Saturday, February 27, 2010

On Being A Bit Horrid

A couple of weeks ago, I wrote an article about a guy called Nassim Haramein who makes a living by giving talks on the nature of the universe, and why I think he's a fake. I kind of pulled him to pieces, and carried on pulling him to pieces until I got tired.

His ideas seem to be extraordinarily popular, and he has quite a following, so my article has caused a bit of a stir. But to a lot of people, I get the feeling it looks like I'm just being horrid. Why else would someone pull another person to pieces? It's not very nice.

Little My: a bit horrid

And it might look a bit horrid to people who've never heard of him too. Why is Bob spending so much time pulling someone to pieces? Why doesn't he write about birds and stars like the good old days?

Anyway, aren't people entitled to hold differing views? Doesn't the human race already spend far too much time putting each other down?

I was thinking about this the other day and I came up with a little story.

Imagine you grew up speaking fluent Mandarin, as well as English. And you'd spent a lot of time in China, living among people in many different parts of the country.

One day, probably somewhere in the US of A, you come across someone giving public lectures on how to understand Mandarin. Lots of people are interested, it seems, because Mandarin is still quite alien to most people in English-speaking countries, yet it's a language that may prove increasingly valuable to learn for the future. You're curious, so you take a look.

What you see is someone making stereotypical Chinese-sounding noises. He utters words that sound vaguely Chinese, and explains what he thinks they mean. He tells his audience that he's studied this language for many many years, and has learned things that most teachers of Mandarin would never even realise. You do recognise some of his words, but they're not put together in a way that makes much sense to you.

You ask his students, who proudly tell you that this is the true Mandarin, and that what they teach in language schools is flawed. When you take issue with this, they insist that obviously that's because you're only able to see what you've been taught, and you've never thought outside of this box, and if you could see the bigger picture then you'd understand what he was saying and what a revolutionary understanding of the language it was. And the reason no other teachers of Mandarin teach this way is because of a massive conspiracy to put down creativity and keep the language in the control of the elite. Or something like that.

Anyway, who are you to tell people how they should speak Mandarin?

He has thousands of followers, and they all happily believe this is the true Mandarin. What do you do?

I guess most people in this situation would decide, after perhaps a little time trying to argue, that what we have here is a bunch of nutters, and walk away. And I probably would too, because, well, what can you do? If they're so keen on believing that this is the true Mandarin, then let them.

It was a little like this for me to find Nassim Haramein claiming he's speaking from years of cutting-edge physics research. The language of physics and mathematics and reasoning is one that I grew up with and use regularly, and I know enough of it to recognise clearly when someone is blagging it.

Science and mathematics is much more like a language than art or music. Learning it is first of all an attempt to get things right – you're trying to get at the way things are, using reason and evidence. Once you're fluent, you can be wonderfully creative with it, but first of all you have to learn to make some sense of the process of rational investigation. Otherwise, no matter how impressive it might sound to some people, you're being as transparently meaningless and ridiculous as the guy who claims that his Mandarin is more true than the one spoken in China.

* * *

I thought I'd devote some time to 'refuting' Haramein because it's clear that there are a good number of people who are curious about him and want to know more, and there's surprisingly little on the web that points out clearly why he's a fake.

I can understand why there's so little on the web analysing him critically and objectively. Firstly, he may have a huge internet presence but he's hardly a household name. Secondly, it's not especially enjoyable to listen to someone when you know they're talking rubbish – it does feel like an awful waste of time. Thirdly, efforts to communicate with his followers isn't entirely pleasurable either. And fourthly, you can end up looking like a proper spoil-sport, taking the side of run-of-the-mill pernickety correctness against the forces of liberated thinking.

Not everyone is a big fan of excessive rationality, but when most of us turn to newspapers, politicians or scientists, we don't appreciate being led up the garden path. However lovely someone might seem, if you can see that they're gathering a following and making money by misleading people, then you do start to feel for the people who are taken in by it.

Of course, we could always view him as a spiritual guide instead of a scientist, as some clearly do – so long as we don't mind our spirituality being served up with delusion, prejudice and an inflated sense of its own importance. (Some would argue that we have a long history of not minding this.)

That's a personal choice. I just wanted to put the information out, so there it is. I've tried not to be unpleasant with it, and to be as objective as I can.

I'm not especially bothered about physics. What I'm bothered about really is the process of searching for truth. (I certainly don't confine this search to physics.) Integral to the search for truth, it seems to me, is the willingness to ruthlessly cast out whatever is obviously false, and then to gleefully jump up and down on its head if it tries to show its face again.

So, well, maybe that means I do enjoy being a little bit horrid sometimes. I'll leave that for you to decide.

You can see my article at
(though you might not find it very interesting unless you happen to know who he is, or have a particular curiosity for people who like to pretend to be physicists).

* * *

In the process of trying to get my head around all this stuff, so that I can argue with people on YouTube and things like that, I've come across some great places to sharpen your understanding of real physics on the web. (I have genuinely been trying to find ways to remain open to everything I've heard Nassim and others say, from all sorts of perspectives... and the more I've tried, the crazier they've looked.)

On YouTube now, not only can you watch the whole of Carl Sagan's Cosmos series, and several programs about the great Richard Feynman, and many other great science documentaries, but if you REALLY want to get to grips with the understanding of reality that modern physics has given us, there's a fabulous selection of lecture series by Stanford University's Leonard Susskind. He's done an entire 15 to 20 hour series on each of Classical Mechanics, Statistical Mechanics, Quantum Entanglements, Quantum Mechanics, Special Relativity, Quantum Field Theory, The Standard Model, General Relativity and Cosmology.

I'm working my way through his presentation of General Relativity as we speak, and it's extremely good. I've been scribbling away deriving Christoffel Symbols to my heart's content, and (when told to) even gone so far as to cut things out of cardboard to explore the nature of curved spaces.

A mostly-flat space with a pringularity at the centre
(a negative curvature singularity; thanks to PV for the word)

As with all physics, though, many of the theories are essentially mathematical in nature, so it's perhaps not for everyone.

(This mathematical nature, oddly enough, isn't because of a massive conspiracy among scientists to keep their ideas out of the reach of those without mathematical training! I've read so much rubbish now, I'm starting to feel obliged to point these things out. It's because using mathematics is the only way to really see that the ideas you read in the popular science books actually work. If all you do is read the ideas in popular science books, you could easily think they're just ideas, and conclude that the ideas of some nutcase from Hawaii might be just as valid. It simply doesn't work like that. It's unfortunate that the only way you can be convinced of this is if you 'do the math'.)

Anyway, don't let me get started on all that stuff again. Give Leonard Susskind a try if you're feeling adventurous (and patient!). I've learnt a lot in the last few weeks, and in some peculiar way it's all down to our friend Mr Haramein. So there we are.

Feel free to think I'm horrid if it makes you happy. I think I'm lovely. (Come on, I used a picture of everyone's favourite mymble! How lovely is that?)

We can argue about it in the comments if you like.

Go to Haramein article
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Saturday, February 13, 2010

Nassim Haramein - Fraud or Sage? (intro)

(Click here if you don't need introducing to Nassim Haramein.)
Recently I've been impressed by the rise to internet fame of Nassim Haramein. He's lauded as a multi-disciplinary thinker, as a scientist, as an inspirational speaker, and as director of research of The Resonance Project.

From the following that he's developed, it's fair to say that he's touched a lot of people's lives. There are a lot of people out there who really think the world of him, and it's not hard to see why. His talks and seminars delve into the heart of reality – the universe, ancient history, particle physics, sacred geometries, mathematics, consciousness – and through the clarity and geniality of his delivery he seems to actually light up his audiences with new ideas.

A brief internet search of his name seems to show only glowing reports. Inevitably, with a little more delving, there are also detractors. There are also a good deal who are curious but unsure, wondering if this guy is for real. He certainly polarises people: a lot of people seem to think he's a nutcase; and there are a lot of people who think he's a genius, and will hold to it in the face of any argument.

I'm not setting out to argue with those who have already made up their minds one way or the other (and who are possibly only looking here to see whether I'm a good guy or a bad guy, and not that interested in what I might say otherwise). We're each entitled to our opinions. But for those who are genuinely curious, I think it's worthwhile taking a look at what he does.

I'd better put my cards on the table now, though. My view is that Nassim Haramein has very little insight into reality from any sort of scientific perspective. I'd like to explain why I believe that any claims on his part of being a physicist, of using any scientific method, or of having any understanding of mathematical principles at all, are utterly bogus. I'd like to give you what I believe are very sound reasons and evidence as to why I say this, and why it is important.

The process of discovering and rigorously testing truths about the universe is something I rate very highly as part of my personal values. Because of this, my personal view is that if he is indeed deliberately selling himself to the public as being at the forefront of scientific knowledge despite having very little scientific insight at all, then he is misleading and even manipulating people for fame and for financial gain. That would be a serious matter of abuse of trust, and it would make him a fraud.

Of course, not everyone holds the scientific method so dear to their hearts. I'm telling you this only to let you know where I stand, not because I think you should agree with me.

I don't want to argue about his qualities as a new age inspirational speaker, or about whether or not he's a great character, or whether or not his ideas make some people happy, or whether or not the pyramids were in fact conceived by people from another planet or anything like that. I only want to look at his scientific claims, to see if he is who he says he is, or whether he's merely manufactured an image and is misusing the language of science to give an air of authority to whatever comes into his head.

Please continue to the main post:

Nassim Haramein - Fraud or Sage?

I'd like to outline here some very sound reasons for asserting that Nassim Haramein is grossly misleading people by claiming to have any depth of scientific understanding behind his ideas.

If you'd prefer to just see some straightforward examples, try some of these (también en español) – but do come back when you're done...

Más discusión en espagñol aquí.

(Alternatively, read this if you think I'm just being a bit horrid.)

[Edit Dec 2011: Anyone curious about Haramein's appearance in some obscure 'peer-reviewed' conference proceedings, please see this note: Feel free to ask questions in the comments.]

[Edit July 2013: He's had an article ("Quantum Gravity and the Holographic Mass") published in a science journal. Does that mean it is science? Please see here or here for details. Links updated May 2016.]


On many of his videos, and on the main page of his Resonance Project's website, he displays a "prestigious" award for one of his physics papers. What is this? His certificate looks at first to have been awarded for best paper in the whole of "physics, quantum mechanics, relativity, field theory and gravitation" at the entire university of Liège, Belgium in the year 2009, and "chosen by a panel of peer reviewers". That would be quite an accolade.

But when you read the wording, it's clear that it was awarded for best paper presented in that category at a single computing systems conference; and that the 'peer reviewers' who awarded it were just the other people on the conference. Most people understand peer review to mean something quite different.

Two relevant questions here. Firstly, how much would the other people on this conference understand about "physics, quantum mechanics, relativity, field theory and gravitation"? Secondly, how many other papers on these subjects do you think were presented at this particular computing systems conference? It's not likely to be many.

It does sound impressive when described on the website and on videos such as this one. If you've looked at youtube comments and so forth, you'll see that plenty of people are impressed by it. In reality it is no more than a certificate for turning up at a conference in Belgium with a paper.

It seems likely that this is the best he has to show from any respectable institution for his twenty years of research, and he really would like to present something from a university that makes him look like legitimate scientist. You can't accuse him of lying here: to his credit, he puts the certificate in clear view right under our noses. As a display of sheer pretentiousness, it's pretty blatant.


Nassim's main current claim to scientific legitimacy is his paper, The Schwarzschild Proton.

It is eight pages of equations and particle physics, and claims to be a significant step towards potentially deriving the strong force from general relativity. Again, it looks impressive. But there are a number of very sound reasons to dismiss this paper as meaningless.

It's presented as a scientific document, so it's not possible to go into the reasoning properly without using technical language and concepts – which is a shame because I doubt that anyone with a good grasp of these concepts would need me to explain the problems with this paper. For those who are curious, I've presented a more detailed analysis of the Schwarzschild Proton as a separate post.

Broadly, though, the main problems with this paper are:

(a) His overall argument is circular, which means it shows nothing. A hypothesis is presented that a proton might be considered as if it were a black hole, and his first conclusion, after a few pages of equations, is that the forces between them would be very strong, like the forces in a nucleus. But this goes without saying! If you pretend that something is as heavy as a thing can be, then it shouldn't come as a surprise to find that the forces would be as strong as a force can be. There's no significance in this whatsoever.

(b) His theory implies that the nucleus of a single atom of hydrogen has a mass of nearly a billion tons. This does seem a bit silly – but theoretical physicists do hypothesise apparently silly things sometimes, so that's not a deal-breaker. For obvious reasons, though, you need a very convincing reason to do something like that, including an explanation as to why we never measure this huge mass when we weigh hydrogen (or anything else), and none is given.

(c) The paper, while using some scientific terms, is presented at a very basic level. This could be considered a plus – all scientists would agree that there's nothing better than a simple theory, if it works. But Nassim is merely playing with equations from student textbooks (these are the only references cited in the paper), things that have been explored thoroughly for decades, and he's using them in a pretty simplistic way. It's unlikely that he'll find anything that hasn't been found before by doing this. What he has found is some values for things that look suspiciously like what he knew when he started. This is often what happens when you go around in a circle.

It's a bit of a joke to claim that anything profound can come from this kind of thing. But again, it looks cool, and it's clearly enough to impress a lot of his followers. And it won a prestigious award! (see above)

As I mentioned above, you can find a more technical look at his paper here.


Nassim often talks about geometries or field equations or things of mathematical significance. Yet watching videos of him presenting ideas, it's painfully clear that he is clueless when it comes to pretty basic mathematics.

Here is a video of him discussing the phi ratio (or golden ratio), a subject he mentions often. From 3:00 minutes onwards, he is using a CAD program to show a relationship between a phi spiral and a W-shape which has some connection to the 'mathematical' ideas of Marko Rodin.

He spots something that looks like a connection – between the emanation point of the spiral and the intersection of the W-shape (jump in at 5:30 into the video to see this) – and he immediately assumes that he's discovered something significant. What does he do? Does he...

(a) investigate it?No. He does zoom in on it a little on his CAD program to prove his point. But he wouldn't have had to zoom much further to disprove it. In this still from the video, it's fairly clear that the spiral doesn't actually emanate from where the lines cross.

(b) calculate it?No. If he had calculated where the spiral starts and where the lines cross, he'd have found that they're not related at all, and that they're not the same point. If anyone is interested, I've done the calculations here. They're not very difficult – no more than the maths I knew from A-level when I was 17.

(c) announce that his 'discovery' relates to interference resonances and has profound implications for Einstein's field equations and matter spiralling into a black hole and that it links his theories to the 'Mathematical Fingerprint of God'?Yes! It's (c). Watch the video. That's what he does.

[Edit 18th Nov: the original video was removed from YouTube, as was the one I found after that, but this third one has most of the same footage in it. Unfortunately it's missing the clip of Haramein relating his work to the 'Mathematical Fingerprint of God', but it wouldn't take you long to find Rodin blurting these claims about the W shape.]

So what? Well to me this is significant. We see the results of this kind of thinking throughout his presentations; this is just one particularly blatant example. It makes it clear that this is not someone who investigates mathematical or scientific ideas when jumping to conclusions will do. Nassim (and indeed the other participants in the video) is someone who is way too ready and willing to make outrageous claims, and to jump on anything that looks kind-of right without stopping to question it. He drags into his explanations as many established scientific concepts as possible to make what he says sound convincing, however irrelevant they may be, and throws in some seriously wacky ones for good measure. This is someone who brings the phi ratio, fractals, dimensions or infinities glibly into his presentations and plays the expert, but meanwhile is clueless about mathematics.

No physicist would ever do this. (Well... one would hope.)

For what it's worth, if you still think there may be some connection, common sense should be enough to tell you that when matter spirals into a black hole it is pulled in faster (begins to dive in at a steeper angle) as it moves towards the centre, rather than completing more and more orbits as it gets closer, as shown on Nassim's spiral. I've explained this a little more in the maths post.

I think this example goes some way to explain why so many people love the 'intuitively right' feel of Nassim's ideas. It feels intuitively right to some people because his approach is simply to spot what seems to be a connection or a pattern, and link it up to the first thing that it reminds him of. He's also a master story-teller. Physics could really do with more people who can communicate like him (but who understand what they're talking about, are a bit less self-obsessed and self-promoting, and will tell the truth). Nassim Haramein is not an investigator, rigorously testing his ideas on the touchstone of reality. What he is doing is not science, it is story-telling.

The appeal of his ideas – making the complexities of the universe graspable and simple to understand – is a false appeal. The Universe far more beautiful and complex than this, and far more of a slippery customer. Getting even a glimpse of how it works has taken the collaborative effort of massive numbers of rigorous, dedicated researchers over the ages. It's an affront to Nature to claim that it can be grasped by whatever models and connections happen to come into one guy's head, untested and unquestioned, however intuitive and exciting and real it may all have seemed to him at the time.

It's a attractive idea. Who wants 'the scientists' to have all the answers? The idea that this one guy-next-door character might have these lovely little insights into physics that have all escaped the entire scientific community, that would be one in the eye for the institutions, wouldn't it. You can see the appeal. It'd be a great thing to be a part of. If he wasn't simply making it all up.


A question. If Nassim's ideas, talks and research are scientific and revolutionary, why is the academic community ignoring it? As far as I can tell, no scientist working in any public university anywhere in the world has responded to any of his research, either in a scientific publication or anywhere online. None of his papers have been published in any scientific journal – certainly not one subject to proper peer review [but see top of article for July 2013 update]. Scientists seem to either treat him as a crank or dismiss him altogether. Which of the following reasons sounds most plausible? Is it...

(a) because the scientific establishment are afraid of having all their precious theories overturned?

Science loves having theories overturned. It's true that individual scientists are human and can be reluctant to accept when their way of seeing things is revealed to be false. Some will be slower to accept new things than others. But all will agree that this is part of the job of being a scientist. In addition, many scientists are deeply competitive, and for every theory beloved to one set of scientists, there'll be another set that is devoted to looking for any serious evidence they can use to pull the rug out from under it.

The world scientific community is an extremely diverse and argumentative bunch. Surely it would be crazy to imagine them being capable of unanimously agreeing to dismiss perfectly good ideas sitting right under all their noses.

This is a fact compatible with even the most cynical view of scientists – that they're more often out to prove each other wrong, even to backstab, than to back each other up. It makes it implausible that any scientist actually sees Nassim's ideas as any sort of threat. His ideas have simply never been taken seriously.

(b) because scientists are incapable of seeing outside the box that they were trained to think in, and are too proud to accept radical suggestion from an outsider?

Scientists can be guilty of narrow thinking. If you specialise in an extremely complex area, the effort of getting your head around the ideas within one framework might be so taxing that the last thing you want to be doing is considering the possibility that the whole framework might be wrong. At the same time, there are many scientists who are mavericks and ready for change, ready to throw it all up in the air. They also have all manner of values, and all manner of spiritual outlooks and practices.

There are hundreds of thousands of scientists in the universities of the world, and their ways of thinking are as various as any other group of hundreds of thousands of human beings - if not more so. There'll always be plenty of scientists hungry for any radical idea, especially in topics as hot as grand unified theories, provided it's got some substance.

There may well be unanimous skepticism about things which have utterly no scientific basis, such as someone claiming to have a theory that the moon is made of green cheese. But this is not because of any inability to think outside of the box.

Regarding outsiders – yes, pride and over-cautiousness can get in the way of scientists taking suggestions seriously from people not affiliated to a university. But would every single one of them fall prey to this? Again, scientists, and even scientific establishments, are surely too numerous and too diverse for this to be plausible.

When Garrett Lisi submitted a potentially revolutionary theory for the unification of particle physics, he was an unemployed surfer living in a camper van on a Hawaiian island with no university affiliation. (Aside from now renting a room in a shared house, it seems he still is.) Perhaps the majority of physicists initially did not take him seriously. But there were certainly plenty who did, who were waiting for someone like this to challenge everything, who looked at his work and thought "you know, this guy really does know what he's talking about. He could be onto something here. And I want in on this."

There are so many other examples of theories being accepted from outsiders (Einstein, for one) that this answer doesn't hold any water. If he isn't getting taken seriously, it certainly can't be blamed on a complete worldwide closed-mindedness among all respectable scientists.

(c) because they haven't come across his ideas yet?

Nassim and his Resonance Project have a massive internet presence, and they've been promoting their ideas to scientific bodies, presenting at university conferences (alongside student projects and industry researchers) throughout the world, and submitting papers to peer-review journals at every opportunity for most of the last decade. Not to mention training hundreds of people to promote their ideas for them.

There have been considerable efforts to put an article about Nassim Haramein, the scientist, on Wikipedia. The results can be seen here – I think you'll find the discussion revealing.

(It's worth noting that all Garrett Lisi did to set the academic world abuzz was to present his ideas at a single relatively obscure conference in Iceland.)

(d) because anyone with an understanding of science can see that his claims and his methods are not scientific in any sense of the term, and that he doesn't actually know what he's talking about?

I reckon so.
The Schwarzschild Proton and other ideas from The Resonance Foundation have also been discussed in depth at


A similar question. How is it that none of his radical historical ideas have any support from any academic institutions either?

I promised I'd stick to the scientific side... but I'd suggest something roughly along the lines of 'ditto'

There was more I had planned to discuss here. I honestly could go on and on with this guy, but it's already rather longer than I anticipated. (I'm open to suggestions, though.) I don't know how much evidence folks feel they need.

[Edit on 8th June: More clear examples of Haramein (a) being clueless about all aspects of physics, and (b) making absurd claims for his insights into physics, can be found in a new post here.]

I'm aware that not everyone understands what evidence is. Some people are even prepared to argue that the more effort we put into 'debunking' someone like Nassim, the more likely it is that he's right, because otherwise why would we go to so much trouble?

No. The reason I want to 'debunk' him is because he's wrong. I teach physics and maths to students, and I think it's important to let them know when something is wrong. It's important to be able to tell truth from falsehood - if we don't, then we lose sight of truth altogether. I don't like it when someone pretends to have insights into the laws of physics that all the scientists of the world are supposedly too dumb to have realised, and misuses their charisma to build an uncritical following. And I noticed that there don't seem to be many detailed explanations on the web of why he is wrong. So I thought, at the risk of looking like a nutter for going on about someone at such length, that I'd try to address the imbalance.

Cultivating the image of being a serious scientist by making misleading and false claims in order to attract paying followers is a serious abuse of trust. There are plenty of others I could have gone for instead. Marko Rodin is one. But you have to start somewhere.

I've posted this on an old and rather silly anonymous blog of mine that happens to still get some traffic (mainly because of the Planck Monkeys), because it means I can go on at length without it giving him any legitimacy.

Now if you just want to listen to him because he can tell an entertaining, inspiring, but rather silly story, full of stuff he's made up, then I wouldn't argue with you for doing that at all.

[Edit 22nd July: Response to this article by Nassim Haramein...]

Response from Nassim Haramein

Nassim Haramein's Resonance Project has published a detailed response to this article. To find out more and to read his response for yourself, please see here. Thank you.

Some links:
The fate of Nassim Haramein on Wikipedia.
Discussion on Bad Astronomy forum
Debate at
Little url for these articles:
A (small) Facebook group[Back to blog]

Some mathematics relating to the phi spiral

This is a more detailed look at one of the points made in my post on Nassim Haramein (number 3 on that page). I've written this in plain text for now, which I appreciate isn't easy to read... I'd like to set out the equations nicely sometime.

In the above video, from 3 minutes onwards, Haramein can be seen arguing that the off-centre location of the emanation point of a phi spiral within an enclosing circle is connected to 9-fold 'resonances'. To illustrate this he divides a circle into 9ths and shows a W-shaped set of chords intersecting at a point that appears to be the emanation point of the phi spiral. You can see this in the video from about 5:30 onwards.

In fact it is straightforward to show that they're not related, and the two points are not the same at all.

1. True Phi Spiral

A phi spiral is a logarithmic spiral which increases in radius by a factor ϕ≈1.618 every quarter turn. The properties of logarithmic spirals can be derived with a bit of basic calculus. A full derivation would be a little too long to show in full here, and it turns out to be irrelevant to what was on Nassim's screen anyway, as he wasn't using a true phi spiral.

Briefly, though... The first step is to calculate the radius of curvature of the phi spiral, which is r√{1+(2 lnϕ /π)²} at a distance r from the emanation point. The second step is to work out the angle between a tangent of the spiral and the radius, which is arctan[(2 lnϕ /π)]. From these, with a little trigonometry, the distance of the phi spiral emanation point from the centre of its enclosing circle works out as
√{1-1/[1+(2 lnϕ /π)²]} ≈ 0.29291 of the way along a radius from centre to circumference.

2. Intersection of Chords[a diagram here you'll have to imagine it for now! Of an isosceles triangle with a vertex of 360/9 = 40º, and another with the same base but a lower vertex of 60º. The vertex of the first triangle is at the centre of the circle, for reasons of 9-fold symmetry; the vertex of the second is where the chords cross. What we're calculating is the distance between the two vertices.]

The distance of the meeting point of the (W-shaped) chords from the centre can be calculated using basic trigonometry. The chords join points 1 & 5 and points 4 & 8 respectively of a regular 9-fold division of the circumference, as can be seen in the video at around 5:40.

The result is {cos(π/9) - √3 sin(π/9)} ≈ 0.34730 of the way from centre to circumference. The 9-fold division of the circumference shown in Nassim's diagram, and which he specifies in the video, is clearly reflected in the formula.

This is nowhere near the emanation point of a phi spiral. The reason it appears close on the presentation is that the spiral used in the video is not a pure spiral at all, but an approximation.

3. Approximated Phi Spiral

Nassim's approximated phi spiral is made from quarter-circles, each increasing in radius by a factor of ϕ. The two versions of the spiral are shown in green (pure spiral) and red (approximation using quarter-circles) on the diagram below. Where they overlap, it shows as yellow. They may look similar, but if you plot continuation circles around them they come out markedly different.

Image from wikipedia; creative commons license; modified from original.

This approximated spiral is constructed from circles embedded in squares, so we can use some basic geometry to calculate the position of the emanation point of this spiral – it lies √{1 - 2/√5} ≈ 0.32492 of the way from centre to circumference. To calculate this, note that the symmetry of the construction implies that it must lie at the point of intersection of the two diagonal blue lines in the diagram above. The eqations of the lines are shown on the diagram, in cartesian form, relative to an origin as shown on the diagram. They can be solved as standard simultaneous linear equations.

This value is close enough to the position of the intersection of the chords to look almost indistinguishable in the presentation. A careful viewer, however, will note that in Nassim's video, the lines do indeed cross further from the centre than the emanation point, as can be seen in the still below.

A still from the video of Nassim's 'discovery'. In this close-up of an area below the centre of the circle, Nassim's diagonal chords are seen to cross below the emanation point of the spiral, not on it. I've added blue cross-hairs at roughly where the emanation point of this spiral would be.

The last two numbers (0.34730 and 0.32492, the ones relevant to Nassim's presentation) can easily be checked by careful construction of the shapes on paper or on a graphics package, and by measurement of the appropriate distances.


There is no mathematical relationship between a phi spiral and a circle split into 9ths. The relationship claimed in Nassim's presentation works only if you don't look too closely, and even then only if the spiral is approximated using quarter-circles.

For him to consequently make claims about the inspiralling of particles into a black hole is preposterous for a number of reasons. Firstly, inspiralling matter doesn't follow any logarithmic spiral (let alone a phi spiral). As matter spirals inwards it is diving in at an ever steeper angle, even without resistance to motion. A logarithmic spiral, in contrast, approaches the centre at a constant angle. The resulting spirals are markledly different (see images below). Secondly, in the model he presents, as it is not a true spiral, the inspiralling matter would in fact have to follow a circular path for 90º and then, suddenly and discontinuously, follow a different circular path for another 90º, which is even sillier. And thirdly, even if it did, the values are still unrelated aside from their happening to be within about 2 or 3 per cent of a radius of each other.

In addition, the 'interference patterns' that seem to 'just appear right out of the phi spiral' when the pattern is replicated (from about 6:40 on this video) are purely an artifact of the approximation that he's used to build the spiral. If he had used a pure logarithmic spiral instead of quarter-circle building blocks, no such patterns could occur. On this topic, as with the others, we see his willingness to jump to vague but profound-sounding conclusions rather than investigate what he is thinking.

I suggest that it is clear from the above that the method of his arguments – if indeed there is one beyond spotting something that looks a little bit like something else – is very deeply flawed, very easily shown to be false, and lacking in both a basic understanding of mathematics and the imagination required to properly investigate straightforward mathematical situations. For this reason (indeed plenty more may be given, but this is reason enough), any of his claims to be employing mathematical or scientific methods to explain the underlying nature of the cosmos or anything else of any complexity should be seen as extremely dubious.

Above: approximate spiral path of matter falling into a black hole (Using dr/dt∝1/r³; and assuming ω².)
a phi spiral; clearly very different.

[Plotted using Wolfram Alpha ]

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