BB #71: Brain Background

Initially I thought, for the first time in the the Brain Bubbles series, I have a bubble actually related to the brain. When I went through the list, though, I saw that #17, Pointers!, was about the brain-mind problem, although the ideas expressed there were very speculative.

As is usually the case when talking about the mind and consciousness, considerable speculation is involved — there remain so many unknowns. A big one involves the notion of free will.

I just read an article that seems to support an idea I have about that.

The article, which I saw in Salon (dot com), is Most brain activity is “background noise” — and that’s upending our understanding of consciousness, by Thomas Nail, Professor of Philosophy at the University of Denver.

The article starts off with why it can be so hard to answer the question, “What are you thinking about right now?”:

95 percent of your brain’s activity is entirely unconscious. Of the remaining 5 percent of brain activity, only around half is intentionally directed. The vast majority of what goes on in our heads is unknown and unintentional. Neuroscientists call these activities “spontaneous fluctuations,” because they are unpredictable and seemingly unconnected to any specific behavior.

It goes on to compare our minds to ships tossed at sea, and I think we’ve all experienced being at sea mentally, our thoughts seemingly directed every which way.

Nail brings up the question of why our brain, which is just 2% of our body’s mass, uses a whopping 20% of our energy to run a system that produces so much noise.

That seems generally contrary to how evolution works. (Although evolution is certainly not without its excesses and outright mistakes. In some cases, traits selected for sexual desirability put a strain on the animal itself. Think of the giant bills, tails, and plumes, of some birds, for instance.)

Still, it doesn’t seem all that likely a noisy brain would be accidental or a byproduct of an evolutionary misstep. The alternative is that it serves an important purpose.


Let me interrupt here to mention an idea I’ve had for a while now about how our brains might be one of the only non-deterministic physical systems that exist.

In part it comes from their sheer complexity, but a big part of my speculation has been that our minds are filled with background thoughts and mental noise, and that our consciousness is able to sift through and select from that in ways that defy physical determinism.

Ways that seem random physically, but which are driven by our consciousness selecting amid the noise of equally available thoughts.

I’ve spent a lot of time watching my mind as I decide what to have for dinner. Especially in cases where I’ve decided soup sounds good, what causes me to select clam chowder over minestrone or lentil or any of the other varieties I keep in my pantry? (I like soup.)

Determinism claims there is some chain of physicality that inevitably leads to the soup I select. A vexing issue about free will versus determinism is why it feels like I’m making a free choice, especially when I go back and forth trying to pick a soup.

The question is, if reality could be rewound to that moment, could I have chosen a different soup? It feels like that’s possible.

But is it? Is the sense we have of free will an illusion? If it isn’t, what’s the mechanism that provides for it?


Back to the Salon article. Nail writes:

Many brain studies of consciousness still look only at brain activity that responds to external stimuli and triggers a mental state. The rest of the “noise” is “averaged out” of the data.

Then he endears himself with me a bit by mentioning computationalism, a topic I’ve spent a lot of blog posts trying to unpack.

Nail continues:

This is still the prevailing approach in most contemporary neuroscience, and yields a “computational” input-output model of consciousness. In this neuroscientific model, so-called “information” transfers from our senses to our brains.

Then came the part that made me smile:

Yet the pioneering French neuroscientist Stanislas Dehaene considers this view “deeply wrong.” “Spontaneous activity is one of the most frequently overlooked features” of consciousness, he writes. Unlike engineers who design digital transistors with discrete voltages for 0s and 1s to resist background noise, neurons in the brain work differently. Neurons amplify the noise and even use it to help generate novel solutions to complex problems. In part, this is why the neuronal architecture of our brains has a branching fractal geometry and not a linear one. The vast majority of our brain activity proceeds divergently, creating many possible associations and not convergently into just one.

Which, yeah, is very much what I’ve been thinking about the brain. One argument I’ve made repeatedly is that, no, neurons are not like logic gates. They’re much more like signal processors, and rather noisy ones at that.

[Note: The article links to Dehaene’s book. I linked to his Wiki page.]


Nail writes that multiple scientists are addressing the issue of spontaneous fluctuations in a new field “known as the ‘neuroscience of spontaneous thought.’ Several critical studies in this area have shown that cognitive flux, or ‘spontaneous fluctuation,’ is not secondary to but rather fundamental for consciousness.”

Apparently the “frequency and distribution of this flux can even accurately predict whether someone is conscious or unconscious.”

Nail suggests this view could be a game-changer for theories of mind.

As a music lover, I liked the analogies to our minds acting like a jazz band:

Our “metastable minds” are emergent properties of lower frequency fluctuations that conjoin into “nested hierarchies” with higher frequency fluctuations. Neuroscientists call this process “cross-frequency coupling.” It works a lot like syncopation in music. At the lowest frequencies, the drums lay down a beat. In-between these beats, the bass plays a rhythm, and in-between the notes of that rhythm, the guitar plays a melody. The song is a sound-wave made of sound-waves.

I like his stream analogy, too:

In most theories, consciousness is “mission control” perturbed by background noises. But consciousness functions more like an eddy in a river in this new model. Just as whirling patterns emerge from turbulent waters, our stream of conscious thoughts and feelings arise from the torrent of spontaneous brain fluctuations.

He actually gets quite poetic about it:

Our brains respond to these frequencies with their own spontaneous fluctuations. They play between the waves with melodies that make up our thoughts and feelings. Like a jazz trio, the world, body, and brain have their own spontaneous fluctuations that are the basis of the creative improvisation we call existence. The world, body, and brain entrain with one another like interlocking eddies floating down a stream.

At the end of the article Nail explores the idea of this cognitive flux and mental health, which is a topic of extra concern in these COVID-stressed times.

If the recent theories of these fluctuations are correct and consciousness emerges noisily from the bottom-up, this suggests a different mental health treatment model. Over time, spontaneous brain activity can become entrained and coupled into negative perceptions and rigid mental habits that constrain the lower frequencies. Higher frequency brain activity can act as a “filter” on our incoming perceptions and feelings about ourselves and the world. In particular, recent research on cognitive flux shows that depressive and anxious rumination occurs at some of the highest levels of nested activity in a region scientists recently named the “default mode network.”

Which ties into the idea that one can work oneself into depression by constantly playing the same mental grooves. Over time, the brain seems to lock into this mode to the point that, traditionally, anti-depressant drugs are necessary to pull it back to normal.

§ §

I liked this so much I couldn’t help quoting so much of it. The article is much longer though, I haven’t spilled all the beans. It’s good reading for those interested in theories of mind.

Obviously it’s speculative, but it does sound well-grounded to me.

And, just maybe, it provides that mechanism for free will.

Stay mentally noisy, my friends! Go forth and spread beauty and light.

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

20 responses to “BB #71: Brain Background

  • Wyrd Smythe

    If you visit Denver, watch out for falling aircraft parts!

  • Wyrd Smythe

    Speaking of noisy brains, there have been some interesting developments with regard to actually communicating with sleepers having lucid dreams:

    I’ve manage to have two lucid dreams, and they were awesome. I keep hoping to have another so I can try to fly.

  • Wyrd Smythe

    (Huh. I’m surprised. I thought this post would get more interest.)

    ION: Apparently, according to one new study, people who curse may be more honest.

  • rung2diotimasladder

    I don’t know about logic gates or signal processors, but Nail’s explanation seems more in line with what we experience too, phenomenologically speaking. One of Husserl’s big points was that we can’t experience the way we do without both the foreground and background of consciousness. Intentionality—the directedness of consciousness—can only occur within a background realm, which is always sitting there, a vaguely experienced ‘outer edge’ of whatever it is we’re focused on, a “something more” that we can possibly explore.

    I like the jazz metaphor too. It gives intentionality something of a boundary without taking away its improvisational nature, its freedom.

  • Michael

    Delayed reaction to a very interesting post, Wyrd! Apologies. When you wrote about syncopation and jazz bands it reminded me of a time at Mike’s place when I suggested that maybe consciousness was related to a novel type of matter: that is, matter that exhibits a high degree of coherence. You told me I was chasing unicorns I think, and I probably said it poorly, and I don’t bring it up because of any other reason that it was really astonishing to see here… that using slightly different words and in a slightly different context, perhaps, you’re at least intrigued by the notion that that the brain is a coherent system, and that this coherence is perhaps one of its most singular and differentiating properties. Coherence is the multi-modal coupling that doesn’t eliminate all degrees of individual freedom. The jazz band is a great analogy. (Check out the Rainbow and the Worm by Mae-Wan Ho. She used the jazz band analogy for living systems for decades, and even published videos [I think I might be able to send you one if you’re interested] of the light patterns formed in the tissue of living organisms.)

    And then you wrote, Let me interrupt here to mention an idea I’ve had for a while now about how our brains might be one of the only non-deterministic physical systems that exist. I perked up over this. I like the idea but what are you saying? You went on to suggest or to quote Nail–excuse me for not looking up which–that maybe the freedom is in selecting a particular thought from among the many. Now I know this isn’t a quantum thing, but even classical coherence has some interesting analogs to what we call wave function collapse, where systems reach bifurcation states and there’s almost no way to predict which path it will take. If it is deterministic it depends on astonishingly small variances in initial conditions. Or… perhaps this is where consciousness itself is able, like you said, to be that vanishingly subtle influence that directs the system onto one path or another.

    I think it’s an interesting proposition.


    • Wyrd Smythe

      Hey Michael!

      “…perhaps, you’re at least intrigued by the notion that that the brain is a coherent system, and that this coherence is perhaps one of its most singular and differentiating properties. Coherence is the multi-modal coupling that doesn’t eliminate all degrees of individual freedom.”

      The limitation here is probably mine, but, other than in the casual sense of “acting together” I don’t know how to interpret coherence with regard to consciousness. (That probably means I’m incoherent!) Coherent laser light, for example, isn’t how I think of brain function — to the contrary, I’d be more inclined to see brain function as highly chaotic.

      But neuroscience isn’t a topic I know that much about. Mike is much more informed about that than I am.

      FWIW, a musical group is coherent in the “acting together” sense, but not in the laser light sense. That, I fancifully imagine, would involved them all playing the same note at the same time. 🙂

      Anyway, the limit in seeing what you’re getting at is no doubt mine.

      I’m always up for suggestions or video links. Just know that my TODO list is, as always, kinda long.

      “I perked up over this. I like the idea but what are you saying?”

      Honestly, it’s almost wishful thinking on my part, because it’s very hard to escape classical determinism. Even chaotic systems are determined — we just can’t predict them through any computation. As you say, tiny variations in input, which are unavoidable, screw the computation.

      Even invoking quantum doesn’t really help, since outcomes are (as far as we can tell) random, which isn’t really much help when it comes to intentional free will.

      But maybe, just maybe, that randomness, or even classical randomness, combined with the no doubt chaotic operation of such a complex system as a brain, does allow a non-deterministic path through the noise.

      It may be a futile idea on my part — somewhat like my hope that spacetime is smooth while energy and matter are quantized (a hope that’s slowly dying in light of arguments I’ve heard for why that just can’t be the case).

      But I can dream!

      • Michael

        Hi Wyrd,

        I don’t know how to interpret coherence with regard to consciousness.

        Me neither. I think the concept of coherence is attractive to me because it has this feel of “wholeness” to it, which I’ll explain more about just below. But how it may or may not cause consciousness, that is totally hypothetical and just intriguing to think about. No idea on the nuts and bolts of it.

        Coherent laser light, for example, isn’t how I think of brain function — to the contrary, I’d be more inclined to see brain function as highly chaotic.

        So, coherence doesn’t just include the laser example, and in fact seemingly (or perhaps actually) chaotic fields can be fully coherent. A jazz band, for instance, is actually a good example. Here’s a paragraph or two I found from a book by Mae-Wan Ho:

        “Coherence can be generalized to arbitrarily higher orders, say, to n approaching infinity, in which case we shall be talking about a fully coherent field. If nth order coherence holds, then all of the correlation functions which represent joint counting rates for m-fold coincidence experiments (where m < n) factorize as the product of self-correlations at the individual space-time points. In other words, if we put n different counters in the field, they will each record with no special tendency towards coincidences, or correlations. The above description is simplified from an account given by American quantum physicist Roy Glauber (who was subsequently awarded the 2005 Nobel Prize in physics for this work).

        "A cohere state is thus one of maximum global cohesion and also maximum local freedom! Nature presents us a deep riddle that compels us to accommodate seemingly polar opposites. What she is telling us is that coherence does not mean uniformity, where everybody must be doing the same thing all the time."

        In a certain sense, it sounds a little like the notion that entanglement produces the structure of space. The "arbitrarily higher orders" of coherence Glauber is describing is (I think) something like an infinite number of correlated modes in a field/(population?) of oscillators. And so everything is fundamentally related, and yet… if you drop a photon detector or two in this field you won't find any thing that is non-random. It's like supercoherence.

        Could it e related to consciousness? Who knows. Leaving that aside, it certainly appears to be related to the production of complexity…


      • Wyrd Smythe

        I have to confess an inability to grasp what’s being said there. It’s like when I first start studying any new topic, and, although the words are English words I know, I can’t understand what they mean used that way. I need so many terms and phrases explained or maybe concrete examples of this in action.

        A lot of the QM math was like that. “Hermitian matrices” as just one example. I look up the Wiki page for it, and it just introduces dozens more terms I have to look up.

        As an aside, it’s always struck me as weird that, QM, the foundation of all reality, and consciousness, which we all experience daily, stubbornly remain our greatest mysteries.

        As another aside, finished The White Boy Shuffle. Awesome. Especially since I lived in Los Angeles from 1967 (just after the Watts uprising) to 1984 (the Rodney King incident and uprising was 1991), so a lot of the descriptions were familiar. Next time I read the book, I’ll do it with a map and see how much he’s made up and how much is real life.

        I’m hooked on Paul Beatty. I bought all four of his books through Apple, even though I’d already read Slumberland and The Sellout. I’ll read Tuff sometime soon.

        Funny thing, when you finish reading an Apple ebook, Apple suggests other books by that author. It suggested Heron Fleet, by Paul Beatty. Which I’d never heard of, but it appeared to be an SF book, and it was only $4.99, so I just bought it. But wrong Paul Beatty, and looking closer, it doesn’t sound that interesting. Ah, well, it was just five bucks. (You’d think at this point in life I would have learned to look before leaping.)

        Yet another aside: I was born in NYC, and this year is the 20-year anniversary of 9/11 (which profoundly affected me, PTSD-style, for about a year after). Reading The White Boy Shuffle I realized it’s the 30-year anniversary of the Rodney King incident, trial, and uprising. Meanwhile, here in Minneapolis they’re in the first stages of the trial for the police officer who killed George Floyd. So little has changed.

      • Michael

        I’ve got to catch up soon on some Beatty! Slumberland is next for me… And yes, the sadness of history repeating. Hoping we can learn a thing or two…

        Okay, so I want to go back to this coherence thing for two reasons: one, I think it’s a fascinating and under-explored area in physics, and two, I think I’ll learn something trying to explain it to someone like yourself who has a good deal of knowledge and interest in related topics.

        So, first, what do we mean by coherence? Well, to quote some Roy Glauber I’ve been reading in preparation for this note, it means correlation. In the simplest example, four student athletes rowing a boat on the Charles River, there is correlation in the peaks and troughs of their rowing strokes. I’d say just like a laser, but reading Glauber has me convinced I don’t really understand lasers. Perhaps a topic for later. Two tuning forks of the same frequency that slip into a resonant oscillation are, like the crew team, coherent.

        But this is an extremely simplistic form of coherence. So, to try and use a classical example, let’s say you have a room full of bongo drummers. Two of them maintain a rhythm of 2 beats per second. The next drummer in does 1 beat per second. The next drummer does 4 beats per second. There are correlations for all of them… Now maybe we have a beat frequency of 3 beats per second, which the next drummer picks up. At 3 bps this drummer has correlations with the beat frequency, but also with each other drummer at different points in time. And so on and so forth. I believe these are what Glauber refers to as “n” orders of coherence in a field–in this case an acoustic field let’s say.

        Glauber’s work was on quantum optics. Let’s take this into the realm of the EM field theory. Per Glauber’s Nobel Lecture, The electromagnetic field in free space has a continuum of possible frequencies of oscillation, and a continuum of available modes of spatial oscillation at any given frequency. A few sentences later he notes, The oscillations of a single mode of the field, as we have noted earlier, are essentially the same as those of a harmonic oscillator. So, the field could be thought of as a shitload of drummers, standing at the ready.

        Empirically, one order of coherence in the field might be detected by placing two photon detectors at arbitrary locations, and discovering a correlation in their detections. This has been done in experiments where a half-silvered mirror splits a beam of light, and to the surprise of physicists, revealed temporal correlations in when photons are detected at both locations. My pea brain thinks this means that what scientists thought would have been a steady, random stream of photons from a light source is actually bands or groups of them, which can be shown to be coherent, or fulfilling a pattern. Probably the 60 Hz of the grid, but whatever… Haha.

        Okay, so if you have this free-field EM, then I’m hoping at this point you can imagine that it could have various oscillatory “modes” and that such modes would represent correlations between the detection of photons at various points in space and time. And now, like the example with the drummers above, we simply start building out “n” additional orders by adding modes. Glauber showed that as the number of modes “n” approaches infinity, in which the EM field is in essence fully and profoundly coherent, there is no detectable correlation we could find between two photon detectors plopped anywhere in the field… This is what Mae-Wan Ho was describing as one of nature’s more profound riddles: the state of maximum relatedness is also one that offers maximum individual freedom… (Maximum may not be correct in this sentence, as one could imagine a truly random field offering “maximum” individual freedom, but I’m not sure such a thing exists?)

        So that’s the astonishing fact of coherence, and why it’s not 100% correct to complex EM states in the brain are not coherent because they’re not like a laser.

        In researching this, I discovered the REALLY wild thing Glauber described in his Nobel Lecture, speaking about a theoretical EM field that is fully coherent–meaning it has infinite modes (I think) of coherence. He notes, It is immediately clear that such states must have indefinite [emphasis added] numbers of quanta present. Only in that way can they remain unchanged when one quantum is removed. This remarkable relation does in fact hold for all of the quantum states radiated by a classical current distribution, and in that case the function ε(rt) happens to be the classical solution for the electric field.

        Trying to say this in plain English: I think this means a fully coherent EM field possesses countless (infinite?) quanta, and yet the observables of such a field are consistent with the manner in which quantum physics explains classical current distributions (e.g. the way it explains the ultraviolet catastrophe). This is starting to sound pretty interesting–almost like Feynman’s notion of light traveling every possible path through the universe, except here we’re saying that light occupies every possible oscillatory mode in the EM field while still resolving into the very specific observables we see…

        Enough for one night. I hope you followed and if you did, I’m hoping it was worth the ride!


      • Michael

        PS – I meant to include these two sentences from the abstract of one of his papers (from 1963): […] coherence does not require monochromaticity. Coherent fields can be generated with arbitrary spectra.

      • Wyrd Smythe

        That actually targets a major confusion I have here, because coherence in physics definitely is about wave forms with the same frequency (i.e. monochromaticity) — it’s defined as the the stability of the phase difference between two wave forms. If that phase difference is 100% constant, the wave forms are coherent. To the degree it’s not constant, the wave forms aren’t. That requires the wave forms be the same frequency.

        The rowers, for example, are all rowing at the same frequency, so even if one was 180° out of phase with the others, they would still be coherent. The bongo players could only be coherent if they were playing the same number of beats per minute. Given my (perhaps very limited) understanding, it makes no sense to say a bongo player at 2 bpm would be coherent with a bongo player at 4 bpm. Given the 4 bpm player is twice the frequency, they could be “in sync” but not coherent, because the phase difference between them is constantly changing.

        The other thing about the rowers and bongo players that strikes me is that in both cases there would be some external force keeping them in sync. It could be, as in the rowers’ case, someone calling out the rhythm, or it could be, as with any band, the members hearing and seeing each other.

        FWIW, in both cases, I would use the term “cohesive” but “coherent” just isn’t a concept I’d apply.

        But maybe I’m just not getting it. That’s always a distinct possibility and certainly wouldn’t be the first time. 🙂

      • Michael

        Okay, you’re right. We might both be right in a sense, but clearly my own concepts around coherence have mentally “broadened” to include a wider range of phenomena that are perhaps non-coherent resonant coupling. But… Glauber also got a Nobel prize for proving there were degrees of coherence, and that arbitrary light spectra (not monochromatic) could be coherent.

        This is very interesting to me, though, Wyrd! I hope you don’t mind if we try to unpack this a bit. I noted with interest the Wikipedia article also linked coherence with entanglement, which I’d never seen clearly written before, but which was bubbling up for me as a possible linkage in the chain of incredible uncertainties here.

        So, if you do a little more web research and look up “optical coherence spatial temporal” you’ll find some links to papers that describe different modes/types of coherence in light. One or two have these graphics showing three or four wave forms that can add together into a wave packet that is repeatable. So you could have multiple disparate contributing waveforms that, if they all repeat, can form a composite waveform that repeats. And this repetition can result in light waves that are spatially and or temporally coherent. Here are two links:

        Link 1

        Link 2

        So the thing is, Glauber’s work does talk about “n” modes of coherence and he talks about how these second, third and fourth order levels of coherence were discovered through experiments in radio astronomy, looking at light from various stars. So I’m curious what these other modes are… Like coherence within coherence or something?

        And then, I guess where my intuition was taking me above is to fields of coupled oscillators which do not all have the same frequency, but do have ways of coupling to one another. I’m convinced I was missing something, as you’ve pointed out, but I’m also convinced there’s something in what Glauber is saying that we’re not understanding either. Because what he’s clearly saying is that a light beam/oscillating EM field can have these “fully coherent” conditions where you have “n” orders of coherence, and that as “n” approaches infinity, you cannot detect coherence in any of those modes. I still find that fascinating.

        But what do these modes really mean or represent…? I’m intrigued there’s something here neither of us quite “groks.”


      • Wyrd Smythe

        As I mentioned, just did my taxes and took a big hit, so I’m going to go have some beers and watch something funny on TV. This is interesting, and I’ll pick it up again later, but it’s starting to look very mathematical, so I’m not sure how much I can contribute. I did go to the Nobel site and download the PDF of Glauber’s lecture and slides for reading later.

      • Wyrd Smythe

        I read Glauber’s lecture, but it starts getting over my head about halfway through. I get that he’s comparing coherent light (per the usual definition of monochromatic with locked phase difference) and chaotic light sources, but I’m not clear on the value or purpose.

        At one point I found myself recalling how bosons tend to clump together whereas fermions cannot occupy identical states (the Pauli exclusion principle). His account of detecting distant radio photons (by Hanbury Brown and Twiss) and their (and later) experiments with local photons seemed almost to be the same thing — that bosons tend to clump.

        At the end of the lecture he says: “It is worth emphasizing that the mathematical tools we have developed for dealing with light quanta can be applied equally well to the much broader class of particles obeying Bose-Einstein statistics.” That made me think there was a connection.

        He further says: “Particles obeying Fermi-Dirac statistics, of course, behave quite differently from photons or pions. No more than a single one of them ever occupies any given quantum state. This kind of reckoning associated with fermion fields is radically different therefore from the sort we have associated with bosons, like photons.”

        This all seems to be about understanding lasers at the quantum level and, as he mentions, “When proper account is taken of the atomic interactions and the non-vanishing atomic masses, the coherent state formalism is found to furnish useful descriptions of the behavior of these bosonic gases.”

        But, as I said, it all gets a bit above my head. I haven’t seen anything that connects it with consciousness or the brain, though. (But I believe this conversation an aside from the post topic? Or am I not connecting the dots?)

      • Michael

        Hi Wyrd,

        Delayed reaction here. Haha. The only connection to consciousness was an improbable and I thought we agreed conjectural one at the start of all this. I think in your post you may have said something about the electromagnetic interactions in the brain or something. And I ran with it. At any rate, Glauber’s work is interesting to me perhaps more philosophically than from an engineering perspective, because he showed that a beam of light that was fully coherent–e.g. possessed n-degrees of coherence where n approaches infinity–would in some sense fail to exhibit correlations in the types of experiments he was doing. That, I think, is pretty amazing. It suggests that an “infinite” form of relatedness or correlation can manifest locally as randomness and independence. And I just think that’s a cool discovery. It was just supposed to relate to your jazz band comment…


      • Wyrd Smythe

        Better late than never! Good to hear from you; I was starting to worry a little!

  • Is Reality Determined? | Logos con carne

    […] this year I was fascinated by an article about the background noise of our brains (see: Brain Background). I especially like the jazz band metaphor; it seems right on several […]

And what do you think?

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: