please empty your brain below
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What do you do at a crossroads (or anywhere there are more than two possibilities?)
Sarah | 09.09.19 - 7:07 a.m. | #
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At a crossroads, only left or right, never straight on.
diamond geezer | Homepage | 09.09.19 - 7:08 a.m. | #
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You introduced a bias by starting facing north. Where would the same sequences of coin tosses have led if you had started facing in a different direction? Of course, on a mathematical grid, the entire walk would just get rotated, but central London is far from a mathematical grid!
Peter Cameron | Homepage | 09.09.19 - 7:31 a.m. | #
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Great that you are using OpenStreetMap in today's post but you need to put in a credit such as “© OpenStreetMap contributors" against, say, the first one: https://www.openstreetmap.org/copyright
Thanks!
OSM Police | 09.09.19 - 7:46 a.m. | #
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I think that by removing the possibility of straight ahead you have altered the probabilities in the results. Not that it matters in the context.
Ian | 09.09.19 - 8:01 a.m. | #
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Recently, I have been wondering what book to re-read. After the blog this morning, I think it will be the Dice Man
cheers...
PJS | 09.09.19 - 8:37 a.m. | #
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What happens if you are directed down a dead-end?
Jon Combe | 09.09.19 - 8:40 a.m. | #
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All junctions with dead ends were ignored.
diamond geezer | Homepage | 09.09.19 - 8:44 a.m. | #
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It will not take an infinite amount of time to get back to your starting point. What the mathematician may have said is that the time to get back is UNBOUNDED. Think of a positive amount of time, however big, and it may take longer than that.
Malcolm | 09.09.19 - 9:14 a.m. | #
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I found as a teen that when I flip a coin the result is predictable. If I put it heads up and flip I get tails, and vice versa.
I can do this ten times in a row.
I've used it to my advantage a couple of times (nearly everyone calls heads).
What's weird is I tell people this, then I demonstrate, and they still don't believe me.
Try it.
(I put the coin on my clenched fist with thumb tucked in, flip, catch in the same hand palm up, then slap onto back of other hand).
Joho | Homepage | 09.09.19 - 9:18 a.m. | #
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Mrs Tiggywinkle says that isn't a proper coin flip, that's a predictable physical procedure.
diamond geezer | Homepage | 09.09.19 - 9:24 a.m. | #
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Oh, I thought everyone did it that way.
Joho | Homepage | 09.09.19 - 9:48 a.m. | #
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this puts me in mind of the referendum that’s caused so much trouble lately.
Jerym | 09.09.19 - 9:55 a.m. | #
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If you rule out straight ahead, that must increase the likelihood of going round in (smaller) circles. Is there a rationale for removing a third, equally random, option (other than the need to determine it by a binary coin toss)?
When I've tried a random walk I've gone out with three different coloured (but same size and shape) beads in my pocket - one for left, one for right and one for straight on. If the first one I picked out was inapplicable, I ignored it and took the next one. It also had the advantage of being more subtle than stopping and tossing a coin at each junction...
Sarah | Homepage | 09.09.19 - 10:11 a.m. | #
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I didn't even know there was a Mrs Tiggywinkle coin.
Paul | 09.09.19 - 10:12 a.m. | #
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Interestingly, you’ll always get back to your starting point in a one or two dimensional random walk, but there’s only a 34% chance that you will in a 3-D one.
Alan | 09.09.19 - 10:24 a.m. | #
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In fact, if you can always get back to your starting point (in an infinite time) then it follows you can always get back to any point on the route (since your walk could have started from there).
And by extension, in a one or two dimensional random walk, you can always get to any point in an infinite time since there is nothing special about the starting point.
Pedantic of Purley | 09.09.19 - 11:11 a.m. | #
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Throwing four queens in a row in Soho? Sounds about right.
Autolycus | Homepage | 09.09.19 - 11:40 a.m. | #
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How long might it take you to get home? What about if you lived 1km away from Oxford Circus? If you used three coloured beads instead of a coin?
Lorenzo | 09.09.19 - 12:28 p.m. | #
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Who the f**k knows.
diamond geezer | Homepage | 09.09.19 - 12:32 p.m. | #
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Came here for quality content, was not disappointed
Thank you, as always, for something unexpectedly interesting.
Webly | 09.09.19 - 1:19 p.m. | #
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As a teen I used to do "Penny Rides" - basically the same thing, but on my bike.
After several attempts that ended in going round the same block each time, I moved on to other pastimes!
Cornish Cockney | 09.09.19 - 1:32 p.m. | #
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The claim that a random walk in 1 or 2 dimensions eventually gets back to the origin needs a bit of exploration.
An apparent disproof is that the sequence "straight on for ever" does not get back, and yet it is one theoretical possibility. I think the point is that infinite sequences which never return are so thinly scattered in probability space, that they occur with probability zero. Which is a sort of mathematical extension of the word "never".
Malcolm | 09.09.19 - 8:38 p.m. | #
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The casual throwing about of non-rigoursly defined terms such as ‘infinite time’ is disturbing and would not be approved my my analysis and Markov Chain tutors.
Madison | 09.09.19 - 9:13 p.m. | #
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