Boolean Logic Quotes

Do not allow the adumbrations of Aristotelian logic to prevent you from seeing a vast spectrum of truths; the post-Boolean continuum of shades of grey where we spend most of our lives.

This page is related to that page. You're reading something constructed using a rhetorical practice, something informed both directly and indirectly by the entire history of composition up until this point, from the Sophists to Derrida. But you're navigating it using pure logical statements, using spans of text or images that, when clicked or selected, get other files and display them on your screen. The text is based in the rhetorical tradition; the links are based in the logical tradition; and somewhere in there is something worth figuring out. ...the entire history of Western pedagogy [is] an oscillation between these two traditions, between the tradition of rhetoric as a means for obtaining power — language as just a collection of interconnected signifiers co-relating, without a grounding in "truth," and the tradition of seeking truth, of searching for a fundamental, logical underpinning for the universe, using ideas like the platonic solids or Boolean logic, or tools like expert systems and particle accelerators ... what is the relationship between narratives and logic? What is sprezzatura for the web? Hell if I know. My way of figuring it all out is to build the system and write inside it, because I'm too dense to work out theories.

when

BC)

1+B

A(B+C) + B(B+C)

Boolean Algebra Circuit Simplification

The methods I’ve described can be used to implement any function that stays constant in time, but a more interesting class of functions are those that involve sequences in time. To handle such functions, we use a device called a finite-state machine. Finite-state machines can be used to implement time-varying functions—functions that depend not just on the current input but also on the previous history of inputs. Once you learn to recognize a finite-state machine, you’ll notice them everywhere—in combination locks, ballpoint pens, even legal contracts. The basic idea of a finite-state machine is to combine a look-up table, constructed using Boolean logic, with a memory device. The memory is used to store a summary of the past, which is the state of the finite-state machine.

The finite-state machine repeatedly executes the following sequence of operations: (1) read an instruction from the memory, (2) execute the operation specified by that instruction, and (3) calculate the address of the next instruction. The sequence of states necessary to do this is built into the Boolean logic of the machine, and the instructions themselves are specific patterns of bits—patterns that cause the finite-state machine to perform various operations on the data in the memory.

The work performed by the computer is specified by a program, which is written in a programming language. This language is converted to sequences of machine-language instructions by interpreters or compilers, via a predefined set of subroutines called the operating system. The instructions, which are stored in the memory of the computer, define the operations to be performed on data, which are also stored in the computer’s memory. A finite-state machine fetches and executes these instructions. The instructions as well as the data are represented by patterns of bits. Both the finite-state machine and the memory are built of storage registers and Boolean logic blocks, and the latter are based on simple logical functions, such as And, Or, and Invert. These logical functions are implemented by switches, which are set up either in series or in parallel, and these switches control a physical substance, such as water or electricity, which is used to send one of two possible signals from one switch to another: 1 or 0. This is the hierarchy of abstraction that makes computers work.

Shannon was interested in building a machine that could play chess—and more generally in building mechanisms that imitated thought. In 1940, he published his master’s thesis, which was titled “A Symbolic Analysis of Relay Switching Circuits.” In it, he showed that it was possible to build electrical circuits equivalent to expressions in Boolean algebra. In Shannon’s circuits, switches that were open or closed corresponded to logical variables of Boolean algebra that were true or false. Shannon demonstrated a way of converting any expression in Boolean algebra into an arrangement of switches.

Each register in the memory has a different address—a pattern of bits by means of which you can access it—so registers are referred to as locations in memory. The memory contains Boolean logic blocks, which decode the address and select the location for reading or writing. If data are to be written at this memory location, these logic blocks store the new data into the addressed register. If the register is to be read, the logic blocks steer the data from the addressed register to the memory’s output, which is connected to the input of the finite-state machine.

Booleans are named after George Boole, an English mathematician who invented Boolean logic. You’ll

Intelligence ultimately isn’t Boolean. It isn’t about logic. It’s physical. It’s a continuous chemical give-and-take with everything around it.

boolean logic is often too primitive to try and express what we're trying to express.

Many religiously minded people have this boolean way of thinking, where everything has to be 'true, false, & null'; whereas it is far more logical to recognize everything is quantifiable in variables.

Selection on one of two genetically correlated characters will lead to a change in the unselected character, a phenomenon called 'correlated selection response.' This means that selection on one character may lead to a loss of adaptation at a genetically correlated character. If these two characters often experience directional selection independently of each other, then a decrease in correlation will be beneficial. This seems to be a reasonably intuitive idea, although it turned out to be surprisingly difficult to model this process. One of the first successful attempts to simulate the evolution of variational modularity was the study by Kashtan and Alon (2005) in which they used logical circuits as model of the genotype. A logical circuit consists of elements that take two or more inputs and transform them into one output according to some rule. The inputs and outputs are binary, either 0 or 1 as in a digital computer, and the rule can be a logical (Boolean) function. A genome then consists of a number of these logical elements and the connections among them. Mutations change the connections among the elements and selection among mutant genotypes proceeds according to a given goal. The goal for the network is to produce a certain output for each possible input configuration. For example, their circuit had four inputs: x,y,z, and w. The network was selected to calculate the following logical function: G1 = ((x XOR y) AND (z XOR w)). When the authors selected for this goal, the network evolved many different possible solutions (i.e. networks that could calculate the function G1). In this experiment, the evolved networks were almost always non-modular. In another experiment, the authors periodically changed the goal function from G1 to G2 = ((x XOR y) or (z XOR w)). In this case, the networks always evolved modularity, in the sense that there were sub-circuits dedicated to calculating the functions shared between G1 and G2, (x XOR y) and (z XOR w), and another part that represented the variable part if the function: either the AND or the OR function connecting (x XOR y) and (z XOR w). Hence, if the fitness function was modular, that is, if there were aspects that remained the same and others that changed, then the system evolved different parts that represented the constant and the variable parts of the environment. This example was intriguing because it overcame some of the difficulties of earlier attempts to simulate the evolution of variational modularity, although it did use a fairly non-standard model of a genotype-phenotype map: logical circuits. In a second example, Kashtan and Alon (2005) used a neural network model with similar results. Hence, the questions arise, how generic are these results? And can one expect that similar processes occur in real life?

I often said I wouldn't have pursued programming as a career if I still did drugs. This is probably true, since weed was always immensely crippling for me. I would have weed hangovers for days, and while stoned, was unable to read or do much of anything besides clean and play video games. Whether or not this would have turned out to be true is academic, but it's definitely true that I wouldn't have become a programmer if I hadn't lost my mind, because the recovery process taught me my most valuable skill as a programmer: how to not think. Programming requires the acceptance that you are entering meaningless symbols into a machine that's going to spit out other meaningless symbols, and this can be hard to accept. It requires abandoning all hope for an answer for the existential "why?" in favour of shuffling boolean values ad infinitum. By no interpretation of the concept of understanding does a computer understand what you're telling it or what it's telling you. On top of that, programming as an act is more often hindered than helped by thinking. Despite zero years of training in computer science, I've found I have an edge in debugging because I never look or ask for an explanation. Ninety percent of the computer bugs in a program are tiny, one-line errors, and you just have to find that error. Holding the entire logical structure of a million lines of code in your mind in futile. The task is to find the references and connections and track them back until you hit the problem. If I get an error message, I copy it into Google, because someone somewhere has encountered and solved the problem, probably by tracking down the people who originally wrote the program. In seven years of programming, I've solved exactly two undocumented bugs via pure deductive reasoning.