What is "Mind?"

Search
Go

Discussion Topic

Return to Forum List
Post a Reply
Messages 16401 - 16420 of total 18368 in this topic << First  |  < Previous  |  Show All  |  Next >  |  Last >>
Ed Hartouni

Trad climber
Livermore, CA
Jul 15, 2017 - 10:04pm PT
so, I'm sure you all have had this sort of experience...

I am in the shower thinking of some particular problem I'm trying to solve, maybe I've been at it for days and I'm deep into its guts, but not at the point where I've got a handle on all of its parts.

My attention is on the problem, completely. I vaguely recollect getting dressed, eating breakfast, saying good bye to Debbie and getting in the car, though I suspect it is a memory recall based on my normal routine rather than the specifics of that actual day.

The next thing I am aware of is walking from my car to my office. I have no recollection of driving to work, none what so ever.

My attention, awareness, conscious activity, all the discursive was focused on that problem.

Somehow, I executed a highly complex activity of driving my car, in traffic, to work, and I made it. Apparently this didn't require any of what Largo is talking about distinguishes me from Curiosity, my sentience was not an issue, my awareness was not an issue, my attention was not an issue.

Apparently the zombie-Ed drove to work, Ed's mind was otherwise occupied, so much so, that there is no experience of driving to work in that mind.

How does that happen?
jgill

Boulder climber
The high prairie of southern Colorado
Jul 15, 2017 - 10:39pm PT
This is where the notion of "awareness" comes apart. I think of awareness as a kind of machine-like response; in this case "George" does the driving for us. And JL's motion sensor does its job. When we take the reins we exhibit both will and "consciousness".

Pretty shallow, I'll admit.

MH2

Boulder climber
Andy Cairns
Jul 15, 2017 - 10:41pm PT
I have no recollection of driving to work, none what so ever.



How does that happen?



Until we know how memories are encoded and stored it may be premature to ask why they are sometimes not formed and stored. For a well-rehearsed task like driving to work the brain may just not waste effort on memory. Novelty seems to be important in how readily memories are formed, and intense emotion helps.


This is one of many areas of research informed and motivated by observations of animal behavior.


http://www.researchgate.net/figure/232706967_fig3_Figure-1-Tinbergen's-experiment-on-homing-in-digger-wasps13-Above-a-digger-wasp

http://www.nature.com/nrn/journal/v3/n7/full/nrn872.html



Can we figure out how it is done in insects?

Might we then be able to answer other questions about memory?


I find memory a much more interesting subject to look into than consciousness.

yanqui

climber
Balcarce, Argentina
Jul 16, 2017 - 07:02am PT
In what way does that statement differ from, "People are just running programs to do things molecules tell them to do?"

The statements aren't so different. However, in the case of the computer we know the statement is true. Perhaps you can tell me the precise details of the "program" my molecules wrote (do you believe my molecules "write" programs? How do they do this?) that produced this reply on supertopo, to demonstrate the proof of the claim above?

Would you consider the way DNA copies itself to be an algorithm?

Beats me.


If an algorithm is a set of rules to follow, how broad is your definition of "rules?"

"My" definition isn't really "my" definition. There is a generally accepted definition in math and computer science. I suppose Turing first formalized this.

yanqui

climber
Balcarce, Argentina
Jul 16, 2017 - 08:44am PT
You got it, Ed. The subjective psychology of the process of problem solving in mathematics (and science, as well, I suppose) is interesting. Ideas seem to bubble up from the subconscious. If the problem is hard, then I need considerable effort to focus my mind (or my brain or whatever you want to say) for an extended period of time (though there is often a natural tendency for my mind to become obsessed or fixated on solving the problem, as well). The process does take some conscious effort as well. Ideas sometimes have to be weighed and considered consciously. Sometimes I need to consciously do some calculations or consider some specific examples. I've even looked at lists of examples generated by computers, when the general cases are not understood. Maybe I realize that what I really need to do is go back and study up some more on what other people have to say. Sometimes I get stuck on a way of solving the problem that is erroneous (or not optimal in some vague sense) and it takes me a surprisingly long to realize that being stuck on one method is exactly what is stopping me. What I need to do is open my mind to other possible perspectives. Strangely enough, the final solution often appears suddenly, with surprising clarity and certainty. I still need to write a proof, but before I do, I know (or perhaps I should say: "feel certain") my solution is correct. The whole process of exercising skills to solve problems (and sharing that with others who have similar skills) is inherently rewarding. That's part of the reason why there were skilled amateur mathematicians, long before professional academics basically took over the stage.

There is some mysterious process going on there (in the brain) and it might be there are some strange super-algorithms, or it might be something else. One thing that leads me to think it's something else is that, so far anyways, computers are surprisingly bad at doing mathematics, in the sense of, autonomously being able to look for interesting problems to solve, and then solving them. I believe if you talk to almost any professional mathematician they would agree that there has never been a computer that has remotely come close to doing that (autonomously selecting an interesting unsolved problem and solving it). Maybe doing such a thing "needs" consciousness, or maybe not. Maybe such a computer could only be built after unforeseen advances in science or maybe we just need better engineering and more complexity. Who knows?
Ed Hartouni

Trad climber
Livermore, CA
Jul 16, 2017 - 09:48am PT
The paper MH2 linked (the first one) has a very early section on the role of the computation model in their research, and it reminds me that a major point of contention is whether or not the mind (or aspects of it) are amenable to that line of research.

First off, we use models to simplify phenomena that are complex and detailed when that complexity is not required in our descriptions. The fact that the Earth is not a point source of gravitation, nor the Sun, nor the Moon was something that bothered Newton, so he went about showing how this simplification was valid. Having explored those boundaries, he could then apply the model of the three point masses circling in space to calculate the Keplerian laws of orbital motion, a largely empirical result, and by the same token, the Galilean description of the ballistic motion of objects near the surface of the Earth. It turns out that both phenomenon are "explained" with the same gravitational force description using the simplified model that the objects are described as "point particles."

We do not say that this model is what exists in the solar system, rather that it describes the solar system to some degree of accuracy and precision. The idea of universal forces, gravity being the first, is a further feature. Maxwell summarizes the electromagnetic force, unifying them and making a theory dynamical, essentially following the Newtonian script.

Later, but not by much, two additional forces are "discovered" in subatomic phenomenon, the weak force governing radioactive decay and the strong force which binds the nucleus together, strong because it has to overcome the repulsion of like-charged particles in very close proximity.

The weak force is unified with electrodynamics to become the "electroweak" force, for which the Higgs Boson is essential, but the program to unify the strong force with the electroweak force has run into some difficulties.

We do not have a quantum theory of gravity, and so there isn't a way forward on the unification path.


These are all models of how the universe acts, and science demands our models provide quantitative predictions of the outcome of the phenomena they address.

A computer model of the mind, or features of the mind, serves a similar role, that the model encodes the features in a computational algorithm which is predictive. The model is not the mind, however, the model, if it is a good one, acts as the mind would.

An observation made by Feyerabend while contemplating the material aspect of mind makes precisely this same point, that a scientific theory (call it a model) will be considered successful when it does this, makes a calculation that "predicts" a behavior.

Now you can object that the model is not the mind, and be completely correct, but you might be incorrect in that there is some physical instantiation of the model in the actual biological system. Knowing the algorithm lets you look for the corresponding physical origin and behaviors, becoming an empirical tool, a hypothesis generator, with which to elaborate the model.

A more elaborate model provides more precise and accurate predictions.


So the statement that AI is not a good model for the mind/brain/whatever has to be sharpened considerably. If it is a statement that AI cannot make predictions that agree with observations the criticism is apt.

If it is to say that AI is philosophically incorrect, well, what does that mean? Philosophy is by its nature a consideration of things that are, not of what might be, and the domain of philosophy expands to explain what we find in nature, but it does not predict what we will find, and it cannot.

Finally, in a very real sense, these algorithms do provide insights that are not otherwise available to our thoughts, especially when a large number of computations are required to make the predictions. That a computer can now beat a chess grandmaster is not to say that the algorithm takes pleasure in that task, there is no algorithm implemented that provides that behavior, but the chess the computer plays is amazing, even astounding, to those humans that play at the highest level. An ancient human game considered an archetypal expression of intellectual power now has only computers as its most competent, imaginative players. Those algorithms executing on my cell phone can beat me every time.

Intention is yet another aspect of behavior, and is certainly a topic of modeling. Human intention is driven by a number of biological factors, most of which are of no concern to the algorithms that we have written, but could be of growing concern in the future. I don't know where that will lead, but it is not so hard to imagine the literary piece of Chiang's I linked above, published in Nature to be more than just imaginative fancy.
MH2

Boulder climber
Andy Cairns
Jul 16, 2017 - 10:57am PT
Perhaps you can tell me the precise details of the "program" my molecules wrote (do you believe my molecules "write" programs? How do they do this?) that produced this reply on supertopo, to demonstrate the proof of the claim above?


Thank you, yanqui.

No, I do not know the precise details of what our molecules are doing. I am fairly sure they do not write programs at all similar to the human kind used to give directions to computers.

However, I do believe that the general principles, or rules, of how molecules interact with one another are known.

Although there is no point in trying to describe a human as a collection of interacting molecules, when you look closely at a small part of a human the shapes and electromagnetic forces of molecules can help you to understand what is going on. For example, it was a tour-de-force of scientific investigation when Bertil Hille characterized the sodium channel in nerve cell membranes.

I've done a little checking on the definition of the word "rule." I find references to rules in math but no definition specific to mathematics.

For computer science the Wikipedia entry on rule-based systems is interesting:

In computer science, rule-based systems are used as a way to store and manipulate knowledge to interpret information in a useful way.

That sounds like a job description for DNA.


But then the entry continues:

Normally, the term 'rule-based system' is applied to systems involving human-crafted or curated rule sets. Rule-based systems constructed using automatic rule inference, such as rule-based machine learning, are normally excluded from this system type.




(I am trying to learn stuff, not to tell stuff. Making mistakes and speculative statements are part of learning. I need the help. Thanks all.)
paul roehl

Boulder climber
california
Jul 16, 2017 - 11:54am PT
WTF Paul... you're going to have to do a better job of explaining your point, obviously you've got a less than conventional view on this Romanticism thing...

My point is simply that within the world of science there is a predilection for the worship of nature that is a vestige of romantic notions from the 19th century and even before. The absolute authority of nature, its sublime presentation, its awe inspiring visions, its trolling curiosities that entice us to study, we view these elements through the distorted lens of “sensibility,” while enjoying a state of denial that declares our observations only products of untainted reason and scrupulous observation. The problem here is a resultant disdain for the human condition, the dismissal of humanity as insignificant in the hierarchy of an evolutionary process in which dolphins and crows might claim some kind of equal status to humanity. The inability to see or admit the intellectual superiority of a human being over a bird, the notion that such a distinction between bird and human is somehow inappropriate or chauvinistic, these are simply the prejudice of a romantic view of nature in which nature and evolution become the only possible final term when, in fact, the final term is the structure predicate to evolution.

I see it this way: in a universe of restrictions, we call them the laws of physics, where certain things can happen and others cannot, “magic” for instance, life and an accompanying awareness have occurred. That is, the logos or construct of the universe allows for life and consciousness to happen. Not only that, but the number of possible planets where that life may be occurring in our own galaxy, let alone the universe, is remarkable. Life seems to be an inevitable outcome of a physical structure or logos that has somehow occurred. That structure, the structure of the physical universe, is the predicate to any evolutionary process, it is the final term behind conscious thought and it is, at this moment, beyond our understanding and it may very well exist permanently as such. If we think of this consciousness and awareness as existing on a continuum with human beings exhibiting an ability to reason intelligently far beyond the abilities of other aware beings, frogs for instance, the implication of that continuum is for intelligences far beyond our own. Repeatedly on this thread folks have touted the potential for superior machine intelligence, for instance. How far can we extend this idea? What is the limit for intelligence in this universe given the constraints of physical laws? What would we call some sort of ultimate consciousness/intelligence/awareness? The sort of self- loathing, disparaging of humanity and humanity’s condition based on our temporary existence both individually and collectively, the notion that our impermanence or smallness trumps our importance and negates our achievements seems not only self -defeating but ignorant of the profound nature and mystery of the gift of knowing. We don’t know the meaning of our understanding but it seems very rare in this solar system and something to be celebrated, honored and explored as the mystery it is. Human thought/consciousness/awareness is an incredible triumph of the process of life, that we as part of nature can possibly know what nature is, really is a kind of crown of creation. Think about it.
yanqui

climber
Balcarce, Argentina
Jul 16, 2017 - 12:35pm PT
MH2 I'm heading out for a hike (it stopped raining) but before I go a few words:

In the previous post I was talking about the the definition of algorithm in math, not the meaning of rule. I don't think anybody makes a big deal about the meaning of rule in math (I don't know about game theory) and it could be used to characterize a lot of different stuff, like definitions (I don't think anyone would have a problem calling the definition of the tangent line to a differentiable curve a "rule"), axioms (the axiom of infinity is a "rule" sounds OK to me). Relations are one kind of rule (in math a "relation" can be thought of as a specified way, or "rule" to relate a set of outputs to a given input) as is the special case of a function (assigns a single output to a given input). Functions are often called rules. The Law of Gravity might be considered a rule, although it's not an algorithm. An algorithm is a (finite, terminating) step by step procedure (formally expressible) to calculate a function. A sort of finite, formal decision process that produces the desired output. Even in math, there are problems that can't possibly be decided this way like the "word problem" in group theory.

I'll come back and look more at your post after I go for a hike!
MH2

Boulder climber
Andy Cairns
Jul 16, 2017 - 01:38pm PT
In the previous post I was talking about the the definition of algorithm in math, not the meaning of rule.


Aha.

And I was not asking about the "true" meaning or definition of what a rule is, but rather your understanding or idea of what a rule is. What you wrote above answers that question well.



As for algorithm

An algorithm is a (finite, terminating) step by step procedure (formally expressible) to calculate a function.

So if a step-by-step formally expressible procedure to calculate a function does not terminate, it is not an algorithm?




I think we are being too picky about the meaning of words and their definitions. But we are getting back to "What is 'Mind?'"


there is no total computable function that decides whether an arbitrary program i halts on arbitrary input x; that is, the following function h is not computable (Penrose 1990, p. 57–63):



Here program i refers to the i th program in an enumeration of all the programs of a fixed Turing-complete model of computation.


Roger Penrose, The Emperor's New Mind: Concerning computers, Minds and the Laws of Physics, Oxford University Press, Oxford England, 1990 (with corrections). Cf. Chapter 2, "Algorithms and Turing Machines."

from

http://en.wikipedia.org/wiki/Halting_problem
Marlow

Sport climber
OSLO
Jul 16, 2017 - 01:46pm PT

This thread reminds me of the old Norwegian adage "å koke suppe på en spiker". The soup may in between taste good, but this is never caused by the nail. It's the other ingredients.
Ward Trotter

Trad climber
Jul 16, 2017 - 03:01pm PT
This thread reminds me of the old Norwegian adage "å koke suppe på en spiker". The soup may in between taste good, but this is never caused by the nail. It's the other ingredients.

Long ago I heard mention of the story of nail soup, although it takes the form of stone soup in other versions. These stories could stretch back millennia and conversely given rise to much newer and more recent expressions-- such as the old hobo poems and tales of "mulligan stew".

The folk tale surrounding nail soup might take the form of a poor bedraggled traveler who comes to a village with just the clothes on his back and an old worn nail in his pocket :

The villagers tried to run him out of town saying that he was going to steal from them. “Oh no, I was coming to share some nail soup with you. All I need is a pot filled with water and I’ll make some soup to be enjoyed by all,” he said. One curious villager brought him a pot filled with water.

The traveler built a fire and got his rusty nail out of his pocket and dropped it in the pot. Soon the villagers started gathering around to see what nail soup was. After a while, the traveler tasted the soup and said, “If only I had some onions, that would really make the soup wonderful.” One of the villagers ran to grab a couple of onions. After adding the onions and cooking the soup for a while, he tasted it again and said, “If I only had a few carrots and maybe some peas, then the soup would be so much better.” Another villager ran to get a few carrots and another got some peas.

The stranger kept tasting the soup and each time he’d mention something else that would make the soup “just right” and each time a villager would run and get that item for the soup. After a while the pot was bubbling with the best smelling soup the villagers had ever smelled.

The traveler fished out his nail, wrapped it in a handkerchief and put it back in his pocket. Then he served up the stew to all the villagers, it was the most wonderful stew they had ever tasted. They were very impressed with the Nail Soup, although they could never replicate the recipe themselves.

Thanks Marlow. If I'm ever to come to Norway we must have nail soup. Who should bring the nail?
jgill

Boulder climber
The high prairie of southern Colorado
Jul 16, 2017 - 04:37pm PT
So if a step-by-step formally expressible procedure to calculate a function does not terminate, it is not an algorithm?


Good point. The definition of "algorithm" might be relaxed a tad to include infinite processes that the programmer intentionally halts at a certain point, for one reason or another (like rounding off a calculation). Is this "halting" a part of the algorithm? If it is then the more restrictive definition applies. But this is a trivial issue in practice.

I've been reading about the famous Einstein-Bergson debate, and how quickly Bergson faded after his refutation of time-contraction in the Twin Paradox. Bergson's notion of 'Time' (what he called duration) contrasted with 'time' as a physicist or mathematician might use the term, but his ideas waned as he was perceived to lack comprehension of Einstein's theory - at least that one part.

I see a similarity with the progress of this thread. JL is similar to Bergson (who was the outstanding philosopher of his time, incidentally) and of course our own Ed resembles Einstein. Can the Wizard pull though here, or will physical reality do him in? Both gentlemen are exceptional in their individual ways.

;>)
feralfae

Boulder climber
in the midst of a metaphysical mystery
Jul 16, 2017 - 05:11pm PT
Paul Roehl, sir:
We had quite a spirited discussion at a recent Intertel conference about this very subject. Or at least this was my point of view. So, I'd like to quote you with any attribution you'd care to have, if I may.
May I quote you elsewhere?:
I see it this way: in a universe of restrictions, we call them the laws of physics, where certain things can happen and others cannot, “magic” for instance, life and an accompanying awareness have occurred. That is, the logos or construct of the universe allows for life and consciousness to happen. Not only that, but the number of possible planets where that life may be occurring in our own galaxy, let alone the universe, is remarkable. Life seems to be an inevitable outcome of a physical structure or logos that has somehow occurred. That structure, the structure of the physical universe, is the predicate to any evolutionary process, it is the final term behind conscious thought and it is, at this moment, beyond our understanding and it may very well exist permanently as such. If we think of this consciousness and awareness as existing on a continuum with human beings exhibiting an ability to reason intelligently far beyond the abilities of other aware beings, frogs for instance, the implication of that continuum is for intelligences far beyond our own. Repeatedly on this thread folks have touted the potential for superior machine intelligence, for instance. How far can we extend this idea? What is the limit for intelligence in this universe given the constraints of physical laws? What would we call some sort of ultimate consciousness/intelligence/awareness? The sort of self- loathing, disparaging of humanity and humanity’s condition based on our temporary existence both individually and collectively, the notion that our impermanence or smallness trumps our importance and negates our achievements seems not only self -defeating but ignorant of the profound nature and mystery of the gift of knowing. We don’t know the meaning of our understanding but it seems very rare in this solar system and something to be celebrated, honored and explored as the mystery it is. Human thought/consciousness/awareness is an incredible triumph of the process of life, that we as part of nature can possibly know what nature is, really is a kind of crown of creation. Think about it.

Thank you.
feralfae
Dingus McGee

Social climber
Where Safety trumps Leaving No Trace
Jul 16, 2017 - 05:18pm PT
the Wizard:


...awareness is beholden to nothing.[citation needed]

Largo, consciousness awareness is just a feeling like loss and hurt. You seem to have miss experienced this detail.

There is no reason to argue this point of awareness with us for you do not know what is going on in your own mind!
Ed Hartouni

Trad climber
Livermore, CA
Jul 16, 2017 - 05:59pm PT
My point is simply that within the world of science there is a predilection for the worship of nature that is a vestige of romantic notions from the 19th century and even before.

I think you do not know much about science, and you probably do not know many scientists.
feralfae

Boulder climber
in the midst of a metaphysical mystery
Jul 16, 2017 - 07:18pm PT
Sirs:
I know I may get whacked in the face with a pie, but may I comment that:

I think that what all of science, philosophy, mathematics are inquiring about is the ultimate algorithm of creation, especially the creation of life. Whether we label our pursuits as the study of physics or the study of religion, a perhaps unstated goal of all search for knowledge is the search for the algorithms of creation.

And that, as Paul R. word-smithed so beautifully, is a remarkable thing. Our consciousness allows us to explore the manifestations of that algorithm, of that creator. I have long stated that I think I live within the Mind of G*d, and around me I observe those bits which draw my attention. It is a wonderful experience of exploration and awe, this life.

So, to me, if we are going to contemplate the Mind, it seems to me we must be willing to acknowledge that there exist strings and structures of functions which we have yet to weave into our version of the fabric of the universe.

And when you posit that "automatic driving," so to type, is perhaps mysterious, then I think we must examine the sophisticated awareness-prioritizing function of the brain, which can be programmed to block out city noise or to be keenly aware of the ticking of a clock. Use of such programming can result in habituated routing of synaptic impulses. But I bet Ed, you'd jump back to high-level consciousness if a deer ran in front of the vehicle: your brain synapses also have been habituated to react to anomalous visual signals during an otherwise habituated routing.

But beyond that consideration, there is the question of how much we know about multiple routing of synaptic signals through various parts of the brain: this routing can be happening on myriad levels and through myriad pathways at once, and so to ask questions as if we must consider a linear structure of consciousness and thought processes strikes me as perhaps a bit naive in light of the sophistication of the brain from what we know so far.

I, for one, think we are in the middle of an evolutionary step, discovering how to advance our own evolution, based on the consciousness and levels of understanding our innate curiosity and other factors seems to be directing. I think that, under a model of cooperative determinism which recognizes a Creator, we are participating in our own evolution at an intentional, conscious level this time. I like it. But one might call it the ultimate algorithm.

Thank you,
feralfae
MH2

Boulder climber
Andy Cairns
Jul 16, 2017 - 10:35pm PT
one might call it the ultimate algorithm.


So perhaps God is the 9th-century mathematician Abū Ja῾far Muhammad ibn Mūsa?


yanqui

climber
Balcarce, Argentina
Jul 17, 2017 - 06:38am PT
So if a step-by-step formally expressible procedure to calculate a function does not terminate, it is not an algorithm?

A failed algorithm, you might say. I doubt many people would buy a computer that just whirred around forever without producing an output.

Examples of algorithms abound throughout the history of mathematics, but the formalization of the concept by Turing (and Alonzo Church) was born in Hilbert's (perhaps unwarranted) optimism about our ability to solve problems. In his 1900 address at International Math Congress in Paris, Hilbert said:

Is the axiom of the solvability of every problem a peculiar characteristic of mathematical thought alone, or is it possibly a general law inherent in the nature of the mind, that all questions which it asks must be answerable?...This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignoramibus.

One of the the problems Hilbert proposed at this congress was the construction of a precise finite decision process to decide if a Diophantine equation (a polynomial equation with integer coefficients in n-variables) had an integer solution. Hilbert proposed:

"Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers."

The Fermat equation x^n + y^n = z^n is an example. When n=2 there are lots of solutions and they can easily be generated algorithmically. Here is a list of all positive solutions up to z=10,000:

http://www.tsm-resources.com/alists/PythagTriples.txt

When n>2 we now know the only solutions are the trivial ones that come from putting in 0s,1s or -1s.

Going against Hilbert's expectations, it was shown in 1970 that there doesn't exist any algorithm that can do what he proposed. In other words: no matter what "computer" you build, there will always be a Diophantine equation it can't handle. This seems to go against the vague optimism expressed in Hilbert's "solvability axiom". We also know other specific mathematical problems (like the "word problem" in group theory) that can't be solved by any finite, formal decision process. These problems are "algorithmically undecidable". Of course to prove something like this, one needs a precise formalization of the concept of algorithm. That's what Turing (and Alonzo Church) gave us.

In fact, Turing's formalization of "algorithm" as a kind of machine that computes (first appearing in his 1937 publication), and his subsequent treatment therein, was specifically done to show Hilbert's optimism about the decision problem (Entscheidungsproblem) was unfounded. After using his machine to prove "relatively few" real numbers are computable, Turing turned his attention to show:

"... there can be no machine, which supplied with any ... formulae, will eventually say whether (the formulae) is provable."

The original paper by Turing is quite clear and free online:

http://www.turingarchive.org/browse.php/B/12

Edit for clarity (there may be some confusion about this): the failure of the computer to solve the Diophantine equation is not that the computer gives a "partial" answer or an "approximation" after it runs a while. The question you ask the computer is: "Does this Diophantine equation have an integer solution?". The computer is built to answer "yes" or "no". Although the computer you build may be able to answer yes or no for some Diophantine equations, no matter what computer you build there will always be a Diophantine equation where no answer comes out. That's what "undecidable" means.
feralfae

Boulder climber
in the midst of a metaphysical mystery
Jul 17, 2017 - 07:04am PT
So perhaps God is the 9th-century mathematician Abū Ja῾far Muhammad ibn Mūsa?

Sure, if that makes you happy. But remember that his work relies on earlier advances by Indian mathematicians. I don't see any human as G*d, but that is just my own system of recognizance which puts me in this mindset. As usual with humans, YMMV.

However, my point was less about identifying a god or gods, and more about the wonder of perhaps being in a position to intentionally, consciously, and actively participate in the evolution of our own species. To be able to simply contemplate such a concept is delightful to me.

feralfae

Messages 16401 - 16420 of total 18368 in this topic << First  |  < Previous  |  Show All  |  Next >  |  Last >>
Return to Forum List
Post a Reply
 
Our Guidebooks
Check 'em out!
SuperTopo Guidebooks


Try a free sample topo!

 
SuperTopo on the Web

Review Categories
Recent Trip Report and Articles
Recent Route Beta
Recent Gear Reviews