Hmmm, so it seems that I keep running into my colleague KC Cole this week. While settling down to drink my morning coffee after a couple of hours of battling dust around the house and leaves outside the house, I found myself looking at the LA Times’ Book Review section, and saw that KC wrote a review of the book entitled “What We Believe but Cannot Prove”, edited by John Brockman. The subtitle of the book is “Today’s leading thinkers on Science in the Age of Certainty”.
(Note to self: Figure out when this “Age of Certainty” thing took place and find out why I did not get the memo.)
It seems that the book is supposed to be a collection of essays about things scientists believe but cannot prove…. KC deconstructs this notion a bit, and I’ll let you go and read the article (which can be found here) yourself, since instead of blogging I’m actually supposed to be running around buying a wedding present and then getting ready to head north to Santa Barbara to attend the actual wedding later today…..
She obviously does not think that this book is as good as it could be, largely because of the brevity of several of the contributions, which “either state the obvious or cut off just as things get interesting, random bursts of intellectualizing designed for compulsive channel surfers”. She likens this to blogging, by the way. (Ahem!) She also says:
Fans (and I count myself among them) of such contributors as Jared Diamond, Steven Pinker, Sir Martin Rees, Freeman Dyson, Daniel Dennett and Howard Gardner would be better off sticking to their wonderful books.
She has a number of positive observations, such as:
The essays worth reading take pains to put beliefs in context: Psychologist Irene Pepperberg studies how gray parrots talk and think (compared with apes, marine mammals and children). She believes birds are the best model for understanding human language. But before making her argument, she offers a highly informative backgrounder on bird song. So, by the time she proposes that the “missing link” between learned and unlearned vocalizing may be found in a recently discovered flycatcher that learns its songs, you’re ready to go along.
There’s also this:
Theoretical physicist Leonard Susskind uses a parable to explain that all proof is ultimately based on probability. He can’t prove that a coin flipped a million times won’t come up consistently heads. But he’d bet his life, soul (and even his salary) on it. Mathematician Devlin admits that he believes Andrew Wiles’ 1994 proof of Fermat’s last theorem only because “experts in that branch of mathematics tell me they do.”
(Hmmm. *All* proof? I’m not sure I would go as far as Lenny in that statement, but maybe I’m being a bit picky. I like the rest of the paragraph quite a lot.)
There are a number of other interesting things about the book, and about the review, but why not go have a look at the site and have a read? Fulfilling KC’s observation about blogging, I’ll cut off my thoughts on this at this point….. because I have to dash out to the shops!
-cvj
March 12th, 2006 at 1:42 pm
Well it is true that absolute proof doesn’t exist outside of mathematics and logic and other such systems, and that we have to take the proofs for some things on trust. I suspect that that was what Susskind meant.
But I can prove a number of things in mathematics and logic, and some of them are so simple and comprehensible that I don’t think that it is meaningful to quibble over the possibility that my reasoning might not be correct or that I don’t understand a proof for one of the premises.
March 12th, 2006 at 2:40 pm
This “Age of Uncertainty” stuff isn’t particularly deep. It’s a rehash of a point made by Hume well over 200 years ago, which was an echo of a point made by Xenophanes over 2300 years before that.
Perhaps what is new is the growing realization that it applies to mathematics as well. This should have been obvious, however. I might make a error in proving the most elementary theorem. I can never be absolutely certain, unlike Sean, that my proof of, say, the irrationality of the square root of 2 is correct. There’s always a chance, however slight, that my brain has a software or hardward glitch that manifests itself only when I attempt to check this particular proof.
March 12th, 2006 at 3:03 pm
Dear Clifford,
okay, I have to write down the same info and ask the very same question on my blog.
Best
Lubos
March 12th, 2006 at 7:36 pm
Belizean, this is not really the point. In some fundamentall sense what you say is tautologic, but I’m not a fan of rendering perfectly good words useless by insisting on considering some abstract absolute tautologies with no relevance whatsoever.
If the likelyhood of the proof being wrong exceeds the likelyhood of earth spontaneously self destructing it becomes operationally meaningless to distinguish certainty from this likelyhood.
The new thing is that mathematical proofs are so complex that we can distinguish likelyhood and certainty.
This is of course a graduall process, but therefore no less real, and no less well described by the words certainty and uncertainty.
March 12th, 2006 at 9:03 pm
Even pure mathematics isn’t always very clear cut, take e.g. Skolem’s Paradox.
March 12th, 2006 at 9:08 pm
FH is right that the sense in which Belizean says even a simple proof, as of the irrationality of sqrt 2, is in some sense “uncertain” distorts the usual meaning of the word “uncertain” to the point of uselessness. However, I think the same is true of Leonard Susskind’s mention of the million sequences of coin flips. It’s actually probably more likely that I’ve somehow made some conceptual error every time I’ve considered the proof of the irrationality of sqrt 2 than it is that a particular fair coin will come up heads on its next million consecutive flips. I’ve discussed this development somewhat on my blog here (talking about the incompleteness of ordinary proofs) and here (talking about the usefulness of probabilistic proofs with certitude as good as Susskind’s coin flips).
March 12th, 2006 at 10:02 pm
I would take issue with Irene Pepperberg concerning parrots. As linguist John McWhorter has pointed out, the parrot will not go out into the forest and teach other birds to speak and, therefore, is a poor example for human speech studies. Native languages are not learned. They happen in humans..There is just a window of time during childhood in which we can utilize the skill. After that we must do some adult rote thing to learn other languages. Bands in Africa called the “Dobe Ju/’Hoansi” (called ‘San’ by others) speak about 7 distinct clicking languages, 3 fluently. Nobody goes to school to learn any of them.
http://www.teach12.com/ttc/assets/coursedescriptions/1600.asp?id=1600&d=Story+of+Human+Language&pc=Literature%20and%20English%20Language
March 12th, 2006 at 11:12 pm
It is indeed the Age of Certainty. For instance, Sean and many other scientists are certain there is no God and that religion is not only useless but harmful. They are as certain as those who have faith.
March 12th, 2006 at 11:37 pm
A Sense of the Mysterious by Alan Lightman Pg 78
It goes on with information that I had mentioned in the “other thread” of KC and string theory, about imaginary numbers and of one called “i”. Another example stated, was “non-euclidean geometry.”
The question is then asked.
Pg 80 to book above
Because maybe we found something that worked?
March 13th, 2006 at 3:04 pm
[…] Bits and bobs accumulated while I was traveling, offered up as I recover from the traumatic trip back to Chicago. (I wasn’t at Don and Crystal’s wedding, but many congratulations to the happy couple!) I had an early flight scheduled Sunday, but I was feeling lazy and unmotivated to arise at dawn to return my rental car, so I called United and asked whether I could go standby on a later flight. They indicated that there should be no problem, as the later flights had plenty of open seats. This turned out to be one of those things they believed even though they couldn’t prove, in fact even though it wasn’t true. After sitting in LAX, watching two flights to Chicago take off full without me, I finally squeezed onto a plane that was scheduled to reach O’Hare at 10:44 p.m. Of course, it took off only after an hour-and-a-half delay, and then landed safely around 12:30 a.m. Sadly, it landed not in Chicago, but in Rockford IL, since it was apparently a bit breezy in Chicago. (Windy city and all that.) After some tense moments when it appeared as if we might all climb aboard busses and drive the rest of the way, the plane did take off again, landed safely in the appropriate airport, and I endured a tense half an hour in which everyone on the flight retrieved their luggage except me. Finally mine came out, allowing me to proceed to the character-building exercise of standing in the rain for another half an hour to get a taxi. Arriving to my chilly lakeside condo at 3:30 a.m., since apparently some bozo left the window open when he left for L.A. For as much as I travel, it’s been a long time since I’ve been subjected to such delays, so I suppose I was due. […]
March 14th, 2006 at 6:32 am
Clifford, even though I answered with #9 here, “a trackback” should have followed to “KC on Mathematics and String” as well, after that entry?
March 16th, 2006 at 9:16 am
On proof and belief. I had thought that mathematicians had shown that there was no proof of anything, fut perhaps I am wrong. To prove something I presume means to have demonstrated it beyond rational disbelief, which would require a definition of belief. Good luck on that.
March 16th, 2006 at 12:19 pm
If one thought one less then the ego developed, strong enough, to venture into the forest, would one have shared the beauty of what propelled the original seer by what “strokes” one could get?
INvention is more then just the mother of, it take its counterpart too, in rearing the young students, to possible futures of independance, in recognition of valid science and the years of school? That we should be lead by, until the day we fall out of the nest:)
There had to be a deeper motivation, for the “seeker of truth” and what remains as, “self evident.”
Graduation to the non euclidean realm, let’s say? GR prepared one on the way, and it’s “historical message” is quite clear?
You are more now then just the student in the way you see, yet there is still ever more to learn in what God/nature might reveal?
Understanding that paradigm change of who you were and how you shall now see in the world, is about change?
Maturity has its psychological reqard having reached the pinnacle of scholastic career? Has it quelled the wanting for more? I don’t think so. Science in regard of age, is still not deserted.
Some, would like to think them senile:)