Apr 24 2012

The Paradox Paradox

Paradoxes exist in science for a very good reason. Science is a human-wide effort to understand how the universe works. When functioning properly it is therefore transparent and open. Further, science is describing one reality, and therefore all of the various scientific models for how bits of the universe work must all be compatible with each other. Science needs to all mesh into one big model of reality. Science also follows rules of evidence, logic, and cause and effect. You cannot invoke magic or arbitrarily suspend laws of physics as needed.

When one bit of evidence or scientific model contradicts another (they both cannot be correct at the same time) we have a scientific paradox. Since our models of reality are incomplete (and arguably always will be) scientific paradoxes pop up all the time.

How one responds to a scientific paradox reveals a great deal about how they approach science and knowledge. Those who crave certainty are made uncomfortable by paradoxes because they point to uncertainty. To a scientist, however, paradoxes are nothing less than awesome, the holy grail, the best thing since sliced bread. To a scientist an apparent paradox (really all scientific paradoxes are temporarily “apparent”) is a bright neon sign proclaiming, “This way for discovery!”

Paradoxes do not exist in reality, only in our current models of reality, and so they point the way to flaws in our current models. They therefore also point the way to further research to improve those models, fix errors, or fill in missing pieces. In short, scientists love paradoxes.

There is another group that also love paradoxes but for an entirely different reason. Science deniers love to exploit current paradoxes in order to argue that either all of science is dubious or that an entire area of science is wrong. This is a strategy of denial, not a legitimate attempt to understand the world. This strategy is also largely based on a logical fallacy – confusing currently unexplained with unexplainable. They assume that the paradox is unresolvable, even when it is based upon preliminary models and there are possible solutions that haven’t even been explored yet.

For example, in the 1990s I had a number of discussions with creationists who were very excited about the “solar neutrino problem.” This was a classic scientific paradox – current astrophysical models are that the sun derives its energy from the nuclear fusion of hydrogen into helium. The standard model of particle physics indicates that this process should produce neutrinos (nearly massless particles that move near the speed of light and interact very weakly with matter). However, neutrino detectors were only detecting about half the number of neutrinos that the standard model predicts the sun should be producing. Aha – a paradox. Scientists were excited. Is our model of how the sun works wrong? Is the standard model of particle physics wrong? Is the experimental data wrong? Or is there some missing piece to this puzzle? Scientists had several theories.

Further I need to clarify what is meant by “wrong.” No scientist was hypothesizing that the standard model of particle physics or solar astronomy were entirely and completely wrong, but rather wrong in one aspect, or perhaps just incomplete.

This is the ordinary process of science and discovery. Yet creationists treated it as if it were an enduring and unsolvable mystery. Creationism.org still cites the solar neutrino problem as evidence for a young sun:

From a creationist point of view, the results of the neutrino-capture experiments are very exciting, for they indicate that the thermonuclear-fusion theory of solar radiation may be entirely wrong. The sun is not emitting the necessary neutrinos.

This is a great example of how science deniers look at paradoxes. They see it as an opportunity to prove an entire branch of science entirely wrong. They really hoped that this one anomaly would kill the fusion-theory of solar physics. They wanted to kill the fusion theory because it allows the sun to be billions of years old. They preferred other models, like the shrinking sun theory, which would only allow for a sun millions of years old. This reveals much about their pattern of thought and arguments – scientific theories are either entirely correct or entirely wrong. You are either 100% certain or you are wrong. They appear to be unfamiliar with the way in which science actually progresses – by modifying and deepening existing theories, but not necessarily replacing them entirely. Current theories may be wrong in one aspect or incomplete, but that does not mean they are entirely wrong.

Also, exploiting the solar neutrino problem is this manner reveals that their strategy is not understanding, but denial. They are not trying to build a coherent theory themselves, just poke holes and cast doubt on existing science. For example, if the fusion theory of stellar astronomy is wrong, then where are the neutrinos we are detecting coming from? Isn’t that a bigger solar neutrino problem than the fact that were are observing only half the predicted number? They don’t appear to care that their alternate “theory” (it’s not really a scientific theory) is full of paradoxes, because they have no problem waving a magic wand to make them disappear.

Even at the time creationists were first crowing about the solar neutrino problem the solution was also hypothesized. Physicists suspected that perhaps some neutrinos were shifting their type on the way from the sun to the earth, and we were only detecting one type of neutrino. In 2001 the solution was presented:

The smoking gun was discovered. The smoking gun is the difference between the total number of neutrinos and the number of only electron neutrinos. The missing neutrinos were actually present, but in the form of the more difficult to detect muon and tau neutrinos.

This was actually not that big a paradox and didn’t keep scientists up at night. They suspected that something like this was the answer, and they soon verified it. The standard model is safe, and so is the fusion theory of the sun. I notice that creationists, however, have largely not updated their science-denying websites.

There is another sun-based paradox that creationists are currently exploiting in the same way – the faint young sun paradox. I will discuss this paradox in my next post.

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55 responses so far

55 Responses to “The Paradox Paradox”

  1. gfb1on 24 Apr 2012 at 9:00 am

    Para-dox?? Vhy no pair uf chickens??

    (sorry, couldn’t resist… )

  2. Ori Vandewalleon 24 Apr 2012 at 11:35 am

    Hm. I’ve always heard that scientists we’re missing two thirds of the Sun’s neutrinos, not half. Wikipedia says: “In various experiments, the number of detected neutrinos was between one third and one half of the predicted number.”

  3. sonicon 24 Apr 2012 at 11:45 am

    a couple quotes of possible interest-

    “How wonderful that we have met a paradox. Now we have some hope of making progress.” Niels Bohr

    “The ‘paradox’ is only a conflict between reality and your feeling of what reality ‘ought to be’.” Feynman

  4. cwfongon 24 Apr 2012 at 1:39 pm

    Paradox: This sentence is false. Solution: Yes, it’s true that it’s false.
    (Axiom or adage: Almost nothing is ever completely true or false.)

  5. siodineon 24 Apr 2012 at 4:39 pm

    You might add a blurb about paraconsistent logic.

  6. Jared Olsenon 25 Apr 2012 at 1:42 am

    I love paradoxes. I’ve always thought that the classical paradoxes (Zeno’s, the Liar’s) were semantic in nature-just presenting language’s inherent lack of precision…

  7. SteveAon 25 Apr 2012 at 2:47 pm

    Jared Olsen: “I love paradoxes. I’ve always thought that the classical paradoxes (Zeno’s, the Liar’s) were semantic in nature-just presenting language’s inherent lack of precision…”

    Zeno’s ‘Achilles and the Tortoise’ paradox has always bugged me.

    And how come I can cut an apple into three equal parts, but when I divide 1 by 3 I get an infinite series: 0.33333… And when I multiply back again I get 0.99999..? Who’s stealing bits of my apple?

    Though these aren’t really the kinds of paradox that Dr S is referencing.

  8. cwfongon 25 Apr 2012 at 3:20 pm

    Because mathematical measurements are at best approximations. As are our truths.

  9. Davdoodleson 25 Apr 2012 at 11:49 pm

    Science deniers believe that “You are either 100% certain or you are wrong”?

    I wonder if they appreciate the irony that science deniers themselves are both 100% certain, and totally wrong.

    Actually, that’s a rhetorical musing.
    .

  10. Ori Vandewalleon 26 Apr 2012 at 1:27 pm

    @SteveA

    1/3 being an infinite series is not a paradox so much as it is an artifact of the decimal system. .999 repeating IS equal to 1, so nothing is actually lost.

  11. BillyJoe7on 26 Apr 2012 at 5:14 pm

    steveA,

    “And how come I can cut an apple into three equal parts…”

    Actually you can’t, certainly not in practice, and aslo not in principle unless the number of each type of molecule in the apple is exactly divisible by three.

    “….but when I divide 1 by 3 I get an infinite series: 0.33333…”

    Or 1/3.
    And, in any case, 0.33333… is equal to 1/3

    “… And when I multiply back again I get 0.99999..? Who is stealing bits of my apple?”

    No-one, because 0.99999…. is equal to exactly 1.

  12. cwfongon 26 Apr 2012 at 5:44 pm

    OriVanderville answered the question and BillyJoe7 proceeded to screw up the answer. Of course you can divide an apple into three equal parts in principle, and the types of molecules have nothing to with it in either practice or principle.
    And 0.99999 is not exactly equal to 1 mathematically even though it’s approximately as equal as you can reliably get to the physical reality of one thing. The same goes for 0.33333.

  13. Ori Vandewalleon 26 Apr 2012 at 5:58 pm

    No, .999 repeating is exactly, mathematically, equal to 1. There are a number of proofs of this, and even a wikipedia article about it.

    http://en.wikipedia.org/wiki/0.999

  14. cwfongon 26 Apr 2012 at 6:04 pm

    Yes, .999 repeating is mathematically equal to one. But not .99999.

  15. cwfongon 26 Apr 2012 at 6:42 pm

    You could also divide an apple as accurately in three parts practically as in principally. You just could not confirm you did it mathematically.

  16. Ori Vandewalleon 26 Apr 2012 at 6:53 pm

    Ah, yes. I misunderstood you for a moment. Carry on!

  17. Jared Olsenon 27 Apr 2012 at 5:05 am

    As I said, our language is just an approximation of reality.

  18. BillyJoe7on 27 Apr 2012 at 7:37 am

    cwfong falls over himself once again:

    “And 0.99999 is not exactly equal to 1 mathematically…”

    But the actual notations used by both steveA and myself (0.33333… and 0.99999…) are correct representations of a repeating decimal.
    And 0.99999… is equal to exactly 1.

  19. cwfongon 27 Apr 2012 at 12:48 pm

    No, BJ7, you made your usual concrete thinking mistake. You didn’t know enough to point out that it was ,999 repeating to infinity. Read the cited article, which also points out that some mathematicians dispute this conclusion as well, not agreeing that the concept of the infinite decimal can be called an exact number.
    I’m not a mathematician, but I tend to agree with the extension to infinity conception.

    In your case, you seem to see the need to point out the obvious, as it wasn’t already obvious to everyone else here. Except that what you can see as obvious never is.

  20. cwfongon 27 Apr 2012 at 12:49 pm

    And the next thing that you post will be wrong as well.

  21. ccbowerson 27 Apr 2012 at 2:49 pm

    I often wonder how much cwfong and BillyJoe7 intentionally misunderstand each other. You have enough things that you actually disagree upon, there is no point in making up more

  22. cwfongon 27 Apr 2012 at 2:58 pm

    ccbowers, are you saying that both our positions are made up? I guess the question then is which one is wronger.

  23. BillyJoe7on 27 Apr 2012 at 5:34 pm

    fongie,

    As usual, when you are wrong, you switch to another argument.
    I named steveA, I clearly quoted steveA, and I clearly responded to steveA.

  24. BillyJoe7on 27 Apr 2012 at 5:36 pm

    Also, try to divide a hydrogen atom into three equal parts. :D

  25. cwfongon 27 Apr 2012 at 5:46 pm

    billyjotistic,

    You were clearly wrong as well.

    Talk about switching the argument, nobody has to divide the atoms to divide the apple. Or did you really think you’d have to?

  26. cwfongon 27 Apr 2012 at 5:53 pm

    Although dividing the hydrogen atom has been accomplished quite well by the fission process developed at my University.

  27. cwfongon 27 Apr 2012 at 5:56 pm

    And the next thing that you post will be dumb as well.

  28. SteveAon 27 Apr 2012 at 7:13 pm

    The ellipsis after the number was meant to represent a series repeating to infinity.

    I mentioned it more as joke really, but it always strikes me as interesting that you can divide 1 by 3 then reverse the process and come up with an answer that is not quite the same. Though I appreciate that mathematically 0.99999… and 1 are the same…sort of.

  29. cwfongon 27 Apr 2012 at 7:33 pm

    BJ7 will now decide he knew that.

  30. BillyJoe7on 28 Apr 2012 at 2:29 am

    “You were clearly wrong as well.”

    But, of course, you are not going to demonstrate how you think that I am wrong.
    Put it this way, if I explain how you are wrong (which I did) and you ignore my explanation (which you did) and simply state boldly that I am wrong (which you did), then that is a miserable failure for you.
    Suck on it.

    “nobody has to divide the atoms to divide the apple. Or did you really think you’d have to?”

    If the number of atoms is not a factor of 3, indeed you will have to.
    That’s was my point.
    But, of course, you are never going to demonstrate how – that I already know from past experience.

  31. BillyJoe7on 28 Apr 2012 at 2:33 am

    SteveA,

    “The ellipsis after the number was meant to represent a series repeating to infinity.”

    Thank you.
    And it’s that that I was responding to.

    “I mentioned it more as joke really, but it always strikes me as interesting that you can divide 1 by 3 then reverse the process and come up with an answer that is not quite the same. Though I appreciate that mathematically 0.99999… and 1 are the same…sort of.”

    Well, that is not exactly correct – but it seems you know that…sort of. :)

  32. cwfongon 28 Apr 2012 at 3:47 am

    BJ7: “Also, try to divide a hydrogen atom into three equal parts.”

    Me: “nobody has to divide the atoms to divide the apple. Or did you really think you’d have to?”

    BJ7, “If the number of atoms is not a factor of 3, indeed you will have to.
    That’s was my point.”

    If? And then if not? Somehow you never put the part in that was supposed to make the point until after you find out the point you thought you were making was not the point you needed to make to cover your obvious mistake. (And by the way, a molecule is not an atom in any case.)

    You never thought about the .999 needing to repeat to infinity until after you were told of it, and you never thought about dividing the atoms nee molecules until you needed another excuse for being wrong again. This pattern of dishonesty repeats itself every time you make what you think is an informative comment.

    You will later say I refused to explain how you were wrong when of course I just explained it again.
    But keep going, the endless pattern of lies and excuses must play out.

  33. BillyJoe7on 28 Apr 2012 at 8:31 am

    You are simply an idiot, cwfong.

    Here is how this developed:

    SteveA’s first comment in this thread:
    “And how come I can cut an apple into three equal parts”
    BillyJoe’s first comment in this thread::
    “Actually you can’t, certainly not in practice, and aslo not in principle unless the number of each type of molecule in the apple is exactly divisible by three.”

    So your comment…

    cwfong: “If? And then if not? Somehow you never put the part in that was supposed to make the point until after you find out the point you thought you were making was not the point you needed to make to cover your obvious mistake.”

    …is way off beam, because both scenarios (divisible by three and not divisible by three) was already contained in my first post in this thread (see bolded part above). There was not any need for me to elaborate later, because it was already there in my first post!

    ====================================

    cwfong; “You never thought about the .999 needing to repeat to infinity until after you were told of it”

    Only if my comments are being read by an absolute idiot!
    Here is another exerpt from my first post in this thread:

    BillyJoe: “0.99999…. is equal to exactly 1.”

    Are you’re really trying to imply that I was not aware that 0.99999… indicates repeating the 9s to infinity! Even when I say that it is equal to exactly 1. Which would only be the case if the 9s repeat to infinity.

    It’s not a sin to accidentally misread what I have written, but to keep insisting I haven’t written it when it is there in black and white for everyone to look back on or for me to quote, is just the height of imbecility.

  34. ngon 28 Apr 2012 at 9:03 am

    Well… this is just a superficial impression, you know. But I think that cwfong is an idiot too.

  35. Dirk Steeleon 28 Apr 2012 at 9:23 am

    BillyJoe

    ‘unless the number of each type of molecule in the apple is exactly divisible by three.’

    Not molecules but quarks surely? Unless of course the apple has no flavour…

  36. anwayaon 28 Apr 2012 at 12:15 pm

    Troll fight! Where’s the popcorn?

    Perhaps it’s time you guys stopped this nonsense.

  37. cwfongon 28 Apr 2012 at 1:26 pm

    I see he’s getting very mad again when his obvious mistakes have been called out.
    He says he must be right about saying .999 is exactly one because it would only be the case if the 9s repeat to infinity. In other words he must be right because his conclusion turned out to be correct even if the initial logic had skipped a few beats. (And I note this is a consistent pattern of his backwards reasoning.)

    And then note this now from him:
    *BillyJoe’s first comment in this thread:: “Actually you can’t, certainly not in practice, and aslo not in principle unless the number of each type of molecule in the apple is exactly divisible by three.”*

    Unless the number of each type of molecule is exactly divisible. Hummm. Is that like exactly dividing the molecule itself? I suppose so, because theoretically you could divide all types of matter into threes,
    again according to theories of the endless divisibility of corporeal substance.

  38. BillyJoe7on 28 Apr 2012 at 6:55 pm

    That’s cwfong resorting to verbal garbage when his argument fails :D

  39. BillyJoe7on 29 Apr 2012 at 3:17 am

    cwrong: “.999″

    Nope. Put your spectacles on and pay attention: 0.99999…

  40. BillyJoe7on 29 Apr 2012 at 3:21 am

    “Not molecules but quarks surely? Unless of course the apple has no flavour…”

    You have to reach into the bottom of the barrel to get a top apple.
    Then, of course, there are the electrons…

  41. cwfongon 29 Apr 2012 at 4:05 am

    But not to infinity? You didn’t know you had to say that or you would have, especially when someone had already done so and you didn’t see the relevance. I say this confidently because it’s what you always do.
    Just as you did with your silly apple division, again ignoring the corollary theories of infinite division. Called them verbal garbage.
    But keep going. Insults always come out when you’re losing.

  42. cwfongon 29 Apr 2012 at 4:48 am

    Note also how I just caught him in an outrageous lie on the Szaszian site. Falsifying the content of a quoted interview with Krauss.
    But as I just said above, it’s what he always does.

  43. BillyJoe7on 29 Apr 2012 at 6:00 am

    Seems cwfong doesn’t know what the ellipsis means. :D

    And on the other thread he has just quoted Krauss proving that what I said was true all along.
    And he doesn’t even realise it :D :D

  44. cwfongon 29 Apr 2012 at 1:05 pm

    No I just quoted the part of the interview with Krauss that you deliberately left out, so that you could continue to lie about what he actually was saying in the book. I had given you the benefit of the doubt that you were just mistaken, but now I know and everyone else knows that you have realized your mistake, especially when Steve Novella pointed it out, and are now simply and deliberately lying.

    You faked an interview that was published in the Atlantic to represent Krauss saying what you wanted him to say by removing the part of the interview where he explained what he had actually said in the book. The interview is here for anyone to read in full:
    http://www.theatlantic.com/technology/archive/2012/04/has-physics-made-philosophy-and-religion-obsolete/256203/
    You lied then and you are lying now, as you always lie when you get caught in a mistake. Your lie about what you now know Krauss was saying was the biggest one you’ve yet been caught at. It proves that your lying is virtually pathological.
    You are a liar plain and simple. You will continue to lie and the next thing you post will not only be wrong, it will be a lie.

  45. BillyJoe7on 29 Apr 2012 at 5:41 pm

    I’ve copied this form the other thread:

    I provided the link so you could read the whole article and I provided a summary in case you didn’t want to read the whole thing. What more can I do. Both the summary and the whole article support what I have always said is in the book.

    I suggest that you actually read the book.

    But, as I have always said, you cannot understand what you read and then just make things up about what you think you read based on preconceived ideas on the subject, so I’m not sure reading the book will make any difference.

    There is really not much else I can do for you to help you understand.

  46. cwfongon 29 Apr 2012 at 6:52 pm

    Bullshit.

  47. cwfongon 29 Apr 2012 at 8:20 pm

    Note, folks, how he’s lied again. He claims he ‘summarized’ the article that he had previously cited, except that he had cited a Scientific American article and falsified the contents of an entirely different Atlantic article. Deftly removing the conclusions in the bargain. Caught in a lie doesn’t seem to phase him at all. Watch him lie again.

  48. Dirk Steeleon 29 Apr 2012 at 11:30 pm

    @SteveA

    ‘And how come I can cut an apple into three equal parts, but when I divide 1 by 3 I get an infinite series: 0.33333… And when I multiply back again I get 0.99999..? Who’s stealing bits of my apple?’

    A similar analogy would be……

    0.3333… of this thread are comments made by cwfong whinging about his special beef
    0.3333… of this thread are comments made by BillyJoe responding to the git
    0.3333… of this thread are comments made by Dirk Steele crying over his spilt beer (actually whisky)

    Who is stealing the bits of any interest in this bloody blog?

    ‘Though these aren’t really the kinds of paradox that Dr S is referencing.’

    Agreed.

  49. cwfongon 29 Apr 2012 at 11:41 pm

    Yet I’ve actually defined a paradox, and you’ve done nothing but bitch and whine for attention.

  50. Dirk Steeleon 29 Apr 2012 at 11:46 pm

    @cwfong

    ‘Yet I’ve actually defined a paradox’

    You would still not understand what a paradox was even if it forced it’s way up your anal passage.

  51. BillyJoe7on 30 Apr 2012 at 12:26 am

    ….actually, I think that’s exactly what he’s after ;)

  52. Dirk Steeleon 30 Apr 2012 at 1:19 am

    BillyJoe7

    ‘….actually, I think that’s exactly what he’s after ;)

    But he will never understand Dirk Steele’s laws of motions.

    And neither will you.

  53. Dirk Steeleon 30 Apr 2012 at 1:25 am

    @BillyJoe7
    @cwfong

    Now, and this is my final word.. will both of you go tidy your bedrooms and finish your homework. Otherwise, and I really mean this, I will confiscate your X-box. And you will definitely not get that Playstation for Christmas…….. And I do really mean this.

  54. BillyJoe7on 30 Apr 2012 at 6:42 am

    “Dirk Steele’s laws of motions”

    Oh, I get it, Daddy Dirk…
    If you get down with dogs you get up with fleas.

  55. Dirk Steeleon 30 Apr 2012 at 9:16 am

    @BillyJoe

    Dirk Steele’s laws of motions”

    Oh, I get it, Daddy Dirk…
    If you get down with dogs you get up with fleas.

    No it is to do with my grand unified theory of constipation. Yet to be peer reviewed but I am still waiting and hoping….. and hoping and waiting….

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