#Cognitive Arithmetic

[omegaphilosophia]

The Philosophy of Arithmetic

The philosophy of arithmetic examines the foundational, conceptual, and metaphysical aspects of arithmetic, which is the branch of mathematics concerned with numbers and the basic operations on them, such as addition, subtraction, multiplication, and division. Philosophers of arithmetic explore questions related to the nature of numbers, the existence of mathematical objects, the truth of arithmetic propositions, and how arithmetic relates to human cognition and the physical world.

Key Concepts:

The Nature of Numbers:

Platonism: Platonists argue that numbers exist as abstract, timeless entities in a separate realm of reality. According to this view, when we perform arithmetic, we are discovering truths about this independent mathematical world.

Nominalism: Nominalists deny the existence of abstract entities like numbers, suggesting that arithmetic is a human invention, with numbers serving as names or labels for collections of objects.

Constructivism: Constructivists hold that numbers and arithmetic truths are constructed by the mind or through social and linguistic practices. They emphasize the role of mental or practical activities in the creation of arithmetic systems.

Arithmetic and Logic:

Logicism: Logicism is the view that arithmetic is reducible to pure logic. This was famously defended by philosophers like Gottlob Frege and Bertrand Russell, who attempted to show that all arithmetic truths could be derived from logical principles.

Formalism: In formalism, arithmetic is seen as a formal system, a game with symbols governed by rules. Formalists argue that the truth of arithmetic propositions is based on internal consistency rather than any external reference to numbers or reality.

Intuitionism: Intuitionists, such as L.E.J. Brouwer, argue that arithmetic is based on human intuition and the mental construction of numbers. They reject the notion that arithmetic truths exist independently of the human mind.

Arithmetic Truths:

A Priori Knowledge: Many philosophers, including Immanuel Kant, have argued that arithmetic truths are known a priori, meaning they are knowable through reason alone and do not depend on experience.

Empiricism: Some philosophers, such as John Stuart Mill, have argued that arithmetic is based on empirical observation and abstraction from the physical world. According to this view, arithmetic truths are generalized from our experience with counting physical objects.

Frege's Criticism of Empiricism: Frege rejected the empiricist view, arguing that arithmetic truths are universal and necessary, which cannot be derived from contingent sensory experiences.

The Foundations of Arithmetic:

Frege's Foundations: In his work "The Foundations of Arithmetic," Frege sought to provide a rigorous logical foundation for arithmetic, arguing that numbers are objective and that arithmetic truths are analytic, meaning they are true by definition and based on logical principles.

Russell's Paradox: Bertrand Russell's discovery of a paradox in Frege's system led to questions about the logical consistency of arithmetic and spurred the development of set theory as a new foundation for mathematics.

Arithmetic and Set Theory:

Set-Theoretic Foundations: Modern arithmetic is often grounded in set theory, where numbers are defined as sets. For example, the number 1 can be defined as the set containing the empty set, and the number 2 as the set containing the set of the empty set. This approach raises philosophical questions about whether numbers are truly reducible to sets and what this means for the nature of arithmetic.

Infinity in Arithmetic:

The Infinite: Arithmetic raises questions about the nature of infinity, particularly in the context of number theory. Is infinity a real concept, or is it merely a useful abstraction? The introduction of infinite numbers and the concept of limits in calculus have expanded these questions to new mathematical areas.

Peano Arithmetic: Peano's axioms formalize the arithmetic of natural numbers, raising questions about the nature of induction and the extent to which the system can account for all arithmetic truths, particularly regarding the treatment of infinite sets or sequences.

The Ontology of Arithmetic:

Realism vs. Anti-Realism: Realists believe that numbers and arithmetic truths exist independently of human thought, while anti-realists, such as fictionalists, argue that numbers are useful fictions that help us describe patterns but do not exist independently.

Mathematical Structuralism: Structuralists argue that numbers do not exist as independent objects but only as positions within a structure. For example, the number 2 has no meaning outside of its relation to other numbers (like 1 and 3) within the system of natural numbers.

Cognitive Foundations of Arithmetic:

Psychological Approaches: Some philosophers and cognitive scientists explore how humans develop arithmetic abilities, considering whether arithmetic is innate or learned and how it relates to our cognitive faculties for counting and abstraction.

Embodied Arithmetic: Some theories propose that arithmetic concepts are grounded in physical and bodily experiences, such as counting on fingers or moving objects, challenging the purely abstract view of arithmetic.

Arithmetic in Other Cultures:

Cultural Variability: Different cultures have developed distinct systems of arithmetic, which raises philosophical questions about the universality of arithmetic truths. Is arithmetic a universal language, or are there culturally specific ways of understanding and manipulating numbers?

Historical and Philosophical Insights:

Aristotle and Number as Quantity: Aristotle considered numbers as abstract quantities and explored their relationship to other categories of being. His ideas laid the groundwork for later philosophical reflections on the nature of number and arithmetic.

Leibniz and Binary Arithmetic: Leibniz's work on binary arithmetic (the foundation of modern computing) reflected his belief that arithmetic is deeply tied to logic and that numerical operations can represent fundamental truths about reality.

Kant's Synthetic A Priori: Immanuel Kant argued that arithmetic propositions, such as "7 + 5 = 12," are synthetic a priori, meaning that they are both informative about the world and knowable through reason alone. This idea contrasts with the empiricist view that arithmetic is derived from experience.

Frege and the Logicization of Arithmetic: Frege’s attempt to reduce arithmetic to logic in his Grundgesetze der Arithmetik (Basic Laws of Arithmetic) was a foundational project for 20th-century philosophy of mathematics. Although his project was undermined by Russell’s paradox, it set the stage for later developments in the philosophy of mathematics, including set theory and formal systems.

The philosophy of arithmetic engages with fundamental questions about the nature of numbers, the existence of arithmetic truths, and the relationship between arithmetic and logic. It explores different perspectives on how we understand and apply arithmetic, whether it is an invention of the human mind, a discovery of abstract realities, or a formal system of rules. Through the works of philosophers like Frege, Kant, and Leibniz, arithmetic has become a rich field of philosophical inquiry, raising profound questions about the foundations of mathematics, knowledge, and cognition.

[teledyn]

The Psychological Scaffolding of Arithmetic

"We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about ‘and’."

— Sir Arthur Eddington

https://psycnet.apa.org/fulltext/2023-84614-001.html

[xyymath]

Why the Number Zero Changed Everything

Zero: a concept so foundational to modern mathematics, science, and technology that we often forget it wasn’t always there. Its presence in our world today seems obvious, but its journey from controversial abstraction to indispensable tool has shaped entire civilizations.

1. The Birth of Zero: A Revolutionary Idea

The concept of zero didn't exist in many ancient cultures. For example, the Greeks, despite their advancements in geometry and number theory, rejected the idea of a placeholder for nothingness. The Babylonians had a placeholder symbol (a space or two slashes) for zero, but they didn't treat it as a number. It wasn't until Indian mathematicians in the 5th century, like Brahmagupta, that zero was truly conceptualized and treated as a number with its own properties.

Zero was initially used as a place-holder in the decimal system, but soon evolved into a full-fledged number with mathematical properties, marking a huge leap in human cognition.

2. The Birth of Algebra

Imagine trying to solve equations like x + 5 = 0 without zero. With zero, algebra becomes solvable, opening up entire fields of study. Before zero’s arrival, solving equations involving unknowns was rudimentary, relying on geometric methods. The Indian mathematician Brahmagupta (again) was one of the first to establish rules for zero in algebraic operations, such as:

x + 0 = x (additive identity)

x × 0 = 0 (multiplicative property)

These properties allowed algebra to evolve into a system of abstract thought rather than just arithmetic, transforming the ways we understand equations, functions, and polynomials.

3. Calculus and Zero: A Relationship Built on Limits

Without zero, the foundation of calculus—limits, derivatives, and integrals—wouldn’t exist. The limit concept is intrinsically tied to approaching zero as a boundary. In differentiation, the derivative of a function f(x) is defined as:

f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

This limit process hinges on the ability to manipulate and conceptualize zero in infinitesimal quantities. Similarly, integrals, which form the backbone of area under curves and summation of continuous data, rely on summing infinitely small quantities—essentially working with zero.

Without the concept of zero, we wouldn’t have the means to rigorously define rates of change or accumulation, effectively stalling physics, engineering, and economics.

4. Zero and the Concept of Nothingness: The Philosophical Impact

Zero is more than just a number; it’s an idea that forces us to confront nothingness. Its acceptance was met with philosophical resistance in ancient times. How could "nothing" be real? How could nothing be useful in equations? But once mathematicians recognized zero as a number in its own right, it transformed entire philosophical discussions. It even challenged ideas in theology (e.g., the nature of creation and void).

In set theory, zero is the size of the empty set—the set that contains no elements. But without zero, there would be no way to express or manipulate sets of nothing. Thus, zero's philosophical acceptance paved the way for advanced theories in logic and mathematical foundations.

5. The Computing Revolution: Zero as a Binary Foundation

Fast forward to today. Every piece of digital technology—from computers to smartphones—relies on binary systems: sequences of 1s and 0s. These two digits are the fundamental building blocks of computer operations. The idea of Boolean algebra, where values are either true (1) or false (0), is deeply rooted in zero’s ability to represent "nothing" or "off."

The computational world relies on logical gates, where zero is interpreted as false, allowing us to build anything from a basic calculator to the complex AI systems that drive modern technology. Zero, in this context, is as important as one—and it's been essential in shaping the digital age.

6. Zero and Its Role in Modern Fields

In modern fields like physics and economics, zero plays a crucial role in explaining natural phenomena and building theories. For instance:

In physics, zero-point energy (the lowest possible energy state) describes phenomena in quantum mechanics and cosmology.

In economics, zero is the reference point for economic equilibrium, and the concept of "breaking even" relies on zero profit/loss.

Zero allows us to make sense of the world, whether we’re measuring the empty vacuum of space or examining the marginal cost of producing one more unit in economics.

7. The Mathematical Utility of Zero

Zero is essential in defining negative numbers. Without zero as the boundary between positive and negative values, our number system would collapse. The number line itself relies on zero as the anchor point, dividing positive and negative values. Vector spaces, a fundamental structure in linear algebra, depend on the concept of a zero vector as the additive identity.

The coordinate system and graphs we use to model data in statistics, geometry, and trigonometry would not function as we know them today. Without zero, there could be no Cartesian plane, and concepts like distance, midpoint, and slope would be incoherent.

[ahuactl]

on mathematical models

the question “is math invented or discovered?” remains to be the most contentious questions in mathematics.

a significant portion of people including mathematicians believe that mathematics holds objective truth insofar as their models, theorems and equations tell the truth about reality in which the Subject: their proposition exists independently of them. this position is familiar among those in the Platonist or Realist traditions of mathematics. common knowledge states that any proposition such as  P: 1 + 1  = 2  is true in which ever universe it is stated in such that its truth is not constructed upon the confines of our society and more strongly, not in our minds or cognitions.

i will present my argument here on why i disagree with this view. first, propositions like P: 1 + 1  = 2 are certainly not true in every construction of a mathematical system. for example, in boolean algebra and nonstandard number systems. even non-Platonist mathematicians would quickly disagree with this as they would claim that the Platonist view holds that the truth of a proposition exists not solely but with the pair (P, S) whereas P is the proposition and S is the system in which it is considered to be in. on such note, this leads me to my next argument.

from the development of set theory in the 19th century, it was discovered by mathematicians that mathematics as a field was built on shaky logical foundations (re: Russel’s Paradox). this thus necessitated the construction of a new structure which must possess the power to rebuild mathematics. this new foundation came with the introduction of ZFC. it is an attempt to systematically rebuild the previously known and accepted results of mathematics while working to eliminate the logical inconsistencies of previous naive set theory. from how it was made, ZFC does not posit the truth of any propositions insofar that it exists as starting axioms in which rules of inference can be applied. as with any theories of logic, its axioms must be decided and chosen. it could be noted that these axioms were posteriori in a sense that they were built to solve the issues such as Russel’s Paradox. it can then be argued that the process by in which these axioms were chosen is contingent upon the values of the persons that chose it as well as the developed culture of mathematics. in fact, it is by no means that ZFC is only the possible theory of mathematics (e.g. Model Theory, Category Theory). no matter the “objective” metaphysical existence of mathematical objects, by the way mathematics was built and practiced, these starting axioms still remain a choice.

to reiterate, the way mathematics has been agreed to be used by mathematicians, whichever system set in place still remains a choice. this reveals its use as pragmatic: the system, that is, ZFC was adapted because it works. this naturally extends out from its foundations to concrete mathematical objects studied in abstract algebra, analysis, etc. for example, a group is not just a set with specific rules with its binary operation; the construction of the properties that denote a Group came a posteriori in a way that it was discovered that the set of properties in the first place proved to be a useful abstraction to study. 

on a related note, i would argue that the existence of abstract mathematical objects actualize themselves by our need and desire for the world to conform to standard rules as appeal to our intuition and senses. the truth value of P: 1 + 1  = 2 in (P, S) in an arithmetic system S signifies an essence in which it “makes sense” that combining abstract objects  result to a set in which it succeeds singular objects by the value of each one of those objects. the value of (P, S) does not reveal a Platonic truth of our universe but instead a declaration of common sensical deductions. in such, a mathematical statement is a “model” the same way a bachelor is “unmarried”.

on usage:

regardless of the metaphysical existence of mathematical objects, it, as a system, is undoubtedly one of the finest works of humankind. i advise that one ought not to use this powerful tool to make claims of absolute truth. in a sense, the existence of mathematical objects remain irrelevant to how it ought be used. one should not at all invoke mathematics to justify repressive systems and to cause grave harm to humanity. as a tool, it must not be used for evil. one must always remain cautious of individuals who use mathematics as arguments by certainty. these individuals who swear by the sharp sword of mathematics is most likely using it to silence thought and keep one from questioning. always look at the mathematics; an equation is not just a set of symbols that denote some property; it is a theory of the world and this theory must be met with most criticisms when it is being used to make claims for human policies. look at the mathematics, specifically which assumptions were made by the ones who present them: it must reveal the true character of such persons.

[justinspoliticalcorner]

Greg Owen at LGBTQ Nation:

In video shared by Fox News on Monday, Donald Trump again claimed schools around the country are “taking” kids and performing “operations” on them. “There are some places your boy leaves the school, comes back a girl,” Trump insisted without proof. “Okay? Without parental consent. What is that all about? That’s like — when they talk about a threat to democracy, they’re a threat,” Trump continued, apparently referring to his Democratic opponent and clearly rattled that her message about his authoritarian nature and cognitive decline are taking hold.

In a rambling answer to a Bronx dad at what the New York Post described as a “surprise” visit to a barbershop packed with Black men who support Trump, the former president, slumped in a barber chair, held forth incoherently on his solution for problems at America’s schools: stopping teachers and administrators from transitioning kids. All of this was in response to the dad’s question about how Trump would help Bronx public schools perform better – the dad didn’t mention trans kids at all. “Could you imagine without parental consent? At first, what I was told that was actually happening, I said, you know, it’s an exaggeration. No. It happens! It happens in areas where it happens. We’re not going to let it happen, but we are going to straighten out a lot,” Trump said, untethered from the facts or syntax.

[...] “I never saw – you don’t need any of them. You know, I want one person and a secretary to just make sure they’re teaching English. Okay. Give a little English,” he said. “Okay? I say reading, writing, and arithmetic. No transgender, no operations.”

Donald Trump pushing anti-trans nonsense yet again, this time by falsely asserting that public schools are helping kids transition and perform gender-confirmation surgery operations.

See Also:

The Advocate: Donald Trump, an actual threat to democracy, claims it’s transgender kids who are a ‘threat to democracy’

[isthenapoleoncute]

This Napoleon is doing some hard thinking!

A lot of people don’t know this, but Napoleons have some remarkable problem-solving and cognitive abilities. They have been found to have an advanced level of cognitive power, above that of even a four-year-old human child. They can understand cause and effect, and use tools to solve problems, such as using a stick to obtain food from a hard-to-reach place, or using artillery to decimate infantry to make way for cavalry. They can even comprehend and use arithmetic, counting well above the number eight.

Studies have found that Napoleons have proportionaly similar sized brains as many primates, which is thought to be the reason for their advanced intelligence.

But their intelligence doesn't stop there, Napoleons have been found to be able to understand, use and combine concepts such as same and different, big and small, and different colors and shapes. They are able to understand the concept of zero and use it to solve problems, demonstrating a level of cognitive sophistication.

Pretty cute, if you ask me!

[daisybslt]

Speech & Language Pathology Stroke Terms

Disorganised list of terms used in slt for stroke- for study/quick reference.

AAC- Alternative augmentative communication.

ABI- Acquired brain injury (anytime after birth).

Agnosia- Inability to process sensory information (in Greek gnosis- "not knowing").

Aphasia- Impairment of language, affecting the production or comprehension of speech and the ability to read or write, depending on the affected area of the brain. (Greek a/without + phásis/speech").

Apraxia- Inability to execute purposeful, previously learned motor tasks, despite physical ability and willingness. (Greek a/without + praxis/action).

Aspiration- Food or fluid accidentally enters the lungs through the windpipe, often as a result of dysphagia.

Bilateral- Involving or affecting both sides, usually referencing both sides of the body.

Capacity- Ability to reason, make decisions and consider choices, express views and receive and understand information (AWI= Adult With Incapacity).

Cerebro-Vascular Accident (CVA)- Stroke.

Cognitive function- Anything involving thinking.

Deep Vein Thrombosis (DVT)- Blood clot forms in a deep vein.

Deglutition- The act of swallowing.

Dementia- Decline of function in the brain causes cognitive problems such as difficulty with memory, understanding and mood.

Dysfluency- Any type of speech which is marked with repetitions, prolongations and hesitations; an interruption in the flow of speech sounds. Commonly known as stuttering or stammering.

Dysarthria- Collection of motor speech disorders.

Dysphagia- Swallowing difficulties.

Embolism- Blockage of a blood vessel by a blood clot or piece of fatty material or other debris in the blood stream. An embolism is a type of stroke.

Enteral feeding- Feeding through a tube connected to the person's stomach.

FAST test- 'Facial drooping, Arm weakness, Speech problems, Time to call 999'

Fluency- Smoothness with which sounds, syllables, words and phrases are joined together during oral language.

Hemorrhagic stroke-  Caused when a blood vessel in the brain bleeds into the brain tissues or the space around the brain.

Hemianopia-  Loss of one half of your visual field. 

Hemiparesis- Weakness on one side of the body.

Hemiplegia- Complete paralysis on one side of the body.

Hypotonia- Abnormal decrease of muscle tone.

Ischemic stroke/ Infarct- Damage to the brain caused by lack of blood flow, usually from a clot. An area of tissue that is dead because of a loss of blood supply. This is the most common type of stroke.

Infarction- A sudden loss of a tissue’s blood supply causing the tissue to die.

Ischemia- Blood flow (and thus oxygen) is restricted or reduced in a part of the body. 

Ischemic penumbra- Areas of damaged but still living brain cells arranged in a patchwork pattern around areas of dead brain cells.

Lacunar stroke/infarct- When a small artery deep in the brain becomes blocked, causing a small area of damaged brain tissue.

Left hemisphere- Controls speech, comprehension, arithmetic, and writing.

Muscle tone- The degree of natural tension in a person's muscles. Abnormally high muscle tone can lead to muscle tightness and stiffness (spasticity). Very low muscle tone can cause floppiness (hypotonia).

Muscle tension- When muscles of the body remain semi-contracted for a period of time in the resting state.

Naso-gastric (NG) tube-  Medical catheter that's inserted through your nose into your stomach.  Used both to deliver substances to your stomach and to draw substances out.

Neglect- Not being aware of one side of the body and/or environment.

Neuron- Nerve cell.

Neuroplasticity- The ability of undamaged parts of the brain to take over the jobs of damaged areas.

Nystagmus- Continuous uncontrolled movement of the eyes.

Paralysis- Partly or entirely unable to move the affected parts of the body.

Percutaneous endoscopic gastrostomy (PEG)- Feeding tube placed through the abdominal wall and into the stomach.

Right hemisphere- Controls creativity, spatial ability, artistic, and musical skills

Stroke- Occurs when something blocks blood supply to part of the brain or when a blood vessel in the brain bursts.

Spasticity- Abnormal increase in muscle tone or stiffness of muscle

Thrombolysis- An early treatment for some types of strokes caused by a blood clot.

Thrombosis- A blood clot that forms in an artery.

Transient Ischaemic Attack (TIA)-  sometimes called a “mini-stroke”. Blood flow to the brain is blocked for a short time, usually no more than 5 minutes.

Vertebral artery dissection (VAD)- A tear in the walls of an artery at the back of the neck, blood can then get between the layers of artery walls and can lead to a clot forming, causing a blockage (a stroke).

Visual field loss- The loss of sight in a particular area of visual field.

[so-true-overdue]

The Gospel of Immunity: A Sermon on the Sacred Shield of Vaccination

Behold, the paradox of human cognition: we champion progress, yet tremble before its fruits.

In a world spinning upon the axis of relentless biological warfare—our cells besieged by microbial marauders—vaccines stand as sentinels, the silent paladins of immunological defense. Yet, their divine efficacy is often questioned by those who worship at the altar of anecdote, forsaking the empirical cathedral of science.

Consider the Magnitude of Their Grace

Vaccines are not mere concoctions of modern alchemy. They are the crystallized wisdom of centuries, born of Pasteur’s tenacity, Jenner’s courage, and the accumulated trials of countless minds wielding microscopes like swords. They have subdued polio’s paralysis, exorcised smallpox’s specter, and shielded countless millions from the venoms of measles, tetanus, and pertussis.

And what of their adversaries? The infinitesimal specter of adverse reactions. Let us quantify the peril: the risk of a severe allergic reaction to a vaccine—a dreaded anaphylaxis—is approximately one in a million. To contextualize, the chance of being struck by lightning in one’s lifetime is 1 in 15,300. Shall we eschew umbrellas next? Or perhaps condemn electricity itself as too great a hazard to endure?

On Negotiation with Risk

Vaccination is not the obliteration of risk; it is a calculated negotiation with uncertainty. To vaccinate is to weigh the scales of harm and benefit, to face the specter of a one-in-a-million reaction and declare that the lives of millions are worth that gamble. Contrast this with the toll exacted by diseases unopposed: measles alone claims the lives of over 100,000 annually, most of them children. This is not conjecture—it is arithmetic, immutable and unyielding.

Shall we refuse the shield because it may chafe? Shall we spurn the ship because it cannot promise calm seas? Such is the folly of those who elevate potential discomfort above the preservation of collective health. They barter statistical insignificance for certainty of peril, trading herd immunity for herd vulnerability.

The Poetry of Immune Memory

The true marvel of vaccination is not merely its prevention but its pedagogy. Vaccines instruct our immune system, training it to recognize the invader before the battle has begun. They are rehearsals for wars that may never come. To vaccinate is to inscribe within the body a symphony of defense, a living testament to humanity’s ingenuity and resilience.

Without this foresight, the immune system becomes a tactician unprepared for the ambush. Disease ravages unchecked, leaving scars upon both flesh and society. Vaccines, therefore, are not just medicinal; they are ethical. They embody the moral imperative to protect not only oneself but the vulnerable—the infant, the immunocompromised, the elder.

A Closing Admonition

Let us not falter in the face of misinformation, for it spreads with a virulence rivaling the diseases we seek to defeat. Let us arm ourselves with knowledge and statistics, with reason and compassion. The act of vaccination is an act of faith—not blind faith, but faith rooted in evidence, nurtured by science, and borne aloft by the unassailable truth that humanity is stronger united.

Go forth, then, and spread the gospel of immunity. For in the armory of progress, the needle is mightier than the microbe.

[t-allyitup]

ed edd n eddy alphabet soup part ii anyone?

may be headed in the direction of a fic me thinks idk i'm just at a point where my brain is experiencing a creative outpouring in the form of ed edd n eddy content

[eddeddy specific i guess. let's see]

cw for substances, implied (but up to interpretation) traumatic events, child abuse/domestic violence mention, double d enjoying calculus

[also ... i may have mentioned this previously somewhere but i'm currently almost 2 years clean from dxm abuse & all drugs so PLEASE know that interactions with substances are not something that should be romanticized or promoted, i'm not trying to do that i just also have been in high school and as a teenager substances are something that exist]

[for purposes of me being me this story features the three ed's as seniors in high school, as well as rolf, kevin, and nazz. johnny & may kanker are juniors in high school, sarah & jimmy are sophomores, and eldest kankers have graduated hs]

[eddy's brother is in the can and staying there cuz i'm not about to deal with his ass sorry]

picking up from double d's brain alphabet soup...

- beginning

but that wasn't productive ruminating for the current task at hand, no.

no, the focus of his current endeavor, as he had been sorely forcing his near non-existent attention span back too, was familiarizing himself with the revision outline for the first calculus ii quiz of his last year of high school.

calculus had been relatively simple, the theoretical aspect of geometry soothingly absent from this branch of arithmetic, with many of the classic formula/solve/answer questions (however tedious the problems may be.) double d enjoyed problems with direct, proven answers, especially ones that would simply be labeled as correct or incorrect. knowing that without a doubt there was a proven, logical, factual answer for a problem was motivating and provided structure.

although he still received excellent markings in his literature classes, and had become especially gifted in theoretical analysis and research investigation, the concept of language left him feeling rather uncomfortable. while there were specific outlines, literary devices, and general frame of composition to guide him, a compelling and well-written piece of writing was largely subjective. personal opinions of the audience were essential to the response of the piece, and therefore effective criticism stemmed often from personal preference rather than execution.

ed, a third of double d’s nearly life-long trio of best friends, had surprisingly excelled in the areas of creative writing and storytelling in the past few years. while his spelling and grammar needed (and likely would always need) some work, his ability to reveal emotion in his writing was pleasantly shocking and impressive to both edd and eddy. double d had scanned ed’s last few impromptu creative writing assignments, and had beamed with pride at each one, offering only some minor suggestions each time that the other teen had taken with great appreciation and warmth. ed had also grown to become interested in cooking, and after nearly burning double d’s house to ash multiple times while trying to cook hot dog burgers, had gotten a strict warning that he'd better work on his scientific skills if he ever considered returning to double d's kitchen again. this had led to double d spending a few grueling hours explaining measurements and proper handling of equipment, but had ultimately paid off in the form of the trio enjoying a delicious ed-cooked meal nearly three times a week.

ed had also joined a d&d league, following a recommendation from a (long overdo) psychiatric assessment that ed had dyslexia and adhd, and would benefit from some time outside of his house. double d and eddy had understood that this was a nice way of the shrink telling ed's parents that their continued domestic violence mishaps and borderline abusive behavior towards their son had been resulting in cognitive decline, and that ed having a productive hobby and solid support system would hopefully be able to keep him stable and shield him from his parents further traumatizing him.

eddy was, to few of the cul-de-sac kid's surprise, quite gifted in the areas of communications, business, and physical education. following his brother’s arrest and eventual incarceration, eddy had been hitting the gym to try and kill off his festering anger and hurt from the abuse. he had made the junior varsity football team the first year, and was quickly promoted to varsity his sophomore year. eddy was still shorter than ed and double d, but was noticeably stronger and better ‘filled out.’ eddy had prided himself on his self-described 'total beefy hunk of a bod,' much to ed's howls of amusement and double d's eye roll of affection. while eddy worked tirelessly on his car, ranting about the 'idiotic lack of, if actually existent, formation strategy’ of the quarterback, double d had become increasingly aware of how eddy's personality had developed. it was clear that eddy had become more confident, in not only himself, but in his abilities. he also showed an impressive talent for pattern recognition, strategizing, and planning. this had been a major asset to their football team, who were mostly 6'2 boulders that had clearly only made the team for their size. of course, it was inevitable that eddy would always be the snarky little attention hog he was, but it was pretty clear to double d that eddy was also becoming observant and (though this may be a stretch) stabilized. he had also gotten tattoos, one of a dragon that matched with ed and a few for other reasons that double d hadn't been paying attention to due to his uncharacteristic staring in shock and (now identifiable) gay panic. eddy had developed an obsession with piercings, too. his ears, left eyebrow, right nostril, and tongue in specific were victims of this endevor, and although kevin had rolled his eyes and scoffed at the look, eddy looked incredible and had remained confident in his appearance.

in fact, it was jimmy, who had grown up more than anyone could imagine, who was the first to compliment eddy on his piercings. jimmy had taken up swimming and diving, as well as student government, and debate team with eddy. his voice was scratchy and soothing, and his ability to tear it up in the pool had astonished and overjoyed everyone. he had been returning to states for swim year after year since the 7th grade, and the legendary smile that had always been the focal feature of his face was now accompanied by a freckling of acne. his baja sweatshirts and acid wash jeans, along with a surprising choice of reebok shoes, had been proof of his own self-settling.

sarah had become distant, although physically present, halfway through freshman year. that october, a rumor had circulated about sarah that double d didn't even want to think about, especially after sarah had told him the truth about what had actually happened.

sarah stayed close to ed the next few years, the rare instance of a unmistakable clang of a sarah laugh present after a particularly goofy joke from jimmy or a swat at the hand of ed trying to steal a french fry was rare, but had become more common. the sound of her laugh was helpful for reminding them that she was healing, and that the blazing force of fire that lies inside, although flickering, hasn't gone out.

johnny had joined a d&d leauge with ed, and was unsurprisingly terrific at arts of all kinds. he had gotten lead roles in the last few student-led visual arts productions, twice as the main supporting character and once as the lead-joseph, in 'joseph and the amazing technicolor dreamcoat.' in the summers, johnny had played baseball, and was playing varsity by junior year. plank remained lodged in his backpack, a comforting reminder that some things never change.

rolf had also become interested in musical theater, as well as baseball. during baseball season, rolf, johnny, and kevin would spend lots of time together, baseball having brought them back. kevin and rolf remained close year round, rolf supporting kevin during football season and kevin supporting rolf at his theater performances, although theater was ‘nerdy’ in his unwarranted opinion.

to everyone's immense surprise, nazz had joined a band. she had joined a rock-n-roll jazz band with marie kanker and rolf, as well as two other boys and the occasional sarah on backup vocals. nazz had also joined the d&d league, per request of ed, and had seemed to be enjoying that. in the summer she played softball, also with marie, and had spent a great portion of each season trying to convince sarah to play.

nazz had grown into someone that double d deeply admired. she was authorative, inclusive, open, and stood firm in herself and her beliefs. she hadn't been interested in showing off, focusing primarily on connection and including others. the other boys in his grade had teased her for her interest in make up and fashion, and nazz didn't care. she enjoyed ‘feminine’ things because they made her happy, just like shredding on her guitar and playing d&d and other typically ‘masculine’ things made her happy. she did what she wanted to do, and she had told double d that even if she was applying make up or learning how to kick start a car engine to impress someone, than what's so wrong with that? what's wrong with wanting to look nice for someone, or wanting to be able to help them? what's wrong with having pride in yourself?

double d had went home after that conversation and started crying. he couldn't stop, and he didn't understand why he had been crying in the first place. he wasn't much of a crier at all-in fact he hadn't cried in months-but when nazz had explained that to him, he supposed he realized how much he cared about her. he realized that the kind of growth it takes to reach that conclusion could only stem from something changing, and he realized that an inevitable and painful part of growth is change.

he had also realized that change triggered advancement, which triggered the discovery of philosophies like the one nazz lived by.

it had also come to mind that to develop such a welcoming and independent philosophy, nazz may have experienced something that was possibly quite traumatizing.

it was the same string of thoughts that double d had regarding the look on eddy’s face before they parted ways for the night. the humid july night buzzed with cicadas and secondhand smoke hung suspended under the artificial buzz of the street light near their houses. a roar of laughter from eddy followed by a the scheming, sly smirk, the kind where you try to stop your teeth from showing but it happens anyway, the light producing a halo effect upon his best friend and leaving double d in a glowy haze. the way eddy’s nose scrunches slightly with the smile and the way his deep, spruce blue eyes stare coyly at him before he takes a final drag of a blunt rolled in a way the should be considered a violation of the herb's personal rights. his eyes mischievous but distant as his lips and lungs kill the joint for good, the image of eddy flicking the discarded paper away and exhaling the smoke upwards. following this dramatic gesture, was what eddy had said to double d moments before he had said goodnight on that warm july evening.

'd, there's no point in me stayin’ after graduation. nothin’ left to stay for once you and lumpy leave for school. i'm leaving this shithole, one way or another.’

double d remembers that moment exactly. the moment that triggered everything to follow, the specific moment when he had realized that he was absolutely terrified of losing his best friend in a way that hadn't previously aligned with his stasis levels. he remembers eddy waving goodbye, calling something about ‘catching him later,’ and double d paced back home and locked himself in his room.

he thought of what nazz had said earlier that day when the older kids of rhe cul-de-sac had gathered at rolf's for table tennis and an excuse to finish a pack of twisted teas. that it isn't wrong to want. it was, in fact, a fundamental function of a sentient creatures existence, and that the external shame that people project on others for having desires in inherently hypocritical. nazz, with her laid back attitude and approachable demeanor, sharing the wisdom of a life once lived through self-criticism.

he thought of what eddy had said about leaving this place, one way or another, and it was then that double d let the pieces of his strained conscious unravel and descended into a fit of choking through tears.

it was becoming very obvious to that eddward that he was entering an entirely different plane of trouble.

- end

if i spelled something wrong no i didn't . gn

[lunechante]

I used to be a bright child. One of those who read a lot, remember everything, think and connect things rapidly, do math as a hobby and need to be intellectually and cognitively challenged all the time. I had a large vocabulary, and although I tended to take things literally, I would always choose the best word to convey exactly what I meant. 

As soon as secondary school began, so did bullying due to my inclination for anything intellectual - from the last years of primary school would be more accurate, but it was still punctuated with great friendships. In order to try and fit - which unfortunately, looking backwards almost twenty years later, did not prove efficient - I depleted my vocabulary to fit society’s “standards”. The ones of my class, that’s to say. Not those that enhance brightness and supposedly allow you to reach for the top. It was like learning a new language, one I was immersed in all the time.

However, slowly, I forgot my “native” kind of French. The language I’d learnt with books through my childhood. Going back to a more formal language register now seems to be an impossible task. Not only is it not instinctive to me anymore, I also have lost the cognitive ability to provide the kind of intellectual labour needed to get it back due to more than a decade of burn out. Nowadays, even navigating between French and English seems hard.

Actually, I lose my words all the time, whatever the language. In the middle of a conversation, I won’t find the word for the most trivial thing. So I often find myself using my foreign language learning skills, discreetly finding circumlocutions to express the idea. Sometimes using the wrong words, or a foreign language or when I’m with someone I trust, showing the thing and admitting I don’t remember how to name it. Most of the time I do manage to keep the conversation going without my interlocutor noticing I could not find my words. But that doesn’t stop the frustration, shame and fear from striking hard. My grandmother had primary progressive aphasia. That’s how it starts. It got noticeable in her early 70s. I try to convince myself that I’m only in my early 30s, that for me, it’s only a matter of burn out, that it will get better when I am not tired anymore - whatever that means. But in spite of rest, it’s happening more and more. But I see that I am not able to get some of my abilities back. Look at my language register. Or my arithmetic. After decades of not practicing, the skills need to be learnt again. Maybe they just need to be refreshed, but even that seems like climbing Mount Everest.

Growing up, puberty hit me young (pathologically) and hard, making me ugly. By the age of 12, I’d been told more than enough to have internalised my ugliness. Still haven’t gotten over it. Having huge problems understanding humour, my only asset was my intelligence. I built myself on that. Even though my peers rejected me for it - or that’s what I understood -, knowledge has always been the most important thing for me. It’s hard to put these feelings into words. The fear, both of change and of losing the only thing valuable about yourself. The frustration from the inability to do anything about it. That shame of what/who you’re becoming, and the self-confidence that just disappears a bit more every day. Not knowing who you are anymore, because that person is far from who you used to be becoming.

In French

[compneuropapers]

Interesting Papers for Week 26, 2023

Saturation of visual responses explains size tuning in rat collicular neurons. Baranauskas, G., Rysevaite‐Kyguoliene, K., Sabeckis, I., & Pauza, D. H. (2023). European Journal of Neuroscience, 57(2), 285–309.

Reconstruction of sparse recurrent connectivity and inputs from the nonlinear dynamics of neuronal networks. Barranca, V. J. (2023). Journal of Computational Neuroscience, 51(1), 43–58.

Population codes enable learning from few examples by shaping inductive bias. Bordelon, B., & Pehlevan, C. (2022). eLife, 11, e78606.

Cerebro-cerebellar networks facilitate learning through feedback decoupling. Boven, E., Pemberton, J., Chadderton, P., Apps, R., & Costa, R. P. (2023). Nature Communications, 14, 51.

The role of the lateral orbitofrontal cortex in creating cognitive maps. Costa, K. M., Scholz, R., Lloyd, K., Moreno-Castilla, P., Gardner, M. P. H., Dayan, P., & Schoenbaum, G. (2023). Nature Neuroscience, 26, 107–115.

Functional geometry of the cortex encodes dimensions of consciousness. Huang, Z., Mashour, G. A., & Hudetz, A. G. (2023). Nature Communications, 14, 72.

Optimal Control Costs of Brain State Transitions in Linear Stochastic Systems. Kamiya, S., Kawakita, G., Sasai, S., Kitazono, J., & Oizumi, M. (2023). Journal of Neuroscience, 43(2), 270–281.

Do cognitive and physical effort costs affect choice behavior similarly? Lim, L. X., Fansher, M., & Hélie, S. (2023). Journal of Mathematical Psychology, 112, 102727.

Deciphering functional roles of synaptic plasticity and intrinsic neural firing in developing mouse visual cortex layer IV microcircuit. Liu, S., & Li, Y. (2023). Journal of Computational Neuroscience, 51(1), 23–42.

Arithmetic value representation for hierarchical behavior composition. Makino, H. (2023). Nature Neuroscience, 26, 140–149.

Altered integration of excitatory inputs onto the basal dendrites of layer 5 pyramidal neurons in a mouse model of Fragile X syndrome. Mitchell, D. E., Miranda-Rottmann, S., Blanchard, M., & Araya, R. (2023). Proceedings of the National Academy of Sciences, 120(2), e2208963120.

Introducing the Dendrify framework for incorporating dendrites to spiking neural networks. Pagkalos, M., Chavlis, S., & Poirazi, P. (2023). Nature Communications, 14, 131.

A statistical foundation for derived attention. Paskewitz, S., & Jones, M. (2023). Journal of Mathematical Psychology, 112, 102728.

Rapid synaptic and gamma rhythm signature of mouse critical period plasticity. Quast, K. B., Reh, R. K., Caiati, M. D., Kopell, N., McCarthy, M. M., & Hensch, T. K. (2023). Proceedings of the National Academy of Sciences, 120(2), e2123182120.

Lingering Neural Representations of Past Task Features Adversely Affect Future Behavior. Rangel, B. O., Hazeltine, E., & Wessel, J. R. (2023). Journal of Neuroscience, 43(2), 282–292.

Evidence for entropy maximisation in human free choice behaviour. Rens, N., Lancia, G. L., Eluchans, M., Schwartenbeck, P., Cunnington, R., & Pezzulo, G. (2023). Cognition, 232, 105328.

Choice selective inhibition drives stability and competition in decision circuits. Roach, J. P., Churchland, A. K., & Engel, T. A. (2023). Nature Communications, 14, 147.

Information-processing dynamics in neural networks of macaque cerebral cortex reflect cognitive state and behavior. Varley, T. F., Sporns, O., Schaffelhofer, S., Scherberger, H., & Dann, B. (2023). Proceedings of the National Academy of Sciences, 120(2), e2207677120.

Transformation of acoustic information to sensory decision variables in the parietal cortex. Yao, J. D., Zemlianova, K. O., Hocker, D. L., Savin, C., Constantinople, C. M., Chung, S., & Sanes, D. H. (2023). Proceedings of the National Academy of Sciences, 120(2), e2212120120.

Hippocampal spatial representations exhibit a hyperbolic geometry that expands with experience. Zhang, H., Rich, P. D., Lee, A. K., & Sharpee, T. O. (2023). Nature Neuroscience, 26, 131–139.

[cyberninja87]

Discover Free Online Hidden Object Games

Embark on a journey into the realm of Hidden Object Games Puzzle Adventures, a captivating genre of video games that challenges you to meticulously spot cleverly camouflaged items within intricate pictures. These games serve as exceptional tools for honing your visual acuity, enhancing focused attention, and nurturing contextual awareness. The digital landscape offers a plethora of complimentary hidden object games, catering to adults and children alike, fostering enjoyment while simultaneously nurturing cognitive growth. https://onlinehiddenobjectgames.com/

Recent psychological studies have unveiled a compelling correlation between engaging in hidden object games and other cognitive exercises, and a noteworthy enhancement in the intellectual capacities of individuals spanning all age groups. This cognitive stimulation appears particularly effective in bolstering short-term memory, fostering strategic planning acumen, and even refining arithmetic proficiency and one's internal locus of control.

In the realms of these immersive games, a quintessential experience entails meticulously scrutinizing a visual canvas to pinpoint specific items. The reward for success often takes the form of credits or bonuses. The diverse array of concealed objects typically encompasses:

Exquisite items rendered in the enigmatic style of artistic mystique.

Alluring female personas.

Treasures or individuals in need of rescue from malevolent clutches.

Romantic and fantastical characters, including mermaids and vampires.

A Plethora of Hidden Object Game Varieties

Presently, the internet boasts an inexhaustible collection of such games. Esteemed purveyors such as Izzy Games and Hidden247 offer an extensive selection of full-screen hidden object games, available for indulgence across desktop computers, mobile applications, and smartphones, with no mandatory downloads.

Moreover, the limits of game access and frequency of visits to these platforms are virtually nonexistent. Practically all these games cater to diverse online and mobile operating systems, encompassing Windows, Apple, Android, IOS, iPhone, and iPad.

Cream of the Crop in Free Hidden Object Entertainment

The plethora of brain-stimulating games and the myriad of individual preferences make the task of singling out definitive recommendations an insurmountable challenge. Yet, rest assured, all these games bear an inherent element of amusement and contribute significantly to the enhancement of cognitive prowess. Simply peruse the extensive roster of games, select those that resonate with you, and relish limitless amusement without incurring any costs.

[explaindeleuze]

post-rave mixology

haunting grounds and liminal spaces are the setting of a new lecture on post-rave economics. the professor starts reciting AI-made poetry from the literature-nobel-winning bot, which operates without prompts and has only been fed rateyourmusic album review's and lyrics. the 87 human students and 32 post-human students all have different interpretations on the professor's lecture; all of which seem to perfectly operate on an hypothetical plane of immanence, only accessible through VR. And as they are turning in their final essay (which is written not in words, but geometric figures, arithmetic operations and emojis), a new synthetic crypto-currency just enters the market and sixteen minutes after its debut, it collapses and generates 17,000 micro-crisis on the cyber-space de-centralized banking system, and generates revenue for the big Capital software, which has operated as a computer virus withouth any intelligence or cognition being aware of it; as it grows, less and less Memory is available for users to install apps and common knowledge starts receding

[xyymath]

Why the Number 7 is Everywhere: Cultural and Mathematical Significance

The number 7 has long captured human imagination—not just as a symbol of luck or mysticism, but also as a profound and pervasive number in mathematics and culture. From ancient myths to modern probability theory, the number 7 seems to appear everywhere, woven into the fabric of our world.

Cultural Significance

In culture, 7 holds a near-universal place of importance. Think of the Seven Wonders of the World, one of the earliest examples of human categorization. Across different cultures, the number appears in the Seven Deadly Sins, the Seven Chakras, and the seven days of the week. These recurring appearances suggest an innate human tendency to group things into manageable, meaningful sets, with 7 striking the right balance between complexity and simplicity. Even the seven colors of the rainbow or the seven notes in a musical scale speak to its symbolic completeness.

But what makes 7 so special in the human mind? It might be related to cognitive biases—our brains tend to favor things in clusters, and 7 is often the number that feels just right. Psychologist George Miller's famous theory of "The Magical Number Seven" suggests that 7 is the optimal number of items we can hold in our working memory, further solidifying its importance.

Mathematical Significance

While cultural significance can be arbitrary, the mathematical characteristics of 7 reveal its deeper properties and importance. 7 is a prime number, meaning it is divisible only by itself and 1. Prime numbers are the building blocks of all natural numbers, playing an essential role in number theory. As an odd prime, 7 also introduces us to the first of the Sophie Germain primes, an intriguing class of primes with particular properties used in cryptography.

In probability theory, 7 makes an appearance in the context of randomness. The famous seven-sided die from various games like Dungeons and Dragons relies on the fact that 7 is the first prime number greater than 6 (the number of sides on a standard die). Mathematically, the probabilities associated with rolling a 7 are interestingly statistically significant in certain games. For example, in a two-dice roll, the number 7 has the highest probability of appearing, giving it a role in games of chance, which enhances its allure.

Moreover, modular arithmetic (a fundamental concept in number theory) often deals with systems that involve 7. For example, 7 mod 3 equals 1. This cyclic behavior, known as congruences, underlies many cryptographic algorithms.

7 in Geometry and Combinatorics

In geometry, consider the heptagon, a 7-sided polygon. Though not as common as the triangle or pentagon, the heptagon still holds significance in various geometric studies, particularly when exploring regular polygons. A regular heptagon can be constructed by dividing a circle into 7 equal parts, and it has intrigued mathematicians, especially in the realm of constructible polygons.

Combinatorics also reveals the number 7’s importance. In the study of permutations and combinations, the number 7 appears frequently when exploring set theory. For example, the number of ways to arrange 7 distinct objects in a sequence is 7! (7 factorial), which equals 5,040 possible arrangements. This highlights the number's mathematical elegance in the context of permutation theory.

The Golden Ratio, Fibonacci, and 7's Appearance

One of the most fascinating mathematical aspects of 7 involves its connection to the Fibonacci sequence and the Golden Ratio. Although 7 doesn't directly appear in the Fibonacci sequence (which begins 1, 1, 2, 3, 5, 8…), the ratio between consecutive Fibonacci numbers approaches the Golden Ratio, which is roughly 1.618. Interestingly, the Fibonacci sequence often appears in natural patterns such as the arrangement of leaves or the branching of trees—processes that, in turn, shape the world around us.

In the context of music, the number 7 takes center stage through the musical scale. The diatonic scale, the basis for much of Western music, consists of 7 distinct pitches, and the octave is seen as a return to the starting note after 12 semitones. This inherent mathematical structure plays a pivotal role in harmony and rhythm, reinforcing 7’s symbolic resonance as the “perfect” number in the realm of sound.

[karansri]

Remedial Education's Benefits for Learning Disabilities

Ananya's Life Skills, as Remedial Classes for Learning Disability, did not feel to be of inferior quality, at fixed times in the day. The effect of the intervention also to be shown has been proven to offer a fourfold higher number of compensations with the best homogeneity and efficiency toward the oldest child. The teachers also started to set the targets for likes, interests and concerns the children are putting in as a measure of how much if at all, might be sellable. There is addressed need in the fields of reading and arithmetic, i.e., how learning topics and arithmetic in schools and elements of everyday life are being studied and kept, and thus, the mathematical and reading concepts together with academic and environmental risks, as well as behavioral and cognitive protective behaviors, would be integrated into preschool and early elementary school.

However, I recalled that none of them had love therapy, whereas their man`s friends, intimate and family members that perhaps even now suggest the contrary, argue neither that they desire nor that such a severe degree of crisis can come to the man nor would transpire. No, I am currently still under training communication in the Ananya Life Skills program.

[cognifitpro]

Are you looking for Cool Math Games?

Cool Math Games by CogniFit offers a unique blend of entertainment and cognitive training to make learning effective and enjoyable. These games are created to engage players of all ages, helping them develop and enhance various mental skills such as problem-solving, memory, attention, and logical reasoning. Whether you're a student looking to sharpen your math abilities or an adult seeking to keep your mind active, CogniFit's games are tailored to meet your needs.

The interactive nature of these games ensures that users stay motivated while improving their cognitive skills. Each game is carefully designed to challenge the brain without overwhelming the player. With engaging visuals, intuitive controls, and adaptive difficulty levels, we provide an experience that's as entertaining as it is educational.

These games are backed by cognitive science and neuropsychological research, ensuring that they effectively target specific brain areas. By playing regularly, users can track their progress and see measurable improvements in their mental performance over time.

The games cater to mathematical concepts, from basic arithmetic and geometry to advanced logic puzzles. For younger users, games focusing on addition, subtraction, multiplication, and division help build foundational math skills. For older players or those seeking a challenge, there are games involving fractions, algebra, and complex problem-solving. This range ensures something for everyone, regardless of age or skill level.

Cool Math Games are also an excellent tool for educators and parents. Teachers can incorporate these games into their lesson plans to make math more interactive and engaging, while parents can use them to support their child's learning at home. With a commitment to making cognitive training accessible, fun, and practical, Cool Math Games are more than just a pastime—they invest in mental agility and lifelong learning.