Hint, heuristic, algorithm

Context: See Tru'eng anew, focus going forward, mathematics.

---

We were wallowing in the muck (it's an election year, so give us a break) wondering what could pull us out of the morass (we do need to get our tops up and spinning). Well, those with oodles of bucks, unless they are extremely careless (read: stupid), find it easier to remove themselves (not exactly, but that's a big T 'truth' issue) from the mess (they leave the crap to others). And, big bucks now are wandering after 'apps' which are oriented, for the most part, toward personal devices (mobile ubiquity).

Aside: Most don't enjoy that opportunity. Someone used baseball to characterize those with large pockets, in the following sense. They categorized the person's success by their starting position. Ellison, of the relational thing, was from the batter's box. Some start from first base. Others already had a home run at birth. You know, most are not even in the ball park. Z of FB was on one of the bases.

So, big bucks HOPE to make more by chasing after dreams (illusions -- as in, chimera). There may be technical aspects to the process that brings things forth, yet one would think that appealing features are more the focus than outright computational prowess. Calling something an algorithm does not make it so (below).

Sidebar: another issues that we'll discuss: A. 3 years with Vista and no BSOD -- only 2 weeks with this newer thing - Windows 7 - and I already have one; B. using the recent version of a program from a famous company, I kept seeing the thing go back to the initial screen. Well, it turns out that this is the default error mode (more friendly than the BSOD?), but it does the unwind without leaving any hint (see below) of what was wrong. It's like going back to square one and starting over (ever heard of Sisyphus?). But, getting a top to spin is not trivial. C. ...

---

So, let's look at this by using the three concepts from the subject line. They can be thought to have a progressive association somewhat like the following describes.

• hint -- We can view this several ways but consider a math problem. Many times, there may be a hint about how to approach a solution. One could say that a hint is sufficient to the wise. Unfortunately, computers are not wise and need explicit instructions. That, folks, is both the boon and the bane. It's the former since we can (try to) know what went into some computation (only under certain restrictive assumptions dealing with things like side-effects, black-boxes, etc.). Another way to think of a hint is that it lays down markers, within a landscape, whose presence helps keep things moving toward an end. Let's face it. Smart folks do not like to follow explicit instructions more than once (why then do we put people into the position where they are, for the most part, automatons? --- stupid, from several sides). You know what? We cannot give a hint to a computer in the same way that we can smart folks (forget the so-called smart devices - dumb-ass'd things, people). Except, if a person is in-the-loop during a computational event of complicated nature, the person can nudge the system away from divergent tendencies (yes, we'll expand at large about this being one way out of the quagmire -- suggesting, of course, human talents not yet developed).  
• heuristic - We could say rule-of-thumb, but it's to mean more than that limiting view. A heuristic view can be fairly powerful approaching, somewhat, the 'nudge' mentioned in the prior bullet. Why don't we hear people talking this, rather than the loud pronouncements about their algorithms? If anything, any decision logic would need to be heuristically based (using real data and analysis thereof) in a real world situation. Developments after Hilbert's question about a program to do all mathematics (Mathematica, and its ilk, notwithstanding) suggest such. 
• algorithm -- There is no agreed-upon definition. But, one strong notion is that an algorithm has (ought to have) more rigor behind it than not. Now, looking at the various characterizations (thanks to Wikipedia editors) can be interesting. Knuth's view probably best fits my experience. Namely, we have this: finiteness, definiteness, input, output, effectiveness. Let's look at those. Finiteness. Some argue that we have this by the vary nature of our domains. Not so. I've seen too many things loop (everyday, operators get lost, for various reasons on the web, which requires redo). Combinations of non-finite spaces can look extremely large from certain viewpoints. Definiteness. Unless there are explicit user requirements, there'll always be a problem here. Convergence, through interest and use, may be the modus operandi, yet it approximates only. Input: thankfully, menu interfaces inhibit problem emergence. But, just a few days ago, someone was trying to show off his new device. And, he started his dialog as if a 'smart' person was on the other side of his Shannon experience. Hah! The thing barf'd. I've seen this too many times, folks. Output: Crap, just look at mangled messages out of supposed smart fixup and fat fingering. It's almost epochal. I've seen too much effort by people to demonstrate that their smart device is such. We dumb ourselves down, folks, in order for this to happen (many, many ways). Effectiveness: As measured by what? Showing off to others? I'll be impressed when we see some type of verification process in places (no, not just testing). However, this is a hard thing to do. 

---

Reminder. See my remarks about Mr. Jobs' little demos from the earlier days. My thought still stands, despite IBM's success on Jeopardy. 

Aside: Don't get me wrong. I love that the software frameworks have evolved immensely. It's nice to open the covers and see the progressive build upon what one hopes is a sound foundation. But, it took oodles of time, effort, and caring work to get here. How do we try to show the extreme tedium, and angst, that has been the case from the beginning? You know what happened, folks? The tide was turned so that computation can be faulty without any user kickback except for not buying. Or complaining? And, the vendor saying: sorry. HOW many millions (billions) of dollars of work has been lost through errors that might be of an egregious type if we could get under the kimono to know for sure? Well, losses are not finite for several reasons (cannot be counted, or accounted for, and the secondary effects are not measurable). 

---

Oh, who with money (yeah, venture people, you) is even interested in the longer term problems? 

Remarks:

01/23/2015 -- Software? Well, we are talking more than apps (latest craze). We are dealing with fundamental questions which, then, gives rise to normative issues in mathematics (and, by extension, to the computational).

01/05/2015 -- See header.

03/23/2014 -- SAT solvers as an example of large class of heuristics.

02/25/2014 -- Put in a context link, up top.

07/20/2013 -- So, today, found out that a new handle for algorithms is algos. Okay.

06/14/2013 -- Moshe's editorial at the Communications of the ACM discusses algorithms. Comments, and subsequent letters responding, to Moshe's thoughts indicate the wide range of opinion in the matter.

05/02/2013 -- This has been a popular post (second most popular), of late. Perhaps, it's the growing awareness of the ever-increasing gap between what we think that we know and what we actually know. Well, the theme of the blog is to look at these types of problems. Perhaps, we can bring something forward from the past (such as, we not learning Anselm's message). I mentioned it somewhere (I'll track it down), but the motivation for this post was in part hearing young guys brag about their algorithms in a public place (of course, weekend situation, so some latitude is allowed). That concept is bandied about these days without people giving the notion its proper respect.

10/05/2012 -- Related posts: Zen of computing (in part), Avoiding oops.

10/05/2012 -- IJCAI has a newer flavor. It, at one time, had a theoretic thrust, mainly. Need to re-acquaint myself with the conference (attended 1987 Milan, Italy 1991 Sydney, Australia 1993 Chambery, France 1995 Montreal, Canada). This talk from IJCAI-2011 relates to the theme of this post: Homo heuristicus.

Modified: 01/23/2015

Celebrating our frailties

In another context, while discussing Ben's largess to business (gamblers) but not to labor (or savers) - though, he claims his rolling out the dough is to create jobs, the notion of someone being perfect came about. Essentially, to err is human. The corollary is true, too: to be human is to err (even for those high-falutin' types that claim to be divine, et al).

To try to be perfect is not human; it's machinations in action. As in, someone doing something 'perfectly' does not mean that the person is perfect. No, that sort of thing is not much different from equating the map with the territory (a real problem nowadays, with ubiquitous computationally motivated intrusions in our lives).

So, does this mean that we cannot be better, etc. (or strive to be so?)? As in, practice makes perfect? No, as systems (and role playing - with effects, of course) are the things that we can have approach perfection. People, while in a system, can get better, to the extent to which they can overcome human limitations. As in, roles and essence are two different things.

But, do we expect that systems are perfect? Well, we do trust them a whole lot more than we ought to. See the comment on the main page about computablity, and problems thereof.

However, we can change the context to that dealing with expectations and realizations. As in, we can get close to fault-tolerant states, even if that comes about from error-fixup techniques that are, undoubtedly, clever.

---

Why do you think that the borg (to wit, Star Trek's type, et al) idea is so strong? People sense that we can have a symbiotic relationship (with what?) that is uplifting. But, too, we can descent into slavery (ah, financial indebtedness is just that).

---

The corollary thought is that 'labor' pertains to a class of people. Whereas, our progress rests upon us seeing that 'labor' relates to roles which are attempted (or fulfilled) by people. No matter that most who descend to this type of activity do so with little choice. Not all people who work with their hands are incapable of more advanced challenges. For some, it's a matter of choice.

Perhaps, that choice is seldom made nowadays. Not true, though, from my experience. One has to listen with the right ear to hear intelligence covered with the detritus from having mostly gross experiences from life. Some never get to shine themselves up. Yet, their potential is there.

---

As an aside, to the young mucks. The thing of having succeeding waves of people entering the market with the latest knowledge running things is part of our problem. Actually, a very large part. That sort of thing is a recent phenomenon, brought on by advances in technology and computation. So, its analysis can be done now since we have had several downturns over the recent times for people to recognize the problem, if it is expressed so as to be obvious (the stench goes all the way to heaven).

Expect some more attention to this theme; too, proposed ways to handle things better will be in the offering. Why not?

Remarks:

09/28/2012 -- One type of hope.

09/21/2012 -- This discussion ties into 7oops7's bailiwick (see Remarks 09/21/2012). We know that we cannot, too much, celebrate our faults. Why? Descent into the quagmire. Oh, wait! Being concerned with the faults of others has the same downward spiral. I have to admit that we need to find a way out of the mess (will it happen in the U.S. any time soon given how screwed up election dynamics have become (partly due to the Court's claiming the fiction that a corporation is a person and that its money is free speech?). Virtues come to mind as essential. Yet, many argue not. From whence, then, we have to ask them, come the motivators (lifters)? Hope is one of the virtues. We hope that we not get pulled into some type of downturn. We just went through one that was caused by those (see prior Remarks) who could run amok yet have not learned their lessons. Ben saw to that with his largess. Well, it's Friday; we'll get back to this later.

09/20/2012 -- It's imperative that I mention the best and brightest. Yes, we've talked of them before. Here is another definition. They might be considered as those whose arrogance causes them to see themselves as perfect. The real tragedy is that these types have always mucked up, and seem to continue to trash, the common world shared by all of us (now, and our progeny in the future). Too, those whose attributes are less stellar (by what is their ascendancy measured anyway? ..., very short term looks? ...) have to clean up after these type whose crap falls on the world from leaks in their diapers.

09/19/2012 -- Rick starts out: perfect memory.

09/19/2012 Let's say, for now, that perfection, like beauty, is in the eyes of the beholder (Wiki has a nice historical view of the concept's breadth of use). See, 09/19/2012 Remark (Fedaerated).

09/19/2012 -- Any sense of 'perfection' would require some way to judge whether something has attained the state, or just is such. All sorts of issues lurk about. So, let's look at the role aspect, for now. We'll get back to the need for 'ídeals' in this matter. That, too, raises considerations for us to look at. In terms of sensors and actions, one might think about adaptability as being an indicator. Yet. we all know about the pejoratives cast'd at the person who is good at playing the chameleon. Thinking of faults, are they not abundantly clear? Oh wait. Much effort goes to covering these up, not unlike our clothes hiding all sorts of imperfections (for the most). So, we're not far from the core issue of truth engineering. How do we know? Even if we can (are allowed to) see under the kimonos, do we know what exactly we're expected to see or even how to do other than react? One approach might be to look at what is considered perfect by category. And, then identify things that are almost perfect in that case, to wit ballplayer, surgeon, and much more. Some might even be 'perfect' in several roles. Others may have few such qualities. Ah, that is nudging up against an important subject, to be discussed later (per usual).

Modified: 09/28/2012

Virtual reality

Lots to catch up on, but this little article from the IEEE Spectrum is interesting. It's written by someone who admits that he made his money getting technology to make things more efficient. Now, he's reflecting on some of the lingering effects that may not be all good.

   http://spectrum.ieee.org/consumer-electronics/gadgets/virtual-reality-is-addictive-and-unhealthy

Somehow, expecting business to have a social conscience is a fool's dream. As we all know, there has been a bifurcation twixt elite and serf, covered here and the related blogs several times, that manifests itself as a gigantic gap between those who have and those who do not have (or have not so much).

But, that's a side issue, for this post. Yes, there is an appeal brought about by those little things (darlings that they are) that allow access (ubiquitously and without cessation) to that which is a mere web, yet it appears to be an endless reality. For some, it's about as close to abstraction as they're going to get. Hence, the pull.

If we taught people how to handle abstractions better, there would be less problem. But, we'll get to that. You see, the interloper is mathematics of the elite whereas it ought to be the purveyor of truth, accessible to all.

---

Elsewhere, there was a mention of Facebook being a metaphor. Actually, it represents this problem from several sides.

The reality is that this overlay being built (of which current technology is only providing a glimmer) upon our casual reality will continue to be and to grow in size and complexity. The elite/serf split has been made worse by that which was done early. It's imperative that we understand better the dynamics so as to make less certain the dire straits for the masses that are inevitable given current thrusts.

Remarks:

08/22/2012 --

Modified: 08/22/2012

Effectiveness, again

Effectiveness? There can be much discussion about this, but, essentially, let's just say that some 'thing' is effective if it works, or produces results, as expected (expectation management might be of interest here, see below -- prior posts in the category). If we take STEM (looking backward), we see a lot of evidence of effective approaches that are remarkably productive. Examples abound: the computer (even if it's within a PDA) being used to read this post, the system behind the blog's use of posts, the communications scheme (WWW, et al), and much more.

Example of effectiveness
Financial Times (08/07/2012)

We have all sorts of others. Take NASA's Curiosity Rover (and its older cousins) or SpaceX, for instance. We could spend hours discussing what is behind that. In this case, mathematics and computation stand out, though a lot of engineering has been involved, to boot (most of which apply advanced computational methods). There's medicine and its marvels to look at.

Business? Well, we can find glimmers here and there, if we discount the idiocy of some finance. But, the mis-application of advanced techniques have put us into deep dodo (see below, as this theme with continue to be described and analyzed so as to propose solutions).

In any case, from a foundation'l view, one has to ask about the effectiveness of mathematics. This has been done; the field is quasi-empiricism in mathematics. Its inception coincides with the wonders related to the establishment of the standard model in support of our understanding of physics, which work used several types of mathematical advances of the past 200 years. The list of accomplishments from applying the knowledge of physics, effectively, is huge (and, is generally known).

---

Publications related to the 'effectiveness' theme have been many, but the paper (1960) by Wigner is seminal: The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Essentially, Eugene suggested that we've been lucky (paraphrase) and that we do not know why this success has come about.

Aside: Listening to some of the practitioners (okay, some are very smart), one can perceive lots of hubris (ah, we'll continue with this, to boot).

Of course, debate continues. The work of Norman Wildberger has some application here (though, this is my put, not the Professor's). He's saying that the current views, in some cases, are too complicated resulting in weaknesses that are insurmountable without some underlying change. Yet, people have been doing this difficult work for several generations now.

Aside: Of course, the populace has bifurcated into the numerant class (in this context, able to follow mathematics - or, paraphrasing von Neumann, able to get used to mathematics) and not. Yet, the importance of mathematics might suggest that it be amenable to all. We'll get back to that.

---

So, an operational question might be: why do we have to understand why the things work, if we can show that they work suitably for repetition and duplication? In other words, the magician's class will be with us ever more (think Poe). By the way, managers are not of that class, rather they expect 'magical' results from the work of others.

---

Now, before going further, let me relate one idea from seeing some videos (see below) by the Prof. He touts rational trigonometry. Okay, I've watched a couple of these (selected by the title's suggestiveness). For one thing, I'm wondering how we might compute with the 'rational' framework, somewhat like this. When doing solution derivation, transforms are the norm. I'll be looking to see how the Prof handles Fourier's work. But, let's take fuzzy logic. As with most abstract approaches, one has to take data related to real (as in being) things, fuzzify these, compute, then de-fuzzify to get results back into the proper domain (talking context, etc.). Now, with the rational approach, it may be better to do long chains of computation after converting to the rational representation. Naturally, one would have to deal with approximations, and such. Yet, during the computation, several troublesome problems would go away since the reals (number) would not be seen. Too, if one is doing things that require limits, or decisions about bounds, the rational approach ought to do this natively. Anyway, it's an interest of mine.

---

Here are three links to the Prof's work:

• Main page:  http://web.maths.unsw.edu.au/
• Foundations videos:  http://www.youtube.com/watch? ...
• Wildtrig videos:  http://www.youtube.com/watch?...

I started the foundations series at MF87 and got hooked. Then, I went back to the beginning. Later, I started the WildTrig series and started to bounce around. I will continue in that vein through the videos. He has additional lecture series: Linear Algebra, Algebraic Topology, Hyperbolic Geometry, and more.

The method that I'm going to follow is to watch and summarize (if motivated). In some cases, I might try to write about the topic before looking at his work just to see how close I can come to his work. Why? I've been at this (applying mathematics through computational systems) for decades (I'm actually quite a bit older than the Prof -- I've seen computation progress from the inside - like our buddy Al). The areas of focus included geometry in modern, advanced types of modelling that are stringent in their demands (that is, not the loosy-goosy approaches we find with gaming).

It's nice to see his focus on Geometry (Euclidean, okay?) which was thought of as a forgotten step-child for a very long time as people ran after topology and differential geometry (ought I say? abstractions following abstractions -- what's the term? abstract nonsense -- the Prof is right, getting a long way from 'reality' - as people try to either be like or to outdo our old friend, Albert). However, in practice, any engineering of products that has mass within the space of our planet (and beyond) makes heavy use of Geometry and Trigonometry.

---

In any case, there were splits between types of duties and responsibilities along a line that could have been troublesome but was never too much so (except, surprisingly, engineers unionized, in many cases). Good engineers, who could handle the mathematics, generally did not become managers (or politicians, for that matter). The really good ones got themselves into the golden handcuffs mode where they were essential, yet overlooked. Well, playing the political games was for the lower-echelon mind (anyway). And, the intellectual workers did magical things (as far as the business mind could see) and had to do so on demand (a source of irritation, to say the least). In fact, the smart companies coddled their good people (perhaps, some of the newer companies know about how to do this better).

But, as you see the nerd revenge coming about in computing (Google, FB, ...), there are still problems (take it from, me, a user, but one who knows what's beneath the skirt even if I'm not allowed to use my eyeballs). Hey, you young guys, you're becoming troublesome for other reasons (we'll get there).

---

So, the Prof's re-do of the foundations might play a role here. No doubt there will still be mental gymnastics required, yet, the underlying basis would be amenable to all (philosophical notion here that has merit in extending the standard model's effectiveness). I saw a lot of contrived efforts at trying to pull out something understandable in a general sense from dense stuff expressed in all sorts of technical media. One goal of this type of thing was to get expectations and progress measurements synchronized between disparate (by their very nature) views.

The Prof mentioned, in MF87, that a lot of the perceived weakness in 'pure' mathematics can be traced to the growing flim-flam (didn't want to use gobbledygook) which comes from an improper basis. In fact, he used smell and sense, many times. Of course, he's not talking naive commonsense, so much. But, intellect (thanks Prof Gardner) is more than we allow. And, we can learn from the Greeks even though the modern view likes to "dis" (take hip-hop, for example) those who went before (whereas, within the fabric - ah, yes, the book and Nova series -- they are there)

Myself, I've been pondering several things, such as, [how] we could get to a modern peripatetic method, even if it would be based upon a flat-world extension (thanks, Hilbert) that has more 'reality' than we appreciate (the earth may be round; the world is definitely flat)? Then, the whole notion of truth engines would use an improved model of human beingness, and the insights related to which would need some type of technical expression. The Prof might be on to something here. He did seem to stress intuition, etc.

Remarks:

08/08/2012 -- The Prof mentions several times his antipathy to thoughts about the infinite and how we may have conquered it (ala Cantor's work, et al). The Prof's approach, as he shows in several videos, can go toward the very large, and small, yet it would not be a convergence (another concept that he does not like). What would be a good term to use?

08/07/2012 -- Since writing this note, I have watched a few more videos. The Prof is thorough in his efforts. Found my first dissonance: MF77, on objects or expressions. Ah! I'll have to dig deeper to see his thoughts on computers. He doesn't like them to be used at crutches. Is he thinking that, perhaps, the computational system might be the realization of some mathematical truth (I can explain -- his focus on code sort of says not -- truth engines are the key, hence the blog). What all this has come to, that is the exposure the past few days to some original though, is that I now know that foundation'l work is being done. I need to pay more attention. Also, my area of work needs to be in meta-mathematics, in part.

Modified: 08/08/2012

Weakness in modern pure mathematics

Several posts, of late, have talked about the need for a re-look at technical issues. This will continue in a, hopefully, coherent fashion with measurable effectiveness (being cheeky).

• Truth Engineering -- Renew, 5 years, Myth 
• 7'oops7 --  Relativistics
• FEDaerated --  LIBOR, a big fudge?

All along, there has been a suggestion here that things are awry because of foundation'al issues. And, this is because of more than the concerns about quasi-empiricism. These issues go way back.

---

There is a chain, folks, that can explain (partly) the source of the problem. Dawkins, in fact, has used the argument. In the sense of science, let's put it this way (paraphrase) -- the biologist talks to the physicist (and chemist), the physicist talks to the mathematician, and to whom talks the mathematician? God. The adage is age-old but worthy of attention.

Aside: What goes along with this is that only some of a cohort set are the ones worthy (of value) enough to push back the horizon. This was fine when things were 'pure' and simple-minded (yes, people, the classic joke of the unaware thinker -- do we really need that?). But, given those considered worthy (yet, they have feet of clay as do the rest) a computer and the web and watch out (yes, people, the crap that we see now is of this ilk -- how did reasoning, smart folks allow such a bad state to develop? - Harvard isn't off the hook - yet, as said before, the theory of multiple intelligence comes from that institution -- so, numeracy (as in, applications of mathematics -- all types) is not the epitome (STEM, a misdirection, of sorts) by any means -- well-rounded-ness? ever heard of that?).

---

Aside: In several posts, there may be use of undecidability and quasi-empirical in the context of computational issues of note. The discussion of this topic will continue under the context of Computability in all of the related blogs.

---

So, the quakings that we see (covered in postings) do deal with mathematics, with those who do it, and with its applications. We will continue to go on about that as the growing computational frameworks are troublesome in very many ways. As I've said, there is no timeline that I'm adhering to (as of yet). We'll follow things to wherever facts and features lead.

In that vein, I just ran across a lecture that is saying similar things, essentially. I'm going to be listening to this and related discussions. The lecture is titled Logical weakness in modern pure mathematics (see on youtube) and is given by Prof. Wildberger at UNSW (New South Wales). What caught my eye was that on the first few frames of Part II we find this list of problems:

• Inconsistent rigour
• Problematic definitions
• Reliance on 'axioms'
• Computationally weak
• Impoverished examples

Then, the Prof shows a partitioning into the troublesome areas and those not so much. The list includes: calculus/analysis, set theory/logic, geometry/topology, probability/measure theory and parts of algebraic geometry.

---

Logical weakness in modern pure mathematics

Aside: The lecture topic has 'pure' in it which study does not generally include applications (that's the whole point, removal via abstraction from anything of consequence). But, the Prof mentions  early on that we need to have examples in order to provide a basis that is more solid (paraphrase - pun intended, to boot). As well, though, the argument here is that those who apply are resting themselves, many times, on what the theorists tell them. In a sense, we cannot have pure without its mappings to usage (I know, philosophically arguable) if we are to overcome the weaknesses alluded to by the Prof. Being cheeky, I feel that a peripatetic approach is required, albeit virtually founded. This type of thing is very much in the interest of the techies to pursue (rather than bigger pockets).

---

This post is a marker as I expect things to get interesting as I follow his arguments. It's real nice to run across this. Why? Many times the problems are as I've mentioned here. Teach a manager a little math and watch out. They'll run amok. Lots of what we see on the web (yes, Google, you, too, mathematicians as you claim to be) is this type of thing. I marvel at how far computational methods have been pushed despite the fact that they have the slimmest of supporting theory.

You question this? Ah, open up your code and let us see.

In another realm, we have program trading. This is the highest type of idiocy possible, even if those propagating the madness have their Doctorates (sheesh, you guys/gals, ever consider foundations?).

Remarks:

06/25/2015 -- ACM Communications had an article (Created Computed Universe) that suggest that our computional prowess ought to lead to agnosticism rather than to anything else. Of course, my initial remark: So many modern minds conjure and contort in order to introduce what is not much different than what some knew many millennia ago in the desert.

08/08/02012 -- On effectiveness. It's there, and we take advantage of it (even if we have no clue as to its origin -- and let hubris reign more than humility). NASA is a very good example with Curiosity Rover. But, the recent Russian failure to launch a satellite says that things can go awry at any time despite good efforts. NASA has had its failures, too. The main issues are at the boundaries (to be discussed) and when extrapolations go way beyond what the basis will support (many examples, we'll get there). But, as the Prof showed with his rational model, we can extend, indefinitely, twixt two rationals. So, the boundary (reference) above has, at least, a dual meaning.

Aside: The Prof mentions several times his antipathy to thoughts about the infinite and how we may have conquered it (ala Cantor's work, et al). The Prof's approach can go toward the very large, and small, yet it would not be a convergence (another concept that he doesn't like). What would be a good term to use?

08/07/2012 -- MF77 deals with object oriented vs expression oriented. The former has some relations with category theory, etc. The latter one might think of as 'code' related. We can think of demonstrating something computationally rather than jawboning (it's good to hear that this is what mathematicians do). The Prof seems to be pushing computer orientation which raise other issues, but we'll keep listening. If he can keep computers from becoming an even bigger mystery, then all would be well. Otherwise, we're talking the development of a monolith, in a certain sense, that would become troublesome, indeed.

08/06/2012 -- We'll jump to the meat and go through the sequence on Rational Trigonometry. His book and papers are available at the UNSW site.

08/04/2012 -- MF3, at 7:38, shows why 'New Math' failed.

08/04/2012 -- Just went through MF1 and MF2. In essence, the Prof is establishing a foundations of mathematics that is amenable to anyone. The analog? Think about the intelligence tests that are supposedly without any cultural bias. The Prof's approach ought to end with a mathematics that will be accessible to any person who wants to make the effort to learn it, not just the elite class. The consequence: we may find discoveries far beyond our imagination since cultural biases are the most limiting especially for those who are of the advanced types whose talent causes them to be forced into (or reinforced toward) the highest (purported, remember?) cultural status.

08/04/2012 -- The first video of the series (count as of now, 101). As of today, the last video.

At 22:56 of MF87

08/04/2012 -- Will do some notes here as we go along. On finishing up MF87, it was nice to hear him say that the youngsters can smell when things are awry. They may not be able to put their finger on what is the problem, but that there is a problem is, somewhat, obvious to them. I'm not going to follow the lectures sequentially but will bounce around by interest and applicability to my work. Notes will be here; there will be occasional summaries posted with comments about how it all applies to the topic of this blog (and its associates).

Aside: von Neumann said that we can't understand mathematics but get used to it. So, that's by use, repetition, etc. Is the Prof arguing the Hilbert side?

Not being critical at this early stage, as I want to hear what he has to say in its entirety. See 22:56 (image), which is right on!

Modified: 06/25/2015

Renewal

Five years ago, the intuition of the blogger was good, in that most advanced work seemed to honor the denseness of semidecidable systems. And, that is being kind, as most argued that we did not have any need for concern for decidability for ‘finite’ systems. Too, we knew that the standard model had been successfully tweaked over a 100 years or so. Having this success made us lean toward hubris.

But, in actuality, if you look at the world (today or anytime), there are many more “unknown unknowns” (recent look via 7óops7) than our old friend Rumsfeld would admit to. Of course, the craziness that occurred late in the year of 2001 had a real and visceral effect; it was too easy prior to that for some to have an unreasonable comfort about our being untouchable in the area bounded by the two large bodies of water. We are still trying to unwind out of effects from those, and later, events.

At the same time, though, some of those who could [have] exploited the observed success of certain methods by growing the ‘chimera’ way beyond its rational basis. That is, the methodical approaches from physics (at many levels) were brought out to build the apparati that run the markets. If you must, sleight-of-hand keeps the take of some as a perpetual sequence (right there is part reason for the bad smells) while obfuscating the reality by trickery and faulty mathematical arguments.

--

From the first post, the blogger has been suggesting that various mis-applications are the norm and that these are enabled by the growing computational frameworks. You see, the basis is essentially undecidable (which we’ll show); our progress has largely been predicated upon the luck of smart people (we’re in deep dodo, people); yet, we have the charlatans arguing that things are (would be) great if we continue to follow them on the path to perdition.  

--

If we can identify the alleged misdeeds, ought there ensue an orderly discussion about what to do? If only. As it then becomes a conflict between truth and power (and we know, just look at the current election, power has its basis in money – truth, on the other hand, is not of money – this, too, we’ll show).

Not that we expect a fairy-tale ending, but one can still think (and cannot be faulted for thinking) that realizations would be required in order to bring some clarity into situations. But, with Corporations seen as people (in what reality is such a thing conceivable?) the whole environment has changed. The blogger will not be the cynic who thinks that resolution is not possible, but we have our work cut out for us.

The initial focus on how abstraction's appeal has led us astray was correct and will continue. The topic needs to be further clarified.

---

Now, in regard to the economic mess, before the time of the start of the blog, some of the rumblings of structures quaking were already heard by some. Many were awakening to the fact that we were going to experience some type of downturn. What was unexpected was the non-stop exposure of stupidity (idiotic notions being widely disseminated by brilliant minds) almost on a daily basis, the deep depth of the crap that was put there by our leaders, and the length of time in which there has been no resolution of the underlying issues (perps still walk).

WTF! Again, WTF!

All sorts of descriptions are possible, such as the old Rip one waking up to this fact, after a couple of decades or so: the best and brightest were given that label precisely for the fact that they could fill the pockets of the fat cats -- to be defined, again – and themselves (ah, FB is more than a metaphor; it’s a poster boy, to boot).

Remarks:

08/08/2012 -- We need the effectiveness (unreasonable or not) to be cast in a new light. Curiosity Rover, et al, is an example of how things can go. 

08/05/2012 -- Added pointer to updated look at unknowns via 7'oops7. Some editing (periodicals have teams plus an iterative process, yet you'll see typos now and then (more frequently nowadays with computer assist being the vogue) -- several lessons in that, perhaps). 

Note: See comment on using another approach, below. Need to tweak it. All the style information that was carried over is troublesome. Oh well. Of course, I know how to filter out and get minimal HTML, but why is it seen as smart (or progressive) to bring in this type of crappy assistance (not any better than it was a few years ago)? 

08/04/2012 -- Weakness? Yes, indeed. 

08/04/2012 -- This was the first post that was developed in a modern editor and then copied to the blog editor. We'll try that for awhile. Having the more intuitive interface ought to help expositions formulate. 

Modified: 08/07/2012

Five years?

It was this day, five years ago, that the blog got its start. The first post asked the question: Can truth be engineered? Of course, to even ponder such a question requires us to cover a whole lot of groundwork. And, bunches of meanderings over the 'landscape' (nod to Susskind, for starters) ensued.

Too, though, there were side-tracks, some of which were quite involved. Why? It was only a few months later (first post with some content related to the problems that started to lurk - anticipating the 99%-ers outrage that would come about later?) that it became apparent that the financial world's transformation of beautiful work (mathematics) from its associated realm of the physical sciences to that of the "money'd" spaces where we find things like greed, and such. It's not that the sciences are pure (though, many would like to think so), yet, none of the putrid smells that we get from the likes of some bankers (and others in that realm) are in the sciences (at least, not as pervasive - after all, people are people). So, we had to look at that whole class of idiocy.

---

At the time of the beginning, truth was to be considered from the small 't' side for a long while. And, the interest was very much directed toward computational aspects. There were many motivations from the effort some of which go back to the blogger's early experiences at knowledge, and messes related thereunto. Of course, that, then, leads to mathematics which, from the beginning, was addressed from the 'effectiveness' angle that is argued under quasi-empiricism (7oops7, FEDaerated). But, too, delving into matters brought out the fact that the focus of the blog ought to be complemented with a couple of other approaches (actually, more), namely the 7oops7 and FEDaerated (referenced in the prior sentence).

During the past five years, there have been many technological changes brought to us in the form of the web. Did you think much of the 'cloud' then? Facebook, in its current mode? Basically, much progress was due to clever use of technology. As things are defined and demonstrated, efforts at standards can help ratchet up the basis shared by everyone. Look at HTML5, for example.

---

So, here we are, after a little hiatus that was spent in a grand search both in reality and virtual worlds. Are we any closer to determining the basis with which to discuss truth? Well, perhaps, if you consider that it would be a type of situational closure (or compactification) for the purpose of attempting definitions with which to found arguments. Example, Either/Or is an example. Actually, the intent there may be to describe some 'meme' like characteristics that would allow pause to vociferous views on either side so that reason (yes, Richard) might be considered in a new light. But, there are many other voices in the mix.

For example, the blogger ran across this one today while doing a specific search (Bing) on Susskind: Closer to truth and Edge. But, someone using truth in a business sense came from another search. That is, when the blog started 'truth engineering' came back with results that concerned 'truth in engineering' which is still the most prevalent search result. Now, this blog will come up, many times. But there are other results, like these two: Truth Technologies, Inc. and Truth Technologies LLC. The former's interest deals with compliance with laws that relate to limiting financial misdeeds (why does that strike a bell?).

---

So, this might be the time for a few words about the approach as things go forward. Expect that the tone will be more considered and technical (as opposed to the groundless 'opinion' that seems to be the main flavor of blogs). One thing about the latter is that mathematical concepts can be expressed in words as we see with Susskind's efforts at explaining his work. At some point, we might actually get formal and rigorous. Even without that, the topic will never be trivial nor can it be exhausted.

---

The 'engineering' focus here has an analog with that which was done with chaos. Some 'truth' determinations will require heavy computation, thereby be reliant on computer assistance. A lot (and this is measurable) will be resolved through human expertise, including educated intuition. The movement outward on the abstraction scale almost everywhere, which is about 300 years in development, has been fun yet it carried a whole lot of trouble with it, the evidence of which abounds around us (very densely, folks).

Remarks:

08/04/2012 -- We'll start our technical trek and look.

07/24/2012 -- Chompsky on the Magna Carta and our rights to Commons.

Modified: 08/04/2012