Faith versus Fact talks a bit about the topic that the Jesus and Mo author covers in four panels in today’s strip:
Here are some gaps that theologians still use:
The origin of life
The mechanism of consciousness
“Fining tuning” of the laws of physics
Why the laws of physics are as they are
The “unreasonable effectiveness of mathematics”
Why humans are able to perceive true things
The “moral law” (humans’ instinctive feelings about right and wrong); this one is a favorite of Francis Collins, who says that the “moral law” MUST come from God.
I cover all these in FvF
Yes – I have seen Templeton ads in New Scientist…
PS “true things” are as meaningless as perfect things & the idea of perfection which religionists love –
“A thing is perfect in which nothing is wanting of its nature, purpose, or end. It may be perfect in nature, yet imperfect inasmuch as it has not yet attained its end, whether this be in the same order as itself, or whether, by the will of God and His gratuitous liberality, it be entirely above its nature, i.e. in the supernatural order. From Revelation we learn that the ultimate end of man is supernatural, consisting in union with God here on earth by grace and hereafter in heaven by the beatific vision. Perfect union with God cannot be attained in this life, so man is imperfect in that he lacks the happiness for which he is destined and suffers many evils both of body and soul. Perfection therefore in its absolute sense is reserved for the kingdom of heaven.” http://www.newadvent.org/cathen/11665b.htm
How meaningless.
Creepy also.
I don’t “get” this one. Of course mathematics is useful. We wouldn’t use it if it weren’t….
b&
It is the religious finetuning argument for the mathematicians universe…
mathematician’s [/finetuned]
This goes back to concepts, a concept being the idea of a class whose members share a certain similarity. The concept named by the word “two” or represented by the symbol “2” is simply the class of all duos; the parts of each member of this class can be put into a one to one correspondence with any other member. This mental integration of many instances into a single mental unit is very economical and thus useful especially given our finite and fallible minds. The concept named by the word “two” enables our minds to make inferences about members of this class that we do not directly perceive.
Mind the Gap.
It is the Templeton Revelation! I like it.
In other comic news, Randall Munroe has – after 1569 strips – made a science mistake.
In _evolution_! :-/
http://xkcd.com/1569/ ; read the Easter Egg [mouse over the comic].
Please pardon my ignorance, but I want to understand. Is his mistake that he’s claiming convergent evolution despite one ‘species’ not being organic, but man-made?
I read that mouse-over as a typical Randall Munroe joke that pokes fun at pseudo-science. I find your lack of faith in Randall disturbing 😉
I think he is being frivolous.
But his easter egg reminds me of the Counting Pines in Sir Pterry’s Discworld.
cr
Templeton: If you build the universe our of metaphysical truths you get a universe with metaphysical truths. You know, the ones that can never be proven.
Your efforts to find the most likely of all unlikely possibilities is the antithesis of science.
It seems to me that “the unreasonable effectiveness of math” is not a gap.
Math is descriptive. The more abstract, esoteric types of math are logical extensions of the more fundamental descriptive math, aren’t they?
This seems to me like saying “the unreasonable effectiveness of English” at communicating ideas between English speakers.
I will soon run out of things to say on this, but I understand that the fact that 2+2 exactly = 4 depends on your point of reference.
Indeed. 2 + 2 = 5, for sufficiently large values of 2.
(And this is a joke, yes…but you can also see real-world examples of it all over the place, especially in computational environments that use truncation rather than rounding. Hell, it can happen with a digital scale….)
b&
You can still buy cheap calculators which will inform you that (8/7)*7 =7.9999997. Less forgivably, my new Android phone informs me that the same quantity is 8 if you enter it directly, but 8.0000000003 if you press = after the first 7 (as you might do to check what you were doing). Come on guys, you could have afforded to carry a few more significant figures.
I think that’s the standard-defined result from one of the IEEE floating point specifications. It’s a result of the round trip from decimal to binary and back to decimal.
You can do precise decimal math, even math on decimal fractions, with computers…but at a performance penalty. Whether any human would notice such a slowdown in a modern smartphone’s calculator I’ve no clue….
b&
Due entirely to round off errors, the following exception toe Fermat’s Last Theorem seems to be true on many calculators.
3487^12 + 4365^12 = 4472^12
I think you must have a typo in there…the values aren’t even close….
b&
The first number should be 3987 not 3497.
It’s taken from this screenshot from an episode of the Simpson’s written by someone fairly mathematically literate.
http://media.npr.org/assets/img/2014/05/08/screen-shot-2014-05-08-at-6.16.50-pm_wide-68c9dd352a5514d2ede51c42ad009b3ec41b4edd-s600-c85.png
That works better.
3987**12 = 1.61344746097513e+43
4365**12 = 4.78421817399473e+43
4472**12 = 6.39766563484867e+43
3987**12 + 4365**12 = 6.39766563496986e+43
The observant will note that the last two figures differ by one in the least significant figure. Which gives this result for the difference:
1.21189378085882e+33
…which is still an humongous number, but one that would be rounded off were this calculation done with one less significant figure….
b&
Would “point of reference” be better termed “working definition”?
Most precisely, we’ve defined “2” as the symbol that signifies the quantity you wind up with if you pick an apple and then pick another one. You can get away with defining 2 apples plus just a little more of another apple as “2 apples” if the context is loose/forgiving enough. But this does not divorce math from physical reality.
That sort of thing only really reliably works at macro scales. Very notoriously, in the quantum realm, you could put one particle in a cage, put another of the exact same particle in the same cage, and, when you open the cage, you might have two particles, or none, or three, or who-knows-what. At the relativistic realm, you might be in your spaceship traveling at, say, several minutes per AU, accelerate your speed by several more minutes per AU, and still only be going several minutes per AU. And Einstein also very famously figured out that there is not 360° in the circle of Mercury’s orbit.
So, if your “frame of reference” is the familiar macro world, basic arithmetic is obvious and intuitive. But in our very own Universe there’re other frames of reference in which it’s next to useless; in those frames, you have to start with different primitives. It’s reasonable to expect that, had we evolved in an environment in which those kinds of primitives predominate, we’d find our own basic arithmetic naïve and useless, save when describing phenomenon in that bizarre macro realm.
b&
Yes, but I think all that is orthogonal to my point.
Quantum physicists are still involved in the project of description. They’re describing the quantum world rather than the Newtonian world, but they produce descriptions of a prior physical reality nonetheless.
My point was to refute the idea that math isn’t tethered to physical reality, that it has its own Platonic existence and it’s miraculous that all those pre-existing equations and formulas happen to map on to physical reality. They are designed to map on to physical reality. Yes, some equations get “discovered” before w discover the physical phenomenon it describes, but this happens in all areas of science. They are called “predictions”.
Even that much will get you into trouble, sooner or later. Math simply doesn’t exist outside of human minds or the symbolic representations of it we’ve constructed.
Trivial proof: you can “do stuff” with math, right? Well, that means action — cognition and computation (and therefore communication) if nothing else. Either math is made up of real-world stuff (patterns of synapses in the brain, for example, or electrical charges in a computer), or it’s a perpetual motion machine doing work without input.
b&
Yes.
“My point was to refute the idea that math isn’ttethered to physical reality…” That is, math is tethered to physical reality.
And I don’t think that refutation has anything to do with the differences between descriptions of the quantum world and descriptions of the Newtonian world.
Ah — sorry. My bad….
b&
No worries!
I’m happy!
b&
I really should’ve avoided the double negative.
It really wouldn’t not be disunconsiderate of you to fail to avoid contemplating the negation of that course of inaction.
No, I’ve no clue what I just wrote means…and I ain’t gonna abandon no double negation, myself!
b&
I agree. The other arguments appeal to something the science might or might not explain some day. But it’s hard to know what would constitute a new and empirical explanation of “why” math is effective.
Also, several of these arguments have been around long before the rise of science (though obviously not the one about fine-tuned constants.)
There’s also the issue that modern science has altered our entire !*concept*! of causality, apparently removing teleology from the universe, and calling into question the theologian’s distinction between main or supernatural causes and secondary causes.
A terrific treatment of this is the book “The Ghost in the Universe” by Taner Edis which takes the reader quite a bit past god of the gaps issues.
I love it when people who’ve based their lives on a book that features a talking snake and a guy who hangs out inside of a whale take a run at mathematics. It’s cute.
The discussions regarding mathematics in this thread are interesting, but obtuse to those throwing theological shade. If they were at all moved by rationality or empiricism, they’d have an altogether different worldview to begin with.
I spent a couple months arguing just that point with a theologian who began his proof of god with the premise “there are moral truths.” I said, hey, wait a minute, there are no moral truths, define your terms; and we never got beyond that point.