## Maxwell Demon – Extracting Energy from a System

Energy and thermodynamics Maxwell's demon is famous for threatening the second law of thermodynamics. But does it? Here we will look at Maxwell original writing, and how we can interpret Maxwell's thought experiment. Thermodynamics is the branch of physics that deals with energy management. Thermodynamics, like all other branches of…

## Mille miliardi di persone

Quanta energia usa l'umanità? Non ci vuole matematica avanzata: così com'è, l'essere umano è lontano dalla sostenibilità. La quantità di energia disponibile non è sufficiente a sostenere la società tecnologica. La potenza (energia per unità di tempo) media usata dagli esseri umani, $$1.8\cdot 10^{13}$$ watt, è un decimillesimo di quanto…

## What's the memory capacity of human brains in bytes?

Some people think that our brain information storage capacity comes from merely switching on and off neurons or synapses. It's not like that. Our brain is a network, and networks store information through different configurations of the relationships between nodes. Although the entropy (and therefore the amount of information stored)…

## Kullback-Leibler Divergence and Cross-entropy Loss

Science is all about data and theories explaining those data. The theory behind coin tossing says that the probability of tail and head is the same, and that given N tosses we expect k heads with a probability $$binomial(trials=N, successes=k)$$. In Bayesian statistics, probability has a nice meaning –it means how strongly…

## Cyberchondria: Why Bayes is a must when looking for web-based diagnoses

The NY Times (and few others) wrote a story entitled Microsoft Finds Cancer Clues in Search Queries: Microsoft scientists have demonstrated that by analyzing large samples of search engine queries they may in some cases be able to identify internet users who are suffering from pancreatic cancer, even before they have received…

## How big can an error be when we estimate something?

Often, when you make an estimation based on many assumptions, people say "There might be errors in all your assumptions, and the error on the result, being the sum of all these errors, is going to be huge". In reality, errors compensate each others. You might overestimate one variable, but…

## Floating Points –Rounding Errors in Algebraic Processes

The floating point representation of numbers is dangerous. With floating points, the computer stores the digits and the position of the point. Imagine a "6-digit decimal computer". This is a computer that uses base 10 numbers, like we human, but can only store 6 digits, the position of the dot,…

## If heat is released from a system, will entropy increase?

Let's ask ourselves this question –will our knowledge about a system increase or decrease when the system cools down? When it's hot, there is high uncertainty about position and speed of the molecules composing the system. The more temperature goes down, the more precise your knowledge about position and speed will…

## Taming Complexity –The Magnum Ice Cream

The Magnum: As Simple as Possible Giacomo, in his "Cremeria Castiglione", explains to me how he is able to make one of the best gelatos in Bologna, and possibly in Italy. This means, for Italians at least, one of the best ice creams in the world. "Making gelato is…

## Can a lion jump 36 feet?

Using data from Rory Young's quora answer: yes, a lion definitely can jump 10+ meters. The horizontal distance D of a projectile with speed V, launched at an angle $$\theta$$ is: $$D = V^2 \cdot sin(2\theta) / g$$ Which gives, for a lion running at 54km/sec, i.e. V=15 m/s, jumping…