A Small Thought About Some Big Numbers

 

I’ve mentioned before that I don’t find the thought of life originating and evolving on Earth through purely naturalistic processes incredible. Five hundred million years — the approximate time we think it took life to get a figurative toehold on our cooling orb — is a long time: multiply that by the number of ponds and puddles and deep ocean vents and, well, there are a lot of places where naturally occurring lipids might self-organize, as lipids do, into little test tubes in which organic molecules can dance.

I find it entirely plausible that that’s what happened.

But I realized today that I’ve been looking at the numbers wrong. Yes, a half a billion years on Earth is a lot of time for chemicals to slosh around, but nonetheless that’s really a drop in the bucket — no, a drop in the ocean.

No, far less than a drop in the ocean.

There’s no reason to think only of the opportunities for life to appear on Earth. More sensible is to think of the opportunities for life to appear anywhere, because, wherever it appeared, that’s the place from which we’ll end up marveling at its improbability.

About a billion lightyears from Earth is a cluster of galaxies named Able 2029. One of the galaxies in that cluster goes by the poetic name IC 1101. It’s the biggest galaxy of which we’re aware, containing on the order of one hundred trillion stars.

That’s 100,000,000,000,000 stars.

In comparison, our own galaxy, the Milky Way, contains a mere quarter of a trillion stars.

There are well over two hundred billion galaxies. Ours is unexceptional — other than being the only one, as far as we know, that contains life.

We now think that most stars probably have planets. Recently, scientists decided that the so-called “Goldilocks zone,” the range of orbits about a star in which the temperature might be “just right” for water to exist as a liquid, is probably much broader than we originally thought. (This has to do with atmospheric dynamics of planets considerably larger than Earth.)

The universe is pretty young (at least it seems that way to me), less than 15 billion years old: life on Earth has been around for more than 20% of the age of the universe. But our sun isn’t a first-generation star: there have been at least two or three generations of stars before ours, perhaps more. So that’s a lot more stars than “merely” the 100,000,000,000,000,000,000,000 stars we can see on a clear night. (I kid, of course, but that’s a rough approximation of how many we think are out there.) So double that number to account for those stars that have come and gone before us.

That’s an awful lot of stars with an awful lot of planets. Multiply that by half a billion years, to give life a chance to start. Think of all those ponds and puddles and deep ocean vents.

Given all that, while I find it wonderful and beautiful and deeply moving that life exists at all, I don’t find it surprising.

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  1. Justin Other Lawyer Coolidge
    Justin Other Lawyer
    @DouglasMyers

    Arahant (View Comment):

    These threads sure do go in crazy directions.

    It’s only the appearance of craziness. Given enough time and enough comments you will no doubt see a beautiful tapestry of logical coherence. 

    • #121
  2. Dr. Bastiat Member
    Dr. Bastiat
    @drbastiat

    Justin Other Lawyer (View Comment):

    Arahant (View Comment):

    These threads sure do go in crazy directions.

    It’s only the appearance of craziness. Given enough time and enough comments you will no doubt see a beautiful tapestry of logical coherence.

    Then again, maybe not…

    • #122
  3. Justin Other Lawyer Coolidge
    Justin Other Lawyer
    @DouglasMyers

    Dr. Bastiat (View Comment):

    Justin Other Lawyer (View Comment):

    Arahant (View Comment):

    These threads sure do go in crazy directions.

    It’s only the appearance of craziness. Given enough time and enough comments you will no doubt see a beautiful tapestry of logical coherence.

    Then again, maybe not…

    Oh. Maybe I’ve misunderstood Henry’s argument then. 😉

    • #123
  4. Dr. Bastiat Member
    Dr. Bastiat
    @drbastiat

    Justin Other Lawyer (View Comment):

    Dr. Bastiat (View Comment):

    Justin Other Lawyer (View Comment):

    Arahant (View Comment):

    These threads sure do go in crazy directions.

    It’s only the appearance of craziness. Given enough time and enough comments you will no doubt see a beautiful tapestry of logical coherence.

    Then again, maybe not…

    Oh. Maybe I’ve misunderstood Henry’s argument then. 😉

    Dang.  I missed your joke.  That was pretty clever…

    • #124
  5. TBA Coolidge
    TBA
    @RobtGilsdorf

    J Climacus (View Comment):

    Henry Racette (View Comment):

    I’m not claiming that it’s possible. I’m just saying that it seems the most likely explanation, to me. It hasn’t been proved to be possible; nor has it been proved to be impossible. So you’re welcome to say you suspect it’s impossible; I’ll continue to say the opposite.

    But you give no evidence for thinking that it is likely, or even, possible. Frankly, it is just a wish. All the evidence we have indicates that it is impossible. That’s the difference between us: I’m not just saying it is impossible: I am drawing a conclusion based on the available evidence.

    Your objection seems to be to the transition from non-living to living. Given that we have a progression of skill in manipulating both non-living and living material, presumably your objection enters the picture when we try to make that critical step, at that instance when our engineered chemistry becomes an engineered life.

    Yes, that’s the step. All the evidence we have indicates that life only comes from life. The evidence is that life is a different kind of thing from non-living matter, and you don’t get life from non-life anymore than you get water running uphill.

    This principle was, in fact, one of the significant findings of modern science. The ancients and medievals thought that maggots spontaneously arose in dead flesh or that diseases sprang forth from miasma. When modern science studied things more closely, and discovered the principle that life only comes from life, the health sciences and management of disease took a great leap forward.

    What is that point? Do you know what is distinct between those chemicals that are just to the inanimate side of the line, and those chemicals just to the living side of the line? What kind of change occurred at that moment? Was it a chemical change? An electrical change? A spiritual change?

    I see no need to engage in speculation about what happened in the distance past. I have no idea how life came to be on this planet or anywhere else. What I do know is that the available evidence all supports the conclusion that life only comes from life.

    Is there one particular step that you think we can’t achieve and, if so, what is it, and why not?

    It seems like your position is driven by the materialistic philosophical belief that life must be reducible to non-life. I can see why, based on that philosophy, you take it for granted that life must have arisen from non-life sometime in the distance past. But that’s a philosophical conclusion, not a scientific one.

    • #125
  6. BDB Inactive
    BDB
    @BDB

    J Climacus (View Comment):

    BDB (View Comment):

    J Climacus (View Comment):
    But you give no evidence for thinking that it is likely, or even, possible. Frankly, it is just a wish. All the evidence we have indicates that it is impossible. That’s the difference between us: I’m not just saying it is impossible: I am drawing a conclusion based on the available evidence.

    Sorry to harp, but you’re doing the exact opposite. Actually “All” the evidence that you are looking at shows that material explanations, physics, will suffice to operate every single piece of the biological world observed so far. When have we ever observed a supernatural phenomenon required to operate some biological process? Where is this evidence that anything —ever — is simply beyond explanation without resort to a special intervention from beyond? (Let us please exclude questions of purpose for now, as a separate topic).

    I have not invoked the supernatural, nor am I claiming life requires a supernatural explanation. I am drawing a straightforward conclusion from the available evidence: Life comes from life, and does not come from non-life.

    Yet life is here.  So without life arising from non-living precursors, either it was created by [something] along the way, or it was created by [something] recently at the same time as everything else.  I could be missing something.  Your thoughts?

    • #126
  7. BDB Inactive
    BDB
    @BDB

    J Climacus (View Comment):

    I may not be able to respond on this thread for some time, or before it goes stale, and I don’t want people to think I’m ignoring them. Henry, thanks for the thought provoking post!

    Thank you for the thoughtful responses as well.  Pardon me if I initially lump apparent similar argument into similar categories of objection.  Hard to tell until you dig, and USUALLY it’s a re-run.

    • #127
  8. BDB Inactive
    BDB
    @BDB

    J Climacus (View Comment):

    Henry Racette (View Comment):

    Stina (View Comment):

    Henry Racette (View Comment):

    Stina (View Comment):

    Henry Racette (View Comment):

    J Climacus (View Comment):
    You seem to take it that the burden of proof is on me to prove that it is impossible.

    Yes, if you wish to claim that it is impossible, the burden of proof is on you.

    I’m not claiming that it’s possible. I’m just saying that it seems the most likely explanation, to me. It hasn’t been proved to be possible; nor has it been proved to be impossible. So you’re welcome to say you suspect it’s impossible; I’ll continue to say the opposite.

    As for progression (e.g., as in travel to Mars being a progression of other travel):

    snip

    To be fair, the claim you are making is more like this:

    “Because we have never seen a unicorn, it is impossible that a unicorn ever existed or ever could exist.”

    That’s the strong claim that you are making. And it’s not a claim I think one can defend scientifically or logically. I mean, assuming that by unicorn we mean a horse with a horn.

     

    So you believe it is possible for unicorns, the Loch Ness monster, big foot, and dragons to exist?

    I suspect that it is possible, given enough billions of years and enough planets, for any biologically possible form to arise somewhere. I don’t know that magic dragons are possible – I kind of think not. And Loch Ness is a specific place that doesn’t contain any monsters as far as we know, so time is running out for something to evolve to fill that niche.

    It’s fascinating that Henry’s suspicion here is a subset of a more general, and ancient, philosophical view of the “eternal return.” If the world has always existed, and will always exist, then every possible event, no matter how improbable, will eventually happen. In fact, it will happen an infinite number of times in the “eternal return.” Similarly, if the universe consists of trillions of planets existing for billions of years (and we take the materialist assumption that life is just a particular molecular arrangement of matter, not different in kind than inanimate matter) then every possible lifeform will arise somewhere. Or, at least, a lot of them will, since the universe in this case is just really big and old, not actually infinite.

    We need not go so far as Poincare time.

    • #128
  9. Steven Galanis Coolidge
    Steven Galanis
    @Steven Galanis

    Henry, your numbers would suggest that man has a humble place in the universe. It is good to be reminded of that from time to time.

    • #129
  10. Front Seat Cat Member
    Front Seat Cat
    @FrontSeatCat

    Jim McConnell (View Comment):

    Henry Racette (View Comment):

    Fritz (View Comment):

    I have no problem with evolutionary biology, but where does the incredibly designed universe originate? There must be a first cause. I choose to believe its divine origin, because nothing else makes sense.

    Fritz, to the extent that things have to make sense, I think divine origin doesn’t make sense either. That is, it doesn’t answer any questions, but merely fobs them off into another universe with another set of completely alien rules.

    Meanwhile, we slowly grasp some of the incredible nuance of the universe we can actually see. And we know that there are holes in what we know, perhaps large holes. We haven’t exhausted the scientific method just yet.

    Let’s just stick to something sensible and scientific for the Creation, shall we?

    Big Bang, anyone?

    Have anything that has ever blown up put itself back together in an orderly and systematic way? 

    • #130
  11. Front Seat Cat Member
    Front Seat Cat
    @FrontSeatCat

    BDB (View Comment):

    Jerry Giordano (Arizona Patrio… (View Comment):

    The flaw in this reasoning is that 100 trillion times zero is still zero. That’s true for 100 trillion trillion trillion, too.

    We don’t know the probability of life emerging by natural processes. It has never been observed, right?

    If the probability is non-zero, then the size and age of the universe would be relevant to the evaluation. If the probability is zero, it doesn’t matter.

    The ability to do math is not as important as knowing what math to do.

    All that we have ever seen are natural processes, and obviously, life has emerged. So our sample size of one serves us pretty well in that regard. Try your math on religion and let me know how that turns out.

    There is no flaw in Henry’s reasoning, and the only shortfall that I see is not taking into account the recent advances in evolution, viz the questionable value of calculus to survival. I don’t mean the study of evolution, although that too is booming — I mean the accelerating specialization of ourselves as supersocial competition machines.

    Evolution does not care about survival, and only rewards it to the extent that it fosters reproduction.

    Are apes evolving into people yet or are they still apes?  Maybe one had a fluke gene, kept going and here we are….. I’d say now evolution is reversing when it comes to man…….

    • #131
  12. Arahant Member
    Arahant
    @Arahant

    Front Seat Cat (View Comment):
    Are apes evolving into people yet or are they still apes?

    That’s not the way it works. First, biologically, people are apes. Second, it is unlikely they would have the mutations to go down that path. The current great apes are each the products of millions of years of evolution in their historical environments, just as we are the products of the environments our ancestors lived in. We did not evolve from chimps. We evolved from something that preceded chimps. It would be like saying that your cousin will become you. Not happening.

    • #132
  13. Arahant Member
    Arahant
    @Arahant

    Front Seat Cat (View Comment):
    I’d say now evolution is reversing when it comes to man

    That’s not the way it works, either. Evolution is not a direction on a timeline. Evolution is the product of thousands and thousands of mutations that are acted upon by the environment. If the mutation better suits a given environment or a niche within the environment, the carriers of that mutation will be more likely to survive and breed. Over time, if a mutation conveys advantages, it gets passed on until most or all of the population has it, not because it’s contagious, but because only those with the mutation survive and breed to pass their genes on.

    There is no reverse switch. It’s always forward in a new direction, depending on the current environment. If the environment changes, other mutations might be selected for.

    • #133
  14. BDB Inactive
    BDB
    @BDB

    Front Seat Cat (View Comment):
    Are apes evolving into people yet or are they still apes?  Maybe one had a fluke gene, kept going and here we are….. I’d say now evolution is reversing when it comes to man…….

    Chimpanzee more likely, and both of us have evolved from a common progenitor, which was a whole lot more like a chimp than a man.  Those which stayed in the jungle got more like modern chimps, which we may suspect are even better adapted for that situation.

    Man, like chimp, continues getting better at some things and worse at others.

    Geographically isolated populations drift without regard to what’s going on in other populations.  Fast-forwarding, the humans who stayed in Africa became optimized for that environment, as did (respectively) those who wound up in other areas, such as Europe and Asia, and then later, an Asia split to the new world.

    Races are what in any other organism we would call subspecies, and they came about in the same way.

    Thanks for asking!

    • #134
  15. Henry Racette Member
    Henry Racette
    @HenryRacette

    Stina (View Comment):

    I’m not declaring abiogenesis possible. I’m merely saying that I see no reason to believe that it is impossible, and quite a lot of reason to think it probably happened.

    God probably does exist, then.

    I am agnostic regarding the existence of God, Stina. I’ve seen nothing that makes me think it’s probable, but nor have I seen anything that makes me think it’s impossible. I think the question is outside the realm of the natural sciences.

    While I think people of faith who try to use science to support their metaphysical claims are making a mistake, I think people who try to use science to debunk faith are worse, because the latter should know the limits of science and refrain from making claims science can’t make.

    • #135
  16. Henry Racette Member
    Henry Racette
    @HenryRacette

    J Climacus (View Comment):

    I may not be able to respond on this thread for some time, or before it goes stale, and I don’t want people to think I’m ignoring them. Henry, thanks for the thought provoking post!

    JC, you too. And, frankly, I’m about ready to disengage from it as well. I don’t want to come off as disparaging of religion, as I think religion is virtually essential to our good character both as a nation and as individuals. (I think that’s particularly true of Judeo-Christian faith.) I’m just of a particularly rational bent, and find cosmology, evolution, etc., fascinating.

    Take care. And thanks for participating.

    • #136
  17. Henry Racette Member
    Henry Racette
    @HenryRacette

    Arahant (View Comment):
    That’s not the way it works. First, biologically, people are apes.

    Arahant’s comments remind me of something the late Stephen Jay Gould used to emphasize in his books about evolution. He liked to remind the reader that evolution is not a progression, in the sense of things getting better, more sophisticated, more advanced. Evolution is merely a continual trimming and fitting of a species into a particular environment. If that meant a species becoming simpler and less complicated — less “advanced” — then that’s where evolution would likely lead.

    A near universal trope of science fiction is that, in the far future, people have huge brains and scrawny bodies — or, alternately, they’re golden Adonis figures of uniform perfection. Genetic engineering and biological augmentation might get us to that, but there’s little reason to think that evolution will.

    The cockroach is as “evolved” as we are — and perhaps more so, if our measure of “evolved” is how well suited an organism is to its ecological niche.

    • #137
  18. TBA Coolidge
    TBA
    @RobtGilsdorf

    Steven Galanis (View Comment):

    Henry, your numbers would suggest that man has a humble place in the universe. It is good to be reminded of that from time to time.

    Not me, I paid for hubris seating. 

    • #138
  19. BDB Inactive
    BDB
    @BDB

    TBA (View Comment):

    Steven Galanis (View Comment):

    Henry, your numbers would suggest that man has a humble place in the universe. It is good to be reminded of that from time to time.

    Not me, I paid for hubris seating.

    4.5 million years of my ancestors didn’t claw their way to the top of the food chain so that I could eat bugs.

    • #139
  20. Justin Other Lawyer Coolidge
    Justin Other Lawyer
    @DouglasMyers

    BDB (View Comment):

    TBA (View Comment):

    Steven Galanis (View Comment):

    Henry, your numbers would suggest that man has a humble place in the universe. It is good to be reminded of that from time to time.

    Not me, I paid for hubris seating.

    4.5 million years of my ancestors didn’t claw their way to the top of the food chain so that I could eat bugs.

    We may not agree on all these details, but I’m with you on the bugs thing.  The modern steer and hog are cultivated to provide us with near heavenly culinary delights. 

    • #140
  21. kedavis Coolidge
    kedavis
    @kedavis

    Justin Other Lawyer (View Comment):

    BDB (View Comment):

    TBA (View Comment):

    Steven Galanis (View Comment):

    Henry, your numbers would suggest that man has a humble place in the universe. It is good to be reminded of that from time to time.

    Not me, I paid for hubris seating.

    4.5 million years of my ancestors didn’t claw their way to the top of the food chain so that I could eat bugs.

    We may not agree on all these details, but I’m with you on the bugs thing. The modern steer and hog are cultivated to provide us with near heavenly culinary delights.

    Indeed!  All wrapped up in the Bacon Cheeseburger!

    • #141
  22. OmegaPaladin Moderator
    OmegaPaladin
    @OmegaPaladin

    I’m sorry @henryracette, but I just don’t see that way.

    Let’s start at the beginning.  Getting amino and nucleic acids is not an easy process.   These are fairly complicated molecules that are not terribly stable.  You can make them fairly easily with the proper conditions and selected starting materials, but then you have to separate the final molecules from side products – good luck having that in nature.    Watch any of NileRed‘s chemical synthesis videos to see just how much purification is involved. 

    Then you have chirality.  We somehow ended up with system based on amino acids with a specific “handedness”  It is really, really hard to resolve different chiral compounds, as they only differ in their reactions with other chiral compounds

    Now you have to properly link the units together.  This is not trivial – synthesizing these building blocks into something functional requires a lot of human intervention.  Typically you will need coupling agents and protecting groups.  Nucleic acids are even worse, with numerous bonding sites on the sugar and the base.  Bear in mind, we still don’t have anything approaching life yet in this process.

    So what is the most basic form of life imaginable?   What you need is self-replication and energy collection.  Energy collection or metabolism turns chemical or other energy into useful work in overcoming the entropy cost of self-replication.  This is still not trivial at all, and we are still talking something so simple it makes a virus look like a human.  This is a level of unlikely akin to predicting every play in the Super Bowl.

    Now, once you have something that is living, you have a long row to hoe on the way to intelligent life.  Natural selection’s biggest weakness is that there is no planning or even determinism.   Every mutation is evaluated immediately, and either provides an advantage, disadvantage, or neither.  Fitness is only determined by whether an organism survives to reproduce and how much it reproduces.  This means a massive improvement can be rendered null by bad luck.  A bacterium evolves a resistance mutation to penicillin.  It is treated with a quinolone or macrolide, and its mutation dies out.  In fact, since many drug resistance mutations are detrimental when the drug is absent, most bacteria will not be resistant in a non-antibiotic treated population.  The normal, wild-type form predominates, with a small number of mutants.  That’s why multi-drug therapy is so effective.

    I only see two explanations for this:  some as-yet undiscovered force that promotes life to form or a designer.  The designer could be any highly intelligent entity.  It is entirely possible the designer is the result of a time loop or is a being of evil who created life to see us suffer.   It has no more religious content than the Big Bang.

    • #142
  23. Henry Racette Member
    Henry Racette
    @HenryRacette

    OmegaPaladin (View Comment):

    I’m sorry @ henryracette, but I just don’t see that way.

    Let’s start at the beginning. Getting amino and nucleic acids is not an easy process. These are fairly complicated molecules that are not terribly stable. You can make them fairly easily with the proper conditions and selected starting materials, but then you have to separate the final molecules from side products – good luck having that in nature. Watch any of NileRed‘s chemical synthesis videos to see just how much purification is involved.

    Then you have chirality. We somehow ended up with system based on amino acids with a specific “handedness” It is really, really hard to resolve different chiral compounds, as they only differ in their reactions with other chiral compounds

    Now you have to properly link the units together. This is not trivial – synthesizing these building blocks into something functional requires a lot of human intervention. Typically you will need coupling agents and protecting groups. Nucleic acids are even worse, with numerous bonding sites on the sugar and the base. Bear in mind, we still don’t have anything approaching life yet in this process.

    So what is the most basic form of life imaginable? What you need is self-replication and energy collection. Energy collection or metabolism turns chemical or other energy into useful work in overcoming the entropy cost of self-replication. This is still not trivial at all, and we are still talking something so simple it makes a virus look like a human. This is a level of unlikely akin to predicting every play in the snip

    Now, once you have something that is living, you have a long row to hoe on the way to intelligent life. Natural selection’s biggest weakness is that there is no planning or even determinism. Every mutation is evaluated immediately, and either provides an advantage, disadvantage, or neither. Fitness is only determined by whether an organism survives to reproduce and how much it reproduces. This means a massive improvement can be rendered null by bad luck. A bacterium evolves a resistance mutation to penicillin. It is treated with a quinolone or macrolide, and its mutation dies out. In fact, since many drug resistance mutations are detrimental when the drug is absent, most bacteria will not be resistant in a non-antibiotic treated population. The normal, wild-type form predominates, with a small number of mutants. That’s why multi-drug therapy is so effective.

    I only see two explanations for this: some as-yet undiscovered force that promotes life to form or a designer. The designer could be any highly intelligent entity. It is entirely possible the designer is the result of a time loop or is a being of evil who created life to see us suffer. It has no more religious content than the Big Bang.

    So what’s one step that, assuming that any required precursor components are available, simply can’t occur without some kind of direction or intervention?

    • #143
  24. kedavis Coolidge
    kedavis
    @kedavis

    Henry Racette (View Comment):
    So what’s one step that, assuming that any required precursor components are available, simply can’t occur without some kind of direction or intervention?

    I don’t know if they can seriously claim “can’t” but that it’s highly HIGHLY unlikely, which is where the trillions and billions might come back in…

    And even if this is the only place in the entirely universe with intelligent life, it still only had to happen ONCE.

    • #144
  25. Henry Racette Member
    Henry Racette
    @HenryRacette

    kedavis (View Comment):

    Henry Racette (View Comment):
    So what’s one step that, assuming that any required precursor components are available, simply can’t occur without some kind of direction or intervention?

    I don’t know if they can seriously claim “can’t” but that it’s highly HIGHLY unlikely, which is where the trillions and billions might come back in…

    And even if this is the only place in the entirely universe with intelligent life, it still only had to happen ONCE.

    That’s pretty much my point.

    When we start throwing out one after another complex molecule or molecular process, it’s easy to feel buried under improbabilities — to the point where “impossible” seems the only answer.

    But if anyone is going to tell me that it is impossible that the sequence arose through undirected natural processes, I want to know which step in the sequence was a leap too far: which smallest increment could not have occurred, even if given a significant fraction of all the time and space in the universe?

    If we can’t convincingly name that step, I think all we’re really doing is saying “wow, it just seems so unlikely that it must be impossible.” When the numbers are as large as they are, gut feelings about plausibility shouldn’t be elevated to the status of demonstrated fact.

    • #145
  26. Arahant Member
    Arahant
    @Arahant

    Henry Racette (View Comment):
    But if anyone is going to tell me that it is impossible that the sequence arose through undirected natural processes, I want to know which step in the sequence was a leap too far: which smallest increment could not have occurred, even if given a significant fraction of all the time and space in the universe?

    By the numbers, every order of a card deck after a shuffle should be unique until well after the heat death of the universe.

    • #146
  27. Henry Racette Member
    Henry Racette
    @HenryRacette

    Arahant (View Comment):

    Henry Racette (View Comment):
    But if anyone is going to tell me that it is impossible that the sequence arose through undirected natural processes, I want to know which step in the sequence was a leap too far: which smallest increment could not have occurred, even if given a significant fraction of all the time and space in the universe?

    By the numbers, every order of a card deck after a shuffle should be unique until well after the heat death of the universe.

    There is at least one verified instance of four perfect bridge hands being dealt. That is, each of the four parties at the table received a hand containing a perfect suit. The odds against that happening are fantastical, much as your 52!.

    But it turns out that if you start with a new deck in sorted order, and you do two perfect riffle shuffles that exactly interleave the card, and then deal, you’ll deal four perfect hands. Someone really good with cards can do two perfect riffle shuffles with a bit of practice.

    None of this has anything to do with my post, but it’s interesting.

     

    • #147
  28. Arahant Member
    Arahant
    @Arahant

    Henry Racette (View Comment):
    None of this has anything to do with my post, but it’s interesting.

    The point is that big numbers do not preclude things from happening.

    • #148
  29. kedavis Coolidge
    kedavis
    @kedavis

    Henry Racette (View Comment):

    Arahant (View Comment):

    Henry Racette (View Comment):
    But if anyone is going to tell me that it is impossible that the sequence arose through undirected natural processes, I want to know which step in the sequence was a leap too far: which smallest increment could not have occurred, even if given a significant fraction of all the time and space in the universe?

    By the numbers, every order of a card deck after a shuffle should be unique until well after the heat death of the universe.

    There is at least one verified instance of four perfect bridge hands being dealt. That is, each of the four parties at the table received a hand containing a perfect suit. The odds against that happening are fantastical, much as your 52!.

    But it turns out that if you start with a new deck in sorted order, and you do two perfect riffle shuffles that exactly interleave the card, and then deal, you’ll deal four perfect hands. Someone really good with cards can do two perfect riffle shuffles with a bit of practice.

    None of this has anything to do with my post, but it’s interesting.

     

    Maybe that depends on how fast they can shuffle and deal.  :-)

     

    • #149
  30. Henry Racette Member
    Henry Racette
    @HenryRacette

    kedavis (View Comment):

    Henry Racette (View Comment):

    Arahant (View Comment):

    Henry Racette (View Comment):
    But if anyone is going to tell me that it is impossible that the sequence arose through undirected natural processes, I want to know which step in the sequence was a leap too far: which smallest increment could not have occurred, even if given a significant fraction of all the time and space in the universe?

    By the numbers, every order of a card deck after a shuffle should be unique until well after the heat death of the universe.

    There is at least one verified instance of four perfect bridge hands being dealt. That is, each of the four parties at the table received a hand containing a perfect suit. The odds against that happening are fantastical, much as your 52!.

    But it turns out that if you start with a new deck in sorted order, and you do two perfect riffle shuffles that exactly interleave the card, and then deal, you’ll deal four perfect hands. Someone really good with cards can do two perfect riffle shuffles with a bit of practice.

    None of this has anything to do with my post, but it’s interesting.

    Maybe that depends on how fast they can shuffle and deal. :-

    Late-night ruminations from the bottom of a glass of bourbon. Let’s give those numbers some thought.

    52!, the number of orderings of a deck of cards, is about 8 x 10^62.

    Let’s say ya gotta be on a habitable planet to shuffle. The number of habitable planets in the visible universe, charitably saying there’re four habitable planets per star, is (perhaps) on the order of 4 x 10^24.

    So 62 – 24 is 38. That means that we have to do about 10^38 shuffles per planet. How long before the heat death of the universe? No one knows, but the shuffling has to end a long, long time before that, let’s say in a million trillion years (which is probably generous: there won’t be much star formation going on by then). A million trillion has 18 zeros.

    So we need to do 38 – 18 = 20… 10^20 shuffles per year per planet for the next million trillion years.

    Figure ten billion people on each planet shuffling non-stop. That’s 10^10 busy shufflers. They have to shuffle 20-10… 10^10 times each year. A year (let’s use Earth years) has about 31.5 million seconds in it, so that means each of those people has to shuffle about 300 times per second to get the job done.

    Shoot. Even Star Trek’s Data doesn’t shuffle that fast.


    PS And the “four planets” assumption was ignored and irrelevant. I blame the bourbon.

    • #150
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