# Tau Function Squared

## Friday, January 17, 2014

### Orch OR latest

I see Hameroff and Penrose have a major new article about their theory that conscious states are quantum states in microtubules, and that the dynamics of conscious states is due to "orchestrated objective reduction"; and there are a number of commentary articles too. I will make my own comment, just as soon as I can read it all.

## Wednesday, March 20, 2013

### Deligne's prize

The eminent mathematician Pierre Deligne just won the Abel Prize. He first won fame for proving the last of the Weil conjectures, which in turn implied the truth of a conjecture by Ramanujan concerning his tau function. The tau function has a special relationship to 24-dimensional spaces that makes it a frequent ingredient in the probability-amplitude formulae of string theory. But much of string theory descends from M-theory, in which the one-dimensional string is revealed to be a two-dimensional "M2-brane".

Although strings and branes live in high-dimensional spaces, one often concerns oneself with the interior of these objects - one-dimensional for strings, two-dimensional for M2-branes - and describes their interior physics using a similarly low-dimensional field theory.

Now, note that the microtubule has a one-dimensional approximation (as a line) and a two-dimensional approximation (as a cylinder). The propagation of certain degrees of freedom within the shell of the microtubule may therefore have an approximate description in terms of a one- or two-dimensional field theory.

Back in the mid-1990s, Nanopoulos et al proposed to describe microtubules in a one-dimensional approximation (neglecting the radial dimension of the cylinder) using a string worldsheet theory. To my knowledge, no-one ever proposed a holographic uplift of this approximation to a brane worldvolume theory - but this is unsurprising given that the worldvolume theory of the M2-brane wasn't even discovered until the next decade.

Also in the 2000s, it became a common thing to apply string theory, via the AdS/CFT duality, to condensed matter physics; the string models are not exact descriptions of their microscopic physics, but rather offer a model, computationally tractable thanks to the duality, of the quantum-thermodynamic class to which the system of interest belongs.

It would certainly be interesting if, say, a holographic uplift of Weil cohomology played a role in describing the quantum fluctuations of the microtubule according to an effective brane theory. I can even imagine the Ramanujan tau function playing a specific role, as the building block of a fudge factor which gives this effective theory the nice properties (like conformality) of a genuine M-theoretic model, thereby making the physics calculable...

Although strings and branes live in high-dimensional spaces, one often concerns oneself with the interior of these objects - one-dimensional for strings, two-dimensional for M2-branes - and describes their interior physics using a similarly low-dimensional field theory.

Now, note that the microtubule has a one-dimensional approximation (as a line) and a two-dimensional approximation (as a cylinder). The propagation of certain degrees of freedom within the shell of the microtubule may therefore have an approximate description in terms of a one- or two-dimensional field theory.

Back in the mid-1990s, Nanopoulos et al proposed to describe microtubules in a one-dimensional approximation (neglecting the radial dimension of the cylinder) using a string worldsheet theory. To my knowledge, no-one ever proposed a holographic uplift of this approximation to a brane worldvolume theory - but this is unsurprising given that the worldvolume theory of the M2-brane wasn't even discovered until the next decade.

Also in the 2000s, it became a common thing to apply string theory, via the AdS/CFT duality, to condensed matter physics; the string models are not exact descriptions of their microscopic physics, but rather offer a model, computationally tractable thanks to the duality, of the quantum-thermodynamic class to which the system of interest belongs.

It would certainly be interesting if, say, a holographic uplift of Weil cohomology played a role in describing the quantum fluctuations of the microtubule according to an effective brane theory. I can even imagine the Ramanujan tau function playing a specific role, as the building block of a fudge factor which gives this effective theory the nice properties (like conformality) of a genuine M-theoretic model, thereby making the physics calculable...

## Friday, January 11, 2013

### Phonon antennae

One of the problems for quantum biology - if you are looking for quantum coherence at the scale of tissues, and not just within a single macromolecule - is, how is quantum coherence created and sustained at those scales? There seem to be two options regarding the mode of interaction: photons and phonons. That is, electromagnetism, and quantized mechanical vibration.

In this regard, the concept of a "phonon antenna", introduced by the quantum biology group at Ulm, looks important - as a type of physical structure that would be an important causal nexus in phonon-induced mesoscopic quantum coherence.

In this regard, the concept of a "phonon antenna", introduced by the quantum biology group at Ulm, looks important - as a type of physical structure that would be an important causal nexus in phonon-induced mesoscopic quantum coherence.

## Saturday, September 22, 2012

### Australian quantum computing

We take a break from biology to bring you the Australian single-atom qubit.

By my understanding, the Australian effort to create a solid-state quantum computer (by doping a silicon chip with addressable phosphorus atoms), which is ten years old, had foundered in recent years; but the enterprise was saved and revived by Michelle Simmons. It's now her job to make sure the world isn't overrun by unfriendly Australian quantum AI. Good luck, Professor Simmons!

By my understanding, the Australian effort to create a solid-state quantum computer (by doping a silicon chip with addressable phosphorus atoms), which is ten years old, had foundered in recent years; but the enterprise was saved and revived by Michelle Simmons. It's now her job to make sure the world isn't overrun by unfriendly Australian quantum AI. Good luck, Professor Simmons!

## Monday, September 3, 2012

### Spin chains as the conceptual bridge

There is a different sort of tau function which appears in the theory of integrable systems, and it may be more appropriate for what I have in mind. Thus we have, on the one hand, "Classical tau-function for quantum spin chains", and on the other hand, "Pseudo-spin model for the cytoskeletal microtubule surface".

(Also see: "A spin chain primer".)

(Also see: "A spin chain primer".)

### Tau meets tau

Hello world. This blog represents a whimsical first approach to some topics that aren't whimsical at all.

Tau is the name of a microtubule-associated protein. It's also the name of a special function from number theory.

Owing to their geometry and complexity, there is a large literature of outre speculation about the biophysics of microtubules. Back when I took a regular interest in that topic, I remember wondering idly if the mathematical tau function would ever turn out to be relevant for the dynamics of tau the protein. This was not a totally arbitrary speculation; the tau function is the sort of high-powered math that is potentially relevant to a low-dimensional physical system with a nontrivial dynamics.

Meanwhile, back in the present day, I affiliate myself in a qualified way with both "transhumanism" and "quantum-mind theories". I stipulate that my affiliation is qualified, because I would dissent from some common transhumanist ideas (such as the idea that a digital simulation of a brain could or would be conscious) and I'd also reject most of what is said about "the quantum mind". In fact, it's because I believe that the locus of consciousness probably has to be something like a quantum condensate, rather than a "program", that I don't believe in conscious simulations.

The occasion for the launch of a "tau-squared" blog is provided by the work and intellectual positions of Athena Andreadis, an American neuroscientist. Her day job involves research into tau's role in dementia - "Tau splicing and the intricacies of dementia" is a nice recent paper where she reviews the state of her field - but she also dabbles as a futurist and culture critic, and she's written polemics against both transhumanism and quantum-mind theories, while nonetheless being into her own version of long-term futurism.

I don't especially want to get into the polemics of these obscure culture wars, at least not here. Instead, what I propose to do is to just return to my old whimsy about the tau function being related to the function of tau, as a step towards more serious engagement with the scientific issues. "One measures a circle, beginning anywhere." If the idea is to investigate whether something highly nontrivial could be going on in microtubule dynamics, a tau-tau conceptual collision is as good a place as any to begin.

Tau is the name of a microtubule-associated protein. It's also the name of a special function from number theory.

Owing to their geometry and complexity, there is a large literature of outre speculation about the biophysics of microtubules. Back when I took a regular interest in that topic, I remember wondering idly if the mathematical tau function would ever turn out to be relevant for the dynamics of tau the protein. This was not a totally arbitrary speculation; the tau function is the sort of high-powered math that is potentially relevant to a low-dimensional physical system with a nontrivial dynamics.

Meanwhile, back in the present day, I affiliate myself in a qualified way with both "transhumanism" and "quantum-mind theories". I stipulate that my affiliation is qualified, because I would dissent from some common transhumanist ideas (such as the idea that a digital simulation of a brain could or would be conscious) and I'd also reject most of what is said about "the quantum mind". In fact, it's because I believe that the locus of consciousness probably has to be something like a quantum condensate, rather than a "program", that I don't believe in conscious simulations.

The occasion for the launch of a "tau-squared" blog is provided by the work and intellectual positions of Athena Andreadis, an American neuroscientist. Her day job involves research into tau's role in dementia - "Tau splicing and the intricacies of dementia" is a nice recent paper where she reviews the state of her field - but she also dabbles as a futurist and culture critic, and she's written polemics against both transhumanism and quantum-mind theories, while nonetheless being into her own version of long-term futurism.

I don't especially want to get into the polemics of these obscure culture wars, at least not here. Instead, what I propose to do is to just return to my old whimsy about the tau function being related to the function of tau, as a step towards more serious engagement with the scientific issues. "One measures a circle, beginning anywhere." If the idea is to investigate whether something highly nontrivial could be going on in microtubule dynamics, a tau-tau conceptual collision is as good a place as any to begin.

Subscribe to:
Posts (Atom)