Mathematics is the domain of all formal languages, and allows the expression of arbitrary statements (most of which are uncomputable). Computation may be understood in terms of computational systems, for instance via defining states (which are sets of discernible differences, i.e. bits), and transition functions that let us derive new states.
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)
[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.
[T]o encode a brain genetically, based on the hardware that we are using, we need something like at least 500 kilobytes of code... actually... it's going to be a little more, I guess. It sounds like surprisingly little... but in terms of scientific theories this is a lot. ...The universe, according to the core theory of quantum mechanics... it's like half a page of code... to generate the universe. ...[I]f you want to understand evolution, it's like a paragraph... a couple lines, really, to understand an evolutionary process. ...[T]here's lots ...of details that you get afterwards, because this process itself doesn't define what all the animals are going to look like. In a similar way, the code of the universe doesn't tell you what this planet is going to look like and you... are going to look like. It's just defining the rule book.
How difficult is it to define a brain? We know that the brain must be somewhere hidden in the genome [which] fits in a CD-ROM. It's not that complicated. It's easier than Microsoft Windows. ...[A]bout 2% of the genome is coding for proteins, and maybe about 10%... tells you when to express which protein, and the remainder is mostly garbage. It's old viruses that are left over and it's never been properly deleted [etc.] because there are no real code revisions in the genome. ...How much of this 10%, [i.e.,] about 75 megabytes code for the brain, we don't really know. What we do know is that we share almost all of this with mice. Genetically speaking, a human is a pretty big mouse, with a few bits changed to fix some of the genetic expressions. ...Most of the stuff there is going to code for cells and metabolism and what your body looks like, [etc.]...
[I]f you look at the progression of AI models, it... went the opposite direction. ...AI started with linguistic protocols, which were expressed in formal grammars, and then it got to concept spaces, and now it's about to address percepts. ...At some point in the near future it's going to get better at mental simulations and at some point after that we'll get to attention directed and motivationally connected systems that make sense of the world, that are in some sense able to address meaning. This is the hardware that we have...
[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.
With this vector space you can do amazing things, [e.g.,] if you take the vector from king to queen, it's pretty much the same vector as between man and woman. ...[B]ecause [these concept spaces are] really a high dimension manifold, we can do interesting things like machine translation without understanding what it means, that is, without doing any proper mental representation that predicts the world. ...[T]his is [a] type of mental representation that is somewhat incomplete, but it captures the landscape that we share in a culture.
[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.
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.
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.
[C]ausal models can be weakly deterministic, basically associative models, which tell you if this state [S<sub>1</sub>] happens, it is quite probable that this one [S<sub>2</sub>] comes afterwards. Or you can get to a strongly determined model... one which tells you, if you are in this state [S<sub>1</sub>], and this condition [c<sub>1</sub>] is met, you're going to go exactly in this state [S<sub>2</sub>]. If this state is not met, or a different condition [c<sub>2</sub>] is met, you go into this state [S<sub>3</sub>]. And this is what we call an algorithm. Now you're in the domain of computation.
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...