The Dome - Indeterminacy in Newtonian Physics

A mathematical proof that Newtonian Physics is NOT strictly deterministic, as well as a demonstration of the possibility of indeterminate systems existing within our universe.

Original animations by randyhelzerman: http://www.youtube.com/user/randyhelzerman
John D. Norton publication: http://www.pitt.edu/~jdnorton/papers/DomePSA2006.pdf
Alternative explanation: http://www.pitt.edu/~jdnorton/Goodies/Dome/index.html

Category:

Education

Tags:

• Dome
• Newton
• Newtonian
• Physics
• Determinism
• Indeterminism
• Random
• Calculus
• Math

[JustinTheAtheist]

I'm sorry, but I'm not going to even bother watching this video. I just don't care as much as I did before. However, I'd just like to get one VERY simple idea across that you're just not understanding:

Whether or not true indeterminacy exists is irrelevant when arguing over the existence or nonexistence of true freewill. For true freewill to exist, all that possess it MUST have ALL information of EVERYTHING, otherwise, their FREE decisions would be compromised by UNCHOSEN ignorance.

[UNFFwildcard]

"For true freewill to exist, all that possess it MUST have ALL information of EVERYTHING, otherwise, their FREE decisions would be compromised by UNCHOSEN ignorance"

If I chose to do something with only 60% of the information, I'm still exercising free will to do so. Free will does not necessitate that all information is available, sinne free will allows imperfect choices.

[LeeHsungWang]

No you're both wrong. You don't need all the information in the world to make a free decision, because if you got all the information in the world your choice would still be either determined by all that information-in case of hard determinism- or undetermined in which case it is random-and the extra information irrelevant-. It is not simply a matter of our world having determinism or not, the whole notion of free will is an illusion.

[alxh89]

2:00 three over tooth power. number fail

[schrodingasdawg]

I somehow missed this video in your uploads list before, only found it while doing a google search (wanted a good video or webpage on the dome to post to my facebook page). You present the example excellently.

Also, I'm sorry that this video was apparently hit by a votebot. =(

[ElasticGiraffe]

Videos like this make me wish I had taken calculus rather than prob & stats. :P

[C0C0nutFace]

Only the expected r(t) =0 solution is physical, the other set of mathematical solutions are non-physical. Also, g is approximated as a constant and should really be described as a function itself (this collapses the 'indeterminacy'). There are many similar examples of physical systems where non-physical 'solutions' are to be 'cut out'. Many philosophers have a hard time getting their heads round this because they can't see the wood for the trees.

[dartplayer170]

Yes it will be different becuse gravity's direction will no longer support the same solution set.

[dartplayer170]

If the domeis upside down then apex would now be the bottom. So how can the ball roll uphill off of the apex? If you're going to introduce a proof against the Dome involving a new scenerio then you need to do a formal proof to show your work because it is a waste of time to argue against a model with no suporting evidence.

[dartplayer170]

You're talking about how he found a model that would violate determinancy. That is not the same as a derivation. A derivation is a mathematical proof for a solution to a problem. I stated that the ball was placed arbitrarily on the dome. Yes it is important, the direction of gravity vs the curvature of the dome is crucial.

[crtx2]

(1/4 disappeared?)The solution set for The Dome was not derived the way you describe it. It was quite the opposite - D. Norton actually started out with a system that violated the Lipschitz condition and had multiple solutions, and THEN tried to come up with a plausible physical instantiation, which became The Dome. Furthermore the ball was placed arbitrarily on the dome (except at the apex). But the way in which it was derived is completely irrelevant.

[crtx2]

(4/4)But the way in which you regard the solution as incorrect in the upside down dome example yet accept the very same for the original dome almost looks as if you regard the solution as not real in certain circumstances, am I right?. I just go one circumstance further. r(t)=0 is the only valid solution at the apex, and nowhere else. Other solutions might be valid elsewhere, but not at the apex.