## Posts Tagged ‘Math’

### 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).

***

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:

***

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.

***

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…)

***

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

### Aphorisms March 2014: Putin, Plutos, Malta, Math, Brain

March 29, 2014

Whip Stops Baffled Bear Momentarily:

Wonderful! Dictator Putin suggests he won’t invade anything today, if a number of changes are made to Ukraine’s constitution, friends, hopes.

Specifically, Putin let it be known that he wants demonstrations in Ukraine, which, says Putin, have been disrupting him for six months, to come to a stop. Demonstrations are a bad example to Russians: too many demonstrations make the kleptocrats flee. There was actually 50,000 people demonstrating against Putin, in Moscow, because he had annexed Crimea.

Speaking of stopping, Putin will stop, if, and only if, he is persuaded that horrendous consequences are coming his way, otherwise. It’s not going to be easy, considering that some German minister said this week that Europe could not do without Russian gas, for the foreseeable future.

And considering that Londongrad is a mighty ally of Putin… In a West ruled by plutocrats. So this is not just about Putin going crazy, it’s about him realizing he is confronting weak and divided democracies, rotten from inside.

Thus, as in the 1930s, plutocrats are playing both sides, hoping for the best. Just as in 1930s, the dictator (Hitler then, Putin now) feels in command of enough plutocratic power in the West to get what he wants, without a world war. Hitler was astounded, on September 1, 1939, when the French Republic and Britain gave him an ultimatum. He had come to believe what his Anglo-American plutocratic friends had told him, that it would never happen, because they, the plutocrats, controlled everything.

***

I Bank Therefore I Tank:

How come Putin has momentarily come to his senses? Sanctions. By closing Rossiya, a bank close to Putin, at a distance, the USA left 495,000 Russian clients without a bank. And that was just a warning shot. Visa, MasterCard and company control the essentiality of Russian banking. Also banks need some international cooperation, and that was going down too.

It goes without saying that the USA, under corrupt president Roosevelt not only did nothing of the sort, but the exact opposite. As France and Britain were in total world war against Nazism, and 45 French division tried to crash through the Siegfried Line, the USA was busy aiding and abetting Hitler’s fascist dictatorship. In a crucial way (lead tetraethyl story).

Not only were Hitler and his followers encouraged, but the German generals who wanted to arrest the Nazis, got very confused: was the USA allied to the Guide, or not?

This time, the early, swift opposition of the president of the USA to tank-born fascism, is not just the most important thing Obama did, but the most important thing any government of the USA did, in generations.

***

Heavens For Sale:

Malta has put for sale 1,800 passports and nationality. First condition: pay 650,000 Euros for the head of the family, at least 250,000 Euros of investment on top of that, plus more per family member. The stratagem is expected to bring in more than one billion Euros. Reassuringly, Malta announced that it did not expect the new Maltese citizens to spend the year there (they will be free to roam the European Union).

Malta is notorious for refusing Maltese nationality, even for those who have resided there more than twenty years, and the EC is not happy about that.

***

The main problem of the socio-economy is plutocracy, though. Plutocracy wants the starvation of the People’s economic activity. That allows to increase the gap between the haves and have-nots, which is the plutocracy’s raison d’être, and ultimate value.

Hence the obsession fabricated by the Main Stream Media against deficits, without saying they are directly related to the plutocracy not been taxed enough. Or the insistence that the People has no skill (thus, presumably ought to be starved in all ways, including access to public education).

***

2.4% population growth in the 1960s. That was the excuse for the creation of massive food exportation machinery then. In the 1980s, that over-production was massively exported to poor countries and frozen European chicken destroyed local food production in poor countries.

Population growth is only 1.3% now. That’s still about 100 million added, a year.

That does not mean that shocks to the world food system are not coming. They are, thanks to the global warming and weirding.

***

Mathematics = Physics

Many modern thinkers have wondered at the remarkable efficiency of mathematics in physics. Galileo said physics was written in mathematics, Plato viewed knowing math as a prerequisite to advanced thinking.

The latter point of view is the correct one. Better: thinking, advanced or not, is, intrinsically, mathematical. Neurology is math.

Mathematics is just a more abstract physics. So if physics is hard, so can mathematics be too. The best avenue to explore what these abstract thoughts mean, is the history of Euclidean geometry. One physical simplistic simplification that Euclid made was flatness. When mathematicians realized that flatness did not have to be, Riemann soon got the idea that geodesic distanciation was equivalent to force (vulgar physicists believe Einstein got the idea).

Euclid also made many other simplifying assumptions about the nature of continuity and … And Quantum Physics violate them, starting with the notion of points.

Patrice Aymé

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