Cosmology Mathematics News

No past infinity? But what about a minus past infinity?

Spread the love

As in “…, -3, -2, -1, zero!” with the three-dot ellipsis comprising an infinite series of numbers.

And we just happen to be on the other side of the zero! end, no less. Further to “There cannot be an infinite past, since we would not reach our ‘here-and-now,’” Kirk Durston responds to this argument from Sean Carroll’s idea that there could be a negative past infinity of time.

Just as it is impossible to count down through the negative integers from minus infinity to zero, so it is impossible in real time, for time t to run from minus infinity to plus infinity. The real past, therefore, must have a beginning, and a key proposition in the cosmological argument still stands.

Now let us try out the idea of time t running from zero to plus infinity, 0, 1, 2, 3, … No problem here. This is what is known in mathematics as a potential infinity. You never actually reach infinity, but you are going in that direction.

Now let us try out the idea of the past being infinite. 0, -1, -2, -3, … No problem here either but, what a minute, real time does not run backward from the present. For an eternal universe, according to Carroll, time runs from minus infinity to zero.

Imagine walking into a room and observing an ageless-looking person sitting on a chair counting, ‘…, -3, -2, -1, zero!’ She then triumphantly looks up and tells you that she just finished counting down, one integer at a time, from minus infinity to zero, taking one second for each integer. I trust that we can all agree that it is impossible to count through the entire set of negative integers, from minus infinity to zero, one integer at a time. Counting down through the seconds of past history is no different. More.

So what happened to all the stuff that must have existed negatively then? Did it just disappear at zero, leaving no trace?

See also: The Science Fictions series at your fingertips (cosmology) on how what started as astronomy and the space race ended up in these kinds of discussions.

Follow UD News at Twitter!

8 Replies to “No past infinity? But what about a minus past infinity?

  1. 1
    Mung says:

    -(infinity * infinity) ^ -infinity

  2. 2
    Barb says:

    “To infinity…and beyond!”

  3. 3
    Mapou says:

    Infinity is a crackpot concept. The very idea of infinity leads to an infinite regress. Materialists and physicists love infinity because without it, they would not have a leg to stand on. Philosophers love infinity because it gives them an ample field in which to pontificate. After all, is not spacetime an infinitely smooth continuum? And do not both Euclidean and non-Euclidean geometries assume infinity? The crackpottery runs deep in the scientific community.

    But let us not wash one hand and ignore the other. Many, if not most, Christians worship infinity because they’ll have you know that the God that they worship is infinitely powerful and infinitely knowledgeable, is he not? Otherwise he could not be God, could he? The crackpottery runs deep in the religious community as well.

  4. 4
    kairosfocus says:

    F/N: Remember, the envisioned countdown is causal, ordered, in finite steps and following a definite temporal succession. Think about what the problem of traversing a past infinity to a zero-point at our observed cosmos’ singularity, then coming forward to now implies. By comparison, think if starting now as k, we can traverse onward to a positive infinity in finite steps. The absurdity of attempting such a traverse should be readily apparent. As will also be the issue that that which begins has a cause. KF

    PS: BTW, there was a bit of discussion on this here at UD a few days ago.

  5. 5
    wallstreeter43 says:

    Correct Mapou , and an infinite regress is the atheistic way of trying to dodge tehe classic first cause argument. It’s such a pesky little philosophical argument isn’t it lol

  6. 6
    Barb says:

    Mapou writes,

    Many, if not most, Christians worship infinity because they’ll have you know that the God that they worship is infinitely powerful and infinitely knowledgeable, is he not? Otherwise he could not be God, could he?

    Psalm 90 reads: “Even from time indefinite to time indefinite you are God.” The words “time indefinite” can refer to things that have an end but the duration of which has not been specified. (see also Exodus 31:16, 17; Hebrews 9:15)

    At Psalm 90:2 and elsewhere in the Hebrew Scriptures, though, “time indefinite” means “eternal.” (Ecclesiastes 1:4) Our minds cannot understand how it is possible that God has always existed. Yet, God had no beginning and will have no end. (Habakkuk 1:12) He will always be alive and ready to help us.

    As a Christian, I don’t necessarily think that “infinity” is a crackpot concept. My mind may not fully comprehend it, but it’s not entirely unreasonable. You could also consider the concept of time: no one can point to a certain moment as the beginning of time. And it is a fact that, even though our lives end, time does not. We do not reject the idea of time because there are aspects of it that we do not fully comprehend. Rather, we regulate our lives by it.

    Also, the concept of space. There doesn’t appear to be a beginning or end to space. The farther they probe into the universe, the more there is. They do not reject what the evidence shows; many refer to space as being infinite. The same principle applies to the existence of God.

    I cannot comprehend temperatures in the millions of degrees, yet astronomers tell us that the heat of the sun at its core is 27,000,000 degrees Fahrenheit (15,000,000° C.). Do we reject that idea because we cannot fully comprehend such intense heat? I also don’t quite comprehend the size of our galaxy. I’ve read that the size of the Milky Way is so great that a beam of light traveling at over 186,000 miles per second (300,000 km/sec) would require 100,000 years to cross it. While my mind doesn’t comprehend the distance, I accept it because scientific evidence supports it.

  7. 7
    GGDFan777 says:

    Some articles that people might find interesting which critique the possibility of an actual infinity or an infinite past :

    “New Zeno and Actual Infinity” by philosopher Casper Storm Hansen

    In 1964 José Benardete invented the “New Zeno Paradox” about an infinity of gods trying to prevent a traveller from reaching his destination. In this paper it is argued, contra Priest and Yablo, that the paradox must be re-solved by rejecting the possibility of actual infinity. Further, it is shown that this paradox has the same logical form as Yablo’s Paradox. It is suggested that constructivism can serve as the basis of a common solution to New Zeno and the paradoxes of truth, and a constructivist interpretation of Kripke’s theory of truth is given.


    “Ungrounded Causal Chains and Beginningless Time” by philosopher Laureano Luna

    We use two logical resources, namely, the notion of recursively defined function and the Benardete-Yablo paradox, together with some inherent features of causality and time, as usually conceived, to derive two results: that no ungrounded causal chain exists and that time has a beginning


    “Infinity at Stake” by Antonio Leon


  8. 8
    Mung says:

    “Infinity is a crackpot concept” is a crackpot comment.

Leave a Reply