Three worlds, three mysteries

Let me clear up another mystery first – where have I been all this time? It’s not so much that I have been too busy to write, but have been embroiled in financial considerations. You may have read in my previous post I have had to take this year out from my personal studies to complete my CFA Level 1 – I passed this in January, and have found myself in the wilderness of not being enrolled to study anything I love. As I have said before, from a credibility perspective I don’t like to dwell on too many matters I have not studied; but I observed my financial mathematics didn’t have a terribly broad platform on this blog. This caused me to go quiet for a while as I ran out of things to say, but I am back.

I am registered to complete all of my second year of my second degree, along with third year studies in complex analysis this coming autumn. In preparation for that I have begun studying two beautiful books;

  • The Road to Reality: A Complete Guide to the Laws of the Universe, Rodger Penrose, in the hope of resharpening a broad overview of physics; and
  • Complex Analysis: A Hitchhiker’s Guide to the Plane, Ian Stewart, a textbook that seems to be horribly underrated on Amazon that saw me good in my first undergraduate.

As such, you can expect random high level physics posts and more technical complex analysis posts until my studies start again, and I hope to post with a little more depth.

Today I thought I would share with you something interesting I read in Penrose’s book – right near the start about three “realms” that live around us and interact, which brings three mysteries. It raises some interesting questions around how the world should be viewed.

The physical world 

This world is easy to understand, it is the world of things which take a physical existence. You would fit into this category, as would a rock or a table. There is a deeper philosophical question around what a physical object actually is, but leave that for those who like to get tangled up in all of that nonsense. For us a physical object is an object in the sense that immediately springs to mind – the sense which is inherent in our everyday experiences of what physically exists.

The mental world

The mental world extends beyond the physical, and includes a whole host of things which are not present in the physical world. Anger is an example – it does not manifest itself in a physical form in the true sense, but it is of course present in the mental world. You know what it is and you know when you feel it – it is within most people’s emotional repertoire.

Platonic mathematical world

The Platonic mathematical world is probably the most contentious of the three worlds, but makes reference to the fact that mathematical entities do not belong in space or time, they are eternal and unchanging. A square for example, lives in this world – you cannot construct a perfect square in the physical world. You can however imagine one, which means it also lives in the mental world – we will discuss the links later. There is a sort of assumption that the mathematical world exists and is eternal, we merely borrow items from this realm and return them when we are done.

There are other more subtle considerations as to what the platonic mathematical world actually means – for example It may be considered a realm of everything which is mathematically true, allowing for mathematical entities to exist even if they cannot all be proven from a consistent set of axioms. I don’t want to get my hands dirty with the philosophy – it’s not my bag and does not interest be greatly.

Penrose’s prejudiced view

The above title is not be being dismissive of the great mathematician, this is how he himself labels his view, which is presented in a diagram below, with the three mysteries numbered. We will discuss them one by one.


Roger Penrose, “The Road to Reality: A Complete Guide to the Laws of the Universe”, Knopf (2005)

  1. The physical world is described in its entirety by the Platonic world of mathematics. This is a large claim, but a belief I certainly hold – that there exists timeless mathematics which can be drawn upon to explain the workings of the entire physical world. Ideas like this, or course, destroy notions of free choice and alike but I think I am OK with that. Only a small portion of the Platonic world of mathematics is required to explain the entire physical world – this makes perfect sense. There are a lot of mathematical beings which exist purely in the mathematical world, we need not imply that every single piece of mathematics explains something in the physical world. It is however interesting, how more and more pure mathematics concepts are finding application in the physical world – applied mathematics seems to grow along with our understanding of the universe.
  2. The mental world is fully and totally contained in a small section of the physical world. This makes perfect sense, but you won’t like it if you believe in certain religious notions. Everything that comprises the mental world, namely brains, products of the physical world – they are made of stuff, just like everything else. This makes sense to me, I don’t view my consciousness to be anything more than the product of physical building blocks. But clearly not everything physical is mental – such as a stone which has , so a small section of the physical world encompasses the mental world.
  3. Finally, a small section of the mental world encompasses the Platonic mathematical world – that is to say anything which is capable of being expressed in “true” mathematical terms can be held in the mental state, by some being or another, but that there are things in the mental state beyond the Platonic mathematical – earlier we used the example of anger, but generally any emotion works.

This arrives us at an interesting predicament – if all of the platonic world is contained within some of the mental world, all of the mental world is contained is some of the physical world and all of the physical world is contained within some of the Platonic something is broken! This would break a basic transitivity law!

Penrose points out that there are many possible explanations for this – most interestingly perhaps these worlds are not as distinct as we are making out in this representation, which means the question of one being contained within another is not a proper question. If there is more overlap than we have drawn in the above diagram, where is it? Or maybe it has been drawn wrong…

The non-prejudiced view 

Like any good and open scientific mind, Penrose presents and considers the alternative view which does embody his own personal views on the world.

Image result for penrose platonic world

Roger Penrose, “The Road to Reality: A Complete Guide to the Laws of the Universe”, Knopf (2005)

Here some alternations have been made:

  1. We have allowed for the mental world containing things which are beyond the physical world – this will appease those who have a more spiritual view on life.
  2. Not all of the platonic world is capable of being contained in the mental world – this will upset those who like me, think we have the theoretical potential to decipher all.
  3. Not all of the physical world can be explained by the Platonic mathematical world – again this goes against the grain to any mathematician or scientist, who will like to believe that the world can be depicted through some continually refined mathematical model.

What is the right answer? At this stage nobody knows. You cannot, for example, tell me mathematics which is incapable of entering the mental state, because in order to do so you have negated your point. I favour Penrose’s view over the one just presented, but I do accept the other opinions.

Of course, there could be a problem with the very way this question is constructed – but none the less it’s good fun to play around.

36 responses to “Three worlds, three mysteries

  1. Although I appreciate the effort to indicate different categories of viewpoints, my own tendencies are to approach the problem from a somewhat different point of view. Our nervous systems are, to my experience, pattern recognizing and matching systems that create and store abstracts of the nerve impulses obtained through the sensory system. Different patterns can be applied to an external source to gain understandings and probabilities of the potentials implied. Just as one particular source, such as an accidental inkblot, can be matched with various stored abstracts each person viewing the same inkblot will match it up with a different personal set of internal abstracts which reveal something individual about him or herself. Different languages are different sets of abstracts with different rules for manipulating them. Chomsky has mentioned that the prime function of language is not communication but rather providing rules for internal thought. I do not endorse that totally, but it has a good deal of viability. There are different ways of viewing reality through the potentials of the nervous system and each avenue of observation displays different potentials and has different utilities. I doubt any limited observer such as ourselves will ever nail down the totality of whatever is out there. Einstein’s famous comment that the mystery of the universe is that it is comprehensible to an observer seems to me rather optimistic. Every observer will understand a great deal with intelligent methods but I doubt that the totality will ever be completely evident.

    Liked by 3 people

    • Hello jiisand, glad to see you are still reading! I like your point, and think I know what you are getting at – I think you are saying that if these realms even do exist then certainly the mental one is likely to be in the eye of the beholder, rather than a general sense of the word!

      Liked by 1 person

  2. Forgive me if I posit anything that is ignorant as I am not a student of science or mathematics but do take much interest in it. I am curious as to your take on which of the worlds you think energy resides in, particularly the type of energy that can control things and the type of energy that people can tap in to to psychically pick up on things, if you will (not the scam artist type of psyhics). I have a theory (as a complete lay person who is only educated at a very base level) and I’m curious what you think.

    Liked by 3 people

    • Wonderful question – but I think in this model it probably fits in the physical world. If you consider the fact that there is an equivalence between energy and mass, it ends up here, but I have to say I never thought about this perspective at all. With regards psychics… unless you meant physics you’ve lost me! I don’t believe in that sort of thing

      Liked by 2 people

      • I pick up on people’s emotions based on their energy, which is not a visible entity. And while I don’t consider myself any sort of crazy psychic, I do have dreams that have come true and I am able to predict things based on feelings that I get. I also will often think of a song and it will come on my playlist a few songs later. And it happens far too often to just label it a coincidence. So I believe that because everything does have a frequency/energy that if you can manifest the same energy or frequency, that the human mind (mental) is capable of being in tune with other frequencies or energies outside of themselves, whether it is another human being (mental) to pick up on how they are feeling or thinking or a radio station or playlist (physical) to send out a signal to play a certain song. I’m not quite sure of the platonic mathematical as that part is a little more abstract and more difficult for me to understand, but perhaps I can rationalize it as such. As a musician, we always try to seek the perfect performance which is a combination of several facets such as rhythm, pitch, expression, correct notes etc. All of those elements coming together are what form the perception of what is most pleasing to an audiences ear. As a performer, I am feeding off of the energy of my audience and the “rush” or “exhilaration” if you will of a live performance, which is energy, and that all affects my “perfect” (platonic mathematical) performance. So my theory was that energy or frequency is what was the connector between all three of those worlds or realms, that line that connected all three of those circles in the model. The only way energy or frequency can actually be seen by the eye is to measure it with a device, even though everything in the physical world does have an energy or frequency, and that becomes the matter, which is physical, there is also energy that dissipates, such as a musical performance once it is past. That remains in the mind, and could be measured during the performance itself, but it is not permanent, correct? So that does not really remain a part of the physical world, except in the minds of those who experienced it.

        Liked by 1 person

      • Reading your reply I don’t know if you are aware that in June 2015 the BBC developed a way people can change TV programs using a brainwave headset. This ability was found to be easier for some people than for others. It has also been shown that a drone can be controlled in this way.

        Liked by 1 person

    • If I may join in Alice, and you may gather from my separate comment below, I appreciate where you’re coming from in both yours. Moreover, to the musical analogy I’d add that of the orchestral conductor because they know and ‘feel’ what notes and instruments are yet to be played and bring them together to produce a harmonious blend of sound and emotive energy.
      It’s one way of explaining how synchronicity and meaningful coincidences are part of spiritual awareness and foretelling events. Another simile is that of pieces of an invisible jigsaw puzzle falling into place; another way is God’s GPS (Global Prophecy Signalling) system, about which I blog.
      Fascinating stuff, and good that you’re on the same wavelength!

      Liked by 1 person

      • I always use what you label God’s GPS or synchronicities as signs that I am in the right place at the right time and on the right path. As when I am reading a very obscure word and hear that same word on the radio or tv at the EXACT same moment, etc…I definitely believe it is all part of spirituality that is a larger universal schematic between a higher being and different dimensions/planes that are scientific in nature that science has maybe not quite found the means for measuring or accessing in a concrete manner as of yet.

        As to your point of conductors, I think it would be fair to label them as energy manipulators/workers (in a positive manner of course). They draw out of the musicians the very best from within them via energy strands.

        Liked by 1 person

      • Having engaged in this type of speculation many times I am wary of getting into religious references and have no need to impose my lack of religion on anybody but insofar as energies are concerned and random coincidences of events that seem significant I hold only vague suspicions about realities that may be fantasies. Energy per se can be useful or immensely destructive depending on whether you are winding your watch or standing too near an erupting volcano so one must be cautious about its nature.


      • It’s true, not only of numbers but also of shapes, colors, scents, sounds, textures, sensations of temperature and many combinations of these in an infinite possibility of sequences. The mind is a pattern sensitive organ and that is its function. ´

        Liked by 1 person

      • Imho jiisand, the ‘proof of the pudding’ is empirical observation of at least triple-synchonicity; ie getting confirmations through double – or more – ‘coincidences’. Occasionally I get a string of them as a concatenation, so it’s absolutely fascinating when they bring both intellectual and spiritual insights and enhance relationship.


  3. Professor Penrose is an interesting character who believes consciousness is some how linked to quantum mechanics and along with Hameroff has extended this novel idea . It is not widely accepted by by other scientists. He believes that computers as we now know them merely play at chess by number crunching and do not understand the game. This is born out by the fact that many puzzles that obey the rules of chess cannot be solved by computers.
    I have just read a book by the late Oliver Sacks a neuroscientist which contains some amazing mathematical facts about twins with an IQ of only 60 who possessed extraordinary mathematical abilities. They did not understand division or multiplication but could name six and eight figure primes. When Mr Sacks dropped a box of matches they looked and said 101 , he asked them how the counted them and they replied we didn’t we just saw 101. This may well imply the mind has mathematical depths we know nothing about.

    Liked by 3 people

    • yes there are a lot of interesting debates around how much a non-quantum computer can ever be expected to behave like a human brain – Godel’s incompleteness theorem of course being the most well known consideration. Godel, Escher, Bach is on my summer reading list – I still haven’t gotten around to it!

      Very interesting book it sounds like! My inbuilt scepticism always takes such stories with a pinch of salt – things tend to get embellished as time goes on, and of course we live in a world where it can be quite lucrative to have such stories – that said, you are not wrong in saying that extraordinary mathematical abilities do exist and continue to be discovered, which just shows how little we truly do know about the limits of our minds.

      Liked by 1 person

      • In his talk ‘ Godel and the End of the Universe ‘ The late Steven Hawking says he was rather disappointed that the ultimate theory cannot be summed up in a finite number of propositions. He appears to believe that Godel came up with theory that will ensure the quest for ultimate explanations in physics is not to be, perhaps it’s a good thing that research shall never end.


  4. I started reading Penrose’s book several years ago then became distracted with other reading/tasks. It’s taunting me from my bookshelf to resume. Interesting predicament, the physical-mental-platonic one you discuss.

    Liked by 2 people

    • Indeed it is. It’s a beast of a book, but very worthwhile. I think it’s one of those books though where you keep looking things up all the time…. the explanations are good but sometimes you need a little more than he offers


  5. I have a few comments / questions. Is physical world really that simple? Doesn’t our view of physical world get limited by our instrument? We define what is physical by what is seen by our eyes. Suppose we have telescopic view or microscopic view? Our physical world may change. We also interpret light signals in our brain. If we have a different chemical composition, say different neurotransmitter, we may view physical world differently. Another question is does mental world reside in physical world or we perceive physical world in our mind. If we shut our mind physical world ceases to exist. We do it everyday when we go to sleep.

    Liked by 1 person

  6. The Three World Hypothesis is a fascinating one i agree, but the diagrams in either case are completely innappropriate and give a deeply dysfunctional impression of the situation it is purporting to display.

    By that i mean that the diagrams imply that each ‘world’ is independent of the other – that each exists ‘outside’ of the other 2 (while implying some mutual connectivity). This is clearly misleading as neither the mental nor the platonic mathematical can be shown to exist independently (outside of) the physical – we need our bodies to prove either exists! Without the physical there is no mental or mathematical.

    The mental is entirely dependent for it’s existence upon the physical (or so those of non-religion seem to believe) while without the mental the platonic mathematical could not be shown to exist. Perhaps there is some branch of mathematics that proves otherwise?? This would imply that the physical entirely contains the mental which in turn contains the platonic mathematical, no? The other issue is of course that we exist in a minutely small part of the physical and yet we can reasonably be said to contain a great portion of the mental world (or at least the majority of examples of it’s different contents and can similarly (if we had the desire and made the effort) could also contain the many parts of the platonic mathematical within our own consciousness(es).

    The diagrams also imply that there is something external to all three worlds with which we are able to establish some viewpoint so as to see how each world is connected. What world are we viewing the 3 from in the diagrams? Is it the physical? The mental? Both simultaneously? ( Something the diagrams do not allow for!)

    It was considering the initial conditions of the Big Bang and how it expanded into it’s current apparent conformation (and how we could define our ‘position’ in the Universe through external observations to our own galaxy) that i first realised the conundrum of viewing something that is supposed to represent ‘everything’ from a position ‘outside’ of that everything.

    We are currently ‘within’ the Big Bang and always have been – while most people who try to conceive of it place themselves ‘outside’ of it and watch it as it explodes, which of course is impossible since there was nothing outside of it before it occurred…. or was there? 🙂


    • The diagram does not imply that the three worlds are independent, which is what yields the paradox (i.e. the diagram shows the entire mental world is contained within the physical). These are what the mysteries are. In terms of if there is no mathematical without the physical… well that is a philosophical point, but I believe mathematics to be timeless. It depends if you believe for example that a square only exists because a human says it does, or if you think it’s an idealised entity which existed before humanity. I belong to the latter camp – but appreciate that isn’t a view point that everyone holds. It is also one of those things that we can’t really prove, so it’s more just what your instincts tell you (which can, of course be flawed).

      I do however agree with your point about how we picture the Big Bang – there are a few interesting points where the idea of nothingness confounds us. I can remember talking to a reader in inflationary cosmology who was explaining to me that the question of what the universe is expanding into isn’t a proper question – you can’t view it like that. Of course our natural experience on Earth will try to make it so.

      There is also the interesting point with the Big Bang, that time began at this instant. If there was no time as we know it before the Big Bang… well it’s hard to assign a notion of really watching anything!

      Interesting thoughts

      Liked by 2 people

      • Thank you Joe for the post that helped inspire them! 🙂

        Just a follow on… if you hold to the idea that mathematics is timeless, does it predate the Big Bang? Did it exist prior to ‘everything’?

        I can comfortably consider it existing before humanity, and certainly before humanity was of high enough consciousness to write the principles down, but before there was any physical Universe? Isn’t that somewhat analogous to the idea that some unifying force existed before time that created the Universe that we are able to contemplate but not prove the existence of? The force some of us have given a human-like personality? How is it different if not? 😉


      • My own ideas involve a strong doubt that we are fully cognizant of the fundamentals of this universe, not to have conjectures on any other universe. I suspect that there are multiple time dimensions and that our consciousness ia aware of only one of them so we each may be aware a section of a being of multidimensional qualities unknown to us. I suspect there are experiences possible of a different time line but adjacent time lines are probably very similar so it is difficult to be sure when slippage occurs, Others have thought of this and a few SF stories have portrayed this. Although I have had a couple of mildly odd experiences I cannot be sure if I am kidding myself or not.

        Mathematics is an exquisite formulation of the relationships of abstracts we use to understand reality and different varieties of mathematics can describe different realities. Observation and experiment can indicate which mathematical architecture is useful in our reality. These are functional operations tied to the way our mind functions and I am uncomfortable in using the term existence in this considerstion.


  7. It’s worth understanding the difference of data stored in static media such as within digital context and in a living neurological setting. Dawkins invented the concept of how mental creations could have a kind of life within themselves that gained a lind of life of a purely mental dimension, Data stored within a living neurological system employs the nerve cells within a complex so that the stored dynamic data reach out s living creatures of a sort and form alliances and connections to become dynamic in contrast to static data storage. These data complexes can change their relationships so that memories within a person can change and vary from original input formation. This flexibility permits creative connections quite automatically and, say, the abstract creations that “live” within a mathematical context or an artistic context or within other formal systems such as music or the various linguistic humans utilize are subject to cultural or religious contexts and emotions in a very dynamic way quite foreign to the static data systems within computers. Memories of relatives and friends within my mind are living creations within my nerve complexes and when I dream of them or even consider them when I am awake the become living dynamics within my mind. This must also be true within other disciplines such as scientific areas or other abstract viewpoints of reality since each of us has constructed our own realities from learning and experience in general. And they are all quite dynamic since they have a life of their own.


  8. Perhaps I should clarify my understanding a bit more. I accept that all we each know and accept about reality exists separate from whatever might have prompted the nerve impulses that I assume originated in whatever may exists in the outside universe. We may divide our understandings into what we assume is reality, what we infer about the patterns we choose to acknowledge as meaningful in mathematics or other internal disciplines we find useful, and a third category which we concede is is intensely imaginative and creative and can be substantially severely divorced from general acceptable actuality. Nevertheless all these different packages exist within our brains alone although they may agree substantially in general acceptance. They are each and all manufactured products of our nervous systems and most likely differ substantially from whatever created the sense inputs to our thinking processes.

    Liked by 1 person

  9. Good that you and Mehki are back-to-blogging – and with back-to-back blogs! Also, like your trinitarian approach to trying to get a handle on our existence, even tho’ very incomplete, and which we’ve discussed some time ago. (You may recall my interest is in the conjunction of science and scripture, especially in Genesis with its Hebraic numerical equivalence and the creative and sustaining power of vibratory energy – eg. Jesus Christ’s ‘upholding’ all things by His word.)

    Liked by 1 person

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  11. Hello again Joe, just to thank you for inspiring me to get around to a brief overview of well-researched data. I’m posting tomorrow and you may want to read via my second pingback to your post, because we can be confident that mathematical principles are an important part of the eternal ‘mysteries of the kingdom of heaven’ (ie. per mystery’s original definition). It develops upon your thesis here and our posts on Euler’s elegant formula of a couple of years ago.


    • Hi Richard, I do sometimes find it most strange the things I inspire! It certainly was never my intention to provide inspiration for religion – but at least I am inspiring something!

      Liked by 2 people

      • Joe, it wasn’t just so much your content as the ‘timing-tandem’ too; yet not as synchronous as in your admiration of the Euler formula. The Penrose diagrams remind me of graphs with x-y-z axes for 3-D coordinates – but how do we draw another axis for 4th dimension of time? So they imply at least another aspect of existence. Moreover, I recalled school physics on electro-magnetic force and James Clerk Maxwell’s 3-fingered aide for determining the directions of current – field – motion (or force): if we consider possible metaphysical aspects, perhaps the hand’s other fingers may point to supra-natural or spiritual (ie not same as religious) influences? There’s similarities between the concepts of quantum tunnelling/entanglement and events described in the Bible – even Sir Roger’s now thinking that consciousness may have quantum origins!


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