From Nereid’s link: (Another endless field!):

“The conflict in science is thus not between theories and experiments but always between rival theories. The problem with sophisticated falsification, however, arises from the fact that it is always a series of theories that are consequently referred to as scientific or non-scientific and never a single theory on its own . . . . calling novel facts corroborated presupposes a clear demarcation between observational and theoretical terms and also that we have a straightforward situation in which no anomalies are involved – both decisions of convention as to what constitutes "basic" or "background" knowledge when undertaking the process. We have the additional difficulty of not knowing whether a potential falsifier refers to the theory being tested – the explanatory theory – or the underlying one(s) used to make sense of it – the interpretive theory.”

Is it because of difficulties like this that scientists come to use the word “model” now? (In the sense of “a schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics”.) It seems the model maker can dismiss as invalid the notion of falsification of what is only a description to be used for further study, like an always incomplete prototype. It is kind of like betting on both sides: you don’t win or lose, you just stay in the game - for fun? Is that cheating?

I believe going back to the roots of the LCDM model may be just as fruitful as tweaking at the new branches. Then you might find some rival theories which, since Ockham’s razor doesn’t seem to apply, might produce a rival model - for example, one which produces a constant universal expansion.

I don’t fully understand this. But (given hazy understanding) if the universal system generates patterns of increasing complexity, if it always produces more “ways to happen” by starting out homogeneous and isotropic, and clumping up into stars, planets, living systems, technology, etc. then it is entropic not only in a physical sense but also in a systematic sense? Or is the universal system itself not subject to grouping - for example, if total energy cannot be defined?

Whether or not some intelligent cause is required is left out of evolutionary theory. It also avoids falsifiability be excluding abiogenesis issues. Big Bang also avoids the first cause type of question, though Inflation was a necessary heavy-duty tweak (ratchet? ).

I think we all want them to, especially if they support our belief system. But, it would no longer be modern science, rather it would be a sophisticated tweaking of 17th century science. The remarkable success of modern science comes from its separation from the subjective realm. All theory tweaking should be objective, even if subjective motivational forces are at work.

I have a feeling I should not have brought it up. [It was stated wrong in the first place, though the correction nit was not been made. (For some reason, I could not edit it late last night.) In the sense I meant -- cart before the horse for humor sake -- entropy is "attracted to" hot regions. I meant to say minimal, or negative, entropy (but even this is confussing). Sorry.]

Only a nut would speculate that it was cold first. So, allow me to retreat to my shell.

Regarding entroyp, look to Ken for someone on top of shoulders, and me on top of toes. I like to think in terms of irreversibility of a process that entropy addresses. Complex systems can develop using energy but at the expense of a limited energy source. Yet, to box the universe up into a closed system is a box too big to buy.

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Lighten up! This is a stellar board!

That's why I prefaced my statement with the words "to me". You are using a different meaning of the word "purpose" than the one I am used to.

I disagree, because it fixes a starting point, a foundation if you will, that is not observationally derived and therefore may be prejudicial and misleading.

Assume, for example, that Darwin had presupposed and written into his theory that the zygote was incapable of passing inherance through the genes; and his basis for this assumption is that a soul is an absolute prerequisite for any physical being. An axiom of this nature could have precluded the conceptualization of, and the funded search for DNA.

On the other hand, if you want to argue that a telelogical view can be derived from existing evidence (such as an extension backward to-and-beyond the BB.), I suppose such a prospective is hard to defeat...until that is, the BB is driven out of the picture by new evidence.

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jwj

It's a big universe out there...is it really unwinding, really burning out?

Entropy is really a local concept, like energy, meant to apply to closed systems in a particular (small) region of space and time. Extending these concepts globally is quite tricky, generally what you do is enter the "comoving frame" and just add up the entropy that each comoving observer sees. You might think that having matter all spread out has more entropy than having it be clumped, but this is not actually the case because of the role of gravity. Gravity means that you can get energy out when you let things contract, and that energy goes somewhere that it can actually increase the entropy. If you did not take that into account, you would think that gravitational instability reduces entropy, but it increases it when you keep track of all the energy released, and that's why it happens spontaneously-- there are simply more ways that you can have stars and planets plus the associated released energy (and all the new things that energy makes possible) than you can have homogeneous uniform particles. That's all entropy ever really means, although it gets very tricky in general relativity so I do not extend this to the entropy of black holes or the global entropy of the universe, just to the local entropy of normal stuff that is comoving with the overall expansion.

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Originally Posted by Jerry I disagree, because it fixes a starting point, a foundation if you will, that is not observationally derived and therefore may be prejudicial and misleading.

Agreed, which is why I stated it is limited in its objective scope. Teleological viewpoints might be helpful, or they may be counter to doing good science. I suspect YEC may serve as an example of the latter. [My midnight post was not very clear on this, I fear.]

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Assume, for example, that Darwin had presupposed and written into his theory that the zygote was incapable of passing inherance through the genes; and his basis for this assumption is that a soul is an absolute prerequisite for any physical being. An axiom of this nature could have precluded the conceptualization of, and the funded search for DNA.

Yes. The one he eventually offered, pangenesis (?), was bad enough, and may have been harmful to his already unaccepted theory. However, in your example, it might have helped him with some of the more staunch [hardshells] Christians which actually supported his theory because it connected with suffering and judgment, as opposed to the mainstream theories of the day.

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On the other hand, if you want to argue that a teleological view can be derived from existing evidence (such as an extension backward to-and-beyond the BB.), I suppose such a prospective is hard to defeat...until that is, the BB is driven out of the picture by new evidence.

Yes, in a night game, when a homerun ball exits the park, many will speculate on who's car will suffer.

My personal view is that science should be seen as a powerful tool to tweak religious, philosophical, and teleological views, the opposite of earlier centuries. Yet, some are holding the pendulum from this reversal, but I'm getting off topic

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Lighten up! This is a stellar board!

This is absolute insanity!!!

Science question?...Does the Universe have initial conditions (assuming finite but unbounded) that orginated Hot or Cold?

Through preconcieved ideas, Laws, and 'supposed observation', and of course a little hypothesis, let's just explore Option "A", and scientifically define Option "B" as Impossible/Woo Woo/Career Suicide!!!

Yeah, there is some 'REAL" scientific Objectivity for YA

I'm not picking on you George!

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RussT
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Everything is, as it should be, otherwise, it wouldn't be!

No problem, I know that the odds my humor will hit just right with everyone are not all that great. The nut, of course, was me and it was me that suggested it could be cold. Yet, given my extensive lack of formal physics, to expect that to be swallowed by many here is a bit.... nutty. I certainly wouldn't be surprised if a cold state of some superstuff preceeded the first Planck time unit. Has any eminent scientist also suggested such a state? If so, are there theories, which meet the requirements of science to be a scientific theory, on the table for pre-Planck time? If not, and to, hopefully, get back on topic, are they popular because they appear tweakable in the reasonable future? Can theories be considered acceptable and tolerable (subjective sense) when they are found with an intolerable conflict (objective sense)?

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Lighten up! This is a stellar board!

Actually rather than thinking about cold and hot, my thought was that the universe would ‘naturally’ begin with no temperature. Then there are two possibilities: it can warm up or cool down. The idea that the science doesn’t address an initial condition of extreme heat is one reason I don’t like the hot big bang idea.

But at present the science most critical to the religious nuts is pointing toward universal doom (at least in the media). How does that work as a religious etc. tweak? And on the other hand, if there is a ‘natural teleology’ to universal evolution, wouldn’t that be a reasonable motivation to seek a scientific model of universal evolution that might indeed provide such a tweak?

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How does that work as a religious etc. tweak?

I suspect it would be similar to our discussions for science tweaking. When new evidence comes along that shows falsification for a given interpretation, than a new interpretation, tweak, will be sought. Of course, science, with its exploratory nature, is much more open and less viscous to change. For an individual, or worse for a group, to accept the idea of a falsification of their belief, even if just a small segment of their belief, is very difficult.

Heliocentricity tweaked certain interpretations of biblical passages, though not many. In the case for an immovable Earth argument, if taken relative to a man or woman, it is not that hard to see it as essentially immovable.

Any tweak in a specific interpretation might only be done when the respective theory of science reaches a level of acceptance by the religious group. This acceptance may go beyond the level of naive falsifiability as the science theory must appear to have been fully stable and fine-tuned.

It is interesting to see how fast the Church scholars, Jesuits, were to recognize the validity of Galileo's results, thus changing to another model -- the Tychonian model. They saw the Copernican model unresolved on the issue of parallax (an intolerable conflict), Tycho's required no parallax and he had resolutions to 1/2 arcminute for some stars (twice the resolution limit of the eye). Then there were the other religious, political, social, philosophical, commercial, etc. issues on the table for them, and at a time of great unrest. The discovery of parallax, a prediction in the Copernican theory, changed things dramatically, and the original intolerable conflict is gone.

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And on the other hand, if there is a ‘natural teleology’ to universal evolution, wouldn’t that be a reasonable motivation to seek a scientific model of universal evolution that might indeed provide such a tweak?

It would be a tweak for some and The Ratcheting (Stephen King sized), but not a break. Catholicism alone has “tolerable acceptance” of evolution.

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Lighten up! This is a stellar board!

The whole point is, there is Option "A" Hot, or Option "B" Cold, or as ngeocorrectly pointed out, No Temperature (But that winds up being absolute zero, the way things are currently defined) so the Universe either warms up OR cools down.

Now, how can it be considered scientific, for a theory to hypothesize HOT and NEVER even consider Cold...or warming up rather than cooling down???

SO, the whole entropy question is only being conidered ONE WAY!

The Causality is only being considered ONE WAY!

Time is only being considered ONE WAY! and "Flipped" inside the Event Horizon!

Yep, they just ASSUME it started with Gamma Radiation, and then say...since the universe started at T=0, and there was nothing before the universe started, saying anything about the before is "UNSCIENTIFIC"/Woo Woo/Career Suicide.

But actually it is a little different than that, because the String/"M" people can talk all they want about "Parallel Universes", or any kind of multi-verse (Inflationary), as long as they don't mess with the Big Bang hot beginning.

The point is, if there is another singularity scenario that can be shown to have evidence for another initial condition scenario that 'might' start of 'cold', shouldn't it be allowed to be explored?

again, how can "SCIENCE" be limited to only one option when there are two

Tim Thompson just linked a whole bunch of alternative stuff...(I can't find it right now) But my point would be the same. They are ALL 'forever universe' models. SO the only competing modles to the Big Bang don't say anything about initial conditions of a finite but unbounded universe! Just saying anything always existed, doesn't describe any mechanisms for how it got here, but supposedly 'somehow' eliminates the creation ex nihilo...beats me???

Like ngeo said, everything has a cause and effect, just as we now understand how oxygen is created by photosynthesis!!!

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RussT
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Everything is, as it should be, otherwise, it wouldn't be!

To the OP:

In my experience, I was once working on a model for the high temperature behavior of some complex materials. This model didn't really say anything about the underlying physics of the material damage mechanis ms. It was basically a large compendium of fudge factors organized in a pretty convolution integral.

Because of the nature of the model, if you ran certain tests, you could pull out the fudge factors and get a model of how the material deformed, but we didn't think for a minute that this model provided us with the ability to generalize to different materials, or to operate too far out of the scope where the factors were derived from.

It seems to me that there are two classes of theory here (or perhaps a spectrum). Certain theories are very powerful, because they amount to a realization of something fundamental about the way the world works, and enable predictions to be made, and can reproduce the results of all prior experimental experience related to them. It seems these relationships are often expressed in terms of invariants - conservation of mass and energy (and lately, mass/energy), conservation of angular momentum, conservation of linear momentum - if you have a few of these, you can usually break down a sytem, apply the equations, and get back it's behavior.

Others tend to be much more situational. If you have some complex system and you poke at it, and tweak it, and generate graphs of the response, and curve-fit to the graphs, you may end up with a model of how that system works, but how about others? What happens off either end of your graphs, in the areas where the system wasn't tested? Do your empirically derived factors still work? Do your curves still fit?

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http://amssolarempire.blogspot.com

The basic question is one of approach.

The scientific method appears to be one of mathematically matching observations to fit the current theory. The idea of producing a model to fit observations appears to be ATM.

Where is a tweak or adjustment required to continue fit or when is it time for consideration of a new model is the question. So far the numbers by scientific method seem to favour tweaks.

Should it become the case that tweaks are the only option that mainstream science uses, which is an option, then I could just as easily rely on any organisation that commands total devotion to unchanging dogma for knowledge.

No, that's nonsense. I have never seen a single ATM idea that even came close to "producing a model to fit observations", and that is precisely what some people have spent a lot of their time demonstrating over there. You have simply inverted the way real science and ATM science actually work, for your own convenience.
There is no "time to consider a new model"-- new models are considered all the time. But they are not interesting until they fit the data better with fewer free parameters or greater conceptual simplicity or generalizability. This quite rarely happens in real science, and I've never seen it in the ATM portions of this forum.

Every observation involves some amount of interpretation. In that sense, you do try to fit what you observe into the frame of reference of your current knowledge. Everybody does this in their lives, not just scientists.

Some people even claim, because of this, that the distinction between observation and model is ficticious: everything is a theoretical construct, even what we call measurements and observations. I happen not to be in this camp, because I think that if all is reduced to theory then it makes no sense to speak of objectivity, and science is reduced to "just another belief system, as valid as any other".

Ignoring those postmodernist perspectives, I would say you are exactly wrong: the scientific method attempts to do the opposite of what you said, which is to let the data speak for themselves as much as possible, and only at the very end of the process to introduce a model that fits the observations.

But you have a point in that in practice there are usually three elements in the process, rather than two: the observations, the new tentative model, and the "tried-and-true" orthodox scientific consensus.

To "read" the obsevations, you need to interpret them in light of some sort of context, which is usually provided by the leading theories in the scientific consensus (what Kuhn called the "paradigm"). For example, when cosmologists nowadays measure a redshift in a distant galaxy, they will normally interpret it as an indicator of how fast the galaxy is receding from ours. Is this information contained in the measurements themselves? No; it's an interpretation based on the scientific consensus.

All this seems sensible to me. While there may be paradigm shifts in science, they don't happen every day, fortunately.

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"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

That's not quite exactly true, but it is a common misconception so I'll just nitpick a moment to clear it up lest it get further vulcanized. Consensus cosmologists view redshifts as a kind of integrated measure of the total amount of expansion that has occured since the light was emitted. Had there been a complicated history of expansion and even contraction, perhaps alternating, through which the light had propagated, then it would all be encoded in that redshift-- not just the current rate of receding. We don't think there has been contraction, but it does appear that the rate of expansion has changed, and that is encoded too. There really is no meaningful way to interpret "how fast the galaxy is receding", which sounds like a current rate, because the core issue is actually "the total factor by which the distance to that galaxy has increased since the emission of that light", which is an integrated effect.

Thank you for the correction. I hope my point is still clear, in spite of the inaccuracy of the example I used.

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"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

You may enjoy the forum in which that essay is posted, ngeo; it seems there are threads (and members) there discussing some of things you seem to be interested in, things which are beyond the scope of BAUT.

A few words on models and tweaking: in modern astrophysics (and cosmology), there are very few theories - General Relativity and theories concerning the strong and electroweak forces. However, these theories require specific values of some parameters, and, as of today, there is no way to determine those values other than 'by hand'. Depending on how you do the counting, there are ~25 such 'constants'.

Getting from the theories, and their constants, to what we actually observe is not easy. We can't put a universe in a test-tube, hold all things constant except the one property we want to look at, and test.

So we develop models - this much of that, connected to this other in these ways, ignoring these aspects, etc. We can then look at the outputs of the models and see how well they match the real universe, as seen through telescopes of various kinds.

Of course, what we see through telescopes is just photons, so there are several layers to the interpretation - what we're matching model outputs to are themselves models! But different models.

In the sense of your question about model makers and falsification, it's not so much that falsification is dismissed as that it's an unproductive way to do science - if you can find a way to tweak the model so that it fits, good; if not, then also good! The point is that without a (sufficiently detailed) model, you can't test anything. And only after you've done lots of testing and tweaking would you be in a position to say 'the mismatch between model and observation is intolerable'.It may be just as fruitful ... but, AFAIK, no one who's tried any alternative - whether from the roots or from left field - has had any success at all.

Yes, it's just a detail-- the point remains that observations by themselves, or theory by itself, is a very incomplete form of science. It is the synergy of the two that gives science its wings. Whether we think of them as different things or just two halves of the same man-made coin, science can only fruitfully be thought of as an interaction between our minds and our environment.

my bold

Even model makers need a start point. To make that point I take just an example of adding a dimension to a point.

People like straight lines and nature likes circles. I forget who said there are no straight lines in nature. I think it was Dr Carl Jung. If you put a pencil on a point a straight line is an outside dimension. If you start at the point and pull both ways it is still a straight line, one way forwards and one way backwards, a time-line.

This is mankind's a = mx + b a line
This is nature r^2 = x^2 + y^2 a circle

Diagram starting point.JPG

Take the formula in say "paint" for a circle and pull from a point you get a circle. Instead of a straight line you get a circle or if you could view a virtual 3D technique a sphere. In one movement thus one dimension you have a round shape. ATM aside what if 'mans' most basic premise is that he forgot to look at nature when trying to describe it.

Let's look at nature, then. What evidence is there that what you have just described has happened?

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"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

The sun round rather than cubic, orbits are round, galaxies are round. Maybe I can't explain perfectly but podhode movement is round.

The point is not that it links to anything specific, so I apologize in advance for any offense caused as the first sentence, it is my sense of humour (a bit of light hearted teasing).

I am not trying to ascribe it to observations as that would be ATM and wrong to bring up. It is right back at basics before even being applied. Can a circle or sphere created in a one directional movement given the right parameters be called one dimension.

Yes it sounds strange but that is because it is, a point can be jiggled around and so describe movement and so can any point on the edge of the circle.

Thank you, Nereid, that is an interesting place. And you are way too smart!

I don't understand most of this part of your post, RussT.

However, you did ask a question that seems directly relevant to this thread, so I will try to answer it.

The question seems to refer to the number of possible alternative cosmological theories. A priori, there is no reason (that I can think of) why there should, or should not, be any particular number of these ... there could be two, ten, ... or ten billion.

However, as I said in my earlier post (replying to one of ngeo's), AFAIK, there are no cosmological theories that have legs ... other than LCDM-based ones.

(Note that 'LCDM-based' includes models in which Lambda is zero, in which there is no CDM, and so on. I.e. these are quite general, and incorporate only GR and certain minimal aspects of theories on the strong force (such as QCD) and the electroweak force).I really don't follow you here ... AFAIK, stuff that incorporates physical regimes far beyond those in which GR and the Standard Model (of particle physics) have been tested are rather speculative, rest on (or incorporate) a theory of quantum gravity (such LQG or String/M Theory), or both.

It would certainly be nice if any such were to be developed sufficiently that observational tests may be possible ... and I think some ideas based on one or more varieties of LQG may well be (as I think you know, the String/M Theory landscape is, today, still so poorly characterised or constrained that no such possibilities exist).

The implication here, is that the 'non ATM' approach has produced a single tapestry. It has not - whatever type of thread you try to weave though inflation and every other black hole always leaves a lot of unconnected partitions.

Once again, it is/can be reduced to a matter of demarcation: How many of the holes need to be patched to produce a superior model, and how many new holes should be allowed to be torn into the fabric?

Without a clear understanding of the limits in the current models, we will never define unresolvable conflicts, and never be able to properly evalute competing solutions.

An example here, would be the simplest of string theories; increasing the allowed number of dimensions from four to eight. With a few extra dimensions, it is easy to bail out of the inflation problem, it is even easy to spindle out some tractor beams that increase the rate of expansion. As many have pointed out, such multi-dimensional solutions are meaningless unless they are also testable; which brings us full circle back to the current standard model: As our observational data does not demonstrate the expected slowing in the rate of expansion, did the theory pass or fail the test? As the sensitivity of the search for gravity waves continues in the null result, when is a point of demarcation reached? Or can another 'wave dampening' parameter (as has already been proposed!) be introduced?

How does one compare two very complex solutions, each with 26 or more independent parameters and declare one or the other more right or wrong?

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jwj

It's a big universe out there...is it really unwinding, really burning out?

I've read this - thrice - and still have only the faintest inkling of what it says - can you clarify please?

In particular:
* which parts of the LCDM model, as used by Spergel et al. (the link is to the arXiv abstract) contain orphans ("unconnected partitions")?
* how many 'holes' are there, in the Spergel et al. paper, which need to be 'patched'?
* specifically, which of the six parameters is either a hole or a patch (or both)?
* what on earth (or not) do string theories have to do with any published cosmological models?
* where did you read that the current (null) results for detection of GW are inconsistent with the entire superset of LCDM models in papers such as Spergel et al.'s?
* what "two very complex solutions, each with 26 or more independent parameters" are you referring to?

For avoidance of doubt, my impression is that your post contains a (hopelessly?) tangled mishmash of misunderstood observational results, theoretical (near-)speculation, and wishful thinking. I do not, in any way, intend to imply that there is no basis for what you write in your post; merely that I, Nereid, cannot make head nor tail of it.

SCIENCE has 2 choices...

Either "A"...the universe is operating as a 'closed system'

OR, "B"...the universe is operating as an 'open system'

IF Massive Black holes 'really' are physical entities, with Event Horizons and singularities...

Then materials can Either "A" Not go 'through' them causing the universe to be operating as a 'closed system'...

OR, Materials CAN "B" go 'through' them causing the universe to be operating as an 'open system'

'You guys/gals'/mainstream/the 'Pros' on this forum, have repeatedly told many many people that the universe doesn't have to conform to the way you 'think' it should be operating!!!

"IF" the Universe is operating as an "OPEN SYSTEM", with materials going 'through' the Massive Black Holes.....................Mainstream Science would NEVER even have a clue as to what that would mean, because mainstream SCIENCE has defined/forced their/its concept of how the universe should be working, by making LAWS without having ALL the information ("Exotic Matter), and actually making the answer to how the universe works IMPOSSIBLE/Career Suicide!

The Big Bang postulates 'energy from the outside' 'somehow' initiated a beginning, BUT in ALL the definitions/arguements........insists that talking about any other 'outside' scenario, besides FLRW EFE 'expanding' solutions are WOO WOO!!!

Either the universe is working with materials going 'THROUGH" Massive Black Holes OR it is not...how can anyone say we are doing science if only Option "A" is allowed?

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RussT
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Everything is, as it should be, otherwise, it wouldn't be!

Where do numbers stop, where do models stop. Perhaps when they don't help or can't get off the ground.

There comes a time when even models exceed their usefulness. For months I have had a model in mind than extends "M" theory beyond super string to the relative world.

This remains the best forum for announcing ideas particularly for relativity and in particular thanks to you Nereid I have tried to form better numbers. Now I mainly give others a few encouraging words and back away if it looks like it is not wanted.

On M.U.F.I.N (multiple universes finite in number) strange connotations like "M" but without progress on earlier work too controversial.

Sometimes it is like you would be prepared to present an idea to the devil himself if it would help but how does one know it it is helping one person or a hundred million people? Even on numbers of a hundred million a year it is a difference the world could handle and still have a large and viable population in a hundred years time. Where does one stop.

I think you have missed the way science works. No one asserts that an open universe is not "allowed", of course it is allowed. The issue is, is it required? Science never makes suppositions except when they are required to make progress. So far, no observation requires we assert that the universe is open, so we do not assert it. It's just that simple-- science is a toolkit, but we only take out a drill when we need to drill something. If and when some observation is more naturally interpreted as the universe being open, then this will become the mainstream notion. At this point, there is simply no such motivation. Can you describe an open scenario that agrees better with all our observations than a closed one? If not, you are holding a drill with nothing to use it on.

Just to add to what Ken G wrote ...

If you, or anyone else, wishes to develop an alternative set of cosmological models, based on assumptions of 'open', or 'cold', or {insert new idea here}, then you are welcome to do so.

For your alternatives to play well, they need to meet the same criteria that the LCDM models have already been shown to meet: internal consistency; consistency with GR, QCD, and electroweak theory*; and consistency with the relevant astronomical observations.

There are, no doubt, a great many ways you could do this.

One, possibly quite powerful, way would be to focus on 'anomalies' - cosmologically relevant, good observational results which LCDM models have an awkward time accounting for (or fail to account for). Perhaps it might be the Pioneer anomaly, or neutrino oscillations, or 'the axis of evil', or globular cluster velocity dispersion 'curves', or primordial ³He or ⁶Li abundance, or ...

*Or some replacement/extension of one or more of these - consistency would then be required with a much wider range of experimental and observational results ...