Uncommon Descent Serving The Intelligent Design Community

What qualifies as science in the wonderful world of Disney

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The scientific enterprise entails:

1. observation
2. hypothesis
3. testing

Consider this passage from the class text of an introductory cosmology class I took once upon a time:

galaxies farther than 4300 megaparsecs from us are currently moving away from us at speeds greater than that of light. Cosmological innocents sometimes exclaim, “Gosh! Doesn’t this violate the law that massive objects can’t travel faster than the speed of light?” Actually, it doesn’t. The speed limit that states that massive objects must travel with v < c relative to each other is one of the results of special relativity, and refers to the relative motion of objects within a static space. In the context of general relativity, there is no objection to having two points moving away from each other at superluminal speed due to the expansion of space.

page 39
Introduction to Cosmology
by Barbara ryden

Let’s say for the sake or argument this is true, an agnostic, science-loving friend of mine expressed the following unease with this claim:

1. we can never observe these galaxies
2. thus we can therefore never test that they are moving faster than the speed of light from us
3. repeatability of the observation? Not even testable in principle
4. things moving faster than the speed of light? We can’t test that directly either!
5. if you add space between two attracting bodies, doesn’t that mean you increase potential energy out of nowhere?

I responded to point 5 by saying, “General Relativity might not implicitly assert the conservation of energy law”, but that didn’t seem to be reassuring to him. I then read this passage in the same book on page 17:

During the 1950s and 1960s, the Big Bang and Steady State models battled for supremacy. Critics of Steady State model pointed out that the continuous creation of matter violates mass-energy conservation. Supporters of the Steady State model pointed out that the continuous creation of matter is no more absurd than the instantaneous creation of the entire universe in a single “Big Bang”.

My agnostic friend just about fell out his chair laughing. We both laughed.

The scenario of faster-than-speed-of light motion can be fit into the Friedmann-LeMaitre-Robertson-Walker solution to Einstein’s field equations of General Relativity, but does that make it true?

Consider Newton’s 2nd law. Suppose we are dealing with a force of 5 Newtons, what are the some of the mathematical (not necessarily physical) solutions to an equation constrained by the assumption that the force is 5 Newtons?

F = ma where F = 5 Newtons
Solution 1:
mass = 5 kg
acceleration = 1 meter/ sec^2

Solution 2
mass = -5 kg
acceleration = -1 meter/sec^2

etc.

Astute readers will notice solution 2, though mathematically consistent with the equation F=ma, is not physically real (in classical or most physics anyway) since it invokes negative mass.

I recall when studying General Relativity the professor assigning us an exercise to analyze geodesic trajectories through a particular solution to the Einstein field equations. This solution yielded incredible possibilities, and I thought to myself, “wow, where can I find such a place in the universe to observe this?”

And then reviewing the solution in class, the professor said something to the effect, “I didn’t tell you, but the solution I gave you describes a wormhole, but I’m not sure wormholes are possible since you need negative mass! This was more an exercise in math.” I and my fellow students had a small laugh, especially after having endured this mathematical exercise. The point being however, just because something is a mathematical solution to an equation of physics doesn’t mean it’s for real.

So with respect to those galaxies which we can’t see, which we will never see, that move faster than the speed of light, we can only postulate their existence as fact via inference. We can’t do it by observation, not by repeatable measurement or direct testing. So is the claim of these unseen entities a scientific claim? It does not accord with 2 of the 3 elements listed above that describe the scientific enterprise. The positivists among us will assert, “well if we can’t see it, we won’t believe it.”

So I would respond, “Ok, so do you believe the unseen galaxies predicted by the Big Bang. You can’t see them, you won’t see them, you can’t verify them, but supposedly they exist, they have properties as galaxies, and to top it off they move faster than the speed of light even though in the lab or anywhere we have access to, we haven’t clocked anything moving faster than the speed of light?”

So is the claim of unseen, unobservable, untestable, unverifiable galaxies a scientific claim? Eh, I leave that to the philosophers of science to decide, but it seems to me if one will admit as scientific the unseen, untestable, unknowable, unobservable, unverifiable entities as existing and having certain properties via inference and without direct evidence, then — well uh — couldn’t we hypothesize all sorts of unseen, untestable, unobservable, unknowable, unverifiable entities as being real via inference, and hence call that hypothesis science? I provided one example of such an entity in the thread: Quantum Enigma of Consciousness and the Identity of the Designer where Richard Conn Henry (a professor at no minor school) argued that Quantum Mechanics suggests God exists. Richard Conn Henry argued God is a permissible construct within accepted physics, and so is consciousness. Whether God is ultimately real is a separate question, but science doesn’t preclude His existence.

Getting back to cosmology, I learned of Alan Guth who speculated the universe expanded briefly at around 1000 times the speed of light in a process called inflation. In fact Andrei Linde speculated Guth understated the inflation speed by a factor of 10^1,000,000. If Guth claims the universe was inflationary, Linde claims it was hyperinflationary. Yikes!

What wasn’t presented in our cosmology class was Guth’s other speculation, which I learned of in a taboo book by William C. Mitchell

Guth is reported to have said, “in fact, our own universe might have been started in somebody’s basement.” Overbye has reported that, Guth and another MIT professor, Ed Fahri, found that, “If you could compress 25 pounds of matter into 10^-24 centimeters, making a mass 10^75 times the density of water…a bubble of false vacuum, or what Guth called a ‘child universe’ would be formed. From outside it would look like a black hole. From the inside it would look like an inflating universe.”

page 229
Bye Bye Big Bang, Hello Reality
by William C. Mitchell

Mitchell further commented of Guth, “can you believe such garbage?” I withhold making such a judgment since Guth is a smart guy, but it seems to me if we admit the possiblity of the universe being created by some tinkerer in a basement, we can surely admit intelligent design of the universe.

On a marginally more serious note, there are a minority of dissenting voices that share some of the reservations about modern cosmology that I’ve hinted of in this thread. One of them is a respected cosmologist by the name of Michael Disney. He argues we have too little data to really form a cosmological model.

Here is an excerpt from Modern Cosmology Science or Folktale

Where Do We Stand Today?

Big Bang cosmology is not a single theory; rather, it is five separate theories constructed on top of one another. The ground floor is a theory, historically but not fundamentally rooted in general relativity, to explain the redshifts—this is Expansion, which happily also accounts for the cosmic background radiation. The second floor is Inflation—needed to solve the horizon and “flatness” problems of the Big Bang. The third floor is the Dark Matter hypothesis required to explain the existence of contemporary visible structures, such as galaxies and clusters, which otherwise would never condense within the expanding fireball. The fourth floor is some kind of description for the “seeds” from which such structure is to grow. And the fifth and topmost floor is the mysterious Dark Energy, needed to allow for the recent acceleration of cosmic expansion indicated by the supernova observations. Thus Dark Energy could crumble, leaving the rest of the building intact. But if the Expansion floor collapsed, the entire edifice above it would come crashing down. Expansion is a moderately well-supported hypothesis, consistent with the cosmic background radiation, with the helium abundance and with the ages inferred for the oldest stars and star clusters in our neighborhood. However, finding more direct evidence for Expansion must be of paramount importance.

In the 1930s, Richard Tolman proposed such a test, really good data for which are only now becoming available. Tolman calculated that the surface brightness (the apparent brightness per unit area) of receding galaxies should fall off in a particularly dramatic way with redshift—indeed, so dramatically that those of us building the first cameras for the Hubble Space Telescope in the 1980s were told by cosmologists not to worry about distant galaxies, because we simply wouldn’t see them. Imagine our surprise therefore when every deep Hubble image turned out to have hundreds of apparently distant galaxies scattered all over it (as seen in the first image in this piece). Contemporary cosmologists mutter about “galaxy evolution,” but the omens do not necessarily look good for the Tolman test of Expansion at high redshift.

In its original form, an expanding Einstein model had an attractive, economic elegance. Alas, it has since run into serious difficulties, which have been cured only by sticking on some ugly bandages: inflation to cover horizon and flatness problems; overwhelming amounts of dark matter to provide internal structure; and dark energy, whatever that might be, to explain the seemingly recent acceleration. A skeptic is entitled to feel that a negative significance, after so much time, effort and trimming, is nothing more than one would expect of a folktale constantly re-edited to fit inconvenient new observations.

Ah, the wonderful world of Disney. Disney wrote a more technical article in The Case Against Cosmology published in the Journal General Relativity and Gravitation..

It should be noted, there is a forgotten article in the Discovery Institute archives by David Berlinski: Was There a Big Bang

Is the big bang model correct? One of my professors, James Trefil, gave his estimate that its about half way confirmed, but he has still some skepticism as he articulated in his book The Dark Side of the Universe.

The answer to the question of the Big Bang is way above my pay grade, but I posted this thread mostly to point out that if we pass off certain unverifiable, unseen, unknowable, unobservable claims as science, by what standard is ID disqualified? After all, according to Richard Conn Henry, quantum mechanics suggests God exists, and if so (though he won’t go so far as I would), imho, ID can then be admitted into to the realms of scientific hypotheses since now we have a theoretical entity with a sufficient skill set to design life.

And finally, with respect to the question of ID being science, in light of considerations above, this passage by Bill Dembski comes to mind:

Thus, a scientist may view design and its appeal to a designer as simply a fruitful device for understanding the world, not attaching any significance to questions such as whether a theory of design is in some ultimate sense true or whether the designer actually exists. Philosophers of science would call this a constructive empiricist approach to design. Scientists in the business of manufacturing theoretical entities like quarks, strings, and cold dark matter could therefore view the designer as just one more theoretical entity to be added to the list. I follow here Ludwig Wittgenstein, who wrote, “What a Copernicus or a Darwin really achieved was not the discovery of a true theory but of a fertile new point of view.”

Comments
Hi Sal,
I think, computer like architectures of necessity cannot be resolvable to purely physical explanations as a matter of principle — based on Shannon, and other considerations.
The problem I see with this reasoning is that it assumes we have a complete understanding of what is physical, which is certainly untrue. QM phenomena are sufficiently counter-intuitive to convince us that we really don't understand what's going on at all (even though the math reliably tells us what we'll find in the end).
I get flak from both sides
I too cannot align my views with either "side". I observe that part of the problem in the ID debate (like in politics and other tribal endeavors) is that people divide up into two "sides", even though there are many subtle issues to consider. Looking forward to your essay, RDFishRDFish
June 27, 2013
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The Morals of the Story 1) Just because we haven’t figured out how something happens in nature doesn’t mean there isn’t some explanation that we currently have no conception of. 2) You can always invoke “intelligent agency” as an explanation of anything, because it doesn’t really mean anything except “something that can do anything”.
Well said. But if I may offer a thought. I think, computer like architectures of necessity cannot be resolvable to purely physical explanations as a matter of principle -- based on Shannon, and other considerations. Finding computer-like architectures in the cell are suggestive of something that acts like an intelligence. Whether an intelligence is really the cause is unprovable, imho, and to that end, I have an essay along those lines of demarcation. I publish it shortly, and you're part of the inspiration for the essay. Thank you for your criticisms. I know I'll get flak from my side for agreeing with a critic. I get flak from both sides. Oh well....scordova
June 27, 2013
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Sal,
Where did I say superluminal velocities between galaxies are impossible? In fact I quoted Ryden’s explantion:
You quoted Ryden's explanation in order to disagree with it:
I only pointed out there no lab experiments to confirm expanding space.
If space doesn't expand, then general relativity is wrong. Yet general relativity is one of the best-tested theories in the history of science. As petrushka pointed out, you're really veering into crank territory when you start contesting GR.
But since you’re quite willing to accept superluminal photons...
Relative to each other in expanding space? Sure. But that doesn't solve the distant starlight problem, and it doesn't help YEC. Look, Sal -- I understand that you're embarrassed to be wrong on such a basic point of general relativity, but just admit it and move on. Trying to cover up your mistake is only going to draw more attention to it.keiths
June 27, 2013
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SCordova, I would like to know more about this field interpretation of general relativity. Do you have a link discussing it?
I've been reluctant to cite my source which was Tom van Flandern, since, like ID proponents he's hated by the mainstream. He passed away before he was able to finish this essay. It was technical, but it cited a very interesting experiment that hasn't gotten the attention it deserved: http://www.metaresearch.org/cosmology/speed_of_gravity.asp Here is a quote:
Lastly, we note experimental evidence from neutron interferometers that purports to demonstrate a failure of the geometric weak equivalence principle, that gravity is due to a curvature of space-time. (Greenberger & Overhauser, 1980) This experiment confirmed the strong equivalence principle (local equivalence of a uniform acceleration and a gravitational field), but its results are incompatible with the geometrical weak equivalence principle because interference effects in quantum mechanics depend on the mass. This is because the wave nature of the neutron depends on the momentum of the neutron, which is mass times velocity. So all phase-dependent phenomena depend on the mass through the wavelength, a feature intrinsic to quantum mechanics. Since the experiment confirms the applicability of quantum mechanics even in the presence of gravity, including this non-geometrical mass dependence, the experiment seems to be a step in the undermining of the purely geometrical point of view, and “tends to bother theorists who prefer to think of gravity as being intrinsically related to geometry”, according to the authors.
I thought the essay was brilliant. I'm not qualified however to judge its correctness, but it was nice to see him reference Einstein's and Feynman's affection for the field versus geometric interpretation of GR.scordova
June 27, 2013
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Well Stonehenge is STILL the result of design. And mother nature is STILL good at making stones...Joe
June 27, 2013
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SCordova, I would like to know more about this field interpretation of general relativity. Do you have a link discussing it?kuartus
June 27, 2013
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A Cautionary Tale About Invoking Intelligent Causation in Science 1) We observe that long, specific sequences of nucleotides in our DNA are needed to encode functional proteins. We find it unlikely that these sequences would occur by chance, and so we compute the probability. Since there are four bases and the gene sequence might be 100,000 bases long, and only a tiny fraction of this astronomical number of possible sequences would result in a functional protein, we compute that the chances of a functional sequence appearing by random mutation are vanishingly small. So we conclude that this can't be happening by mere chance. The only thing we know of that can look ahead at what sequence of bases will be needed to create a functional protein is an intelligent agent, and so we conclude that the best explanation for the information encoded in our DNA is intelligent causation. 2) Now imagine we're living 275 years ago in Boston, Massachusetts. We see that during thunderstorms, two out of every ten lightning strikes hits a church steeple. We find this peculiar, and compute the probability that this might happen by chance. We measure the city and find that it covers over 3 billion square feet, and the church steeples cover only 3000 square feet total. This means the chances of lightning hitting a church steeple is only one in a million, and so the odds against the observed frequency of strikes happening by chance are vanishingly small. So we conclude that this can't be happening by mere chance. We see that the lightning leaves the cloud at a high altitude and heads for these church steeples, and so it appears that the lightning bolts are aimed from the clouds toward the steeples. The only thing we know of that can look around from the clouds, identify the church steeples, and aim something at them is an intelligent agent, and so we conclude that the best explanation for lightning hitting our churches is intelligent causation. The Morals of the Story 1) Just because we haven't figured out how something happens in nature doesn't mean there isn't some explanation that we currently have no conception of. 2) You can always invoke "intelligent agency" as an explanation of anything, because it doesn't really mean anything except "something that can do anything".RDFish
June 27, 2013
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The seems like an unwarranted claim. Why not? If there is an intelligent mind directing the chemical assembly of molecules, why shouldn’t that force equally be in action today?
Intelligent agencies can decide to stop doing things.
How would you test whether your claim is correct?
Maybe you can't, but there are lots of things in science where we can't repeat an observation or mechanism like Guth's inflation. Do you accept Guth's inflation? Many do, but strictly speaking, it's not in operation today. That was the issue the essay raised -- do these things qualify as science because they are not repeatable observations? They are accepted only via inference (and in Guth's case piles of unprovable speculation coupled with inference). Do you accept Guth's idea of Big Bang in a basement? If so, that's ID. I have no problem accepting speculation as science, but then, by that standard ID is science. My position is ambivalent on whether ID is science or not, but I'm just highlighting the double-edged sword of insisting on repeatability. It will disqualify many legitimate fields of inquiry.scordova
June 27, 2013
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Elizabeth, ID does not require the designer(s) to still be designing today. And it appears no one is designing living organisms from non-living matter- humans are trying- on this planet.Joe
June 27, 2013
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KeithS overreaches:
That reflects a serious misunderstanding of general relativity. GR doesn’t forbid galaxies from moving faster than light relative to each other; it only forbids them moving faster than light relative to space itself.
Where did I say superluminal velocities between galaxies are impossible? In fact I quoted Ryden's explantion:
The speed limit that states that massive objects must travel with v greater than c relative to each other is one of the results of special relativity, and refers to the relative motion of objects within a static space. In the context of general relativity, there is no objection to having two points moving away from each other at superluminal speed due to the expansion of space.
And you have a dubious at worst and uneccesary at best claim here:
it only forbids them moving faster than light relative to space itself.
I merely pointed out we don't have lab experiments to confirm this possibility. But since you're quite willing to accept superluminal photons, and if we admit, as a general possibility, superluminal mechanism for photon travel then YECs can have a solution to distant starlight, it just won't use the FLRW solution, maybe something like the Carmeli-Hartnett-Humphrey's or some other solution. GR can be a doubled edge sword, eh? Thanks for advocating superluminal photons. I'm all for superluminal velocities. Yeah baby!scordova
June 27, 2013
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Sal
The mechanism of intelligent design of life is no longer in operation today.
The seems like an unwarranted claim. Why not? If there is an intelligent mind directing the chemical assembly of molecules, why shouldn't that force equally be in action today? How would you test whether your claim is correct?Elizabeth B Liddle
June 27, 2013
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Sal, There is a far more serious error in your OP:
So I would respond, “Ok, so do you believe the unseen galaxies predicted by the Big Bang. You can’t see them, you won’t see them, you can’t verify them, but supposedly they exist, they have properties as galaxies, and to top it off they move faster than the speed of light even though in the lab or anywhere we have access to, we haven’t clocked anything moving faster than the speed of light?”
That reflects a serious misunderstanding of general relativity. GR doesn't forbid galaxies from moving faster than light relative to each other; it only forbids them moving faster than light relative to space itself.keiths
June 27, 2013
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We are also addressing the amended argument at TSZ.keiths
June 27, 2013
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The error is we can see presumably superluminal galaxies that are less than 3.26 x 4300 MpC away, however we cannot see superluminals farther than that. The thrust of the OP however stands. That is a minor amendment.scordova
June 27, 2013
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Thanks keiths. I noticed Neil Rickert's cowardly equivocation:
Evolution has been very fruitful, and continues to be fruitful.
Darwinian evolution hasn't been fruitful, Neil. Biology under darwinian evolution can't even tell us what makes an organism what it is. All it does is say "such and such an organism emerges from the interactions of matter (ie its genome) and energy." Darwinian evolution can just tell us why some organisms are eliminated. It doesn't say anything about how multi-protein configurations arose. OTOH Intelligent Design Evolution, in the form of EAs and GAs, has been very fruitful.Joe
June 27, 2013
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Sal just cross-posted this OP over at TSZ, where we immediately noticed a very basic error. This statement is wrong:
1. we can never observe these galaxies
See the comments at TSZ for details: What qualifies as science in the wonderful world of Disneykeiths
June 27, 2013
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Axel @57, it's hard to say what exactly was going on there. But his mind was certainly modeling the game in some inexplicable way, and his intuitions seemed to be informed by whatever was going on with that model. I couldn't rule out that luck was involved to some degree, but pulling three 21's on three 7's seems a little like a miracle hand. I wonder if he'd be able to play for that sort of success on a regular basis. If so, he wouldn't be welcome in casinos for very long. ;) The Boy with the Incredible BrainChance Ratcliff
May 19, 2013
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Religios-like adherents, explanations - ad hoc-ad nauseum, continuously 'surprising' observations. All the signs of a dinosaur theory completely lost.
Einstein’s Gravity Theory Passes Toughest Test Yet – Apr. 25, 2013 Excerpt: A newly-discovered pulsar — a spinning neutron star with twice the mass of the Sun — and its white-dwarf companion, orbiting each other once every two and a half hours, has put gravitational theories to the most extreme test yet.,,, “We thought this system might be extreme enough to show a breakdown in General Relativity, but instead, Einstein’s predictions held up quite well,” http://www.sciencedaily.com/re.....142250.htm
'Pulsars' are imaginary, any tests done on them are suspect.butifnot
May 19, 2013
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His mind had quickly adapted to the medley of the card game's dimensions, making his usual lightning calculations, but matching his memory of the positions of the remaining cards in the pack with his now 'trifurcated' hand. Was his mind being informed before he understood it? Or did he understand it first? Sounds like the former was his m.o.Axel
May 19, 2013
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What was mind-boggling that when Daniel Tammet consciously tried to beat the bank at blackjack in the casino, he kept losing. When he relied on his intuition, and made COUNTER-INTUITIVE (there.. I've said it!!!) decisions/choices, splitting his cards, his intuitive calculations must have been much more complicated and difficult than his earlier, conscious, 'ratiocinative' ones, and were eerily successful. Or did I misunderstand that?Axel
May 19, 2013
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Cosmology is as lost as Darwinism. Ruled by math and oblivious to reality. It is interesting that these two subjects generate so much anger.butifnot
May 19, 2013
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Gödel's philosophical challenge (to Turing) - Wilfried Sieg - lecture video http://www.youtube.com/watch?v=je9ksvZ9Av4 "Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godelbornagain77
May 19, 2013
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Kurt Gödel: Modern Development of the Foundations Of Mathematics In Light Of Philosophy (1961) - A reading of the best lecture never delivered - video http://www.youtube.com/watch?v=CgZ_9gQfitcbornagain77
May 19, 2013
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OT: Kurt Gödel Centenary Full Lectures from the Princeton Institute for Advanced Study - video http://www.youtube.com/watch?v=IvbnxT3VL1Ebornagain77
May 19, 2013
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Bornagain77 @50, yes it does. I wouldn't mind seeing things the way Daniel does, even if only for a short time. Perhaps someday we will. :D I wonder if there are any protein engineering savants out there somewhere. I'm not even kidding.Chance Ratcliff
May 18, 2013
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Daniel is amazing, walking through the 'landscape of pi'! Simply amazing! Being faced with such wondrous things sort of puts things in proper perspective doesn't it?bornagain77
May 18, 2013
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Bornagain77, glad you liked it. I've watched it a couple of times over the last few years. I'm always amazed by him. Thanks for that list! I've seen a couple of them, but that is a good list, and something to look forward to. With all those links, I'm surprised I was able to add to your collection. ;) One of the interesting things about Daniel Tammet is that he's otherwise normal, and that's not typical for savants from what I understand.Chance Ratcliff
May 18, 2013
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Amazing video Chance! :) seeing as there is a 'spiritual' aspect to stuff like this, people with amazing abilities that is, I've collected a few videos along this line: Jake: Math prodigy proud of his autism – 60 Minutes – CBS News – video http://www.cbsnews.com/video/watch/?id=7395214n&tag=re1.channel Quote of note at the 12:00 minute mark of the preceding video; ‘The whole randomness thing, that’s like completely against all of physics’ Jake Barnett – Math Prodigy Attack results in Savant Syndrome, Jason Padgett, Beautiful Mind, The Man who draws pi - Fractals - video http://www.youtube.com/watch?v=yCvYKiNW4vQ This following man denies the autistic label, but is very ‘gifted’ none-the-less in his ability at math; The Human Calculator – Ruediger Gamm – video http://www.metacafe.com/watch/4200252 Autistic Savant Stephen Wiltshire Draws the City Of Rome From Memory – video http://www.metacafe.com/watch/4200256 The boy in this following video rivals, or maybe even surpasses, Nikola Tesla as an example of innovative ideas coming fully formed to the mind without any need for trial and error: Bluejay: The Mind of a Child Musical Prodigy – video http://www.cbsnews.com/video/watch/?id=7186319n Derek Paravicini on 60 MINUTES – Musical Autistic Savant – video http://www.metacafe.com/watch/4303465 Kim Peek - The Real Rain Man - MegaSavant [1/5] http://www.youtube.com/watch?v=k2T45r5G3kA This following girl, though written off as severely retarded, reveals that there is indeed a gentle intelligence within her that is trapped behind that wall between her mind and body. A wall that others see only as severe retardation, and nothing more hidden behind that veil of retardation: Severely Handicapped Girl Suddenly Expresses Intelligence At Age 11 – very moving video http://www.youtube.com/watch?v=vNZVV4Ciccg Music and verse: Evanescence – My Heart Is Broken - music video http://www.youtube.com/watch?v=f1QGnq9jUU0 Psalm 139:13 For you created my inmost being,,,bornagain77
May 18, 2013
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Bornagain77, you might enjoy this documentary about Daniel Tammet, a numbers and language savant. He recited PI to 22,500 decimal places and learned Icelandic in a week. The Boy with the Incredible BrainChance Ratcliff
May 18, 2013
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Sal, again I'm sorry if I wrote anything to hurt you personally.,,, In regards to humbleness, I'm reminded that whenever anyone claims superior knowledge over another in a matter, such as in math,, I remember this,, Is Integer Arithmetic Fundamental to Mental Processing?: The mind's secret arithmetic Excerpt: Because normal children struggle to learn multiplication and division, it is surprising that some savants perform integer arithmetic calculations mentally at "lightning" speeds (Treffert 1989, Myers 1903, Hill 1978, Smith 1983, Sacks 1985, Hermelin and O'Connor 1990, Welling 1994, Sullivan 1992). They do so unconsciously, without any apparent training, typically without being able to report on their methods, and often at an age when the normal child is struggling with elementary arithmetic concepts (O'Connor 1989). Examples include multiplying, factoring, dividing and identifying primes of six (and more) digits in a matter of seconds as well as specifying the number of objects (more than one hundred) at a glance. For example, one savant (Hill 1978) could give the cube root of a six figure number in 5 seconds and he could double 8,388,628 twenty four times to obtain 140,737,488,355,328 in several seconds. Joseph (Sullivan 1992), the inspiration for the film "Rain Man" about an autistic savant, could spontaneously answer "what number times what number gives 1234567890" by stating "9 times 137,174,210". Sacks (1985) observed autistic twins who could exchange prime numbers in excess of eight figures, possibly even 20 figures, and who could "see" the number of many objects at a glance. When a box of 111 matches fell to the floor the twins cried out 111 and 37, 37, 37. http://www.centreforthemind.com/publications/integerarithmetic.cfm Geometric Principles Appear Universal in Our Minds - May 2011 Excerpt: Villagers belonging to an Amazonian group called the Mundurucú intuitively grasp abstract geometric principles despite having no formal math education,,, Mundurucú adults and 7- to 13-year-olds demonstrate as firm an understanding of the properties of points, lines and surfaces as adults and school-age children in the United States and France,,, http://www.wired.com/wiredscience/2011/05/universal-geometry/bornagain77
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