"Interesting Things" :- Microtubules, L- Functions and P- adic numbers among them...

 

The variety and depth of subjects that you can find on YouTube these days are remarkable. I came across these two series while generally surfing for ideas about what consciousness might be, and then separately while trying to understand the math behind, counter to all common sense, the result that the sum of all numbers from one to infinity is in some way equal to minus one-twelfth.

While watching the videos on consciousness, one idea came up, that Quantum Processes might be the means for it to happen. Roger Penrose contended it couldn't be purely algebraic/mathematical and that it must involve a Quantum Process, such as the collapse of the wave function. Stuart Hamerhoff, an anesthesiologist, suggested that one place where quantum effects could occur within a cell was within structures called  microtubules.

If so, these tiny tubes within cells might be working below the level of the trillions of neurons and synapses processing and predicting information, adding even more complexity to the nervous system and also explaining how single cells could exhibit some signs of consciousness and memory. 

Another YouTube video about infinite sums told me more about the Langlands program, L-Functions, and alternative number systems like the P-adic numbers. 

It struck me that evolution was only looking for things that worked reliably to represent, process, categorise, and predict, and it may well use forms of mathematics that are not what we are used to in everyday life. 

Conventional ideas about how neurons and synapses work could be undercut by how great long tubes of resonant carbon rings could store and calculate "data" in various forms - as well as set up Quantum states that collapse to create"consciousness". How could complex information get into systems like these? How would the processed data to be acted on, or remembered, be stored, or get out to the wider organism?

So, to trying to explore these ideas further, first of all, what are microtubules?

The strange tubes in cells are Microtubules. You can follow the link above to see what Wikipedia has to say about them, but to summarise, they are responsible for many things. They act as a cytoskeleton and "muscles" to move or shape a cell, and they provide "pathways" to move things and signals around the inside of a cell. They are what move a cilia or flagella that propel cells about, and when a cell divides, they are the scaffolding that assembles and then pulls the chromosomes carefully and exactly apart into two halves. 

In single cells, at least, they seem to be involved in memory and in choice of action... and yet they are just hollow tubes of two different protein subunits, Tubulin A and B (which are 50% the same). They link together and come apart with ease, but can stay coupled indefinitely. They come together to form tubes made of 13 strands, and even in a hot, wet cell, they can exhibit quantum properties inside the tubules. 

Roger Penrose and Stuart Hameroff have advanced a theory that a quantum collapse that occurs within the microtubule  and that "IS" consciousness. They call the theory ORCH-OR (Orchestrated Objective Reduction)

Here is Roger Penrose talking about it , and here Stuart Hamerhoff gives his ideas.

Other ideas I have been interested in, very much as a layman, is the maths around infinite sums and expansions of the idea of what "number" is. The until now rigidly defined way of dealing with combining and calculating with them. Whole new number systems are out there, even the concept of number is up for debate.

The everyday numbers we use have "prime" numbers only divisible by themselves and one, and there are also equations that are similar and can be manipulated mathematically like numbers. They have been called L functions.

The simplest case of an L-function is the Riemann Zeta function, an infinite sum, and central to an understanding of much of the maths we rely on.

In P-adic numbers the conventional ideas of bigger and next to cease to apply - in some P-Adic systems you can even show a square root of minus one.

So thinking about things like modular arithmetic and watching the PEAKMATH videos on the surprising underlying connections between different areas of maths I found myself noticing how the various operations on L- functions seemed to operate on long (in theory infinite) strings of related information and the thought occurred to me that something like a microtubule could hold information in the resonances of individual tubulins that could be operated on in a similar way to the operations on l-functions, in addition to them being in quantum states of possibility. 

It also seemed possible that the Tubulin could hold "information" in more than our usual binary, on/off or 0/1 way - for example +/0/- that would be very different from our way of working in computers, ven without having to resort to quantum strangeness.

 L- Function videos

This series of Videos from Peakmath is about some of the mathematics of L-functions, I linked to one above to explain what an L-function is and what they represent and can do. The Langlands program that also studies them as the bridge between so many areas of Maths.

It occurred to me that as Life has been constantly evolving, one of the things that can help survival is efficient processing of information. 

Why should it just be the sort of maths and software that our brains have so far understood or discovered? 

For evolution, it only needs to work better and better to flourish, and perhaps it has therefore discovered a few tricks in processing, comparing, and predicting that we haven't learned yet - even our clever AI.

Quantum Conciousness Videos

Then we come to some ideas that were mentioned above that try to explain actual consciousness. The "Hard Problem," as stated by David Chalmers, is more than just information processing at a massive scale it is, they say, not computable. Penrose posits it is actually a collapse of a wave function or a "Quantum event". 

A gentleman called Justin Riddle has been working on a series of videos about this and all of them are worth watching. He talks of the philosophy, mechanics, ideas, and systems and so much more. They are developed from a lecture series he gave at Berkeley.

So that's a brief summary of some ideas, put down imperfectly on this blog as an "aide memoire" to try and make sense of them - I expect to be constantly rewriting and expanding on it - but if you get a chance, if indeed anyone reads this, check out at least the first few videos in the series above.

PS - I forgot P-Adic numbers, that's for another day.