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Post by Paddy on Mar 30, 2009 23:11:25 GMT
Doesn't Maths. start with Axioms?
And aren't Axioms presumptions? I'd hate to be a theorem so, Sir.  Must be tough trying to get started with nowhere to start from.  'Twould never get anywhere!  Paddy |
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Post by postscript on Mar 31, 2009 9:09:38 GMT
Hi Graham. An old adage on the difference in thinking between exponents of the sciences and the arts! However, having spent some time as a NONscientist working with scientists, I know they do possess souls. Despite all their science (and I am thinking of medically-orientated scientists, which may make a difference) I have always been encouraged by the numbers that are convinced of life after death, for which belief there is no scientific explanation!
Peter S.
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Post by martindn on Mar 31, 2009 21:12:13 GMT
Hi Peter,
I should hope so too! As a scientist myself, once in my sixth form days described as a "cold hard scientist" by an arts student, only half in jest I think, I have some understanding of that percetion.
But scientists are still as human as anyone else, we just have to learn to separate our logic from our feelings. The scientific method is a powerful epistemology - the error some make is in believing it is the only one.
Martin
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Post by gra7890 on Apr 1, 2009 17:18:10 GMT
An old adage on the difference in thinking between exponents of the sciences and the arts! Hi Peter, Not exactly ..... although the Sciences use Maths there are important differences. Science either 1 ) observe a real life situation and then try and fit a Mathematical model to it. If it fits fine, if not they 'tweak' the model until it does fit. e.g Newton's laws work well ( but not perfectly ) for most situations. Then Einstein et al had to modify them for relativity etc. .... or 2) Use Maths to predict something then go look for it. e.g The recent 'big bang' experiment in Geneva. Hunting for a Mathematically predicted particle. At the risk of now annoying all the Sciences  their world is continually moving and the latest model will always need to be modified. Mathematics gives an exact solution to a problem but if the problem changes then the exact Mathematics will have to change to accommodate this. My point is that Maths is exact hence a rule is exact. ( Unless of course Maths is trying to predict a random event ..... e.g chaos theory ) Hope That makes sense Best Wishes, Graham |
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Post by gra7890 on Apr 1, 2009 17:53:55 GMT
I'd hate to be a theorem Must be tough trying to get started with nowhere to start Hi Paddy, It is not so tough really ! For advanced Theorems, like us , you build on other Theorems :2fun: And if in doubt look at a picture Best Wishes, Graham |
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Post by Paddy on Apr 1, 2009 20:27:27 GMT
I'd hate to be a theorem Must be tough trying to get started with nowhere to start Hi Paddy, It is not so tough really ! For advanced Theorems, like us , you build on other Theorems And if in doubt look at a picture Best Wishes, Graham Yes! We can count the squares ok!. Some people even colour them in.  But, if theorems are based on previous theorems, what about the very first theorem? Its proof must have depended on an Axiom or presumption, since it preceded all other theorems. Therefore, all further theorems (that depend on the first theorem) must also rely on presumption. So, since the first if may actually be unfounded, whatever Maths has 'proved' ( then) could still be either true or false. And we may never be able to tell which! Maybe we do know where we stand with Maths - nowhere at all.  No wonder Pythagoras turned to Music .... Paddy |
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Post by Paddy on Apr 1, 2009 20:47:57 GMT
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Post by gra7890 on Apr 1, 2009 22:43:08 GMT
Hi Paddy, Pythagoras did not ‘ turn’ to Music from Mathematics. Exactly the opposite in fact, he believed everything could be explained by numbers. Music was one of his main studies to this end. As it is the 1st of April I assume your other conjectures are ‘tongue in cheek’ or are you suggesting that two points cannot be joined by a straight line Graham |
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Post by Paddy on Apr 1, 2009 23:14:04 GMT
Hi Paddy, Pythagoras did not ‘ turn’ to Music from Mathematics. Exactly the opposite in fact, he believed everything could be explained by numbers. Music was one of his main studies to this end. As it is the 1st of April I assume your other conjectures are ‘tongue in cheek’ or are you suggesting that two points cannot be joined by a straight line Graham Hi Graham, I meant Pythagoras turned to Music for comfort every so often! Is there any such thing as a 'line' (or a point) - except in theory? Try drawing one and it will have thickness, so it's not really a line at all! So, how could we prove that no (insubstantial) point(s) on such a (non-existent) line were 'out of line'? If, but, maybe .... Paddy |
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Post by comet on Apr 2, 2009 8:44:40 GMT
 Cat Stevens had an album called Numbers - A Pythagorean Theory Tale in 1975. It didn't do very well in the charts, Maybe it was to abstract for it's time. It seems to be music for fun and is very light and playful to listen to. I had it as an LP since it's innitial release and was delighted to get it again on CD in 2001 a full 26 years later.
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Post by Jeff on Apr 2, 2009 9:19:21 GMT
Hello Paddy ! Its a shame some people get hung up about errors in others' punctuation !!  |
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Post by Paddy on Apr 2, 2009 10:21:19 GMT
Hello Paddy ! Its a shame some people get hung up about errors in others' punctuation !! Yes! Much ado about nothing! A little knowledge can be a dangerous (and hurtful) thing! Ironically, apostrophes were introduced (erroneously) into English only as recently as the 18th century. But, sadly, modern-day intolerance can take much more sinister forms: political bigotry, racial discrimination, religious intransigence, 'holier than thou' morality, personal intimidation, etc. ................ |
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Post by stevemacdonald on Apr 2, 2009 16:39:59 GMT
"The beginning of wisdom is to call things by their right names." -- Chinese proverb,
My peeve of the day is that some names are just too hard or tricky to pronounce, and yet people take offense or become excessively patronising if you get it wrong. That makes me want to mispronounce it all the more! Unfortunately, letters of the alphabet don't sound the same in every language. What the world needs is a universal phonetic spelling system that will eliminate confusion.
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Post by gra7890 on Apr 2, 2009 17:28:32 GMT
Hi Paddy, Ah.....….. now we are getting somewhere ! A point is a location in space. Points are dimensionless. That is, a point has no width, length, or height.. A pencil line is just a way to illustrate the idea on paper. You may specify a line by specifying any two points within the line. For any two points, only one line passes through both points. So yes what you say is true, BUT you are not dealing with a Mathematical line or point......as Mathematics has to be precise! So that brings us back to where we began i.postimg.cc/9fYxy370/smilie-big-grin.gif a Mathematical rule is always true, if there was a exception then it would not be a rule. Therefore to prove something it must be done in general e.g Proof by Induction. No amount of particular examples will prove it, as it could break down later. However it only takes one 'counter example' to disprove something and show a proposed ‘rule’ is not a rule !. I meant Pythagoras turned to Music for comfort every so often! I can appreciate that...... after all that is why we are here Best Wishes, Graham |
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Post by postscript on Apr 2, 2009 17:50:05 GMT
Hello Paddy ! Its a shame some people get hung up about errors in others' punctuation !! No Jeff, I do not agree. I earlier refrained from commenting as I could only riposte in a very strong manner which might well upset at least one Moderator! Instead, I have recently received an email which was a friend quoting from TheTimes , so I will copy that in here and challenge any Mod to think TheTimes language is in an y way unacceptable. "AN OBITUARY PRINTED IN THE LONDON TIMES. Interesting and sadly true. 'Today we mourn the passing of a beloved old friend, 'Common Sense', who has been with us for many years. No one knows for sure how old he was, since his birth records were long ago lost in bureaucratic red tape. He will be remembered as having cultivated such valuable lessons as: Knowing when to come in out of the rain; why the early bird gets the worm; Life isn't always fair; and maybe it was my fault. Common Sense lived by simple, sound financial policies (don't spend more than you can earn) and reliable strategies (adults, not children, are in charge). His health began to deteriorate rapidly when well-intentioned but overbearing regulations were set in place. Reports of a 6-year-old boy charged with sexual harassment for kissing a classmate; teens suspended from school for using mouth wash after lunch; and a teacher fired for reprimanding an unruly student, only worsened his condition. Common Sense lost ground when parents attacked teachers for doing the job that they themselves had failed to do in disciplining their unruly children. It declined even further when schools were required to get parental consent to administer sun lotion or an Aspirin to a student; but could not inform parents when a student became pregnant and wanted to have an abortion. Common Sense lost the will to live as the churches became businesses; and criminals received better treatment than their victims. Common Sense took a beating when you couldn't defend yourself from a burglar in your own home and the burglar could sue you for assault. Common Sense finally gave up the will to live, after a woman failed to realise that a steaming cup of coffee was hot. She spilled a little in her lap, and was promptly awarded a huge settlement. Common Sense was preceded in death, by his parents, Truth and Trust. His wife, Discretion, his daughter, Responsibility, his son, Reason. He is survived by his 4 stepbrothers; I Know My Rights; I Want It Now; Someone Else Is To Blame; I'm A Victim. Not many attended his funeral because so few realised he was gone. If you still remember him, pass this on. If not, join the majority and do nothing. " Peter S. |
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