nobody says the oldest observations we see, can be viewed by looking out in any angle due to light bending; same exact thing is everywhere.

Say our earth reference, was inside of the 1 light year sized early universe. If we are not in the center of the expansion, shouldn't there be more universal matter/energy on one side of us, compared to the other side? Should this asymmetry of matter relative to us, in terms of GR and SR,  create asymmetry in the microwaves we see? Some of the microwaves has to travel longer, on the long side, thereby altering the energy density since there is not enough time for the farthest end to reach us when all the close side is counted.
« Last Edit: 24/12/2015 13:57:27 by puppypower »

#### dlorde

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« Reply #70 on: 25/12/2015 22:35:06 »
We are considering three dimensions of space so yes, they all have a centre.
So how does one identify the centre of an unbounded 3D space?

#### dlorde

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« Reply #71 on: 25/12/2015 22:48:47 »
If we reverse the expansion of the universe and space-time; play it backwards, this leads us to the singularity of the BB. If we could see energy burst, from that original event, shouldn't that event appear as a single point in space; center of the universe?
It may be worth pointing out that if you reverse the observed expansion of any explosion by extrapolation, you'll get back to an apparent origin smaller than whatever it was that exploded; so there's really no compelling reason to suppose there actually was a singularity at the BB.

Also, given that spacetime seems to be topologically flat, it's apparently possible that it was not finite in extent at the BB, i.e. it was an infinite expanse of hot, dense stuff that started expanding. The part we see, the observable universe, would have been a tiny part of that infinite extent. This isn't a scenario I'm particularly comfortable with, but I'm told it can't yet be ruled out; I'm not particularly comfortable with quantum 'weirdness' either, but it's a demonstrable fact, suggesting that reality doesn't care what I'm comfortable with  [8D]

#### Ron Maxwell

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« Reply #72 on: 26/12/2015 01:26:57 »
We are considering three dimensions of space so yes, they all have a centre.
So how does one identify the centre of an unbounded 3D space?

I can't see why one would want to as there is,as far as I'm aware, no such thing. The idea that the universe is infinite makes no sense to me.

#### dlorde

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« Reply #73 on: 29/12/2015 00:43:23 »
So how does one identify the centre of an unbounded 3D space?
I can't see why one would want to as there is,as far as I'm aware, no such thing. The idea that the universe is infinite makes no sense to me.
It doesn't have to be infinite, I'm asking about an unbounded finite 3D volume, i.e. closed in 4 dimensions, so it is unbounded in 3 - in the same way the surface of a sphere is an unbounded but finite 2D area, closed in 3 dimensions. It's one of the more popular topological models for a finite 3D universe.
« Last Edit: 29/12/2015 00:45:02 by dlorde »

#### Ophiolite

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« Reply #74 on: 29/12/2015 02:13:45 »
I can't see why one would want to as there is,as far as I'm aware, no such thing. The idea that the universe is infinite makes no sense to me.
Your lack of understanding is probably not a sound basis upon which to reach such definitive conclusions.