It From Bit - The Whole Shebang
    By Johannes Koelman | August 8th 2010 07:06 PM | 49 comments | Print | E-mail | Track Comments
    About Johannes

    I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune


    View Johannes's Profile

    In the It-From-Bit series I have reported extensively on Verlinde's 'entropic gravity' concept. I have also provided you with an illustrative 'mikado universe' picture of entropic gravity. This got topped off with my own intuitive notion that in an entropic universe, not only gravity, but also accelerated cosmic expansion emerges. As a result, in one fell swoop, entropy eliminates the need for a fundamental force of gravity as well as the need for dark energy. 

    All of this can be summarized succinctly by expanding on an analogy put forward by Dennis Overbye in the New York Times:
    There is no elementary force that causes mass to accelerate together and neither is there such a thing as dark energy causing the universe to accelerate. It is just that the big bang made the universe wake up to a bad hair day.
    In this fourth It-From-Bit blog post, I will attempt to provide you with an intuitive graphical picture of how entropy effects lead to the emergence of gravitational as well as cosmic acceleration. The first causes matter at short distances to accelerate together, and the second causes matter at large distances to accelerate away. By the time you finish reading this post, you should understand how entropy can be responsible for both these, seemingly opposite, effects.

    On the origin of bad hair days
    If you make a habit of falling asleep with nicely combed hair, and invariably wake up with a hairdo resembling a knotty mess sprouting in all directions, you might be tempted to ascribe this emergence of disorder to a 'hair knotting force' in combination with an 'expansive hair pressure'. This gets even more tempting when, despite vigorous combing, you keep observing hair springing back in a disordered state. Clearly you have to overcome significant randomization forces to restore your hair in a nicely ordered compact configuration. 

    Celebrity bad hair day: victim of knotting forces and expansive hair pressure spotted in the wild (1949).

    When reasoning like this, you have fallen into a conceptual trap. 'Hair randomization forces' do not exist. Just the fact that there is many more ways for your hair to be tangled up rather than being nicely ordered, makes your hair to evolve into a statistically more probable messy state. By tangling up, knotting and expanding disorderly, hair gets more room to express itself.

    Are we making the same conceptual error in reaction to the universe's bad hair day?

    If so, to avoid this error, we must accept that both gravity and the mysterious cosmic tension referred to as dark energy both cease to exist at a fundamental level. Gravity and dark energy are no more than the large scale consequences of the universe seeking more probable configurations. Mass clogs together and the cosmic expansion speeds up as a result of the universe seeking room to express itself. Some call it a bad hair day, others refer to Murphy's law, while physicists prefer the more quantitative term entropy. No matter what name you attach to it, fact is increasing disorder needs no force to guide it, it's the way things evolve statistically. 

    Physical bits: entropy, quanta and degrees of freedom

    To understand the entropic origin of gravity and dark energy, we first need to grasp entropy. In essence, entropy is the number of bits required to describe a physical system in all its microscopic details. Rather than speaking about bits, physicists tend to talk in terms of 'the number of degrees of freedom' or the 'number of quanta'. We don't need to be bothered about the differences. For the present purposes we can think of the quanta constituting a physical system as encoding the bits specifying that system.

    Physical systems statistically tend to seek configurations that require more bits to describe them. Reason is that a configuration described by, say, 8 bits corresponds to 28 = 256 different microscopic states, while a configuration described by only half of that number of bits would correspond to 24 = 16 microscopically distinguishable states. Physical systems don't have a preference for any of their micro-states, and as a result they do show a tendency towards configurations rich in micro-states, and therefore corresponding to more bits.

    This, in a nutshell, is the statistical basis for the second law of thermodynamics: the number of bits or amount of entropy of a system tends to increases due to the microscopic dynamics being impartial to the accessible micro-states. In layman's terms: physical systems seek configurations that allow them more room to express themselves.       

    Entropic Gravity

    Whereas in Newtonian context one can investigate universes consisting of point particles, in general relativity such idealizations do not exist, and we are forced to consider more interesting elementary massive objects: black holes. So let's investigate a model universe consisting of black holes.

    In my last post I elaborated on black holes and the holographic principle. The picture that emerges is that for outside observers black holes can be thought of as spherical surfaces capable of accommodating a finite number of quanta. Key result of black hole physics is that the number of quanta is proportional to the surface area. With the mass (or energy) of individual quanta scaling with the inverse of the black hole circumference, the black hole mass (the total mass of all quanta) is proportional to the black hole's circumference.

    Combining these black hole results with the above entropy maximization principle, one is tempted to conclude that individual black holes will increase their entropy by growing in size. That would be true, were it not that also black holes have to adhere to the law of conversation of energy. The entropy (or area) of an individual black hole can not grow without increasing its energy (or circumference). 

    So how does nature satisfy its hunger for entropy?

    That is simple, if one black hole doesn't suffice, add a second. If two black holes of equal mass merge, a black hole will result with a mass equal to the sum of the two.* This means that the resulting black hole circumference will equal the sum of the two initial circumferences, and therefore the resultant entropy (or surface area, which scales with the square of the circumference) will double.

    Two equally sized black holes merging together (cross-sectional view). The net effect is that the total circumference doesn't change, while the total area (entropy) doubles.            

    From the second law of thermodynamics, it follows that black holes will tend to move together and merge, thereby forming a configuration richer in entropy. We have given this effect the name 'gravity', and for many years assumed it to be associated with a fundamental force. It is not, it is a statistical (entropic) effect.

    Studying in more detail two black holes approaching each other, it becomes evident that both will undergo surface area (or entropy) increases, even when their mutual distance is much larger than their individual diameters. When doing the math, it follows that for large distances these entropy increases correspond to an entropic acceleration given by Newton's one-over-distance-squared law. This is what is at the heart of Verlinde's observation that gravity is an entropic effect.     

    Entropic cosmic acceleration 
    Ok, so black hole mergers lead to entropy increases. Is there another way for our black hole universe to increase entropy? You might be surprised to hear that there indeed is an alternative way for total surface area (and thereby entropy) to increase. In fact, it is a much more straightforward way: the total surface area of a system of black holes will increase when additional black holes enter the system. 

    How could that happen in our model universe? Well, we have to be a bit more precise here: often when we are talking about 'the universe' what we really mean is the observable universe. This observable universe is bounded by a cosmic horizon. The term horizon is very appropriate here, but denotes a more fundamental limitation than we are used to. The cosmic horizon indicates the cosmic depth beyond which observation is physically impossible. It is the distance at which the cosmological redshift becomes unbounded, and time seems to get to a stand-still. For an expanding universe, the cosmic horizon and distant objects all recede. Objects will enter the observable universe causing its entropy to increase, provided the cosmic horizon recedes faster and overtakes the most distant objects. This mechanism is illustrated in below animation.            

    Entropic cosmic acceleration at work in the black hole universe (cross-sectional view). While the black holes (white circular holes) move away from each other, the cosmic horizon (the edge of the observable universe indicated in dark blue) overtakes the receding black holes. Although no black holes merge, the entropy of the observable universe (total surface area of the black holes contained within in the observable universe) obviously increases.

    It should be clear that nature's hunger for high entropy configurations will lead to a combination of affects shown in the two animations above. Entropy increases by black holes merging, as well as by the observable universe expanding. When doing the math, both effects result in accelerations: massive bodies accelerate toward each other, and the observable universe undergoes an accelerated expansion. The key conclusion to be drawn from all this is that these effects do not require a fundamental force of gravity, and neither do they follow from a mysterious dark energy dominating the universe, yet unobservable other than by it's effect on the cosmic expansion. Both acceleration effects are the direct result of what one should expect to happen statistically without a fundamental force of gravity or dark energy to be present.

    Word of warning
    To conclude, a word of warning: although since my original entropic universe post several research groups have embraced the entropic universe concept described above, not all it's consequences have been derived yet. In particular, the entropic expansion of the universe differs from the expansion described by the standard model of cosmology, the lambda-CDM model. Further investigations are required to compare the behavior resulting from the entropic expansion model to the same data used to fit the parameters in the lambda-CDM model. 

    No matter how appealing these ideas might seems, if they don't fit the data we need to scrap them. Watch this space.   

    * This would be true if one could execute a controlled merger. In reality, black hole mergers are uncontrolled explosive events that will cause some of the mass to be ejected. As long as less than about 29% of the total mass gets ejected, there will still be an entropy increase albeit not an entropy doubling.


    On counter argument I read to Verlinde's ideas on gravity was that if gravitational attraction is caused by a change in entropy, how this can be squared with the second law.

    For instance, if an object moves around another mass in an elliptical orbit, it will come closer at one time => Entropy increases, and more distant at another => Entropy decreases.

    If entropy decreases at one place, it must increase in another. But where? I am sure this is too simple a view of gravitational interactions and the second law. But it does puzzle me.


    Johannes Koelman
    Rob -- the main focus of the above post was to provide a simple non-relativistic picture of entropic gravity, and in particular how entropic effects can generate attraction (gravity) as well as repulsion (dark energy). (I got quite some questions about this.)

    The question you raise widens the discussion to how energy/momentum-conservation fits within the entropic framework. It was stressed by Verlinde in his paper that this is an essential part of the entropic approach (he made it plausible that Newton's F=ma fits into the conceptual picture), and one that needs to be addressed in the still-to-be-devised (!) holographic entropic gravity theory.

    I think it is fair to say that at this moment all we've got is some simple hints that entropy gives the right instantaneous accelerations ( both for gravity as well as for cosmic expansion), but we have no idea how to cast this into a full theory. In the absence of such a theory, we can still test the entropic dark energy concept against hard cosmological data (it does make predictions different from lambda-CDM). That will make clear whether or not the search for such a theory will be a waste of time. To come back to your specific question: I don't think it's right to assume that relative motion leaves the entropy (horizon surface areas) unaffected.
    Johannes says: "I don't think it's right to assume that relative motion leaves the entropy (horizon surface areas) unaffected."

    Maybe this article provides a clue to a potential "relativistic entropic" approach:"

    "We will show that the entropy associated with a simple localized matter system in flat and otherwise empty space is not an invariant quantity defined by the system alone, but rather depends on which observer we ask to measure it."


    "An inertial observer will assign the usual, naive entropy given by the logarithm of the number of internal states. However, an accelerated observer (who sees the object immersed in a bath of thermal radiation) will find the object to carry a different amount of entropy."


    Thanks for the link

    Amateur Astronomer


    The reference to Marolf, Minic, and Ross 0310022v2.pdf from 2004 has a few problems.

    The obvious problem is it calculates entropy differences from internal energy in the first law of thermodynamics with out accounting for the mechanical energy that is required to boost the object into a frame relative to the second observer.  So the whole article is suspect of a systematic error, even if it is the second observer who is boosted.

    Next the Lorentz contraction apparently puts the object and its entropy into a smaller volume with a smaller surface relative to the second observer. The second law doesn’t allow this without expending mechanical energy on the object or the observer.

    From these two problems it appears likely that the observers will have to be included inside of the system that is being measured, if the entropy is to be regarded as a path independent state function.

    The article makes assumptions from the Unruh effect and the second law of thermodynamics, but attempts to rewrite the third law of thermodynamics without actually saying so. The writers started with an attempt to show that the entropy change from a series of generalized thermodynamic processes is different from the entropy change from a corresponding sequence of quantum state changes.

    I would guess that the conclusions are more of a result from the mathematical assumptions that were made, than they are from the physical states of the system. In the widely accepted Copenhagen representation the state of a system is not established until a measurement is made.  Then the measurement apparatus becomes part of the system and contributes to the measured state.

    So where can we find the answer to this riddle? See whether I understand it.

    An inertial observer will see the three laws of Thermodynamics always observed. According to the equivalence principle, a free falling observer will also see all three laws to hold.

    So this means that an observer in an orbit will see no change in the entropy while she moves around. Even if she is in some elliptical boundary around a mass.

    There is no reason to assume that an accelerating observer will observe that the three laws hold. So, a stationary observer in a gravitational field could measure a change in entropy from a mass in orbit at different points in orbit. Or not?

    Or would such a change only be observed when the mass crosses a horizon, black hole or Rindler? If a horizon is crossed, all the entropy of the crossing mass will be displayed on the horizon (holography), never to leave that again.

    I assume I need to think this over some time.

    At the consciously taken risk of being evacuated from this board as the ultimate crackpot... about the following line of reasoning:

    Mass is a property of both matter and ‘pure’ energy. It is a measure of the inertia we feel when we try to accelerate it. We can increase the mass of a body of matter by for instance stretching a spring in a closed box (thereby adding static energy). Its mass will increase a tiny bit and the box will be (slightly) more difficult to accelerate. Another way to increase ‘mass’ is by accelerating a body of matter (thereby adding kinetic energy). The inertia (carefully avoiding the word ‘relativistic mass’ here ) against any incremental (relativistic) acceleration will increase with the acquired speed. And the light speed (c) is the unattainable upper limit.

    Now from mass back to entropy.

    If we add energy to a closed system of matter, its entropy must also increase (assuming the volume of the body remains the same). Hence we could reason that a box with a pulled spring has a higher entropy. But also an (relativistic) accelerated body must have a higher entropy than a body at rest. Einstein has shown that acceleration and gravitation are two equivalent and indistinguishable concepts, so, if (relativistic) acceleration increases entropy then also gravity should have a similar effect. A mass that is accelerated by a gravitational field should therefore also show (or induce) an increase in entropy. This is in line with Johannes model that shows that two masses are being attracted to each other based on the simple statistical fact that this is the most probable outcome for any system seeking higher entropy (nuance added in the next paragraph).

    However, when we look at Johannes’ Mikado model we see another relation between mass (i.c. a black hole) and entropy. Mass (in the form of matter) reduces entropy by blocking ray paths and the reason that two masses are inclined to move towards each other is based on a statistical 'preference' towards a state that MINIMIZES the total entropy REDUCTION (a full merge would be the optimal state). My guess therefore is that mass (let’s assume as an attribute of matter) is a form of ring fenced, dense energy that has a reduced number of degrees of freedom compared to energy in its ‘purest’ state. We could use our human body as an analogy. It’s a piece of highly improbable skinned mass that therefore has a reduced entropy compared to its environment. But then there is the Second Law of Thermodynamics which implies that this highly unlikely, local reduction of entropy caused by our body mass, needs to be compensated somewhere else in the universe (probably in the mass’ vicinity). Since we know that mass also curves the space-time metric, maybe the induced curvature is precisely the incremental entropy required to satisfy the Second Law of Thermodynamics (i.e. entropy reduction of mass = entropy increase of the deformed space-time metric).

    Since in this model mass and space-time curvature exactly mirror each other in entropic terms, we could take one additional step and see space-time as the bookkeeper of the incremental information required to fully describe mass. Inertia would then be no more or less than the bookkeeper having a capped writing speed to record the behavior of mass. Since I assume that an accelerated (relativistic) mass or a larger (rest) mass have a higher entropy, it would require more bits to keep track off it in the space-time metric and you can feel the bookkeeper ‘push back’. The maximum writing speed is then probably capped at c.

    Or in other words: mass can never travel faster than its own (holographic) shadow in space-time .

    How could this be a counter argument? This is like saying Newtonian gravity is incorrect as it makes the gravity force point in the direction of lower gravitational energy:

    If an object moves around another mass in an elliptical orbit, it will come closer at one time => gravitational energy decreases, and more distant at another => gravitational energy increases.

    All of this is irrelevant. If a force points in a certain direction, it doesn't mean the resulting movement is in that direction. So an elliptic orbit describes a constant entropy situation, although the entropic force is pointed inward.

    Quentin Rowe
    Hi Johannes,

    Verlinde's entropic gravity ideas, when applied to the arrow of time, strike me as a kind of cosmic sequential sorting algorithm of Hawking state-space. A legitimate question to ask therefore, is why does the universe exibit a preference for this the kind of entropic evolution, rather than a totally chaotic kind of order of events? What is implied, when pondering this question, is some kind of connection between each state, that gives a bias to the order of successive states. If each state is independant of the other, there should be no order at all. If the states themselves direct the order, then the universe would be deterministic, rather then probalistic.

    Another question: Does a holographic universe include the property of laser holographs such that a small piece of the image contains the whole image, but with less information/lower resolution? If so, then it would be appropiate to look for patterns on the micro-scale that reflect the shape of macro-scale phenomena, even to the cosmos as a whole. For example, particle-antiparticle pairs and negative/positive volumes as suggested by Diracs equations. Also, the black-hole ideas in Verlinde's theory appear to reflect this principle in some small way.

    Besides all that, just because there is an entropic force biasing probabilites to order these states along a certain direction, that doesn't mean that there won't be a physically manifested mechanism to carry out this work. Gravitons may still be legit in Verlinde's universe.

    This is a good topic to introduce readers to the work of the late Gevin Giorbran, who while not a scientist, has thought deeply about the laws of thermodynamics, and suggests an extension to Boltzmann's  work to include two orders: one of Grouping order, and one of Symmetry order. Each order acts as a boundary to all possible states of space-time, and Giorbran argues for these orders as the driving forces of gravity and cosmic expansion, very much the same as Verlinde's suggestions.

    Another key idea of Giorbran is that flat (empty) space, at zero Kelvin is in fact not empty, but a singularity that is the sum of all possible physical states.

    A couple of quotes for you from his website:

    "The underlying nature of grouping order involves dividing and separating things into individual groups. The best example, a sort of prototype idea to represent grouping order, is to imagine setting up a game of checkers or chess."

    "Where grouping order separates things apart into many groups, symmetry order mixes and combines things together ever more evenly."

    Johannes Koelman
    "a bias to the order of sequential states" Hi Quentin -- a reaction to the above statement (will read the info you link to later): Not sure if I understand you correctly, but the whole idea of entropic gravity assumes an absence of any bias. Think in terms of a chaotic dynamics that effectively makes each state equally probable. Entrpoic acceleration would also result if each next state is drawn at random with equal probability (see post 'entropic gravity for pedestrians').
    Quentin Rowe
    Thanks for your reply...

    I guess what I'm not too clear on what the idea of state-space in general is. Do states in state-space exist independently of each other, or are they physically generated from each other in a cause-effect relationship? Why should the universe care if it plays out all possibilities in a certain order?

    For example, if a being is able to choose to perceive the order of state-space to play out in reverse order, consistently and without a break, then a broken egg reassembling would not be illogical, nor break any known laws of physics.

    This seems a crucial issue for my understanding. If we bring a point-of-view analysis into the picture, say from a human observer, or down to an electron's P.O.V., we might ask, why doesn't the experience of an observer in state-space randomly jump about from state to state, if there is absolutely no coupling between states? Is consciousness driven by probability, or does a conscious POV bring order into state-space simply to make it more comprehensible? If so, why does it even have to be comprehensible?

    For an electron orbiting a proton, thus taking on a bit-part in the identity of a hydrogen atom, how would it know or care which atom or local it is playing this role in? All the identifiers of it's locality play out almost identically across the cosmos. In essence, the amount of state-space for an electron to occupy is very limited compared to the amount of electrons in existence. Does quantum uncertainty result from this?

    Taking it to another level, Max Tegmark has explored these ideas in depth. One particular calculation he did in his 2003 paper "Parallel Universes" related the probability of finding an identical copy of oneself to distance in an infinite ergodic universe. He got the tremendous distance of 10^10^29 metres. No matter what the distance, the important idea to note is that there is no communication possible between these two versions, as they are way beyond each others light horizons.

    Or is there? An unexplored consequence of this calculation is a macro-scale "spooky action at a distance", or non-locality. Assuming I am that individual's copy, if my next action/state/event diverges from my other self so far, far away, which one am I to be next? If my action/state/event converges to coincide with my distant self, then have I travelled faster than the speed of light to arrive and occupy the body of my other self? If Tegmarks calcuation is correct, it brings into question the whole notion of time and space in relation to conscious perception.

    I would go so far to argue, based upon that key calculation in Tegmark's paper, that in an infinite physical universe, it is an inherent property of consciousness to give rise to 'physical laws' and order, and therefore entropy, merely by how it chooses to navigate state-space... assuming there is indeed a choice.

    Specifically with this approach, consciousness does not emerge from physicality. I am arguing that consciousness is simply missing from the equations of physics, and that there is no need to separate it or give it locality, like many reductionists tend to think. It shows up in mathematics of multi-verses, and should and can be taken seriously.
    Amateur Astronomer


    our comments about conscious thought in state space are related to the Copenhagen interpretation, where the states are not resolved until a measurement is made. Most scientists are supporting the Copenhagen interpretation because it predicts the correct outcome of physical experiments. In your question the conscious observer has become part of the state space and has contributed to the resolution of the states. Before the states are resolved the system contains a great many potentials that are configured on a scale smaller than the resolved states. To me it looks like Johannes is describing the smaller scale where the potentials reside, rather than the larger scale where the states are resolved. This larger scale is still smaller than the Planck units.

    Two months ago we had a discussion about the results from beam splitting experiments in which the conclusion was that it all makes sense from the photon’s point of view. Your question on state space looks like it is leading to the same type of conclusion. From the electron’s point of view, there is a jump from one state to another, but the jump is a shorter distance and a smaller energy change than is observed from a different point of view.

    Quentin Rowe
    Yeow, Copenhagen!
    At first I was a little taken aback to be associated with this view, but after some research, I can see it is a broad and often ill-defined approach, so it's easy to get tangled with.

    I wish to make clear, I'm not advocating wave-function collapse, or any sort of mysterious conscious observer effect. The main objection I have with such mystical approaches is, frankly, all the myst!

    What I'm attempting to do is to better distinguish the dilemma with the macro/micro-scale argument, as presented for example in the 'Schrödinger's cat' thought experiment or even the 'Wigner's friend' extended version.

    In these thought experiments, if one were to replace the quantum-event chance mechanism with that of a macro-scale mechanical device, the observer problem remains - regardless of the device. I'm believe that that was Schrödinger's original intent, but his experiment, perhaps unintentionally, fingered conscious perception as central to the argument. To me it shifts the emphasis away from quantum-uncertainty, to perception of change.

    How does an electron 'know' of an event? It changes state. It is effected by other events. If there is no change of state, then there is no perception. It even has a basic memory of an event: it's new momentum. It can know it's position when it takes another 'peek'.

    Consciousness, in this light, lies between events. Consciousness could be defined as 'change' itself, or as making a choice between one state or another. To identify an awareness, or a separate conscious identity, would become an exercise in system boundaries.

    If I were to pick a general principal to emerge from this discussion, it is that for any physical system or state (observer included) that cannot distinguish itself from another system, then for all intents and purposes, it is the same system no matter the localities. Conversely, any change in the system, no matter how small, requires a change in locality. Thus locality can be seen as emerging as a property of the systems state.

    I think I've wandered off topic now. Johannes' articles, as you pointed out, covers ground at the Planck scales, and I seem to have hijacked the discussion to the direction of consciousness.

    I still remain confused as to whether states exist completely independently. It's a rich subject, so I'm sure further research will illuminate my understanding.

    Cheers Jerry!

    Johannes, thanks for answering my hologram question.
    Amateur Astronomer

    Thanks Quentin,

    Copenhagen interpretation was argued by the best minds in science, and never brought to an agreement. The best chance to understand it still appears to be from looking at the fundamental processes as you have done from the point of view of the interacting particles. Then the results can be transformed into any number of other reference frames for other points of view.

    An example is in the beam splitting experiments where the laboratory is measuring the results from 4 possible choices at different times and different places. The laboratory must be regarded as something real. However the results can best be understood when it is realized that the photon is making all of the choices at the same time and in the same place. The photon must also be regarded as real.  So the conclusion is that the perception of reality is not invariant in gage transformations. If reality is not invariant, then consciousness is not likely to be invariant either.

    The prevailing opinion seems to be that the most fundamental quantum potentials are not interacting with each other.  I’m not really happy with that.  It sounds like a quick way to get an easier math problem to solve.  The definition of what constitutes a measurement is important here. Unfortunately it hasn’t been defined in a way that makes a consensus.

    I would argue that a very large number of quantum states get resolved by physical laws without a conscious observer, at least not one of higher intelligence.  Then we would need to say what conscious means, and what higher intelligence means.  I prefer an explanation where the quantum potentials do interact with each other at least to the extent that is necessary to produce a statistical distribution. That is a distribution with one central tendency and one standard deviation from the central tendency.  Without interaction there is no way to avoid having more than one central tendency, or in other words, more than one most likely answer to each question.

    If the quantum potentials do interact, then they can be continually measuring each other in ways that resolve the quantum states and the statistical distributions leading to the classical laws. It removes a lot of pending operations and parallel universes. This point of view is popular with a large number of scientists, but is also opposed by another large group. Everyone accepts the successes of Copenhagen interpretation, but the different groups give different significance to the results.

    Thanks, Q, for that little counter argument to Copenhagen. That "conscious observer dependent" interpretation has always bothered me. Schrodinger's cat would surely know if it were dead or alive. More importantly, particles would "know" if they collide. There would be a change of state, as you point out. Every collision is an observation, in that sense. When defined in this way, the mysticism disappears. Every event is observer dependent AND everything that changes state is an observer. Problem solved. :-)
    Citizen Philosopher / Science Tutor
    Hi Steve,

    Yes, that neatly sums it up!

    Another issue I have with the Schrodinger's Cat thought experiment is that if you replaced the quantum trigger with macro-scale trigger, like a coin flip for example, you still have the same observer problem.

    This implies that superposition of states is an every day part of the macro world. So what's the big deal... or is this what Schrodinger was meaning to show?


    Johannes Koelman
    "Another question: Does a holographic universe include the property of laser holographs such that a small piece of the image contains the whole image, but with less information/lower resolution?" Forgot to answer this question: Yes, the information on the horizon/screen must be non- local. Each bit on the screen relates to a region in 'real' space. Although not necessarily all space. The word 'holographic' is very appropriate in this context.
    Thanks. Your post not only explains entropic gravity in layman's terms, but also gives an intuitive understanding of the second law, which I've always struggled with.

    I have an idea for an experiment, but I'm afraid I may have suggested it before in this series and just forgotten. Apologies if this is the second time it's been suggested:

    Get a pick-up truck where the trailer portion is completely flat and level. Start the truck, and drop a bunch of ball bearings in the middle. Would you see ball bearings close to one another come even closer, and those far away spread apart? In order to not suffer from the edge effects, you'd probably need a sufficiently large pick-up truck.

    Johannes Koelman
    You're welcome, Sunny. "Get a pick-up truck where the trailer portion is completely flat and level. Start the truck, and drop a bunch of ball bearings in the middle. Would you see ball bearings close to one another come even closer, and those far away spread apart" Not sure if I understand you here. Are you wondering whether the combined effects of gravity and accelerated expansion would be measurable on a small scale? The answer to that question would be 'no'.
    I may have attached too much drama. I just meant get a flat, level surface, put ball bearings on it, and make the surface vibrate. This isn't meant to replicate the real universe, but give some insights as your toy universes do. For example, I'm guessing the ball bearings would move away from one another, because this maximises their entropy. This is a different kind of expansion to the edge-of-the-universe one you describe here, but it does work OK as a sort of reverse Mikado universe that you describe in your earlier "It from Bit" (, where the balls are trying to be free instead of the rays. I was hoping there could be more surprising results, but maybe not. Maybe there's some other experiment that one could physically do that works as a toy universe...

    Amateur Astronomer
    The gravity parameter G is required for defining all of the Planck units. If gravity is not fundamental, then are the Planck units also not fundamental? I would argue that the potential for gravity to occur is a fundamental property of space time, just as much so as Planck’s constant h and the speed of light c are fundamental, even if the realization of a gravity field is not fundamental. That doesn’t mean the statistical processes have not created the gravity potential. The statistical processes probably do create the gravity potential, but also create the other properties of space as well. In the zero point, a potential for gravity puts a limit on the total energy, without which energy in space would be infinite. Entropic gravity represents both energy and information connected together. That entropy must have a database stored in space time and connected to a thermal reservoir. It means a group of physical objects must exist in space time where ever the entropic gravity can emerge. That is just about everywhere, except near a black hole. Verlinde’s presentation in Paris used Planck units of surface area as the storage locations for entropic information. By implication a certain amount of energy is assigned to each of the storage locations. I guess the conclusion is that the statistical processes are more fundamental than anything else, even more fundamental than the Planck units. Then gravity G must emerge from the statistics, but c and h must also emerge.
    Johannes Koelman
    "guess the conclusion is that the statistical processes are more fundamental than anything else, even more fundamental than the Planck units. Then gravity G must emerge from the statistics, but c and h must also emerge." Yes, one can speculate that one day it would be natiral to define Planckian units starting from the area associated with one bit, the maximum energy for such a bit, and the speed (or spacetime-orientation) of the bit area.
    Hi John,

    Nice explanation regarding how the entropic force can lead to both gravity and the cosmic acceleration.

    However in the animation for the expanding universe you say that as the universe expands more black holes start coming into the universe. However if one started with the big bang how would this work because there wouldn't be any black holes in the initial universe?

    I had another idea though quite similar to your animation regarding how the cosmic acceleration might work. Suppose space is quantized and the number of available states/positions depends on the presence of matter and this number decreases with increasing distance from this matter then one could possibly define a sphere of influence surrounding any matter.

    So starting at the point of big bang as matter expands would the total sphere of influence increase leading to more states of space and therefore increase in entropy?

    Johannes Koelman
    Thanks Anon. Don't forget the big bang is a singularity in time, not in space. The big bang created seeds for observable universes everywhere, each of them growing into the other ones. So you can think of the expanding universe as an infinite space of black holes getting more-and-more separated (Hubble expansion), with the size of the (overlapping) observable universes growing as the square of the black hole separation.
    "The big bang created seeds for observable universes everywhere, each of them growing into the other ones."

    Is this the current consensus among physicists? I thought big bang was a singularity in space too. (I'm not very knowledgeable in physics though I've immense interest in it).

    Somehow what you are saying seems very specific to black holes and requires the presence of black holes to explain the expanding universe. Would this argument explain why there's a gravitational attraction between say the earth and the moon (or any non-blackhole object)? Maybe I misunderstood the post.

    Johannes Koelman
    "Is this the current consensus among physicists? I thought big bang was a singularity in space too."

    Yes, this is the current consensus. Imagining the big bang as an explosion located in space is a (very common) misunderstanding fed by poor analogies (and the very term 'big bang').

    "Somehow what you are saying seems very specific to black holes and requires the presence of black holes to explain the expanding universe. Would this argument explain why there's a gravitational attraction between say the earth and the moon (or any non-blackhole object)?"

    I used black holes for the same reason point masses are used to explain Newtonian gravity. But Newtoniun gravity also applies to extended objects (like the earth and the moon), and the same is true for entropic gravity. Using black holes avoids ambiguity in 'screen selection'. (Verlinde is very liberal on this point, and assumes there is a freedom to select any gravitational equipotential surface as 'entropy surface'. I am not so sure if that is indeed correct. In any case, it renders the argument much more complex.)
    "Yes, this is the current consensus. Imagining the big bang as an explosion located in space is a (very common) misunderstanding fed by poor analogies (and the very term 'big bang')."

    Could you provide any links to this (e.g. to Wikipedia, or elsewhere)? The pop cosmology books I've read all seem to indicate a normal GR singularity model for the early universe, not a collision of multiple singularities. Thanks!

    Amateur Astronomer
    Fundamentals of physical statistics have been talked around in science for about 35 years. In more recent times the topic is called Sub-Quantum Mechanical Kinetics. It is popular in some of the fringe areas of physics. There are similarities to the statistical fundamentals Johannes described. A Planck unit is theoretically the smallest physical thing that can be measured without an electrical charge attached to it. Any thing smaller in statistical physics will have to be measured indirectly. Supposedly there are such smaller things, especially in the virtual objects of the vacuum. A zero point oscillator is usually described as filling a Planck volume, but with a number of sub parts that are smaller. Oscillators in space are essential parts of optics and quantum mechanics. The Planck volume looks like just a bit of space that is calculated as an average of the surrounding bits. Best estimate at present from equal partition is that each ZPE oscillator contains something like 8 or 16 virtual mass particles in pairs, containing an average of about 14.66 virtual electric charges. The electric charges are also grouped in pairs of opposite polarities. The fine structure constant is related to the number of charges. Then the variety of different objects has to account for all four of the fundamental forces or some aspect of them that propagates farther than one Planck length. A question was asked about the big bang and black holes entering our light cone. Johannes gave one aspect of physics described by black holes. I don’t believe it was intended to be a complete explanation of cosmology. Notice that Verlinde also described a very small part of physics carefully chosen to support holographic theories without adding unnecessary parts. For cosmology there is a theory of radiant focusing that accounts for how energy accumulates slowly from the uncertainty principle and the third law of thermodynamics in non random actions. It comes from Boltzmann and Schrödinger and provides an explanation of why entropy was low in the past. Johannes was writing about random processes that dominate space time on the smallest scale. That explains why the accumulation is slow. The non randomness is a small part of the total process, possibly occurring by chance. Using the Planck scale energy, equally partitioned, with radiant focusing, it is possible to calculate the age of the cosmos, compared to the age of the universe since the big bang. The answer comes out to be a cosmos very much older than the universe. I believe this is an answer to one of the questions about the big bang. There is a lot of guess work in the universe creation, but the best information is saying that space and time were fairly well developed before the big bang. There could have been other universes in the cosmos before our universe, as well as the other things that were created outside our light cone during the big bang. So the view that Johannes gave about objects crossing into our light cone is very reasonable. There isn’t a good theory to tell why a big bang occurred at just that particular moment. Some scientists believe the fine structure constant changes slowly over time, possibly related to the accumulation of energy. There are some limits that the fine structure constant must be within to have space and time like our universe. The limits relate to between 8 and 16 electric charges per ZPE compared to 14.66 at present. If the ZPE average is less than 8 charges each, then space is predicted to collapse into something very small. If the average charges increase to 16 per ZPE then the Planck volumes explode into a new big bang. It isn’t a complete theory, just the outline one. Holograms around closed volumes of space have been represented as containing information about the contents inside the closed space. I would argue that information flows both ways. The hologram must also contain some information about things that are outside the closed surface, maybe not a complete description, but enough entropy to control how the energy fields behave. One example is the two black holes of equal size approaching each other from an intermediate distance, each surrounded by a holographic surface. The two objects interact through entropic gravity before the holograms touch each other.
    Hi Johannes Thank you for the informative article. I did have a few (probably trivial) questions. Firstly about the bad hair day analogy - with bad hair days, there are a multitude of forces (friction, humidity, movement, static electricity, etc) at work to increase the entropy of the system. Although this is only meant as an analogy, doesn't an entropic universe require such and interaction of forces to cause the entropic effect? If so, wouldn't gravity just be a derivative of the other forces? Or is there an actual entropic force that substitutes gravity as a fundamental force. Even the second law of thermodynamics is a statement of observation of systems and not actually governed by a single force. Secondly, is there a definite link between Information theory entropy and the entropy defined by Verlinde's theory? I am familiar with channel and source coding (transmission and compression) algorithms which are based on Claude Shannon's work, and would be very interested to know how they fit into this theory. Also does the Shannon Limit manifest itself in the black hole universe that you mentioned? I am looking forward to understanding more about this interesting subject. Regards Siju
    Johannes Koelman
    Hi Siju -- the bad hair analogy indeed goes astray on this point. Unlike messy hair, entropic gravity and entropic cosmic acceleration do not require forces to explore the 'state space'. To appreciate this point, you may want to read my earlier post 'Entropic Gravity For Pedestrians'. Entropy in physics is the very same thing as Shannon's quantification of information content. In its barest essence, entropy is the the amount of information (as defined by Shannon) needed to fully specify the physical state.
    Thanks Johannes

    I did as you said and read your Entropic article for pedestrians, and I think I understand the basic idea behind the entropic "force" but there is still one thing I do not understand - why would the particle move from one state at all? I hope this isn't a stupid question - I looked at the tetrahedron model first, and while I understand the logic of why particles at a single vertex has lower entropy - isn't the motion of the particles from one vertex to another just one of the arbitrary rules of the universe they are in. If it is an accurate analogy of something akin to reality, then shouldn't there be a similar arbitrary rule in our universe?

    Also with the Mikado universe, I think I understand how a path for the 2 particles to come together can develop, but I just don't really get how a more probable open path actually pushes the 2 black holes together. Maybe I'm viewing the problem too naively, but I don't understand. Please could you help

    Johannes Koelman
    Siju -- the key thing to note is that when a configuration with some masses is described by a certain number of bits, and a similar configuration with the masses slightly more closely together needs, say, five more bits to be described (e.g. in the mikado model 5 more Ray paths that can be occupied), then the configuration with the masses closer together is 2^5 = 32 times more likely to occur.

    It is this statistical effect that generates a 'drift' towards high entropy (higher number of bits) configurations.
    Like Siju, I still don't get it. What is the force 'drawing cards' from the state space? It seems we need to specify that there is some clock or transition rule that pushes on the universe to move it from one state to the next. (I do not mean that objects in space must be nudged by a physical force for entropy gravity to work.)

    Amateur Astronomer
    Carl, in this article Johannes wrote about how systems can operate, not about what makes them run. The question you asked relates to the storage of energy. When there is energy stored in a system the microscopic parts oscillate with a frequency and amplitude related to the quantity of energy. Entropy is a way to measure and report about how many energy states can be filled by random action. There is a huge disagreement among specialists about how much energy there is in the universe. Johannes has written other articles that suggest the total energy is zero with negatives and positives canceling out. On the other hand he comes for a dissertation program in quantum mechanics where the local energy of a microscopic system is thought to be quite high. Johannes has been clever to avoid the dispute about local energy density. In the topic of entropic gravity it is not the information of entropy that makes things happen. The entropy describes an energy storage device that makes the systems run.
    Amateur Astronomer
    Siju, The two types of entropy for information and energy are always exactly equal as long as the thermodynamic energy is assigned (1/2) k for each degree of freedom, using Boltzmann’s constant k. This is the connection that Verlinde applied in his Paris presentation.
    Probably you have been asked this already, but I am wondering if you have any response to the criticism of Lubos Motl



    Johannes Koelman
    I have addressed this issue in
    (see section 'Reversible Entropic Forces')
    Thanks Johannes, I had seen that. But is this the same issue as that regarding the double slit experiment on neutrons? If so perhaps you could explain how. That is the criticism I was referring to.

    Johannes Koelman
    Anon -- yes, it is the same non-issue. The criticism is based on a misunderstanding of the concept 'entropic force'. Entropic forces occur in real life situations described by Hamiltonian (reversible) dynamics. Such Hamiltonian systems can be quantized without any problem. There is no problem with decoherence due to 'changes of the number of micro states' for the very reason that the microscopic dynamics is reversible.

    The funny thing is that following the lines of thought in the blog post you linked to, one would be able to 'prove' that diffusion processes are not possible. Sometimes formalism gets in the way of true understanding....

    Would love to have your opinion on the latest:

    The author states, "The last two terms in the parenthesis in the above equation represent a deviation from the standard Hamiltonian. This deviation is a general and unavoidable consequence of the entropic description of gravitation and is independent of the details of microscopic physics behind such description..."


    Amateur Astronomer

    Luboš is more expert than I am on the topics he discussed. So I don’t intend to debate him on his content.

    Verlinde made it clear that his representation was not intended to be a dynamical system or a complete model, only a few snap shot photos of momentary situations.

    In the displacement of Δx, there is obviously a dynamical transformation left out, and it appears to be a deliberate choice to make the simplest possible explanation. Then it isn’t surprising that there would be a disagreement with the dynamical experiment described by Luboš. On the other hand, Verlinde derived the law of gravity by his method.

    My own opinion is that gravity must be emergent from the vacuum of space, because the law of gravity appears to be the same everywhere. If the simpler explanation of entropy is not sufficient, then something can be added to it, but there is no reason to throw away the concept of entropic gravity. All of the physical laws must emerge from the vacuum, because they are the same everywhere, and the vacuum is the only thing that goes everywhere.

    <!--[if gte mso 9]>


    <![endif]--><!--[if gte mso 9]>

    <![endif]-->I finally got around to reading Erik Verlinde’s Jan 6, 2010
    paper “On the Origin of Gravity and the Laws of Newton”

    Very interesting indeed. I first heard about it this summer on CNN TV of all
    places. I have a long background interest in all of this, yet I am little more
    than a hobby physicist. I am posting here on the topic eight months late, but
    not in vain. I think it has plenty of staying power and fertility. Further down
    is a quick review of Verlinde’s paper. For the more advanced readers, I will
    pose a few tough questions right now.

    Coarse Graining. A lot has been written about it since
    people started trying to derive the 2nd Law of Thermo from
    statistical mechanics. The mathematics can be daunting. In more recent times
    (1980s), this coarse graining was used by Hawking, Page and company to group
    things (complexions, whatever) into equivalence classes and do Feynman-like
    path integrals in cosmology. How does one get a grip on the right approaches is
    my question.  I have tried to wade through parts of Feynman’s original book on path integral and I have looked at the much older work by Boltzman and Planck to name two examples. Even with my
    degree in mathematics, I found it all to be very heavy going.

    Coarse graining is not done the same in the quantum physics
    as it is done in classical physics. The objects that are created using
    complex-valued superpositions are not like the phase-space points in classical
    physics. The classical way of doing equivalence classes and lumping uses the
    set theory of Venn Diagrams. The “kets” of quantum mechanics have different
    mathematical machinery -- things like dot-products and projections that one does not do with
    classical points. Superpositions are not unions of states. The classical AND is
    very different from the quantal AND. A consequence of this is the fact that a
    quantum random walk can spread out much faster than a classical random walk.
    Below is an excellent link (a Wolfram Demonstration) of this interesting fact,
    which surely is relevant to Verlinde’s interests. Or is it?

    ya ya …  OK …

    Below is a quick review of Verlinde’s Jan 6, 2010 paper.

    The not-so-glittering central mechanism that Verlinde uses to derive Gravity is
    called the “entropic force”. He uses this force to DERIVE Newton’s F=ma,
    Newton’s F = GMm/R^2, and also more general formulae like the Poisson equation
    for Newton’s gravitational potential. Verlinde also uses the “entropic force”
    to derive Einstein’s Field Equations (via an advanced use of Killing vectors).

    Sidebar: Einstein’s curved space-time does not give one a
    mechanism for gravity. It instead informs one that if you know the mechanism
    for gravity, then you also get the mechanism for curved space-time, because the
    two are hand in glove. For curved SPACE, one can think of terms of matter
    deepening/creating space in the sense that a given volume of space with matter
    can be enclosed with less surface area than a space without matter. For curved
    TIME one can think in terms of redshifts and the way wavelengths are stretched
    as signals rise up from regions of high density. This stretching also applies
    to de Broglie’s matter waves.

    Via the “entropic force”, Verlinde rather elegantly
    and efficiently derives curved space-time and also the laws of motion.

    This is quite a triumph. The basics are not complicated. The physics and
    predictions are not necessarily new. What is new is the order in which
    everything is derived.

    An essential ordinary parameter that Verlinde works from is Temperature T. The
    more obscure one is called Entropy and given the symbol S. Entropy is sometimes
    related to information or bits. More precisely, it is in proportion to the
    amount of HIDDEN information -- what you do NOT know. There are a number
    “mechanisms” for information to be hidden. One of the more prosaic ones is when
    we mentally do what is called “lumping” or “stereotyping”. Verlinde does not
    use these terms. He instead uses industry standard terms like “coarse
    graining”, “averaging” and “holography”.

    There are also LESS subtle and arbitrary ways in which information can be hidden.
    An object, the Earth itself for example, may block the view of more distant
    objects with its curvature and horizon. The size and distance to that horizon
    can depend on how tall one is. There is a measure for the degree of hiding that
    runs from zero to one, with the horizon of black holes being at the maximum of
    one. Another surface of maximum entropy density is the cosmological horizon
    caused by portions of the distant universe accelerating away from us at speeds
    greater than that of light. For these boundaries, the amount hidden of
    information is maxed-out -- its density is as saturated as it can ever be.

    What is really fascinating is how much it can all be brought down to earth; one
    need not focus on the extremes of particle physics and astrophysics. The
    entropic force drives the action at all “macroscopic” scales. It can even be
    used to explain tensions in social arenas wherein groups of people are “lumped”
    in coarse ways and are in conflict.

    Instead of following the money, follow the shifts in entropy.

    [edit: testing the editing functions here; changed a "to" to a "two".]
    <!--[if gte mso 9]> Normal 0 <![endif]-->

    Looks like I missed the boat and will have to try to answer my own questions ….

    For a higher reference on the distinction between the Boolean operations of Classical Physics and the Hilbert Space cross-products, inner products and projections of Quantum Physics, one can try parts of Leonard Susskind’s YouTube Lecture 5 on Quantum Entanglement.

    Sidebar: The video quality is terrible; the whiteboard is overexposed making it near impossible to read the equations. One would expect that a physics department would know how to run photographic equipment. Alas, such is not the case with this lecture. Frankly, I think that classrooms are much more “cozy” with blackboards. Equations look best written in chalk. Maybe it is the security police who thought that whiteboards would be a good idea and brighten classrooms.

    Susskind uses Venn Diagrams to prove Bell’s inequality. He then shows that Bell’s inequality is violated when one uses the vector space mathematics of quantum mechanics and inserts various projections of the singlet state |ud>-|du> into Bell’s inequality.

    Grasping the distinction between Venn diagram logic and non-Venn diagram logic is difficult, especially for beginners who are used to seeing a semi-classical approach to quantum physics. This approach was pioneered by Bohr himself and is standard fare in introductory courses. It unfortunately gives one the feeling that quantum physics is little more than an extension of Newtonian and Maxwellian physics with the addition of a postulate for Planck’s constant. That it instead involves a different type of non-Boolean logic gets lost if one does not use the full machinery and higher mathematics of quantum mechanics.

    The one thing that people remember from the Bell inequality violation with states like |ud>-|du>  is that it is telling us something about how quantum mechanics is non-local in ways that classical physics is not. Exactly how it pulls this off is subject to debate. Be that as it may, a look at Erik Verlinde’s website shows that he feels that this non-locality is also at the heart of Holography and essential to understanding how gravity and space can be emergent from entropic gradients. Below are a few quotes from his site:

    “[T]he microscopic degrees of freedom on the holographic screens should not be seen as being associated with local degrees of freedom in actual space. They are very non local states. This is what holography tells us. In fact, they can also not be only related to the part of space contained in the screen, because this would mean we can count micro states independently for every part of space, and in this way we would violate the holographic principle. There is non locality in the microstates.”

    “There is action at a distance hidden in gravity, even relativistically. The ADM and Komar definitions of mass make this non-local aspect of gravity very clear. This  non local aspect of gravity is precisely what the holographic principle is about.”

    “The logic here is: thermodynamics + holographic principle -> gravity.

    In my paper I claim that gravity follows in a very simply fashion from holography, but that the direction the other way is much more complicated.”

    I do not know very much about entanglement, but I know a lot about optics and interference. In optics exist a very particular holographic screen. It is the hole in the wall of a camera obscura. I also know a lot about the OTF, MTF and PTF. I was involved in writing the standards for STANAG, ISO, IEC an DIN for these imaging quality characteristics. I know one thing very sure. For characterizing imaging with incoherent light it is sufficient to measure the modulus, the MTF. This is so because in incoherent light all phases are scrambled. For incoherent light imaging research ray tracing is a valid method. It means that the light quanta behave as particles. In contrast, for holographic imaging the PTF is of far greater importance than the MTF. Here all effort is done to keep the phases in proper order, because they transfer the most important part of the information. This story tells an important thing. If you want to understand entanglement and want some closeby demos of its effects, then you might look at holographic imaging or just at light interference. Wave mechanics is just like optics but then taken one dimension higher. This means that the hole of the camera obscura is an equivalent of the holographic screen that surrounds a black hole. Don't travel to the other end of the world to see something that you can find nearby.
    If you think, think twice
    Quentin Rowe
    Christchurch living room undergoes sudden increase in entropy... earthquake tramped my living room and rearranged my bookshelves. Bits are averywhere! Dammit, I don't have the energy to get them back in order right now... too many aftershocks.

    Verlinde was right, entropy is a force to be reckoned with.

    Want to SLEEP!

    Thank you, Johannes, for this wonderful "It from Bit" series. I just finished reading all four articles and I have learned quite a lot. (Now I must make time to go back and read all your other articles!)

    I especially enjoyed this Whole Shebang article, which summarizes very elegantly the link between entropy, gravity, and expansion.

    In my mind, however, there still remains the question, which is primary? Does entropy cause geometry or does geometry cause entropy? I remember reading once that the direction of entropy can be explained by the fact that the universe is expanding. That is, energy and matter flow from high density to low density (one way to state the 2nd law) because of the ever expanding space. Should the universe start to collapse, presumably time would reverse and flow would be from low concentration to high. From this perspective, it is geometry that drives entropy (up or down), not the other way around.

    Still, the equivalence worked out by Verlinde is a fantastic step forward. This is all very exciting. Thanks for making it accessible to the non-specialist.
    Citizen Philosopher / Science Tutor
    Speaking of geometry …. Steve, why are you posting here with a picture that is my spitting image (pardon my English)… right down to the shirt and hat? It’s uncanny.

    Question for Johannes: will you be in Europe around Christmas? Parijs?


    Hypothesis #1: Great minds dress alike (you handsome devil, you).
    Hypothesis #2: You are my evil double from a parallel universe and have slipped through a tear in the fabric of space-time to steal my identity as a jet-setter in Paris.
    Hmmm... I have to go with #2. It is not falsifiable, so it must be true. :-)
    Citizen Philosopher / Science Tutor