Thema: Mathematik

Findings

“To believe in progress does not mean believing that progress has already taken place. This would not be belief.” — Franz Kafka, Reflections on Sin, Suffering & Hope

The groovi and gyri of your cerebral cortex identify you like your fingerprint.

“If — as some physical theories speculate — there is only one possible initial state of the universe and only one self-consistent set of physical laws, then the initial state required no bits of information to describe.” — Seth Lloyd

Goldbach’s conjecture: Every even number greater or equal to 4 is the sum of two prime numbers.

Doogie mice are mice that have been genetically altered to be smarter. Enrichment of the environment improves the cognitive performance of control animals but not of Doogie mice.

A state of a multiplayer game is Pareto optimal if there is no solution which is better for ALL participants. A state is a Nash equilibrium if NO player can improve his situation by changing only his own strategy.

Subliminal (16ms) unconscious stimuli have a measurable influence on your consumption behavior IF you are thirsty. And you will not be aware of the fact that such stimuli were shown to you.

Thermodynamic depth, a complexity measure for physical systems, relates the entropy of a system to the number of possible historical paths that led to their state.

If the same odor is present during slow-wave sleep that is present during learning new things, this improves performance. Induced slow oscillations by electric stimulation also improve declarative learning.

Distinguish horizontal from vertical explanations. Horizontal explanations correlate events on the same level of detail, they tell us why a certain event happened. Vertical explanations are explanations in terms of the level(s) below. They tell us why a certain generalization holds. If you get a horizontal explanation and still feel the need to ask “why?”, look for vertical explanations.

“We say we measure time with clocks, but we see only the hands of the clocks, not time itself. And the hands of a clock are a physical variable like any other. So in a sense we cheat because what we really observe are physical variables as a function of other physical variables, but we represent that as if everything is evolving in time.” — discovermagazine.com

Epistemic actions are actions that are intended not to change the world but to minimize the computational load on your brain. For example, walking around a chessboard, reshuffling your cards. Actions that could have taken place in your mind, were your mind not extended into the world.

The majority of the connections from the prefrontal cortex to other brain areas is inhibitory. Is what we perceive as conscious control not so much involved in the creation and execution of plans but mostly in their inhibition?

Is the distinction between autopilot and deep thought not a distinction between planning vs. not planning, but a distinction between attention vs. no attention?

Duality: Map your problem to another space, find a solution there and map it back to get the solution you need. Think Category theory.

Patients with brain damage that prevents REM sleep do not appear to have a memory deficit.

Children below the age of four do not have a concept of what other people know. They believe that their knowledge is equal to other people’s knowledge. As soon as they learn something, they suppose that others know it, too.

Apes seem to understand basic intentions, but not cooperative intentions.

A brain area could respond to a stimulus by not responding while most other areas are active.

Use machine learning to create thousands hypotheses for lots of small patches of a brain in parallel, test the predictive value of each of them and discard all but those that work.

Four challenges to mind reading based on machine learning: The temporal and spatial resolution of current scanners; the potentially “unlimited” number of thoughts vs training on specific patterns; some types of brain activity have stereotypical patterns across people (e.g. lying), others seem not to; individuals change over time.

1 is not a prime number because factorization needs to be unique.

Perfect numbers are numbers that are equal to the sum of their proper divisors. 6 = 3 + 2 +1. Are there any odd perfect numbers?

Goal-directedness means equifinality: Different initial states lead to the same final state. Goal-directedness implies a reduction in entropy.

We know no good reasons why neurons have dendritic trees beyond increasing the surface area for synapses from other neurons.

Four different types of answers to the question why a certain animal behaves in a certain way: Proximate cause; current survival value; ontogeny (development of the individual); phylogeny (development of the species).

Humans were linguistic 100.000 years ago.

All of your mitochondrial DNA is from your mother.

Acheulean hand axes have been produced practically unchanged for over a million years. Many have been found in a state of not having been used at all. Social artefacts?

We are the only species vulnerable to ideas. Think religion. Freedom. Democracy. Justice.

Language digitizes.

In an experiment, children and chimpanzees try to get food out of a box after being shown a technique with an unnecessary additional step. Chimpanzees leave out the unnecessary step. Children copy the whole procedure.

Be precise.

Machine Learning from Scratch

Ich habe einige Zahlen, will die nächste in der Folge vorhersagen und weiß nichts über die Herkunft der Zahlen. Kann ich eine Vorhersage treffen? (Nein.)

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Nun habe ich dieselben Zahlen, darf aber annehmen, dass einfache Erklärungen wahrscheinlicher sind als komplizierte. Kann ich jetzt eine Vorhersage treffen? (Nein.)

1010101010101010101010101010101010101010_

Ich nehme zusätzlich an, dass die Folge auf irgendeine Weise berechnet werden kann. Kann ich jetzt die wahrscheinlichste nächste Zahl vorhersagen? (Nein, nicht in endlicher Zeit. Das allgemeine Vorhersageproblem ist unlösbar.)

1010101010101010101010101010101010101010_

Kann ich einen Algorithmus schreiben, dessen Ausgabe gegen die wahrscheinlichste nächste Zahl konvergiert, wenn die Laufzeit gegen unendlich geht? (Ja. Dovetailer über alle möglichen Programme, angefangen mit dem kürzesten; die Ausgabe des kürzesten Programms, das die Zahlen und eine zusätzliche ausgibt, ist die aktuelle Hypothese.)

Wir Menschen treffen jeden Tag Vorhersagen. Der Vorteil, den wir gegenüber derzeitigen Algorithmen haben, liegt in den zusätzlichen Annahmen, die wir unbewusst machen, in der Art von inductive bias, mit dem uns die Evolution ausgestattet hat. Die Aufgabe von Forschern auf dem Gebiet des maschinellen Lernens ist es, den Suchraum von Algorithmen derart einzuschränken, dass die Laufzeit der Algorithmen polynomiell wird, und dabei möglichst wenige Lösungen für Vorhersageprobleme auszuschließen, die für unsere Welt relevant sind.

Cognitive Science in Osnabrück

Was ich gerne vor Beginn meines Studiums in Osnabrück gewusst hätte.

Unter anderem: Wie das erste Semester aussieht. Was man in den einzelnen Fächern lernt. Wer das Studium nach zwei Semestern abbrechen wird. Wie die Bachelor-Note zustande kommt. Was Cognitive-Science-Studenten nach dem Studium machen. Bonus: Zusammenfassungen der Vorlesungen, Mitschriften und Beispielaufgaben.

Lies weiter und du erfährst, ob du Cognitive Science studieren willst und wie du das erste Semester überstehst. Weiterlesen »

Neuronale Netze in Theorie und Praxis (Facharbeit)

Der Begriff “neuronale Netze” bezeichnet das Netzwerk aus Nervenzellen im Gehirn von Mensch und Tier, das für jegliche Denkvorgänge verantwortlich ist. Im Bereich der Informatik steht der Begriff in der Regel für künstliche neuronale Netze, d.h. für stark vereinfachte Modelle der biologischen Systeme. Durch solche Modelle wird es möglich, Computer auch für Aufgaben einzusetzen, die nicht — oder nur schwer — explizit programmiert werden können, sondern Lernvorgänge erfordern. Weiterlesen