Miles Mathis: More on the Golden Ratio and the Fibonacci Series

Posted: August 27, 2013 by tallbloke in Analysis, Maths, Phi, solar system dynamics

More on the Golden Ratio

and the Fibonacci Series


by Miles Mathis : First posted March 16, 2013

A couple of years ago I wrote a long paper on the golden ratio, showing how the unified field caused a
field constraint that could lead to the golden ratio in natural situations. I now have something
important to add to that.

That paper was somewhat complex as a matter of influences and kinematics, but this one will be much
simpler. I was looking at a simplified expression of the golden ratio today, one I wrote myself instead
of getting it from the textbooks, and it led me in a somewhat different direction. The golden ratio is
commonly written in terms of φ, which has the value 1.618. But it can also be written in terms of what
is called the conjugate Φ, which has the value of .618.

Historically, that was the initial esoteric thing about the golden ratio: it was the number that had an
inverse that was equal to 1 + itself.

1/.618 = 1.618

It was that curious equality that initially intrigued mathematicians, not any infinite surds or Fibonacci
series or anything else. Phi is normally written in equation form as

1/φ = φ – 1

But if we write it in terms of the conjugate—as we should—it is

1/Φ = Φ + 1

As you see, that is the more natural way to write the first number equation above. If we then multiply
both sides by Φ, it becomes

Φ2 + Φ = 1

We do that not because we are really interested in the number Φ2 = .382, but simply to get rid of the
ratio, allowing us to look at it more like a power series—or simply a power equation.
Now, the series form of the golden ratio—which leads to the Fibonacci series—is still interesting, and I
am not here to overturn it or argue it down (I will confirm it below). But this simpler form may tell us
something as well. I showed in that previous paper how we can look at the golden ratio as a field
equation instead of a series, and we can look at this simpler expression as a field equation, too. If we
let the number 1 represent “the whole field,” then we see that the other side of the equation is giving us
just two terms, not an infinite number of terms. This expression appears to be telling us that the whole
field is made up of some subfield, and also of a second subfield that is the square of the first. This may
be of interest to us, since it is what I found of my unified field. When the gravity field is changing by
the square, the charge field is changing by the quad. Which means the charge field is the square of the
gravity field, as a matter of change.

I haven’t found that the energy of either field is the square of the other, notice. The charge force on a
particle isn’t the square or square-root of the gravity force. The square only applies to the field
changes. Gravity falls off by the inverse square while charge is falling off by the inverse quad. Does
this fact have anything to do with the golden ratio?

We are seeing that it does, which makes it curious that the golden ratio has never been connected to the
inverse square law of physics. Even though no one before me had the two subfields as we do in my
unified field, it seems someone should have noticed that the golden ratio concerns squares and squareroots.
It would have been pretty easy to connect phi to the inverse square law, since phi and gravity
both fall-off by the square.

And even without gravity, phi should have been tied to the sphere. Why? Because the surface area of
the sphere also falls off by the square. Any real field emitted by a sphere would fall off by the square.
That would include gravity or anything else.

SA = 4πr2

Now, it may be that others have made this connection, but it isn’t reported in the mainstream literature.
It isn’t at Wikipedia, for instance, and it seems a thing worth reporting, if you have it in your briefcase.
I assume it isn’t reported because no one has figured out how either the sphere or gravity can be the
cause of the Fibonacci series in nature. The confirmed instances we see in nature don’t seem to be the
result of gravity or of spherical emission. For instance, although plants are in a gravity field, obviously,
and this field is spherical, the field seems too big to explain the small changes we see. The gravity field
of the Earth is very big, in other words, and curves very little. But the tendril is very small, and curves
a lot. So the connection is not made.

However, my unified field gives us answers to both problems, and allows us to make the connection
logically. It isn’t the gravity field that is influencing the tendril, it is the charge field inside the gravity
field. Since the charge field changes to the square of the gravity field, it changes very much faster.
That is, it curves more over the same given distance. This allows it to explain smaller field changes
like tendrils. The charge field is also a field of particles (photons), which allows us to track the real
influence in the field. We already know that plants respond both to the light field and to the E/M field,
so the mechanism is no longer mysterious.

In the same way, the spherical nature of the field is explained. It isn’t the large sphere of the Earth that
is emitting here, forcing us to follow the small local curvature of that field. It is the nucleus and the
proton itself that is emitting the charge field, allowing us to explain Fibonacci curves down to the
smallest sizes. The real curvature of the tendril is then explained by the diminishing influence of some
local spherical charge field, probably one centered in the plant itself. Some local bundle of ions is
creating a charge field, and we are seeing the natural fall-off with distance of that spherical bundle.
I will be told that the connection wasn’t made because the Fibonacci series doesn’t fall off by the


But it does if we analyze it correctly. I can show you how to do that straight from this mainstream
diagram. Start by ignoring the largest box. The box with a side of 1 won’t help us study squares since
1 squared is 1. We will look only at the second box and the third. Now, ignore the boxes and look only
at the curves in those two boxes. You can see we have the quadrant of a circle in each. The length of
the side of the box tells us the radius of the circle. The radius of the second box is r = 1/φ. The radius
of the third box is r = 1/φ2. I would call that an inverse square relationship. If we then compare box
four directly to box three, we get the same relationship, and so on.* If we look at each box as a field
component (or fractal) instead of as part of a series, we do have an inverse square fall-off.

In other words, the problem is they are writing and expressing the golden ratio as a series instead of a
field. The Fibonacci series is actually the same as the unified field, and they both are based on the
inverse square. Another way to say that is that they are writing the series as a series where each
number is based on the first number in the series rather than as a series where each number is based on
the previous number in the series. Notice that if you assign any box the length 1/φ, the box below it is
its square.

If you still don’t follow me, look here:


You can see phi falling off by the inverse square with your own eyes, by an equation called the infinite
surd. That isn’t my equation, that is Wikipedia’s. That is written as a sum rather than as a series,
allowing us to see the fall-off by inverse square. I will be told that is falling off by the square-root, but
the square-root is the inverse of the square. Some have said I often seem to mistake the square-root for
the inverse square. They aren’t the same.

1/r2 ≠ √r

That’s true in a lot of situations. You can’t just substitute one for the other in an equation. However, if
you are doing relative field calculations—as I often do—and you know you are in a field that varies by
the square, you can us the square-root in your calculations. I have done that often in my papers on
Bode’s law, axial tilt, and others. There, I use it as an inverse field manipulation, not as a substitution
for 1/r2 . We are seeing a similar thing here with the infinite surd equation, which—by the way it is
written—stands as a diminishing square rather than as a series.

You should also notice something else about the infinite surd. The basic term is 1 + √1, which matches
in field form our equation above Φ2 + Φ = 1. In other words, what we see again is a field with two
subfields, and one of the fields is the square root of the other. Because one field is inside the other
field, we get this infinite regression when we write the field as a series. We are seeing clear evidence
of the charge field inside the gravity field, creating the unified field.

How could so many people miss this? As usual, it is because they have too much math and too little
mechanics. Instead of trying to visualize this as field mechanics, most people have been analyzing it as
pure math. Most of the current and historical math not only doesn’t help us see the field mechanics, it
blocks it. And this example stands as a near-perfect indictment of modern physics, which has been
hampered by a lack of visualization and physicality for at least two centuries. Since the Copenhagen
Interpretation in the 1920’s, it has been even worse, since visualization was no longer simply a rarity
(due to the normal or average abilities of physicists); beginning with Bohr and Heisenberg, it was
outlawed. Banned, verboten, förbjudet.

What this means is that the Fibonacci curve is just a sign of the charge field. The charge field falls off
by the square inside the gravity field, creating this pattern of fall-off we see as the Fibonacci tendril. It
curves rather than falling off in a line, because everything curves in the charge field. See my paper on
the Coriolis effect, where I explain that curve. The Fibonacci tendril can best be understood as a field
combination of the Coriolis effect and the inverse square law, both of which I have shown are caused
by the charge field. The strength of the spherical charge field (which we call electrical when it moves
ions) causes the fall-off, and the spin of the charge field (which we call magnetic) causes the curve.
If you don’t understand what I mean by that last part, go back to the Fibonacci curve diagrammed
above. Notice they turn the series 90o by hand in between each box. Meaning, they just turn it because
it fits the tendril that way, not for any mechanical reason that they explain. If you ask them, “why are
you turning the boxes each time?” They can only answer, “Because that gives us the pretty tendril.”
But they don’t use some sort of righthand rule to justify it. They just do it. They can’t use a righthand
rule to explain it, because that would imply the tendril has something to do with E/M, and they don’t go
there. But I do. The curve actually is related to the righthand rule, and this motion is related to the E/
M field. Both are caused by the charge field, by the same fundamental mechanics.

I consider this paper to be a complement to my earlier paper, not a replacement for it. But I will admit
that this paper is far easier to digest. This paper is a refinement and simplification of the fields
described there, and should appeal to those who want just the barebones, with extreme clarity but very
little exhaustiveness (or exhaustion). That first paper was better at explaining how charge causes the
(a + b)/a = a/b relationship and the parameters of celestial bodies like the Moon. This paper is better at
explaining the Fibonacci series.


*We know that box 4 is to 3 as 3 is to 2, so if there is an square relationship between 3 and 2, there is a square
relationship between them all. The reason we don’t find that square relationship between box 1 and 2 is that box
1 is arbitrarily assigned the number 1. But our series is not based on the number 1, it is based on the number .
618. That is why box 2 is our foundation, not box 1. This is also why we don’t find a square relationship
between box 4 and 3, with the given numbers. The given numbers are written as functions of 1, not of .618. In
other words, if we divide 1/φ2 by 1/φ3 , we don’t find a square. But again, that is because the series is not a
function of 1/φ2 . It is a function of 1/φ. So the only relationship that will directly tell us that the series IS based
on the square law is the relationship between 3 and 2, as I showed.

  1. tallbloke says:

    Thanks to ‘Kuhnkat’ in the comments to the previous thread for flagging this one up.
    I wrote to Miles in February after I posted my Phi/fibonacci paper on the solar system asking him if he had any ideas on how phi might be related to the inverse square gravity law.

    Looks like he wrote this paper after that but had already forgotten why he’d started thinking about Phi again.
    Too busy writing a paper every three days. 🙂

    I think We’re now more than 0.618 of the way to a full solar system solution, and an answer to the question; “Why Phi”

  2. NikFromNYC says:

    A new English translation of Pacioli’s book called The Divine Proportion that was illustrated by Da Vinci has been delayed indefinitely now for years, so I can’t read their final interesting diagram:

    Pacioli’s long lost book on chess was recently found in a palace and it included a funky chess set:

  3. Bloke down the pub says:

    An interesting post, even if my pay-grade might not stretch that far. Still, if it means we can now build a warp engine then I’m all in favour.

  4. tallbloke says:

    Nik: Nice, I think I’ll turn me up one of those sets on my old dad’s lathe.
    There are a couple of Italian friends reading this blog, so we might get a translation of the book illustration. A lot of it is obvious, but the paragraphs need an expert.
    The heading is clearly:

    “Tree of proportion and proportionality”

  5. tallbloke says:

    Bloke dtp: What it means is I now have the underlying cause of the Phi relationships I found in the orbital and synodic periods throughout the solar system. I suspected it was gravity (and if Mathis is right, electro-magnetics too). But I don’t have Miles’ mathematical insight. His genius is in seeing things in simple equations that others have missed for centuries. It is his vision and elucidation of a ‘proper pool ball mechanics cosmos’ that has enabled him to see this relationship between Phi and the inverse square law. That in itself should be enough reason for people to take an interest in the rest of the corpus of his work.

    Now I need to re-visit my discovery and apply the Phi-inverse-square relationship to further elucidate the orderly nature of the solar system.

  6. Roger Clague says:

    Miles asks

    “How could so many people miss this? As usual, it is because they have too much math and too little mechanics. Instead of trying to visualize this as field mechanics, most people have been analyzing it as pure math. Most of the current and historical math not only doesn’t help us see the field mechanics, it blocks it. “

    I asked myself why I found it difficult to see the correct field mechanics, even when explained brilliantly as in this post. The difficult part for me was visualising “the charge field inside the gravity field, creating the unified field.”

    I was thinking of an empty space with fields in it as Newton did. So fields have separate existences, each in the same empty space.

    Now I visualise the first field ( gravity ) like a real field ready for a crop. The second field ( charge ) is the furrows and ridges made in it.

    Is this problem because we see less bumpy ploughed fields now than 100 years ago ? We see flat sports fields with straight or curved lines added on top of the grass field by us.

  7. Paul Vaughan says:

    Stated concisely: _1_ _2_ _3_ _4_

  8. Paul Vaughan says:

    Note that the discrete case (i.e. stepping by integer numbers of squares) can be generalized to continuous fractions. The Fibonacci spiral is the solution to a differential equation. In polar coordinates the differential scaling factor is (φ^2)/π. The narrative can be both generalized and simplified.

  9. tallbloke says:

    Paul: Excellent, thank you. I think most of us will have to go the long way round to be able to visualise this. Hopefully we’ll catch up with you in a while. 😉

    I wonder at what solar wind speed the Parker spiral most closely resembles the fibonacci spiral.

    Time for the less mathematically gifted among us to get the tracing paper out I think 🙂

  10. mkelly says:

    1/.618 = 1.618

    This is true depending on the accuracy you will accept. 1/.618= 1.61812297735 at least. Granted we are talking a smidge over a 1/10000 off.

  11. tallbloke says:

    mkelly: Mathis is giving Phi (big ‘P’ or Φ) to 3dp. It’s value to a few more is 0.61803398874989484820458683436564…
    A nice way to calculate the value is to add 1 to the square root of 5, divide the result by 2, and finally take the reciprocal (i.e. divide 1 by your result so far). Before taking the reciprocal (or inverse), notice that you have Phi+1 = phi (small ‘p’ or φ) = 1.6180339887…

    The above method is a slightly roundabout route so you can see both Phi and phi. The quick method is (1-√5)/2 and change the sign from neg to positive.

  12. tallbloke says:

    Not sure where I’m going with this yet but a full turn in of the spiral from box 2 with radius 1/φ in Miles’ illustration is the radius in box 6, with a radius of 1/φ5. We can multiply this value by φ*(√5+2) to get back to the original 1/φ radius one turn of the spiral out in box 2

  13. J Martin says:

    I find Miles work appealing but difficult to follow. Some of his ideas are basically alarming, such as expansion, the world and all matter and the universe (?) are doubling in size every 28 minutes, iirc.

  14. tallbloke says:

    JM: The expansion thing is a mathematical trick which enables Mathis to perform relativistic calculations without the tedious mucking around with complex maths. It also avoids the notion of an attractive force which doesn’t fit well with his vision of a ‘poolball mechanics’. But you don’t have to take it literally.

  15. wayne says:

    Uh, I’m lost, always thought
    Phi = Φ = (√5)/2 + 1/2 = [1;1,1,1,1,1,1,1,…..]
    phi = φ = (√5)/2 − 1/2 = [0;1,1,1,1,1,1,1,…..]
    it forms the the grand galactic unity at Φ − (√5 − 2)^(1/3).

    😉 Just kidding.

    Maybe just reading this again slower, phis reversed this time, and everything might become a bit clearer.

  16. tallbloke says:

    Hi Wayne. Easy mistake to make. You’d naturally think the capital greek letter Φ would refer to the bigger number. But no:

    “Mathematician Mark Barr proposed using the first letter in the name of Greek sculptor Phidias, phi, to symbolize the golden ratio. Usually, the lowercase form (φ) is used. Sometimes, the uppercase form (Φ) is used for the reciprocal of the golden ratio, 1/φ.”

  17. Brian H says:

    That works handily in my PC Windows calculator. (5^.5 + 1)/2 = 1 + phi, then the 1/x function key shows the relation, back and forth.

    Just discovered (1+phi)^2 = 2 + phi. Spooky.

  18. tallbloke says:


    I’m not really bothered what people think of Miles Mathis’ grand theory so far as this thread is concerned. The key observation he has made is that Phi contains an inverse square falloff in the way its magnitude is constituted. Given the inverse square falloff in the strength of gravity from the Sun outwards, and the phi relationships I discovered in the periodicity of the planetary orbits for which we are seeking a plausible physical explanation, this observation is the best yet in terms of finding a viable solution. That’s what I want to concentrate on here.

    So it seems to me that the best line of approach is in considering why the orbital distances tend to ‘quantise’ at phi related points. I put a comment on the other Mathis thread which may help in this regard. here it is again:

    This illustration might help us understand what is going on:

    “The idea is to try to fill a right-angled triangle with an infinite number of maximally-sized squares.
    Although you can try this with any right-angled triangle, there are certain critical proportions at which the dimensions of the filling-squares snap into simple quantised relationships.
    The first quantised solution happens with a triangle with angles of 90°, 45°, 45°. For that ratio, the squares form a cascading series where each square is exactly half the size of the last, and the quantity of squares in each size goes up in factors of two (1, 2, 4, 8, 16, 32, … etc.).
    The next solution doesn’t turn up until we use the proportions above, which turn out to be those of the Golden Section.
    For this solution, the sizes of the squares form a Golden-Section series, and their quantities form a familiar pattern. There’s one large square in the corner, another single square one size down alongside it, then two identical copies of the next square (alongside #2 and above #1), three of the next, then five, then eight ….
    This series runs 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 … It’s the Fibonacci Series!
    So while it’s already well-appreciated that the ratios between consecutive Fibonacci Series numbers converges on the Golden Ratio (as do an infinite number of other similar series), it’s less well appreciated that if you start with the Golden Section, you can generate the Fibonacci series from it by quantisation.
    As we make the shape of the triangle “sharper”, we hit an infinite number of further solutions.”

    Since nature often seems to follow the ‘principle of least action’ it seems plausible that planetary orbits would settle where there are the least number of perturbatory interactions with other planets which lead to complex instabilities. Perhaps this is illustrated by the fact that Earth’s orbit changes from more to less rounded over a cycle of around 100,000 years, rather than some shorter period. That leads to the further thought that since the Phi arrangement observed in the solar system causes repeating patterns in the alignments of various groups of planets, the effect of those alignments might be a negative feedback to perturbations which might otherwise grow too large and threaten the stability of the system. I’m fishing for ideas on how we could test such a proposal.

  19. Steve C says:

    For recreational maths enthusiasts, an earthbound ‘phi’ approximation from a long time ago which suggests that we humans have been mathematically aware for some time:

    Interesting to see it in the heavens too.

  20. tallbloke says:

    As well as this unusual property whereby the Golden Section is the proportion that the fibonacci series tends towards, and also the fibonacci series emerges from the quantisation of the Golden Section, there is another property we need to remember.

    The fibonacci series exhibits something called a lognormal distribution. i.e when you plot the log of the values against the number of terms, you get a straight line. In nature, logormal distributions turn up in various ways in nature.

  21. tallbloke says:

    Steve, fascinating, thanks. It is said that the fibonacci series came from India, and that it appears in Sanskrit poetry dated to 420BC.

  22. Steve C says:

    Glad you liked it, TB. I reckon the Fibonacci series is older than the Sanskrit poetry, though, having come across that link while doing some followup after reading some of Graham Hancock’s stuff. If he’s even half right, those alignments are likely to be over four times the age of the poetry, and facts on the ground (like the Sphinx’s well-weathered flanks) suggest he may well be.

    The older I get, the righter Socrates seems: “All that I know is that I know nothing” … 😉

  23. tallbloke says:

    Steve: The way I think about it is this.
    The clever ancients weren’t ‘primitive’. Human societies devolve as well as evolve, and it’s likely that in the last 10,000 years, some pretty smart people have spent time thinking about things. Without the distractions of modern life, and with a desire to understand the cosmos, they went to a lot of care and trouble to make observations, calculations, picking the right locations, aligning their observation stations etc. We know from inscriptions at doorways in ancient constructions that there was awareness of azimuthal positions of the celestial bodies at various latitudes, and that the constructions were sited at specific latitudes where there were significant geometric reasons for the choice. To try to divine the secrets of the heavens, the inner workings of heaven’s geometry was replicated on the Earth. The great circle at your link runs to a maximum of 30° north at the longitude of ‘the Holy land’ and at 30° south of the equator. the Earth’s tilt to the plane of the ecliptic is about 23 degrees. The Moon’s declination swings from -28.8° to +28.8° at the peak of the 18.6yr declination cycle. The tilt of the Earth may have changed a degree or so over the last few thousand years. A couple of the sites are at the latitude where a vertically placed stick would have cast no shadow under the midday summer solstice Sun.

  24. crikey says:

    Well Done TB.. Enjoying following your research..
    Enjoying also the mathis hypothesis..

    I loved his simple algebra to explain the forces of the universe.

    and also when he transposes the algebra to equal one
    Where one is the universal force

    Φ2 + Φ = 1

    A simple yet powerful relationship.

    Charge + Gravity = The entire universe Unified field

    .381 + .618 = 1

    Charge + Density = The entire Universe Unified field

    Ev + ( mass/volume) = 1

    All the charge plus all the mass and space in the universe = the universe

    Is that what he is saying. ?

    Phi ( conjugant ..0..618) is inherent in charge and density/gravity in the universe

    A general unified force equation ..
    Φ2 + Φ = 1

    So when you study Planets and phi..TB .You are studying one component of the equation. The density of the solar system?

    Anyway that my best shot at understanding Mathis . No laughing..

  25. tallbloke says:

    Hi Crikey. No units, it’s a relationship of the relative change not of the magnitude of either of the forces.
    “I haven’t found that the energy of either field is the square of the other, notice. The charge force on a
    particle isn’t the square or square-root of the gravity force. The square only applies to the field
    changes. Gravity falls off by the inverse square while charge is falling off by the inverse quad. Does
    this fact have anything to do with the golden ratio?
    We are seeing that it does, which makes it curious that the golden ratio has never been connected to the
    inverse square law of physics.”

    I made the connection at the end of February and emailed him about it. I hadn’t found a solution though, only recognised that there must be a relationship between Phi and the inverse square law. It’s still not clear to me how we integrate Mathis’ observation into the laws of planetary motion, but at least we have something to ponder. It’s a step forward.

  26. mkelly says:

    tallbloke says:

    August 27, 2013 at 8:40 pm

    mkelly: Mathis is giving Phi (big ‘P’ or Φ) to 3dp. It’s value to a few more is


  27. Roger Andrews says:


    Another interesting feature of the Fibonacci sequence is that it’s been identified in the orbital periods of planets in the solar system, which covers gazillions of cubic miles and weighs gazillions of tons, and in things that mostly weigh a few ounces or less, such as shellfish, flowers, mineral crystals and the magnetic resonance of cobalt niobate mesons.

    And so far as I know, nothing in between.

    Maybe there’s something to be learned from this.

    Incidentally, a crude but effective way of determining whether a physical variable is related to Fibonacci is simply to plot the variable against the Fibonacci number. Here’s what we get with planetary orbital periods:

    I have other some other plots that I could post if anyone wants to see them.

  28. tallbloke says:

    Roger A: Thanks for those obs. nice plot, feel free to put up others. Although the low fibonacci numbers wander quite a long way off the Golden Ratio, so to see that Mercury Earth and Venus fit well, you need to use a different method, like the one in my February paper, which starts the series from the outer solar system and works inwards to higher numbers.

    As an easy obs to they are related to phi, I made up a little word picture which goes like this.

    Jupiter makes TWO THIRDS of an orbit, while Earth and Venus meet FIVE times, as Earth orbits EIGHT times and Venus THIRTEEN, while being passed TWENTY ONE times by Mercury as it orbits the Sun THIRTY FOUR times. 2,3,5,8,13,21,34

    Regarding your obs about relative sizes, big trees weighing many tonnes also exhibit fibonacci, both in their branches and fruit and cones, and some say the continents are fractal too. Breeding populations also display fibonacci sequences in their generation numbers, and the total mass of rabbits on the planet is huge!

  29. Roger Andrews says:


    As I mentioned, the approach is crude. The idea is to spend a few minutes confirming that there is a Fibonacci connection before you spend a lot of time proving that there isn’t.

    The heaviest tree on earth is the General Sherman sequoia, which weighs in at 1,900 tonnes. The combined mass of the planets in the solar system is 2,700,000,000,000,000,000,000,000 tonnes. So including trees doesn’t do very much to reduce the scale problem.

    Neither does including rabbits. The world rabbit population is estimated at around 7 billion, which with an average rabbit weight of 1kg gives us 7 million tonnes of rabbits. This is still 380,000,000,000,000,000 times less than the weight of the planets.

    I also note that the connection between breeding rabbits and Fibonacci is based on a model that makes a number of assumptions, including immortal rabbits and that the female produces one male and one female rabbit every month. Is there any observational verification of this model?

    Back shortly with more graphs. 🙂

  30. Stephen Fox says:

    Phew thanks for the calming words about expansion,TB. I’ve got enough on my hands with actual expansion due to middle age…
    But mainly, thanks for bringing Miles Mathis to my attention. I went to read his work on Einstein and almost felt I understood. Also, there’s a nice little drive-by on dark matter.
    I hear Trenberth’s missing heat is now officially ‘dark heat’. Feels right, somehow…;D

  31. tallbloke says:

    Hi Roger A: Good stuff. I freely admit the rabbits is a numbers game, not obs. 🙂
    Anyway, general sherman ups the ante from your “few ounces” you have to admit.
    I suppose I could turn the question back to you and ask what large things there are between 1900 tonne trees and the planetary scale where Phi might manifest itself. Snowflakes perhaps? Not individual ones, but the total mass of polar ice is pretty big.

    Good to see your first crude pass reveals that there is a Phi relationship between the planetary orbital periods. I already knew that, but you’re being a wise sceptic by confirming it for yourself.

  32. tallbloke says:

    Stephen F: Welcome. Miles says he’s found that the latest sum of mass of dark matter as proposed by the mainstream theoreticians equals his mass equivalence for the total of photons comprising his fundamental charge field he predicited which he says underlies atomic particles and electrical and magnetic fields.

  33. Roger Andrews says:


    Some pics to look at. First four more solar system variables. The relationship between Fibonacci and orbital distance is about as good as the one between Fibonacci and orbital period, suggesting that with a little extra work you could get a close fit between Fibonacci and orbital distance too – unless of course you’ve already done it. 🙂 The fits with planetary mass and density aren’t so encouraging, but there may be other ways of plotting the data that would improve them.

    Second, four plots of Fibonacci against terrestrial variables. The atmospheric pressure and earth’s internal temperature plots show no match – I think because these variables are distributed lognormally while the Fibonacci distribution is semilognormal, but then I didn’t expect much from these comparisons anyway. The lack of a good match in the tectonic plate case was, however, a little disappointing because tectonic plates are born, grow, die and move around like flowers and shellfish and I think can also be characterized by fractals. I was also hoping that the percentage of elements plot would show something because the proportions of chemical elements in some crystals are reportedly related to the Fibonacci sequence, but the plot shows an almost exact anticorrelation with Fibonacci, almost as if Fibonacci was acting in reverse. Don’t know what to make of that.

    I’d be happy to plot up comparisons for trees and rabbits if I had any numerical data to plot, but there doesn’t seem to be any.

  34. tallbloke says:

    Roger A: Good work. One of the great dead astronomers, lavoisier maybe or laplace, noted that the densities of Venus, Earth and IIRC Jupiter followed the inverse square law approximately. My aim in this thread is to work out how to apply Miles’ insight on the inverse square hidden inside Phi to planetary orbital parameters. So we might find a relation in the end, but obviously not the direct one your plots show isn’t there.
    I did find a couple of interesting pages on phi in chemistry and physics for you to peruse:

    If hydrogen has a phi factor, then protons dancing with electrons in the solar wind maybe do too…

    I’m offline for 24 hrs.

  35. oldbrew says:

    @ Roger Andrews

    What might the effect of ‘pairing’ planets be on the data you supplied, i.e. combined figures for Me+V, E+Ma, J+S, U+N ?

  36. Roger Andrews says:

    TB: Interesting links. Thanks. It seems that the golden ratio is alive and well at the molecular, atomic and subatomic levels.

    I find this kind of analysis a lot more compelling than the photos of shellfish, flowers and trees you find on the web. The golden ratio doesn’t work in all shellfish anyway (it works in gastropods but not too well in lamellibranchs, brachiopods and echinoids) and not in all trees either. I have a palm tree in my garden which grows straight up for about 30 feet and then splits into into ten fronds, each of which has about 150 leaves, and that’s it. Not much sign of Fibonacci there.

    However, the fact that water molecules cluster in groups that exhibit golden ratio properties doesn’t mean that these properties will be identifiable in rivers, lakes or oceans, which contain uncountable numbers of molecules that are free to move wherever gravity and fluid flow takes them. The golden ratio also reportedly controls the structure of snowflakes, but you won’t see it replicated in a snowdrift. This might go some way towards explaining the “scale” problem.

    So why do we see Fibonacci in action in something as large as the solar system? Well, I haven’t a clue, but I find it intriguing that the golden ratio governs the Bohr radius, which defines the distance between the proton and electron in a hydrogen atom (your second link), and that the “acceptor” bond in the first Figure of this link looks like Miles Mathis’ “squashed” moon.

    Oldbrew: “What might the effect of ‘pairing’ planets be on the data you supplied, i.e. combined figures for Me+V, E+Ma, J+S, U+N ?” I’d be happy to try this but I’m not certain how to ‘pair’ them or what you think might happen if I did. Could you elaborate?

  37. tallbloke says:

    Roger A: Glad you found the links interesting. regarding your palm tree:
    “I have a palm tree in my garden which grows straight up for about 30 feet and then splits into into ten fronds, each of which has about 150 leaves, and that’s it. Not much sign of Fibonacci there.”

    Have a look at the spiral growth on the trunk. You might find the angle between the successive dead frond branch stumps is some multiple or subdivision of 137.5 degrees. 360-(360/phi). The arrangement maximises sunlight on leaves.

    “What might the effect of ‘pairing’ planets be on the data you supplied, i.e. combined figures for Me+V, E+Ma, J+S, U+N ?” I’d be happy to try this but I’m not certain how to ‘pair’ them or what you think might happen if I did. Could you elaborate?”</em

    Oldbrew and I are meeting up on Saturday. He has indeed been working on planet pairs, and yes, we do have interesting discoveries to report in due course.

    Right, gotta go.

  38. oldbrew says:

    @ Roger A

    ‘I’m not certain how to ‘pair’ them or what you think might happen if I did. Could you elaborate?’

    Don’t worry, there aren’t any certainties but I didn’t want to put more than one idea into your head. Let’s leave it open to interpretation for now, so if anything springs to mind along those lines why not try it out.

  39. Tenuk says:

    The rings of Saturn display Phi relationships with the planet. As the rings are made up of comparatively easily to move fragments, rather than a large solid lump, perhaps no surprise.

    Nice illustration here!

  40. John in France says:

    I am in no sense a mathematician, but have over twenty years of experience with phi by way of practical ruler-and compass drawing practice.
    To me, the spiral shown and its description have the whole process arse-up’ards and make a very simple drawing process look fiendishly complicated. The simple process entails NOT ignoring the largest “box” (or rather, square) but starting with that square divided into two 2 : 1 rectangles. If you then set your compass to the diagonal of the outer rectangle and produce it down to the extended base line of the square, you can form a rectangle that will automatically have phi proportions or extreme and medium ratio. This phi rectangle (of irrational proportion : 1.618 0339 887 …) combined with the original square will also have phi proportions, extendable to infinity by adding squares to the longest side. A square inscribed within a phi rectangle corresponding to the shortest side will give the same result. No other rectangle has this property. It can also be the basis of the spiral shown. This procedure has proved invaluable to me in musical instrument design without resorting any calculation or numeric measurement whatsoever (the results of crunching irrational numbers will always be relatively inaccurate anyway).

  41. Roger Andrews says:


    Here’s a photo of the top of my palm tree. Growth lines on the trunk are flat and evenly-spaced, not spiral, and there’s no growth pattern I can see that comes close to an angle of 137.5 degrees. The frond branches get narrower away from the trunk and I guess they might show an inverse Fibonacci relationship, but I’m not going up there to take measurements because the picture begins about 25 feet above the ground and I don’t bounce as well as I used to. 😉

  42. Roger Andrews says:


    I did some crude “pairing” by calculating the ratios of orbital periods and distances between adjacent planets and plotting them, with the idea being that in a perfect Fibonaccian world they would all plot along a horizontal line at y=1.618. They of course didn’t, and Jupiter/Mars generated a big spike when I used only the nine planets:

    Interestingly, however, the spike went away when I added the asteroid belt:

    With the asteroid belt included the orbital period ratios are significantly higher than the golden ratio (mean 2.19, standard deviation 0.41) but the orbital distance ratios are encouragingly close (mean 1.68, standard deviation 0.23).

  43. oldbrew says:

    Thanks RA, looks interesting. Given Kepler’s law that the ratio of orbit² to (distance from Sun)³ is a constant, can that be reduced to one graph?

  44. tallbloke says:

    Roger A: Could you try the ratios of adjacent synodic periods of planetary pairs for us? E.g. m-v vs v-e vs e-m vs m-a etc

  45. oldbrew says:

    TB: what is ‘m-a’?

  46. Roger Andrews says:

    “Roger A: Could you try the ratios of adjacent synodic periods of planetary pairs for us? E.g. m-v vs v-e vs e-m vs m-a etc”

    Dunno about that. The synodic periods don’t look very encouraging:

  47. oldbrew says:

    RA: those are the synodic periods with Earth so they don’t show Mercury-Venus, Jupiter-Saturn etc.

  48. tallbloke says:

    I’ll put together a list for Roger A.