|From Gödel, Escher, Bach: An Eternal Golden Braid |
by Douglas Hofstadter.
A 3D block projects three different
letters when illuminated along the three axes.
This is the fifth in a planned multi-part posting that includes portions of our email dialog.
Click for Part 1 - His 2008 Paper
Click for Part 2 - Determinism vs Probability
Click for Part 3 - QM and Chess Analogy
Click for Part 4 - Property Dualism
The following excerpts are from emails from Ira Glickstein to Howard Pattee (Oct 19 11:06 PM, Oct 21 11:56, Oct 23 10:21 PM, Oct 22 12:34 AM) and his replies (Oct 21 3:01 PM, Oct 23 10:21 AM).
[IRA GLICKSTEIN] Howard, THANKS for your prompt and courteous replies to my questions and critique on your 2008 paper. If I have your permission, I am considering putting a new Topic on my Blog linking to your newly posted 2008 paper and possibly including our recent email dialog. … I think a new Pattee Topic with a specific paper link will be welcomed by your many admirers. So, please let me know how you feel about this "opportunity" :^)
[HOWARD PATTEE] Ira, You have my permission to publish my more-or-less "scholarly" email discussions with you, but notify or link me to it so I know what's being discussed. …
[IG] Thanks for permission to publish your scholarly replies to my probing response to your 2008 paper. I will certainly link it to you when I publish it …
[HP] Other thoughts. Within a few years 90% of the population will have smartphones, and I estimate that much less than 1% will have any idea of how they work, or even have the background knowledge to understand how they work.
The world is already divided into the very rich and very poor, and all the large financial institutions owned by the rich have proven to be corrupt without help from technology. Technology divides us further into a priesthood of techies (good and evil) and the Luddites. This is now a very unstable situation as we are already experiencing with the NSA/CSS leaks and all the international hacking activities (e.g., Stuxnet and who knows what else?).
Experts say our infrastructure (power, transportation, finance) is at risk. I would say that compared to this technological instability global warming is a minor risk. What do you think? Howard
[IG] Well, as you know, I am a Guest Contributor to the world's most popular climate website. I accept that the mean surface temperature of the Earth has increased since 1880, and that part of that increase is undoubtedly due to human activities such as unprecedented burning of fossil fuels increasing Atmospheric CO2 from about 270 to the current 400 ppmv. However, I am sure the official Intergovernmental Panel on Climate Change (IPCC) has over-estimated the Equilibrium Climate Sensitivity - ECS (how much the surface will warm given a doubling of CO2) by at least a factor of two, and perhaps three. That is why all IPCC warming predictions since their first in 1990 have been on the high side compared to measured temperatures.
That IPCC error explains why temperatures have stabilized over the past 17 years even as CO2 levels continue their rapid rise. Thus, most of the warming is due to Natural Cycles, not under human control. The moderate warming and moderate CO2 increase experienced so far may be net beneficial to human civilization, and, in any case, poses no real danger. (And, even if it does pose a risk, since most of it is due to Natural Cycles we humans cannot control, we really cannot stop it, so we will have to adapt, using TECHNOLOGY.)
So, I agree with you that technological instability IS a greater risk than global warming. Technological instability includes, IMHO, a genetic engineering disaster, nuclear disaster, political chaos disaster due to runaway debt triggering riots and class warfare leading to tyranny, etc. But, the only way we can continue human civilization given the inevitability of Natural Cycles of global warming (and global cooling - see the ice core record of alternating ice ages and warm ages about every 100,000 years) IS adaptation using technology.
Thus, we have to accept the risk of technological instability as the price of survival. Ira
[IG] Howard, you earlier brought up property dualism, where a single Material Substance can have both "physical" and "mental" properties as described in the linked Wikipedia entry. I think of these properties as being different aspects or views of a single material thing, such as continuous vs discrete, finite vs infinite, particles vs waves, energy vs matter, mind vs brain, etc. Thinking about it, I came up with the following analogy to Flatland, …
[HP] Ira: … Your idea of knowledge as projection from higher dimensions is essential. It also shows us that there is no one right answer. Complementary views are necessary, even when they appear contradictory …
[IG] … a 3D cylinder (like a can of soda) intrudes upon the Flatlander's 2D plane of existence. If it approaches slowly and side first, they will initially sense a line segment. Then, as it penetrates further they will sense a long, narrow rectangle. Further penetration will result in a somewhat wider rectangle. On the other hand, if the can approaches end first, they will sense a circle of constant diameter.
[HP] See jacket of Hofstadter's Godel_Escher_Bach [NOTE: Illustrated above] where one block's projections cast three different letters. … I think the earliest example of projection is the allegory of Plato's_Cave. …
[IG] So, what is it? A line, a rectangle, or a circle? …
[HP] Projections from higher dimensions is basic in quantum mechanics where we model the "states of reality" by an infinite dimensional, complex, normed vector space (Hilbert space). A measurement is a projection of this space rotated by the choice of the basis vectors. Nobody agrees on what the "states of reality" means. Read a little of Schlosshauer's Elegance_and_Enigma: The Quantum Interviews (The Frontiers Collection) Maximilian Schlosshauer ...
[IG] Thinking about aspect dualism further, if the can approaches at an angle, it will appear to the Flatlanders to be in any of a variety of shapes. It could look like a trapezoid, an ellipse, a triangle with one curved side, etc. However, when in circle mode, a cylinder will always have a constant diameter.
If a sphere (ball) approaches their plane of existence, they will initially sense a point, then a small circle, increasing in diameter. However, the sphere will never appear to be an ellipse nor anything containing a sharp angle. Flatlanders distinguish a cylinder from a sphere by it having a variable diameter and by never having a sharp angle.
So, if we humans are stuck (evolved) in a world where sensing 3D plus time is all that is needed to survive and replicate, we will forever be limited in how we sense 4D and higher material objects that intrude upon our 3D solid of existence. Sometimes material objects will appear to be continuous (like the edge if a can when it is in its circle mode in Flatland) and sometimes discrete (like the edge of a can when it is in it's rectangle mode in Flatland. Sometimes the intrusions will seem to us to be particles, sometimes waves, and so on.
But what about material vs "information" (otherwise known as brain vs "mind")? Well, I would say that "information" is an abstraction that may never be absolutely true, and will seldom be absolutely false. The Flatlanders may all agree that an intrusive object of type “C” has multiple modes (line, rectangle, trapezoid, circle, ellipse, and so on) and that it never has the ability to change diameter, and that an intrusive object of type “B” may change diameter but never have sharp angles, and thus correctly call them by different names (which we -but not them- understand to be a can and a ball), but that "information" is a mere abstraction that does not capture the material truth. …
[HP] Many physicists interpret the mathematics of QM as an expression of the statistical information that is just sufficient to give the best predictions. The wave function or a vector in Hilbert space is just a strange kind of potential distribution from which we calculate probabilities of measured events (N.B. Born's_Rule and Gleason's _Theorem appear to rule out determinism). When we get new information from a measurement, the probability distribution is immediately changed ("collapse of the wave function").
Born argued that this is also the case in classical mechanics because empirically it is not deterministic. I agree with Born that all dynamic models should be understood as change of probability distributions in time. …
[IG] Thus we (scientists) gather "information" and come up with ways to measure and distinguish different hyper-dimensional objects that intrude upon our solid of existence, and notice and document and quantify the correspondence between "electrons" or "photons" when in their "particle" mode or in their "wave" mode, but we will never really, really apprehend what these hyper-dimensional objects "really" are!
We know how to convert "matter" to "energy" (nuclear energy) but we will never know what they "really" are.
Like the child (or senior citizen) who knows how to skillfully operate his or her HDTV set and DVR and PC and iPad, but has no real knowledge of radio frequency waves or computers or software, we will forever possess incomplete "information" that is a rough abstraction of real, real, "reality"!
[HP] This should be called Ira's modern view of Plato's Cave-- the Allegory of the iPad. Howard