Question Why the universe looks the same irrespective direction and position?

[Wonderip]

According to Friedman, the universe looks the same irrespective of direction and position. But I don't get it.

 

[Hayseed]

I'm not sure what characteristics he or you are referring to. I'm going to assume it's the distribution of mass. Maybe temperature. Not only is it the same, but the farther out one looks, the denser it gets. Something is out of kilter. Something is senseless. It's always been hard for me to think of astronomy as a science. No solid foundation. Everything is indirect, and usually wrong. Like elliptical orbits.

 

[Hartmann352]

I'm not sure what characteristics he or you are referring to. I'm going to assume it's the distribution of mass. Maybe temperature. Not only is it the same, but the farther out one looks, the denser it gets. Something is out of kilter. Something is senseless. It's always been hard for me to think of astronomy as a science. No solid foundation. Everything is indirect, and usually wrong. Like elliptical orbits.

The cosmological principle is usually stated formally as 'Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers.' And the Standard Model of Cosmology also relies on the fundamental assumption that we don’t occupy a special place in the Universe, an idea known as the Copernican Principle*.

This amounts to the strongly philosophical statement that the part of the Universe which we can see is a fair sample, and that the same physical laws apply throughout. In essence, this says that "the Universe is knowable and is playing fair with scientists."

In a perfectly homogeneous and isotropic Universe the CMB would look likewise perfectly homogeneous and isotropic. However, during the very early phases of the Universe history (particularly, during a period known as inflation), this otherwise slightly boring picture was spiced up a bit and small perturbations were created in this smooth landscape in the form of curvature fluctuations. These incidentally, went on to form all the structure we know today – galaxies, clusters of galaxies, etc., and are the reason why we can exist today and discuss anisotropy! These perturbations can be studied by analysing the tiny temperature and polarization differences that were imprinted in the CMB as a result, which are represented as colored blots in the CMB map below. They are really tiny perturbations: 1 part in 100,000. As far as we can see, large-scale isotropy is at least, a very good approximation. As far as homogeneity is concerned, we can only comment on the portion of the Universe we see, but here large-scale homogeneity certainly seems to also hold.


The Cosmic Microwave Background (CMB) as seen by the Planck satellite. Credits: ESA and the Planck Collaboration.

In the standard picture, only these tiny fluctuations generated during inflation leave their imprint on the CMB. A distinctive feature is that some randomness is involved in their generation; their statistical behaviour is constrained by physics, but what exact perturbation will appear at a precise spot is random. If we were to make an analogy with a coin toss, we could say that physics chooses the coin, but the particular outcome of a toss is then random.

Looking out into the night sky, we see a clumpy universe: planets orbit stars in solar systems and stars are grouped into galaxies, which in turn form enormous galaxy clusters. But cosmologists assume this effect is only local: that if we look on sufficiently large scales, the universe is actually uniform.

The vast majority of calculations made about our universe start with this assumption: that the universe is broadly the same, whatever your position and in whichever direction you look.

If, however, the universe was stretching preferentially in one direction, or spinning about an axis in a similar way to the Earth rotating, this fundamental assumption, and all the calculations that hinge on it, would be wrong.

Now, scientists from University College London and Imperial College London have put this assumption through its most stringent test yet and found only a 1 in 121,000 chance that the universe is not the same in all directions.

To do this, they used maps of the cosmic microwave background (CMB) radiation: the oldest light in the universe created shortly after the Big Bang. The maps were produced using measurements of the CMB taken between 2009 and 2013 by the European Space Agency's Planck satellite, providing a picture of the intensity and, for the first time, polarisation (in essence, the orientation) of the CMB across the whole sky.


Four potential CMB patterns for universes with direction

Previously, scientists had looked for patterns in the CMB map that might hint at a rotating universe. The new study considered the widest possible range of universes with preferred directions or spins and determined what patterns these would create in the CMB.

A universe spinning about an axis, for example, would create spiral patterns, whereas a universe expanding at different speeds along different axes would create elongated hot and cold spots.

Dr Stephen Feeney, from the Department of Physics at Imperial, worked with a team led by Daniela Saadeh at University College London to search for these patterns in the observed CMB. The results, published recently in the journal Physical Review Letters, show that none were a match, and that the universe is most likely directionless.

Daniela Saadeh from University College London added: "You can never rule it out completely, but we now calculate the odds that the universe prefers one direction over another at just 1 in 121,000. We're very glad that our work vindicates what most cosmologists assume. For now, cosmology is safe."

See: http://www.earlyuniverse.org/does-the-universe-look-the-same-in-all-directions/

See: https://earthsky.org/space/our-universe-has-no-direction

See: https://universeadventure.org/big_b...se,look around, the universe will be the same.

See: https://phys.org/news/2016-09-scientists-universe.html

* The Copernican Principle is a basic statement in physics that there should be no ``special'' observers. For example, the Aristotelian model of the solar system in the Middle Ages placed the Earth at the center of the solar system, a unique place since it ``appears'' that everything revolved around the Earth. Nicolaus Copernicus demonstrated that this view was incorrect and that the Sun was at the center of the solar system with the Earth in orbit around the Sun.

The implications of Copernicus' work can not be exaggerated. His views challenged the literal interpretation of Scripture, the philosophical and metaphysical foundations of moral theory, and even common sense itself. The result was a massive opposition to his reported ideas. It was the slow, sure acceptance of the heliocentric theory by natural philosophers that ultimately quieted the general clamor, however the name of Copernicus is still a battle cry against the establishment in religion, philosophy and science. In later years with Freud, man lost his Godlike mind; with Darwin his exalted place among the creatures of the Earth; with Copernicus man had lost his privileged position in the Universe.

The lesson learned by future scientists is that if a theory requires a special origin or a particular viewpoint in order to work, then it is not plausible.

See: abyss.oregon.edu

The contributions of the Planck Satellite and the COBE, Cosmic Background Explorer, combined with the Hubble Ultra Deep Field** (where every dot and squiggle of light is a distant and therefore early galaxy), must be applauded for providing scientists and astrophysicists with the data and images necessary to show that the universe, on the largest scales imaginable, is isotropic. The sheer size and majesty of our universe is daunting but understandable and every article is a building block in our quest for knowledge.
Hartmann352

**

 

[Vladimir Leonov]

According to Friedman, the universe looks the same irrespective of direction and position. But I don't get it.

I believe that the universe is much larger than we see it in the most powerful telescopes. Moreover, we cannot look at the universe from the side in real time. Since we see that galaxies are flying with acceleration, there must be an expansion front for galaxies. We do not know the width of this front and its curvature. This expansion front should be spherical and it looks like a rubber shell whose thickness we do not know. This is a consequence of Einstein's theory and this fact was pointed out by other scientists.

Inside this spherical expanding shell is the visible region of the Universe. The visible part of the Universe is located inside this spherical expanding shell. Therefore, we perceive our universe as flat and homogeneous. It seems astronomers have already measured the curvature of the universe. But the main thing is that if we are inside the visible region of the Universe, which is much smaller than the spherical front of expansion, then galaxies should have different speeds and different acceleration of expansion.

Then we can have a map of the expansion of galaxies with vectors of the expansion rate of galaxies. Next, we can calculate from this map the curvature of the universe, the width of the expansion front and the direction to the center of the expanding universe and our position on this map. This work must begin to be done. It seems astronomers have already established that galaxies are expanding at different speeds. Then this fully confirms the spherical shape of our universe inside the spherical front of the expansion of which there are galaxies. It is like a rubber shell of a ball and inside this shell are galaxies. Therefore, we observe that all galaxies move away from each other when such a shell expands.

I am repeating that this is the generally accepted model of an expanding universe according to Einstein's theory. We have to make only one addition, that the visible area of the spherical universe is much smaller than its actual size.

 

[lauredurr]

I love astronomy, but there's one question I have.

If the universe is expanding, can't we measure that compared to distant galaxies and triangulate the origin point of the universe? That'd be cool.

 

[Lariliss]

The first thing to understand is what the theory of gravity is. The way Newton did: as a fixed, unchanging set of coordinates that you could place your masses down onto. When Newton first conceived of the Universe, he pictured space as a grid. It was an absolute, fixed entity filled with masses that gravitationally attracted one another.

Einstein recognized that this imaginary grid wasn't fixed, wasn't absolute. Instead, it was like a fabric, and the fabric itself was curved, distorted and forced to evolve over time by the presence of matter and energy.

Alexander Friedmann showed that if you didn't add this extra cosmological constant, and you had a Universe that was filled with anything energetic (e.g. matter, radiation, dust, fluid, etc.) there were two classes of solutions: one for a contracting Universe and one for an expanding Universe.

The mathematics tells about the possible solutions, but you need to look to the physical Universe to find which one of these describes us. Hubble was the first to discover that individual stars could be measured in other galaxies, determining their distance.

Nearly concurrent with this was the work of Vesto Slipher. Atoms work the same everywhere in the Universe: they absorb and emit light at certain, specific frequencies which depend on how their electrons are excited or de-excited. When he viewed these distant objects, other galaxies, their atomic signatures were shifted to longer wavelengths than could be explained.

The two ways to make sense of this:

1. Either all of relativity was wrong, we were at the center of the Universe, and everything was moving symmetrically away from us.
2. Or relativity was right, Friedmann was right, and the farther away a galaxy was from us, on average, the faster it appeared to recede from our perspective.

It's as though the fabric of space itself is getting stretched over time, and all the objects within that space are being dragged apart from one another.

The farther away an object is from another, the more "stretching" occurs. If all you had was a Universe filled uniformly and evenly with matter, that matter would simply get less dense.

But the Universe isn't perfectly even and uniform. It has underdense regions, like great cosmic voids where there are virtually no massive objects present at all.

On small scales, like the scales of living creatures and below, the electromagnetic and nuclear forces dominate. On larger scales, like those of planets, solar systems and galaxies, gravitational forces dominate.

On the largest scales of all, the expansion wins. The most distant galaxies are expanding away so quickly that no signals we send out, even at the speed of light, will ever reach them.

The superclusters of the Universe, stretching for over a billion light years, are being stretched and pulled apart by the Universe's expansion. In the relatively short term, over the next few billion years, they will go extinct. Still, the Milky Way's nearest large galaxy cluster, the Virgo cluster, at just 50 million light years away, will never pull us into it. Despite a gravitational pull that's more than a thousand times as powerful as our own, the expansion of the Universe will drive all of this apart.

Nearby, the Virgo cluster itself will remain gravitationally bound. The Milky Way and all the local group galaxies will stay bound together, eventually merging together under their own gravity.

Because the expansion of the Universe only has effect where another force (gravitational, electromagnetic or nuclear) hasn't yet overcome it. If some force can successfully hold an object together, even the expanding Universe won't affect a change.

The reason for this is subtle, and is related to the fact that the expansion itself isn't a force, but rather a rate.

If there's a force binding those objects together that's greater than the background expansion speed, there will be no increase in the distance between them.

The fabric of space itself may still be expanding everywhere, but it doesn't have a measurable effect on every object.

 

[Lariliss]

I love astronomy, but there's one question I have.

If the universe is expanding, can't we measure that compared to distant galaxies and triangulate the origin point of the universe? That'd be cool.

The thing to keep in mind with the Big Bang and the expansion of the universe is that it wasn’t an “explosion” like a detonation here on earth, with a definite center, and the universe spooling outwards into a pre-existing space.

- Not the whole universe is observed.

- Even from what we are able to observe now. If you take every point in space that exists now, and trace it backwards, all those points get closer and closer together until they reach a mathematical singularity. The Big Bang is, quite literally, everywhere, because the singularity would contain all energy, mass and space.

- There is quite a lot of evidence pointing to the idea of a very tiny universe at the very beginning of our universe; one of the more important being the detection of the cosmic microwave background (CMB). CMB is a fundamental glow in the microwave,any other observations you’re making at this wavelength will be in addition to the CMB.

 

[Hartmann352]

I believe that the universe is much larger than we see it in the most powerful telescopes. Moreover, we cannot look at the universe from the side in real time. Since we see that galaxies are flying with acceleration, there must be an expansion front for galaxies. We do not know the width of this front and its curvature. This expansion front should be spherical and it looks like a rubber shell whose thickness we do not know. This is a consequence of Einstein's theory and this fact was pointed out by other scientists.

Inside this spherical expanding shell is the visible region of the Universe. The visible part of the Universe is located inside this spherical expanding shell. Therefore, we perceive our universe as flat and homogeneous. It seems astronomers have already measured the curvature of the universe. But the main thing is that if we are inside the visible region of the Universe, which is much smaller than the spherical front of expansion, then galaxies should have different speeds and different acceleration of expansion.

Then we can have a map of the expansion of galaxies with vectors of the expansion rate of galaxies. Next, we can calculate from this map the curvature of the universe, the width of the expansion front and the direction to the center of the expanding universe and our position on this map. This work must begin to be done. It seems astronomers have already established that galaxies are expanding at different speeds. Then this fully confirms the spherical shape of our universe inside the spherical front of the expansion of which there are galaxies. It is like a rubber shell of a ball and inside this shell are galaxies. Therefore, we observe that all galaxies move away from each other when such a shell expands.

I am repeating that this is the generally accepted model of an expanding universe according to Einstein's theory. We have to make only one addition, that the visible area of the spherical universe is much smaller than its actual size.

Mr Leomov, you are absolutely correct when you mention that "...the universe is much larger than we see it in the most powerful telescopes."

That is because the light from the most distant reaches of the universe will never reach us due to its increasing expansion.

The universe's expansion is determined by something called the Hubble constant, which is approximately equal to 71, measured in the technically useful but conceptually confusing units of "kilometers per second per megaparsec*."

In more sensible units, the Hubble constant is approximately equal to 0.007% per million years -- what it means is that every million years, all the distances in the universe stretch by 0.007%. (This interpretation assumes that the Hubble "constant" actually stays constant over those million years, which it doesn't, but given that a million years is extremely short on cosmic timescales, this is a pretty good approximation. When we talk about the "distance" between two galaxies, we are referring to the distance between them right now -- that is, the distance we would measure if we somehow "pressed the freeze-frame button" on the universe today.


(Upper) The arrow points to the most distant galaxy in the universe, Gn-Z11. (Lower) Carbon emission lines observed in infrared. When it left the galaxy, the signal was ultraviolet light in the region of 0.2 micrometers, but it was redshifted and stretched to over 10 times that to about 2.28 micrometers. Credit: © Kashikawa et al.

If we only use the definition of distance given above, then the Hubble constant tells us that for every megaparsec of distance between two galaxies, the apparent speed at which the galaxies move apart from each other is greater by 71 kilometers per second. Since we know that the speed of light is around 300,000 kilometers per second, it is easy to calculate how far away two galaxies must be in order to be moving away from each other faster than the speed of light. The answer we get is that the two galaxies must be separated by around 4,200 megaparsecs (130,000,000,000,000,000,000,000 kilometers).

if you use a value of around 1.4 for z (the redshift), you get the required distance of 4,200 megaparsecs. Therefore, any galaxy with a redshift greater than 1.4 is currently moving away from us faster than the speed of light.


Sloan Digital Sky Survey: arrow denotes Z of 4.90.

The speed of each individual galaxy with respect to us will increase as time goes on**. If we assume that this acceleration continues indefinitely, then galaxies which are currently moving away from us faster than the speed of light will always be moving away from us faster than the speed of light and will eventually reach a point where the space between us and them is stretching so rapidly that any light they emit after that point will never be able to reach us. As time goes by (billions of years in the future), we will see these galaxies freeze and fade, never to be heard from again. Furthermore, as more and more galaxies accelerate past the speed of light, any light that they emit after a certain point will also not be able to reach us, and they too will freeze and fade. Eventually, we will be left with a universe that is mostly invisible, with only the light from a few, very nearby galaxies (whose motions are strongly affected by local gravitational interaction) to keep us company.

How we can possibly see a galaxy that is moving away from us faster than the speed of light! The answer is that the motion of the galaxy now has no effect whatsoever on the light that it emitted billions of years ago. We can easily see where the galaxy was not moving faster than the speed of light at the moment the light was emitted; therefore, the light was able to "outrun" the expansion of space and move towards us, while the galaxy moved away from us as the universe expanded. We can immediately see that once the light is emitted, the galaxy moved away from us faster than the point where the light was given off, and that this disparity will only increase as time goes on and the galaxy and light separate even more. Therefore, we can have a situation where the galaxy keeps on moving away faster and faster, eventually reaching or exceeding the speed of light relative to us, while the light which it emitted billions of years ago leisurely coasts on, never having to move across a region of space that was stretching faster than the speed of light, and therefore reaching us.

As time goes by (billions of years in the future), we will see these galaxies freeze and fade, never to be heard from again. Furthermore, as more and more galaxies accelerate past the speed of light, any light they emitted after a certain point will never be able to reach us, and they too will fade away. Eventually, we will be left with a universe that is mostly invisible, with only the light from a few, very nearby galaxies (whose motions are strongly affected by local gravitational interaction) to keep us company.

Galaxies at a distance of 4,740 megaparsecs and redshift of 1.69 are just reaching the critical point, while galaxies at a redshift of 1.4 are still emitting light that will eventually reach us.

* Megaparsec - a measurement of distance equal to one million parsecs or 3.26 million light years.

** Saul Perlmutter in 1997, Biography," ...we were analyzing our haul of 42 Type Ia supernovae at redshifts about z~0.5 and finding an odd result: the universe’s expansion was apparently dominated by a cosmological constant, or more generically a “dark energy” pervading all space, so it was actually speeding up – this didn’t fit with known models of physics! We announced this startling evidence for a cosmological constant at the American Astronomical Society January 1998 meeting. Because both our team and the team -including co-Laureate Adam Riess – independently announced matching results at conferences in the beginning of the year, by the end of the year most of the scientific community had accepted the extraordinary findings."

"When we started the project we thought that whatever answer we found would be exciting: if the universe were decelerating enough we would know that the universe is finite and is coming to an end in a Big Crunch; if not then we could establish that the universe is likely infinite in space and time, and the inflation theory would have a successful prediction. We could not have hoped for the actual outcome, a surprise that presents a new puzzle to fundamental physics."

See: https://arxiv.org/pdf/astro-ph/0310571.pdf

See: https://www.forbes.com/sites/starts...-8-billion-year-old-universe/?sh=f5971a940bcf

See: https://scitechdaily.com/astronomer...the-very-boundary-of-the-observable-universe/

See: http://curious.astro.cornell.edu/ab...g-faster-than-the-speed-of-light-intermediate

We have moved very far beyond the Earth centric universe of the ancients with it its series of crystalline spheres enclosing the sun, planets and the realm of the stars. We can observe the very edge of the visible universe, some 13.8 billion years in time and space as the universal expansion picks up speed as found by Saul Perlmutter, Adam Riess and their two teams. Having received the Golden Guide to Stars from my mother as a child, my appetite was whet for exploration and reading. Today, we, all of us, stand on the shoulders of giants as we stare into the oncoming infinite darkness resulting from the universal expansion.
Hartmann352

 

[Hayseed]

If the universe was expanding as theorized, we wouldn't see as many stars. I believe our science has made many serious errors.......not in the measurement........but in the interpretation of those measurements. Any linear oscillation....any and all......changes frequency thru a gravity gradient.

Our atomic clocks, still use linear oscillations for our clocks. It's so hard to fathom, why an educated person could believe that the rate of time can be changed. Time is omnipresent.

The light shifts seen......are caused by extreme gravity, not velocity.

Science even has the arrogance to compare and equate linear motion with angular motion. And this of course, is an impossibility.

A linear oscillation has four changes in acceleration during a period. And two complete stops. A rotation has but one and no stops. And that is only the acceleration of direction, not speed.

When we start using rotational clocks, we will see that time does not change. It does not change with acceleration or gravity.

AND...AND.....IF time does not change........ALL of our science falls apart.

As it should. The eclipse-star experiment and gravitational lensing are used as proof that space-time is real. Both of these dynamics can be explained with classical mechanics........just as light can be explained in the same manner. With omnipresent time.

A rotational clock.....the demise of quack science.

 

[Lariliss]

If the universe was expanding as theorized, we wouldn't see as many stars. I believe our science has made many serious errors.......not in the measurement........but in the interpretation of those measurements. Any linear oscillation....any and all......changes frequency thru a gravity gradient.

Our atomic clocks, still use linear oscillations for our clocks. It's so hard to fathom, why an educated person could believe that the rate of time can be changed. Time is omnipresent.

The light shifts seen......are caused by extreme gravity, not velocity.

Science even has the arrogance to compare and equate linear motion with angular motion. And this of course, is an impossibility.

A linear oscillation has four changes in acceleration during a period. And two complete stops. A rotation has but one and no stops. And that is only the acceleration of direction, not speed.

When we start using rotational clocks, we will see that time does not change. It does not change with acceleration or gravity.

AND...AND.....IF time does not change........ALL of our science falls apart.

As it should. The eclipse-star experiment and gravitational lensing are used as proof that space-time is real. Both of these dynamics can be explained with classical mechanics........just as light can be explained in the same manner. With omnipresent time.

A rotational clock.....the demise of quack science.

In my opinion, there are three issues:
1. Mixing several subjects into one. For instance, time existence, light existence, zero-mass. The science has its exact branches and subbranches and should be followed for correct comprehension, not messing theories, approaches and facts.
2. Confusing terms. Often, observation and conclusion, mass and zero mass, velocity, time, spin. Every time it should be given within context and with explanatory notices.
3. Confusing myths and evidences. Postulates, basic theories and still developing theories, paradoxes.

 

[Hayseed]

The whole and complete goal of science......is to unify all dynamics. Hello.

If the science you study, can not be related to all other science..........it is worthless.

This is one reason modern science can not unify. Look at the definition of energy. If we know what energy is.......why so many definitions. Same with mass. No one can define mass. Look at E=Mc2.

E and M have mussy definitions......OR very specific definitions for that equation.....but not others. This is not the way to organize science study. Energy is simply motion, any and all motion. Mass....is simply confined motion....the more confinement of motion, the more mass. The c2 dynamic....is what confines the motion. A perpendicular acceleration is needed to confine it.

Take any one branch of science, and the underlining theories will have contradictions......that you will accept. Every branch has these. These do not add.....they multiply.

And they puzzle you.

But classical mechanical science leave no contradictions and a puzzle that is solved. And cooperates with other dynamics.

The reason this is so hard to believe......is that you have been told, that you have been taught, classical physics. You have never been taught classical physics.

The only classical physics that you have been taught.......is the puzzles of long ago .......and as a basis for space-time and QM..........to explain "classical failures".

But there were no classical mechanical failures. Only intellectual failures.

It wasn't until the Parson's model in 1915,(before the discovery of neutrons) that the structure of sub atomic mass(and the entire and future periodic table) was explained. And only after that.....that the dynamic......the physical motion of emission......of that light could be understood.

Once the structure of a particle and the dynamic of light was realized........all and everything else......fell into place.

But no one is taught this. If time and space can't be warped, no one cares. The old professors of today were star trek freaks.

But there is a unity of all motion with omnipresent time. Physical Reality. Without time warps, to the dismay of many.

 

[Stan]

"Inside this spherical expanding shell is the visible region of the Universe. The visible part of the Universe is located inside this spherical expanding shell. Therefore, we perceive our universe as flat and homogeneous. It seems astronomers have already measured the curvature of the universe. But the main thing is that if we are inside the visible region of the Universe, which is much smaller than the spherical front of expansion, then galaxies should have different speeds and different acceleration of expansion."

Some of us find it difficult to think 4 dimensions. Spacetime is 4 dimensional. As you say "looking outward" is going forward in time. Nothing you can see is your "now". Space and time - in this universe -
are indivisible.

This has a consequence; our ability to understand a 4d sphere. The universe being spherical is a possibility of course, but it is not like a tennis ball being blown up with the galaxies on the inside of it. The galaxies in this analogy are on the SURFACE of the ball. Technically a sphere is simply the surface of the ball. The universe is (in the present) the surface of a 4d ball - a hypersphere cross section (?)

The surface of a sphere (in a hypersphere) is spacetime (correct me someone if I get this wrong) . we cannot view this model in all of its dimensions so we "drop" 1 or sometimes 2 depending on how deep we go. To imagine "space" in 3d we use the analogy of the of a ball surface. The inside of the ball does not exist in our "present". The universe we attempt to describe only exists in the present for each separate place (position) upon it.

The nice analogy to make things easy is to imagine our universe as the surface of a balloon as it is being blown up. If galaxies were dots marked on the surface you would see the distance between the dots increasing as the balloon got larger. They would not be travelling along the balloon surface !

So, if you wish to consider the "visible universe" it would be (so far as most opinion is concerned) simply a circular AREA drawn on the surface of the sphere.. The universe then would be a sphere whereas the visible universe would be a circular patch writ on the surface. NOTE that this describes a universe where no matter how long you travelled you could not leave the surface - it has a boundary but you can travel forever.

I think