Good afternoon ladies and gentlemen, welcome to this week’s SDA distinguished lecture, documentary & interview series installment. Today, for your delectation, here is Dr. Gregory Chaitin, from IBM’s Thomas J. Watson Research Center, giving his Alan Turing Lecture on Computing and Philosophy, Epistemology as Information Theory: from Libnetz to the Omega Number, II, III, IV, V, VI, & VII, at Mälardalen University, Västerås, Sweden, in 2005. If you find that interesting, and would like a little more information, here is Professor Chaitin’s Carnegie Mellon University School of Computer Science Distinguished Lecture in 2000: A Century of Controversy Over the Foundations of Mathematics, II, III, IV, V, VI, VII, & VIII. Please note that this is not Reader Tips, our regular Reader Tips entry will appear tonight as scheduled.
vitruvius – he rambles and rambles! It could all have been said in half an hour!
Well, my ‘take’ on it, is that we are exploring that basic conundrum, the FACT that our world is not a reductionist amalgamation of actualized bits, but is both those actuals..and the ‘potential to be actual’. It’s this latter that is the interesting area for it governs the former (potential governes actual).
Chaitin’s ramble outlines how the computable real numbers define, with ever more precission, an actuality. That suggests that an actuality becomes more embedded within the local contextuality. OK..but can the world exist within such a mode? The scholastics, for example, imploded intellectually as they tried to define ‘how many angels on a pin’, so to speak.
And panda bears have defined themselves to such a degree of food (bamboo) that they are unable to adapt. That’s what happens with precission, you lose the ability to adapt.
The uncomputable real number, on the other hand, refers to the Potential Force, the Universals, the General Rules..of which the computable real number is only an ‘insignificant example. And that includes us; I distinctly heard him say that we, as computable Reals, are insignificant.
So, the incomputable Real, is the potential-to-be Actual, and only a small amount of potentiality becomes actual.
Naturally, you can’t compute the future, i.e., the halting probability, because that would suggest that the Potential is as specific and articulated as the Actual..and all we insignificants need to do, is find out what the Potential is ‘actually’ made up of. That’s reductionism.
Very much Godel (whom he mentioned). Also Aristotle (whom he did not mention); and Charles Peirce (whom he did not mention).
Nice lecture but Vitruvius, he rambles.
Back to my Delice….( I am NOT sick); it’s a great cheese and I have a limited exploratory capacity.
Quite so, ET; I like your potential/actual dichotomy, and the various Delices do tend to have limited shelf life, thus one must attack when the time is ripe. Yet what I found most interesting about Dr. Chaitin’s ramblin’ man is the way he goes about trying to get a rope around the notion of maximally unknowable. That’s really a brilliantly creative piece of work he’s done there. It opens some very interesting doors. Is theology the mechanism evolution invented to cope with maximally unknowable situations? Is the human notion of god the name of the maximally unknowable?
Because, you see, folks, man invented philosophy in order to have something high-falutin’ to talk about while enjoying symposia, so if you’re not doin’ that now, well, then, we’re not on the same page, are we ?-)
If you would be so kind as to re-submit that last comment of yours, the one I unpublished, without the gratuitious insults, then I think that would be a good thing, Rabbit.
Don’t have a friggin’ clue what the topic is, let alone the content of the thing.
Guess I’m just one of those unedumicated idjits that rely on common sense and life’s previous experiences to deal with things of an earthy nature.
I do understand the roman numerals, however.
The insults weren’t gratuitous. They were thoroughly deserved.
I have read vastly worse insults – for far less provocation – on SDA. Why don’t you post my submission as is, and see if other readers don’t agree with my assessment?
Look, Rabbit, I think your points were well taken, but if you look up symposia as linked supra, you will find that “A symposium would be overseen by a symposiarch who would decide how strong or diluted the wine for the evening would be, depending on whether serious discussions or merely sensual indulgence were in the offing”. It’s in that sense that I’d rather not descend to the level of your first attempt to participate here this afternoon, at least not yet, deferring to Euboulos‘s note to the effect that:
If you would like, I’d be happy to republish your comments without the gratuitous insults, should you no longer have access to them (I do), just let me know, old chap.
Vitruvius: Very well…
ET:
Naturally, you can’t compute the future, i.e., the halting probability, because that would suggest that the Potential is as specific and articulated as the Actual..and all we insignificants need to do, is find out what the Potential is ‘actually’ made up of. That’s reductionism.
You’re *&%!# in *&%/!@. The Halting Problem is a mathematical question that is cast as one of “future computation” only for convenience. At its root it concerns the properties of certain mathematical systems, and has nothing to do with the future.
Nor is the solution of the Halting Problem – that you cannot write a program that decides whether any other program will halt for any input- obvious, as you claim. Indeed, it takes considerable study to understand why no such program can be written.
Theology states that the ‘ultimate’ is unknowable. After all, Adam and Eve were living in the potential world; then, they connected themselves with particular or actual information – and you know the result. They became actual, which is to say, finite.
But all peoples, everywhere on earth, have some notion of the ‘unknowable’, of the ‘infinite’ – and I don’t mean the monotheistic religions. Nor even polytheism. But animism. Belief in spirits, in..whatever that is not actual but that ‘might’ affect the actual.
I think, however, that when we refer to the potential, we also move into, not a rational analysis, but an emotional one. Benedict’s Faith, so to speak. The faith that there WILL be a future; that the future is open to change; that ‘hope’ is a reality.
I hate to say it but that focus on the emotional depths of the potential brought the arrogant and ignorant Obama to power. The fact that he can’t, himself, connect with the actual reality, and doesn’t realize that there is no direct linear connection between His Description of the Potential, and Actual Reality – is our Big Problem.
Thanks, Rabbit, I appreciate that. Now the thing about the temporality of the halting problem. Sure, according to some models, such as yours, it’s just as you say. Yet keep in mind that the most interesting thing about tonight’s lectures is, as was introduced in the first video clip, that Gregory is trying to look at what’s going in the margins that form between disciplines. It’s all well and good for you to go dwell in the center of your discipline, I support you there, but that does not justify your slagging those who are at least keeping an eye out toward what might be going on at the margins of epistemological growth.
Bingo on the Regensberg reference, ET. Say, while we’re here,
would you do me a favour, ET? f*ck off with the Obama shit
in this symposium, ok? Is there no sacred space remaining?
ET:
Questions of computability are mathematical questions which are solved through mathematics and not philosophy or theology. That we actually have machines that approximate (but only approximate!) these mathematical entities is besides the point. Ultimately this is about logic – any association with reality (e.g., “the future”) is spurious.
rabbit – you are the one who doesn’t understand. I said nothing about writing a program that will have the capacity to halt a process. Obviously, since the articulation (writing) of a program is an ACTUALITY, then, it can, in a linear manner, most certainly decide on another Actuality. And it can most certainly halt a process.
What is being discussed is whether a General Set of Rules, so general as to be not articulated as anything specific, but merely general, has the logical capacity to not merely stop a particular Actual, but even Start one. I say: No.
This means that there is no essentialist force that makes a lion evolve and emerge, over a species that we, who are actual, don’t know. The evolution of that particular species, the lion, is in effect, a ‘halt’ on computation. And there is no ‘code’ in the potentiality that is evolution that predetermines a halt, i.e., that lion.
And that, is the great strength of the potential. That it consists merely of a few general rules and the actualization into specific morphologies, is subject to the informational input from chance and context.
vitruvius – alright, alright. Watch your language. Ladies are present.
rabbit – I disagree with your definition of logic, which most certainly can focus on the future and to general or abstract rules. I refer not only to the syllogism, which requires a universal, but also to propositional logic, which focuses on the future.
I also happen to think that reality IS a logical process.
The whole point of the keynote address in tonight’s symposium, Rabbit, is that it is in fact not the case that, as you alluded to, “Questions of computability are mathematical questions which are solved through mathematics and not philosophy or theology”. If you are going to claim a mathematical definition of computability, then you’re bust on just the Godel, Church, and Turing theses that Gregory referred to. So where do you go? You go outside of mathematics to the broader area of epistemology, or perhaps as you would prefer, Rabbit, ontology. Still, It’s not about me, sir. It’s not about ET, sir. It’s about Dr. Chaitin’s lectures, sir, and you will note, that his position is not without a temporal aspect.
By the way, you’re a Platonist, aren’t you, Rabbit?
Did you know that ET and I are Pythagoreans?
Can I get you something at the bar ?-)
Hold on, wait a second, whether or not ET is a
Pythagorean is not for me to say. Sorry about that.
ET:
What is an “Actual” or “Potential” in mathematical terms? I need to know this since the Halting Problem is a mathematical result, and we it can only be used to draw conclusions about reality if we first cast those aspects of reality in rigourous mathematical terms (e.g., a propagating wave is cast as a vector obeying a partial differential equation).
Potential is like real number, actual is like computable real number. But we’re not doing mathematics here, Rabbit, we’re doing epistemology. After all, we can draw conclusions about our knowledge of the reality of human nature without putting it into a formal mathematic form, Rabbit. Of course, sometimes we’re wrong. On the other hand, as Dr. Chaitin makes so abundantly clear, sometimes mathematics pales in comparison to the maximally unknowable.
Vitruvius:
Platonist? If I knew what that meant I’d be insulted.
I am, however, an applied mathematician, and so know something about the relationship between logic and reality. And here’s something I know: the bridge between logic and reality must be crossed with care. Casuallness and flippancy are repaid with nonsense.
The financial industry has, on a number of occassions, fallen in love with its mathematical models without proper understanding of their limitations. The Gaussian Copula model is a notable example. The reward has been a couple of multi-billion and trillion dollar bailouts to prevent global economic catastrophe.
It may be, as ET asserts, that reality is governed purely by mathematical systems. There are certainly many parts of reality that appear so. But to tie reality to mathematics you must cross treacherous waters.
Exactly, Rabbit. You see it, as you said, as a mathematician, I see it as an engineer, and ET can speak for herself. The question remains, what do you think about tonight’s keynote lecture? The question isn’t, particularly, what you think about what ET thinks, or what you think about what I think, or even, technically, what you think about what you think. The question is, what do you think about what Dr. Chaitin thinks? That’s the topic here.
V:
What did I think of Ray Gumb’s lecture? It was a good summary of issues in metamathatics over the last century. And … that’s about it. I was reasonably familiar with most of the things he saidi, and well aquainted with a few things he said, and could find nothing to disagree with.
His last bit on where we go from here was a little wild – the mathematical difference between a rock and a deer? I was hoping for more on current issues on the foundations of mathematics rather than its application to life, the universe, and all that. Are there any “crises of mathematics” now out there?
Who is Ray Gumb?
Mathematics derives answers from given or accepted postulates.
Epistemology attempts to circumscribe that which is “knowable”.
See
http://en.wikipedia.org/wiki/Epistemology
for the quick and dirty version of the types or categories of knowledge.
Of course mathematics introduces the concept of the infinite, with some useful degrees of success.
The atheist however is arbitrarily ontologically limited usually by reductionist attempts at empiricism.
For example one cannot ‘see God’ or the infinite in the conventional sense by ocular sensitivity. Or more properly one cannot “know God” in the sense that you know your neighbour or your spouse.
One cannot in the usual sense sit down on a rock in the desert and say “Hey God, what’s up with that?” Well I suppose you could, but the infinite may not answer back in the conventional way.
You can’t even share a beer with the infinite God, even if you wanted to, as those may be ‘treacherous waters’ as rabbit has pointed out.
That may however count as a ‘spirited’ discussion.
* Agnosticism
* Belief
* Certainty
* Determinism
* Doubt
* Epistemology
* Justification
* Estimation
* Fallibilism
* Fatalism
* Nihilism
* Probability
* Solipsism
* Uncertainty
The extreme sceptic of course, is one who engages in solipsism; who knows only his own mind; which of course is rather lonely.
Some might argue that the solipsist has ‘lost his mind’; but a trip into the desert will assure you will soon find it.
One can posit that humans can know love, but how do you define it. One can’t point out love and say “Hey there goes love!” unless of course it happens to be one’s proposed spouse. 🙂
As Chaitin points out n bits of precision posits n axioms which may or may not be true. Hence the monster modeling of Glow Ball Warming.
In short the very act of measuring or modeling irretrievably leaves out orders of precision.
If one tries to measure the infinite you will always come up short no matter how discrete you get, which of course is a bit of a conundrum.
Cheers
Hans-Christian Georg Rupprecht, Commander in Chief
1st Saint Nicolaas Army
Army Group “True North”
I agree, rabbit – logic and reality are two different realms. They are both required of each other – logic cannot exist as logic without being articulated as reality. And reality must be organized in a logical manner or..it is entropic chaos. This is basic Aristotle.. (not Plato).
And I fully agree; it is incorrect to posit that a model of reality is equivalent to reality. That’s not quite what Chaitin is talking about, however. He’s not talking about the logical model vs the actual reality. He’s talking about a potentiality-to-be-actual. Once that potential is actualized as a model or as a thing, it’s not longer potential.
Is reality governed purely by mathematical systems? Only if we admit the mathematics of real numbers, both in their non-computable as well as computable forms. Both are required; the potential as well as the actual.
Sorry. I meant Chaitin. Gumb introduced Chaitin in another lecture. I read the written version of the lecture, since my computer is mute.
Excellent. I too thought that Dr. Chaitin’s talk was a good summary of issues in metamathatics over the last century. Fascinating stuff. Well, we’re into our second krater now 😉
so the universe might implode while mathematics(the tool of other sciences) has figured out the penultimate equation of neoreality, or something.
chaos is part of reality.
The universe might implode? Where?
in a teleprompter near Wash.D.C., i guess..oops..-forgot about creeping Ohmatics into all discussions, sorry.
hans – to suggest that unless one believes in god, one cannot accept the reality of the infinite, of the potential, is, well…it’s illogical.
The universe can’t implode into a teleprompter,
Reg; a teleprompter isn’t big enough to hold it.
When, ET, do we say whether or not logic is illogical?
Not in practice of course, in culled domains; but in theory.
heh, vitruvius. It may be illogical to us, but logic is never illogical. Otherwise…it wouldn’t be logic. So there.
Logic is all about relations. Now, can there be valid and invalid logic or relations? Yes. The invalid ones can’t last longer than the single articulation. They can’t reproduce. So, a bird with no head might be born, but…
But…, let me guess: but “a bird is not logic”?
vitruvius – of course a bird is an articulation of logic. The one with the head is valid; the one without is invalid. My point is that it, alas, could not reproduce.
By the way, rabbit, since you are a mathematician, then, you might be interested in the work of Daniel Dubois, mathematician, and his work in strong and weak anticipation. Strong anticipation is what we’ve been referring to here as ‘potential’, while weak anticipation is the models to which you refer. Two very different processes. Google him.
Also, Mark Burke, another mathematician.
You might be interested in the AIP, American Institute of Physics publications of Dubois’s conferences on ‘Computing Anticipatory Systems’.
A headless bird is an invalid articulation of logic?
You’re straining my suspension of disbelief, ET.
Broken, maybe, but invalid, I don’t see how.
wow you guys sound so smart using those big words.
pppptthhh
It does appear the words are epistemologically far beyond some peoples mental ken.
So you do understand that by trying to look smart you just end up looking snooty.
Nah, we’re just havin’ fun, Free. Sorry if the noise bothers you.
Yet perhaps you could try some other channel over here. And
if we’re lucky, perhaps some of these thoughts we’re studying
will benefit your children, or their children. Chin up, old chap.
OK, vitruvius, invalid probably means ‘broken’ in your terms. Or, hmm, maybe not. Logical propositions – and all reality – are always triadic and are either valid or invalid. That is, given the input and the mediation (major and minor premises) ..if they are valid actions of organization, then the output (the bird) has to be valid.
But, what if you have the same triadic morphological process of input/mediation and output, but the output was, well, broken. That suggests that something invalid in organization occurred in the major and/or minor premisses.
I’m saying that the headless bird is a result of organization of mass to mass, so to speak. The fact that it existentially exists, as such, even for only a few nanoseconds, is a result of mass being organized in a particular way. An invalid way.
This particular sad specimen of matter has been organized, lacking the capacity for continuity, both in its metabolism as an individual and in its reproductive membership in a collective.
Free- don’t be such a snob. Just because you don’t get what we’re talking about doesn’t mean that you should insult us. Oh – and are we just trying to look smart, or..are we???
I fail to see why you need to be mean to Free, ET.
Because, vitruvius, I’m tired of being called names and denigrated, personally. I prefer to have the issues and opinions I express debated and criticized.
But I don’t like it when people reject that approach, and turn to personal attacks. Discussing these issues isn’t an attempt to show any of us up as ‘snooty’. It’s a genuine exploration of fascinating areas of reality.
Heck – there are lots of topics I don’t dare to discuss on this blog – such as the Wheat Board, or computer programs; and lots of other areas. But I don’t need to go into those threads and tell them they are incomprehensible (and to me, they certainly are)..and just being snooty.
Hey guys, don’t worry about it. I love it when you talk dirty.
FREE, they’re not trying to be snooty. They’re just some philosophical / scientific types brainstorming and having some fun.
Just relax and enjoy the discussion.
Regrettably, I’m not able to participate because I am a philosophical / literary … / thug type and therefore just have to enjoy from the sidelines.
Correct, ET, you don’t need to do that. Not that I’m a saint, or anything like that. But at the end of the day, you’re not going to surf the wave unless you rise above the tide. Or maybe it’s just that that Thielemans and Wonder tune over in the Late Nite Radio thread has got me off my game. Or, perhaps, it’s that we’re now on the third krater 😉
Hey, Greg, Happy Independence Day, sir!
Vitruvius, thank you very much, sir. You’re a gentleman and a scholar.
Are those fireworks I hear, or are they gunshots?
ET, 90% of the people at SDA admire and respect you. Seldom do we have an opportunity to have that kind of renown.
Vitruvius, you seem to have worked through whatever introspective dilemma that was troubling you a month ago. At least that’s the way it appears from my end. I certainly hope so.
Onward and upward.
I’ll second Vitruvius’s greeting, Greg. There’s nothing like your Declaration of Independence for its sheer love, respect and toleration of mankind. …When in the course of human events…We hold these truths to be self-evident…Life, Liberty and the pursuit of Happiness..consent of the governed..
Oh, and when one reads the list of grievances, hmm, some of them remind me of Obama. [Sorry, vitruvius, I couldn’t resist. I’m leaving now.]
That’s ok, ET, we’re on the third krater now. Anyway, I don’t see the introspective dilemma, Greg, from this side of the corporeal dermis (you know how that works), but I suspect that it’s an ongoing project. I’m still a little bit annoyed that people aren’t appreciating how good they’ve got it, historically speaking, but I’m starting to also appreciate that that’s just an aspect of my personality type, and that it’s not for me to hold that against them. Perhaps it’s vaguely reminiscent of Dr. Chaitin’s maximally unknowable: in practice, there’s not much I can do about it (except recommend good cheeses). Anyway, at a minimum, this is a multi-year project, not a multi-week one, after all, Greg, you and I have been discussing this for, oh, about five years now, if you think back about it 😉
My head hurts.
I do enjoy these discussions, although I feel like a couch potato running a race with well-trained athletes. They are way far in front of me, but I enjoy getting off the couch and going for a run, even if I can’t keep up.
Thanks for the lecture, Vitruvius.
Here’s my ‘take’ on it, pace ET, who was the right track about a kind of actual and potential ontology, but got all messed up in the big words.
The key is to listen to the question period in 7th lecture about 4 minutes in. That’s where Chaitin summarizes what he was trying to say (and never actually said!) during his ramble.
His point is to argue in favour of a ‘discrete metaphysics’, which means a metaphysics that starts from simple, computable laws/principles from which great complexity arises. I take it he meant to use the epistemological principle that explanations must be simpler than the explananda to infer that ontological phenomena (ET’s actuality) are somehow complex decompressions of simpler ontologically prior realities (ET’s potential to be actual). The most ontologically prior realities are laws of nature and/or some kind of mathematical entities (or both are the same). Yet for these simple realities to yield more complex realities, they must be computable, and thus discrete in some way.
That’s why he was trying to argue that real numbers (which are infinitely more uncomputable than computable) aren’t really real. He can more easily argue that reality has this computable simple/complex structure if he can show that uncomputable numbers can’t physically exist and are problematic even from a mathematical point of view. He was definitely not saying that uncomputable real numbers refer to ‘the Potential Force, the Universals, the General Rules’ as ET would have it. On the contrary, the general rules must be (or involve?) the computable numbers if they are to ‘compute’ out some result, i.e. the physical phenomena of the world. And this is also why Chaitin was opposed to a non-deterministic quantum mechanics. For if the universe were non-deterministic in some way, then phenomenal reality and its principles would ultimately be uncomputable.
About the relation between logic and reality (or epistemology and metaphysics), Chaitin did seem to want to suggest that they come together somehow, but it wasn’t at all clear to me what he meant. This idea, at any rate, is certainly nothing new – probably as old as Pythagoras, almost certainly as old as Plato, and explicitly present in the 3rd century AD neoplatonists like Plotinus (e.g. the ‘One’ is the first principle of all, metaphysical, epistemological, and ethical). It’s funny why he kept giving Leibniz (not Libnetz, see posting above) all the credit. Which reminds me, Vitruvius, why do you oppose Pythagoras and Plato on points like these? There surely are differences in their views, but I’m not sure there’s a significant one at the level on which we’ve been speaking.
Anyway, that’s enough waxing for now. Any feedback would be appreciated.