Fourth dimension surfing

The second image below has marked time in the drafts section of my dashboard for well over a month. It was taken at the Jacoby Falls on one of the very first mild weekends of our Pennsylvania spring. An earlier post which described that visit concerned a topic altogether divorced from that of tree trunks, and so too does this one. I have thought much, as part of my professional responsibilities, about a construct called morphospace. Let me explain. Imagine how you might describe, by measurement, an animal such as a garden snail, for example. You’d have to measure the length of the shell, the width of the shell, and the dimensions of the shell opening … and then you’d have to count the number of whorls and somehow determine their rate of expansion. When you were done you might have ten measures. Now consider that this shell, because you have collected ten variables, occupies a point in ten-dimensional space, morphospace, a cloud of points which describes the totality of snail shells. Below is a famous representation of the (three-dimensional) morphospace occupied by molluscs (mostly snails and clams).


Let us now consider physical, rather than mathematical, dimensions. The first dimension is a point on a line, the second is a surface, and the third is a cube. The fourth dimension is, of course, time. And, that’s what this post is about. In particular I’ve been thinking about how it is that the lives of plants play out, in this fourth dimension, very differently than ours. Generation times vary across organisms. Humans have an average generation time of twenty-five years. This figure drops to five days for an aphid, and just several minutes for a bacterium. Most plants, in comparison, live life at a very different pace. If you’ve ever been fortunate to view a time-lapse sequence of a growing plant you know that they do indeed move. These movements however are not driven by muscles (as is the case in animals) but are generated by changes in water pressure and in the absolute size of cells. Movement notwithstanding plants, once established, stand, rooted, stately, stoically, and quietly. They are subject to environmental influence, come-what-may, for they cannot move. I am most impressed by the lives of especially long-lived woody dicots. The oldest tree known is a Great Basin Bristlecone Pine thought to be more than 5,000 years old. Although such antiquity is rare, trees dating between 1,000 and 3,000 years old are quite common. [The oldest known clonal (vegetative) tree is a Quaking Aspen thought to be more than 1,000,000 years old.] The lives of plants play out on a much longer time horizon than ours. Trees are in no hurry. Can we learn anything from this? I often wonder.


As a postscript, and with a nod to my geekier followers, I point to a series of radio broadcasts entitled Ruby, The Adventures of a Galactic Gumshoe in which the sport of Fourth Dimensional Surfing is described. And, finally I present this video clip, produced by Mother Nature Videos which presents one videographer’s view of surfing in the fourth dimension.

34 thoughts on “Fourth dimension surfing

  1. I have nominated you for my freshly minted blog award. It is called The ILFB Award: Intelligent Life-Forms in the Blogosphere. You may or may not pass it on. I am looking forward to feedback on the consistency of my nomination policies. You are an excellent initial nominee for so many reasons! I addition to the reasons described in the nomination itself I believe a blogging biologist is most qualified as an intelligent life-form in the blogosphere himself on the one hand and to bring a new award to life in the other hand.

  2. I have often thought about this. Thank you for illustrating it so beautifully! The ‘time horizon’ of things is, in my opinion, one of the most defining qualities of the thing as a whole. As humans we constantly count our own rings, and there are many ways to do this. At a certain point, perhaps when the rings behind are more in number than the rings we’ve left to grow, we are confronted with mortality.

    On a different note, I am studying the theory of relativity now and dealing with the implications and the mathematics of time dilation. I have learned a lot from this, and still am not sure what this new knowledge does to my philosophical ideas about time, but I am sure they will be upended soon enough.

    1. Thanks very much for the observations Johannes. So many interesting things to consider. While reading your comment something clicked in my mind and I was reminded of a statement made by a famous ecologist. He pointed out that humans have been around for perhaps 200,000 years and that the earth has been around for a bit more than 4,000,000,000. So, if you take the fraction of earth time that we’ve been here (0.00005) and round DOWN (0) … we don’t exist! Poof. Magic. Have a great day and swing back around sometime to see what’s going on here at Pairodox.

      1. I began teaching a 7th grade Ancient History class with a similar idea. Compressing the history of the universe into a single calendar year –the Big Bang occurring at midnight Jan 1.

        I don’t remember the exact number of seconds, but the take-away was that human beings were born on Dec 31 at 11:59:57. Something like 3 seconds out of the whole year!

        It was fun to start class that way because then we zoomed in on a certain era within those three seconds, and it really got the kids thinking about time in an unfamiliar way.

        1. Yeah … this is a classic ‘experiment’ which is carried out in a variety of ways. Next time you want to do this, give each pair of students a roll of toilet paper! You’ll have to take the entire class to the gym where they can roll out the entire roll. The full length of the roll represents 4.6 billion years of earth time. Have them do the math and figure out where on the roll a series of earthly events occur. The origins of life, the rise of the dinosaurs, the demise of the dinosaurs, the great extinctions, the rise of plants, and then of course the rise of Homo sapiens. If I remember correctly we arise well within the last piece of tissue and, in fact within the last centimeter of material I believe. Just another way of doing the very same thing as the clock protocol. Thanks for your response. D

  3. Very cool and something I’m very, very interested in bordering on obsession… 186,282 ᴍɪʟᴇs ᴘᴇʀ sᴇᴄᴏɴᴅ something I just posted, I have a couple of other ones but hope you might enjoy. Peace!

    1. Hey digitalhegemon. The ‘thumbs up’ is (are?) appreciated. I will drop by shortly to see what you’re about – always looking to connect with like-minded, and thoughtful, folk. D

      1. I read some more of your posts and I think we have much in common with that subject. I truly look forward to talking more especially regarding the graphical representation of what you are talking about. It’s very cool to find someone else following that tip.

        1. Hi Digitalhegemon, I was reading an older post of yours a while ago. It was very long and I couldn’t finish it, and now I can’t find it. It was a fiction piece about dream writing. Can you reply with a link to the post? Thank you. I suspect that given D.’s description of memory formation, this might be of interest to him, too.

  4. What an interesting and thought provoking post. I had a quick look this morning but wanted to wait and come back to it when I had a chance to read and digest it slowly! I couldn’t agree with you more about the beautiful difference between time experienced by ourselves and tress. I often think about this, and about the speedy ( to our eyes) lifetime of a butterfly. Because we inhabit and experience the same place in time, but at different speeds there is surely much that we miss of each others worlds 🙂

    1. Absolutely. What a topic for contemplation. The span of our lives. Trees, bacteria, tortoises, cameleons, the list goes on, endlessly. I understand that all of these organisms are without our brand of consciousness but still .. they perceive the world within which they live .. but how? No, I don’t mean literally ‘how’ because I think I understand their neural and sensory systems. But, I mean what do they make of their existence? Or are they even capable of this kind of though? If not – how sad. And even if they are, I do not believe we can ever know its nature – but we can think about it can’t we? And, how does their absolute life span influence how they experience their lives? Cool. D

  5. Your comments have exploded, I see. Well, I’m back because I wanted to take some time to let the dust settle in what was, for me, a huge creative bomb that went off when I encounter your post. As you know from an earlier conversation, shells are turning up as a significant metaphor in my creative writing, and snail shells are particularly abundant! A couple of weeks ago I was searching for a way to understand how a snail shell could be measured, mathematically. Of course, I’m very interested in how time becomes another factor for measurement, like rings on a tree, and layers of memory and experience in a human life… the connections are so rich. I’m still going to come back and read this a few more times. Actually, I should probably print it and put it with my book notes, then I can properly attribute your influence if the book is published. 🙂 I love how you’ve connected the Fourth Dimension with plants and trees. Thoughts of this are influencing my next post, already drafted.

    1. I am happy to add more to this explosion of comments now 🙂 I agree with Michelle – the more often you read it the more new associations spring to your mind. I will also get back to this post in one my next posts – I am following up on something I had announced already twice in a cryptic way. Technical question: What timezone does this blog live in? There seem too be only two hours time difference to my time zone which does not seem correct.

      1. I’ve got several layers of comment to respond to this evening … but for now I’ll respond to the easy query … I’m in EST = UTC -5. I assume you are CEST = UTC +2 … 7 hours ahead of me? In either case I’m not sure where the WordPress servers are and have never taken the time to figure what the relationship between time stamps on posts and my EST is. D

    2. Thanks M. I’m glad your reflections have been fruitful. Yes, the way in which time influences information processing is something to be considered. As a biologist I have always been fascinated by the information we are able to store and retrieve. Where is it? Can you, or anyone, point to it? Experts say that cognition is reflected in the formation of neural circuits … newly formed connections between and among neurons. But, certainly we cannot be talking about physical connections, for memories, thoughts, and ideas may form instantaneously. I’ve always wondered whether it is unreasonable to view neurons as suspended in a cytoplasmic matrix … something not unlike Jello. When one neuron communicates with another the connection is electrical. Perhaps that transient electrical connection leaves a trace through the matrix such that bits of knowledge or memories are represented by those paths. And a path, once established, may easily be retraced. Just something to THINK about! D

      1. I posted something new, and you’ll notice that I’ve been giving much thought to your post here; there should be a ping back from the link I embedded to your site.

  6. Reblogged this on Theory and Practice of Trying to Combine Just Anything and commented:
    If anybody ever said biologists and biology aren’t geeky, this post disproves it. Have you been aware of the three-dimensional morphospace occupied by molluscs or can you surf four-dimensional waves? This post covers so many different aspects – it needs to be reblogged at a blog that aims at “combining everything”.

    1. Technical update: I have shared the link to this post also on Facebook now – and this time FB did not complain about the “unsafe” link (as with the post on farm humor).

  7. But you just KNEW Elke and I would be all over this, didn’t you? The only reason I’m late is that a cold I have is slowing me down just a tad. Yesterday I didn’t read anyone’s stuff so this morning I’m playing catch up. And you’re not making it easy, what with giving me videos to watch too. As I write this I’m looking across the room at the 30 cm cactus plant I bought around 18-20 years ago when it was just a 2-3 cm baby. It’s slowly growing and has been transplanted several times. This one is the fourth pot I think and it now has its own stand. While on its previous perch it was stressed by some nearby plants and developed an awkward bend – it looks more like a pickle now. A VERY prickly pickle. Respect for those spines caused me to delay in transplanting it so now I have a nasty bend to work out. For the past 6 weeks it’s been placed in a corner so that sunlight comes from only one direction and I’m slowly turning it this way and that every few days in an effort to straighten it. It’s working. There’s just one bend left and I figure that in a couple of months it will be straight enough.

    1. Thoughtful and brilliant solution to your ‘thorny’ problem. Not one that many would have had the sense to figure out. Plants do indeed move but oh so very slowly. We used to think that marine and freshwater sponges were entirely sessile … I have seen a time-lapse (taken perhaps over several days) which showed an individual ‘walking’ over the substrate. It was fascinating to see. The organism essentially disassembled itself, slimed its components (cells) across the substrate a bit, and then reassembled itself. It cycled through rounds of assembly and disassembly and, over time, moved quite nicely from here to there. It’s all about perspective. D

      1. Yes, and as you pointed out a different sense of time. I found your description of how the sponge moves to be completely fascinating. Always something new! Back to the cactus – it’s very difficult to work with while transplanting. The spines easily pierce leather work gloves. I finally hit upon a solution. Now when I need to manipulate the plant I use two pairs of linesman’s pliers with vinyl handles. I use them in reverse, ‘pinching’ the plant between the handles. Since I have to use the ‘wrong end’ of the pliers this ensures I have a gentle touch.

      2. This description of the walking sponge reminds of a video that went viral a while ago – in particular your mentioning of slime and disassembling. The video I am thinking of shows “magnet putty eating a rare metal cube”. It really looks like a lifeform: You got me thinking about the characteristics of “life” again!

  8. Of course this is appealing to the physicist in me – we use all kinds of abstract spaces incl. many dimensions (not only the 4D spacetime). It is probably one of the most useful things I learned when studying physics – to build a model of basically anything that can be described as “events” or “points” in an abstract space. Currently I am struggling with creating sort of a matrix including communication protocols in smart metering, their features and how they fit into the physical networking topology. “How much” mathematics are using on a daily basis as a biologist? In passing I noted that there are new fields called biomathematics or something.

    1. As a classically trained zoologist I don’t have much opportunity to include mathematics in my work. Several years ago however, I became quite interested in modeling feeding behaviors which occur within the land snails (would you say ‘Schnecken’). It was fun, but didn’t really go anywhere. I was interested, when I booted my computer this morning, to find a distinct lack of response to this post. I don’t think the typical WordPress reader cares much for esoterica. D

      1. My theory on the lack of interest is as follows: Most readers react immediately or not at all. A post like this might take bit more time to digest, so you need to “flag” it and come back after some time. I do this flagging, but I don’t know how common it is. I “process” blog postings in a similar way as e-mails (and flag the notification e-mails).

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