William M. Briggs

Statistician to the Stars!

Page 4 of 414

There Is No Difference Between A Forecast, A Scenario, or A Projection

There are all kinds of models.

There are all kinds of models.

This is a tad incoherent, but the gist is here. I had the opportunity of submitting an abstract to the AGU fall meeting, and had only a couple of hours in which to do it. This is the, eh, plain-English rendering of that abstract. Stand by for more news.

People trying to escape the implication of a bad forecast often claim their forecast wasn’t a forecast but a projection or scenario. The implication is that a bad forecast means a (possibly beloved) theory is no good. Therefore, if the forecast wasn’t a forecast, but a projection or scenario, the theory can still be admired (or funded).

This won’t do. Forecasts are scenarios are projections. And bad forecast-scenario-projections means bad theories.

These misunderstandings are not only found in making predictions, and in classifying which future-statements count as predictions, but also under which circumstances predictions must be verified. There is general recognition that good models produce good forecasts, but bad forecasts can’t be ignored by calling them a projection or scenario.

Now the finer points. For a start, the remarks below are general and apply to any data not yet seen, but for ease, predictions of future events are illustrated.

All forecasts are conditional on two things: a theory/model and a guess about what the future holds. Neither need be quantified or even rigorously defined, of course, but since scientists are keen on quantification, models usually have numbers attached to them.

Imagine the simplest model, which is a function of the past data, of time, and some set of premises which specify the model form (say, an ARMA process). This model can make a forecast. It will be conditional on the theory—which is the past data and model-form premises—and on a guess about what the future holds—which here is just that the future will come at us in discrete time points, t+1, t+2, etc.

Suppose the forecast is for time points t+17 and t+18. Here you stand at t+3, well short of t+19, but you still want to “verify” the forecast. Well, you can’t. The guess of the future has not obtained, therefore the forecast hasn’t, in effect, really been made. It is null. It is impossible to discuss the quality of the theory: it may be good or bad, we can’t know which.

Nothing changes if we add to the model other propositions of interest. Suppose we augment our simple time series model with “x” variables, propositions which, for the sake of argument, say something about matters probative of the thing forecasted. Now if the forecast does not change in any way regardless of the state of the “x” propositions, then these items are irrelevant to the theory. Irrelevant items shouldn’t even be part of a theory, but these days, in this heyday of the politicization of science, anything goes.

For illustration, add another component to “x”, say, the price of oil exceeding some level. Point is this. If the guess of the future is t+1 and t+2, and here you stand at t+3, you have met the time criteria, but still have to check whether the price of oil exceeds the stated level. If it does, you can check the validity of the forecast; if not, not.

Nothing changes if we add other “x” variables, or turn the model into physics instead of statistics. Get it? There is no difference between a physics and statistics models in terms of forecasts. (Most models are mixtures of both anyway.) If the guess of the future conditions obtains, then the forecast may, even must, be evaluated (the technical term is “verified”).

A difficulty arises with the word scenario, which is “overloaded”. It can mean guess of what the future holds, the time points plus the price of oil, i.e. the “x”, and is therefore not a forecast but part of one, or it might mean a forecast. To avoid confusion, this is why only “forecast” or “prediction” should be used.

It’s time t+3 and the price of oil did not exceed the stated level, so the forecast is null. But, since the price of oil is probative, we could make a new (after-the-fact) forecast assuming the appropriate price. In this way, we can still verify the model.

If we’re using that model for making decisions, particularly in government, we must verify it. We must input the “scenarios”, i.e. the “x”s that obtained, and then recompute the forecast. If the forecast has no skill, the model must be acknowledged as unworthy, to be abandoned of overhauled.

Update Reading is a difficult art, rarely mastered. Many after reading a title feel they have assimilated all the material there under. Strange. Many others gloss. More than a few shot right by where I said scenarios were sometimes the “x” and sometimes the forecasts themselves.

But it sure is nice to have an opinion, isn’t it?

What I Have Learned From Global Warming: Contest Winner Essays 2. Plus Secret Bonus!

Global warming will cause an increase in clement afternoons.

Global warming will cause an increase in clement afternoons.

Another essay from the winners of the Rename Global Warming Contest is here! Plus, a special bonus, a treat for all readers! See below! Don’t miss it!

John Buckner, “Climactic Climatic Calamity”

I learned how HARD it is to rewrite the past record in order to reflect the true past record.

This actually happened to me back in 2003. I paid GOOD MONEY to see the Viking Exhibit featured at the Minnesota Science Museum in St Paul. I’m looking through all the cool exhibits about Viking life and conquest back in their day. I was admiring their accomplishments despite the fact that it was as cold then as it was today.

And then I saw it. It was so offensive and wrong. Michael Mann had recently PROVED that this display could NOT be correct.

The exhibit showed three depictions of a non-descript “mountain” purportedly in Iceland circa 1000, 1400 and Today.

The 1000 picture showed this mountain (hill actually) lush and green from bottom to top. The 1400 picture showed this hill with a snow cap. The Today picture showed the mountain entirely covered in snow.

I fumed and seethed all the way home. Not having won this prestigious award, I had no say or power to effect the change required by the exhibit to show the true past.

Not long after 2003, I started hearing rumors about the fact that the Medieval Warm Period (WMP) may have occurred but it was a regional thing. Only the Vikings enjoyed the benefits or suffered the consequences of the MWP.

The “deniers” harped about how the MWP benefited the Vikings and today’s improving temperatures would benefit us. Thank God, er Gore, someone answered this with the “Tipping Point” of Arctic Methane (that is a proper noun isn’t it?) that would overheat the entire globe not just the Arctic.

WAAAIIIITTTTT. If I HAVE to accept that the Viking’s had perhaps experienced warmer temperatures than today, then wouldn’t the Tipping Point have occurred then? NO! The WMP really MUST be expunged…and all those warmer times before could NOT have occurred. We’ve never had a time when climate changed naturally—ONLY MAN can change a climate!

(Or was that ONLY MANN can create a Yamal Tree?)

Mike Hulme “Climate Change and Virtue: An Apologetic” (Quotations from his peer-reviewed article in Humanities, 2014, 3, 299–312.)

Tim Flannery closes his recent book Here on Earth: A New Beginning with the words “…if we do not strive to love one another, and to love our planet as much as we love ourselves, then no further progress is possible here on Earth.”

In all the climate models I have examined, used and criticised over 30 years I have not yet come across a variable for love or an equation for calculating humility. The thermometer may have been essential to tell the story of a warming world, but environmental scientists have not yet invented or seen the need for a hope-ometer.

And there are those who still believe in this project [i.e., pinning hopes on The Consensus]. They excoriate others who obstruct and obscure this pure guiding light of rationality—a position adopted, for example, by Naomi Oreskes and Erik Conway in their recent book Merchants of Doubt.

At the time [~1990] it seemed entirely reasonable that with one of the last “enemies” of progressive Enlightenment liberalism having been swept away (i.e., communism), a new irrepressible world order would emerge. And it would be one that would now fully exploit the predictive power of fruitful globalised science.

Far from the end of history, then, and the inexorable onward march of the secular project, we are witnessing an overdue reconsideration of the place of rationality in human knowing. There is a challenging re-examination underway of the role of religion in the public sphere.

In my pursuit of the idea of climate change I want to focus attention on the ancient idea of virtue, the possibility that the “wickedness” of climate change as a problem demands a flowering of human “goodness”.

But listen carefully to the new voices speaking in the desert—some of whom I mentioned at the beginning—and one will hear a new language emerging around the fringes of climate change research, discourse and action…the language of empathy, story-telling, trust, wisdom, humility, integrity, faith, hope and love [ellipsis original].

I need to be clear. A focus on human virtue is not a political programme. This is no techno-fix for climate change, no system for Earth governance, no exercise in social engineering.

[Yours Truly admits to being charmed by Hulme's simplicity.]

Judgments About Fact And Fiction By Confused Researchers

miracl

Good news first. The peer-reviewed “Judgments About Fact and Fiction by Children From Religious and Nonreligious Backgrounds” by Kathleen Corriveau, Eva Chen, and Paul Harris in Cognitive Science is so awful that it automatically enters the short list for the First Annual WMBriggs.com Bad Science Award (to be announced each October). Congratulations!

The article opens, “Children often learn about people such as Cinderella, Tom Sawyer, George Washington, and Rosa Parks in the context of a narrative. However, these protagonists vary in their status.”

Bad Science of the First Kind re-packages commonsense as if were new and certifies it by official card-carrying researchers. Pace: “Five- and 6-year olds are able to use one important heuristic in assessing the status of story protagonists (Corriveau, Kim, Schwalen, & Harris, 2009). When hearing a story about an unfamiliar protagonist, they use the nature of the events in the narrative as a clue to the protagonist’s status.”

See what I mean?

Yet Bad Science of the First Kind is not harmless. It foster scientism and leads, all too often, to Bad Science of the Second Kind. This is malignancy, where what is not so, or is unknown, is said to be certain. Corriveau has done us a service by showing us the progression. Let’s watch.

“Woolley and Cox (2007) found that pre-schoolers increasingly claim that the miracles in religious (i.e., biblically based) story-books could have really occurred. Moreover, as compared to children from nonreligious families, children from Christian families were especially likely to regard such events as plausible” (p. 3).

Don’t see the problem because, obviously, miracles in religious “story-books” really for real could have happened, and that religiously educated children would more likely know this? Hint: She meant it negatively.

“The analysis offered by Corriveau et al. (2009) implies that, in the absence of a religious education, children will regard miracles as implausible because they involve ordinarily impossible outcomes. Accordingly, they should conclude that the protagonist in a story that includes a miracle is a fictional character rather than a real person” (p. 4).

The lack of philosophical training tells. Miracles are not “ordinarily impossible outcomes.” They are not impossible at all. If they were impossible, they could never happen, n’est ce pas? Anyway, here come the “experiments” on “religious”, by which she meant Christian (Jews were excluded), and non-Christian kids.

Kids were read stories like the following, and then shown a picture of the person and asked to put that picture into a “real [person]” or “pretend [person] box.”

Religious
This is Peter. One night he and the disciples were sailing a boat and got caught in a bad storm. Jesus walked on water to save them and Peter jumped out to walk toward him. Peter started to sink but Jesus caught him and they both jumped into the boat. The storm passed and everyone was safe.

Fantastical
This is Peter. One night he and his friends were sailing a boat and got caught in a bad storm. Peter fell into the water and started to sink. A fairy flew toward the boat to save them and used her powers to get him back onto the boat. The storm passed and everyone was safe.

Realistic
This is Peter. One night he and his friends were sailing a boat and got caught in a bad storm. Lightning flashed and Peter fell out of the boat. Peter started to sink, but his friends threw him a rope and pulled him back into the boat. The storm passed and everyone was safe.

Lo. “Religious children…were more likely than secular children…to categorize these characters as ‘real.’” The scare quotes are hers. By “Religious”, I must emphasize, she meant Christian—and not Muslim, Buddhist, Hindu, Shintoist, Zoroastrian, Jew, etc.

What elevates this beyond Bad Science of the First Kind is not just that was accompanied by an unjustifiable and unverified quantification of the results, topped by an overly complex statistical model with wee p-values. No, sir. It was the extrapolations which followed.

“It is possible that religious teaching, especially exposure to miracle stories, leads children to a more generic receptivity toward the impossible, that is, a more wide-ranging acceptance that the impossible can happen in defiance of ordinary causal regularities” (p. 13).

Miracles, when they occur, are always caused. How could they not be? Which strongly suggests the question: Shouldn’t a person experimenting on children to plumb their understanding of causality understand causality herself? Or do Corriveau et alia take the dogmatic, against-all-evidence position that miracles are everywhere impossible?

Or was her purpose to make Christianity into a pathology? I’ll let Corriveau have the last word (from the conclusion).

“By contrast, secular children displayed little recognition of God’s special powers. When presented with religious stories that included ordinarily impossible events, they categorized the protagonists as pretend” (p. 21).

“[E]ven if children have no natural inclination to believe in divine or superhuman agency, religious instruction can readily lead them to do so”. And, “An alternative possibility is that children are disposed to credulity unless they are taught otherwise by their families” (p. 23).

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Thanks to Nicholas Senz at Catholic Stand where we first learned of this, uh, study.

Philosophic Issues in Cosmology IV: Creatio Ex Nihilo—Guest Post by Bob Kurland

From the Hubble deep field.

From the Hubble deep field.

Bob Kurland is a retired, cranky, old physicist, and convert to Catholicism. He shows that there is no contradiction between what science tells us about the world and our Catholic faith.

Read Part III.

In the beginning God created the heavens and the earth. The earth was formless and void, and darkness was over the surface of the deep, and the Spirit of God was moving over the surface of the waters…[Gen 1:1-2 (KJV)]

“The laws of nature themselves tells us that not only can the universe have popped into existence like a proton and have required nothing in terms of energy but also that it is possible that nothing caused the big bang,” Professor Steven Hawking (Discovery Channel broadcast).

“When men choose not to believe in God, they do not thereafter believe in nothing, they then become capable of believing in anything.” G.K. Chesterton

Historical

The Hebrew for formless and void in Gen 1:1 is tohu-bohu (or tohu va vo-hu), though one Hebrew told me the translation was topsy-turvy, a mess, confusion. That would be more in accord with notion held by many physicists that Creation arose from quantum fluctuations.

Where did ex nihilo come from? Besides scripture (2 Maccabees 7:28, Hebrews 11:3), the first Christian writer to promote the doctrine of creatio ex nihilo was Theophilus of Antioch in the late 2nd Century, who wrote:

[B]ut then they (the Platonists) maintain that matter as well as God is uncreated, and aver that it is coeval with God. But if God is uncreated and matter uncreated, God is no longer, according to the Platonists, the Creator of all things, nor, so far as their opinions hold, is the monarchy of God established. And further, as God, because He is uncreated, is also unalterable; so if matter, too, were uncreated, it also would be unalterable, and equal to God; for that which is created is mutable and alterable, but that which is uncreated is immutable and unalterable. And what great thing is it if God made the world out of existent materials? For even a human artist, when he gets material from some one, makes of it what he pleases. But the power of God is manifested in this, that out of things that are not He makes whatever He pleases;

Theophilus was contesting the view of Greek philosophers, Platonists, neo-Platonists, that the universe was eternal, that a demi-urge had created it from pre-existing stuff. Theophilus’s theologic cudgel was wielded against the Gnostics by later Christian theologian/philosophers and fully developed by St. Augustine. It was St. Augustine who developed arguments about time, that time could have begun with creation, which is a view remarkably in accord with much of modern cosmology, e.g. “…no time passed before the world, because no creature was made by whose course it might pass,” St. Augustine, City of God bk 11, ch.4.

As Keith Ward (Quantum Cosmology and the Laws of Nature) puts it: “For Augustine, God brought about time and space as well as all the things that are in them. Just as God did not create space at a certain place, but non-spatially caused all places to exist, so God did not create time at a certain moment, but non-temporally caused all time to exist.”

Note that Ward’s interpretation above does not require a first moment of time, a “t=0″, although Augustine did accept, on the basis of Revelation, that the Universe (which to him was much smaller than our conception) had a definite beginning.

St. Thomas Aquinas also contended against the Greek philosophers’ version of Creation. He agreed with Aristotle that creation required a First Cause, which Aristotle called the Prime Mover and which Aquinas called God. However, he believed that only Revelation, not reason, could assert that Creation began at an instant in time (ST, P1, Q46):

By faith alone do we hold, and by no demonstration can it be proved, that the world did not always exist…it cannot be demonstrated that man, or heaven, or a stone were not always. Likewise neither can it be demonstrated on the part of the efficient cause, which acts by will. For the will of God cannot be investigated by reason, except as regards those things which God must will of necessity; and what He wills about creatures is not among these, as was said above.

Even though the world might be eternal, Aquinas maintained that God’s creative agency would be and is continually active, as a creatio continua.

Time

Some comments about the forms “time” might take in a cosmological description of the evolution of the universe, and whether creatio ex nihilo requires a beginning, an instant in time about which we can say this is t=0, and there is no t<0.1

Our ordinary understanding of a universal time is confounded by the prescriptions in special and general relativity. Special relativity requires that the time of an event depends on the frames of reference of the object and observer; thus, an event A might be in the future for observer X in one frame of reference and in the past for observer Y in a different frame.

A further complication is found in general relativity, gravitational time dilation. To take these complications into account, spacetime is divided into space-like slices, for which some proper time, t, is assumed to be the same everywhere in the slice. This proper time can be replaced by another parameter (varying with time) such as R (the radius of the universe) which is constant in a slice.

The uncertainty principle of quantum mechanics introduces still another complication: uncertainty in time x uncertainty in energy > h/(2pi). This means that to specify t=0 exactly there would have to be an infinite uncertainty in the energy of the system.

Contemporary

For the most part opinions of contemporary theologians are reactive to various cosmological theories about the origin (or non-origin) of the universe. Focus on the Big Bang (t=0) hypothesis and the Hartle-Hawking model (no beginning). Then, if God is eternal and timeless, how does God act in a world that progresses in time; in other words, what can we say about the temporality of God? This question is addressed in Quantum Cosmology and the Laws of Nature by several of the authors:

  • The Big Bang hypothesis confirms creatio ex nihilo by showing the Universe began at a definite time (t=0): William L. Craig, Ted Peters
  • The Big Bang hypothesis might be true, but it is also possible that the Universe could be eternal, with creatio continua by God: George F.R. Ellis, Richard Swinburne, Keith Ward*
  • The Big Bang hypothesis and cosmology, for one reason or another, are not all that relevant to theological ideas about creation: William Alston, Ian Barbour (in Robert John Russell’s article), Karl Barth, Wilhelm Drees, Arthur Peacocke (in Robert John Russell’s article), William Stoeger
  • The Hartle-Hawking model offers theologic possibilities (see Summary below): Wilhelm Drees, Chris Isham, Robert John Russell

Summary

The science/physics of creation is not settled with respect to creatio ex nihilo, either as a beginning in/of time or as a component of creatio continua. In terms of treatments of General Relativity (GR), the FLRW model yield a singularity at R=0 (t=0), the Penrose-Hawking singularity theorem showed that singularities are generally found as solutions of the GR field equations, and the Borde-Guth-Velenkin theorem demonstrates for classical relativity, if the Universe has an average positive expansion, it has to have a beginning. But GR fails in the domain near R=0, t=0, such that quantum gravity theory would have to be invoked—but there is no theory of quantum gravity.

None of the theories which have a purported quantum mechanical base have any empirical support. In the Hartle-Hawking model the introduction of the imaginary, it, to replace the time variable, t, in the general equation for the universe wave-function (if such were to exist) is arbitrary, done only for aesthetic reasons (to remove a singularity).

Robert J. Russell and Chris Isham claim that the Hartle-Hawking model is consistent with creatio continua, with nothing at the boundary of the closed universe. Robert J. Russell also argues that a finite universe is consistent with Creation theology, even if there is no definite beginning (as in Hawking’s argument that the south (or north) pole is not the beginning of the earth.) George F.R. Ellis points out that Hawking’s argument that the universe is pre-existent, caused by nothing other than gravity, is not correct since the Hartle-Hawking model includes (pre-existent Hilbert spaces, quantum operators, Hamiltonians,etc.) whose existence is if anything more mysterious than that of the universe itself,” quoted by Robert J. Russell.

My Take

The science/physics/cosmology of creation does show empirical evidence for a creation event, a “Big Bang”: the red shift showing a universe expansion; the COBE microwave background radiation showing the burnt embers of a very initial epoch; the hydrogen/helium ratio and lack of carbon-12 in ancient (far distant) stars; the more recent B-mode COBE results showing effects of early inflation.

Theologians seem to be wary about falling into a “God of the Gaps” pit, using the deity to explain what science cannot. That fear I believe is unfounded. At some point a God of the Gaps argument has to be introduced, as a prime mover, to explain why there is a science illumined by mathematical theory. There are theological and philosophical issues that are not yet (and may never be) settled: What is time? Does God change with time, or is He eternally fixed and, if so, how does he act in time?

Theologians and scientists have not improved very much, if at all, on the insights of Sts. Augustine and Aquinas. Faith and revelation give insight. The arguments of the Catechism are as forceful now as they were when first propounded by Theophilus of Antioch. And finally, we should keep in mind the aphorism of St. Thomas Aquinas: “It is not that God is irrational but that our understanding is limited.”

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1Objections have been made to the use of t=0 as a “beginning” in that arbitrary mathematical mappings can change t=0 to t = -infinity (logarithmic transform) or t= +infinity (inverse transform). I don’t consider such objections to be substantive, since they are artificial—we don’t perceive the passage of time in a logarithmic or inverse transform way, although as any husband knows who has waited for his wife to finish shopping, the subjective passage of time is not necessarily linear with a clock.

Summary Against Modern Thought: God Is Eternal

This may be proved in three ways. The first...

This may be proved in three ways. The first…

See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles. All posts are under the category SAMT.

Previous post.

Short, sweet, and entirely obvious proofs today. But I add some material from Aristotle on which St Thomas relied, which itself is fascinating and makes you wonder why people stopped reading the former. Review: for any change, there must be a first and unique (single) Unchanging Changer. What does that imply?

Chapter 15: That God is eternal

1 FROM the foregoing it is also clear that God is eternal.i

2 For whatever begins or ceases to be, suffers this through movement or change. Now it has been shown[1]ii that God is altogether unchangeable. Therefore He is eternal, having neither beginning nor end.

3 Again. Only things which are moved are measured by time: because time is the measure of movement, as stated in 4 Phys.[2]iii

Now God is absolutely without movement, as we have already proved.[3] Therefore we cannot mark before and after in Him. Therefore in Him there is not being after non-being, nor can He have non-being after being, nor is it possible to find any succession in His being, because these things cannot be understood apart from time. Therefore He is without beginning and end, and has all His being simultaneously: and in this consists the notion of eternity.[4]iv

4 Moreover. If anywhenv He was not and afterwards was, He was brought by someone out of non-being into being. Not by Himself; because what is not cannot do anything. And if by another, this other is prior to Him. Now it has been shown[5] that God is the first cause. Therefore He did not begin to be. Therefore neither will He cease to be: because that which always was, has the power to be always. Therefore He is eternal.vi

5 Furthermore. We observe that in the world there are certain things which can be and not be, namely those that are subject to generation and corruption. Now whatsoever is possible to be has a cause, because, as in itself it is equally related to two things, namely being and not being, it follows that if it acquires being this is the result of some cause. But, as proved above[6] by Aristotle’s argument, we cannot go on to infinity in causes. Therefore we must suppose some thing, which it is necessary to be.vii

Now every necessary thing either has a cause of its necessity from without, or has no such cause, but is necessary of itself. But we cannot go on to infinity in necessary things that have causes of their necessity from without. Therefore we must suppose some first necessary thing which is necessary of itself: and this is God, since He is the first cause, as proved above.[7] Therefore God is eternal, since whatever is necessary of itself is eternal.viii

6 Again. Aristotle[8] proves the everlastingness of movement from the everlastingness of time: and thence he goes on to prove the everlastingness of the substance that is the cause of movement.[9] Now the first moving substance is God. Therefore He is everlasting. And supposing the everlastingness of time and movement to be denied, there still remains the argument in proof of the everlastingness of substance. For if movement had a beginning, it must have had its beginning from some mover. And if this mover had a beginning, it had its beginning from some agent. And thus either we shall go on to infinity, or we shall come to something without a beginning.ix

7 Divine authority bears witness to this truth: wherefore the Psalm[10] reads: But Thou, O Lord, endurest for ever, and again:[11] But Thou art always the self-same, and Thy years shall not fail.

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iEternal, which is to say, outside time, not part of time, unchanging. Eternal does not mean now, one second from now, two seconds from now, etc. It means no time.

iiThis is what Aquinas did in Chapter 13.

iii From the Philosopher, and don’t forget that when these gentleman use motion they mean change:

But neither does time exist without change; for when the state of our own minds does not change at all, or we have not noticed its changing, we do not realize that time has elapsed…So, just as, if the ‘now’ were not different but one and the same, there would not have been time, so too when its difference escapes our notice the interval does not seem to be time. If, then, the non-realization of the existence of time happens to us when we do not distinguish any change, but the soul seems to stay in one indivisible state, and when we perceive and distinguish we say time has elapsed, evidently time is not independent of movement and change. It is evident, then, that time is neither movement nor independent of movement…

Now we perceive movement and time together: for even when it is dark and we are not being affected through the body, if any movement takes place in the mind we at once suppose that some time also has elapsed; and not only that but also, when some time is thought to have passed, some movement also along with it seems to have taken place. Hence time is either movement or something that belongs to movement. Since then it is not movement, it must be the other…

But we apprehend time only when we have marked motion, marking it by ‘before’ and ‘after’; and it is only when we have perceived ‘before’ and ‘after’ in motion that we say that time has elapsed. Now we mark them by judging that A and B are different, and that some third thing is intermediate to them. When we think of the extremes as different from the middle and the mind pronounces that the ‘nows’ are two, one before and one after, it is then that we say that there is time, and this that we say is time. For what is bounded by the ‘now’ is thought to be time—we may assume this.

iv This is from Summa Theologica[4]—the debt to Aristotle is obvious:

As we attain to the knowledge of simple things by way of compound things, so must we reach to the knowledge of eternity by means of time, which is nothing but the numbering of movement by “before” and “after.” For since succession occurs in every movement, and one part comes after another, the fact that we reckon before and after in movement, makes us apprehend time, which is nothing else but the measure of before and after in movement. Now in a thing bereft of movement, which is always the same, there is no before or after. As therefore the idea of time consists in the numbering of before and after in movement; so likewise in the apprehension of the uniformity of what is outside of movement, consists the idea of eternity.

Further, those things are said to be measured by time which have a beginning and an end in time, because in everything which is moved there is a beginning, and there is an end. But as whatever is wholly immutable can have no succession, so it has no beginning, and no end.

Thus eternity is known from two sources: first, because what is eternal is interminable–that is, has no beginning nor end (that is, no term either way); secondly, because eternity has no succession, being simultaneously whole.

vIt’s high time to resurrect this word; so much more evocative than whenever.

viSince the first cause of the here-and-now change must exist, and cannot be caused by anything else, and therefore cannot change, this first cause must be eternal, i.e. outside time.

viiReview Chapter 13. What is not cannot cause what is. You can’t get something from nothing.

viiiWhatever is necessarily true, in the logical sense, will not be false at some point in the future, when circumstances change. True is always true, true outside of time, i.e. eternal.

ixThese proof by contradictions are, I think, especially convincing when they involve infinities. We’ll end with a portion of the footnote to Aristotle, more for the flavor than anything else (the paragraph break is mine):

Now the existence of motion is asserted by all who have anything to say about nature, because they all concern themselves with the construction of the world and study the question of becoming and perishing, which processes could not come about without the existence of motion. But those who say that there is an infinite number of worlds, some of which are in process of becoming while others are in process of perishing, assert that there is always motion (for these processes of becoming and perishing of the worlds necessarily involve motion), whereas those who hold that there is only one world, whether everlasting or not, make corresponding assumptions in regard to motion.

If then it is possible that at any time nothing should be in motion, this must come about in one of two ways: either in the manner described by Anaxagoras, who says that all things were together and at rest for an infinite period of time, and that then Mind introduced motion and separated them; or in the manner described by Empedocles, according to whom the universe is alternately in motion and at rest—in motion, when Love is making the one out of many, or Strife is making many out of one, and at rest in the intermediate periods of time…

Asserted by all not fearful of where this admission leads, that is.

[1] Ibid.
[2] xi. 5.
[3] Ch. xiii.
[4] Sum. Th. P. I., Q. x.
[5] Ch. xiii.
[6] Ibid.
[7] Ibid.
[8] 8 Phys. i. 10 seqq.
[9] vi. 3 seqq.
[10] Ps. ci. 13.
[11] Ibid. 28.

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