Comments for musings on interesting ideas http://treepax.com/blog postings about idea generation, how we block our thinking and innovation Fri, 05 Dec 2008 02:58:34 +0000 http://wordpress.org/?v=2.3.1 Comment on Simultanity and Sequency by Ian Moore http://treepax.com/blog/2007/11/28/simultanity-and-sequency/#comment-17 Ian Moore Fri, 30 Nov 2007 11:32:09 +0000 http://treepax.com/blog/2007/11/28/simultanity-and-sequency/#comment-17 The number of fingers trick is a classic "fences and gateposts" problem. Which are you counting - the things themselves (the gateposts) or the things in between them (the fences)? Obviously when you are counting down on one hand you arrive at the 6th finger. You have not counted fingers but the number of the finger. Not sure if this relates to Xeno's paradox at all actually. Xeno's paradox is "wrong" because he assumes that an infinite number of finite things must be finite. If you think if the series: 1 + 1/2 + 1/4 + 1/8 + ..... given an infinite numbers of terms this is = 2 (or more precisely "as the number of terms tends to infinity the sum of the terms tends to 2). Whereas the series: 1 + 1/2 + 1/3 + 1/4 ....... constantly increases as the number of terms increases (i.e. the sum is infinity when the number of terms is infinite). So going back to Xeno's paradox - just because there are an infinite nuber of (finite) time periods this does not mean that the sum of them is infinite. There is another problem with Xeno's paradox becuase it assumes that you can keep dividing the distance by a half. It assumes that their is no indivisible unit of distance! The number of fingers trick is a classic “fences and gateposts” problem. Which are you counting - the things themselves (the gateposts) or the things in between them (the fences)? Obviously when you are counting down on one hand you arrive at the 6th finger. You have not counted fingers but the number of the finger.

Not sure if this relates to Xeno’s paradox at all actually.

Xeno’s paradox is “wrong” because he assumes that an infinite number of finite things must be finite. If you think if the series:

1 + 1/2 + 1/4 + 1/8 + …..

given an infinite numbers of terms this is = 2 (or more precisely “as the number of terms tends to infinity the sum of the terms tends to 2).

Whereas the series:

1 + 1/2 + 1/3 + 1/4 …….

constantly increases as the number of terms increases (i.e. the sum is infinity when the number of terms is infinite).

So going back to Xeno’s paradox - just because there are an infinite nuber of (finite) time periods this does not mean that the sum of them is infinite.

There is another problem with Xeno’s paradox becuase it assumes that you can keep dividing the distance by a half. It assumes that their is no indivisible unit of distance!

]]> Comment on Simultanity and Sequency by graeme http://treepax.com/blog/2007/11/28/simultanity-and-sequency/#comment-16 graeme Wed, 28 Nov 2007 13:45:08 +0000 http://treepax.com/blog/2007/11/28/simultanity-and-sequency/#comment-16 Re Xeno's paradox. I remember encountering a similar problem (given to me by my elder sister) when I was a child, concerning the number of fingers I had! Counting backwards from 10, starting with my right hand, I counted 10...9...8...7...6 and I then added the 5 fingers I was sure I had on my left hand. As 6 + 5 = 11, (and I said as much!), my sister required an explanation of the discrepancy. Now I'm not sure of this (!?) but doesn't the explanation lie in the direction of travel (i.e. my starting point) and wouldn't this explain the Xeno paradox too? Re Xeno’s paradox. I remember encountering a similar problem (given to me by my elder sister) when I was a child, concerning the number of fingers I had! Counting backwards from 10, starting with my right hand, I counted 10…9…8…7…6 and I then added the 5 fingers I was sure I had on my left hand. As 6 + 5 = 11, (and I said as much!), my sister required an explanation of the discrepancy.

Now I’m not sure of this (!?) but doesn’t the explanation lie in the direction of travel (i.e. my starting point) and wouldn’t this explain the Xeno paradox too?

]]> Comment on one red paperclip by graeme http://treepax.com/blog/2007/11/22/one-red-paperclip/#comment-13 graeme Fri, 23 Nov 2007 15:41:16 +0000 http://treepax.com/blog/2007/11/22/one-red-paperclip/#comment-13 This is a perfect illustration of the economists' 'Buyer Utility'. From the classic demand and supply graph, the market (clearance) price is found where he demand curve intersects the supply curve - but remember, before reaching the intersection (left side of the demand curve), many people are prepared to pay more than the market price because they get more utility i.e. its more valuable to them than the asking price. This is a perfect illustration of the economists’ ‘Buyer Utility’.

From the classic demand and supply graph, the market (clearance) price is found where he demand curve intersects the supply curve - but remember, before reaching the intersection (left side of the demand curve), many people are prepared to pay more than the market price because they get more utility i.e. its more valuable to them than the asking price.

]]> Comment on Nouns and verbs by ian-contributor http://treepax.com/blog/2007/11/14/nouns-and-verbs/#comment-7 ian-contributor Thu, 15 Nov 2007 14:09:14 +0000 http://treepax.com/blog/2007/11/14/nouns-and-verbs/#comment-7 I know that people are researching various animal languages e.g. dolphins, parrots and such but I don't think these studies have come up with any real understanding of whether they use anything that we would recognise as a language as yet never mind how that language might be structured. I know that people are researching various animal languages e.g. dolphins, parrots and such but I don’t think these studies have come up with any real understanding of whether they use anything that we would recognise as a language as yet never mind how that language might be structured.

]]> Comment on Nouns and verbs by graeme http://treepax.com/blog/2007/11/14/nouns-and-verbs/#comment-6 graeme Wed, 14 Nov 2007 14:55:39 +0000 http://treepax.com/blog/2007/11/14/nouns-and-verbs/#comment-6 I think you are making the link between 'cause and effect' and the structure of our language ('noun and verb'). As an alternative to going 'extraterrestrial' (i.e. Klingon), for alternative language structures, has anyone tried to decypher languages of other species that are based here on Earth?! I think you are making the link between ’cause and effect’ and the structure of our language (’noun and verb’). As an alternative to going ‘extraterrestrial’ (i.e. Klingon), for alternative language structures, has anyone tried to decypher languages of other species that are based here on Earth?!

]]> Comment on rotating snakes by Ian Moore http://treepax.com/blog/2007/11/12/rotating-snakes/#comment-5 Ian Moore Mon, 12 Nov 2007 17:01:24 +0000 http://treepax.com/blog/2007/11/12/rotating-snakes/#comment-5 I am not sure but I don't think so. I think it may be related to the speed at which your eyes scan the image and how quickly they <a href="http://en.wikipedia.org/wiki/Saccade" rel="nofollow">saccade</a>. I am not sure but I don’t think so. I think it may be related to the speed at which your eyes scan the image and how quickly they saccade.

]]> Comment on rotating snakes by graeme http://treepax.com/blog/2007/11/12/rotating-snakes/#comment-4 graeme Mon, 12 Nov 2007 16:41:28 +0000 http://treepax.com/blog/2007/11/12/rotating-snakes/#comment-4 How profound! Does the speed at which the snakes rotate tell me anything about my brain processing speed? How profound!
Does the speed at which the snakes rotate tell me anything about my brain processing speed?

]]>