Pausing to rest for a moment at *New Scientist:*

You might think that the universe started with a big bang. Ten years ago, that is what I thought too. But then I came to realise that the issue is far from settled. Pursuing this question prompted me to change the tack of my career and become a cosmologist, even though I had just completed a PhD in the philosophy of quantum physics. What I have discovered since then supports a radically new response to the question that irked Augustine – what came before the beginning? The answer, thrillingly, may be that there never was a big bang, but instead a universe with no beginning or end, repeatedly bouncing from an epoch of contraction to expansion, and back again.

Anna Ijjas, “What if there was no big bang and we live in an ever-cycling universe?” atNew Scientist(paywall)

The war on the Big Bang as an actual beginning can never stop and never will. The main question is whether the war on evidence will settle the issue by allowing whatever view would prevail most “thrillingly” to stand in for science.

Evidence isn’t really at issue; many people today need a universe other than the one we live in and they will theorize their way to it, if only in their own imaginations. But “science” will cooperate if science knows what is good for it.

Experimental physicist Rob Sheldon, our physics color commentator, writes to say,

Anna Ijjas was a post-doc for Paul Steinhardt, and in the past 5 years they have written a number of papers very critical of “inflation”. It’s ironic, because Steinhardt was one of the 3 founders of inflation theory. Just last week we had a mention of his 2017 SciAm blog describing the death of inflation. The problem is that no one knows how to solve all the designed features of the universe without inflation. Evidently Steinhardt and Ijjas came up with a solution (which turns out to be 40 years old), the “Big Bounce”. They argue that all the smoothness of the universe produced by inflation, can also be produced by repeated expansion-contraction-bouncing expansion-contraction-bouncing expansion…

Here’s their 2019 cyclic universe paper:

Abstract: Combining intervals of ekpyrotic (ultra-slow) contraction with a (non-singular) classical bounce naturally leads to a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically, but the scale factor grows by an exponential factor from one cycle to the next. The resulting cosmology not only resolves the homogeneity, isotropy, flatness and monopole problems and generates a nearly scale invariant spectrum of density perturbations, but it also addresses a number of age-old cosmological issues that big bang inflationary cosmology does not. There may also be wider-ranging implications for fundamental physics, black holes and quantum measurement.

(open access)More.

Sheldon also offers some thoughts on the paper:

Two points:

1) What is really recycling is not the universe, but this theory.

2) None of the previous objections to a “Bouncing Universe” are addressed, rather it is now seen (by Ijjas and Steinhardt) as less objectionable than the justifications for inflation, multiverse, etc. In other words, its new-found attraction is simply by comparison to all the other badly aging theories out there.

*Note:* Rob Sheldon is the author of *Genesis: The Long Ascent.*

*See also:* The Big Bang: Put simply,the facts are wrong.

and

What becomes of science when the evidence does not matter?

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“And if there were a pre-Big Bang state and you had some bounces, then that fine tuning (for entropy) gets even finer as you go backwards if you can even imagine such a thing. ”

Dr. Bruce Gordon

The recycling universe conjecture has also been totally crushed by the hard evidence for a ‘flat’ universe found by the ‘BOOMERANG’ experiment as well as other experiments.

Verse

nice article.

the same reason so much push back vs a big bang to start is having to deal w/ a start, is a start attests to The One supernatural-designer creator aka G-d of Abraham, just as described by Moses to begin with.

all the empirical observations do align with a start, by one hyper-dense miniscule area that contained the entire physical universe, than hyper rapid cosmic inflation expansion, into the mature size and density universe, by the end of that cosmic expansion, relatively early in the history of the universe. So if you are into steady state oscillation, as a PhD thereon on our team is, we are stable on the first plateau. reference the YeC Moshe Emes series for Torah and science alignment volume II aka ‘SPIRAL’ http://www.amazon.com/dp/B07DP4TBZ5

From a purely objective point of view, there is the FACT that chemical elements appeared in stages, with the “creation” (construction?) of lighter elements (hydrogen & helium) first, and stuff like iron showing up MUCH later. That is, the chemical elements “evolved”.

And so 1st and 2nd generation GALAXIES, not stars but entire galaxies, CANNOT produce Life because they don’t contain “heavy” elements like carbon and iron. It was only with the appearance of 3rd & 4th generation galaxies that there were enough heavy elements around to allow the formation of things like H20 and CO2. Similarly, the newer galaxies, which formed from the 3rd & 4th junk, have TOO MANY heavy elements (radium, uranium, thorium, etc.) to allow life to SURVIVE. If the amount of thorium in Earth’s crust was only SLIGHTLY higher, the crust would MELT and Earth would have no solid ground.

So, any Cycling Universe should have similar problems with each new instance BEGINNING with too much stuff heavier than helium. And we can observe galaxies in our instance of the universe that we can reliably label as lacking heavy elements.

So, as the song says: First, when there’s nothing…

https://www.youtube.com/watch?v=ILWSp0m9G2U

Vince

Wouldn’t cyclic universes have a problem with junk being left behind on top of the fact that it also might produce effects that could be seen throughout its entire existence?

I only asked this question because I can’t imagine that it would be able to perfectly pull back every particle that it had spewed out in the first place

It would leave litter

Or that’s what I would think I could be wrong

As to the evidence for a flat universe, (which, as mentioned in post 1, was a major line of evidence that helped rule out the conjecture that we live in a ‘bouncing’ universe), there are some further interesting consequences, besides overturning the ‘bouncing universe’, to the universe being exceptionally flat.

One consequence to the universe being exceptionally flat, the tiny temperature variations in the Cosmic Microwave Background Radiation (CMBR) correspond to the largest scale structures of the observable universe. “If the universe was curved in any way, these temperature variations would appear distorted compared to the actual size that we see these structures today.”

Moreover, the large scale structures of the universe, (i.e. quasar and radio galaxy distributions in the universe), reveal a “surprising rotational coincidence for Earth,”

Moreover, when they ‘smeared’ and/or ‘averaged out’ the tiny temperature variations in the CMBR, they were able to detect the anomalies in the CMBR which ‘strangely’ line up with the earth and solar system.

At the 13:55 minute mark of this following video, Max Tegmark, an atheist who specializes in this area of study, finally admits, post Planck 2013, that the CMBR anomalies do indeed line up with the earth and solar system

Here is an excellent clip from “The Principle” that explains these ‘anomalies’ in the CMBR that line up with the earth and solar system in an easy to understand manner.

In other words, the “tiny temperature variations” in the CMBR, (from the large scale structures in the universe, to the earth and solar system themselves), reveal teleology, (i.e. a goal directed purpose, a plan, a reason), that specifically included the earth from the start. ,,, The earth, from what our best science can now tell us, is not some random cosmic fluke as atheists had presupposed.

On top of all that, in the following paper, Robin Collins found that photons coming from the Cosmic Microwave Background Radiation (CMBR) are ‘such as to maximize the intensity of the CMB as observed by typical observers.’

However we turn it we keep coming back to an uncaused first cause or an eternal “something” Neither is particularly acceptable but, for the life of me I can’t think of an alternative. We must be missing something.

If, as theists claim, God is an uncaused being, why can’t a cycling universe be uncaused.

Brother Brian@ 7Good question. And of course a cycling universe would be more environmentally friendly than one belching pollution out of a tail-pipe.

BB,

>If, as theists claim, God is an uncaused being, why can’t a cycling universe be uncaused.

Because a material universe (cycling or one-time) ultimately requires an explanation that lies outside of the material. (“Where did the entire system come from?” is just one question that needs an extra-material answer. At least for the curious.) It’s not as obvious that an immaterial being needs a cause.

The uncaused effect. That will be a boon for science.

EDTA

Why? Just like God, if the universe, in a cycling fashion, always existed (is eternal), it doesn’t need a cause.

>if the universe, in a cycling fashion, always existed (is eternal), it doesn’t need a cause.

Something has to be responsible for the cyclical system as a whole existing, even if one can conjure up an explanation for why it doesn’t run out of energy. (It can’t be because we’re close to the “start”, because it supposedly didn’t have one.)

BB @ 7:

“If, as theists claim, God is an uncaused being, why can’t a cycling universe be uncaused.”

Well, let’s assume it can. That means uncaused causes are possible.

When we boil reality down to its basics, we know that it seems to consist of two ‘ontological primitives’:

1) Matter

2) Mind

The question then is, ‘which of these is the uncaused cause from which the other derives?’

At the moment, the consensus of the Academy is that mind emerges from matter.

However, there are many problems with this theory, much of which has been discussed on this Forum.

The alternative, that matter emerges from Mind, is gaining traction. Some heavy hitters have held this view, notably Max Planck: “We cannot get behind consciousness. I regard matter as derivative from consciousness.” Contemporary scholars who postulate Mind as the ground of all being, include astrophysicist Richard Conn Henry (see his famous – or maybe infamous – essay in Nature, ‘The Mental Universe’, in which he proposes that monistic idealism is an inescapable conclusion from the scientific evidence) and double-PhD philosopher/computer scientist Bernardo Kastrup.

So yes, you could have always-existing matter. But once you admit the possibility of uncaused causes, the opposite pole – always-existing mind – becomes equally likely. The old canard ‘Who made God?’ is then disposable; nothing needs to have made God if one accepts the possibility of uncaused causes.

It then becomes a matter (pun not intended) of evidence and Ockham’s Razor. And Conn Henry will tell you (and prove to you with mathematics) that the evidence favours uncaused Mind, while Kastrup will demonstrate that uncaused Mind is a more parsimonious explanation for existence than uncaused matter; William of Ockham would approve.

F/N: An oscillating universe model faces ever-mounting entropy, degradation of energy concentrations, leading to it not being plausible that an eternally cycling cosmos as a whole is the root of reality. KF

PS: It is ever so interesting to see refusal to cogently address logic of being in action. There are candidates to be as suggested. Some are impossible of being as core characteristics are mutually contradictory, e.g. square circles. Others are possible i.e. would be in at least one possible world. If in some but not others, contingent and so dependent on external enabling causes, e.g. a fire. If in all, then framework for a world to be, called NECESSARY BEING (the term BB dodged). Where, if N is a serious candidate necessary being, either it is impossible of being or it is possible — and as framework for any world to be — actual. Utter non-being (= no reality) has no causal powers and were such ever the case no world would exist. That a world is implies a necessary, world-framework independent being exists as causally adequate framework for this and any other world. God is the most serious candidate for many good reasons (start with us as morally governed creatures and what adequately grounds such), and either is impossible of being or is actual. Given state of issues, we may freely summarise that there is no cogent reason to see God as impossible of being, so there is every good reason to hold that he is actual.

CB

Not if the universe is eternal. If it had no beginning then it requires no cause. The same argument used for God.

KF

Yes, entropy etc. is the law for an expanding universe. But if our universe were a contracting one, would this still apply? I doubt it.

The universe is physical, consisting of matter and energy. God is not. Only a fool would try to compare the two.

Brother Brian is a desperate troll.

BB, whether a system is expanding or contracting the degradation of energy connected to temperature will continue. That is a microscopic process, recall statistical thermodynamics (a component of Chemistry as well as Physics) and Prevost’s theory of heat exchanges. Next, I did not say that the concept of a wider cosmos as a whole is not put up as a candidate world root necessary independent being, just that such is not plausible. Heat death and its effect on oscillating models is one thing. Another is the basic logical challenge of traversing a past explicit or implicit infinity of time in successive finite stages, a supertask. We can have an ever-growing potential infinite going forward (which always only attains a finite value of states) but traversing such from the past to now is a different problem. Regardless of Russell’s refusal to see. KF

PS: No composite entity made up from independent proper parts can be necessary. The composition implies contingency, as does having a beginning or end.

KF, the heat death concept was contingent on an ever expanding universe.

BB, I used it more generally to speak of energy degradation, which is independent of expansion or contraction of a system’s scale. Entropy rises with time in a temporal-causal system, given the energy moving downhill driver at work. Try, say a white dwarf formed and then cooling down by radiation, that will not change in a contracting cosmos until average temperatures shift the flow direction, which is a fourth power law. Go back to the three laws (plus the zeroth) and consider microscopic underpinnings. The basic statistics involved will not change and you get the famous arrow. KF

BB@ 15:

“If (the universe)had no beginning then it requires no cause. The same argument used for God.”

Well, I agree, but the gist of my comment @13 still applies. If one accepts the possibility that matter can exist eternally, then one must accept the possibility that mind can exist eternally.

Unless, of course, one assumes that mind derives from matter – which is the very point at issue. Some scientists and philosophers believe that matter derives from mind; including (as quoted in #13) people of the stature of Planck.

Of course, none of the above suggests that this ‘Mind’ must equate to the ‘God’ of the Torah/Bible/Quran – although it might do.

Many psychonauts down the ages (mystics, NDErs, entheogen ingestors) have encountered what they believe is God, but it’s not an old dude with a white beard; rather it is, and contains, all of existence (including us), and is in its essence nothing but infinite love.

This is NOT ‘pantheism’ BTW – the notion that the universe is God or that ‘coffee mugs are conscious”. Rather it is panentheism – everything is an outflowing of God and is contained within God.

In much the same way that your dreams conjure a whole apparently-real world, but the coffee mug in your dream isn’t ‘conscious’, it’s *within your consciousness*.

Prof. R. C. Henry, who I mentioned @13, was a lifelong atheist until he concluded (by the study of physics, not any kind of theology) that the only reality is Mind – and that we are, as he put it, “dreams in the mind of God”.

(He was a bit late to the party. Shakespeare got there first when he wrote that “we are such stuff as dreams are made on”.)

CB

I don’t have a problem with that as a possibility. Although, it still has yet to be shown that a mind can exist without matter.

Brother Brian:

Yes, it has. Just because you are too afraid to check it out for yourself doesn’t mean the evidence just goes away.

BB,

Let’s look a bit more at your implied transfinite (beginningless) past and what such a form of words runs into. Where, we may make all sorts of forms of words or symbols by imagining things. However, for such a form to accord with actual or possible reality may be a very different challenge.

Consider now, N, and some past finitely remote time K, counted as k finite, causal-temporal, cumulative stages prior. Thus, K +1, K+2 . . . K+n accumulates causally-temporally to now. And, as these stages are causal, energy degradation occurs but that is not primary here (save that it highlights that time is linked to thermodynamic processes tied to causal succession).

Proceed backwards beyond K, K-1, K-2, . . . K-m. We are obviously still finitely remote from N.

Go beyond, K-(m+1), K-(m+2), K-(m+3) . . . K-(m+p) for reference.

You will see that we are laying out another count effectively 0,1,2,3 . . . p steps removed beyond K. And of course from K (effectively set at 0) we go forward some n steps to N.

A first consequence is that we may be justified in speaking of some K, finitely removed from now. K can be arbitrarily large (in principle) but is only finitely removed. Finite steps to now can be justified.

Next, look at what is happening beyond K. We obviously can in principle go to m, finitely further removed. However, as we try to count onwards, we see an up-count appearing in countable steps, m, m+1, m+2 etc. We can justify reaching successively to some finite m+p, but we can never justify a count like k-(m+[w-1]), k-w, where w is transfinite, omega. That is the transfinite remove beyond k cannot credibly be spanned in finite stage successive steps.

We are only justified in speaking of a finitely remote past that accumulates in finite stage steps [think, years for convenience] to reach now.

This still obtains if we do not explicitly refer to a specific transfinite value but leave it implicit in the ellipsis.

While we may use a loose form of words to talk about a beginningless temporal-causal past that accumulates in finite stages to now, that has serious challenges to be credibly justified on examining causal succession by cumulative finite stages. Where, causal is crucial, we have contingent successive stages. I suggest, a succession of contingent stages does not attain cumulatively to independent, necessary being as causally adequate world root.

We need an entity that rises above the contingent, temporal-causal physical order.

Where, as a reminder, no-thing is just that, non-being. Were there ever utter non-being or no reality, such has no causal capability and no world would ever be. No-thing would forever obtain. As a world is, something always was which is also causally adequate for a causal-temporal world such as ours. One that is credibly contingently set up at a deeply isolated operating point for C-chem, aqueous medium, cell based life. Further, for life that is embodied but rises beyond GIGO-limited computational substrates to morally governed insightful rationality.

That points, again, to a different order of existence for necessary being: minded and capable of creating such a world, grounding moral government. Thus, inherently good and utterly wise as well as powerful and independent as being. We are justified to speak here, of an eternal, transcendent, inherently good, utterly wise, minded order of being as world root.

A fairly familiar picture and one Plato spotted oh so long ago in his inference to the good soul as creator of the world, in The Laws Bk X.

KF

BB,

you have improperly reversed the issue.

It has been repeatedly highlighted to you that a computational substrate such as a brain cannot credibly account for insightful, intentional rationality. As Reppert highlights, again (and as you have studiously side-stepped any number of times):

Matter in the form of computational substrates and what may emerge from them by physical processes does not account for mind. Though, we may profitably discuss quantum influence interfaces etc that may run both ways. The Smith cybernetic loop model then allows us to see how a two-tier controller with a supervisory oracle could account for effective, embodied mind.

And as was already noted we need a causally effective world root with deep intelligence to credibly get to a physically expressed causal-temporal world set up for cell based life. Where morally governed rationality multiplies the constraints.

Mind antecedent to and causing a material world with intelligent, insightful, morally governed creatures is a very plausible world-frame.

Perhaps, you should reconsider the crooked yardstick of default atheistical presumptions and consider it.

KF

BB @ 23

“it still has yet to be shown that a mind can exist without matter.”

Once again, I agree – but once again, the opposite scenario also applies:

Have we got evidence of matter existing without mind? Where is such evidence? Absent the existence of mind, how could we ever have any evidence of matter? How would it be possible to demonstrate the existence of matter which persists independently of mind, without the existence of mind?

(This is beginning to seem like some sort of ontological koan!)

re 25: Omega is not a real number, so the expression k-w is meaningless in respect to the real number line.

I’m currently reading a poorly written but interesting book on the history of the concept of infinity and its difficulties. I’m not yet to the part on Cantor et al, but I’m confident the above sentence is correct.

re 28: Omega refers to the transfinite, which pertains to actual numbers. Perhaps the book you are reading isn’t poorly written but instead poorly read.

Omega is not a real number in the mathematical sense of being a number on the number line. I don’t think you could find a reference that says it is. There are numbers such as imaginary numbers; transfinite cardinals such as aleph-null, aleph-one; hyper-reals, etc. that are “actual” numbers in that they are well defined and have mathematics associated with them, but they are not real numbers in the sense of representing a point on the real number line.

hazel, You aren’t even paying attention. Omega, in the context of what kairosfocus is saying, refers to the transfinite. And just like infinity, it is not a number. But it does pertain to actual numbers on the number line.

So, ET, what is the meaning of k-w, where k is a real number and w is omega?

Omega is (the) transfinite. So, from some real number, k to the transfinite, Omega

But “the transfinite Omega” is not a place on the real number line that you can “get to”. Omega is a number

aboutthe real number line (actually the natural numbers on the number line), but it is not a numberonon the number line.Charles Birch at 27 is in VERY good company when he asks,

To wit

To add insult to injury, due to advances in science, especially advances in quantum mechanics, it turns out that atoms themselves are found not to be the solid indivisible concrete particles, as they were originally envisioned to be by materialists, but it turns out that the descriptions we now use to describe atoms themselves, the further down we go, dissolve into “abstract conceptual tools for describing nature, which themselves seem to lack any real, concrete essence.,,,”

In fact, according to quantum theory, the most fundamental ‘stuff’ of the world is not even matter or energy, (as Darwinian materialists originally presupposed) but is ‘abstract’ immaterial information itself

Thus, in irony of ironies, not even the material particles themselves turn to be are ‘real’ and concrete, (on the materialistic definition of what is ‘real’ and concrete), but turn out to be “abstract” immaterial information.

This puts the die-hard materialist in quite the conundrum because, as Bernardo Kastrup further explains in his article, to make sense of this conundrum of a non-material world of pure abstractions we must ultimately appeal to an immaterial mind. i.e. we must ultimately appeal to God!

Or to put it much more simply, as Physics professor Richard Conn Henry put it at the end of the following article, “The Universe is immaterial — mental and spiritual. Live, and enjoy.”

Of supplemental note:

The Darwinian materialist, in his rejection of God, simply has no anchor for reality to grab onto:

As I have pointed out several times now, assuming Naturalism instead of Theism as the worldview on which all of science is based leads to the catastrophic epistemological failure of science itself.

Thus, although the Darwinist may firmly believes he is on the terra firma of science (in his appeal, even demand, for methodological naturalism), the fact of the matter is that, when examining the details of his materialistic/naturalistic worldview, it is found that Darwinists/Atheists are adrift in an ocean of fantasy and imagination with no discernible anchor for reality to grab on to.

It would be hard to fathom a worldview more antagonistic to modern science than Atheistic materialism and/or methodological naturalism have turned out to be.

Omega is the name. That’s all. And yes it pertains to real numbers on the number line. And you cannot get to infinity, either. But there are numbers all along the journey…

ET, you write, “And you cannot get to infinity, either.”

However, if you can’t “get to” infinity, then saying that k-w means “from some real number, k to the transfinite, Omega”, which you wrote earlier, is contradictory.

But, to repeat in different words, k-w is meaningless because the only thing you can subtract from a real number is another real number, and w is not a real number.

hazel, buy a dictionary and look up the word “transfinite”.

Transfinite refers to a number larger than any finite number. Omega is the first (smallest) transfinite ordinal number.

You can’t subtract a transfinite number from a finite number, so k-w is meaningless. Omega is not a number or quantity on the real number line.

I’ll note that you have not addressed these specific points.

hazel:

That explains why kairosfocus said:

“… but we can never justify a count like k-(m+[w-1]), k-w, where w is transfinite, omega.”Or do you not understand that?

kf followed that with “That is the transfinite remove beyond k cannot credibly be spanned in finite stage successive steps.” But there is no such thing as a “transfinite remove” beyond k. That is my point. If all kf means is we can always keep counting, then of course that is true. But his use of k-w and “transfinite remove” are not mathematically meaningful.

And so it is with the alleged transfinite past- not mathematically meaningful. That was the point.

BA77 @ 35

That Wigner quotation was nice; I hadn’t seen that one before. Especially:

“Our knowledge of the external world IS the content of our consciousness and …… consciousness, therefore, cannot be denied.”

Precisely! So again, how can one present evidence for matter existing without mind? (Any more than, as BB pointed out, mind existing without matter.)

Here’s a thought experiment for materialists. How do you know a table exists? The materialist might answer “because I can see it and touch it”.

Well, what about if you’re blind and have massive peripheral neuropathy? “Well,” the materialist might say, “I might smell the wood of the table; I might hear it creaking; I guess I could taste its surface.”

OK, so what if ALL your senses were non functioning? How would you know the table existed? The materialist might answer “I personally wouldn’t, but other people would, and that’s enough.”

OK, now what happens if there are NO other people? Come to that, imagine ALL sentient life from bacteria to amoebas to self-aware beings, is suddenly removed from the universe. How then could the table be said to exist? How indeed could the universe be said to exist?

There would be no shapes, textures, colours, sounds, brightnesses, darknesses, smells or spatial relationships in such a universe. If it existed at all, it would consist of a swirling mass of mathematical probability functions – which could hardly be said to be “matter”.

So yes, BB is right – we have yet to observe mind disconnected from matter. But we are also yet to observe matter disconnected from mind – indeed, the very act of observation would be impossible!

Hazel,

Let’s observe my phrasing in 25 above, noting that there were remarks leading up to:

As for the legitimacy of w as a number that may be referenced in the general context of natural counting numbers and their additive inverses etc, I am always bearing in mind the surreals framework and the hyperreals, as I have discussed in this blog and in this general context of concerns many times across the span of years. Notice,

my phrasing above highlights that we cannot extend from some imagined last finite to a successor step by increment of one step which is suddenly becoming transfinite.Where also, let us not overlook transfinite induction. Here, Wiki’s summary:

Clearly, it is reasonable to envision a succession of ordinal numbers (notice, successive steps) that ranges out into the zone of transfinites. And as the surreals show, we can form and use a mirror image on 0, giving negative values.

Now coming back to your objection in 28:

First, I was NOT speaking to reals as such but to ordinals, ranked successive steps, which are perhaps the easiest context to bring out transfinites.

(I add, the easiest way to get to a hyper-continuum is to use reciprocals tied to the span of ordinals that goes beyond the naturals, so 1/x is a catapult function, allowing a cloud of reciprocal values between 0 and 1 including first for 0 infinitesimals closer to 0 than any 1/n n a natural. Use the usual interpolation property to identify that there is no distinct nearest number to any particular number in the span [0,1] Then in effect shift by addition so between successive ordinals we interpose a continuous block. Bring on the surreals, and see that for reals any particular value is in effect an w-length succession of closer steps, effectively a power series that has a whole part and a fraction that eventually traps the desired value pi or e or whatever. This views say decimal numerals as compressed power series.)

Coming back, let us notice that my argument was that we cannot justify a causal-temporal succession of finite stages (years is convenient but not strictly correct) from a claimed beginningless past to now. We can justify a finite succession, bound in the past, i.e. implying a beginning. I used a suggested reference point K, n steps antecedent to now and then took up going beyond K. As we did so, we saw how beyond some K, we face a supertask to see beginningless antecedent stages. We are only justified to speak of a finite past, even in the case where the transfinite past claim is left in an ellipsis.

And my pivotal point is not that far removed from your objection that w is not found on a reals line: given, the reals interpolate the natural counting numbers (which are ordinals) we do not have any particular n in N such that its immediate successor is w. Which, can be mirrored to the negatives. What I did at 25 was to take that mirror to show that ascending by succession from a claimed beginingless past does require traversing the transfinite in successive finite stage steps. Which will fail. Even if the transfiniteness is left implicit in an ellipsis.

I did so as much has been argued here over several years on the point. That argument I recently revisited using the development of hyperreals to justify comments I made over three years ago originally, which were in fact justified.

Coming back to the issue in the main, a physical, causal-temporal succession by finite stages world is not plausibly beginningless, that is it is not a good candidate necessary, world-framework being. Causal-temporal successive physical worlds are credibly contingent, with a beginning (even if one goes beyond a big bang to say a quantum foam sub-verse with spacetime inflating bubbles).

The workaround on the obvious beginning at the bang, is unsuccessful, Despite forms of words that may at first seem plausible (as BB suggested and before him Lord Russell et al).

We need a necessary being world root with adequate causal capacity to account for our world, with us in it. That points to a powerful being capable of being the source of a world with morally governed creatures that also rise beyond computation on GIGO limited substrates to insightful rationality. Where, rationality is inescapably morally governed. After Euthyphro, Hume and so forth this points to a necessary being world root that is inherently good and utterly wise.

KF

PS: The surreals allow all sorts of weird and wonderful combinations under which w can be stepped down from to say w/2 in steps (of course transfinitely many), and w+1 or w-1 can be made as reasonable ideas. In 25 above K was a finitely remote value stepped back from N by n steps, which can be interpreted as subtraction. The summary above IN THAT CONTEXT suggests going back w steps beyond K in finite stages precisely in order to show why we cannot do it, transfiniteness here being precisely an emergent property that does not suddenly arise but is recognised. Thus w is the order type, thus stepwise successor, to the naturals. It cannot be stepped up to leading to [w-1] being finite then +1 and poof, magic, w is now suddenly transfinite. As dealing with the negatives is harder (stepping down from implicit transfinitely remote values) I took several steps to get there. Baldly taking the mirror of the positives will be objected to.

kf, I think when people think about time they use the real number line as the model. Your inclusion of ordinals and hyperreals is idiosyncratic, I think.

Enough for me.

The transfinite resides on the real number line, hazel. Time, like the transfinite and infinity, is a journey.

Yes, the number line is infinite in that you can keep counting forever, so I agree that traversing the number line (and time if modeled by the number line) is a journey that cannot be completed. But there is is no “transfinite point” that “resides” on the number line: there is no place “transfinitely remote” from any finite point. No two points on the number line are an infinite distance apart.

That’s all fairly simple and entirely orthodox math.

kf writes, “The summary above IN THAT CONTEXT suggests going back w steps beyond K in finite stages precisely in order to show why we cannot do it, transfiniteness here being precisely an emergent property that does not suddenly arise but is recognised. Thus w is the order type, thus stepwise successor, to the naturals. It cannot be stepped up to leading to [w-1] being finite then +1 and poof, magic, w is now suddenly transfinite.

I agree with that (except I’m not sure about the “emergent property” sentence means). My point is that transfinite numbers are not on the real number line. Do you agree with what I wrote ET at 47? (A nice short answer to that question would be appreciated.)

Hazel, with all due respect you come across as looking for a strawman caricature based on taking out of context. I am not claiming that we can descend from the beginningless (so transfinite) past in finite stage steps (“years”) BB and before him others such as Russell are or were, at least by implication. What I am highlighting is why such a claim implies traversing a transfinite span in finite stage steps which is an infeasible supertask. You cannot get your transfinite beginningless past by leaving that character behind the curtain of an ellipsis. Beginningless plainly implies that the past in countable causally-temporally successive stages — with before leads to after through causal processes involving energy flows and thermodynamics — is remote beyond any finite K however large the n stages to now are. As to countability, a once now gives rise to a successor and this chains step by step. We can therefore in principle tag them and arrange them, with +1 increments in the succession direction and -1 increments in the antecedent direction. This can be mapped to an integer number line. Beginninglessmess implies transfinite TEMPORAL-CAUSAL extension leftwards. It is that which runs into the supertask I drew out. Your explanation as to how a behinningless transfinite character past extending beyond ANY finitely remote past stage K of finite duration can be traversed in finite stage steps is ________ ? KF

PS: I have been dealing with hyperreals and/or surreals, the reals line with Z as mileposts is irrelevant to my concerns. I will say that any particular K on it reachable in finite steps or bracketed in finite stage steps is inherently finite. But the line has an indefinite extension that gradually points to the transfinites beyond. On the hyperreals model — closer to what ET is fishing for — a transfinite M can feed into 1/M –> m closer to 0 than any 1/N –> n for a natural counting number. Such an m is on a continuum to 0 the hyperreals, and as M is operated on within a given class of numbers the hyperreals, there is arguably a one line that takes in all. Just it is not called the reals. I add, m is an infinitesimal leading to nonstandard analysis and Calculus, dx dt etc.

kf, you are addressing all sorts of issues that I am not.

Concerning the real number line, do you agree with these statements? If not, please explain.

1. The number line is infinite in that you can keep counting forever, so traversing the number line is a journey that cannot be completed.

2. There is is no “transfinite point” that “resides” on the number line: that is, there is no place on the real number line that is “transfinitely remote” from any finite point.

3. That is, no two points on the number line are an infinite distance apart.

Can you address just these three points?

I just read the PS to 49. kf wants to include the hyperreals in this discussion, and I don’t, as I don’t think that is the model many, or any except kf, have in mind when they discuss time. Therefore, no further discussion is necessary.

Hazel,

you are trying to rule arbitrary datum lines. The issue is to address the claimed beginningless physical world, and whichever framework of quantities and structures that best allows us to frame such is applicable. So, we go where we find what we need to accurately describe and model.

It turns out that surreals and hyperreals allow this best, framing the naturals and reals in a way that brings out how R connects to transfiniteness. My observation is that we often put the trasnsfinite character of the claim of beginninglessness behind a curtain of an ellipsis, and not even a four dot ellipsis. The applicability of counting numbers comes from successive, causal-temporal finite stages, so we can start at now N and count back in -1 increments to some K, in n steps, and beyond K to k -m, then onward to k – (m + p), then we can raise the issue of increasing m + p without limit.

That is what brings out that there is no definable last finite counting number or integer so going one further step is no longer finite. That is the ellipsis implies a zone of onward continuation so the whole indefinite set is transfinite. Continuum can be filled in using shifts of [0,1]. Where, our ability to use the catapult function 1/x lets us see the connectedness of the hyperreals. For a transfinite hyperreal H, 1/H –> h, closer to 0 than 1/N –> 0 for any natural but h and n are obviously in the same interval [0,1].

Saying n is a real but h is not simply tells me that the reals as defined are not the set relevant to my concerns, because of the happenstance of definitions; I think calling R the “reals” lends it an aura that it turns out it cannot live up to. Worse, having valid infinitesimals opens up vistas for calculus related processes and linked physics; so, so much the worse for good old set R.

Old model, now retired.

We have enough to settle the substantial matter, now settled that we have no plausible basis to speak of a beginningless past.

KF

PS: You ask questions, I will comment:

>>1. The [counting] number line is infinite in that you can keep counting forever, so traversing the number line is a journey that cannot be completed.>>

–> In finite step stages.

–> Numbers extends to the transfinite and infinitesimal, with complex numbers as vectors.

–> As I based my argument on, one cannot count up from 0 in finite stages and reach a transfinite. Beyond any K finitely removed from 0, we have k+1, k+2, . . . so we can just as readily initiate the counting from K on.

>>2. There is is no “transfinite point” that “resides” on the [counting] number line:>>

–> Irrelevant to our interest, and there are hyperreals and surreals connected to N, Z, Q, R which can be seen as linked through say hyperreal H –> 1/H –> h near 0 in the interval [0,1]

>> that is, there is no place on the real number line>>

–> reals interpolate counting numbers,

>>that is “transfinitely remote” from any finite point.>>

–> “place” implies specific identified value. Such a value can be incremented depending on which side +/-1 and exceeded.

–> But all that tells me is the STRUCTURE continues on without limit and is transfinitely bound by w the order type of the counting numbers and by -w its additive inverse taking in negative integers.

–> This comes out very naturally in pondering surreals. There is a well known diagram that brings it out very well.

>>3. That is, no two [specifically identifiable] points on the counting, [integer or real] number line are

~~an infinite distance apart.~~[–> transfinitely algebraically different on subtraction] >>–> I find it important to highlight that once we specify or identify or symbolise particular values in N, Z or R we may exceed by increment. However, it is part of the STRUCTURE of the sets that they are without FINITE bound, i.e. the ellipsis we use is pregnant with huge meaning.

–> That is why I no longer trouble myself overmuch over the so impressively named “reals” which unfortunately suggests psychologically that other relevant and valid numbers are somehow less than real, are somehow an arbitrarily invented figment of our imagination.

–> It turns out the hyperreals and surreals were what I was interested in and needed, I am happy to have R, Q, Z, N bracketed inside transfinites [with w the first transfinite ordinal but there is plenty room for related surreals around w] and to have 0 surrounded by an infinitesimal cloud of values like h of smaller magnitude than the reciprocal of any particular n in N

Watch https://www.youtube.com/watch?v=BBp0bEczCNg

I’ve watched that before, kf, and read other stuff: I know about hyperreals, and know how they work. That is not my point. My point is that I am virtually certain that everyone from Aristotle to people like William Lane Craig have had the real number line in mind when discussing time: my bet is that you are the only person who wants to introduce the hyperreals as a model for time.

And, I know full well that the “real” numbers have no special status just because of their name. I used to give a whole lecture in calc class about the history of numbers, with an emphasis on what a bad choice “imaginary” was for the square roots of negative numbers.

hazel just refuses to understand the point. Oh well.

Hazel, R is a subset of *R, and by setting it in context we better appreciate what a beginningless past entails. Where, it is a key part of the structure of Z and R that any particular value we can count to or bound by counting just past (whether by incrementing or decrementing), will be finite. So, a finite stage successive process will not span an explicit or implicit transfinite span. Consequently we do not have a good reason to claim a beginningless past that by finite stage causal-temporal succession has attained to now. In discussing the real past we are only warranted to speak of finitely remote stages, not stages that have passed beyond any finite limit. KF

ET, a beginning points to a very unwelcome thought, a begin-ner. KF

KF- And that is where Stephen Hawking made his living- the beginning just happened. Given the state of matter, heh, it just had to happen. And the laws that govern nature “just are (the way they are)” (“A Briefer History of Time”).

This is pointless, I know, but kf writes, “So, a finite stage successive process will not span an explicit or implicit transfinite span.”

Ifwe are thinking about the real number line, thereare no“transfinite spans”, assuming that the phrase “transfinite span” means that there are two points spanned by (or separated by) an infinite distance.Let me make a few things clear:

1. I am not arguing for a beginningless past: that is not a subject I have addressed. I am just discussing the nature of the real number line and the concept of infinity.

2. I know very well, of course, that counting in successive steps doesn’t ever end. If that is all kf’s sentence means, then of course I agree. If “transfinite span” just means the always continuable process of counting onwards, forever and without limit, then we have no disagreement.

3. If kf is still talking about the hyperreals, then he can just ignore this post.

Hazel,

I use the natural counting numbers as a framework for counting stages, so let us explore their pattern via von Neumann:

{} –> 0

{0} –> 1

{0,1} –> 2

. . .

{0,1,2 . . .} –> w

Notice, how the RHS is the ORDER TYPE of the LHS and gives us a label for the set? It introduces no additional quantity.

The implicitly transfinite nature of the natural counting numbers as a whole is captured in the three dot ellipsis, and the w is a short hand for the set viewed as ordinal, having cardinality Aleph null.

In this context, the claim, there is a beginningless traversed actual past of cumulative temporal-causal stages to now can be understood as implying traversal of the transfinite. Let now, N, be 0, and let’s just roll over to the negative integers, mirror image to the positive counting numbers. So, N has antecedent N-1, next N-2, . . . N-K, N-[K+1], . . . where on this hype EVERY and ALL -ve integers -K are matched to actual past causal-temporal stages. The order type of this suggested span is patently w and the span is implicitly transfinite. (This is best seen by pulling back the zoom and seeing i/l/o the hyperreals and surreals.)

That the set is transfinite can be seen by how running a count onwards from K will replicate the process as though K were zero. That is, a proper subset can be placed in 1:1 correspondence with the whole set to N. That is a diagnostic sign of a transfinite set.

The claim, that there was a beginningless transfinite past implies a claim to have traversed a transfinite span in finite step cumulative causal-temporal stages.

This is an infeasible supertask.

We have no warrant to claim actual transfinite traverse in finite stage steps.

By contrast, posit some H such that 1/H –> h where h is less than any 1/n n in the natural counting numbers will catapult over the span of the naturals with the interpolated continuum that leads to R. The hyperreals help us see the big picture.

KF

PS: The context of the discussion is the beginningless past claim.