Lyfe, Thoughts

My Take on LYFE Part II: Principal Component Analysis I/II

To understand this post, it is advised to read the previous one first.

Through this post, I will try to get a sense of the 4 functions (or “pillars”) assigned to the definition of Lyfe and eventually start bridging those towards a more information theory-like approach by determining over what those functions act upon and to what extend in order to isolate the key components we’ll need. more like 2 functions because that’s longer than expected
In other words; we have been given the recipe and we will look for the ingredients to eventually apply it for a dish of our tastes.

And, regarding my own job search, I found that EU project named Marie Skłodowska Curie Innovative Training Network “SmartNets”; they are trying to study and model mice and zebra fish brains from the molecular level to the larger scope of interconnected graphs. It’s ambitious and it looks amazingly cool! I cannot postulate in my own country, but there are many interesting opportunities in the neighborhood and they even come with a renewable 9 months contract for young researcher and the opportunity for a PhD thesis in computational neuroscience *giggles*.

Although I have more the vocation than the grades, and my application is currently an underachieved mess, it would feel like a deep mistake if I had to pass on such a cool opportunity bridging neuro and computer sciences while getting researcher experience !

How it’d feel like to be taken for a neuro-computing thesis vs How it’d feel to fruitfully obtain it !

Ok, let’s get back to business! So the first question to ask is…

What is a Dissipative system ?

The most obvious dissipative system I could think of

This is one of those concepts that physicists have been mesmerizing about way too much.
I could say that it is any system that is not lossless (conservative) when energy flows through it; but any non-idealized (or “real”) system is dissipative as reality always have friction so… let’s not get there.

If you really want to get to the formalism, the KU Leuven has some nice slides (to nicely overcomplicate it as Science should be).
The real key to this being:

  • Energy flows through the system, or a part of it.
  • The amount of power (energy per time) is superior to the variation of stored energy by the system (what it gains as energy per time).
  • Energy being a conservative property, that inequality means something is lost; usually as heat.

To get back to my resistance, I apply a power source to it which makes some energy flow through it and, as it doesn’t store electric current, it will dissipate the electric energy as heat energy, meaning it will become hotter. (So does every electric component, as they all have a non-null resistance property; but we said we were only using idealized components).

Non-dissipative system, prosaically called “conservative” system.
Energy flows while always peaking at the same value

BUT… that was much too easy!
Let’s push this concept around a bit. In a conservative system such as the pendulum, we will have our energy flow between 2 states: a kinetic energy and a potential energy, oscillating between a gain of height against gravity or a gain of speed against inertia.

Therefore, in a pendulum, there’s just a transformation of energy. But isn’t it also the case when my resistance changed electric energy to heat energy ?
Here comes the slippery slope!

Hierarchy of energy flows conservation efficiency
Having Mechanical below electrical is not that weird. A rock on top of a mountain conserves well its energy but, if you want the energy to flow from a power plant to your house, you’ll have a lot more loss with Mechanical energy

Think of it that way: there is some sort of hierarchy between the energies. A thermal energy is the lowest form: you only extract power by allowing it to balance two systems with one of them having a lower temperature (less thermal energy) than the other. Then, entropy is maximal, nothing else to do there.

But it is not the same for other forms of energy who could still degrade (usually as heat; in thermal energy). When we have our pendulum energy flowing between potential and kinetic, it actually stays at the same level. These are 2 sorts of mechanical energies, so “in idealized case” no entropy is produced and therefore no lower level of energy (heat). But, if you convert electric to mechanical energy, you will have a loss going back and forth.

This is where I want to extend that idea of dissipative system; it’s not simply “losing” energy as it flows through the system (received > stored) but it’s losing energy level which also accounts as entropy production. Therefore, if my electric energy becomes mechanical energy which becomes thermal energy; my system has a cascade where 2 different dissipative inequalities will apply.

For instance, if I have a robot producing entropy both by processing information (electricity -> heat) and by manipulating actuators (electricity -> mechanism -> heat).

What is an Auto-Catalytic system ?

I can remember my late chemistry teacher explaining that a catalyst is something used in a chemical reaction but then given back. It is not consumed by the reaction but it either allows it or enhances it.
For instance, considering a chemical reaction using A and B as reactant and D as a product :
A + B + C -> D + C

would logically be simplified to A + B -> D, as the catalyst C wouldn’t be consumed.
But this notation doesn’t show the kinetic of the reaction which would better illustrate C acting as the catalyst. There might be an intermediary component AC produced in order to react with B and gets to D; or it might be required to reach some level of energy that the reaction cannot on its own.

As a general definition, a catalyst is something helping the transition from a state to another more stable state without being consumed.

But then we are after an “auto”-catalysis; meaning the reaction will create the condition to facilitate itself.

I could get back to a chemistry example but those are boring and abstract. Instead, I’ll take the opportunity to advert for a strongly underrated vulgarization channel called The Science Asylum that I’ve been heavily consuming for a month with the pleasure of (re-)discovering cool physics concepts.

In this crazy video, he explains how it is possible to terraform Mars with a (reasonably) giant magnet to regenerate its magnetic field (I guess it’s ok to be a little crazy… check it out!)

In the case depicted in the video, it is proposed to use a magnet in order to strengthen Mars magnetic field and gets it to regenerate.
The part not explicited in the video is the auto-catalytic behavior we will end up with.

Think of it that way: Mars is a cold rock with a thin atmosphere because most of its remaining constituent are frozen at the poles. If you allow the planet to augment its atmosphere density (by retaining it with a stronger magnetic field, for instance), the greenhouse gases will start to retain more of the sun radiation. This will lead to a warmer planet surface which will evaporate more iced atmosphere which will augment its atmosphere density which will augment its greenhouse effect… and that’s how aliens built our sun!

Well, not really as that method won’t actually work for many reasons; one of them being that the atmosphere will eventually run out of fuel (reactant) and saturate. But there you got it: that positive loop effect accelerating its own action is the auto-catalytic phenomenon.

Fichier:Enzyme catalysis energy levels 2.svg — Wikipédia
Example of the effect of a catalyst to reduce the energy required in order to transit to a new state

What you can get out of it is that, in order to get a catalysis, you need to move from a given state to a new state which is more stable (meaning it has less energy to release). You start from a static state and end up with a saturation meaning reaction is not possible anymore (reactant are all used or the environment is saturated).
Weirdly enough, I conceptualize it more like the behavior of magnetic permeability.

Saturation (magnetic) - Wikipedia
The permeability µ reaches a peak and declines when the ferromagnetic material gets saturated

An important observation in the catalysis is the increase in local entropy as your final state has a lower level of energy.
The hardest part is to put the “auto-” in front of the catalysis. It has to be a system like a marble that needs a gentle push to go all down the hill, or a campfire that just requires an ignition to keep producing the heat in order to continue burning until it runs out of wood.

What’s next ?

I split this part into 2 sub-parts as it gets much longer than expected.
As usual, I’m trying to avoid too much reworking on this blog and to approach it more like building a stair step-by-step, that means an eventual reworking at the end as I’m not fully sure yet where I’m going with it.

Next time, I’ll write about homeostatic systems, learning systems (if this was an easy one, this blog would be a single post) and maybe compare them to existing experiment in the real-world or to the most general notion of a program (a Turing machine of course).
So far my feeling is that, if it gets somewhere, this technology would be limited to what’s currently done by batch processing in large data systems.
Well, let’s see…

Leave a Reply

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

WordPress.com Logo

You are commenting using your WordPress.com 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