What is Mathematics? - an addendum to the comments between Talbert and Maggot

GSTalbert1

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Your point? You're not actually claiming that that's mathematics and not merely mathematic grammar?

http://crookedtimber.org/2014/01/26/whats-the-math-made-of-ding-dong/


“Y’all’s fakes!”


If you’re impatient you can skip ahead to 3:20 or so. Tl;dw: the overly scientific Princess Bubblegum, having snuck into Wizard City dressed in wizard gear along with Finn and Jake, is buying a spell from a
head shop place that sells potions and spells and all that schwazaa. But she wants to know what the spell’s made of. “Magic?” Then she asks…read the post title. Then they get busted.
 

uberfukken

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Your point? You're not actually claiming that that's mathematics and not merely mathematic grammar?

http://crookedtimber.org/2014/01/26/whats-the-math-made-of-ding-dong/
That was an integral, written in a way that's difficult to read. The proper way to do it would be one straight line. Philosophy does that quite a bit, taking rudimentary ideas and infusing it with an elitist way of speaking to make it seem more deep and thought provoking than it actually is.

For example:

The word “philosophy” ought always to designate
lolok

 

GSTalbert1

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That was an integral, written in a way that's difficult to read. The proper way to do it would be one straight line. Philosophy does that quite a bit, taking rudimentary ideas and infusing it with an elitist way of speaking to make it seem more deep and thought provoking than it actually is.
No it does the reverse of this. The topics of philosophy always sound that way because it starts with taking an elitist way of speaking to make it seem more deep and thought provoking than it actually is and looking at the rudimentary ideas.
 

uberfukken

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No it does the reverse of this. The topics of philosophy always sound that way because it starts with taking an elitist way of speaking to make it seem more deep and thought provoking than it actually is and looking at the rudimentary ideas.
Looks more like mimicking if anything else.

The point is that mathematics is a tool. The only thing that philosophy has to do with it is that certain philosophers used it.
 

GSTalbert1

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Looks more like mimicking if anything else. The point is that mathematics is a tool.
Philosophy is the love of wisdom i.e. clarity.

The only thing that philosophy has to do with it is that certain philosophers used it.
Yes, precisely. Like John Searle devastating A.I. with his Chinese Room, like Hertz providing a philosophical shift in the "tool" as you speak of force, as in what is it we mean by force: the way we use "force", or Decartes and his coordinates. These are historical examples that by improving understanding of principles by which we construct our question, our hypothesis, before we even begin is more than helpful; clarity is a value in itself.
 

GSTalbert1

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Relevant Copypasta:
There's this weblog:
Alex the parrot’s last experiment shows his mathematical genius

but you can just as easily access the horse's mouth.
Further evidence for addition and numerical competence by a Grey parrot (Psittacus erithacus)
Abstract:
A Grey parrot (Psittacus erithacus), able to quantify sets of eight or fewer items (including heterogeneous subsets), to sum two sequentially presented sets of 0–6 items (up to 6), and to identify and serially order Arabic numerals (1–8), all by using English labels (Pepperberg in J Comp Psychol 108:36–44, 1994; J Comp Psychol 120:1–11, 2006a; J Comp Psychol 120:205–216, 2006b; Pepperberg and Carey submitted), was tested on addition of two Arabic numerals or three sequentially presented collections (e.g., of variously sized jelly beans or nuts). He was, without explicit training and in the absence of the previously viewed addends, asked, “How many total?” and required to answer with a vocal English number label. In a few trials on the Arabic numeral addition, he was also shown variously colored Arabic numerals while the addends were hidden and asked “What color number (is the) total?” Although his death precluded testing on all possible arrays, his accuracy was statistically significant and suggested addition abilities comparable with those of nonhuman primates.
There's some things to note on the capacity of the parrot to engage in meaningful mathematical communication -

Alex demonstrated some competence in summing two Arabic numerals, each representing quantities less than or equal to 5, to a total of 1–8, and three quantities of differently shaped and sized items of quantities less than or equal to 4 to a total of 1–6. In both studies, the numbers of correct trials requiring a response of a vocal numerical value reached statistical significance.

The paper makes a common error in assessing mathematics, at least in my opinion,

No pattern could be distinguished in his responses (correct or incorrect) to suggest his use of a particular mechanism. Conceivably, he may have used different mechanisms for the different tasks, or different mechanisms depending upon the numbers of items involved.

This is a strange way of putting it, how automatically there is that extra assumption that it is mathematics framed as the learned experience rather than merely it's communication. For instance take Skinner's box:




Can't we say too that these mice are doing "maths" as it were because clearly they are responding, with remarkable precision I must say, to what amounts to an environmental change that is at heart merely a complex mathematical regiment. You cannot say they do not know, in some fashion, "what's up" without resorting to some strange Cartesian dueling paradox in which there exists two different kinds of matter that have no relation to each other and yet they somehow interact.

At any rate, I believe that mathematics is merely the results of a philosophical inquiry into our senses, senses that are not possessed solely by any mere mathematician. There is often great confusion between the ways we investigate life and the proper way in which we communicate our results.

There are some points of note in the paper:


Introduction:
Many nonhuman species exhibit various forms of number related abilities (see citations and review in Beran 2011; Dehaene 2011), but only those trained to represent quantity symbolically with Arabic and/or vocal numerals (notably, apes and a Grey parrot) appear to exactly map such numerals to precise cardinal values of sets. Some apes and the parrot spontaneously transferred to novel arrays, demonstrated comparable levels of competence in comprehension and production, understood ordinality, and exhibited abilities extending well beyond levels possibly explained by non-exact strategies (e.g., subitizing, estimating, analog magnitude, or object file representations: Biro and Matsuzawa 2001; Boysen 1993; Boysen and Berntson 1989; Boysen and Hallberg 2000; Boysen et al. 1993; Matsuzawa 1985; Matsuzawa et al. 1991; Murofushi 1997; Pepperberg 1987, 1994, 2006a, b; Pepperberg and Gordon 2005; note Carey 2009). Interestingly, only two nonhumans—Boysen’s chimpanzee Sheba (Boysen and Berntson 1989) and the Grey parrot, Alex (Pepperberg 2006a)—could label the quantity of a summed set, an ability once thought to be uniquely human and based on language skills (Spelke and Tsivkin 2001). Sheba could sum arrays of 0–4 food items (to a total of 4) that were placed in two of three possible sites; Alex could sum arrays of 0–6 items of variously shaped and randomly sized food or nonfood items (to a total of 6) that were placed in two sites. In both cases, the nonhumans were asked about the sums when the addends were no longer visible; that is, they had to remember the separate addends, perform the summation, and then either touch (Sheba) or produce vocally (Alex) the label that represented the exact total quantity. Unlike other studies involving addition (or subtraction) of objects (e.g., review in Beran 2011; Rugani et al. 2009), neither Sheba nor Alex were making judgments based on relative quantity between or among sets, but rather were exactly mapping numerals to the cardinal value of the total number of objects present; their results were not subject to issues such as Weber’s Law (i.e., a discrimination between two quantities determined by the ratio of those quantities, not their absolute difference). Sheba, furthermore, transferred, without training, to summing the Arabic numerals themselves, a unique behavior among numerically trained nonhumans, and one demonstrating further knowledge of the representational
nature of the numerals. The present studies were designed to determine whether Alex could demonstrate similar levels of numerical competence. Success would demonstrate that such abilities are not limited to humans and nonhuman primates, but may also be available to other nonhuman, nonprimate, nonmammalian species with training in exact symbolic representation of number. Two experiments were thus initiated. One study tested whether Alex could duplicate Sheba’s ability to sum Arabic numerals: He was sequentially shown two Arabic numerals and, in their subsequent absence, was asked to vocally produce a label to indicate their sum. In a separate small set of trials, he was shown the same stimuli in the same manner, but was also presented with various Arabic numerals of different colors, and asked for the color of the numeral representing the sum; colors changed on each trial. The second set of trials ensured that Alex could not learn a particular pattern over time (e.g., ‘‘if I see X ? Y, I say Z’’); that is, had he lived longer, this procedure, with its additional step, would have allowed testing the same sums many more times without training him to produce a specific response, unlike tasks given other nonhuman subjects. A second study tested whether Alex could remember and sum sets of objects in three separate locations under the same constraints as had been in place for two locations (Pepperberg 2006a); that is, could he maintain numerical accuracy under what could be an additional memory load, in an experiment that required two updates in memory rather than one? Neither study was completed because of Alex’s premature death; however, preliminary data, consisting of first and rarely second trial results—and thus lacking any possibility of training—were statistically significant and suggest his ability to perform these more difficult tasks.

Discussion:
Alex demonstrated some competence in summing two Arabic numerals, each representing quantities less than or equal to 5, to a total of 1–8, and three quantities of differently shaped and sized items of quantities less than or equal to 4 to a total of 1–6. In both studies, the numbers of correct trials requiring a response of a vocal numerical value reached statistical significance. Although neither study contained enough trials to test all possible sums and combinations of addends or to repeat most queries, the Arabic numeral study contained at least one trial for each sum from 1 to 8, and the three-cup study contained at least one trial for each sum from 1 to 6. Alex made few errors overall. The lack of replication of the various sums over trials, however, emphasizes the first trial nature of the results and shows that no training could have been involved. Even the data for the few trials requiring him to respond with the color of the Arabic numeral representing the sum suggest a capacity for exact number representation. Conceivably, his one error, on the first trial, may have represented a misunderstanding of the task: He might have responded to the number of objects rather than their values, given that no training of any sort had preceded questioning on this novel task. Note, however, that he did not persist in this response but was correct when asked a second time and responded appropriately on the next two trials. Given that Alex died before finishing either experiment, that is, before being subject to complete sets of questions involving all possible types of sums, no pattern could be distinguished in his responses (correct or incorrect) to suggest his use of a particular mechanism. Conceivably, he may have used different mechanisms for the different tasks, or different mechanisms depending upon the numbers of items involved. Learning about the correct responses for a given array, however, can be discounted, given that almost all queries are first trial responses for each array. Also, given that all objects in the three-cup task were always of different shapes and sizes within and between trials, Alex’s responses were not likely to have had a nonnumerical basis (e.g., mass, contour, density, etc.). Clearly, just as for the chimpanzee Sheba, all of the addends in the three-cup task were within subitizing range (Pepperberg 2006a); thus, he could easily have tracked these without specifically counting. However, he, again like Sheba, still would have needed to remember the values under each of the three cups, for several seconds for each cup, and update his memory after seeing what was under each cup, even if nothing was present. In contrast to Sheba, however, the possible total sum tested reached 6. Possibly, Alex may have summed sets sequentially, rather than representing three addends separately before summing—that is, summed the first two, kept that sum in memory, then added the third, or, after seeing the first set,
‘‘counted up’’ for the next two (see Boysen and Berntson 1989). Such procedures are not unlike those used by children (Fuson 1988) and argue for somewhat different, but still advanced, number representations. In the first case, Alex would have had to retain numerical representations longer than if he were summing only two sets; that is, add the first two sets, update memory, then add the third and again update memory, all in *15 s. In the second case, he would have had to understand the number line—that each successive number denoted one more item than the previous number—a fairly complex notion (see Pepperberg and Carey, submitted). As discussed in Pepperberg (2006a), other mechanisms were possible but unlikely. For example, had Alex used a nonverbal accumulator, he would have had to visually partition and scan individual items in each addendum at a constant rate (an event for each pulse) and not reset his accumulator for the next addenda. The system is inherently inexact because of the variability in scanning sets of static items (i.e., the rate of pulses; see Mix et al. 2002); it produces errors normally distributed around the correct response and shows increasing errors with increasing set size, specifically above three; it would not provide the exact numerosities Alex’s task requires. Similarly, an object file represents number only implicitly (i.e., with no mental symbols for cardinal values per se). Mental models in working memory are created for small sets of individuals, with one symbol for each individual, and although these models also support computations of numerical equivalence and order, and addition and subtraction, based on 1-1 correspondence, the system cannot capture, even implicitly, any number beyond working memory limits (*4; see Carey 2009, Pepperberg 2006a).

In the Arabic numeral task, Alex, like Sheba, had had no training on summing the Arabic numerals, and, like Sheba, spontaneously transferred from summing items to summing symbols. He was significantly above chance on the task that asked him to produce vocally the label for the sum in the absence of any visible numeral. His data on the related task—although extremely limited—which was somewhat more like that of Sheba’s, in that possible responses were available from which to choose, tended toward significance. In contrast to Sheba, however, he had to indicate the label not just for the sum but for the color of the numeral that represented the correct numerical sum (an additional step), and the total summed quantity on which he was tested could reach 8. Specifically, despite the small number of trials, several aspects of the data support, although cannot prove, Alex’s competence. (1) Alex was not simply using his biggest number as a default response when sums were large. Interestingly, when he erred with two Arabic numerals whose sum was large (trial 9, using the numerals 5 and 3) his error was to state ‘‘seven’’, not ‘‘eight’’. (2) He proficiently summed the contents of all the cups, whether the sum involved specific objects or numerals that represented sets of objects. The only times he produced a label for only one of the addends in the three-cup task was when such a response was appropriate, that is, in trials when nothing was under the other cups. In the Arabic numeral task, the only time he made such an error was on the first trial of the color response task, which, as noted above, could have been a different type of error. Nor was he merely avoiding using the label of an addend as a response, as multiple other options were available. (3) If, in the Arabic numeral summation task, the numerals had only approximate meanings, Alex’s errors would likely have exhibited a range close to the correct response. In contrast, such was the case only once; his other two errors appeared to involve some fixation on responding ‘‘eight’’, even though trials were held weeks apart; thus, his data surpassed what would be expected if he were using the kinds of systems employed by most nonhumans or preverbal infants—for example, analog magnitude systems or object files, which cannot represent any positive integer above 4 exactly (see Carey 2009, for a review). In the three-cup task, his two errors occurred within the subitizing range, where he should have been exact. Interestingly, Shimomura and Kumada (2011) report increased errors for humans within the subitizing range when memory load is increased (as is the case in the threecup task), but possibly because of encoding errors and not from working spatial memory per se. Taken together, with previous studies on addition (Pepperberg 2006a), number comprehension (Pepperberg and Gordon 2005), and ordinality (Pepperberg 2006b), these data provide additional evidence that Alex likely understood the cardinal representation of his Arabic numerals, vocal and graphic; that his capacities with respect to addition were, like those of Sheba, spontaneously transferred from object sets to symbolic representations of the sets; and involved sums slightly beyond those of chimpanzees (e.g., Boysen and Berntson 1989). The reported data, despite involving only partial results, support previous studies on the number competence of a Grey parrot, suggesting that such abilities are not limited to humans and nonhuman primates but may also be available to other species that also have training in exact symbolic representation of number.

Sauce
 

Fingerdawg

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Math is that thing people always fail at and when they don't fail at it they are yelled at by faggots for being good at it while proving humanity really do have more than 2 brian cells
 

Barrabas

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Alright, I just finished the first post, so I can't even be bothered to read your fucking arguments for two pages.

First of all, there's something of the Kants Joke, as described by Nietzsche in the LOLGAYscience:
Kant’s joke. — Kant wanted to prove, in a way that would dumbfound the whole world, that the whole world was right: that was the secret joke of this soul. He wrote against the scholars in favor of popular prejudice, but for scholars and not for the people”
Not so directly, but more in the ironic sense of egalitarianism and, something like hope, I guess, that came through that. You start and end with mathematics, ultimately, I think anyway, trying to make the point that axioms, while used quite a bit in math, are not necessary, nor should they be included in the definition of something like "Pure Mathematics", or rather, you raise and at least stab at the question of "what is math ITSELF a priori"? Yeah, maybe not original, but it's a question worth bringing up.

In the middle though, this became less a critique on math, and more social commentary, which I found it rather shrewd of you to sneak in, mostly because it makes you seem like you're a nice guy.

I liked the Heidegger quote: "Everything functions". That's one to remember. But that part particularly interested me, because it went so far around the grid so fluidly, which is what I most enjoyed about it. It was neither the time nor place to mention it, but Ted Kasczinsky talks alot about this "function" of technology, as an independent entity, and it's at least interesting to note that he was an Ivy League educated mathematician. His prognosis wasn't good, although I've certainly read more optimistic opinions from others Ivy League mathers.

It's good that you question the value of technology though, because I think it's a very real problem, and if we end up proving the unibomber right, with his predictions of ever increasing indignities against humanity, we'd be throwing away Eden all over again.

Other highlights included the Meno dialogue. I always love when Socrates proves the guy is a moron.

I don't know if arguing is really necessary for me, since I believe you've framed this as your (well thought out, based on certain facts, and well articulated) opinion on a specific matter? I mean, at the least it certainly began with "What I find problematic about axioms...", so that's the way I read it anyway, but I ain't no big city pheelosopher like you dun find up at tha tharr Youu-nee-varseeetay.
 

GSTalbert1

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Ted Kasczinsky talks alot about this "function" of technology, as an independent entity.
Teddy's off his rocker. He's not stable.



But technique and science develop not in a vacuum but in human society, which consists of classes. The ruling class, the possessing class, controls technique and through it controls nature. Technique in itself cannot be called either militaristic or pacifistic. In a society in which the ruling class is militaristic, technique is in the service of militarism.

In the middle though, this became less a critique on math, and more social commentary, which I found it rather shrewd of you to sneak in, mostly because it makes you seem like you're a nice guy.
[/quote] A good part of math is social enterprise, that is to say math is political. If you're proof only convinces you, then it proves nothing. Take Sudoku or chess. Both are games that can be reduced to mathematical functions but you cannot perform calculus with chess. Both involve certain common faculties of the human condition in order to play; for instance a person can play chess blind. The next question begins with the nervous system.

Now...

'Porn Studies' Is a Serious Academic Journal for Serious Academics

LOL
But first, check out all the action at the journal's website. You can get unfettered access, not just to thumbnails but to full-length essays with titles like "Humanities and Social Scientific Research Methods in Porn Studies," "Positionality and Pornography," "Authenticity and Its Role Within Feminist Pornography," and my personal fave, "Deep Tags: Toward a Quantitative Analysis of Online Pornography." And if you prefer your quantitative analysis completely raw-dog, here's a link to a spreadsheet of the entire dataset from the study. Kinda freaky, but, ya know, some people are into that shit.
MUCH DETAIL:

Young women with crisp fake tans, long platinum blonde hair extensions, silicon breasts, and acrylic nails are fucking cocks that are artificially erect. They vocalize a performative sense of pleasure with moans and squeals as their male counterparts lead them through a formulaic equation of sexual positions that ‘opens’ the penetrative action up to the camera for the viewer's pleasure—not their own. This assemblage of ‘fast food’ pornographic sex continues until the female performer is instructed to ‘fake’ an orgasm and receive a load of hot cum on her face.
 

Barrabas

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I respectfully disagree with Trotsky on this one, and ask you to reconsider the stability of Ted. When I read Technological Slavery not too long ago, the thing I noticed was his lucidity, but also coupled with a very real fear. When you read his rationalizations for said fear, his research, understanding of the left, including his somewhat scathing review of the Anarcho-Primitivist movement, and correspondence with people in the philisophical fields, speaking for myself anyway, I couldn't help but feel somewhat "enlightened", or rather, "as though a scales had fallen from my eyes" after very seriously considering his positions, and hearing out his points.

After a couple of weeks of chewing on it, and sharing his very real fear (I have a bad habit of living in the philosophy of the person I'm reading at any given time), of course I was able to reassure myself that there are always alternatives, and I would say it can be argued he isn't being rational on this point perhaps, in his insistence of there being just one way (the total overthrow of technology) with which to solve the problem, but the problems he indicates, and the visible manifestations of his observations in the digital age we live in today are rather alarming.

If TK is insane, it is only in his ultra-rationality. Like I said, the fear is very real, and I feel valid, whether or not his reactionary prescriptions are the only remedies being a moot point.

And I never figured you would throw Marxism at me; I'd be surprised, if I was surprised.

But you say there will be a "next question", and there's never a next question! You just go into Porn Studies, which of course is a thing, because it's fucking errwhere, and a huge part of our social culture. Frankly, I had just figured shit like this would get lumped into a specialized psychology degree, but this is funny, because when I watch porn, I ruin it alot by thinking about this same shit, and instead of fapping, I find myself absorbed in the camera angles, and judging the acting and chemistry between the two stars. Why X is attractive, and Y is distasteful? What the fuck is the obsession with the underneath shot where I'm just watching a dick smash a vagina, like an animated GIF for like 10 minutes without a break in the shot? What sort of person would want to watch this? Is it an older generation thing? What is the mindset of a person who likes Z? Stuff like that, sort of ruins the good time. It's rather depressing when I write it all down like that, actually.

This, of course is the natural evolution of this topic, it's wordy intro, the subsequent arguments with Maggot, the outrage of the plebs, and then my own reaction. We went from Platonic Forms, to HXC Porn in three pages. Sounds about right for EDF. If anything it should have happened sooner.
 

Barrabas

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Oh, and so far as Math being political, I read something by Hannah Arendt awhile back, and fuck all if I can remember what it was, but Imma see if I can find it, because it was about the nature of what constitutes a "political action", and it was good, and apt to this conversation.
 

Barrabas

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Between Past and Future said:
Marx, when he leaped from philosophy into politics, carried the theories of dialectics into action, making political action more theoretical, more dependent upon what we today would call an ideology, than it ever had been before.
The whole of the quote can be found in section 1, here. But the treatsie itself is a good critique of the modern position of philosophy itself, as viewed through the works of Marx, Kierkegaard, and Nietzsche, explaining how each of these philosophers broke long-standing traditions of philosophy in order to advance philosophy-- i.e, Marx taking philisophical thought, and jumping into the political arena with it, which had been rather a no-no until this time.
Moar said:
OUR tradition of political thought had its definite beginning in the teachings of Plato and Aristotle. I believe it came to a no less definite end in the theories of Karl Marx. The beginning was made when, in The Republic's allegory of the cave, Plato described the sphere of human affairs all that belongs to the living together of men in a common world in terms of darkness, confusion, and deception which those aspiring to true being must turn away from and. abandon if they want to discover the clear sky of eternal ideas. The end came with Marx's declaration that philosophy and its truth are located not outside the affairs of men and their common world but precisely in them, and can be "realized"
only in the sphere of living together, which he called "society,"through the emergence of "socialized men" (yergesellschaftete Menscheri). Political philosophy necessarily implies the attitude of the philosopher toward politics; its tradition began with the philosopher's turning away from politics and then returning in order to impose Ms standards on human affairs. The end came when a philosopher turned away from philosophy so as to "realize" it in politics. This was Marx's attempt, expressed first in his decision (in itself philosophical) to abjure philosophy, and second in Ms intention to "change the world" and thereby the philosophizing minds, the "consciousness" of men.
Regarding traditions/axioms though:

moar said:
Kierkegaard, Marx, and Nietzsche are for us like guideposts to a past which has lost its authority. They were the first who dared to think without the guidance of any authority whatsoever; yet, for better and worse, they were still held by the categorical framework of the great tradition. In some respects we are better off. We need no longer be concerned with their scorn for the "educated philistines," who all through the nineteenth century tried to make up for the loss of authentic authority with a spurious glorification of culture. To most people today this culture looks like a field of ruins which, far from being able to claim any authority, can hardly command their interest. This fact may be deplorable, but implicit in it is the great chance to look upon the past with eyes undistracted by any tradition, with a directness which has disappeared
Tradition and the Modern Age from Occidental reading and hearing ever since Roman civilization submitted to the authority of Greek thought.
I think this fits rather well in your discussion of axioms, and does a bit to defend the position you've taken.
 

GSTalbert1

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I respectfully disagree with Trotsky on this one
You are disagreeing with the fact that the effect of technology, as in science, is autonomous in regards to who designed it and what it is designed for? Math can never give you a blueprint for a Boeing 747.


and ask you to reconsider the stability of Ted. When I read Technological Slavery not too long ago, the thing I noticed was his lucidity, but also coupled with a very real fear. When you read his rationalizations for said fear, his research, understanding of the left, including his somewhat scathing review of the Anarcho-Primitivist movement, and correspondence with people in the philisophical fields, speaking for myself anyway, I couldn't help but feel somewhat "enlightened", or rather, "as though a scales had fallen from my eyes" after very seriously considering his positions, and hearing out his points.
Ted uses various systems of logic depending on what he's talking about. The reason why his logic seems so very ration is because he is extremely passionate. He feels a certain way about a situation and then he ad hoc rationalizes his feelings. At one point he's spouting 1950s political justifications for methodological individualism, all of which generally posit strong positivist inclinations. He then completely abandons this line of thinking when speaking about "leftists" and then takes up strains of thought from 18th century eurpoean imperialist historical propaganda. He then drops both these concepts to muddle his way to an extreme form of anarchic collectivism towards mutual suicide. There's logic only in context within a very shattered system.

The concern over the effect of technology on the stability of society is by no means a new line of thought:

Leo Strauss said:
If we seek, therefore, for the origins of political science, we merely have to identifiy the first man not engaged in political activity who attempted to speak about the best regime. His name was Hippodamus from Miletus. Hippodamus’s best regime had three chief characteristics. His citizen body consisted of three parts, the artisans, the farmers, and the fighters. The land belonging to the city consisted of three parts, the sacred, the common, and everyone’s own. The laws too consisted only of three parts, laws regarding outrage, laws regarding damage, and laws regarding homicide. The scheme is distinguished by its apparent simplicity and clarity. But, as Aristotle observes, after having considered it, it involves much confusion. The confusion is caused by the desire for the utmost clarity and simplicity. Outstanding among the particulars which Hippodamus suggested is his proposal that those who invent something beneficial for the city should receive honors from that city. When examining this proposal, Aristotle brings out the fact that Hippodamus hadn’t given thought to the tension between political stability and technological change. We suspect the existence of a connection between Hippodamus’s unbridled concern with clarity and simplicity and his unbridled concern with technological progress. His proposal as a whole seems to lead not only to confusion but to permanent confusion, or permanent revolution. The unusual strangeness of the thought induces Aristotle to give an unusually extensive account of the man who had fathered it. I quote, “He also invented the division of the cities into planned parts and he cut up the harbor of Athens. In his other activity too he was led by ambition to be somewhat eccentric so that some thought he lived in too overdone a way. He attracted attention by the quantity and expensive clothes which he wore not only in winter but in summer periods as well. And he wished to be known as learned in giving an account of nature as a whole.” It looks as if a peculiar account of nature as a whole, an account which used the number three as the key to all things, enabled or compelled Hippodamus to build on it his triadic plan of the best city. It looks as if Hippodamus had applied a formula elaborated in a mathematical physics to political things in the hope to achieve the utmost clarity and simplicity. But in fact he arrives at utter confusion since he has not paid attention to the specific character of political things. He did not see that political things are in a class by themselves.
 
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