July 15, 2021

The butterfly effect 4/5

Gravity, entropy and self-organization


After explo­ring the his­to­ry of chao­tic sys­tems and begin­ning to put chaos theo­ry into pers­pec­tive with Nassim Haramein’s theo­ry of the connec­ted uni­verse, I conti­nue my explo­ra­tion of the links bet­ween entro­py and self-organization that can be obser­ved throu­ghout the universe.

Ilya Prigogine ope­ned the box of iso­la­ted sys­tems by pro­po­sing a phy­sics of dis­si­pa­tive struc­tures. Nassim Haramein has shown that there is no box to get out of ! Because in a uni­verse where eve­ry­thing is connec­ted, nothing is iso­la­ted from nothing. So, if the uni­verse is not a clo­sed sys­tem but is inter­ac­ting with other uni­verses, what hap­pens to the notion of entro­py, which is inti­ma­te­ly lin­ked to clo­sed systems ?

In this article, I invite you to exa­mine the idea that in a uni­verse made up of black holes connec­ted at all scales by a feed­back of infor­ma­tion, the notion of entro­py is entan­gled with that of gra­vi­ty. In other words, I am explo­ring the pos­si­bi­li­ty of recon­ci­ling the increase in entro­py pre­dic­ted by the second law of ther­mo­dy­na­mics with the increase in self-organization in the uni­verse. Let’s go !


A formula for entropy

« You start with a ran­dom group of atoms, and if you light it long enough, it shouldn’t be so sur­pri­sing that you get a plant. »

An article [2] publi­shed in 2014 in Quanta Magazine des­cribes how the phy­si­cist Jeremy England [3] deve­lo­ped a simple mathe­ma­ti­cal for­mu­la des­cri­bing entro­py. It explains the abi­li­ty of cer­tain groups of atoms to cap­ture ener­gy from their envi­ron­ment and dis­si­pate it in the form of heat, under cer­tain conditions :

- Being dri­ven by an exter­nal ener­gy source (such as the sun for example)

- Being sur­roun­ded by a bath of heat (like the ocean or the atmosphere)

These atoms manage to gra­dual­ly self-structure them­selves in order to dis­si­pate more and more ener­gy. To deve­lop his for­mu­la, England relied on the work of phy­si­cist Chris Jarzynski and che­mist Gavin Crooks. These scien­tists have shown that the entro­py pro­du­ced by a ther­mo­dy­na­mic pro­cess cor­res­ponds to a simple ratio : the pro­ba­bi­li­ty that atoms under­go this pro­cess divi­ded by their pro­ba­bi­li­ty of under­going the oppo­site pro­cess. This ratio increases as the pro­duc­tion of entro­py increases : the beha­viour of the sys­tem then becomes more and more « irreversible ».

According to this for­mu­la, in prin­ciple appli­cable to any ther­mo­dy­na­mic pro­cess, sys­tems far from equi­li­brium can the­re­fore keep their entro­py low by consi­de­ra­bly increa­sing the ener­gy of their environment.


Example with pho­to­syn­the­sis. During this phe­no­me­non, a plant absorbs sun­light, which is extre­me­ly ener­ge­tic. It uses it to make sugars and then rejects infra­red light, which is much less concen­tra­ted. Thus, as sun­light dis­si­pates, the ove­rall entro­py of the uni­verse increases. However, during its life­time, the plant will prevent itself from decom­po­sing by kee­ping its inter­nal struc­ture in order.

Jeremy England shows that the absorp­tion and emis­sion of light are due to reso­nance phenomena.



For optimised energy dissipation

« We can show very sim­ply from the for­mu­la that the most like­ly evo­lu­tio­na­ry out­comes will be those that absorb and dis­si­pate the most ener­gy from exter­nal envi­ron­men­tal inputs to achieve them. »

« This means that clus­ters of atoms sur­roun­ded by a bath at a given tem­pe­ra­ture, such as the atmos­phere or the ocean, should tend to orga­nize them­selves to reso­nate bet­ter and bet­ter with the sources of mecha­ni­cal, elec­tro­ma­gne­tic or che­mi­cal work in their envi­ron­ment. » [5]


Jeremie England talks about dissipation-induced mat­ter adap­ta­tion. He iden­ti­fied two mecha­nisms that allow an increa­sing amount of ener­gy to be dis­si­pa­ted over time (increa­sing entropy):

- Self-replication : According to him, the theo­re­ti­cal mini­mum dis­si­pa­tion that can occur during the self-replication of RNA mole­cules and bac­te­rial cells is very close to the actual amounts that these sys­tems dis­si­pate during repli­ca­tion [6].

- Structural orga­ni­za­tion : under cer­tain condi­tions, par­ticle sys­tems will spon­ta­neous­ly orga­nize them­selves by adap­ting their struc­ture to bet­ter dis­si­pate ener­gy. For non-living sys­tems, we can cite the vor­tices of tur­bu­lent fluids. They repro­duce spon­ta­neous­ly (self-replication) accor­ding to a frac­tal law (struc­tu­ral organization).


On the right frequency

anevrisme-structure-dissipativeAs I explai­ned in article 2, these vor­tices form in an aneu­rysm [7]

when blood rushes into it because its beha­vior becomes tur­bu­lent. There are many spa­tial and tem­po­ral scales in the aneu­rysm sac. The size, loca­tion and orien­ta­tion of twirls are constant­ly changing.

However, these vor­tex dyna­mic sys­tems behave more like dis­si­pa­tive struc­tures than chao­tic sys­tems. In fact, they repro­duce spon­ta­neous­ly by dra­wing their ener­gy from the sur­roun­ding fluid. Precisely, they accu­mu­late ener­gy by reso­nance. And in doing so, they also dis­si­pate a large amount of it. Thus, the increase in order inside the struc­ture appears in depen­dence with the increase in disor­der outside.

Dynamic sys­tems are ulti­ma­te­ly sen­si­tive not to ini­tial condi­tions but to reso­nances. Henri Poincaré high­ligh­ted it with the pro­blem of the three bodies, Ilya Prigogine deve­lo­ped it with the dis­si­pa­tive struc­tures : reso­nances invite us to think dif­fe­rent­ly than in terms of tra­jec­to­ries.

« The notion of reso­nance cha­rac­te­rises a rela­tion­ship bet­ween fre­quen­cies (…) Resonance occurs when (…) two fre­quen­cies (…) cor­res­pond to a simple nume­ri­cal ratio (one fre­quen­cy is an inte­ger mul­tiple of the other) (…) Frequencies, and in par­ti­cu­lar the ques­tion of their reso­nance, are at the heart of the des­crip­tion of dyna­mic sys­tems. »


Turbulent fluids behave as such because the rota­tio­nal forces due to gra­vi­ty out­weigh the fric­tio­nal forces due to vis­co­si­ty. And they even have a link with black holes !


Towards black hole entropy

Indeed, a black hole can be des­cri­bed as a bubble of vis­cous fluid, then its beha­vior being close to that of a tur­bu­lent fluid. We’re tal­king about a fluid-gravity match.

Moreover, in the holo­frac­to­gra­phic model, a black hole behaves as such because the rota­tio­nal forces of space-time exceed the fric­tio­nal forces. The frac­tal cha­rac­ter of a tur­bu­lent fluid is found in the geo­me­try of the hori­zon of a black hole when it is modi­fied by the absorp­tion of a mate­rial object. The black hole emits gra­vi­ta­tio­nal waves, whose dis­si­pa­tion by cas­cades of ener­gy allows it to return to its equi­li­brium form.

Jeremie England’s work shows that par­ticles tend to dis­si­pate more ener­gy when they reso­nate with a dri­ving force. Could the source of the elec­tro­ma­gne­tic work that this phy­si­cist is tal­king about be the gra­vi­ty that Nassim Haramein is tal­king about ? Indeed, what bet­ter than a black hole in the theo­ry of the connec­ted uni­verse to absorb and dis­si­pate energy ?

Let us add that this theo­ry esta­blishes that black holes are lin­ked by a frac­tal law from the infi­ni­te­ly small to the infi­ni­te­ly large, and this dyna­mic can be explai­ned at all scales !


Information, gravity and entropy

The holographic principle


At first glance, tal­king about entro­py for a black hole isn’t very intui­tive. In the stan­dard model at least. Entropy is rela­ted to tem­pe­ra­ture. Black holes do not emit radia­tion. Therefore, they have no tem­pe­ra­ture and no entropy.

In 1972, Stephen Hawking sho­wed that the sur­face area boun­ded by the hori­zon of a black hole can­not decrease. Jacob Bekenstein then saw an ana­lo­gy with the second prin­ciple of ther­mo­dy­na­mics and, in 1973, he argued that black holes do indeed pos­sess entro­py, repre­sen­ted by their event horizon.

At the time, this theo­ry was unac­cep­table to Stephen Hawking, who set out to prove that it was false… until his own cal­cu­la­tions pro­ved it to be cor­rect. Using quan­tum phy­sics to explain the mecha­nism of radia­tion, he sho­wed that the shape of this radia­tion is exact­ly that of an object in ther­mal equi­li­brium. And that its tem­pe­ra­ture is pro­por­tio­nal to sur­face gra­vi­ty. Finally, in 2004, he reco­gni­zed that black holes have entro­py, that infor­ma­tion can be retai­ned, and that black hole hori­zons absorb and emit coherent information.

According to Bekenstein, the infor­ma­tion has a mini­mum size equi­va­lent to a Planck sur­face, a quan­tum pixel the size of a Planck length of side. Based on this work, Gerard ‘t Hooft sho­wed in 1993 that all the infor­ma­tion contai­ned in the volume of a black hole can be expres­sed in terms of infor­ma­tion on the black hole hori­zon. The infor­ma­tion is then sto­red in the form of a fin­ger­print. This is what Hooft cal­led the « holo­gra­phic prin­ciple » [9]. The infor­ma­tion absor­bed by a black hole is ful­ly res­to­red during the quan­tum eva­po­ra­tion pro­cess. The holo­gra­phic solu­tion found repre­sents the entro­py of the black hole, it’s equi­va­lent to the tem­pe­ra­ture.


The quantification of information

The entro­py of black holes is a mea­sure of the amount of infor­ma­tion they contain, but to which we do not neces­sa­ri­ly have access [10]. The inter­pre­ta­tion of this defi­ni­tion is deba­table accor­ding to :

  • The theo­ry and the­re­fore the frame of refe­rence used (stan­dard or holofractographic)
  • The basic unit used to quan­ti­fy the infor­ma­tion (area or volume)

The entro­py of a black hole is less than a quar­ter of the sur­face of its horizon.

entropy-black-holeIn the stan­dard theo­ry, a Planck area is used as the fun­da­men­tal unit of infor­ma­tion. Thus, a black hole whose hori­zon consists of Planck’s areas A has a maxi­mum entro­py of A/4 units. From an infor­ma­tion point of view, it is as if the entro­py is writ­ten on the black hole hori­zon and each bit of infor­ma­tion, as 0 or 1, cor­res­ponds to four Planck areas.


Nassim Haramein’s model is much more ele­gant. By using spheres and not sur­faces as units of infor­ma­tion, he esta­blishes a direct rela­tion­ship bet­ween the volume of a black hole and its sur­face, and thus its entropy :

  • The volume of a black hole is a sphere made of small Planck spheres.
  • There is a natu­ral ratio of 1/4 bet­ween a sphere and its equa­to­rial sur­face [11] (4πr² / 4 = πr²).
  • The sur­face of the black hole is lined with equa­to­rial sur­faces arran­ged in the pat­tern of the flo­wer of life.

Entropy can thus be quan­ti­fied in a very simple way [12].


Feedback information

« Information is the inter­con­nec­ted fabric of our uni­verse. What are the dyna­mic pro­cesses invol­ved ? Feedback sys­tems (like a frac­tal), which lead to non-linear evo­lu­tion and local unpre­dic­ta­bi­li­ty
[13]. The inter­ac­ti­vi­ty (inter­com­mu­ni­ca­tion) of such a sys­tem, with its crea­tive and inno­va­tive aspects, leads to expo­nen­tial assi­mi­la­tion and syn­tro­py. Far from the ran­dom and mecha­ni­cal pro­cesses fore­seen by the law of entro­py, which is in itself a high­ly theo­re­ti­cal case of an iso­la­tion and divi­sion sce­na­rio. » [14]


Order and disor­der coexist thanks to this feed­back dyna­mic. Information is always trying to orga­nize itself, it tends tire­less­ly towards more com­plexi­ty and towards the advan­ce­ment of conscious­ness. The feed­back of infor­ma­tion is esta­bli­shed by constant to-and-fro bet­ween the infi­ni­te­ly small and the infi­ni­te­ly large : it goes from the quan­tum vacuum to mat­ter and vice ver­sa. Particles appear and disap­pear conti­nuous­ly through the fun­da­men­tal pro­cess of materialization/dematerialization of the vacuum. The ori­gin of the mate­rial « order » is the feed­back bet­ween mat­ter and vacuum. This exchange hap­pens in such a short time that it eludes us.

But if each inter­ac­tion with the vacuum per­ma­nent­ly breaks the conti­nui­ty of the mani­fes­ta­tion of mat­ter, how can we explain that forms are pre­ser­ved in time ? Thanks to the enco­ded infor­ma­tion about the struc­ture of space, which, as it inter­acts with mat­ter, pro­vides a memo­ry for the struc­ture. In the end, from moment to moment, eve­ry struc­ture is recrea­ted fast enough and close enough to the pre­vious one that it gives us the illu­sion of expe­rien­cing conti­nui­ty in form.

So be it. But in this case, shouldn’t there be a pat­tern, a struc­ture at the base of all the others, which would serve as a refe­rence ? What if it’s the vacuum structure…


The vacuum structure

Vacuum is not only ran­dom, it also has a struc­ture. Which grows in a… frac­tal fashion. From then on, we can bet­ter unders­tand how cer­tain pri­vi­le­ged phy­si­cal quan­ti­ties — such as the mass of the pro­ton, the speed of light or the gra­vi­ta­tio­nal constant — keep their res­pec­tive values no mat­ter what hap­pens. Why are the constants constant after all ? Because they obey a pre­cise and per­pe­tual­ly rene­wed divi­sion of the struc­ture - and the­re­fore of the ener­gy — of the vac­cum. It is not the value of these pri­vi­le­ged magni­tudes that is constant, it is the dyna­mics of the uni­verse to which they obey.

And here are the notions that have just been dis­cus­sed in infographics :


In summary

The information

  • The uni­verse is an open system.
  • The uni­verse is an expan­ding black hole.
  • It is made up of black holes dis­tri­bu­ted accor­ding to a frac­tal law, from the infi­ni­te­ly large to the infi­ni­te­ly small.
  • A frac­tal is an open equa­tion that allows feed­back from one scale to ano­ther (or from one black hole to another).
  • The exchange of infor­ma­tion in the uni­verse is based on the prin­ciple of reso­nance (simi­lar fre­quen­cies attrac­ting and « wor­king » together).
  • The infor­ma­tion is sto­red in memo­ry, enco­ded on the space-time structure.



  • The exchange of infor­ma­tion in a region of space creates an ener­gy cal­led mass.
  • Mass ener­gy creates gravity.
  • Gravity is the result of an exchange bet­ween the infor­ma­tion contai­ned in the volume of a black hole and that present on its surface.



  • The entro­py of a black hole is a mea­sure of the amount of infor­ma­tion it contains.
  • The volume of a black hole is made up of Planck spheres (the smal­lest unit of infor­ma­tion that defines our rela­tion­ship to the universe).
  • The infor­ma­tion contai­ned in the volume of a black hole is pro­jec­ted onto its sur­face (holo­gra­phic principle).
  • The sur­face of a black hole is lined with Planck’s equa­to­rial surfaces.
  • An equa­to­rial sur­face of Planck is pre­ci­se­ly one quar­ter the sur­face of a Planck sphere (4πr² / 4 = πr²).
  • The tota­li­ty of the equa­to­rial sur­faces repre­sents the neces­sa­ry and suf­fi­cient sur­face to quan­ti­fy the entro­py of the black hole.
  • As the uni­verse expands, the sur­face area of our black hole-universe increases.
  • Thus the entro­py of the uni­verse increases. However, its gra­vi­ta­tio­nal field is also increasing.
  • Since gra­vi­ty is a ratio bet­ween the volume and the sur­face of a black hole, entro­py is pro­por­tio­nal to volume and inver­se­ly pro­por­tio­nal to gra­vi­ty.


  • So yes, the entro­py of the uni­verse is increa­sing, but it can never increase dis­pro­por­tio­na­te­ly because it inter­acts with gra­vi­ty, which constant­ly balances it by crea­ting order.
  • Gravity is a source of reso­nance and self-organization ; it keeps struc­tures in an ever-changing order.
  • Entropy and self-organization appear in depen­dence.


This is how the uni­verse orga­nizes itself, at the cost of a large amount of ener­gy. In the next and last article of the series on the but­ter­fly effect, we will go back down to Earth and see how this dyna­mic applies to the scale of the MeToo move­ment.



Notes and references

A formula for entropy

[1] ENGLAND Jeremie, quo­ted by Natalie Wolchover, A new phy­sics theo­ry of life, in : Quanta maga­zine, 2014
[2] WOLCHOVER Natalie, op.cit.
[3] Jeremie England is an assis­tant pro­fes­sor at the Massachusetts Institute of Technology. Its theo­re­ti­cal results are gene­ral­ly consi­de­red valid, but the inter­pre­ta­tion of its for­mu­la has not been proven.


[4] Jeremie ENGLAND, quo­ted by Natalie WOLCHOVER, A new phy­sics theo­ry of life, op. cit.
[5] Ibid.
[6] September 2013 article publi­shed in the Journal of Chemical Physics
[7] An aneu­rysm is a dila­tion of the wall of an arte­ry that causes the crea­tion of a pocket inside which the blood changes its beha­vior.
[8] PRIGOGINE Ilya, La Fin des cer­ti­tudes[The end of cer­tain­ties], Paris, ed. Odile Jacob, 1996, p.45

Information, gravity and entropy

[9] See also the article The holo­gra­phic uni­verse : the under­lying uni­ty to unders­tand the link with holo­gra­phy, from which the prin­ciple takes its name by ana­lo­gy.
[10] To get an idea of what I mean, you can read this alter­na­tive inter­pre­ta­tion of Schrödinger’s Cat expe­rience.
[11] The equa­to­rial sur­face is the flat sur­face obtai­ned when cut­ting a sphere per­fect­ly in two.
[12] Note that this approach also allows us to find a quan­tum solu­tion to gra­vi­ty, as well as a solu­tion to the infor­ma­tion para­dox.
[13] Authors’ note : « A local phe­no­me­non appears to be unpre­dic­table when it depends on the glo­bal evo­lu­tion of the uni­verse. »  
[14] BROWN William and HARAMEIN Nassim (2014, January 23) Space-time as Information — An Ordering Principle of Living Systems


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