Mathematics and mind are supernatural, therefore God exists?


Therefore, Cthulhu exists

If you ever want to publish some poorly written drivel in a popular “news” magazine, there’s an easy recipe: make sure it’s pious drivel. It’s like these rags have a mandatory quota of religious crap they have to spread around, and quality is no criterion. So Newsweek published an article titled, Does god exist? Some scientists think they have proof. Guess what? They don’t have proof, and it’s not written by a scientist. The author is an economist, or more precisely, working at the intersection of economics, environmentalism and theology. It shows. He has a couple of bad arguments that don’t justify what he claims.

His first argument is basically that math is magic. It’s not matter, and it’s not energy, therefore it’s something independent of physical reality.

In other words, as I argue in my book, it takes the existence of some kind of a god to make the mathematical underpinnings of the universe comprehensible.

Did I mention that he’s peddling a book? Of course he is.

I’m not a mathematician or a philosopher, I’m just a pragmatic biologist, so I find the whole point of this line of reasoning to sail right over my head. It seems more than a little self-referential — god created logic; I’m making a logical argument; therefore god exists — and they want to argue not that god is mathematics, but that god is something outside of mathematics who created math, so it’s not clear how demonstrating that the universe operates on a consistent set of logical principles argues for something outside that universe. That math works does not imply that a god, especially the specific deity of myth and folklore, Jesus, also works.

But it’s typical of this guy’s approach. If he can’t see it or touch it, it must be a mystery, and must be supernatural, therefore god. He has another example, besides the math he doesn’t understand: consciousness.

How can physical atoms and molecules, for example, create something that exists in a separate domain that has no physical existence: human consciousness?

It is a mystery that lies beyond science.

That consciousness exists in a separate “domain” is nothing but an assertion.

The workings of human consciousness are similarly miraculous. Like the laws of mathematics, consciousness has no physical presence in the world; the images and thoughts in our consciousness have no measurable dimensions.

The complex, patterned flow of electrons inside the computer he typed that on also lacks “measurable dimensions”, therefore Microsoft Word is supernatural. Probably satanic, even.

…I would argue that the supernatural character of the workings of human consciousness adds grounds for raising the probability of the existence of a supernatural god.

Except…the workings of human consciousness are not supernatural. You can swallow a pill that affects the level of neurotransmitters in your brain, and change your mood. You can have a stroke that knocks out regions of the brain and get changes in personality and behavior. You can lie in an MRI and think about math problems or poetry and see changes in the pattern of oxygen consumption in your brain. It’s complicated and we’re far from understanding everything about consciousness, but it is clear that it is profoundly physical, a product of shifting patterns of ionic flux and material patterns of connectivity and chemistry.

Dualism just doesn’t work.

This being a pseudoscientific essay on god, he’s also got to throw in his two cents about evolution. He doesn’t understand it.

As I say in my book, I should emphasize that I am not questioning the reality of natural biological evolution. What is interesting to me, however, are the fierce arguments that have taken place between professional evolutionary biologists. A number of developments in evolutionary theory have challenged traditional Darwinist—and later neo-Darwinist—views that emphasize random genetic mutations and gradual evolutionary selection by the process of survival of the fittest.

Oh? Really? What are these arguments? Of course random genetic mutations are part of the story. Of course selection occurs. There are arguments about the relative contributions of different processes in evolution, but no real challenges to the big picture. Where does he get this idea that there are major shake-ups going on that make the supernatural a plausible alternative theory?

Would you believe…Stephen Jay Gould?

From the 1970s onwards, the Harvard evolutionary biologist Stephen Jay Gould created controversy by positing a different view, “punctuated equilibrium,” to the slow and gradual evolution of species as theorized by Darwin.

No. Punctuated equilibrium is not a different view (although Gould himself contributed to the confusion by inflating the significance of an argument about the tempo of evolution). There is nothing in PE to defy our understanding of how evolution works. What this is is simply more of the standard creationist lack of comprehension of both evolutionary theory and punctuated equilibrium.

I recommend this overview by Douglas Theobald on the misconceptions about PE.

Much confusion has surrounded the concept of Punctuated Equilibrium (PE) as proposed by Niles Eldredge and Stephen Jay Gould in 1972. This essay addresses a few of the erroneous views held by many creationists and even some evolutionary biologists concerning PE. In this article I make the following main points:

  1. There are two common uses of “gradualism,” one of which is more traditional, the other of which is equivalent to Eldredge and Gould’s “phyletic gradualism.”
  2. Darwin was not a “phyletic gradualist,” contrary to the claims of Eldredge and Gould.
  3. PE is not anti-Darwinian; in fact, the scientific basis and conclusions of PE originated with Charles Darwin.
  4. PE does not require any unique explanatory mechanism (e.g. macromutation or saltation).
  5. Eldredge and Gould’s PE is founded on positive evidence, and does not “explain away” negative evidence (e.g. a purported lack of transitional fossils).

Aside from mangling ideas by Gould, who else is claiming that natural mechanisms are inadequate to explain evolution? It’s James Shapiro.

In 2011, the University of Chicago evolutionary biologist James Shapiro argued that, remarkably enough, many micro-evolutionary processes worked as though guided by a purposeful “sentience” of the evolving plant and animal organisms themselves. “The capacity of living organisms to alter their own heredity is undeniable,” he wrote. “Our current ideas about evolution have to incorporate this basic fact of life.”

Shapiro is a crank. The only people who promote his theories all seem to be intelligent design creationists. The Newsweek article seems to believe he’s supporting the god-hypothesis.

For my part, the most recent developments in evolutionary biology have increased the probability of a god.

You know, I’m a little bit familiar with current developments in evolutionary biology, and none of them involve magic or the supernatural. Once again, he’s just making an assertion without evidence, in contradiction to the actual state of affairs, and somehow leaping to the conclusion that evolution is evidence for a god.

Oh, hey, did you know that the existence of science is evidence for gods, too?

The development of the scientific method in the 17th century in Europe and its modern further advances have had at least as great a set of world-transforming consequences. There have been many historical theories, but none capable, I would argue, of explaining as fundamentally transformational a set of events as the rise of the modern world. It was a revolution in human thought, operating outside any explanations grounded in scientific materialism, that drove the process.

That all these astonishing things happened within the conscious workings of human minds, functioning outside physical reality, offers further rational evidence, in my view, for the conclusion that human beings may well be made “in the image of [a] God.”

Again with the claim that human minds function outside physical reality. If that were true, maybe he could make a case, but he hasn’t demonstrated what he claims.

Furthermore, from this broad, diffuse, non-specific set of sloppy arguments for a god who is some generic force behind mathematics and consciousness and evolution, what do you think: will he promote a pantheistic vision of a deity? Maybe he’ll plunk down on the side of one of the Hindu gods. Or maybe it’ll be Anansi or Huitzilopochtli.

Nah, you know it was coming. He thinks this nebulous nonsense is evidence for the god of the Christian holy book. So predictable…

That the Christian essence, as arose out of Judaism, showed such great staying power amidst the extraordinary political, economic, intellectual and other radical changes of the modern age is another reason I offer for thinking that the existence of a god is very probable.

But he even mentions Judaism — which is significantly older than Christianity, and still extant. If endurance is the metric, shouldn’t it win? Hinduism and Zoroastrianism are even older.

I’d also have to argue with the idea that the Christian essence, whatever that is, has been stable. Ever heard of the Reformation? The Thirty Years War? And which Christianity is he talking about: there are thousands of denominations, and all of them would look really weird in contrast to Christianity in the first century, or the tenth century.

Also, I have to point out that the fact that people believe in something is not actually evidence that what they believe is true. People have believed in ghosts for millennia, that does not mean that ghosts exist.

Comments

  1. Ed Seedhouse says

    Seems to me to be just another “God of the gaps” position. “Science doesn’t understand it, therefore God!”

    No, science doesn’t understand it therefore we need to think and observe and experiment better.

  2. remyporter says

    When people start talking about the magic of consciousness, I always challenge them to prove that I am conscious. No one ever has.

  3. jaybee says

    Is it the author’s contention that, since God created math, God could change the rules to, say, make 1+1=3 and 1+2=2? If God is powerless to change the rules of math, then God wasn’t required to create those rules — the rules are independent of that God.

  4. evodevo says

    Or levels of consciousness – has this guy tried talking to a dementia patient? Or one, like my aunt-in-law, who had bouts of ischemia and would exhibit definite personality changes, and then a month later be back to normal and not remember the ischemic events? Or go off their rocker like my mother-in-law because the hospital gave her ambien? This guy obviously hasn’t read any actual neurology or even Ramachandran or Pinker or Sacks … his understanding of “consciousness” seems to be rudimentary at best, as is his understanding of evolution.
    Just another attempt by the MSM to cater to the Templeton crowd …

  5. cartomancer says

    I love the way the entire discipline of History is dismissed in a single sentence: “There have been many historical theories, but none capable, I would argue, of explaining as fundamentally transformational a set of events as the rise of the modern world.”

    So historians of the Late Medieval and Early Modern world have achieved precisely nothing, because “it was a revolution in human thought” is enough to explain everything? I’m glad my old undergraduate tutor passed away last year, before it was revealed that his entire life’s work was a waste of time. Looks like I’d best burn my copy of Peace, Print and Protestantism then, and all the other books on that period I still have. What a relief my historical skills are still relevant to my own fields of Ancient and Medieval history!

  6. Nerd of Redhead, Dances OM Trolls says

    My laugh is always, and especially so in this case, if you don’t posit an imaginary deity, there is absolutely no need for one to explain things.
    The mental masturbation to get there is very self-satisfying, but is meaningless to anybody else.

  7. Rich Woods says

    If human consciousness exists outside physical reality then how am I able to express my conscious thoughts in a physical medium? I’m pretty sure I’m typing this on a keyboard using my fingers to press each key down in turn rather than applying my world-renowned powers of telekinesis.

    (Given the number of typos I’ve just corrected, it would be so much simpler if I could just will my message into existence in each of your non-physical minds.)

  8. bryanfeir says

    And, of course, the ‘measurable dimensions’ bit is just flat-out false, too. There actually is a measurable dimension to consciousness, and it’s the same measurable dimension we would use for electrical patterns in computers: entropy, at least as defined in information theory.

    Sure, actually measuring it is non-trivial, but it is at least theoretically measurable.

  9. The Very Reverend Battleaxe of Knowledge says

    But, but, but…

    Roger Penrose assures us that all we need to explain consciousness is a workable theory of quantum gravity to see how it acts on microtubules in the brain….

    See, humans create proofs for mathematical propositions where the Halting Problem for the Turing Machine associated with them is undecidable–Therefore: impossible. Therefore: Quantum gravity. It must be the action of unknown physics on the mictotubules in the brain (since we don’t know what they’re doing, anyway.)

    To quote the great Dave Barry: “I swear I’m not making this up”. See The Emperor’s New Mind and Shadows of the Mind.

  10. Zeppelin says

    Why are people so eager to confuse the map for the territory when it comes to mathematics, anyway?

  11. Feline says

    As a mathematician I keep getting annoyed at “mathematics => God”. Because believing the notion that “mathematics aren’t real” necessitates an ignorance of mathematics that any person with a college education should be ashamed of.

  12. Sean Boyd says

    God coulda helped us out a bit with this by, say, proving the Riemann Hypothesis. Also, I didn’t realize I was studying magic all those years ago…did I miss the line for magic cloak, wand, and familiar at registration?

  13. consciousness razor says

    In other words, as I argue in my book, it takes the existence of some kind of a god to make the mathematical underpinnings of the universe comprehensible.

    We notice various things and events in the universe, and we either do or don’t comprehend a certain amount about them. When we do comprehend something, we use mathematical, logical, verbal, artistic or various other means to represent what is comprehensible about it. Otherwise, we haven’t yet found a good way to do that. Anyway, we do that, and we do it for ourselves, because comprehension is incredibly useful — it at least passes the time and can maybe pay the bills. That isn’t at all mysterious. This is just people making sense of our world, in any way that we can.

    We don’t in fact live in a world that is absolutely incomprehensible, one with no discernible consistencies or patterns or relationships; and in a world like ours, we are bound to get something useful out of a project like that. Maybe not much, but it’ll be something.

    Would a god create an utterly formless world, which wouldn’t be able to support anything interesting or even something with regular features or consistent sets of properties, such as for example stars or molecules or living organisms or whatever you like? I have no clue. Let’s say that it’s more likely that a god, if it has any intelligence or any interest in what it’s doing, would create something else if it could. That doesn’t actually tell us much of anything, because we couldn’t even begin to list all of the possibilities here. And it likewise puts extremely loose constraints on what an atheistic universe might look like, if you just picked a random one out of a hat. (Whatever that may mean, if the collection inside the hat is infinite.)

    Anyway, let’s grant that it’s extremely weak evidence for a god, which brings the chances up from 10^-1000 to something more like 10^-999. Perhaps that’s being too generous. Play around with those made-up tiny numbers if you want, but any way you slice it, that’s no reason for theists to throw a party.

    But it’s not just that. This same type of bullshitter claims incomprehensible stuff (or stuff which currently isn’t well-understood) is also supposed to be evidence of the supernatural. This makes no sense. That can’t be evidence of the same thing, to start with, just given what it means to be evidence for something.

    Also, it’s hard to even see how the thought process is supposed to work here, if there is supposed to be any actual thought process (and not just bullshit propaganda). Would a god be likely to make a world which is incomprehensible? Would he be inclined to put any incomprehensible stuff in it, much less fill the whole world with nothing but that? Again, no clue. But that doesn’t seem like an especially promising idea, as I tried to say, if the assumption is that a god would make a universe in order for it to have interesting properties (or a specific one that he really deeply wanted more than anything else).

    Still, maybe god needs to find a better hobby, or he just had nothing better to do with eternity except make a garbage universe which is nothing remotely like ours. Fine. If a god is interested in structureless noise, or if that’s the best he could do, then he would make that type of world instead, not ours. One thing he can’t have the power to do is make that same structureless bizarro-world so that it is also structured (or interesting, comprehensible, etc.) and has the features this bullshitter was blathering about. You may say god is omni-whatever and can do everything (including impossible things); but we don’t need to delve into that or why that’s untenable, because that has no bearing on the world, which isn’t omni-whatever. The world is the thing which is supposed to satisfy both of those contradictory criteria, and it can’t do that.

  14. slithey tove (twas brillig (stevem)) says

    Colbert and Brad Pitt addressed similar question during his “looking at the sky” skit. “Did mathematics create the world or did we create mathematics?” asked Colbert.
    without even waiting for Pitt’s answer, I turned to my partner to comment “yes we invented it.” Mathematics is just a system we invented to describe reality. It is not the underlying mechanism of the universe that we occasionally discover a rule now and then.
    Math equations are descriptions someone developed that allows one to plug in numbers and test whether the result of the equation matches the real world result. Sometimes there’s a mismatch, that means the equation needs to be reformulated not that reality is violating the rules. Perfect example is Einstein noticing discrepancies between Maxwell’s equations and measured results, reformulated the equations into what is now known as “Special Relativity”.
    uhm wheram am I going. dunno.
    math we created to describe, and talk about with precision, reality. I doubt it is the underlying “rules” of reality we occasionally dig up. Our equations are just more accurate ways to make predictions about how reality works.
    Thank you for reading my ramble.
    I’ll see myself out…

  15. Azkyroth, B*Cos[F(u)]==Y says

    Is it the author’s contention that, since God created math, God could change the rules to, say, make 1+1=3 and 1+2=2? If God is powerless to change the rules of math, then God wasn’t required to create those rules — the rules are independent of that God.

    I think it’s fair to say that math IS math’s rules.

  16. alkisvonidas says

    @The Very Reverend Battleaxe of Knowledge

    This guy’s claims go far, far beyond anything Roger Penrose has ever proposed.

    Penrose, AFAIK, is a mathematical Platonist. The Platonist position is not about mathematics being supernatural, or of supernatural origin, but rather about whether mathematical objects can be thought of as well-defined outside of any historical context or convention.

    For example, a Platonist would say that the mathematical constant pi in a sense exists, and has always existed, regardless of our ability to calculate it to a given precision. We have discovered and not invented it. Other civilizations, possibly alien, would stumble upon the same concept, and it would BE the same concept of pi, regardless of whether they called it glooble, for example (or anything at all, for that matter).

    There are other approaches to mathematics, most prevalent of which is the formalist approach: mathematical objects do not exist beyond what can be proven and constructed formally. In the case of pi or the natural numbers, the distinction is not really important, because their definitions are uncontroversial. But in the case of “deeper” concepts, such as the axiomatization of arithmetic, a number of distinct formalist approaches are possible, and there the distinction between platonism and formalism matters. A formalist, faced with such a choice, would say that we can pick whichever “fork” of the axioms we like/need for our specific purposes. A platonist would consider some choices “right” and others “wrong”, based on whether or not they feel it describes that intuitive entities they call “natural numbers”.

    But all this has nothing to do with the drivel of “mathematics, therefore God”. The author makes a classic reification mistake: we shouldn’t think that everything that can be given a name describes an entity. I can talk about “justice”, “faith”, “freedom”, or “a mild concussion”, doesn’t mean these are things floating out there, in a reality of their own, subject to being observed and described.

  17. rietpluim says

    Nelsons argument basically comes down to: the proof that God exists is that there is proof that God exists. Has he ever considered joining Tautology Club.

  18. rietpluim says

    Re: math and reality.

    People sometimes express how miraculously reality “obeys” mathematical rules. While in reality, reality does not more often than it does. If you take an apple, and add another apple, you don’t get two bicycles. One plus one is two only in a very limited number of occasions.

  19. Bill Buckner says

    #16

    Perfect example is Einstein noticing discrepancies between Maxwell’s equations and measured results, reformulated the equations into what is now known as “Special Relativity”.

    What discrepancies with Maxwell’s equations are you referring to?

  20. slithey tove (twas brillig (stevem)) says

    re 21:
    oops. you’re right, no discrepancy within Maxwell’s eqns, discrepancy was between Maxwell and Newton’s eqns.
    Sorry to continue so vague, it was something about measuring speed of light. Einstein had a choice between two sets of variables as which were Constants, which were Malleable. Einstein chose Maxwell’s as Constants and let Newton’s be the Malleable ones.

    Good point Buckner, not such a good example of the point I was trying to make @16.

    Still, it is a single example of how math is our description of reality and can be adjusted to fit reality, not the reverse.
    BRB
    ?

  21. Scientismist says

    Erlend Meyer #4:

    I don’t understand this, and I really don’t want to either, therefore GOD!

    Worse. The conclusion is “I really don’t want you to understand this either, because my GOD (which any fool will now understand obviously exists) has given me the right to tell you what to do, and since you don’t want to, that just proves you are evil so I get to burn you at the stake. (You can provide the match.)”

    “Math and consciousness, therefore God” sounds a lot like philosopher Alvin Plantinga, who argues (as near as I can tell) that since (1) human thought leads to perfection (the perfect knowledge of the existence of God), and (2) evolution works by preserving mutational errors in the physical world (and so cannot be perfect), therefore (3) human thought must be independent of physical evolution. I believe PZ has previously expressed his disdain for this argument.

    Back when I was studying math in college (too many decades ago), I was told that one theory of the early development of math that is supported by archeological evidence is that sheep herders sent sheep off to market with the most trusted slave. But just to help that slave’s honesty, he carried a clay envelope prepared by the seller filled with little clay marbles, one for each sheep. The buyer could open the envelope and remove one marble for each sheep that went through the gate, knowing that they should match. Or, later on, he could just interpret the marks on the outside of the envelope and count the sheep. Still later, the seller and buyer could dispense with the marbles and just use a clay tablet with the symbols.

    I don’t know if professional mathematicians would agree, but in my own mind, I have always figured that the rest of mathematics consists of ever more sophisticated tools for manipulating those symbols while not losing track of any marbles. It works well in studying the physical world because that world is itself pretty good at conserving and keeping track of its marbles.

    But now this guy is saying that 3 packets with 4 marbles each matching up with 12 sheep is a non-physical divine miracle. But if we have the packets, we can open them up and by golly there are 12 marbles — or are there? If we do the experiment, and it indeed counts up to 12, proving (according to this guy) that the envelopes and marbles are a non-physical miracle, will we witness the packets with their symbols and the 12 marbles being taken up in a cloud of holy rapture?

    Nah. I think this guy has just lost his own marbles.

  22. KG says

    Scientismist@23,

    Lunar calendars go back to the Paleolithic, long before slaves would have been taking sheep to market! Sequences of 29 marks, sometimes with shapes differing along the sequence in a systematic way. I’d say one-to-one correspondence between nights and marks is definitely mathematical. And what sort of human beings tend to find it most useful to keep track of monthly cycles?

  23. alkisvonidas says

    And what sort of human beings tend to find it most useful to keep track of monthly cycles?

    I dunno, werewolves?

  24. Rob Grigjanis says

    KG @25:

    And what sort of human beings tend to find it most useful to keep track of monthly cycles?

    Those humans who wanted a reliable unit of time longer than a day and shorter than a year?

  25. consciousness razor says

    alkisvonidas:

    The Platonist position is not about mathematics being supernatural, or of supernatural origin, but rather about whether mathematical objects can be thought of as well-defined outside of any historical context or convention.

    That’s not how I would put it. Platonists say mathematical objects exist. Others don’t necessarily have any argument that they’re not well-defined, a concept which is logically separable from “historical context or convention.” Non-Platonists may think a circle is perfectly well-defined, no matter what the context may have been like whenever people defined it.

    It is true that not all Platonists would say math is supernatural. Some would, including Plato himself (and it wasn’t just math but all Platonic Forms). But that’s not central to mathematical Platonism. You may think mathematical objects are abstractions, but being abstract isn’t being supernatural. To make just one possible distinction, abstractions don’t cause anything physical, which is not to say they don’t exist. In contrast, supernatural things (if any existed) are supposed to be capable somehow of causing or influencing physical things/events/etc.

    For example, a Platonist would say that the mathematical constant pi in a sense exists, and has always existed, regardless of our ability to calculate it to a given precision.

    Alright, now you shifted to a better formulation: they say it exists. It should be fairly clear that’s not the same thing as being well-defined. I can define a unicorn just fine; but I’m going to tell you it’s nonexistent, or fictional if you feel like talking about any sense in which a fictional entity exists (in your mind, in a book, in our culture, etc.).

    But would I say that a unicorn “has always existed”? Err… no, I probably wouldn’t define my unicorns that way, although I guess that’s not totally out of the question. A unicorn may have to be in time (in a fictional world or a real world other than ours) in order to count as a unicorn, otherwise it can’t move around and do unicorn-type activities…. But the number pi presumably isn’t a temporal thing at all, so maybe “always existing” isn’t such a great way to put it. It just is, according to Platonists, independently of physical time, space, matter, and so forth.

    There are other approaches to mathematics, most prevalent of which is the formalist approach: mathematical objects do not exist beyond what can be proven and constructed formally. In the case of pi or the natural numbers, the distinction is not really important, because their definitions are uncontroversial.

    But you can’t literally “construct” anything which gives all of the digits of pi (nor can you give me a list containing every natural number). You can converge on it through various methods or build up pieces of it or something like that; but some people are suspicious of basically anything that’s infinite (and never mind continuously infinite or even larger). They think that sort of thing can’t “exist,” at least not in our physical world if at all, by virtue of being infinite. That sort of finitist position is different from thinking that certain stuff like the number 58 doesn’t exist, by virtue of being a number.

    slithey tove:

    Sorry to continue so vague, it was something about measuring speed of light. Einstein had a choice between two sets of variables as which were Constants, which were Malleable. Einstein chose Maxwell’s as Constants and let Newton’s be the Malleable ones.

    Maxwell’s theory implies the speed of light is constant. That of course doesn’t just mean it fails to vary over time, which isn’t too surprising, but that you get the same results no matter what state of inertial motion you or the light source are in. That definitely is surprising. However, like everything else according to SR, light doesn’t have an absolute speed. So you have to be really clear about what it means to say that it doesn’t have a speed, while maintaining that it’s also somehow “constant.” It’d be pointless, at best, to try to measure something it doesn’t have. You can observe phenomena that you had associated with its absolute speed, and you’re saying what everybody will agree those phenomena will be like.

    SR was fixing mechanics so it would be consistent with electromagnetism, since Maxwell’s theory was a fantastic success and Newton’s hadn’t been tested in such regimes. It more or less updates Galilean relativity by stipulating that “the speed of light is constant,” when that phrase is understood properly. It’s not clear what you mean by saying he picked a “set of variables” from Maxwell, instead of picking a different set from Newton. And it’s not like Einstein just made an arbitrary “choice” there. The evidence was building for Maxwell and against Newton, which makes it an easy “choice” if you really want to call it that. He went with the evidence and tried to make a good theory based on that.

  26. says

    I would think any god worth his salt would have created a system with a set of axioms both complete and consistent. Whence the Incompleteness Theorem?

  27. Rich Woods says

    @feralboy12 #29:

    Whence the Incompleteness Theorem?

    Oh, that God, he’s just teasing us! And why wouldn’t he? It shows he’s really human at heart. Go on, tell me you’ve never tried to persuade your kids that Jurassic Park is actually a documentary.

  28. Rob Grigjanis says

    cr @28:

    It more or less updates Galilean relativity by stipulating that “the speed of light is constant,”

    Much more than that. It really is important to stress that SR requires another postulate: that physics equations should look the same in any inertial frame. It’s the requirement that all* of Maxwell’s equations take the same form in any inertial frame that cannot be satisfied with Galilean transformations.

    *Two of them actually are invariant under Galilean transformations.

  29. consciousness razor says

    Rob:

    Much more than that. It really is important to stress that SR requires another postulate: that physics equations should look the same in any inertial frame. It’s the requirement that all* of Maxwell’s equations take the same form in any inertial frame that cannot be satisfied with Galilean transformations.

    Sure. But I’m happier with your second version: that all of Maxwell’s equations take the same form in any inertial frame. I wouldn’t say it’s genuinely new, since as you correctly pointed out, Galileo had already said essentially the same thing in the 1600s, and 2/4 already satisfied that condition (which was no accident). It did need to be applied consistently, to new laws Galileo didn’t know about and couldn’t have accounted for, requiring new transformations that would do the same old job Galileo had wanted, of “making the equations the same.”

    But the basic idea had been around for a long time; it was still alive and kicking, etc. For a while it just wasn’t obvious to anybody how they could make a theory like SR which would solve their problems (and various people had all sorts of other views of course, including not realizing/admitting there was a problem). So, it seems wrong to say Einstein really had to make that additional postulate, since that makes it sound like he just pulled it out of thin air.

    I guess it’s fair to say it had to be added to Maxwell’s theory in some sense, or reformulated and applied consistently to it — not really the perspective I was taking, but fair enough. Still, it’s not added to the whole existing structure of physics at the time.

  30. Rob Grigjanis says

    cr @32:

    So, it seems wrong to say Einstein really had to make that additional postulate, since that makes it sound like he just pulled it out of thin air.

    First of all, no postulate worthy of the name is ever pulled from thin air. And yes, Einstein had to make that postulate to derive the transformation properties of the electric and magnetic fields. Don’t forget that aether theory was still around. From “On the Electrodynamics of Moving Bodies“;

    These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies. The introduction of a “luminiferous ether” will prove to be superfluous…

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