Posts Tagged ‘Neural Networks’

WHAT DREAMS ARE AND WHAT THEY DO

December 20, 2020

Dreams are fundamentally simulations of situations which can be imagined. This is their main function and evolutionary utility. That’s why and how they appeared. Dreams prepare our neurobiology to react to potential real worlds… which we have not experienced yet, like a bear appearing suddenly after making itself as flat as rug…

Dreams also are also… built to help guess new interpretations of situations that we may have encountered already. Yes, dreams are built! Dream machinery is the fundamental scientist, setting up thought experiments in universes we can’t imagine yet… before the dream happens.

Indeed, before the experiment, there is always the thought experiment. Before the idea, there is always the dream. Dreams are more about construction of appropriate neural networks… than interpretation… although dreams can also make neural interpretations of situation which have been encountered.

To understand how that could be, how these simulations… and stimulations… which we call dreams, could occur and leave a trace, one has to understand the consequences of a completely revolutionary idea: ideas and dreams correspond to neural networks within the brain… One has also to understand a further step in complication: that emotions derive, in part from generalizations of neural networks (and the topological influences, not to say computation, the neurohormones they secrete… operate).Neural networks are real objects, not dreamy stupidities a la Plato not belonging to the “real’ world. Existence in the real world means energy and inertia. Thus dreams appear from energy and inertia, and acquire existence from them. It matters, literally, matters in the physical sense, what we dream. Dark Dreams Matter.  

It’s not us who do stuff in dreams, but rather dreams which make us into what we are.

In other words, ideas, dreams and emotions all have physical reality, they are sets of physical objects (embodied categories to use mathematics). But they are also different notions from each other: ideas can be consciously visited (that’s probably enacted by sets of connection to a higher level “meta” layer of neurons… probably in the frontal cortex)… 

Dreams are only preparations of ideas… ideas, the stronger networks, can get consciously inspected, because they are stronger and connected to the meta-conscious layer. The weaker networks correspond to the subconscious (or the nearly conscious) and when those are activated, in sorts of chain reactions, we experience what we call dreams… Shall we have them again and again, Hebbian reinforcement occurr, making them stronger and thus into emerging consciousness…

The mechanism fostering dream states is the shutting down of parts of the brain which actively, or passively, suppress other parts of the brain. This happens naturally during sleep (it can also happen from variegated training, for example meditation, deepsea apnea diving, etc.). Hence the connection of dreams with sleep… But day-dreaming is definitely possible, whether in awake or “woke” states: it’s just a matter of shutting down inhibitions. (The woke/cancel culture is then a giant dream-like state of freedom from a previous perception of reality, and inhibitions…)

Having the capacity of dreaming, and that of imagination, which is related, means that human beings are ready to handle, as if they had experienced them, situations which never occurred before in experienced life… Or which were not even imaginable consciously! But those circumstances did occur in dream life… and left behind half-cooked neural networks…. But half ready networks means that they can turn into functional networks quickly. Hence the capacity of human beings to adapt to situations unforeseen in real life, but already experienced in dreams…  

Dreaming, and imagining, make human beings more intelligent, as the brain trained with the science of the imaginable in anticipation of whatever may come along.

We are the thinking animal, and that means thought experiments upon not just the realities we experienced, but also thought experiments upon the realities which live only in our minds.

According to Plato, Socrates enjoyed the advice of “daemons”, and many thinkers have argued that some inner voice advised them to do some things, or prevented them to do some things. When philosophers look inside themselves. they are searching for this inchoating neural networks… where the future, or alternate, often better, more real versions of reality lay [1].

Patrice Ayme

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[1] “You have often heard me speak of an oracle or sign which comes to me, and is the divinity which Meletus ridicules in the indictment. This sign I have had ever since I was a child. The sign is a voice which comes to me and always forbids me to do something which I am going to do, but never commands me to do anything, and this is what stands in the way of my being a politician.” — Socrates, Plato’s Apology

The point being that politicians do not do introspection, searching for this inner, tentative networks. All politicians do is read. manipulate and exploit public logical and emotional networks: politicians’ minds are intrinsically about the past and the mob, that’s why they should be cancelled, as the end-all, be-all . Whereas intelligence is all about creativity and the future. And creation starts always with new neural networks… Deep inside.

What Are Numbers? Math is most abstracted physics!

June 27, 2019

German mathematician Richard Dedekind (1831–1916) published in 1888 a paper entitled Was sind und was sollen die Zahlen? What are numbers and what should they be? 

Here is my answer: forget what you know. 

Numbers are neural networks. Small numbers have small networks, big ones, big networks; so the nature of numbers, change, as they get bigger…(According to me, listening, delighted, to the indignant screams of distant mathematicians ).

Diagram Chasing all of them: not a coincidence. Instead of having “It from Bit”, one has it from action (arrow in Cat theory, action potential with neurons, fundamental process in physics…)

A few immediate applications of this master idea:

  1. Numbers are learned, because neural networks are learned.
  2. Advanced animals, having advanced neural networks, should be capable of having those neural networks we call numbers.
  3. Big numbers are different from small numbers, because big neural networks are different from small ones. Here again is the idea that energy should matter in mathematics (the conventional thinking being just the opposite: energy doesn’t matter).

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Kronecker’s also quipped: “God made the natural numbers. Everything else is the work of man.

Kronecker proceeded to define numbers from Set Theory, invented for the purpose. Later Bertrand Russell found a problem with Set Theory, the set of sets which are not elements of themselves brought a contradiction. Russell tried to get out of that with a hyper complicated theory. In modern times, mathematicians prefer to use Category Theory. [1]

I go beast on how to construct numbers. Beasts have brains, and brains have neural networks.

Kronecker thought mathematics is the work of man. But, actually all advanced animals move in a way proving they are capable of differential calculus. Far from being the work of god, differential calculus is the “work” of dog. Without differential calculus, that dog can’t hunt. OK, dog is not conscious of god, or of the calculus it’s using. So what?   

Now for a few easy bits:

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Let’s notice that numbers are definitely the work of the genus Homo: 

Consider the integer 152. 152 is the work of man. Just like “Yes” is the work of the Englishman. 

152 means: 100 + 5×10 + 2. But that’s only in base ten. In base 60, that would be: 60 x 60 + 5 x 60 + 2… Which converts to 3,902  back in base ten. 

So “152” is not an absolute notion. For that integer to make sense, the basis in which it lives has to be expressed (and what the notation means, such as 2 = 1+1…). The Babylonians invented base 60 to handle big numbers in astronomy. We still use base 60 to this day, for angles and time. So “152” is a cultural construction. In several ways. 

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So how come Platonists claim that numbers live out there, in a special realm of their own, if there is so much human explanation and convention to provide, with just basic numbers? Most mathematicians also believe their are exploring that realm of Plato. But actually all they are exploring is the possible connections which can be built within the neural networks inside their brains. So they are exploring physics, a bit like a child on a beach explores which sand castle she can get away with. A difference with building sand castles is that the possibilities are few and are carefully recorded, becoming the body of that culture and language called “mathematics”. 

An example is the Archimedean axiom. The Greeks knew about it well: it’s in Euclid, and it says that, given two magnitudes, A and B, there is always an integer n so that: nA > B.

If one denies that axiom, one gets infinitesimals… That was made rigorous through Model Theory, in the 1950s, three centuries after Leibnitz first introduced infinitesimals, starting a fight with Newton.

No Plato universe of “forms”… or rather, they exist, but live as geometries inside brains…

Even more dramatic are hyperbolic and elliptic geometries: they were discovered at least a century before Euclid. Then they were forgotten, and a stupid debate occurred for 21 centuries about whether the parallel axiom (one parallel to a line, one only, through a point off the line) was independent of the others. Mathematicians, even the brightest, had forgotten that their ancestors had found geometries with many, or no, parallels…)

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Let’s recapitulate: culture is composed of (vague, but good enough) descriptions of neural networks, which can be transmitted. Once contracted, those neural network templates modify brains in similar ways. Those similarly modified brains behave all similarly, mimicking innate characteristics.  

Language enables a transmission of neural geometries, topologies, logics, and categories. Language is primitive in most advanced animals, consisting in grunts, cooing, gestures, etc. But in Homo language became an advanced mental cultural duplication system (and some of the mentality passed is mathematical, but not only). 

True, advanced animals have a sort of pseudo-innate capability to evolve neurobiological mathematical structures: through trial and errors mimicking their relatives, or experimentation with what works, young animals brains learn to optimize trajectories: the brains of many predators in pursuit make subsets of themselves into differential calculus machines. 

So if Plato’s “forms” are real forms in (generalized) geometry and topology… what are the latter made of? Good question! Therein come our old friend, the Quantum Wave… 

Clearly, math is the most abstracted physics.

Patrice Ayme


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