Columbia mathematician Peter Woit offers some interesting comments on Max Tegmark’s The Mathematical Universe. We’d noted it last weekend, because the New Scientist review comprised one of the few instances of critical thinking on multiverse theory we’ve encountered in popular science media. Anyway, here’s Woit:
Tegmark’s career is a rather unusual story, mixing reputable science with an increasingly strong taste for grandiose nonsense. In this book he indulges his inner crank, describing in detail an utterly empty vision of the “ultimate nature of reality.” What’s perhaps most remarkable about the book is the respectful reception it seems to be getting, see reviews here, here, here and here. The Financial Times review credits Tegmark as the “academic celebrity” behind the turn of physics to the multiverse:
As recently as the 1990s, most scientists regarded the idea of multiple universes as wild speculation too far out on the fringe to be worth serious discussion. Indeed, in 1998, Max Tegmark, then an up-and-coming young cosmologist at Princeton, received an email from a senior colleague warning him off multiverse research: “Your crackpot papers are not helping you,” it said.
Needless to say, Tegmark persisted in exploring the multiverse as a window on “the ultimate nature of reality”, while making sure also to work on subjects in mainstream cosmology as camouflage for his real enthusiasm. Today multiple universes are scientifically respectable, thanks to the work of Tegmark as much as anyone. Now a physics professor at Massachusetts Institute of Technology, he presents his multiverse work to the public in Our Mathematical Universe.
It’s part of the “mainstreaming” of the multiverse—quite apart from any evidence in support—that I wrote about here:
Hailed as the “world’s smartest man,” with cameos to his credit on The Simpsons and Star Trek, Stephen Hawking has blessed the multiverse for popular culture. Denouncing philosophy (and religion) as “outdated and irrelevant”, he announced that science dispenses with a designer behind nature because the law of gravity explains how the universe “can and will create itself from nothing.”
Those who want to be in the know, whether or not there is anything to know, will not know enough not to ask about evidence.
Especially when they learn things like this (Woit’s post is must reading):
1. The Templeton Foundation gave Tegmark and Anthony Aguirre nearly $9 million for a “Foundational Questions Institute” (FQXi)
2. Tegmark has little interest in mathematics, it turns out, and
There are no mathematicians among those thanked in the acknowledgements, and while “mathematical structures” are invoked in the book as the basis of everything, there’s little to no discussion of the mathematical structures that modern mathematicians find interesting (although the idea of “symmetries” gets a mention).
3. The book closes with a plea for scientists to “get organized to fight things like ‘fringe religious groups concerned that questioning their pseudo-scientific claims would erode their power’.” This, let’s understand, is from a well-funded multiverse advocate whose discipline rests on no evidence at all.
Woit says he doesn’t understand the attraction of the multiverse. If he means “scientific” attraction, I don’t either. If he had meant “political” attraction, the answer is obvious. Stay tuned.
See also: The Science Fictions series at your fingertips and
Popular science writer “sort of” gets it about the multiverse scam
Hawking [now] says there are no black holes?
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71 Replies to “Mathematician wonders about the respectful reception new multiverse book is getting”
As even Tegmark himself admits in this recent concession to the problems with the inflation conjecture (whatever level that is in his scheme of things), multiverse scenarios are epistemologically self defeating:
Actually, contrary to Tegmark’s philosophical druthers, infinity is not ever going away, and infinity itself shows that the scientific idea that needs to be retired is naturalism/materialism:
Moreover, despite Tegmark’s love affair with conjecturing ‘random’ infinite multiverse’s, of all flavors, to ‘explain’ any anomalous effect, that he may stumble across, that needs a cause to explain it, the ‘theory’, (if inflation can rightly be called a theory rather than wild speculation), that needs to be retired, rather than infinity, (and exactly what finite parameter could he possibly postulate that would be up to the task of retiring infinity? 🙂 ), to prevent the epistemological collapse of science itself, is clearly inflation itself (as well as the multiverse in general).
The most succinct rejoinder to multiverse conjectures, that I’ve personally seen, is the following:
Aren’t these the people who speak dismissively – if ever so gently so – at QM as woo-woo?
‘Mathematics-based, sure, but a hopeless topic on which to base theoretical assumptions….’ More like Buddhism!
‘at QM’, should be ‘of QM’, of course.
My apologies. It was a relic of ‘scoff at’, but they can’t be too ‘up front’ about it, since the modern world is largely based on it.
I saw an estimate of the scale of QM’s significance, recently, of approximately two thirds of global, industrial output.
Tegmark may be a crank but he is right about infinity. Infinity is nonsense. Heck, it’s not even wrong. And I say this as a Christian. That said, what caught my attention in the OP is this:
How did an obvious crackpot/con-man like Stephen Hawking ever acquire such fame? This is a sad commentary on the status of modern science.
To further reflect on Tegmark’s notion of ‘retiring infinity’ from science so as to avoid ‘anything goes’ conundrums, conundrums that he himself, (apparently obliviously), is instrumental in invoking every-time he appeals to an unconstrained ‘random infinity’ to try to explain the universe, or to try to explain some facet of the universe, it is interesting to note where infinity actually pops up as a result of real science instead of infinity being a philosophical add on from naturalists.
In this endeavor, it is first important to note that ‘higher dimensional’ mathematics had to be developed before Einstein could elucidate General Relativity, or even before Quantum Mechanics could be elucidated;
In Quantum Mechanics we find that the higher dimensional mathematics, that was required in order to elucidate it, is defined as a ‘infinite dimensional Hilbert space’
Along that line, it is found that a ‘uncollapsed’ photon, in its infinite dimensional quantum wave state, is mathematically defined as ‘infinite’ information:
It is interesting to note that many times when I have pointed this amazing fact out to Atheists that they responded that the infinite dimensional quantum wave state was just a abstract mathematical description that had no ‘real’ correspondence to reality. Yet, despite what those atheists held beforehand, here was a rigorous measurement of the infinite dimensional quantum wave function, in 2011, that established it as ‘physically real’;
The following experiment actually encoded information into a photon while it was in its infinite dimensional quantum wave state, thus destroying the notion, apparently held by many atheists, that the wave function was not ‘physically real’ but was merely an ‘abstract’ description. i.e. How can information possibly be encoded into something that is not physically real but is merely abstract?
The following paper mathematically corroborated the preceding experiments and cleaned up some pretty nasty probabilistic incongruities/conundrums, in quantum mechanics, particularly incongruities dealing with quantum entanglement. Conundrums that arose from, not so surprisingly, a purely statistical/probabilistic interpretation of the infinite dimensional wave function.
Of note: Since I believe, in my unqualified opinion, that the Many Worlds interpretation of quantum mechanics insists on treating the wave function as an abstract probabilistic construct, then, again I believe in my unqualified opinion, that the preceding work refutes the Many Worlds interpretation of quantum mechanics.
On the reality of the quantum state – Matthew F. Pusey, Jonathan Barrett & Terry Rudolph – May 2012
Abstract: Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state truly represents. One possibility is that a pure quantum state corresponds directly to reality. However, there is a long history of suggestions that a quantum state (even a pure state) represents only knowledge or information about some aspect of reality. Here we show that any model in which a quantum state represents mere information about an underlying physical state of the system, and in which systems that are prepared independently have independent physical states, must make predictions that contradict those of quantum theory. (i.e. Any model that holds the Quantum wave state as merely a abstract representation of reality, i.e. as not a real representation of reality, must make predictions that contradict those of quantum theory.)
Hey @bornagain77 speaking of quantum states I recently saw a documentary on BBC about counciosness. At the end of the documentary the host joins up with John-Dylan Haynes a neuroscientist in Berlin. The host did a experiment with a MRI scanner and pressed a button by choice. After the experiment he showed results of a pre-determined state in the brain that showed that the neuroscientist could predict what he was going to press 6 seconds before he actually made the choice. The documentary had showed the picture of his material brain already choosing something before his counciosness mind did. Just wanted to know if you saw this documentary what are the implications of this!
to continue on from post 5: Another interesting place infinity pops up as a result of science, instead of it being a philosophical add on of naturalists, is from Quantum electrodynamics (QED)
In fact QED does not so much “‘solve’ the problem of infinities associated with charged point-like particles” as it ‘brushes the problem of infinity under the rug’,
Richard Feynman comments further here,,,
I don’t know about Feynman, but as for myself, being a Christian Theist, I find it rather comforting to know that it takes an ‘infinite amount of logic to figure out what one stinky tiny bit of space-time is going to do’:
Moreover, besides this brushing infinity under the rug with QED, we also find the conflict of reconciling General Relativity and Quantum Mechanics appears to arise from the inability of either theory to successfully deal with the Zero/Infinity problem that crops up in different places of each theory:
I guess the mathematicians are having a much harder time ‘brushing infinity under the rug’ here. Yet, to continue on, the unification, into a ‘theory of everything’, between what is in essence the ‘infinite Theistic world of Quantum Mechanics’ and the ‘finite Materialistic world of the 4-D space-time of General Relativity’ seems to be directly related to what Jesus apparently joined together with His resurrection, i.e. related to the unification of infinite God with finite man. Dr. William Dembski in this following comment, though not directly addressing the Zero/Infinity conflict in General Relativity and Quantum Mechanics, offers insight into this ‘unification’ of the infinite and the finite:
And if we allow that ‘God can play the role of a person’, (for who could deny Him that possibility “IF” He exists), as even the author of the incompleteness theorem himself allowed that god could do,,
,, if we allow that possibility that ‘God can play the role of a person’, then we find a very credible reconciliation between the finite and the infinite that does not wind up in the ‘anything goes’ epistemological pit of logical absurdities,,,
,,,in fact, unlike all thiese outlandish multiverse scenarios which have no empirical support, we find a reconciliation between General Relativity and Quantum Mechanics that has a surprising amount of empirical support. For instance, it is now shown that the process in which the image was formed on the Shroud of Turin was a ‘quantum process’, not a classical process:
The absorbed energy in the Shroud body image formation appears as contributed by discrete values – Giovanni Fazio, Giuseppe Mandaglio – 2008
Excerpt: This result means that the optical density distribution,, can not be attributed at the absorbed energy described in the framework of the classical physics model. It is, in fact, necessary to hypothesize a absorption by discrete values of the energy where the ‘quantum’ is equal to the one necessary to yellow one fibril.
Scientists say Turin Shroud is supernatural – December 2011
Excerpt: After years of work trying to replicate the colouring on the shroud, a similar image has been created by the scientists.
However, they only managed the effect by scorching equivalent linen material with high-intensity ultra violet lasers, undermining the arguments of other research, they say, which claims the Turin Shroud is a medieval hoax.
Such technology, say researchers from the National Agency for New Technologies, Energy and Sustainable Economic Development (Enea), was far beyond the capability of medieval forgers, whom most experts have credited with making the famous relic.
“The results show that a short and intense burst of UV directional radiation can colour a linen cloth so as to reproduce many of the peculiar characteristics of the body image on the Shroud of Turin,” they said.
And in case there was any doubt about the preternatural degree of energy needed to make such distinct marks, the Enea report spells it out: “This degree of power cannot be reproduced by any normal UV source built to date.”
Music and Verse:
Jaceli123,,,, if you would have googled a bit, you may have found this (or something along this line)
Do Benjamin Libet’s Experiments Show that Free Will Is an Illusion? – Michael Egnor – January 15, 2014
Excerpt: Materialists often invoke the experiments of Benjamin Libet when they deny free will.,,,
(Yet) Libet himself was a strong defender of free will, and he interpreted his own experiments as validating free will. He noted that his subjects often vetoed the unconscious “decision” after the readiness potential appeared.
,,,”The role of conscious free will would be, then, not to initiate a voluntary act, but rather to control whether the act takes place. We may view the unconscious initiatives for voluntary actions as ‘bubbling up’ in the brain. The conscious-will then selects which of these initiatives may go forward to an action or which ones to veto and abort, with no act appearing.” – Libet
Libet even observed that his experimental confirmation of free will accorded with the traditional religious understanding of free will:,,,
as well, (as if that were not enough),
in the following experiment, the claim that past material states determine future conscious choices (determinism) is falsified by the fact that present conscious choices effect past material states:
Quantum physics mimics spooky action into the past – April 23, 2012
Excerpt: The authors experimentally realized a “Gedankenexperiment” called “delayed-choice entanglement swapping”, formulated by Asher Peres in the year 2000. Two pairs of entangled photons are produced, and one photon from each pair is sent to a party called Victor. Of the two remaining photons, one photon is sent to the party Alice and one is sent to the party Bob. Victor can now choose between two kinds of measurements. If he decides to measure his two photons in a way such that they are forced to be in an entangled state, then also Alice’s and Bob’s photon pair becomes entangled. If Victor chooses to measure his particles individually, Alice’s and Bob’s photon pair ends up in a separable state. Modern quantum optics technology allowed the team to delay Victor’s choice and measurement with respect to the measurements which Alice and Bob perform on their photons. “We found that whether Alice’s and Bob’s photons are entangled and show quantum correlations or are separable and show classical correlations can be decided after they have been measured”, explains Xiao-song Ma, lead author of the study.
According to the famous words of Albert Einstein, the effects of quantum entanglement appear as “spooky action at a distance”. The recent experiment has gone one remarkable step further. “Within a naïve classical world view, quantum mechanics can even mimic an influence of future actions on past events”, says Anton Zeilinger.
In other words, if my conscious choices really are just merely the result of whatever state the material particles in my brain happen to be in in the past (deterministic) how in blue blazes are my choices instantaneously effecting the state of material particles into the past?,,, I consider the preceding experimental evidence to be an improvement over the traditional ‘uncertainty’ argument for free will, from quantum mechanics, that had been used to undermine the deterministic belief of materialists:
Why Quantum Physics (Uncertainty) Ends the Free Will Debate – Michio Kaku – video
What Does Quantum Physics Have to Do with Free Will? – By Antoine Suarez – July 22, 2013
Excerpt: What is more, recent experiments are bringing to light that the experimenter’s free will and consciousness should be considered axioms (founding principles) of standard quantum physics theory. So for instance, in experiments involving “entanglement” (the phenomenon Einstein called “spooky action at a distance”), to conclude that quantum correlations of two particles are nonlocal (i.e. cannot be explained by signals traveling at velocity less than or equal to the speed of light), it is crucial to assume that the experimenter can make free choices, and is not constrained in what orientation he/she sets the measuring devices.
To understand these implications it is crucial to be aware that quantum physics is not only a description of the material and visible world around us, but also speaks about non-material influences coming from outside the space-time.,,,
How Free Will Works (In Quantum Mechanics) – video
Just repeating over and over that infinity exists does not make it so. Most of your arguments are arguments from authority. They sound like propaganda. I distrust authority, especially human authority. Here’s the reason that infinity is nonsense.
Compared to the infinitely large, everything is infinitely small. And compared to the infinitely small, everything is infinitely large. So, if infinity existed, everything would be infinitely large and infinitely small while also being finite at the same time. This is absurd on the face of it.
Now, I know you have religious (Biblical) reasons for pushing infinity. In my opinion, your reasons are wrong, whatever they are. Now stop appealing to authority and refute what I wrote above. Let’s see some actual logic for a change and not some useless reference to authority.
Some infinities exist in reality, some do not.
For example, if I draw a line that’s one meter long, and then poke a pinhole somewhere on that line, there are an infinite number of places on that line, all irrational number distances from one end, where the hole could appear.
Mapou, I’m quite happy to let what I wrote, and referenced, stand on its own merits, as I am quite happy to let what you wrote fall by the same standards. Infinity is a wild, wild, horse and any material explanation will be thrown off into the dirt of epistemological absurdity. Only God, who is infinite, not infinity, can tame infinity. Only God who is omniscient, knows every number in pi, or possesses the infinite knowledge necessary to collapse the infinite dimensional quantum wave state to a photon of one bit.
The Supreme God is a Being eternal, infinite, absolutely perfect;,,, from his true dominion it follows that the true God is a living, intelligent, and powerful Being; and, from his other perfections, that he is supreme, or most perfect. He is eternal and infinite, omnipotent and omniscient; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things, and knows all things that are or can be done. He is not eternity or infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures for ever, and is every where present:
Sir Isaac Newton – Quoted from what many consider the greatest science masterpiece of all time, his book “Principia”
Your reply to my comment @11 is exactly what I expected from you. You would rather believe in lies than change your doctrine. Your doctrine IS your God. You worship your idea of God more than you worship God. That makes you an idolater in my book. Good luck with that.
Saying that there is an infinite number of places on that line does not make it so. It is an assertion, not a proof.
PS. Please, don’t circumvent my proof against infinity @11 above with other arguments. Either prove me wrong (if you do, I’ll bow down to your superior understanding and apologize for my foolishness) or accept that I am right (in which case, you must bow down to my superior understanding and make amends). Anything else is just useless talk.
Mapou, actually I did not presuppose that God, through Christ, could ‘tame the irreconcilable infinity problem’ that had popped up between General Relativity and Quantum Mechanics. In fact I did not even know the infinity problem between the two existed until a few years ago, but I can not deny that I was very pleasantly surprised that Christ offered such a ‘neat’, very credible, empirically backed, reconciliation between the two grand theories of physics. You accuse of me that I would ‘rather believe in lies than change your doctrine’, but I strongly disagree with, what I find to be, your emotional assessment. I came to the table of science many years ago willing to let the evidence speak for itself, and to not try to force fit the evidence into any preconceived notions that I may have had. Thus my Christian belief was very vulnerable to falsification at the time. But what I have found through the years is that, not only has my basic Christian belief not been threatened by the findings of modern science, the findings of modern science actually require Christianity to be true in order for a ‘theory of everything’ to truly be successful in the reconciliation of General relativity and Quantum Mechanics (not to mention the reconciliation of perfect God with imperfect man)!
“So you think of physics in search of a “Grand Unified Theory of Everything”, Why should we even think there is such a thing? Why should we think there is some ultimate level of resolution? Right? It is part, it is a consequence of believing in some kind of design. Right? And there is some sense in which that however mulrifarious and diverse the phenomena of nature are, they are ultimately unified by the minimal set of laws and principles possible. In so far as science continues to operate with that assumption, there is a presupposition of design that is motivating the scientific process. Because it would be perfectly easy,, to stop the pursuit of science at much lower levels. You know understand a certain range of phenomena in a way that is appropiate to deal with that phenomena and just stop there and not go any deeper or any farther.”,,, You see, there is sense in which there is design at the ultimate level, the ultimate teleology you might say, which provides the ultimate closure,,”
Professor Steve Fuller
quote as stated At 17:34 minute mark of the following video
In Cambridge, Professor Steve Fuller discusses intelligent design – Video
@bornagain77 thanks also what are the implications of this video!
Jaceli123, sorry I’m not watching any of your off topic rabbit trail videos anymore. You have to do your own homework!
Mapou, it is also humorous to note that you simply cannot wish infinity away by demanding everyone else bow to your will that infinity should be stricken from discussion in science. Science simply does not work that way! (Much less do scientists work that way). If you want to be taken seriously then you have to provide a rigorous mathematical/logical proof as to why infinity is persona no gratis in science.,,, Which I wish you luck in, because it was through the ‘logic of infinity’ that Godel was able to bring the incompleteness theorem to fruition.
It is also interesting to note in the following video, that documents the lives of several mathematicians who were studying infinity, that there was a strange streak of madness that followed them in this endeavor:
Personally I find the fact that man should even be able to contemplate the infinite to be a wonderful mystery. A mystery I hold is related to the fact that we were created by infinite God, in his image, to have a personal relationship with Him.
Verse and Music:
Ok sorry this subject has me really worrying because if brain states occur and we have no control over this what does this show for free will. Anyway sorry again!
Unless you are prepared refute my argument @11 against infinity, everything you write from now on is unimportant to me. In fact, my respect for you has taken a precipitous dive. See you around.
Mapou, in your argument, you are trying to understand the infinite from a finite materialistic/naturalistic perspective. OF COURSE it is logically absurd from that position. Why should I try to refute your argument when I agree with you 100% that materialism/naturalism cannot handle the infinite? i.e. non sequitur!
Your self-deception is as bold and in-your-face as that of a Jerry Coyne or a Richard Dawkins. But it does not fool me. Why should anybody try to understand something that does not exist? The non-existence of infinity has absolutely nothing to do with materialism of naturalism.
Another thing that bothers me about you is your constant use of this world’s pathological science to prove your Christian faith. Don’t you know that Yahweh’s science makes a mockery of human science? Yahweh and the host of his angels laughs at the stuff you bring up to defend your doctrine. I, too, join them in poking fun at it. Don’t you know that this world’s science is carefully designed to deny God and his glory? But those of you who truly have faith in Yahweh will not have long to wait to see His science manifested in this world and crush the science of this world like one crushes a bug underfoot.
Funny Mapou, you rail against infinity being real on the one hand but then on the other you say the ‘science of this world’ will be crushed by, what I assume is, the infinite wonder and glory of God. Which is it, does the infinite not exist? or does infinite power exist in God? And if you don’t think God is infinitely powerful, just how much finite power are you willing to grant him? Just asking, inquiring minds and all that!
The science of this world is hopelessly infatuated with infinity. Black holes, wormholes, Big Bangs, infinite parallel universes, etc., are all based on continuity, which assumes infinity.
The concept of infinite power is both absurd and stupid. It is a concept created by weak men who do not understand that they, too, are gods.
Sure, Yahweh’s power and wisdom are enormous and can continue to grow indefinitely, if he so wishes, but that is not the same as saying that they are infinite. Show me a single quote from the scriptures where Yahweh says, “I am infinitely powerful” or “I have infinite knowledge of the past present and future.” This stuff is not even wrong. It makes a mockery of God and opens a door for the forces of evil to come in and mock God and his people.
Interesting Mapou, never heard anyone claim God is not infinite in power and knowledge. Does it not bother you that you have a finite god instead of a infinite God? What church were you brought in? or what church do you currently go to that teaches this strange doctrine?
“Remember the former things long past, For I am God, and there is no other; I am God, and there is no one like Me, Declaring the end from the beginning, And from ancient times things which have not been done, Saying, ‘My purpose will be established, And I will accomplish all My good pleasure’;
The Lord Reveals His Omnipotence to Job
38 Then the Lord answered Job out of the whirlwind, and said:
2 “Who is this who darkens counsel
By words without knowledge?
3 Now prepare yourself like a man;
I will question you, and you shall answer Me.
4 “Where were you when I laid the foundations of the earth?
Tell Me, if you have understanding.
5 Who determined its measurements?
Surely you know!
Or who stretched the line upon it?
6 To what were its foundations fastened?
Or who laid its cornerstone,
7 When the morning stars sang together,
And all the sons of God shouted for joy?
8 “Or who shut in the sea with doors,
When it burst forth and issued from the womb;
9 When I made the clouds its garment,
And thick darkness its swaddling band;
10 When I fixed My limit for it,
And set bars and doors;
11 When I said,
‘This far you may come, but no farther,
And here your proud waves must stop!’
12 “Have you commanded the morning since your days began,
And caused the dawn to know its place,
13 That it might take hold of the ends of the earth,
And the wicked be shaken out of it?
14 It takes on form like clay under a seal,
And stands out like a garment.
15 From the wicked their light is withheld,
And the upraised arm is broken.
16 “Have you entered the springs of the sea?
Or have you walked in search of the depths?
17 Have the gates of death been revealed to you?
Or have you seen the doors of the shadow of death?
18 Have you comprehended the breadth of the earth?
Tell Me, if you know all this.
19 “Where is the way to the dwelling of light?
And darkness, where is its place,
20 That you may take it to its territory,
That you may know the paths to its home?
21 Do you know it, because you were born then,
Or because the number of your days is great?
22 “Have you entered the treasury of snow,
Or have you seen the treasury of hail,
23 Which I have reserved for the time of trouble,
For the day of battle and war?
24 By what way is light diffused,
Or the east wind scattered over the earth?
25 “Who has divided a channel for the overflowing water,
Or a path for the thunderbolt,
26 To cause it to rain on a land where there is no one,
A wilderness in which there is no man;
27 To satisfy the desolate waste,
And cause to spring forth the growth of tender grass?
28 Has the rain a father?
Or who has begotten the drops of dew?
29 From whose womb comes the ice?
And the frost of heaven, who gives it birth?
30 The waters harden like stone,
And the surface of the deep is frozen.
31 “Can you bind the cluster of the Pleiades,
Or loose the belt of Orion?
32 Can you bring out Mazzaroth[a] in its season?
Or can you guide the Great Bear with its cubs?
33 Do you know the ordinances of the heavens?
Can you set their dominion over the earth?
34 “Can you lift up your voice to the clouds,
That an abundance of water may cover you?
35 Can you send out lightnings, that they may go,
And say to you, ‘Here we are!’?
36 Who has put wisdom in the mind?[b]
Or who has given understanding to the heart?
37 Who can number the clouds by wisdom?
Or who can pour out the bottles of heaven,
38 When the dust hardens in clumps,
And the clods cling together?
39 “Can you hunt the prey for the lion,
Or satisfy the appetite of the young lions,
40 When they crouch in their dens,
Or lurk in their lairs to lie in wait?
41 Who provides food for the raven,
When its young ones cry to God,
And wander about for lack of food?
You are indeed a deceiver and you are not to be trusted.
This line is not found in the book of Job. It is an editorial addition by the translators of the New King James Bible.
In other words, you have nothing to show but deception. And you know what? You will never have anything because you are lying to yourself and to others. Stop doing that. You’re not doing God a favor.
So Mapou, you hold that the God who spoke Job 38 is a finite being? I certainly don’t! In fact I can’t even conceive of such knowledge and power, as was manifested in the verses of Job 38, being confined to a finite being.
As well, I noticed you didn’t comment on Isaiah 46:9-10 which directly contradicted your claim that there was no verse that said God was omniscient. Or was that, in your eyes, just me misinterpreting the scripture again so you didn’t bother to acknowledge your mistake?
Enough theology in this one thread for a divinity school. Anyone noted how Tegmark’s philosophizing (with a clearly religious turn) can be advanced in science publications (SciAm comes to mind)? Odd that it bothers so few.
Stephen Hawking/No Black Holes, by the way, reached 76 m on Google search.
Mapou @ 11
Consider the set of counting numbers 1,2,3,4,5,6,7,8,9,10. There are 10 of them. Notice that the set of even numbers is 5. Do the same for the set of counting numbers to 100, 1000, a million, and a trillion. There are still half as many even numbers. Extrapolating, if you divide the infinite number of counting numbers by the infinite number of even numbers in the series, the answer will be exactly 2. Thus, there are larger and smaller infinities, falsifying your first statement.
Calculus is based on finding the sums of infinitesimally small slices of areas under 2D curves, from which we can calculate many things including the thermal efficiency of a Carnot engine (although it’s easier to use the formula 1-T1/T2). The sum of an infinite number of infinitesimally small numbers is not infinitesimally small. For example, the thermal efficiency of a typical steam engine is about 0.4, and not zero. This falsifies your second statement.
Divide the length of the circumference of a circle by the length of its diameter. How many digits are in the answer? From memory, the answer starts out 3.14159265358979323846264338327950… Thus, infinity exists in mathematics and in reality, falsifying your conclusion as well.
“And the truth shall set you free”, that is exactly why reading posts from BA77, Q, KF, VJT and others like them makes us die-hard fans of them and makes us want to read more and more. Kudos!
The cardinalities of “counting numbers” and “even numbers in the series” are both the same. So the answer is 1, not 2.
F/N: Pardon, but attempted division does weird things with transfinites and is a forbidden operation as a result. Think of p / q as find multiplicative inverse of q, q’ and multiply: p x q’. Now, what is the multiplicative inverse of aleph-null? H’mm, that requires a div. by zero error if there ever was one! Verboten, tut, tut! Better view is that we identify transfinite sets by seeing the cardinality of a proper subset is the same as of the full set. Yes, that is strange, but it works. Doff hats for Cantor on that, knowing the price he paid for messing with ant trying to tame infinity. KF
Q: There actually is a non-standard development of calculus on hyper reals that takes up the infinitesimal and conceptualises it into something tractable, as opposed to the usual infinite series limits approach. KF
As to Querius’s comment here:
This is another place where the findings of modern science give us clear indication that ‘the infinite’ must reside in God. As Querius indicated we know that pi is infinite, although no finite being (or finite computer) has been, nor will ever be, able to elucidate all the numbers of pi. But whatever, or more precisely Whomever, brought this universe must have had/has knowledge of every number of the infinite number of pi. This is apparent since ‘He’, if I may be so bold as to use that pronoun, designed the universe along the parameters of pi, using the infinite pi as a sort of a template if you will.,,,
The following is very interesting since, with the discovery of the Cosmic Microwave Background Radiation (CMBR), the universe is found to actually be a circular sphere which ‘coincidentally’ corresponds to the circle of pi within Euler’s identity:
Moreover, there is now known to be an unexpected ‘flatness’ to the universe that also corresponds to the diameter of pi in Euler’s identity:
That the fine-tuning of the roundness and flatness of the universe are unexpected from a naturalistic perspective is revealed by the fact that naturalists attempted to ‘explain it away’ by postulating rapid inflation during the initial stages of the Big Bang, which, as Tegmark himself concedes,,
Thus Tegmark concedes that postulating a unconstrained random infinity, as was done with inflation, to explain the roundness of the universe is a epistemologically self-defeating proposition. Yet, in irony of ironies, he calls for retiring the concept of ‘unconstrained infinity’ from science altogether. A concept that he, as news pointed out in the OP, Max Tegmark himself was instrumental in championing in the first place:
Besides the evidence that Dr. Ross listed for the 1 in 10^120 finely tuned expansion of the universe, this following paper clearly indicates that we do live in universe with a ‘true cosmological constant’. A cosmological constant that is not reducible to a materialistic basis. Thus, the atheistic astrophysicists are at a complete loss to explain why the universe expands in such a finely tuned way, whereas Theists are vindicated once again in their beliefs that the universal constants are truly transcendent!
Querius, I agree with you. Cantor never proved anything wrt infinite sets and he is not God. Not only that there isn’t any utility in saying all countable and infinite sets have the same cardinality.
Cantor’s is more dogma than mathematics.
Ladies and gentlemen, here is my argument again:
Unless you have a counter argument that either directly refutes it or agrees with it, you are wasting both your time and mine. Sorry.
Querius @ 30, nope, that’s not it.
By the way, those of you who are under the false impression that calculus uses infinity, consider that digital computers routinely solve calculus problems and yet, nothing is more discrete and finite than a computer.
First, I just note that your “ratios” — note, your use of compared to — are not the same as the things themselves.
A subtle but important difference.
The same finite distance, measured in light years will be a small fraction, but measured in Angstroms, it will be a large number. But all along it is the same distance, say from Papine to Half Way Tree in Kingston, Jamaica, or the length of Long Beach in Christchurch, Barbados [a mile].
On the way, a corrective note for me, if we try to assign a multiplicative inverse, say v, to the transfinite aleph Null, say A0, we see v * A0 –> 1. The cardinality of evens AND of natural no’s will both be A0, and the division you proposed “translates” to v*A0 –> ??, or the same 1. But this is “toying” the real point is that cardinality of a transfinite countable set has different properties from that of a finite set. And in fact it is sets we are really dealing with here.
To see that 1, 2, 3, . . . and 2, 4, 6 . . . have identical cardinality, let us do a transformation:
So the logic forces us to accept that N and the set of evens hold the same cardinality, A0.
Being strange to us given our current concepts and being absurd in itself are different things.
A simple case is how it is possible to stand at one and the same point and be due North of London, New York, and Tokyo.
At first it seems odd, but the geographic North Pole is due North of every other point on the Eart’s surface.
This also holds for many concepts in theology and philosophy, that seem strange until worked through.
You are imagining things. There is no mistake to acknowledge. Here is the verse again:
Where in this verse does it say anything about Yahweh being either infinitely powerful or infinitely knowledgeable? Enlighten me.
PS: A computer does not solve a calculus problem, the programmer does. And if you mean evaluating a numerical solution to say volume of a solid of revolution between defined points, that is a numerical approximation. If you program the machine to analytically integrate, it gives an analytic solution worked out elsewhere. Try to get it to solve for an analytic expression for integral of e^(-x^2). It will predictably fail for the obvious reason.
I fail to see the truth in what you’re saying here. Is it a refutation of my argument?
This proves nothing. Be a hero and go right ahead and measure your finite distance using an infinitely small unit. Good luck with that.
The rest of your argument @39 does not address my argument. Sorry. Notice that your argument assumes the very thing (the existence of infinity) it is trying to prove.
F/N: Is God eternal, a necessary being? Your answer will give us a clear view of the matter, and of your particular theology . . . and closely linked philosophy. Similarly, is God all knowing, all-powerful, all-good, all-wise, etc. These questions help clarify what is meant when God is said to be “infinite-personal.” KF
PS: This, from Wiki, will be interesting. The world has some really strange things in it.
M: I am not trying to prove the existence of an infinite set, thus of an infinity. That reality, has long been obvious. Set up a mirror. Locate images behind it, then understand it poses a virtual half-universe. Then, put two in parallel with a pin with a bright red knob on top in the middle, yielding (mathematically, if you will) an infinity behind each. Similarly, observe a line, the real number line and observe the property that between any two neighbouring values we can define a third, etc. Perhaps, your problem is with the logic involved, as is suggested by challenging on the supertask of measuring an infinity in finite succession. All that succeeds in doing is highlighting that one cannot traverse an infinity in steps. The whole set must be delivered at once. That a transfinite set may have strange properties should be no more surprising than negative numbers, zero, the incommensurate nature of sides and diagonals of squares, the sqrt(-1) = i, etc. And BA77 is dead right to highlight how all of these things (including implied infinite series) come together in the Euler expression 0 = 1 + e^(i*pi). KF
so this verse
‘Declaring the end from the beginning, And from ancient times things which have not been done,’
Is not reflective of God’s omniscience in your book? I must say, I have never met anybody, and I mean anybody, that holds to your strange interpretation of scripture (and mathematics). I find omniscience and omnipotence to be integral to Theism. For instance how people going to give an account for ‘every careless word uttered’ on the day of judgement if God is not omniscient?
But I tell you that everyone will have to give account on the day of judgment for every empty word they have spoken.
And just because you personally believe God is not omniscient and omnipotent, in your own private interpretation of scripture I might add, what in God’s green earth gives you the audacity to believe that you can change thousands of years of Monotheistic thought on God’s omniscience and omnipotence, by throwing, what I perceive to be, a rather childish tantrum on a out of the way blog?
If changing Theological thought were not enough for your unconstrained ambitions, you also want to exclude infinity from role in mathematics because you find absurdities with it that you, personally, have not been able to work your way through. But you offer no rigorous proof, in any system of logic, as to why infinity should be stricken. Just because you are stuck in a personal mental mire on the infinity matter why do you think the world of mathematics should suddenly stop and take notice of you. Do you really think that name calling, and such as that as you have displayed here, is going to have any effect on the preeminent mathematicians of the world? Perhaps you should call Gregory Chaitin up with your insight that infinity should be stricken from math?
The Limits Of Reason – Gregory Chaitin – 2006
Excerpt: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.,,,
I’m sure he could probably use a good belly laugh at your suggestion!
In that case, this discussion is futile because my argument is that infinity is nonsense. Unless you are trying to disprove my argument, I fail to see the purpose of our debate, assuming this was a debate to begin with.
If humans, with their feeble means, can make predictions, imagine what a being who can create a universe can do. Not only can such a being make very accurate predictions, he can make his predictions happen by actively manipulating physical events. I fail to see the need for omniscience (infinite knowledge) here. Besides, the Yahweh of the scriptures is never presented as knowing everything. If one knows everything, one cannot have regrets. Did not Yahweh regret having created humans? The answer is yes, of course, because this is what the book of Genesis says in plain language that cannot be denied or futzed with unless one is a liar.
On another note, is not Jesus God? If so, as God, he should know everything according to your theology, right? And yet we know from reading the scriptures that Jesus does not know everything. How can that be? Well, Jesus himself said that he did not know the exact time of his return, only the father knows.
Methinks the holes your theology would let a Mack truck through.
I am sure there is a point you are trying to make here but I can’t place a finger on it. Sorry.
Simple. Everything that occurs in the physical universe is being recorded in what I call “the lattice”. It’s a finite universe and a finite lattice.
It is not audacity. I just don’t trust anybody, especially those who hold on to thousands of years of dogma at all costs. That’s idolatry, in my opinion. I question everything this world throws at me.
Your personal opinion of my behavior is irrelevant to me.
I do offer a simple solid proof @11 above but I’m still waiting for your refutation.
I simply call a spade a spade. I am not a politician.
I don’t give a rat’s posterior about Gregory Chaitin’s opinion or the world of mathematics and their preeminent mathematicians. I know my priorities. I always write for the simple man or woman. Those are my peers.
Mapou, to borrow your words, ‘you are deceiving yourself’!
You got me, Mr. born again man. I yield to the infinite superiority of your arguments. NOT. LOL.
Mapou you state:
But alas Mapou, I am not the one who said this:
And yet you expect us to ‘yield to the infinite superiority of your arguments’, and indeed you act like a spoiled child when no one takes your strawman argument seriously, when you yourself don’t take the entire field of mathematics seriously. Someone has an seriously hyper-inflated opinion of their own infallibility on this matter!
Maybe I have a hyper-inflated opinion of my infallibility in this matter but the same can be said about you.
PS. I am still waiting for your logical refutation of my argument @11. I guess I’ll have to wait until chickens grow teeth and evolve into predatory birds. LOL.
Mapou, you want a ‘logical refutation’ of your ahem ‘argument’ when you have rejected the entire logical world of mathematics as to having any purchase over your own self-exalted infallible thinking in this matter in the first place? i.e. cart before horse!
To shine a light in a darkened room it is first necessary to, at least, open a window!
There’s none so blind as those who will not see.
Prov. You cannot make someone pay attention to something that he or she does not want to notice.
It is precisely because I have read the so-called proofs of infinity that I reject them. My argument is a direct refutation of those proofs. You avoid it like the plague because you don’t have the mental ability to even think about formulating a rebuttal, let alone refute it. You’re weak. You know it and I know it. A true follower of Yahweh is strong, not weak.
That being said, I don’t challenge you specifically to refute my argument @11. I know you can’t. You are a propaganda artist, not a thinker. I challenge everybody. It’s a logical argument. If I am proven wrong, I will repent and acknowledge my foolishness.
This is not what is wrong with Querius’s argument. The glaring problem with his argument is that he is assuming the existence of infinity (e.g., “if you divide the infinite number…”) while arguing for its existence. Querius should man up or woman up, as the case may be, and acknowledge that his argument is invalid or lose face.
Well, according to Georg Cantor, the inventor of the classification of infinities, I’m wrong about comparing counting numbers with even counting numbers. He recognized that there are different orders of infinities, which he called Alephs, and that counting numbers and even counting numbers are both in Aleph-0.
My original thought was more in line with L’Hopital’s rule where you take ratios of expressions as some part in the numerator or denominator goes to infinity. The *rates* of which each expression goes to infinity or to zero are compared. My thought was that in pairings of the two infinite sets, the the ratios are not 1 in this case; any element of one set is always double its pair in the other. Hmmm, but now I’m talking myself out of my position. The infinities are equal in number despite the fact the values of the numbers in one set are always double that in the other.
However, Georg Cantor does assert that the infinity of real numbers is greater, because you cannot pair off real numbers with counting numbers (or natural numbers for that matter). In turn, you also cannot pair off the numbers of curves with the real numbers, so these are in different Alephs.
My point about an infinite number of real numbers on a line of finite length still stands.
Mapou, your ad hominem undermines your claim of ‘being strong’. Claiming to be ‘strong’ while disparaging other people who may disagree with you is certainly not a sign of strength but of weakness. A truly strong person does not try to exalt himself by belittling other people, but a truly strong person tries to help those he considers less fortunate than himself/herself.
But you got it wrong. I am not trying to help you at all. I have very little respect for you, especially after this exchange. You’re a typical doctrinairian and I don’t like doctrinairians. I don’t think you’re less fortunate. You have access to the same knowledge sources as I do. That’s the way I feel. And I tell it like I see it.
This is so true. One of the most brilliant people that I work with is humble and soft-spoken. He carefully considers the technical questions and challenges put to him, and he answers them with both kindness and precision.
Mapou, you continue to want me (or anyone) to ‘refute’ your argument at 11, which is as such,,,
to which I responded to your argument in 13 as such:
and to which I again responded to your argument at 22:
And Mapou to further show you that I agree 100% with your argument against a naturalistic/materialistic interpretation of infinity, which is once again,,
,,,I think you may find the following site very interesting:
The preceding interactive graph points out that the smallest scale visible to the human eye (as well as a human egg) is at 10^-4 meters, which ‘just so happens’ to be directly in the exponential center of all possible sizes of our physical reality (not just ‘nearly’ in the exponential center!). i.e. 10^-4 is, exponentially, right in the middle of 10^-35 meters, which is the smallest possible unit of length, which is Planck length, and 10^27 meters, which is the largest possible unit of ‘observable’ length since space-time was created in the Big Bang, which is the diameter of the universe. This is very interesting for, as far as I can tell, the limits to human vision (as well as the size of the human egg) could have, theoretically, been at very different positions than directly in the exponential middle;
also of note:
So thus Mapou, I agree 100% with your argument, and nature itself agrees you, that a finite naturalistic/materialistic infinity, with space-time, cannot exist. Where I think your argument goes off the rails is when you try to extrapolate the obvious absurdities that are apparent for infinity in the material (space-time) realm,,,
,,,off the rails when you try to extrapolate the obvious absurdity in the material, space-time, realm to the transcendent (i.e. higher dimensional) realm that is above this material realm. Yet how did this material, space-time, realm come into being if not from an infinitely powerful, omniscient, transcendent Being who had mastery over infinity so as to be able to do it?
i.e. Mapou, your argument from the infinitely large and from the infinitely small against the validity of infinity itself addresses the issue from the wrong conceptual basis to begin with! i.e. I NEVER disagreed with you that infinity within the space-time of the material realm was completely absurd. You are the one who erroneously assumed that such absurdities for infinitely in the finite material realm hold for the timeless-spaceless transcendent realm that is above this one, and indeed the transcendent realm that brought this universe into being, but you simply are not justified in such an radical extrapolation from the material realm to say that the infinite does not exist in God who brought this material realm, all the space-time matter-energy of it, into being by his word and who continues to uphold it in his infinite power.
Verse and Music:
Q. Is God eternal, a necessary being?
A. Yes. But eternal is not synonymous with infinite. It simply means immortal or indestructible. Why? Because God is the greatest power in the universe.
Q. is God all knowing? A. No.
Q. All-powerful? A. No.
Q. All-good? A. I have no idea what this means. Something is either good or bad.
Q. All-wise? A. If God can make mistakes and can regret making such mistakes, then the answer is no. Yahweh admits that he made a mistake creating humans on earth.
Cantor was a self-important crackpot and a con artist, IMO. His contribution to society amounts to a disaster, considering the enormous amount of time wasted by the world’s acceptance of infinity as a logical concept. Even after Planck discovered that the universe was discrete, physicists still continue to act as if infinity is a valid concept. It’s painful just to think about it.
Doesn’t the Big Bang presuppose a beginning, i.e, a starting pooint? That would make the universe finite, not infinite. Hawking uses imaginary numbers in his theorems, but according to William Lane Craig, when he converts the numbers to real integers, a singularity appears (the beginning point). I don’t see at all how Big Bang cosmology supports infinity.
There is no question, at least in my yin-yang, dualistic philosophy, that reality consists of both a physical realm and a spiritual realm. The word “transcendent” means nothing to me. Here is how I define the two.
1. In the physical realm, everything can be created, destroyed or modified. Everything has a beginning and can have an end.
2. In the spiritual realm, nothing can be created, destroyed or modified. Things just are.
I see no reason to believe that the spiritual realm is infinite. It contains as many entities as are necessary, no more and no less. Personally, I could not worship a God who is infinitely knowledgeable and powerful. Setting aside, for argument’s sake, the fact that such a God is logically absurd, the problem I see is that everything would come easy to such a God. He would have no merit in my view. I prefer the idea of a self-made God who spent trillions upon trillions of years perfecting his wisdom and power through trial and error and hardship. That’s the kind of God that appeals to me and that’s the kind of God I am not ashamed to call Master. And I believe that’s the God that scriptures refer to as the “ancient of days.”
I truly believe that humans were made in the image of the Gods (Elohim). The Gods have brains just like us and learn through trial and error just like us. The main difference is that Yahweh Elohim has honor whereas humans don’t.
“The word “transcendent” means nothing to me.”
What Properties Must the Cause of the Universe Have? – William Lane Craig – video
Wherefore should the heathen say, Where is now their God?
Our God is in heaven; he does whatever pleases him.
M: Just a note, eternal in the context of being the necessary being at the root of reality is already infinite, of endless duration. KF
PS: Other necessary beings such as the proposition 2 + 3 = 5, are endlessly contemplated by God as eternal mind. Another infinity in aggregate.
PPS: Your ad hom on one of the most significant mathematicians in history — who, similar to several others suffered bipolar depression — is unworthy and verges on being offensive. Cantor is a founding father of Set Theory, and in that context a main pioneer of the mathematics of the infinite . . . or better, the transfinite (the Absolute Infinite, he reserved for the Godhead). His reputation is not on trial. Period. This one is in the league of a Gauss, or a Newton. If one can show his work and its cumulative legacy materially in error or in need of limitation and generalisation, fine, but a trash-talk dismissal is simply not acceptable.
PPPS: I see your framing of your own system of theology. Your privilege, but not compelling. The interested onlooker may wish to refer to say Hodge here on . . . 3 vols (with defense of approach in an ultra-mod era here) or to the alas incomplete (he passed on . . . ) magisterial work by the Angelic Doctor, here. Grudem’s contemporary Systematic Theology is a short [relatively speaking], simple [ditto] survey. Onlookers may like to look at the humble street level course here on, and yes, it starts with where to go for more, including the heavy artillery.
I’m sorry but anybody who legitimizes infinity as a viable concept in science is a crackpot in my view. The belief in continuous structures (which presupposes infinity) in the physics community is probably the biggest impediment to progress in the field, IMO. Worse, thanks to the belief in infinity, physics has been inundated with crackpottery, what with time travel, parallel universes, wormholes, black holes, etc. Even Einstein, Mr. Continuity par excellence, had serious doubts about it as seen in this partial quote from a letter he wrote to a friend near the end of his life:
Too bad Einstein did not live long enough to work on that angle. The only reason that physicists, including Einstein during his heyday, still cannot figure out why C is the fastest possible speed in the universe is that they believe in continuity and infinity. If they could only get rid of those shackles, they would understand that, not only is C the fastest possible speed, it is also the only possible speed. Nothing can move faster or slower, period. Surprise!
So I don’t care how great a contribution Cantor has made to set theory. His obsession with the legitimacy of infinity and his ability to captivate and deceive the minds of so many generations of thinkers with his crackpottery is unforgivable, IMO.
PS. The veneration that some people (mostly Catholics, I think) have for the Angelic Doctor (Thomas Aquinas) borders on the idolatrous, IMO. Talk about worshiping doctrine.
M: The validity of infinity has nothing to do with whether or not there is a multiverse, for instance. The continuum is not primarily a scientific concept but a mathematical one and is just as valid. And, with al due respect people may differ on big issues without being crack pots all on one side. KF
PS: I am about as Protestant as they come, and the angelic doctor is one of the greatest minds in the history of Christendom, with Paul, Augustine, Calvin and Wesley up there too in that league — warts and all.
Eternal is most certainly synonymous with infinite.
You claim that God is the greatest power in the universe, yet below you claim that He is not all powerful. See the contradiction in your own beliefs?
You and I are reading entirely different Bibles then.
You didn’t know what eternal meant, either.
No, He did not. I’m not sure what scriptural reference you’re using here. At times, God changes his attitude toward people. For example, more than once, the ancient Israelites left Jehovah and followed other gods. Jehovah then took away his protection. However, when the people felt sorry for their error and called to God for help, he changed his feelings toward them, or ‘felt regret.’ (Judg. 2:18)
God is perfect and never errs in judgment, so it is not that he feels regret in the way that a human does when he has completely misjudged a matter. Rather, Jehovah feels regret by adjusting his dealings, responding to the change of heart he observes.
This is not just a cold rescinding of a sentence. Jehovah’s feelings change toward repentant sinners. According to some scholars, the origin of the Hebrew verb translated “feel regret” in the verses cited above is thought to reflect the idea of “breathing deeply,” maybe with a sigh. This may indicate that when Jehovah sees genuine remorse in a human heart, figuratively he breathes deeply, as with a sigh of relief. God can show the repentant person the loving attention enjoyed by those having His approval. That sinner may still face certain consequences, yet God is pleased with his change of heart. He softens “the calamity,” or divine discipline, that otherwise might be due. (Jer. 26:13)
You also never answered my point about the Big Bang, either.
I no longer want to discuss this topic. Thanks for the comments.
M: While you may no longer wish to debate the topic, you may find the already linked readings helpful. Again, I commend to you the street level survey with reference links here on. KF
Ok. I cannot let this go without a response. Some dumbass over at antievolution.org who calls itself CeilingCat, wrote the following as a refutation of my argument @11:
LOL. CeilingCat has no clue as to what a comparison is. A comparison is a question or test that demands a true or false answer. For example, given the finite values X and Y, we can ask:
X is greater than Y, true or false?
or, within the context of my argument against infinity, if Y is given as an infinitely small value, we can phrase the question thus:
X is infinitely greater than Y, true or false?
or, if Y is given as an infinitely large value, we can phrase the question thus:
X is infinitely smaller than Y, true or false?
The answer is a resounding YES to both questions. CeilingCat should claw its way back to the ceiling and let grownups take care of grownup business.