tag:blogger.com,1999:blog-4724592643224262209.post6322903871995213305..comments2023-05-08T02:52:16.953-07:00Comments on Cognition and Evolution: Flatland and Free WillMichael Catonhttp://www.blogger.com/profile/01017910055699348111noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-4724592643224262209.post-10943732189811766602011-06-09T09:40:55.208-07:002011-06-09T09:40:55.208-07:00I definitely took this quite literally and knew I ...I definitely took this quite literally and knew I could be doing so erroneously; but it's a good vehicle for thinking about it. But my question is that I'm not sure what an addtional dimension can mean if it can in principle not be traveresed (i.e. R^2 x R in the representation you used). I'll visit your post and see! Thanks for your comment.Michael Catonhttps://www.blogger.com/profile/01017910055699348111noreply@blogger.comtag:blogger.com,1999:blog-4724592643224262209.post-13303656003866770132011-06-08T19:03:16.303-07:002011-06-08T19:03:16.303-07:00A very interesting post! It gives great food for t...A very interesting post! It gives great food for thought, however I fear that you may be taking too literally, the idea that time is a +1th dimension. To simply "tack time on to space as an extra dimension" does not work as in your analogies. Just because we can traverse space does not mean that we can traverse time in a lower dimensional space. To put this mathematically precisely, a two dimensional world with time is represented by R^2 x R. That is, a 2-tuple consisting of a two dimensional space vector and a time scalar. One can still only traverse the two dimensional space vector.<br /><br />That said, I find your post very interesting and it made me think. I have recently started thinking of such things in my blog (http://www.thinkdepository.com/?q=blog/3), with a post firstly on determinism in flatland, and then a subsequent post on the implications this has on free will in flatland.Borishttp://www.thinkdepository.com/?q=blog%2F3noreply@blogger.comtag:blogger.com,1999:blog-4724592643224262209.post-60450874101382662472009-10-23T13:29:01.420-07:002009-10-23T13:29:01.420-07:00I still think Flatland is a useful analogy for tho...I still think Flatland is a useful analogy for those who see a pre-destined universe as a four-dimensional block of frozen space-time, which some do. You're correct that in this model, we ourselves as three dimensional beings must have a fourth dimension across which the state of the other three can change, so that we can change states in the third dimension, and climb around on Flatland's 3D block of plane-time. If time as the fourth dimension is taken literally by various models of the universe (six in the standard model I think?), there are multiple dimensions above us, but as long as there aren't infinite dimensions then the highest would necessarily be static.<br /><br />The backdrop of this issue for me is that I do believe there is such a thing as free will, but I recognize the incompatibilities between this belief and our understanding of the physical world (and therefore, nervous systems) so far. Consequently I'm actually happy that the concept of "now" seems incoherent in a deterministic universe because it's apparently incoherent.Michael Catonhttps://www.blogger.com/profile/01017910055699348111noreply@blogger.comtag:blogger.com,1999:blog-4724592643224262209.post-70277007710445345282009-10-23T07:04:02.516-07:002009-10-23T07:04:02.516-07:00I think the Flatland analogy confuses the issue of...I think the Flatland analogy confuses the issue of free will more than it clarifies it. Maybe some fifth-dimensional sadist told the fourth-dimensional sadist that he was always going to tell you about your third-dimensional smooshing (into a two-dimensional object, right?) thus transferring the question of free will up n dimensions.dbonfittohttps://www.blogger.com/profile/08787420987976232701noreply@blogger.com