tag:blogger.com,1999:blog-1219943390209086498.post7880772787546992199..comments2020-11-12T15:19:30.653+08:00Comments on A Shed Down Under: How Science Works II: The Prequel.John S. Jacobhttp://www.blogger.com/profile/07136673809517474111noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-1219943390209086498.post-3279072396757779902012-12-02T17:55:05.873+08:002012-12-02T17:55:05.873+08:00Hi John,
the point about Wittgenstein is that lang...Hi John,<br />the point about Wittgenstein is that language constrains thought, and in fact is a template for it. Not that he was paranoid. Only you control language in your own mind. How you control it to a large degree determines the way you think. That is one reason why "The Forbidden Experiment" is forbidden!<br /><br />Just as human languages are constructs, mathematics is also. Both are symbolic representations of reality. Your answer suggests that you intrinsically understand this, when you mention peering "beneath the syntax". Mathematics isn't the reality, mathematics is a representation of the reality, quite possibly a higher fidelity representation of reality than language, but none the less just a representation. (Where on the number line does the square root of -1 exist? Yet think of the utility of this little tool, this non-real representation!)<br /><br />My teaching experience suggests that we don't teach rigour in language because it is possible to have an imprecise understanding and get by. This is not the case in mathematics. I was startled by how many of my 80%+ year 11 physics students scored under 40% on the force concept inventory to assess their understanding of forces and motion. Close analysis showed that these guys had eaten up the maths in year 10, without much understanding of the physics. Multiple choice can help here - it is the only teaching and assessment tool that I have ever found which is up to the task of teaching nuance and discrimination between related concepts. Language, precise language, coupled to a deep understanding of the patterns of misconception formation in our kids, is needed to fix this. <br /><br />By the way, strongly disaggree with your comment <br /><i> is there empirically one instance of modern physics being advanced by work conducted in purely qualitative language without the aid of mathematics? Therefore I am forced to stand by my original statement. Qualitative language: usually (but not always) necessary; certainly not sufficient. Mathematics: always necessary for scientific advances; but arguably not sufficient </i><br /><br />Maths and language are both essential tools in the advancement of science. There are no advances which have occurred in the absence of language, and none in the absence of mathematics. Language and mathematics are intrinsic tools for quantitative sciences (but note that the language is intrinsic, and the word quantitative pulls in the mathematics)!<br /><br />One final point: people develop intellectually in a language influenced and language dominated environment. The fact that you can, at a certain advanced level of development dispense with the tools that got you to that advanced stage does not prove that those tools were unnecessary. Polylinguist assertions aside, no one knows whether high level thought without language is possible, because no one has ever tried it. I don't think they could, either.<br /><br /><br />Do have fun!<br />I don't think we think about this stuff nearly enough!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1219943390209086498.post-60586928115349354742012-11-05T09:00:14.815+08:002012-11-05T09:00:14.815+08:00Hey, Leon! Long time. How's it going? I thin...Hey, Leon! Long time. How's it going? I think we can now safely dismiss the paranoid ramblings of Wittgenstein, since in this the Information Age it is evident that no government, agency or private concern is even remotely capable of controlling language. No one controls language because everyone controls it. <br /><br />We have to differentiate between the qualitative languages and the quantitative language in one fundamental way: the qualitative languages are subjective creations of humans acting collectively. On the other hand, if you care to peer beneath the syntax and take in the underlying meaning of mathematics you will observe that it is not a human creation at all, but a discovery. Maths is the discovery of necessary and fundamental relationships between quantities, functions and conceptual objects.<br /><br />Your valid point about the necessity of qualitative languages as a means of thinking about things is true for all monolinguists, but not absolutely true. It is possible, as some polylinguists can attest, to think purely conceptually without words to guide or hinder. That is not to say that it is very common, however, and language remains for the majority the one means of thinking fluently about anything including science, philosophy, religion or, say, cosmetics. <br /><br />But more to the point about science and math: is there empirically one instance of modern physics being advanced by work conducted in purely qualitative language without the aid of mathematics? Therefore I am forced to stand by my original statement. Qualitative language: usually (but not always) necessary; certainly not sufficient. Mathematics: always necessary for scientific advances; but arguably not sufficient without that indefinable human inspiration that often leads us through as it were a darkened room in exactly the right direction.<br /><br />Another related point: human language is barely adequate for even discussing science. Most of the time we are reduced to using mere analogies and metaphors (and in a broader sense, every word we use was once just a metaphor of the idea that it points to). Schrödinger's Cat? No such thing is even remotely possible in reality. Einstein's Riding on a Beam of Light? Not physically possible at all. Therefore talking and arguing linguistically about these analogies does not lead to new science, only to confusion and crackpot ideas. Maths is the only way to actually progress science and is the ultimate, unavoidable way that people must access in order to understand science at a functional, contributive level.<br /><br />Fortunately, anyone can do maths. It isn't a closed, controlled language. Unfortunately, we do not typically teach it in that way and many people feel excluded from the "club." Human subjectivity and beliefs strike again whenever someone believes that they could never work mathematically. It is usually teachers that unwittingly communicate that unconscious belief, because they haven't woken up to it either. <br /><br />Most teachers (and I mean no disrespect to you, Leon) still try to teach maths as a distinct thing stripped of all meaning and context. This is ludicrous! People don't learn ANYTHING without context or meaning or a personal investment in the subject. The very few who seem to get on well with maths are those with a personal belief that it is somehow pleasurable. <br /><br />But everyone is interested in something, and if that something can be shown to benefit enormously from maths as a tool, then you literally couldn't PREVENT kids from snapping it up faster than you can teach it. John S. Jacobhttps://www.blogger.com/profile/07136673809517474111noreply@blogger.comtag:blogger.com,1999:blog-1219943390209086498.post-22147962295037756492012-11-04T17:47:41.973+08:002012-11-04T17:47:41.973+08:00I have to disagree with the statement that Mathema...I have to disagree with the statement that Mathematics is its only useful language - it is not.<br /><br />Language (english, or any other) allows you to chunk concepts together, and dramatically decrease the load on your short term working memory. This allows you to think about complex things. F=ma is next to useless without the chunking of concepts into "force", here represented by F (-> direction<br /> -> magnitude<br /> -> member of an opposing pair<br /> -> etc )<br /><br />Wittgensteins comment "he who controls language controls thought" rings true here, and throughout the history of science you can see how disciples open up and expand once the necessary language and conceptual tools become available. (Eg, Dawkins "selfish gene" concept/terminology).<br /><br />Only/One true way - that way of thinking about puzzles in science just limits your toolset.<br />My dremel is my favourite tool, but is by no means the only one I use to make stuff. I like my soldering iron too!<br /><br /><br />As always, keep up the good work. It is good to give people a bit of a prod, it gets them thinking.<br />Leon<br />Anonymousnoreply@blogger.com