All our access to mathematics... is because we do computation. We can understand mathematics because our brain can compute some part of mathematics, very very little of it and to a very constrained complexity, but enough so we can map some of the infinite complexity and noncomputability of mathematics into computational patterns which we can explore.
cognitive scientist
, also known as “the wizard of consciousness”(born 1973 in Weimar, Germany) is a cognitive scientist focusing on cognitive architectures, models of mental representation, emotion, motivation and sociality. Achievements include research in novel data compression algorithm using concurrent entropy models; development of microPsi cognitive architecture for modeling emotion, motivation, mental representation. In 2000, Bach graduated with a diploma in Computer Science from Berlin, followed by a Doctor of Philosophy at Osnabrück University, Germany, in 2006.
Before joining , he worked as a visiting researcher at the and the Harvard Program for Evolutionary Dynamics. Fact finding reports by the and found that Bach’s research was supported with more than $150,000 by the Foundation.
From: Wikiquote (CC BY-SA 4.0)
Showing quotes in randomized order to avoid selection bias. Click Popular for most popular quotes.
[T]he genome defines the rule book by which our brain is built. The brain boots itself, in a development process, and this booting takes some time... formation learning in which some connections are formed, basic models are built of the world so we can operate in it. How long does this booting take... about 80 megaseconds. That's the time a child is awake until it's 3 1/2 years old. By this age you understand Star Wars, and I think everything after Star Wars is cosmetics.
In cognitive science, we currently have two major families of architectures... One, the classical school... characterized as Fodorian Architectures, as... the manipulation of a language of thought, usually expressed as a set of rules and capable of . ...The other family favors distributed approaches and constrains a dynamic system with potentially astronomically many until... behaviors [of] general intelligence are left. This may seem more "natural" and well-tuned... Yet many functional aspects of intelligence... as planning and language, are... much harder to depict using the dynamical systems approach.
[O]ur best bet is not just to have a single classification with filtering. ...[I]nstead... take the low level of input and get a whole universe of features that is interrelated. ...[W]e have different levels of determinations. At the lowest level we have percepts. At a slightly higher level we have simulations, and on an even higher level we have a concept landscape.
If we want to understand music we have to go beyond understanding sound. We have to understand the transformations that sound can have if you play a different pitch. We have to arrange the sound in a sequencer that gives you rhythms, and so on, and then we want to identify some kind of musical grammar that we can use to... control the sequencer. So we have stacked structures that simulate the world. ...If you want to model a world of music you need to have the lowest level of the precepts, then the higher levels of mental simulations, which give the sequences... and the grammars of music... [B]eyond this you have the conceptual landscape that you can use to describe the different styles of music. ...[I]f you go up in the hierarchy, you get to more and more abstract models, more and more conceptual models, and more and more analytic models. ...[T]hese are causal models...
Attempts in psychology at overarching theories of the mind have been all but shattered by the influence of behaviorism, and where cognitive psychology has sprung up in its tracks, it rarely acknowledges that there is something as "intelligence per se", as opposed to the individual performance of a group of subjects in an isolated set of experiments.
For Turing it wasn't quite so bad. ...[T]uring could see that the solution is to understand that mathematics was computational all along. ...For instance pi in classical mathematics is a value. It's also a function, but it's the same thing. In computation, a function is only a value when you can compute it, and if you cannot compute the last digit of pi, you only have a function. You can plug this function into your local sun, let it run until the sun burns out... This is it. This is the last digit of pi you will know. But it also means that there can be no process in the physical universe, or in any physically realized computer that depends on having known the last digit of pi. ...Which means that there are parts of physics that are defined in such a way that cannot strictly be true, because, assuming that this could be true leads into contradictions.
For a long time people have thought that the universe is written in mathematics... In fact nothing is mathematical. Mathematics is just the domain of formal languages. It doesn't exist. Mathematics starts with a void. Just throw in a few axioms and if those are nice axioms, then you get infinite complexity. Most of it is not computable. In mathematics you can express arbitrary statements, because it's all about formal languages. Many of these statements will not make sense. Many of these statements will make sense in some way, but you cannot test whether they make sense because they're not computable.
The last big things that we discovered was the constructivist turn in mathematics... to understand that the parts of mathematics that work are computation. That was a very significant discovery in the first half of the 20th century. ...[I]t hasn't fully permeated philosophy and even physics yet. Physicists checked out the code libraries for mathematics before constructivism became universal. ...Gödel himself ...didn't get it yet. Hilbert could get it. Hilbert saw that [e.g.,] Cantor's set theoretic experiments in mathematics led him to contradictions, and he noticed that with the current semantics we cannot build a computer in mathematics that runs mathematics without crashing, and Gödel... could prove this.
[W]e saw that mental representation is about percepts, mental simulations, conceptual representations... [C]onceptual representations give us concept spaces, and... these concept spaces... give us an interface for our mental representations we can use to address and manipulate them, and we can share them in cultures. [T]hese concepts are compositional. We can put them together to create new concepts. ...[T]hey can be described using higher dimensional vector spaces. They [vectors] don't do mental simulation and prediction, and so on, but we can capture regularity in our concepts with them.
PREMIUM FEATURE
Advanced Search Filters
Filter search results by source, date, and more with our premium search tools.
[T]here is another type of mental representation that is linguistic protocols, which is... a form of grammar and a vocabulary. ...[W]e need these ...protocols to transfer mental representations between people ...by scannning our ...representations, disassembling them ...and ...we use a discrete set of symbols to get this to somebody else... [who] trains an assembler that reverses this process and builds something that is... similar to what we intended to convey.
[Y]ou don't know this state in which you don't have a self. You can turn off yourself... You can... meditate yourself [into] a state where you are still conscious, where still things are happening, where you know everything that you knew before, but you're no longer identified with changing anything. ...[T]his means that your self ...dissolves. There is no longer this person... you know that this person construct exists in other states and it runs on this brain... but it's not a real thing. It's a construct. It's an idea... and you can change that idea, and if you let go of this idea... If you don't think you are special, you realize it's just one of many people, and it's not your favorite person even... It's just one of many, and it's the one that you are doomed to control... and that is... informing the actions of this organism as a control model. This is all there is, and you are somehow afraid that this control model gets interrupted, or loses the identity of continuity.