Robert J. Marks: The logical consequences of a literally infinite past are absurd, as a simple illustration will show:
The story starts with Slow Sam who is a very slow writer. Sam is writing his autobiography. But it takes Sam a week to write the account of a single day of his life. Poor Sam. He is falling further and further behind in his writing.
But in the world of infinities this need not be the case. If the universe has always been in existence and Slow Sam has been writing for this entire infinite time, then the number of days and number of weeks today — counting from an infinite time ago — are the same. The consequence of this is crazy. If he has been writing forever, Sam can have completed his autobiography if he dies today!
This conclusion is, of course, ludicrous. Although not a definitive mathematical proof that the universe was created a finite time ago, the observation is solid evidence that our universe had a beginning. Otherwise, we would have to deal with infinity weirdnesses like Slow Sam’s autobiography.
To avoid the ridiculousness of Slow Sam finishing his autobiography, we must conclude the universe had a beginning.
Robert J. Marks, “2. Infinity illustrates that the universe has a beginning” at Mind Matters News
Takehome: The absurdities that an infinite past time would create, while not a definitive mathematical proof, are solid evidence that our universe had a beginning.
Here’s Part 1: Why infinity does not exist in reality. A few examples will show the absurd results that come from assuming that infinity exists in the world around us as it does in math. In a series of five posts, I explain the difference between what infinity means — and doesn’t mean — as a concept.
You may also wish to read: Yes, you can manipulate infinity in math. The hyperreals are bigger (and smaller) than your average number — and better! (Jonathan Bartlett)
Traversal of a transfinite span in stepwise stages is an infeasible supertask
You cannot get to the end of an infinite future.
How can you possibly get to today from an infinite past?
Everyone misses the obvious.
If the universe was infinite, or if there are/were an infinite number of universes, everything physically possible must have happened.
If you disagree, please explain why?
Then exploring the possibilities is what destroys this concept not absurd examples like Sam and his biography.
Infinity is what people who don’t like the finite (reality) appeal to.
It’s a psychological reaction.
Andrew
There seems to be a lot of confusion about infinity.
I see no logical or mathematical problems with an actual infinite past. Infinite sets that can be put into a 1-1 correspondence are not necessarily identical. Every week Sam runs 6 days behind, so if he has been writing from infinity, then he is infinitely far behind in his book. Of course, this assumes that the past had a specific beginning point, which an infinite past denies.
And why should an infinite universe entail that “everything possible must have happened”?
Suppose there were a proof that the past is finite . Then there must a maximum possible past age, say N. But why not N+1? or NxN? If you can’t specify a precise upper limit for N, does this not entail that N is infinite?
If actual infinity is to be banned, does this mean that God has a finite past? or a limited knowledge of the future?
“I see no logical or mathematical problems with an actual infinite past.”
Then you aren’t being consistently logical.
Andrew
“If actual infinity is to be banned, does this mean that God has a finite past?”
God doesn’t have any kind of past or future. His creation does. Finite.
Andrew
Explain why something did not happen.
At any point in time, there is an infinite past. This means every possible combination of matter and energy would at some time happen. If you disagree, then explain why it didn’t happen? Remember one has postulated an infinite amount of time but has ruled out certain combination as possible.
You just answered your question.
There is nothing larger because nothing existed then. Even if one could imagine a larger number, it does not relate to anything real.
Similarly someone says give me an N and I will give you a larger N which N+1. The only problem is that while N may point to something, there comes a point where N+1 will not point to anything. Also if there is a finite amount of time, then one will run out of opportunities to say there is a N+1 thus, there will be no larger number than N. In other words in order to postulate an infinite number of numbers, there has to be infinite time to do it.
Jerry at 8,
Insufficient data. This is wild speculation at best. No actual answer is possible.
“But why not N+1? or NxN? If you can’t specify a precise upper limit for N, does this not entail that N is infinite?”
If the imagination is where these exercises exclusively take place, then it’s all… well… imaginary, and you haven’t demonstrated anything.
Andrew
“A journey of a thousand miles begins with a single step.”
— The Dao De Jing
CD at 11,
‘A journey to infinity would take an infinite number of steps, so you can forget about that one.’
— The Me De Jing
“A journey of a thousand miles”
Finite.
“begins with a single step.”
Finite.
Andrew
By definition if a thing does not happen in an infinite number of attempts, then it is “not possible”.
Therefore, in an infinite number of attempts, everything that could possibly happen must happen.
Asauber at 7.
“God doesn’t have any kind of past or future. His creation does. Finite.”
The Biblical God has a present, past, and future (“who is, and who was, and who is to come” Rev.1:4), and, moreover, is “from everlasting to everlasting” (Ps.90.2), which means a beginningless past and an endless future. Infinite in time in both directions.
Capalas,
You are interpreting Bible passages in light of your own understanding. Yours might not be the correct interpretation.
Andrew
Capalas at 15,
God has no beginning and no end. He is the same yesterday, today and tomorrow.
Silver at 14
“And why should an infinite universe entail that “everything possible must have happened”? “By definition, if a thing does not happen in an infinite number of attempts, then it is “not possible”. Therefore, in an infinite number of attempts, everything that could possibly happen must happen.
Not so. Suppose event A can happen only if, say, some universal property P (mean density, or temperature, etc.) > 1. And suppose in the infinite past P was always less than 1 . Then simply because A is possible (i.e., P might become >1 in the future) does not entail A must have already happened. An infinite number of attempts at A failed because the proper conditions were not (yet) present.
This is a simple explanation of what I was trying to say.
Now take this to the next step and try to understand what is then possible. The answer is that very shortly there will be an infinite number of unlikely scenarios. One of the most interesting conclusions will be that an infinite number of entities with infinite intelligence and power must exist.
Again I highly recommend the Asimov short story, “The Final Question” which is about this very possibility. But with a twist. It was Asimov’s favorite thing he wrote.
https://www.physics.princeton.edu/ph115/LQ.pdf
“And suppose in the infinite past P was always less than 1”
Couldn’t be. In an infinite past there would be an infinite number of moments when P=1 and P>1
Andrew
See you can’t invoke infinity and then say something didn’t happen in it. Everything happened an infinite amount of times.
Andrew
Including this same internet thread.
“Including this same internet thread.”
Jerry,
Weird.
Andrew
SA at 14,
If I have a car but there’s no gas in the tank, I can try to start it an infinite number of times and still get nothing.
Capalas
There’s no “yet” in an infinity. You can’t add anything to an infinity. In an infinite number of attempts, you can’t add one more. If I tell you, “drive an infinite number of miles and then just add one more mile” you cannot do it.
So, you can’t wait for something that “hasn’t happened yet”. You cannot traverse an infinity and then expect something else to happen.
Everything has already happened. You can’t get to a present tense and then just add another day to a beginningless infinity.
I notice by your phrasing you are confusing a mathematical conception of infinity with “actual infinity”.
The universe is real. It is something that exists. It’s not just a mathematical construct.
A universe without a beginning would require the movement across an infinite distance in time to arrive at today. No mathematical propositions can change that.
It’s just not possible in real life.
Silver: “You cannot traverse an infinity and then expect something else to happen.”
Consider “one-bounce” cosmologies, where the present expansion of the universe was preceded by a single, infinitely long contraction. The present was preceded by an infinite past, but after that, there was only one bounce, one history of human life, etc.
Infinite past time does not in itself demand that everything possible happened, let alone an infinite number of times.
“If I have a car but there’s no gas in the tank, I can try to start it an infinite number of times and still get nothing.”
Relatd,
Just keep trying till gas is put in the tank. You have an infinite amount of tries. In an infinity gas will be in the tank an infinite amount of times.
Andrew
“Consider “one-bounce” cosmologies,”
We’re right into full-blown fantasy . Yawn. It was inevitable.
Andrew
“Infinite past time does not in itself demand that everything possible happened”
You don’t understand infinity. You think you can just give it properties that are finite. Confusion.
Andrew
Perhaps Davies and Walker will help:
That should clear up the point.
KF
PS, for more on the anthropic principle from Lewis and Barnes https://uncommondescent.com/intelligent-design/hitchhikers-guide-authors-puddle-argument-against-fine-tuning-and-a-response/#comment-729507
There’s a few new folks joining this conversation, so I will throw out Ben Waters argument for the finitude of the past again. Nobody here has refuted it so far, but feel free to give it a try: https://philarchive.org/archive/WATMDA-2
F/N: Basic logic of being problems attach to claims of infinite past temporal-causal thermodynamically constrained worlds. Where, at cosmic scale, time relates to just that sort of energy constrained flow of events, from finite stage to finite stage. For convenience, think in terms of years. This allows us to start from the integer mile posted reals with points at infinity to set a framework for consideration, the hyperreals. An explicit or implicit transfinite past implies a successful traversal of ACTUAL past stages . . . k –> k+1 –> k+2 . . . now –> . . . constituting a completed transfinite traverse. We can talk about that, but it takes but little effort to see that a completed transfinite, stepwise traverse like that is an infeasible supertask, as we can only ever reach a finite number of successive stages in succession, bound by onward possible ones. That is, inherently this sort of world is strictly finite in the past and while it may be unlimited in onward succession at every stage only finitely many steps will have occurred; this is a potential infinite, as opposed to an actually traversed one. Worlds like ours inherently have past finite limits, and are subject to heat death onward [effective dissipation and degradation of energy concentrations useful to be reservoirs for physical work] if left to themselves. KF
I’m curious. Wouldn’t the invention of the calculus of infinitesimals by Newton, which allowed the successful solution of a number of previously insolvable problems, show that one class of infinities (infinitely small things) must exist in order for the math solutions to exist?
Doubter, it can be readily shown that the abstracta N, Z,R,C,R* exist in any possible world as part of its logical framework of structure and quantity. See the linked. KF
No.
At Doubter #33 “infinitesimals ” can be considered in the same fashion of the infinite… and yes while both help mathematics in their most extreme boutique type concepts one can show just how absurd they can get.
For example – I think i can show that there are just as many points on line A-B, as there are on a square that consists of 4 lines the length of A-B (square A-B-C-D-A) .
I believe Using infinitesimals, there are an infinite number of points on line A-B. There can be no number greater than an infinite (number of numbers, amounts of amounts, days of days)…hence the absurdity of it becomes apparent. In this creation, we live in the finite and only mathematically dabble in the infinite…..
re 36, to Thumper.
1. Showing that there are just as many points on the line segment AB as there are in the square ABCD is what Marks wrote about in part 3 of his series. That is one of the many things that are true about the mathematical concept of infinity that is counter-intuitive in respect to our understanding of finite items. See here for part 3 of Mark’s series.
These are only “absurd” in respect to a comparison with finite sets, but not absurd if seen as a coherent and logical part of the mathematics of the infinite. The history of mathematics is full of the original resistance to some new ideas as “absurd” that were eventually accepted as new mathematics with powerful meanings and uses, such as irrational numbers, negative numbers, and imaginary numbers.
2. You write, ” There can be no number greater than an infinite (number of numbers, amounts of amounts, days of days).” Here you are wrong. The number of points on a line represented by the real numbers is a greater order of infinity than the number of counting numbers {1, 2, 3…} or the number of rational numbers on a line. This is basic mathematics at the advanced high school level. If you don’t know that, you should read up. See this article in Marks’ series: here
3. You write, “In this creation, we live in the finite and only mathematically dabble in the infinite…..” I think everyone that I know of that has ever posted here agrees that the real world can’t instantiate a true infinity of things. There is no controversy here about that.
However, to dismiss the mathematics of infinity, especially the infinitely small and the principle of continuity that it implies as “dabbling” or a “boutique” really shows a lack of appreciation, I think, for the power of our mathematical models that uses infinity, as embodied in calculus among other places, to accurately describe the world, as Doubter mentioned in 33.
@Viola Point 1…cool so I was not off the mark, I’m sure he was more eloquent than I about it.
Point 2 … I don’t think you have any mathematical proof of any number being higher than an infinite. So if you re-read my post, you will see we are dealing with the infinitesimals…the fractions… ( the old Plato/Zeno example of going half the way from point A to point B ..and then halfway again..and so on and so on … infinitely )…and that point right there is where those are in lock step with the infinite…or ‘counting numbers as you stated’…same thing…but you missed that point. (they both go on and on and of course…on to no end) So I pretty much disagree with your point on that. This can be shown (explained actually) that the set of numbers that are infinite…will always include the highest known number +1… in all situations one can ever imagine. in fact about the only path that one could take is a rather esoteric-ish example of the use of numbered ‘sets’. By this I mean that it was shown that there will always be a higher number of ‘sets’ (be it numbers or what have you) ….than there are in all of the numbers that make up these sets. For example, no matter the amount of numbers you state …there will always be a higher number of ‘sets’ that contain those numbers and classify those numbers than there are numbers. But then we are now drawn into the ever expanding absurdity of infinity…yes, while it supports edge math…it is never able to be quantified. and by that I propose that you show the value of pie to the 10 to the tenth to the tenth value …and if it really matters at that level for any calculations ever done.
Sorry if I am not being congruent as I wish to be… I don’t dismiss the value of infinite concepts at all… but I accept that we don’t correctly value them..as we can’t mathematically comprehend their true nature. they do very much have value….. but there is so so much more deeper aspects that we don’t and can’t grasp in this realm….it will have to wait.
“infinitesimals…the fractions… ” No, the infinitesimals are not the same as fractions.
“… I don’t think you have any mathematical proof of any number being higher than an infinite” Did you read Professor Marks post on this very subject, which is a proof that there is an infinity “bigger than” the infinity created by the counting numbers.
If I had a list of all the natural numbers, that list wouldn’t be as big as a list of all the real numbers.
In fact, there are too many real numbers to put on a list – so the real numbers would be a “bigger infinity” than just the infinite list of the natural numbers.
Let’s say I had a piece of paper of infinite size – tall and wide.
Then, I typed all the natural numbers on it.
Now, I took the exact same sized paper and then tried to type all the real numbers on it.
Of course, the real numbers wouldn’t fit.
Why?
Obviously, the real numbers are a bigger infinite. So, you need a much bigger piece of paper.
EDTA @31,
Thanks for the link to Ben Waters’ paper on the finitude of the past. Whenever I see an argument involving something infinite, I simply substitute in n/0 (where n does not equal 0).
There are all kinds of interesting things one can prove with n/0. For example
a = 1 . . . given
b = 1 . . . given
a = b . . . reflexive property, substitution property
a^2 = ab . . . multiplying both sides by a
a^2 – b^2 = ab – b^2 . . . subtracting b^2 from both sides
(a + b) (a-b) = b(a – b) . . . factoring out (a-b)
(a + b) (a – b)/(a-b) = b(a – b)/(a – b) . . . dividing both sides by (a-b)
(a + b) = b . . . result of the division
(a + b) – b = b – b . . . subtracting b from both sides
a = 0 . . . result of the subtraction
But a = 1 was given, therefore 0 = 1 . . . substitution
Of course, ratios of rates toward zero and infinity can found using L’Hôpital’s Rule. But that’s another subject.
-Q
And on the controversy about the sizes of infinities:
https://www.quantamagazine.org/to-settle-infinity-question-a-new-law-of-mathematics-20131126/
-Q
That’s the problem. Infinity with endpoints. Infinity bounded and limited to a completed set.
We didn’t hear anything from that group, but i’m happy to count myself a member of it.
…” Did you read Professor Marks post on this very subject, which is a proof that there is an infinity “bigger than” the infinity created by the counting numbers. ” Clearly I did not, and should now to better try to comprehend this. But with my limited math skillz i understand that there is always going to be another number n + 1…no matter what…there can always be 1 added to the previous.
It becomes hard to comprehend the factual nature of an infinity, while we can certainly converse philosophically on it….(and yes have our best processors to continually press out and into infinitude)
I thought I just added a sort of ‘proof’ that yes – there is something ‘larger’…or ‘more’ than an infinity of counting numbers by stating that no matter what…. there will be a list of ‘sets’ that will always be ‘larger’ or ‘more’ than the components that make up the sets. (in the case above the use of counting numbers were used..and one can always create unique ‘sets’ of all counting numbers in ways that produce more ‘sets’ than counting numbers)
Getting back to the philosophical…. maybe something in our nature has some aspect of infinity built in… I try to understand the spiritual aspect and nature of God…. but only as is capable in this realm
@SA Post 40:
First thanks for pulling those quotes…. helps
But is there such a thing as infinity to the 10th power? It does not feel right to even consider something being larger than something that can’t be quantified. the example of counting vs real numbers is a good example – I don’t think one can try to define infinite is a ‘different’ type of infinite’ for one set of numbers vs another set of numbers…. infinity is self descriptive? iow…. you don’t plug in a different value for infinity for different situations…. I don’t think infinity is specifically inclusive nor exclusive of anything if it restricts the nature of an infinite…
So while i get the point of real numbers, counting numbers…. ect… infinity is just that… infinity… no matter how you use it…. a piece of paper infinitely wide as it is tall will have to infinitely grow to and infinite size to hold the infinitely growing number of real numbers or counting numbers…. never stopping…. For example – there are no amount real numbers that can’t be counted…..both are infinite… and infinite is not limited as far as I know.
Trumper
No, there isn’t. Infinity does not have a boundary. In order to raise an infinity to a power, you have to circumscribe it – you have to put a boundary around it, and then say, “this infinity”. But if you can put a boundary on it, then it’s not infinity. That’s the mental trick that the mathematicians have fallen into. Once they say “this infinity is a completed set” – they’ve violated what infinity is.
Agreed because it’s simply incorrect. Infinity cannot be quantified. Nobody can say how large it is. To then say “there’s a bigger infinity” is nonsense.
We know this because the stories about how “one infinity is larger than another” are often prefaced with a comment something like: “‘This will seem very surprising but actually some infinities are bigger than others!”
Then the story will go directly to the (deceptive) proof and end: “See? Isn’t that amazing?”
But the thing is, they haven’t solved the obvious problem: “How can you even say that one infinity could be bigger or smaller than anything?” But they don’t answer that.
It’s like asking: What weighs more, an infinite number of golf balls or an infinite number of elephants?
Then they’ll say “of course, there’s no real infinity in the world, that would be absurd”.
But the math itself is absurd.
Instead of golf balls and elephants, it would be the same as asking:
What weighs more, an infinite number of unicorns or an infinite number of leprechauns?
If an infinity does not exist in realty, why do theorists talk of how cardinality associates one point from one infinity to one from another – matching them point by point?
Exactly. A piece of paper of infinite size has no edges. You never get to the end of the paper and say “well, it just won’t fit any more numbers”. An infinite space will fit every possible thing – it has no boundaries. Real numbers will fit and natural numbers also – and there won’t be any unfilled space. Neither number set runs out of numbers all of a sudden and just stops. They both have unlimited, uncountable amounts.
@Querius
Not sure what kind of made up math you’re doing here, but in math you can’t devide by (a-b), if a=b.
SA #47
Nicely stated. exactly what I was attempting to get at but bumbled about it fully. The absurdity of infinity….. it’s a great concept…and fringe in its practicality.
AndyClue @48,
Exactly! My point was that dividing by zero–or rather, with a number approaching zero–yields a result that approaches infinity, one can get all kinds of weird results, including the bogus “proof” that 1 = 0.
This is why working with infinity requires one to be extremely suspicious of the result. It’s also why in mathematics dividing by zero is “undefined” and that 0/0, when expressed as a limit, is “indeterminate.”
-Q
Infinity as a concept as opposed to infinity in reality is a little akin to us never getting anywhere or never being able to pickup an object.
For me to pick up an object I have to reach my hand out and pick it up , but for my hand to reach out and pick it up it has to first travel half the distance between my and the object , then half again then half again , and so on thus my hand never reaches the object , in reality it never moves at all.
Marfin: For me to pick up an object I have to reach my hand out and pick it up , but for my hand to reach out and pick it up it has to first travel half the distance between my and the object , then half again then half again , and so on thus my hand never reaches the object , in reality it never moves at all.
A good example of why logic and/or mathematics is rarely the entire picture of what is going on in a practical sense. Can’t remember who said it but: all mathematical models are wrong but some are useful.
In 1976, a British statistician George Box wrote “All models are wrong, some are useful.”
Exactly. And this is why ID is powerful–not that it’s necessarily true, but that the expectation of intelligent design (purpose) in biology has been historically more accurate than the expectation of random junk.
-Q
Querious at 53,
Which is correct?
Living things only look designed but they they are not designed.
Living things are designed and there are ways to determine design in living things.
The scientific consensus prefers “Living things only look designed but they they are not designed,” PLUS, the expectation is that anything new and surprising is random junk without any useful function. This fits in perfectly with the current Darwinian narrative, which is assumed to be true despite massive amounts of falsifying evidence.
Science currently has no objective way of quantitatively measuring design or information.
While I believe in a brilliant Creator who is the originator and sustainer of all creation, this belief is outside the capabilities of science as it is for most of the most important things in life:
Can one measure beauty in BTUs?
How about measuring compassion in candelas?
How about using inches to measure integrity?
In science, none of these exist.
-Q
“Science currently has no objective way of quantitatively measuring design or information.”
What?
The Human Genome Project followed by the Human Genome Reference Program.
“These new tools were put to good use, and on April 1, 2022, the Telomere-to-Telomere (T2T) consortium published a collection of papers that report the first truly complete sequence of the human genome. The sequence — over 3 billion base pairs long across 23 chromosomes — is entirely gapless. The T2T consortium further used this newly completed genome sequence as a reference to discover over 2 million additional genomic variants. Such information is valuable for gaining a comprehensive view about how human genomes vary as well as for investigating how these newly discovered variants influence health and disease.”
https://www.genome.gov/Funded-Programs-Projects/Human-Genome-Reference-Program
Relatd @56,
The Human Genome Reference Program is extremely impressive. Please understand that I’m denying the presence of functional information. What I’m asserting that there’s no measure for the amount of design or the amount of information (or information density).
Here’s an example. Let’s say that the design solution or specified information for something is 42 (as claimed in the Hitchhiker’s Guide to the Galaxy). This number can be expressed as:
42
Forty two
XLII
101010
etc.
Would you say that the information density of each of the above is identical?
-Q
Querius at 57,
The goal of the Human Genome Project is to identify functional information. How does everything work? How do all the parts of the genome affect and communicate with the rest? ID is knowing that this system was designed. It is not possible by chance. The amount of functional, specified information is growing. As scientists determine the role played by all parts, it will be obvious that ID is the correct answer.
Relatd @58,
No argument. But my question remains: How can one *quantify* information or design.
Yes, we know design or the appearance of design is present but exactly how much? Let me ask you another question:
a. You find three rocks stacked in a column in a desert. There’s no question of human intervention.
b. There’s a house not far away. Again, no question of human intervention.
Question: How much more design/information is there in the house than in the stack of three rocks?
-Q
Querius at 59,
All forensics work begins with questions based on history, based on patterns and based on similarities. The same with archaeology.
I find a laptop and next to it is a damaged, no longer functional Terminator straight out of the movie. Both are far beyond the abilities of chance in terms of their construction.