The conscious, mathematical brain!

A new week!

As I have frequently mentioned, I so enjoy having guest posts being sent to me.

They give you, dear reader, a break from yours truly and so very often they offer a new and interesting perspective on dogs, on us, and on the world.

This week there are three guest posts, in various guises, lined up and, who knows, there may be a couple more heading in.

But to the first of those guest posts.

Well, technically, more of a reposting today than a pure guest post. That reposting is of a most fascinating post published by Patrice Ayme on the 25th. January. It was called WE ARE MATHEMATICS. But there were parts of Patrice’s post that I struggled with so I am offering it to you with a rather long introduction.

I hope you enjoy it.



The sound of  an object falling to the floor of the shower, suddenly and without warning, nearly caused me to jump out of my skin.

I was washing my hair and had my eyelids tightly closed lest the shampoo suds got into my eyes. Inadvertently, I had felt my right elbow dislodge something from the top of the small corner shelf that held the bar of soap and the bottle of hair shampoo.

I let the flowing warm shower water rinse the suds from my face, opened my eyes and looked down. The object that had made such a sudden, loud noise was a plastic brush maybe three or four inches long. It had fallen to the wet shower floor some five feet below the corner shelf where the brush normally lived.

As I stared down at the brush, the warm water cascading comfortably down my body, I reflected that in the space of a fraction of a second my mind had computed the distance that the unknown object had fallen and offered me a sense of the speed it must have been traveling when it hit the floor.

Now don’t get me wrong! I didn’t come up with a precise answer to that question of how fast the brush was going but in that moment of thought I sensed both the distance the brush had fallen, five feet; plus or minus, and the effect of gravity in accelerating that brush even over such a small distance. (Later I calculated the brush hit the shower base going at around 10 fps.)

Now it would have never occurred to me that my brain was capable of almost instantaneous calculations, as in mathematical calculations, if I hadn’t read in the previous twenty-four hours a recent essay from Patrice Ayme. An essay that convinced me completely that, in Patrice’s words:

The world is not as astonishingly understandable, as Einstein would have it. Neuronal grid cell studies show that we are the world. Understanding the world is understanding ourselves.

The world is not just written in mathematical language, as Galileo found out. We are made mathematically. We think mathematically, because we are made of math. We are mathematics.

Patrice had opened my eyes, more accurately opened my mind, to something that was then immediately clear to me and will be to you, dear reader: Our brains have an intuitive and instinctive sense of space. Not space in some abstract sense of the term but space in the sense of spatial awareness.

Think how easily, how quickly, you understand distance. Whether it is a measure of distance in your own home or assessing how far away that bird is flying towards and setting down on a high branch of a tall pine tree.

Think how even with our eyes closed we can navigate around a familiar part of our lives. Think how the sailors of ancient times (and trust me not so ancient times) used ‘Dead Reckoning’ (DR) to navigate safely and securely across vast oceans.

Our brains could only do this if they were computing these spatial assessments mathematically.

OK, that’s enough from me. Here’s that essay from Patrice.



Mathematically Built Brain: The Example of Grid Cells, Incarnating Algebraic Geometry.

Understanding how the cognitive functions of the brain arise from its basic physiological components has been the final frontier in logic and rational science for thousands of years. (As I tried to explain yesterday, the superstitious religious fanatics tried their best to bury all of science, and the scientific mindset, the essence of humanity; they nearly succeeded!)

The 2014 Nobel was given to John O’Keefe (a “half”!), the rest jointly to May-Britt Moser and Edvard I. Moser “for their discoveries of cells that constitute a positioning system in the brain.” I will develop here the philosophical viewpoint, which is broader (O’Keefe’s career was steered by the influence of Hebb, the famous psychologist, who got the idea of the outside patterns imprinting the neurocircuitry of the brain).

Here is Hebb: “Let us assume that the persistence or repetition of a reverberatory activity (or “trace”) tends to induce lasting cellular changes that add to its stability.[…] When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased.”

Well it turns out that evolution has had even more imagination than that. I will even propose Patrice’s Neural Theory, a vast generalization.

Galileo famously said the language of nature was written in mathematics. It turns out that it is much more than that. Our brain is mathematically organized. What Descartes consciously discovered, a coordinate frame in which to set-up calculus, is automatically generated in the brain. This is the meaning of grid cells.

Grid cells are neurons that fire when an animal moving of its own free will traverses a set of small regions (firing fields) which are roughly equal in size and arranged in a periodic triangular array that covers all of the available environment. They were discovered in 2005 by a couple (literally) of Norwegian researchers, the Mosers, and rewarded by the Nobel Prize in 2014 (shared with O’Keefe, from London, who invented the basic experimental technique, and discovered “place cells)

Once set, navigation can be done in the dark, blinded. Scientists’ discovery that rodents, bats and nonhuman primates have a system in the brain for so-called “dead reckoning navigation”… “Dead reckoning” refers to the ability to navigate without external cues. The term comes from ship navigation. A crew will “take a sighting” via cues such as the stars or landmarks to determine where the ship is on a map. Then, when the ship moves, ‘dead reckons’ to update location on the map paying attention to speed and direction. The Greco-Romans already had such systems, with little paddled wheels counting the distance covered over the sea. It turns out that ‘dead reckoning’ is enabled by the grid cell system, inside the brain.

Recording Of Grid Cells Activity Inside Rat Brain (Jeffery Lab and others.)
Recording Of Grid Cells Activity Inside Rat Brain (Jeffery Lab and others.)

Kate Jeffery, a professor of behavioural neuroscience at University College London puts it this way:

“The importance of grid cells lies in the apparently minor detail that the patches of firing (called ‘firing fields’) produced by the cells are evenly spaced. That this makes a pretty pattern is nice, but not so important in itself – what is startling is that the cell somehow ‘knows’ how far (say) 30 cm is – it must do, or it wouldn’t be able to fire in correctly spaced places. This even spacing of firing fields is something that couldn’t possibly have arisen from building up a web of stimulus associations over the life of the animal, because 30 cm (or whatever) isn’t an intrinsic property of most environments, and therefore can’t come through the senses – it must come from inside the rat, through some distance-measuring capability such as counting footsteps, or measuring the speed with which the world flows past the senses. In other words, metric information is inherent in the brain, wired into the grid cells as it were, regardless of its prior experience. This was a surprising and dramatic discovery. Studies of other animals, including humans, have revealed place, head direction and grid cells in these species too, so this seems to be a general (and thus important) phenomenon and not just a strange quirk of the lab rat.”

We should have looked for Plato’s cave. It turned out that this cave has been built, is being built inside our heads all along! This cave is built-in two ways: automatically (grid cells) and as a response to the environment,, from the outside, from the environment, in.

(So it matters what our brain experienced before to mold afterwards what comes in anew from the outside! No experience is a neutral experience!)

That cave is both a topology (what’s near and what’s not, the logic of place), and a basic geometry (the grid and its grid cells). To have a grid built automatically is the equivalent of having a reference frame in mathematics. It makes sense if one wants to make mathematics!

And not just mathematics, but even Infinitesimal Calculus! It is indeed clear that animals such as dogs have a mastery of calculus: experiences have shown this, and anybody with a dog throwing a stick sideways in water will see the dog running along the shore a bit, and then jump in the water, so as to minimize the time to reach the stick, a typical calculus problem. Dogs can do calculus, because they can make algebraic geometry in their brains, having a reference frame made of these grid cells! (If they had no grid cells, they would not be able to do calculus.)

Thus Descartes rediscovered, consciously, something which had been found, evolved and calculated by evolution half a billion years ago (or more!). The reference frame, also known now as the neuronal grid cell system, is basic to all of mechanics, even Poincare’-Lorentz Relativity.  (An open question: Quantum Physics uses even more general reference systems, Hilbert spaces; I will therefore predict that the brain has also that sort of organization!)

The world is not as astonishingly understandable, as Einstein would have it. Neuronal grid cell studies show that we are the world. Understanding the world is understanding ourselves.

The world is not just written in mathematical language, as Galileo found out. We are made mathematically. We think mathematically, because we are made of math. We are mathematics.

We are not just looking at shadows in a cave, as Plato would have it. And the cave was not given to us by the gods, as Socrates had it. We are the cave, we, and our personal history, built it.

Any new experience, idea or emotion, taught or experienced, is another brick in that wall of perception and analysis, we better consider it carefully, before indulging in it. Call that the Principle of Mental Precaution But that Principle extends also to what we chose NOT to experience, which can be just as bad, if not worse.

You are not just what you think. You mentally are what you were submitted to, and what you decided to submit to. Fate is written in mathematical patterns, one theorem made out of neurons, their axons, dendrites and supporting glial cells, at a time.

Such theorems are written with the physics of minds, just as sturdy as the physics of stars. Just as hopeful, just as ominous.

Plato thought mathematics were “forms”, out there, outside of the physical world. This is not what science is finding. There are not “forms” out there, and physics, nature, somewhere else. Our minds are literally made of math.

So here is my theory:

Whatever exists in mathematics exists in the brain. And reciprocally.”

Patrice Ayme’


I do so hope that this essay from Patrice fires you up as it did me. If it leaves you with questions, then offer them to me as a comment to this post and I will take it upon myself to have Patrice answer them.

Finally, did you pick up on the fact that it isn’t just our human brains that are mathematical organs, it applies to the brains of dogs as well!

Mathematics in action. (Photo courtesy of Pinterest)
Mathematics in action. (Photo courtesy of Pinterest)

32 thoughts on “The conscious, mathematical brain!

    1. Dear Mincs1: It’s not just a thought, but a flower which has been picked up. An unexpected blossom! It’s for us to look at, and to go further, then, where no thought, or even feeling, has been before…


    1. Dear petspeopleandlife: Even those not “remotely” interested by math are still made of maths. So the essay was about you! Most people don’t hate themselves… or pets, themselves full of math, as Paul, me and others have pointed out…. ;-)!

      Liked by 1 person

  1. Thanks Paul for re-publishing my essay! Your introduction is absolutely excellent I will reproduce as a comment to my essay, as it illustrates it so well. It is true that such subjects call on long meditation, as you point out. I had plenty of time to ponder the essence of mathematics, as a researcher in the discipline… And I think you studied electrical engineering, which calls on mathematics such as infinitesimal calculus, so it’s easier for people like us…


  2. One of the basic ways to communicate is through mathematics. This is the go to language for future space exploration and possible interaction with intelligent life forms. Sounds sci-fi but it is based in reality. Terrific article, Patrice!


    1. Of course! Hadn’t thought of that aspect. That mathematics is the language of the whole universe. (Takes me back to my teenage days to when I learnt Morse code en route to becoming a British Radio Amateur: G3PUK.)

      Liked by 1 person

      1. So where did that interest come from? Meandering back to my days of amateur radio, I can still recall being amazed in discovering how quickly the brain associated one’s callsign as a personal ‘name’. One could be practically fast asleep, albeit wearing headphones, yet hear one’s callsign in Morse code and be instantly fully awake. Just like someone calling your name out when you are asleep in bed.

        G3PUK – Dah dah dit, di di di dah dah, dit dah dah dit, di di dah, dah di dah.

        Ah! Nostalgia!

        Liked by 1 person

      2. Honestly, my deep & abiding love for Star Trek. I wanted to be Captain Kirk. I loved the idea of being in space, being an explorer. Now, I can do that with my writing!


    2. Hello Susan, and thanks! The idea is that mathematics is not just a language (that idea was written, black on white, by Galileo. He spoke of circles, triangles, lines: the ellipses of Kepler had no sunk in, and Galileo did not know about brand new Descartes’ algebraic geometry and even newer Fermat’s calculus). The idea is that our very substance is mathematics itself.
      Our minds are unknown, because our maths are unknown.
      As far as SETI is concerned, I am rather skeptical (I have personal addition to the Drake equation…)

      Liked by 1 person

  3. I had half written a comment here Paul and I enjoyed Patrice’s take on the Conscious Mathematics.. Then got called away..
    We are all of us upon this planet part of the Jigsaw within the mathematics of Energy.. Our Energy is constantly emitting and radiating outwards at the speed of thought.. 🙂 As we move.. Energy around us moves and all particles within our space then move also.. For there is no Empty Space.. But its full of invisible Energy

    I am sure Brian Cox the scientist could explain it much better than I.
    I feel each of us contribute to the Conscious Maths of the Universe.. As we give out either our Negative or Positive rays of thought..
    Each thought we think is energy, we too are Energy.. and are generating our future with what we think right now..
    One only has to look at the paint upon our walls, the fabric of our clothes.. All once someones thought put into motion via Action projected into our reality..

    Which is why we should be careful what we wish for.. For we really do attract like for like as energy is energy it neither knows what is Good or bad.. it will gather momentum regardless and follow the pattern of mathematics like a magnet.. Positive or Negative..

    And this is why I try to keep my vibration in the energy of Love, Unity, Harmony and Peace…

    A very interesting Read..
    Thank you for sharing Paul


    1. Thanks Sue!
      As far as Brian Cox and Al., exposing modern physics, the truth is that we know some things, which are astounding. But we are far from knowing the full story. We know a spectacular bit: plenty of energy in empty space. BUT we don’t know how MUCH there is (some attempted theories are off by a factor of 10^60, a one followed by 60 zeroes…). And we don’t know what causes “it”, whatever “it” is: the theory of virtual particles is controversial (I debated this subject with the creator of the theory, Richard Feynman!!!!!). By the way, I have my own theory.

      Thus, really grand extrapolations by grand physicists are just like claims in the primary school yard.

      It would be better to teach only what we really know for sure, and that’s amazing enough…

      Liked by 1 person

      1. I totally agree Patrice.. Even those great Scientists who think they know the workings of the Universe from their own theories of Mathematics.. In reality know nothing in the scheme of things.. We are very primitive I am sure..
        And I doubt our brains are wired up to take the data of how this Universe and Energy operates.. For it is beyond our human capabilities of understanding..
        I am sure Science has not progressed far enough to even understand One tenth of the possibilities out there within the Matrix of Creation.

        And like all things.. What we discover today as Truth.. Tomorrow may well change that Truth.. For we are evolving all the time as parameters change..

        For instance at one point in our History.. Science told us not to sail over the oceans horizon, for they told those who sailed they would fall off the edge of the world..
        Well exploration proved otherwise and Science had to be rewritten..

        Which is why nothing is ever written in stone.. For we are not held within our man made laws.. But we are all subject to Universal Laws.. Which fascinate me. 🙂

        And thank you Patrice. I always love our rare but positive exchanges in dialogue..
        Many thanks..
        Blessings Sue 🙂


  4. I should also have said Patrice is so right here with his thoughts
    ” But that Principle extends also to what we chose NOT to experience, which can be just as bad, if not worse.”
    I so agree.. putting our INTENT is pouring energy into a thing.. a thought.. When we keep pouring that energy into not wanting something to happen we then can well be attracting that very same thing towards us.. because that is the prominent energy we are focusing upon


    1. Very true, Sue! Some of the Trump phenomenon just arose that way. For decades “democrats” have been busy denying what their leaders were really doing. More and more energy was put into denial and lying. The Main Stream Media, all plutocratically owned, got used to lying ever more bluntly and subtly.

      Finally all too many voters (who last voted for Obama in 2012, studies have shown) had enough… They voted for those using the same methods, but with the avowed aim to serve them. Evil has grown.

      Liked by 1 person

  5. As regards to your latest point, Sue, I am writing a little essay on this today. I have a slightly different take, even more ominous… Much more present. Not a question of particular “leaders”. Obama viewed himself as a great “leader”. In truth, he was led by the nose, by the real leaders, thus leading from behind as the average circus bear used to be… The same happened with… Hitler. What is more important is to find out who, what, the true leaders are.


  6. Seriously you two, I am delighted with the exchanges. Just read them out to Jeannie and we have both been humbled by the knowledge and intelligence displayed in your ‘conversation’. Thank you!


  7. I only wish I were mathematically inclined. While I’m sure that post made sense to a certain segment of your readers, it was written in Yugoslavia by my mind.
    Liberal Arts Major 😆


    1. I’m certain you are doing yourself down!

      Just keep a little part of your mind open to how quickly you react to some things over the next couple of days and I am certain that you will see where Patrice is coming from.

      Plus don’t equate how well or otherwise you are in ‘doing’ maths with how your brain functions. That’s not what we are speaking of. Just be an observer of your actions. For example, I’m sure you are pretty good at catching something; say a ball. Listen to your mind as it measures the speed of the incoming ball, tracking the decreasing distance to your hands, and then directing your hands to intercept that ball. It will have computations written all over it: mathematical computations.

      Oh, by the way, I can’t speak Yugoslavian! 😉

      Liked by 1 person

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