Sunday, August 28, 2011

Math error in news: divorce rates

I heard an egregious math error the other day on NPR (from the morning of Friday, August 26. The story was about divorce statistics in the United States, regional differences, and changes over time.

The statement in questions was worded something like this:
The South has one of the highest rates of divorce in the country. One reason is that it has more marriages than elsewhere.
Sounds plausible right? Only if you redifine the concepts of what you are hearing. This is an egregious type mismatch of a rate to a number. a rate is the ratio of the subset to the whole (whatever the whole is), and a number is..well... it's just the count with no division going on. The rate is presumably the number of divorces per capita (entire population of the region).

The statement, as is, is inferring a number (more marriages) from a rate (higher divorce rate).



So maybe you have a large number of divorces and that can be because here is a large number of marriages (which may or may not be because of a large number of people). That is a reasonable inference to make.  

Or you might have a large marriage rate leading to a large marriage number in the region and (assuming people tend to get married within a region) this could lead to a large number of divorces in the region, and so immediately a large divorce rate.

But note this is all relative. A region could have a large divorce rate but small number of marriages or divorces. (or contrapositively, a lower -number- of marriages and high divorce -rate-). Much too unspoken is the relevant contexts for ratios and number comparison.

I don't think this is shoddy math exactly just shoddy use of language (which arguably -is- shoddy mathematics).

First, disclaimers: this is a paraphrase from memory, and I cannot find a transcript to corroborate my hearing.

Comments on Tractatus: 1 The world is everything that is the case

1 The world is everything that is the case.
Right off the bat he starts off with an empty tautology. Is 'empty tautology' an empty tautology? No, a tautology is a statement that is true under all interpretations. Something is empty when there is nothing instructive to be gained. This is collegiate late-night study-avoiding intellectual bullshit (I remember it well!). In my high school yearbook, we had to give a quote next to our picture (something pithy and meaningful, "If you love something, set it free,...") One guy just said 'Everything is'. That's it. Genius. A you-can-all-go-to-hell slap in the face, Anyway, W is being serious here. Wanker.

1.1 The world is the totality of facts, not of things.
OK...Come on. Really?

I'll bite. So he's in some sense redefining what you want people to think of as 'the world', 'facts, and 'things'. He's trying to pull the shades down (oops, I mean 'up' :) ) and show you that you're wrong to think of the world as sense objects (what I understand he means by 'things') and it is correct to think of it as statements. Almost Platonic. He's being kind of arrogant, and by 'kind of' I mean 'totally'. Anyway, why couldn't he just say 'let's talk about items of knowledge as opposed to sense objects'?

1.11 The world is determined by the facts, and by these being all the facts.
More stipulation then. He's defining 'world' to be a set of knowledge rather than, well, we've already forgot about all those other things.


1.12 For the totality of facts determines both what is the case, and also all that is not the case.
'Determine' is just a fancy way of saying 'let's think of them as'. Considering the negation, as being specified at all, is clever and Taoist, but is just encouraging us to being perceptive of form and ground, that's all.

If one can take this as substantive, W is presenting in a sideways manner the ideas of correctness and completeness, that what we are talking about is propositions ('facts') and that 'the world' )a domain of discourse) is a set of propositions, and that set is complete (everything about the world is said in those facts -and- anything -not- in that set is -not- true of that world), something that would be said nowadays as sort of a closed world assumption: for a given world, there is no more and no less what is stated in a set of 'facts'.


1.13 The facts in logical space are the world.

Kind of empty repetition of the previous.

1.2 The world divides into facts.
Kind of empty repetition of the previous. Or could be taken to be a deep deep principle of mathematics that 'is' is not a symmetric in English, that one must state (if not show) both directions the world is made up facts and (the other direction) nothing else. Or it could be bullshit.

1.21 Any one can either be the case or not be the case, and everything else remain the same.

I have little to say here (!!) other than this is pretty empty, that is, he is saying things that we already know. Is a statement of obvious simplicity ('the king has no clothes!') interesting or useful? Sometimes yes. Here it is hard to see.

Or is this just an expression of there's no middle between true and false?

This set of propositions (is that what these are, or are they recursively self-defining 'facts'?) is pretty sparse, but intended to introduce. Was this outline produced linearly or refined as needed? Of course both, but section this looks like a quick start to get the rest.


Now a comment on commenting. Obviously, I have something against Wittgenstein here. It could easily turn out to be the kind of sophomoric disdain one has for elementary knowledge that wasn't once so elementary. Fine. Revolutionary in his time (he made possible/motivated/kick started/inspired the school of logical positivism/the Vienna circle?), but boring now?

Wednesday, August 10, 2011

Comments on Mythical Man-Month: Chapter 7


Chapter 7. Why Did the Tower of Babel Fail?
(cursory comments here, there is hardly any discussion to be made  because it is too easily true; needs to be said, but I can't really add anything).
7.1 The Tower of Babel project failed because of lack of communication and of its consequent, organization.
This is the same as noting the benefits of standards. There's having a standards, and making sure everyone uses the standard, 
Communication
7.2 ''Schedule disaster, functional misfit, and system bugs all arise because the left hand doesn't know what the right hand is doing." Teams drift apart in assumptions.
Pretty obvious.
7.3 Teams should communicate with one another in as many ways as possible: informally, by regular project meetings with technical briefings, and via a shared formal project workbook. (And by electronic mail.)
By documentation? yes, it is all needed but has the same difficulty as any documentation in that it is hard to make it follow reality once written down.
Project Workbook
This is an entirely new concept to me, but is very easily implemented using a wiki nowadays.
7.4 A project workbook is ''not so much a separate document as it is a structure imposed on the documents that the project will be producing anyway."
-
7.5 ''All the documents of the project need to be part of this (workbook) structure."
-
7.6 The workbook structure needs to be designed carefully and early.
designed how?
7.7 Properly structuring the on-going documentation from the beginning ''molds later writing into segments that fit into that structure'' and will improve the product manuals.
Document early? I guess really one should document continuously and this is just a reminder not to put it off until afterwards.
7.8 ''Each team member should see all the (workbook) mate- rial's (I would now say, each team member should be able to see all of it. That is, World-Wide Web pages would suffice.)
This device (workbook) still needs behavioral 'technoloy', people should be encouraged to use a wiki in this manner.

7.9 Timely updating is of critical importance.
duh?
7.10 The user needs to have attention especially drawn to changes since his last reading, with remarks on their significance.
Current wiki technology (MediaWiki) enable comparing, but it is of questionable facility (ain't so easy to use).
7.11 The OS/360 Project workbook started with paper and switched to microfiche.
Good for them. I remember when we had to use the chits thrown away by card readers. And no pen, just a stick and excess oil from the sides of the printer housing.

7.12 Today (even in 1975), the shared electronic notebook is a much better, cheaper, and simpler mechanism for achieving all these goals.
yes.
7.13 One still has to mark the text with (the functional equivalent of) change bars and revision dates. One still needs a LIFO electronic change summary.
The current implementation of good behavior, a version control system, takes care of this.

7.14 Parnas argues strongly that the goal of everyone seeing everything is totally wrong; parts should be encapsulated so that no one needs to or is allowed to see the internals of any parts other than his own, but should see only the interfaces.
Without reference to the next item, I find this total encapsulation questionable. Yes, data hiding is good at every level, reducing the unnecessary expense of mental energy. But seeing what is available and how other things look is a good way to learn design too.
7.15 Parnas's proposal is a recipe for disaster. (I have been quite convinced otherwise by Parnas, and totally changed my mind.)
Parnas's view has been totally vindicated by the open source movement. But Brooks brings up an interesting contradiction, that of data-hiding as a laudable goal. I'm not sure how to reconcile the two. Maybe it is that for unit construction purposes, making large knowledge necessary is undesirable, but for finding the tools you need (without knowing exact details), seeing the larger catalog is better.

Organization
7.16 The purpose of organization is to reduce the amount of communication and coordination necessary.
Just like in -programs!-
7.17 Organization embodies division of labor and specialization of function in order to obviate communication.
Just like in -programs!- 
7.18 The conventional tree organization reflects the authority structure principle that no person can serve two masters.
Reduces communication and trust complexity (trust complexity is how many varieties of similar but conflicting messages one gets. Yes, I just made that up.
7.19 The communication structure in an organization is a network, not a tree, so all kinds of special organization mechanisms ("dotted lines") have to be devised to overcome the communication deficiencies of the tree-structured organization.
Right. A single tree is too simplified for humans. More than one tree, or a network is better. But not haphazard.

7.20 Every subproject has two leadership roles to be filled, that of the producer and that of the technical director, or architect. The functions of the two roles are quite distinct and require different talents.
The difference needs to be explained better. A producer is... and an architect is...

Really, I thought he was going to say a technical architect and a human resource type manager.
7.21 Any of three relationships among the two roles can be quite effective:
. The producer and director can be the same.
. The producer may be boss, and the director the producer's right-hand person.
. The director may be boss, and the producer the director's right-hand person.
I think this is too localized to his situation. Interpersonal conflicts and connections may make this a good fit or a bad one. This is too losely judgable by scoial engineering experiments.

Comments on Tractatus: 2 What is the case, the fact, is the existence of atomic facts.


(As things get longer, I won't comment on everything, I'll just quote those things I comment on)

2 What is the case, the fact, is the existence of atomic facts.
Twelve words to say "let's dance around defining 'atomic'". -Atomic- facts? Are these facts that are unanalyzable/unsplittable? Prime facts?...Isn'tthat just axiomatics? Did Euclid (and Eudoxus etc) figure do that taxonomy already?

2.01 An atomic fact is a combination of objects (entities, things).
I guess the answer would be 'no' to previous. That is, 'atomic' means um...not atomic.A combination is not atomic right, because you can split it into constituents.

2.011 It is essential to a thing that it can be a constituent part of an atomic fact.
Wow. Not my particular definition of 'atomic'. I'd hope that something called 'atomic' would not have parts at all.

...hm...mea culpa. Sadly, in reading a classic text about philosophy of language, and in philosophy where defining terms and playing with their vagueness and amphiboly is most of the activity, I failed to consult the original text and alternate translations. The original term is
Sachverhalten
which is translated by Ogden as 'atomic facts'. Not having facility with German, I can only consult dictionaries and see that this is usually translated by just plain 'facts'. Pears' translation uses 'states of affairs'. So any failings of the text ascribed to the use of the term 'atomic' where it is irrelevant, misleading, and/or wrong, I blame these on Ogden. I don't have any idea what the connotations of 'Sachverhalten' are in distinction to the other 'fact' word, namely 'Tatsachen'.

What this says to me is that depending on translations, is like depending on ones native understanding of connotations of particular words, and can therefore be terribly misleading. If you are taking the course of the narrative based on unspoken definitions of the language being used then it will be terribly misleading. And unfortunately this is exactly what most philosophers do, extrapolate on unspecified connotations, which are inherently language and culture specific.

So, two meta comments...in the rest of this commenting, I will try to translate in my head 'atomic facts' to 'states of affairs' with some sort of internal meaning attached to 'Sachverhalten'. Also, I withdraw my above comments I stand on 2.01 and 2.011, but 2 stands. These points are self-explorations mutually defining statements about 'Fall' (a 'case'),  'a fact') and 'Sachverhalten' ('states of affairs'). Hilbert famously remarked that

"One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs".

and this is exactly the Wittgensteinian 'use implies meaning' thesis. But where does W give that thesis? Here in TLP somewhere? Later in PI? Created out of thin air by commentators? Something in between?

2.012 In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing.
So before this statement, W and the translations were unwittingly -showing- what is the case, but now he is telling us...but badly.

This statement is pure philosophy, in that it is an analysis of how analysis happens.

The rest is a bit of 'meaning' play trying to tease out what exactly a 'fact' should be.  Given the above difficulty with the pivotal term 'atomic fact', consider it to be uninterpretable, unanalyzable (but not indivisible, that is something else) and that its use is telling you how it..well, how it is to be used.

2.0121 It would, so to speak, appear as an accident, when to a thing that could exist alone on its own account, subsequently a state of affairs could be made to fit. If things can occur in atomic facts, this possibility must already lie in them.
(A logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.) Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connexion with other things.

... (lots of stuff (that I don't care to comment on) omitted)...
2.0232 Roughly speaking: objects are colourless.
This just comes out of nowhere. Totally irrelevant to everything else and doesn't 'do' anything. Nonsense in the Edward Lear/Lewis Carrol sense.  

...
2.063 The total reality is the world.
Summary: let's talk about 'facts'.
2.1 We make to ourselves pictures of facts.
The rest of this section is an enforced slippage in meaning of 'picture' from whatever you think it is to 'metaphor'. As to the original German, I can't really say.

2.21 The picture agrees with reality or not; it is right or wrong, true or false. 
2.22 The picture represents what it represents, independently of its truth or falsehood, through the form of representation.
'Everything is'
2.221 What the picture represents is its sense.
This actually comes close to saying something. And then falls away into nothingness.
2.223 In order to discover whether the picture is true or false we must compare it with reality.
This says something. A 'picture' (whatever it really is supposed to mean) is not reality, but representing reality. I'd go further with what I think he should be getting at ("a picture is an attempt to represent reality, a theory, whose correctness depends on comparison with data..." but that has the latter-day benefit of 100 years of further exploration). But he dosen't go in that direction. He just adds further emptiness.
2.224 It cannot be discovered from the picture alone whether it is true or false.
Maybe he is going that way. Anyway, it stops here.
2.225 There is no picture which is a priori true.
I barely understand what 'a priori' means outside of this, so I certainly don't know what he means here. So i he saying that a 'picture' is a -representation- of a statement that can be either true or false and that a picture isn't necessarily one or the other, but must be checked? (against what? 'reality'? but then a 'picture' is an experimental hypothesis? I find it hard to believe this is where he's going with this.)

Monday, August 8, 2011

Comments on the Tractatus: Intro and Preface and quick general observations

I'll begin here with comments on the motto and Russell's introduction.

Motto: . . . und alles, was man weiss, nich bloss rauschen und brausen gehört hat, lässt sich in drei Worten sagen. 

To translate loosely, "pretty much everything can be explained in three words". A justification of aphorisms and the style of the book, which is certainly written aphoristically. As long as the words are chosen well, I think this is a good thing in general...too many words, too much explanation, is often just too much. But also sometimes philosophers tend to use words...extrapolatively. Yes, there is a dictionary definition, and common unspoken connotations, but these are then metaphorized beyond comon limits. As long as they stay on this side of line of incoherence, it works (take any work with 'Being' in the title, they're getting pretty close) with a lot of leeway.


I won't do interlinear on Russell's intro, just selections:
What is meant is somewhat less complicated than it sounds.

This is purely in reference to W's mathematical symbolism.
... a good notation has a subtlety and suggestiveness which at times make it seem almost like a live teacher
A classic statement by Russell, of which I had never thought that this is where it would have appeared.As prefacing TLP, It is preceded by "Wittgenstein’s fundamental thesis that it is impossible to say anything about the world as a whole." and that this may have been suggested by notation. This leap seems pretty far to me so I can only guess that what Russel means is that a notation is a purposeful limitation, instead of trying to say things about the world, just say them about something very small and particular (maybe that's just me saying that about notation). I think this is the major benefit of mathematical language (and further this 'notation'). It is what makes mathematical language the goal for philosophical language, precise and limited.

There are some respects, in which, as it seems to me, Mr Wittgenstein’s theory stands in need of greater technical development
I think Russell is being polite here, -very- polite, a back-handed compliment, damning with faint...no, it's not even praise. I read it as, from the perspective someone who had completed a three volume master opus of an attempt to develop all mathematics from a few logical principles, that he doesn't want to be the giant squashing a bug. So in a sense, he's holding back quite a bit.

What causes hesitation is the fact that, after all, Mr Wittgenstein manages to say a good deal about what cannot be said...
Exactly. W's manner here is 'sober', serious, sometimes metaphorical, but never cynical, and not mercurial. So when W says in his own preface, you will understand his book when you consider it nonsense, he really -means- that rather than trying to be clever. W may mean it, but it is not necessarily the case (I find that TLP is -full- of extrinsic meaning and that W is giving a contrary message from outside the work).

...to have constructed a theory of logic which is not at any point obviously wrong is to have achieved a work of extraordinary difficulty and importance. This merit, in my opinion, belongs to Mr Wittgenstein’s book, and makes it one which no serious philosopher can afford to neglect.
"not at any point obviously wrong"...this is another 'read-between-the-lines'...Russell is trying very hard not to say anything negative. It's almost of the level of 'fills a well-needed gap in the literature', or 'the text was well-formatted with undeniable taste in choice of font'.


Now for W's preface.
How far my efforts agree with those of other philosophers I will not
decide. Indeed what I have here written makes no claim to novelty in
points of detail; and therefore I give no sources, because it is indifferent
to me whether what I have thought has already been thought before me
by another.
What this says to me is that he doesn't bother with distinguishing original thought and repeating what he's heard elsewhere. To me this is consistent with the knowledge that most of his sections 5 and 6 were well established mathematical logic at the time of his writing...

I will only mention that to the great works of Frege and the writings
of my friend Bertrand Russell I owe in large measure the stimulation of
my thoughts.
 ...and what good he got out of mathematical logic he got from Frege and Russell (the machinery of truth-functions) and anything else is a poor, mangled presentation by W of what others laid out before him.

Other statements in the intro are bizarrely immodest ("This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it—or similar thoughts.", "I am, therefore, of the opinion that the problems have in essentials been finally solved")


As to the general form of the book though, I am particularly fond, the ever expanding outline, the analytic tree, the commentary, elucidation, step by step as opposed the weaving self overlapping narrratives common in most humanities. Though it is an attempt at having the form of systematicity (like the obvious example of Spinoza), whether it is even close to success there, the attempt is what matters. I say systematization because, in disagreement with most commenters, it is not an attempt to be Euclidean, like Spinoza, in a statement-proof-statement-proof manner, but rather it is simply an outline, where shorter numbered items are explained further by numbers with suffixes. To be topical however, I suppose I should mention that this has affinities with bullet point mania in Powerpoint slide decks. I think it works well here; a narrative would be as boring as...ahem...Kant.


Comments on Tractatus-Philosophicus

You read things and you want to vent about it. Wittgenstein has been on my bedside table forever (which means for me that I totally ignore it). But every so often I'll pick up something or read online. So I'm going to do another interlinear comment stream on a classic, Wittgenstein's Tractatus. I am not a scholar of philosophy, but I am interested, have read naively a fair amount, and have lot's of comments that have built up over the years.

My main online source is:

   http://www.kfs.org/~jonathan/witt/tlph.html

a hypertext version with original German, and the Ogden English translation, and Russell's introduction.

Other sources are:

   the PDF of side-by-side German and two English translations

So coming soon are my interlinear comments plus some thematic comments.

Wednesday, August 3, 2011

Metaphors in Software Engineering

Deploying web applications

- like doing open heart surgery on someone in the swimming stage of a triathlon

Fixing bugs

- like trying to open a locked door, with no keyhole or handle, the sign says 'push' but