https://www.tutorialspoint.com/compu...ogic_gates.htm
https://www.circuitcrush.com/circuit-analysis/
My current view is that circuit analysis is (mainly) processed by the left hemisphere. This is how "the computer engineer" is different from "the mathematician".
Language is probably not possible without symbols and abstractions. Otherwise, a group of people would have to experience the exact same things to be able to communicate them.https://www.quora.com/What-part-of-y...mplex-thinking
“What part of your brain is responsible for logic or complex thinking?”
Short answer: all of it.
Longer answer: it’s a symphony.
First level answer: the cerebrum. The cerebellum is responsible for trained activities of the body, including speech, but it is directed by the cerebrum.
Of course, the cerebrum consists of two hemispheres. The hemispheres each have a different construction of the world, and it is the synthesis of their views that makes us human.
A quick summary of the hemispheres follows. Their full relation is much too complex to describe in a Quora answer. The right hemisphere, having access to the entire visual field, sees the larger picture and understands how the larger picture changes over time. You might say it understands the world from the top down. The left hemisphere, having access only to the right half of the foveal vision, sees the pieces of the world and how they are related. You might say it understands the world from the bottom up. No other animal that we know can hold both of those views and synthesize them.
The left hemisphere’s bottom-up view provides a symbolic understanding of the world. Its symbols are held at various levels of detail, and it understands how those levels relate to one another. So it sees a chair as a seat, four legs, and a back. It is also aware of variations of this description, but if you ask most people to draw a chair, that is what you will get. The left’s symbolic understanding includes words to denote most of the symbols, along with rules for using words to construct sentences and larger utterances. The left sees time as a set of symbolic relations (“before”, “during”, “depends on”, etc.).
The right hemisphere’s top-down view provides a holistic understanding of the world. It understands how all the pieces fit together, and how they work together as processes. It sees a chair as one or more images of chairs it has been exposed to, and it knows how chairs are used by people. If you ask some people to draw a chair, they will draw one of the many chairs they have seen, picking one to match the context of the question. The right side understands context and provides context to all our thoughts. The right side has words, and they are attached to experiences and processes. The right side senses and understands the flow of time and how context, experiences, and processes fit into the flow.
Now for an answer to the question.
The left hemisphere understands the symbology of logic and complex thinking. It knows all the parts (objects and rules) and can talk about them in the abstract. People with right hemisphere lesions can talk quite convincingly about abstract systems they have learned. Moreover, complex thoughts and processes are almost never understood in a vacuum; they are learned and shared and taught. The left hemisphere and its understanding are heavily involved in such discourse.
The right hemisphere understands the context of logic and complex thinking. It knows what a logical inference means in a particular context, and it understands how various contexts can change the meaning. It understands how complex thinking and processes vary in time. It understands the context of discourse involving complex thoughts and processes.
A discipline often considered a domain of logic and complex thoughts is mathematics. (I have a degree in math.) The left hemisphere understands the proper construction and manipulation of equations, but the right hemisphere knows what they mean. The left hemisphere can construct and understand the graph of a parabola, but the right hemisphere sees the parabola and intuits the sign of the derivative at each point. Going further into advanced analysis, the equations get more complicated and abstract, which the left hemisphere manages, but the meanings become ever more abstract, and the right hemisphere needs to follow those meanings or the equations are useless. As an extreme example, only the right hemisphere can understand and manipulate high dimensionality spaces, though the left hemisphere is needed to share that undertanding.
History also requires cooperation of both hemispheres. The left hemisphere can understand all the events and static relations of a time period, but it is the right hemisphere that sees the patterns and understand the flow. And so it is with every discipline.
The answer to the question depends on its context.
https://www.youtube.com/watch?v=dFs9WO2B8uI
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4684024/
(Iain McGilchrist ... The Master and His Emissary: The Divided Brain And The Making of The Western World)
https://en.wikipedia.org/wiki/Prefrontal_Analysis
If a person has primary PFS then he/she has primary PFA as well.
Both intuition/creativity and logic/comparison depend on PFA and PFS.https://psyarxiv.com/skxwc/
"Typical IQ test tasks involving PFS of several objects: (A) requires the combination of two objects. The top two rows of the matrix indicate the rule: 'the object in the right column is the result of the combination of the two objects shown in the left and middle row' (the solution in the 5th square). (B) shows a question that relies on the PFS of four objects. (C) shows a question in which PFS of two objects has to be conducted according to the following rule specified in the top row: 'the object in the middle column goes on top of the object in the left column' ( the solution in the second square)."
Shape (geons), size, quantity and direction are processed by the parietal lobe.
Verbal patterns and visual patterns (faces etc) are processed by the temporal lobe.
Creativity (i.e. "intuition") and comparison (logic, categorization, verbal reasoning and visual reasoning) depend on PFA/PFS and working memory.
https://en.wikipedia.org/wiki/Baddel...working_memory
https://en.wikipedia.org/wiki/Working_memory#Theories
Anders Ericsson and Walter Kintsch have introduced the notion of "long-term working memory", which they define as a set of "retrieval structures" in long-term memory that enable seamless access to the information relevant for everyday tasks. In this way, parts of long-term memory effectively function as working memory. In a similar vein, Cowan does not regard working memory as a separate system from long-term memory. Representations in working memory are a subset of representations in long-term memory. Working memory is organized into two embedded levels. The first consists of long-term memory representations that are activated. There can be many of these—there is theoretically no limit to the activation of representations in long-term memory. The second level is called the focus of attention. The focus is regarded as having a limited capacity and holds up to four of the activated representations.
Oberauer has extended Cowan's model by adding a third component, a more narrow focus of attention that holds only one chunk at a time. The one-element focus is embedded in the four-element focus and serves to select a single chunk for processing. For example, four digits can be held in mind at the same time in Cowan's "focus of attention". When the individual wishes to perform a process on each of these digits—for example, adding the number two to each digit—separate processing is required for each digit since most individuals cannot perform several mathematical processes in parallel. Oberauer's attentional component selects one of the digits for processing and then shifts the attentional focus to the next digit, continuing until all digits have been processed.
A)
John Nash, Bill Gates, Mark Zuckerberg: introvert, a planner, primary PFS, leading Se, the right hemisphere, logical (comparison)
"the mathematical physicist" (type/subtype)
https://en.wikipedia.org/wiki/Isaac_Newton#Mathematics
Newton's work has been said "to distinctly advance every branch of mathematics then studied."
https://www.youtube.com/watch?v=8w3FR4gT7e0 (Tom Rocks Maths ... Creative Thinking in Science with Robbert Dijkgraaf)
https://www.youtube.com/watch?v=m6rfpQXzXu0 (Numberphile ... Math vs Physics - Numberphile)
https://www.youtube.com/watch?v=6EIW...8g5yic&index=3 (Classification of sets - Lec 03 - Frederic Schuller)
"the strategist"/"the leader": extrovert, a planner, primary PFA/PFS, leading Si, the right hemisphere, intuitive
https://www.youtube.com/watch?v=h-JGqEiNs-I (John Bartholomew ... Chess Fundamentals #4: Pawn Play)
https://www.youtube.com/watch?v=GgMN2dka23s (Want to Improve Your Chess? Don't Copy YouTubers!)
"the industrialist" (usually a mechanical engineer): extrovert, a planner, primary PFA/PFS, leading Se, the left hemisphere, intuitive or logical
https://www.youtube.com/watch?v=hoh5rEVMtsI (Honest Careers ... What do Mechanical Engineers do? ($87,300 Average Salary))
Theoretical physicists often use thought experiments and they constantly compare one idea with another, so they are not creative all the time.
The key difference between "the mathematical physicist" and "the theoretical physicist" could be analysis vs. synthesis instead of comparison vs. creativity. Both subtypes use PFA and PFS, though.
https://www.youtube.com/watch?v=LKYDNDIpoiQ (Gene Bellinger ... Analysis and Synthesis v3 xRev)
"the mechanical engineer": extrovert, not a planner, primary PFA/PFS, leading Se, the left hemisphere, analysis or synthesis
https://www.youtube.com/watch?v=9XB4Be6TjHU (Adam Savage’s Tested ... Adam Savage's One Day Builds: Snub-Nosed Blade Runner Blasters!)
https://www.youtube.com/watch?v=co_qcndNa44 (RiverTechJess ... 21 Reasons Why I Love Engineering / Should I be an Engineer? / Why Engineering is Awesome)
https://www.youtube.com/watch?v=c3S9P9A4els (Day in the Life of a Mechanical Engineering Student | Engineering Study Abroad)
"the mechanical engineer": extrovert, not a planner, primary PFA/PFS, leading Se, the left hemisphere, analysis or synthesis
https://www.youtube.com/watch?v=9XB4Be6TjHU (Adam Savage’s Tested ... Adam Savage's One Day Builds: Snub-Nosed Blade Runner Blasters!)
https://www.youtube.com/watch?v=co_qcndNa44 (RiverTechJess ... 21 Reasons Why I Love Engineering / Should I be an Engineer? / Why Engineering is Awesome)
https://www.youtube.com/watch?v=c3S9P9A4els (Day in the Life of a Mechanical Engineering Student | Engineering Study Abroad)I think this is incorrect ... "the mechanical engineer" and "the industrialist" are probably right hemisphere types."the industrialist" (usually a mechanical engineer): extrovert, a planner, primary PFA/PFS, leading Se, the left hemisphere, intuitive or logical
https://www.youtube.com/watch?v=hoh5rEVMtsI (Honest Careers ... What do Mechanical Engineers do? ($87,300 Average Salary))
"the mathematician" does not exist. Instead, (most) mathematicians have superior PFA/PFS and working memory since their objects/geometric shapes are more complicated.
https://www.youtube.com/watch?v=5RSMLgy06Ew (MIT OpenCourseWare ... Lec 7 | MIT 6.042J Mathematics for Computer Science, Fall 2010)
https://en.wikipedia.org/wiki/Discrete_mathematics
Discrete mathematics (logic, set theory, number theory, theoretical computer science ...) suits a left hemisphere type (i.e. "the computer engineer" or "the experimental physicist").
"the experimental physicist" could be a right hemisphere type so I will use "the programmer" instead (i.e. leading Se, a planner, left...).https://www.youtube.com/watch?v=5RSMLgy06Ew (MIT OpenCourseWare ... Lec 7 | MIT 6.042J Mathematics for Computer Science, Fall 2010)
https://en.wikipedia.org/wiki/Discrete_mathematics
Discrete mathematics (logic, set theory, number theory, theoretical computer science ...) suits a left hemisphere type (i.e. "the computer engineer" or "the experimental physicist").
https://www.youtube.com/watch?v=1LoSV1sjZFI (Approximating Irrational Numbers (Duffin-Schaeffer Conjecture) - Numberphile)
James Maynard's type is most likely "the computer engineer".
https://en.wikipedia.org/wiki/Handed...uage_dominance
"One common handedness theory is the brain hemisphere division of labor. In most people, the left side of the brain controls speaking. The theory suggests it is more efficient for the brain to divide major tasks between the hemispheres—thus most people may use the non-speaking (right) hemisphere for perception and gross motor skills. As speech is a very complex motor control task, the specialised fine motor areas controlling speech are most efficiently used to also control fine motor movement in the dominant hand. As the right hand is controlled by the left hemisphere (and the left hand is controlled by the right hemisphere) most people are, therefore right-handed. The theory implies that left-handed people have a reversed organisation.
However, this theory does not address the fact that the majority of left-handers have left-hemisphere language dominance - just like right handers. Only around 30% of left-handers are not left-hemisphere dominant for language. Some of those have reversed brain organisation, where the verbal processing takes place in the right-hemisphere and visuospatial processing is dominant to the left hemisphere. Others have more ambiguous bilateral organisation, where both hemispheres do parts of typically lateralised functions. When tasks investigating lateralisation are averaged across a group of left-handers, the overall effect is that left-handers show the same pattern of data as right-handers, but with a reduced asymmetry. This finding is likely due to the small proportion of left-handers who have atypical brain organisation."
------
I should probably use symbolic vs. real instead of left hemisphere vs. right hemisphere since 30% of left-handed people process language differently.
https://math.mit.edu/directory/profile.php?pid=144https://www.youtube.com/watch?v=5RSMLgy06Ew (MIT OpenCourseWare ... Lec 7 | MIT 6.042J Mathematics for Computer Science, Fall 2010)
Tom Leighton's type is "the programmer".
One could argue that "superior PFA/PFS and working memory" etc should be a subtype since primary PFA/PFS vs. secondary PFA/PFS is a dichotomy.https://www.youtube.com/watch?v=1LoSV1sjZFI (Approximating Irrational Numbers (Duffin-Schaeffer Conjecture) - Numberphile)
James Maynard's type is most likely "the computer engineer".
James Maynard's subtype is "the logician".
https://www.youtube.com/watch?v=cyvDG8qjt-M (BBC Magic Numbers Mysterious World of Maths)
https://www.ucl.ac.uk/bartlett/casa/dr-hannah-fry
Hannah Fry's type is the introverted version of "the mechanical engineer", and her subtype is "the mathematician".
"the physicist" is a right hemisphere type, and "the experimental physicist" and "the theoretical physicist" are subtypes.
This is not a good description ... less concrete, tangible etc or more envisioned, imagined etc is much better. (btw, this is not about abstraction)I think this is incorrect ... "the mechanical engineer" and "the industrialist" are probably right hemisphere types.
"the mathematician" does not exist. Instead, (most) mathematicians have superior PFA/PFS and working memory since their objects/geometric shapes are more complicated.
... and "the mathematician" refers to a type here, not a subtype.
https://www.shu.ac.uk/about-us/our-p...katie-steckles
https://www.youtube.com/watch?v=NWBToaXK5T0 (Langton's Ant - Numberphile)
Katie's type is "the computer engineer" and her subtype is "the logician".
https://physics.anu.edu.au/contact/p...le.php?ID=1934
https://www.youtube.com/watch?v=I_Df_mx8Hxo (Tibees ... Books for Learning Mathematics)
Toby's type is the introverted version of "the mechanical engineer" and her subtype is "the mathematician".
http://web.math.princeton.edu/~mchudnov/
https://www.youtube.com/watch?v=xBkTIp6ajAg (Planar Graphs - Numberphile)
Maria's type is "the programmer".
https://en.wikipedia.org/wiki/Dianna_Cowern
https://www.youtube.com/watch?v=n2RhC4JNS7M (Physics Girl ... My Path into Physics (at MIT))
Dianna's type is "the physicist" and her subtype is "the experimental physicist" .
https://en.wikipedia.org/wiki/Julia_Galef
https://www.youtube.com/watch?v=vpnxd31y0Fo (Big Think ... Julia Galef: The Sunk Costs Fallacy | Big Think)
Julia's type is "the chess player".
Maria's subtype is "the computer scientist".http://web.math.princeton.edu/~mchudnov/
https://www.youtube.com/watch?v=xBkTIp6ajAg (Planar Graphs - Numberphile)
Maria's type is "the programmer".
A)
John Nash, Bill Gates, Mark Zuckerberg: introvert, a planner, primary PFS, leading Se, the right hemisphere, logical (comparison)"the mathematical physicist" (type/subtype)
https://en.wikipedia.org/wiki/Isaac_Newton#Mathematics
Newton's work has been said "to distinctly advance every branch of mathematics then studied."
https://www.youtube.com/watch?v=8w3FR4gT7e0 (Tom Rocks Maths ... Creative Thinking in Science with Robbert Dijkgraaf)
https://www.youtube.com/watch?v=m6rfpQXzXu0 (Numberphile ... Math vs Physics - Numberphile)
https://www.youtube.com/watch?v=6EIW...8g5yic&index=3 (Classification of sets - Lec 03 - Frederic Schuller)
Isaac Newton's, Robbert Dijkgraaf's and Frederic Schuller's subtype is "the mathematical physicist".
Bill Gates' and Mark Zuckerberg's type is "the programmer" and their subtype is "the computer scientist"
John Nash's subtype is either "the mathematical physicist" or "the theoretical physicist".
Tom's subtype is the extroverted version of "the mathematician".
https://en.wikipedia.org/wiki/Fluid_...d_intelligence
This is my current view on fluid intelligence.
1. awareness of spatial relations and categories (including comparison) ... which is (mainly) processed by the parietal lobe
2. strategic thinking and planning (including cognitive flexibility) ... which is processed by BA 10
3. PFA/PFS and working memory (imagination) ... which is (mainly) processed by DLPFC
https://en.wikipedia.org/wiki/Brodmann_area_10
"Present research suggests that it is involved in strategic processes in memory recall and various executive functions."
"Although this region is extensive in humans, its function is poorly understood. Koechlin & Hyafil have proposed that processing of 'cognitive branching' is the core function of the frontopolar cortex. Cognitive branching enables a previously running task to be maintained in a pending state for subsequent retrieval and execution upon completion of the ongoing one. Many of our complex behaviors and mental activities require simultaneous engagement of multiple tasks, and they suggest the anterior prefrontal cortex may perform a domain-general function in these scheduling operations. Thus, the frontopolar cortex shares features with the central executive in Baddeley's model of working memory."
"This area has also been implicated in decision making prior to the decision being available to conscious awareness."https://pubmed.ncbi.nlm.nih.gov/21930138/https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3572161/
"Our findings provide a novel strong evidence for a specific involvement of right frontopolar cortex in visual-spatial prospective memory. In the context of previous data providing evidence for left BA 10 involvement in verbal prospective memory, our results also suggest material-specific lateralization of prospective memory processes in BA 10."
"A role for rostral prefrontal cortex (BA10) has been proposed in multitasking, in particular, the selection and maintenance of higher order internal goals while other sub-goals are being performed. BA10 has also been implicated in the ability to infer someone else's feelings and thoughts, often referred to as theory of mind."
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3086290/
"FPC has been associated with planning (Koechlin et al., 1999, 2000; van den Heuvel et al., 2003), envisioning/predicting future events (Partiot et al., 1995; Okuda et al., 2003), reasoning (Christoff et al., 2001; Kroger et al., 2002), maintaining rules guiding subsequent cognitive activity (Sakai and Passingham, 2006), and endogenous set switching (Rogers et al., 2000; Weidner et al., 2002)."
https://www.youtube.com/watch?v=uOgnlSUuYjI (Footnotes2Plato ... Intro to German Idealism (1/2))
"the philosopher" is probably a subtype of "the chess player" (or "the politician", or "the scientist"...).
From now on, I will only use these names for subtypes.
These are possible subtypes:
These are possible dichotomies:
1. comparison vs. creativity (less likely)
2. analysis vs. synthesis
3. deductive reasoning vs. inductive reasoning/abductive reasoning
Last edited by Petter; 05-01-2021 at 08:40 AM.
https://www.youtube.com/watch?v=qHwjG5611V4 (Fields Institute ... Relating Topology and Geometry - 2 Minute Math with Jacob Lurie)
The key difference between "the mathematical physicist" and "the theoretical physicist" could be analysis vs. synthesis instead of comparison vs. creativity.
Some mathematicians focus on synthesis.
I think the key difference between "the mathematical physicist" and "the theoretical physicist" is deductive reasoning vs. inductive reasoning/abductive reasoning.
... or an analytical method vs. a numerical method.
I think the key difference between "the mathematical physicist" and "the theoretical physicist" is deductive reasoning vs. inductive reasoning/abductive reasoning.
https://www.quora.com/What-is-the-di...merical-method
"the philosopher" is a deductive subtype and "the scientist" is an abductive subtype.
If deductive reasoning vs. inductive reasoning/abductive reasoning is an actual dichotomy, so a person prefers one cognitive process over another, then "the philosopher" and "the scientist" are different types. (The names still refer to subtypes, though.)
I think a subtype should mean a gradual difference within a dichotomy.
https://math.stackexchange.com/quest...e-or-deductive
"Mathematics is deductive. To be more precise, only deductive proofs are accepted in mathematics. Your "inductive proof" of the distributive property wouldn't be accepted as a proof at all, merely as verification for a finite number of cases (1 case in your question)."
https://en.wikipedia.org/wiki/Problem_of_induction
"induction is the glory of science and the scandal of philosophy"
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