Comments

  • Rational thinking: animals and humans
    Why does 'reasoning' require a modifier?Vera Mont

    If the reasoning isn't correct, things can go very wrong. That is why it is important to have the correct facts and think things through carefully. Democracy is not about what one person thinks but together after we argue with each other and check our facts, what is true. This is akin to scientific thinking. It is not basing our understanding of reality on a myth that can not be supported with factual statements.

    We have a big problem in the US. Our understanding of rational thinking is very weak. In general people don't know the difference between an opinion and a fact. All thinking is confused with being rational and that is a serious problem.

    It is your opinion that I hold rational thinking as a human thing based on language that animals do not have because I want to exploit animals, is an opinion, not a fact. Let me make it clear, I care that we know the difference because it is the only chance we have of not destroying our planet. If we do not distinguish between correct reasoning and incorrect thinking, the planet is doomed and there is no other animal on earth that can do that reasoning.
  • Rational thinking: animals and humans
    This is why the definition and meaning of the phrase "Rational thinking" needs to be clearly listed and agreed upon first. If we all have different viewpoints of what the phrase "Rational thinking" means, we're never going to come to an agreement. as to whether an instance of a crow using a tool is an instance of rational thinking.Philosophim

    I can think of three major elements to rational thinking: its form is linguistic, its structure is logical, and its orientation is (ostensibly) self-interest (either direct or indirect). Under that definition, animals do not have rational thinking because they lack language. And intuitive thinking, which allows for action without explicit knowledge of the reasons for action is similarly excluded.Baden

    @Manuel said "I suppose a bare minimum has to be symbolic representation akin to something that arises with language use. Animals do not have language, if by "language" one has in mind propositional knowledge."

    Perhaps we can focus on logic.

    Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. https://en.wikipedia.org/wiki/Logic
    .

    I like that the definition begins with "correct reasoning". Lenching someone does not involve correct reasoning. In court, we aim at correct reasoning. But then I think of the ancient Greeks and the argument against rhetorical speaking which may appeal to emotions more than reason.
  • Rational thinking: animals and humans
    Do you mean animals besides humans?LuckyR

    Yes. I don't think anyone here is arguing humans have not evolved from an ancestor that would be classified as an animal. The transition from prehumans to humans is better documented today and with our improved knowledge of animals having culture, our understanding of the transition is getting better.

    facial anatomy suggests that A. ramidus males were less aggressive than those of modern chimps, which is correlated to increased parental care and monogamy in primates. It has also been suggested that it was among the earliest of human ancestors to use some proto-language, possibly capable of vocalizing at the same level as a human infant. This is based on evidence of human-like skull architecture, cranial base angle and vocal tract dimensions, all of which in A. ramidus are paedomorphic when compared to chimpanzees and bonobos. This suggests the trend toward paedomorphic or juvenile-like form evident in human evolution, may have begun with A. ramidus. Given these unique features, it has been argued that in A. ramidus we may have the first evidence of human-like forms of social behaviour, vocally mediated sociality as well as increased levels of prosociality via the process of self-domestication—all of which seem to be associated with the same underlying changes in skull architecture. A. ramidus appears to have inhabited woodland and bushland corridors between savannas, and was a generalized omnivore. https://en.wikipedia.org/wiki/Ardipithecus_ramidus
    .

    Their challenge was most likely climate change making life in the trees more difficult, forcing this species out of trees and making them land animals with culture and physical changes improving vocalization and indication of less aggressive behavior.

    I have to change what I said about climate change. There is new information and it makes more sense.
    Hominid fossils predating the emergence of Australopithecus have been sparse and fragmentary. The evolution of our lineage after the last common ancestor we shared with chimpanzees has therefore remained unclear. Ardipithecus ramidus, recovered in ecologically and temporally resolved contexts in Ethiopia’s Afar Rift, now illuminates earlier hominid paleobiology and aspects of extant African ape evolution. More than 110 specimens recovered from 4.4-million-year-old sediments include a partial skeleton with much of the skull, hands, feet, limbs, and pelvis. This hominid combined arboreal palmigrade clambering and careful climbing with a form of terrestrial bipedality more primitive than that of Australopithecus. Ar. ramidus had a reduced canine/premolar complex and a little-derived cranial morphology and consumed a predominantly C3 plant–based diet (plants using the C3 photosynthetic pathway). Its ecological habitat appears to have been largely woodland-focused. Ar. ramidus lacks any characters typical of suspension, vertical climbing, or knuckle-walking. Ar. ramidus indicates that despite the genetic similarities of living humans and chimpanzees, the ancestor we last shared probably differed substantially from any extant African ape. Hominids and extant African apes have each become highly specialized through very different evolutionary pathways. This evidence also illuminates the origins of orthogrady, bipedality, ecology, diet, and social behavior in earliest Hominidae and helps to define the basal hominid adaptation, thereby accentuating the derived nature of Australopithecus. https://www.science.org/doi/abs/10.1126/science.1175802
  • From numbers and information to communication
    Animals do not put together an argument to arrive at a conclusion. A valid/sound conclusion is the goal when one is engaged in reasoning. For example, if I have some information on the chance that it's going to rain this morning -- atmosphere, clouds, radar -- I can conclude validly that it's going to rain this morning.L'éléphant

    That point seems to be what is being argued in the Rational thinking: animals and humans thread, @Vera Mont is making strong arguments in favor of animals being rational thinkers. Can I copy and paste your argument there?
  • What should the EU do when Trump wins the next election?
    Sis, we have competent economists to answer your question. Yes, they know enough.L'éléphant

    :lol: Who is they? How many of them are there?
  • Rational thinking: animals and humans
    They already have a language. The argument is over whether and how well they learn some version of a human language.Vera Mont

    No animals don't already have a language. Language is next to culture, it has to be learned. The ability to learn a language varies across species and within the species are individual differences and the age of our ability to learn changes with our age. Older children have a greater learning ability and there are some things that if a child does not learn or experience at a certain age, the child will never be able to incorporate it in its being.

    That said, many animals have warning sounds. Those sounds are instinctively known to all species because as math explains, the sounds are irritating and can not be ignored. A group of chimps may have different sounds for different threats- this would be cultural and something that has to be learned before one could know if the threat is an eagle coming from the sky, or large snake hanging in the tree or a predator coming by ground. Those warning sounds, even the more complex ones are not propositional thinking. The great ages are not going to discuss what humans are doing to their habitat and what they can do to defend it.
  • Rational thinking: animals and humans
    Intuition is rational thinking.Vera Mont

    I will use a link to explain why intuitive thinking is not rational thinking.

    Intuition is defined as the ability to acquire knowledge without the use of reason [1]. Some liken intuition to a gut feeling, or to unconscious thinking. Rational thinking is defined as the use of reason, the capacity to make sense of things, and the use of logic to establish and verify facts [2].

    Intuition versus Rational Thinking: Psychological Challenges ...
    https://www.sciencedirect.com/science/article/abs/pii/S1546144012003791#:~:text=Intuition%20is%20defined%20as%20the,and%20verify%20facts%20%5B2%5D.

    As @Manuel explains rational thinking begins with a proposition. I am learning as I read and reply and use links because I do not have a strong understanding. So here is an explanation of propositional knowledge.

    Propositional knowledge is the knowledge of a proposition, or fact, that can be justified, true, and believed. It can be applied to a wide range of subjects, including science, geography, math, and self-knowledge. https://www.google.com/search ? <a href="https://en.wikipedia.org/wiki/Declarative_knowledge#:~:text=Propositional%20knowledge%20asserts%20that%20a,referred%20to%20as%20knowledge%2Dthat" target="_blank" rel="nofollow">https://en.wikipedia.org/wiki/Declarative_knowledge#:~:text=Propositional%20knowledge%20asserts%20that%20a,referred%20to%20as%20knowledge%2Dthat</a>.

    Now here is where the rest of the animal realm fails. It took us centuries but we now of an amazing comprehension of pi.

    Succinctly, pi—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14. https://www.scientificamerican.com/article/what-is-pi-and-how-did-it-originate/#:~:text=Succinctly%2C%20pi%E2%80%94which%20is%20written,of%20pi%20is%20approximately%203.14.

    The importance of our present knowledge of pi is mind-blowing! It tells how organism grow, and helps with navigation of air planes. This link is very complex so I am leaving just the link for those who want to know what pi has to do with the creation of the universe and how things grow. https://www.biophysics.org/blog/pi-is-encoded-in-the-patterns-of-life

    This link is a little simpler..
    Tracking Aircraft with a Raspberry Pi - Stephen Smith's Blog

    Stephen Smith's Blog
    https://smist08.wordpress.com › 2023/01/27 › tracking-...
    Jan 27, 2023 — A tutorial, by Tony Roberts, on connecting a Raspberry Pi to an SDR radio to retrieve flight information from nearby aircraft.

    Any way even though many of us struggle with math, it is an important component to rational thinking.

    Sciencific thinking is nothing like our every day thinking.
    Scientific thinking is the process of reviewing ideas using science, observations, investigational processes, and testing them to gain knowledge. The goal is to make outcomes of knowledge that may be meaningful to science. The scientific method is how scientists and researchers apply their scientific thinking. https://study.com/academy/lesson/scientific-ways-of-thinking.html#:~:text=Scientific%20thinking%20is%20the%20process,researchers%20apply%20their%20scientific%20thinking.

    Oh man :nerd: A thought came up as I worked on the explanation.

    Modern thinking is nothing like the thinking of the Middle Ages and around the world are people still far from proposition knowledge and thinking. Our understanding of the different modes of thinking and how far we have come in the last hundred years is still outside of our consciousness but we are not the same human beings we once were. We only had to potential to become as we are. Other animals do not have this potential.
  • Rational thinking: animals and humans
    (Experiment: have a trusted human teach a baboon to do it, then let him in among a troop of youngsters.)Vera Mont

    I am excited because you have gotten to the core of the subject. Baboons to not have the attention span of great apes. Baboons are monkeys not apes. The difference is genetic. I don't know if anyone has tried as hard to teach a baboon or done an experiment as you suggest. I think not because from our present judgment of baboons it would be futile.

    Here is a link...

    Monkey species include baboons, macaques, marmosets, tamarins, and capuchins. Ape species include humans, gorillas, chimpanzees, orangutans, gibbons, and bonobos.

    In evolutionary and genetic terms, ape species are much closer to humans than monkeys are. In addition to having similar basic body structures, apes are highly intelligent and can exhibit human-like behavior. For example, chimpanzees, which are closest to humans genetically, can create simple tools and use them effectively.

    Although monkeys communicate with each other, apes possess more advanced cognitive and language skills. They can't speak like humans, but they can use sign language and other bodily movements to communicate with humans effectively. Communication skills help gorillas, chimps, and bonobos develop complex social groups and even exhibit some aspects of culture. Like humans, apes can think and solve problems in their environments. https://www.wonderopolis.org/wonder/whats-the-difference-between-apes-and-monkeys#:~:text=Monkey%20species%20include%20baboons%2C%20macaques,to%20humans%20than%20monkeys%20are.
  • Rational thinking: animals and humans
    So then if we took a human, and they did the same thing as the crow without saying any words, we would think that wasn't rational thinking? How did the crow arrive at that conclusion to do what it did to begin with?Philosophim

    That is the intuitive question. As @Manuel warns, when we know something intuitively, it is important to check and double-check that intuitive thought. An intuitive thought may be the result of past experiences or spending many days trying to answer a question. We can not be sure why but the thought is just in our heads whole and complete. Because I am studying the brain I read or hear time and time again, that our brains are very active and we are not aware of all its activity.

    We know humans can be aware of some of that thinking in a way we call rational thinking. Rushing out to hang someone for committing an offense with other men dressed in white sheets, is not rational thinking even if the men are aware of their reasoning. Their reason is not the careful reasoning of science. Men's behavior in times of war had little to do with rational reasoning. :heart: I hope we all gain better knowledge of different modes of thinking and different codes for thinking. How do our brains work compared to how do the brains of great apes work?
  • Rational thinking: animals and humans
    As far as your idea of the significance of the chimpanzee recognising his or her image in the mirror, it may suggest a form of personal identity based on an image of one's bodily appearance.Jack Cummins

    You made me ask the question, can a chimp recognize a picture of himself in a line up of chimp pictures? That is different from a mirror image. In the mirror, our movement is reflected. What if the chimp realized the movement in the mirror was his movement but that does not mean he could pick out an image of himself in a line of pictures?

    I am watching college lectures about humans and primates and the thing that impresses me the most is how extremely picky researchers are! The question must be asked exactly right. They must be as sure as possible that they identify exactly what causes something and their peers are quick to jump on them if everything is not exactly right. This is not normal everyday thinking. It is very disciplined thinking.

    About you and I thinking along the same line at the same time, you and I have experienced this often. It is enough to make me ask if we have a psychic connection but then is that even possible? I think that is unlikely but not impossible. I have a very old book about logic and the author warns us never to be too sure of what we think because we can never know enough to be certain. Science is about being as certain as we can be and history is a series of times when the general experience of the moment moves people to think and act the same, such as the hippie movement and then a fascination with drugs such as we have today.
  • Rational thinking: animals and humans
    Yes, some animals can think rationally. It depends on how you define 'rationally' of course. If you define it as, 'the brain processing humans do', then its not. I don't ascribe to this definition, but many do implicitly.

    Here is a crow using a stick to get food. Do you think this is rational?

    https://www.youtube.com/watch?v=cjfrxkEpfX8
    Philosophim

    By definition of "rational," I would say no, the crow's behavior is not the result of rational thinking.

    I like @Manuel's used to Propositional Knowledge. If the crow questioned if the stick would work, and proposed an experiment and then explained the results, the stick must be this long and have this strength to work, and we tested his experiment and found it to be true, then we have rational thinking. I hope once I learn the language of math I will be able to understand math better. Reading about Propositional Knowledge helped my brain form a degree of understanding about rational thinking. How do we understand anything without the right words?

    Your example is very important because we thought only humans used tools, and we made that ability the defining marker of being human. Next, we thought culture is what defines humans and then we discovered social animals have culture. But we still have people who believe humans were made of mud and it was a god who made them so we aren't really animals like all the other animals. I don't think that belief would pass the test for rational thinking, but then when someone comes up with a crazy explanation for believing in something, we call that rationalizing.

    Help, my thoughts may not be in the proper order or maybe I am not using the right words? I think I destroyed my argument. :chin:
  • Rational thinking: animals and humans
    suppose a bare minimum has to be symbolic representation akin to something that arises with language use. Animals do not have language, if by "language" one has in mind propositional knowledge.

    There may well be other aspects to thinking that are not related to language, but we don't know what they are. We are back to speaking about these things through language. So, until we have some proposal as to what non-linguistic thought is, we are stuck.

    As for communication? Yes, they do, and they seem to be highly efficient at it. Look at bees or birds or dolphins, they have some amazing capacities for communication that we lack.

    Intuition is somewhat hard to describe. I don't think it's better than non-intuitive thinking, just different. Though we should keep in mind that our intuitions can be quite wrong.
    Manuel

    Very nicely said and so the debate goes on. I had to look for an explanation of propositional knowledge because that is a new term for me.

    Propositional knowledge is a type of knowledge that involves knowing facts, and is also known as declarative or descriptive knowledge. It can be defined as justified true belief, which means that a person has propositional knowledge if they:
    Believe something to be true
    Are justified in believing it to be true
    The thing they believe is actually true

    Propositional knowledge can cover a wide range of subjects, including: Science, Geography, Mathematics, Self-knowledge, and Any other field of study.
    https://en.wikipedia.org/wiki/Declarative_knowledge#:~:text=Propositional%20knowledge%20asserts%20that%20a,referred%20to%20as%20knowledge%2Dthat.

    Having the right language for this discussion is very helpful. Thank you, Manuel.
  • Rational thinking: animals and humans
    Post-hoc rationalisation probably was the original form of 'rational thinking', as social group-animals it was pretty important to justify/rationalize our actions.

    So you know, it seems that Plato/Socrates (contra the Sophists) got us on the wrong track with this weird ideosyncratic notion of rational thinking to arrive at the truth.
    ChatteringMonkey

    Is it rational to believe illnesses are caused by the gods? Is it rational to believe a god created man from mud?
  • Rational thinking: animals and humans
    Reason and one's relative facility in reasoning has very little to do with verbal proficiency or fluency. Individuals with too deep a regard for what is said by those who speak authoritatively are some times fooled into believing what they're told rather than what they themselves are able to discern.Vera Mont

    The argument about chimpanzees and their ability to communicate is more complex than whether they learn a language or they can not.

    As a matter of learned culture, some Chimpanzees in the wild do have warning calls that identify a predator. In the learning stage, a young chimp may see a leaf fall and make the sound for an eagle, or see a wild pig and make the sound for a predator cat. The adults will look for the pedator and ignore the warning if they do not see it, or if they see it, they will repeat the warning. In time the young will make the correct sound at the correct time. Our cats and dogs may be very good at communicating with us but wolves do not have that kind of relationship with humans. The difference between domestic and non-domestic animals in the genes. Just as the learning difference between chimps and baboons is in the genes.

    Here is a link explaining rational thinking requires language, not just warning sounds for predators.

    Abstract
    This article deals with the relations between language, thought, and rationality, and especially the role and status of assumptions about rationality in interpreting another's speech and assigning contents to her psychological attitudes—her beliefs, desires, intentions, and so on. Some large degree of rationality is required for thought. Consequently, that same degree of rationality at least is required for language, since language requires thought. Thought, however, does not require language. This article lays out the grounds for seeing rationality as required for thought, and it meets some recent objections on conceptual and empirical grounds. Furthermore, it gives particular attention to Donald Davidson's arguments for the Principle of Charity, according to which it is constitutive of speakers that they are largely rational and largely right about the world, and to Davidson's arguments for the thesis that without the power of speech one lacks the power of thought. https://academic.oup.com/edited-volume/34534/chapter-abstract/292961457?redirectedFrom=fulltext
  • Rational thinking: animals and humans
    Intuition is a shortcut to an answer in the absence of sufficient evidence to draw a logical conclusion. It is based on recalled experience and knowledge.Vera Mont

    I think Baden gave a good explanation of why all thinking is not equal to rational thinking.

    We could get into what emotions have to do with our thinking and question how rational we are when we are emotional. The book "Emotional Intelligence" explains how emotions mess with our thinking, and the more recent study of what hormones have to do with emotions and judgment. I used to clean a bar and on football game nights, the bar would be trashed! Watching football increases a man's testosterone level, which results in more aggressive behavior than adding a few beers, reducing one's inhibition and I should have gotten a bonus for cleaning on those nights. :grin:

    Your post triggered the next thought about experience and knowledge. Individually, we are different in our ability to learn. More dramatic is the fact that baboons like to eat termites as much as chimps. They watch the chimps make tools to fish the termites, but they do not imitate the behavior, although they want the termites just as much as the chimps. I think that is equal to me wanting to understand math, and I just don't get it.

    I hope we think as much about how we think as we think about how another animal thinks. Intuition is not rational thinking because there is no language involved. My point about going through the gate is knowledge can prevent us from knowing.
  • Rational thinking: animals and humans
    I can think of three major elements to rational thinking: its form is linguistic, its structure is logical, and its orientation is (ostensibly) self-interest (either direct or indirect). Under that definition, animals do not have rational thinking because they lack language. And intuitive thinking, which allows for action without explicit knowledge of the reasons for action is similarly excluded.

    Animals do have communications systems though, and therefore skills, and human intuitive thinking can be a better (esp. faster) way of solving problems, avoiding danger, dealing with people etc. In fact, think about most real life conversations--they are almost entirely intuitive. Who's thinking explicitly about what to say next?
    Baden

    I know all that but hell will freeze over before I can explain it as well as you did. :heart:

    :lol: My arguments are based on my own struggle with language and especially ordering my words so they make sense and rational thinking. Such as choosing the right words to title a thread. I am terrible at that.

    I led a team of volunteers to help a young woman in a nursing home. When leaving, a young man with a very low IQ made it through a locked gate, that I could not get through because obviously the gate was locked and obviously it was necessary to have a code to get out of the secured building. But my dim-witted friend did not take time to think through the problem. He put his hand through the gate and opened it from the outside. Quite obviously our "thinking" can make us stupid. And if I were to be lost in the wilderness, I would want him to help me get out. I have known a few low IQ people who think more like animals and I mean this as a complement.

    I knew a gentleman who ran from the WWII soldiers who killed everyone in his family. As a young child, he had to survive on his own in the forest. I asked him how he did that and he said he watched the animals and learned from them.

    "Who's thinking explicitly about what to say next?" I am thrilled you got why I thought this thread was important. The more I thought about our thinking versus animals, the less sure I was about our own thinking! I know there is soooo much I do not know and how many books I try to read are over my head. I never habituated the steps of logical thinking so my struggle to learn seems futile. I have gone through life in a state of daydreaming and it is amazing I got this far.
  • Rational thinking: animals and humans
    Even within the categories it appears that there are vast differences in consciousness, intelligence and behaviour repertoires.Jack Cummins

    I remember when there was a lot of excitement about chimps recognizing their image in a mirror. Of course much more research has been done since then.

    The ability to recognize one’s own reflection is shared by humans and only a few other species, including chimpanzees. However, this ability is highly variable across individual chimpanzees. In humans, self-recognition involves a distributed, right-lateralized network including frontal and parietal regions involved in the production and perception of action. The superior longitudinal fasciculus (SLF) is a system of white matter tracts linking these frontal and parietal regions. The current study measured mirror self-recognition (MSR) and SLF anatomy in 60 chimpanzees using diffusion tensor imaging. Successful self-recognition was associated with greater rightward asymmetry in the white matter of SLFII and SLFIII, and in SLFIII’s gray matter terminations in Broca’s area. We observed a visible progression of SLFIII’s prefrontal extension in apes that show negative, ambiguous, and compelling evidence of MSR. Notably, SLFIII’s terminations in Broca’s area are not right-lateralized or particularly pronounced at the population level in chimpanzees, as they are in humans. Thus, chimpanzees with more human-like behavior show more human-like SLFIII connectivity. These results suggest that self-recognition may have co-emerged with adaptations to frontoparietal circuitry.
    https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5390703/#:~:text=The%20ability%20to%20recognize%20one's,highly%20variable%20across%20individual%20chimpanzees.
  • From numbers and information to communication
    I don't know. Rational processes have come into being through it. Does that make it a rational process?Patterner

    We really need a thread for that discussion. I started a thread but left it in the logic and philosophy of math category. That might not be the right thing to do but there are reasons for doing so. https://thephilosophyforum.com/discussion/15426/evolution-animals-and-humans
  • From numbers and information to communication
    To think rationally is to use (valid) reasons for your actions. If an animal can learn new information that it was not born with (instincts) and use that information in a way that provides some advantage to its survival then we could say that it is capable of rationally thinking. For instance, my cat has learned some English words like, "treat" and "outside", and has even learned to communicate to me her needs to receive treats and to go outside even though she does not have the ability to say those words. Rational thinking provides the ability for the animal to make predictions using the patterns it has experienced in its environment.Harry Hindu

    I agree with you and would gladly discuss it in another thread.
  • From numbers and information to communication
    By "evidence of rational thinking" I have in mind that animals can learn and having learned appear to apply what they have learned, replicating the actions of their lesson learned to obtain a desired result. But a greater challenge to you is for an account of "problem solving" by animals - and that won't be easy. Perhaps a start would be a quick description of the process.tim wood

    Monkey see monkey do. I think we need a different thread for discussing animals. I have been watching and re-watching lectures about arthropods and was really looking forward to sharing information with you, but not in a math thread. The language skills of some great apes is amazing and they can teach their children. I can not make strong arguments about this but it is an interesting subject.
  • From numbers and information to communication
    Nature or nurture? Why not both? Instinct - nature - given, but any pet owner can recite occasions when the animal exhibited evidence of rational thinking. My guess is that the both killing and mistreatment of animals makes it a necessity to resist acknowledging their "personhood."tim wood

    What do you mean by rational thinking? I have no doubt that animals are good at problem-solving.

    In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. In this case, one speaks of a rational function and a rational fraction over K. The values of the variables may be taken in any field L containing K. Then the domain of the function is the set of the values of the variables for which the denominator is not zero, and the codomain is L.
    https://en.wikipedia.org/wiki/Rational_function

    Math is not a knee jerk reaction to someone walking across the yard. It does not come to us naturally but we must first learn how to learn math. How do you propose to teach your best friend (dog) to use math?

    I can fully appreciate the sentiment of humans being animals. But I think the awareness of other animals is different from ours. I will never be able to tell what used the path by sniffing a spot on the ground. I can not detect that a person has cancer, or is autistic, or has dangerously high blood sugar levels by smelling it. Services dogs can. I would love to think like a dog but I will not experience life as a dog does.
  • What should the EU do when Trump wins the next election?
    Well, I do not know about 'better' but they are different forms of government and that is because they have a different constitutional system. The constitution has everything to do with the amount of power a president has and also which checks and balances are in place. Not just the constitutional document as such but the whole constitutional order. Now in the German constitutional order the president is mostly a ceremonial figurehead, an elder statesman. Currently it is Walther Steinmaier. He is not the head of government though, the head of government is the chancellor, similar to a prime minister, a title unknown in the US. It is precisely the constitution that creates such differences. Now the German constitution (Basic law) has been written just after the second world war, with the prime imperative being to prevent a power grab by any one person or party. Germany has coalition governments also something unknown in the US. That is because it does not have a 'winner takes all' constitutional system. The funny thing is the German basic law has been inspired by the constitutions of the allied nations, including the US.

    See, things are never clear cut. Of course the US has taken over ideas from German education because Germany was arguable the most advanced country in the 19th century, However, the Germans must have learned a thing or two about bureaucracy from the French, bureau being a French word after all.

    Currently I think serious flaws in the US constitutional system are appearing, but so are they in Europe. Constitutional systems and institutional designs can add to the resilience of a political system, but they can never make it endure. The US constitution is actually a logical one given the US history and the wish to curb the dominance of the most populous states, but it ends up being a system in which only a few votes from people in a few states really matter. The US system, especially the politicization of the supreme court, leads to a very partisan and competitive democracy. It has its good sides, people are connected to their politicians, but it also has its bad sides, a tendency for polarization.

    As for the minimum wage question, I am no economist. I will therefore pass on that question. I think there might be options though, you could for instance bring top tier incomes down through taxation to name one...
    Tobias

    Wow! that is a wonderful post! You made me order a book The German Polity. I can not trust my brain to remember what you said of a week from now, find my way back to your post.

    Germans may have learned bureaucratic order from others but I think what put them over the top was the Prussian military order. I hate this, when I go to explain something, I realize I don't have enough information. I will be watching my mail box for 3 books now. :roll: My daughter may have to take my bank card. :lol: But obviously I need more information.

    Can we make a million copies of you and disperse them through the US so perhaps the citizens of the US will begin having reasonable discussions of the political and economic problems? It is so bloody obvious to some of us that extremes of income are problematic. It is also obvious that human beings are more likely to be civil if they have a good education, full bellies, and decent housing. Now this is way off topic so I will stop.

    Thank you for being such a nice and well-informed person.
  • Identity of numbers and information
    I am not sure if there should be a separate thread for communication because we are getting far from the identity of numbers and information and when this happens a thread loses its cohesiveness and cognizance.

    I am creating a thread for communication. "From numbers and information to communication".
  • Identity of numbers and information
    1 + 27 + 4,534 = I eat apple.Patterner

    :heart: I absolutely love that example. :rofl: That makes as much sense as spell-check programs that obviously don't have a clue about the intended meaning. Or don't know it is a quote and not something to correct. And AI can do better why?
  • Coping with isolation


    Oh my goodness! What an awful horror story! That was not fair.
  • Coping with isolation
    Wine and chocolate! TV and popcorn!Shawn

    Ah, want kind of wine goes best with chocolate?

    I would love the popcorn and a movie, but must void it because it put me in the hospital twice. Diverticulosis, means avoiding food that may not easily digest, popcorn, nuts, seeds. It usually takes 3 days with an IV in my arm to break the dam, and by the third day I am ready to kill if they don't let me out! Like they won't even let me have chocolate or a cup of coffee! :scream:

    I have a do not resuscitate order because if I can not get on with my life, I don't want to keep breathing. I used to think if I could at least play computer games I could manage but my experience is a 3-day limit and the homeless guy I befriended, ended up confined to a hospital bed and incapable of communicating more than "yes'"or "no" for about a year before he passed. Visiting with him through that changed my mind. Let me go!
  • Coping with isolation
    I might sing some of the old songs though, now and then.unenlightened

    I started watching movies I don't normally watch and kicking up feelings I was not aware of having, and crying to cleanse my soul. With nothing to distract us can we avoid soul searching or do we even want to?
  • Coping with isolation
    You can always do art projects or read, if those things are fun and you're not consigned to one room. Recently discovered ice tie dye. Though there be so many things to do (or nothing at all) if I was the last person on earth.Nils Loc

    I can work with that. I actually love walking along the river and communing with nature. Some days I am overwhelmed by appreciation of the beauty of nature. I have reacted to trees as beings in a different form and you hit upon a very important point! I wanted to walk along the river but didn't want to wear a mask, nor risk exposing someone to the virus so I was confining myself to my apartment.

    On the good side, the confinement led to better organizing and I want to continue the effort of making my living space more attractive. Yes! to hell with the rules against putting holes in the walls. I have a large picture that absolutely has to go on the wall. I don't even want to go through the winter months without some improvements. Thank you for opening my mind to the possibilities. :heart:
  • Coping with isolation
    The idea of finding a library sounds good to me. I wonder if I would write though, without the expectation anyone would ever read it. That turns into a kind of philosophical question on the value of art, I think.Baden

    Never give up hope! I am quite sure I would write with the hope that someday my written record would be found by another earthline or maybe a being from another planet. Such thoughts being helped by TV shows like Star Trek. Philosophically, my imagination is pretty good, so I might be able to keep myself motivated with that hope.

    It is obvious to me how helpful the Bible is to people who can have faith. I think, how we experience life is very tied to self-talk. You know the saying "It isn't what happens to you that matters, but you make of it". It is so hard to know if I feel psychologically awful because of what I think, or are my hormones running the show, causing me to feel good or bad. I tend to be my worst enemy, beating myself up if I don't force myself to be positive. While people who have faith have a mental trick that can actually be very helpful. Like Robin Crusoe. Such classical novels can be helpful to us and some prisons have found the classics can correct the population who need a better perspective on life.

    Congradulations for writing such a good story.
  • Coping with isolation
    Then again since Big brother is around and about, one must become more paranoid.Shawn

    :lol: No thank you! I am having a very visceral reaction to what you said. I am also thinking of a professor's lectures about philosophy and the Intelligence of Emotion. I did not stop and think through what you said. I just immediately felt dread and thought I would rather be totally alone compared to the only other being, being a Big Brother that is as totally impersonal as some mods in other forums. What is that relationship and emotion of rejecting the possibility of existing with Big Brother? Why is that worse than complete aloneness?
  • Coping with isolation
    Did you see the episode where there was a guy that got isolated on an abandoned island, which was suddenly evacuated because of--as it turned out--unfounded fears of a tsunami? And somehow he was the only one who got left behind--can't remember why--but there is loads of food around and no issue of physical survival etc. He's just on his own and expects to be for a long time, the other inhabitants having permanently relocated.Baden

    Thank you for the interesting story. That was a lot of work putting in all those words so I feel sincerely cared for. You relayed a sense of comprehension of my unpleasant feelings of Isolation and that meets my need to communicate with someone. I am thinking something philosophical could be said.

    Last night I watched an anthropology professor's lectures about primates and humans. And after reading your story, I thought if I were truly isolated I would look for a library. I once worked for the University of Oregon library in the microfilm department when it was in the basement and they had the original newspapers. My job was to microfilm them and I had such a sense of connection with all the souls who lived in the past.

    I have a video made by a man who lived alone for many years by a lake in Alaska. He had a few human contacts who would bring his supplies but most of the time he was truly isolated. I am in awe of his ability to do that!

    Yesterday and today I had negative COVID test results so I am out of isolation. I am out of prison. :grin: I am not sure if I feel so much better because my health is better or if I feel so much better for psychological reasons. I just know my mental health today is a whole lot better. :grin:
  • What should the EU do when Trump wins the next election?
    What I mean is, you seem to equate the promise 'you will never need to vote again' on a par with the promise to raise minimum wages. The first comes down to the abolition of democracy the second may have good or bad economic consequences. They are not on the same level. You seem to present them as a dilemma, but they are not. One is an outright attack on the constitutional order the other a rather mundane policy proposal. The constitution has everything to do with the power of the president as the constitution circumscribe his or her power, that is what constitutions do, among other things.Tobias

    I appreciate the distinction you made between the candidates. They are both stupid promises! Can I please have another choice? :lol:

    However, saying the constitution has everything to do with the power of the president makes no sense to me because I know more and more power has been given to the president. On the other hand things completely out of our control happen and talking as though one person is responsible for that is lacking in logic. That lack of logic seems to go with believing this one person will give us something we want. :brow:

    The president of the US has a lot more power institutionally speaking than say, the president of Germany.Tobias

    Please tell more about Germany because this is so paradoxical. The US adopted the German models of bureaucracy and education and picked up German military ideas as well. However, I have come across info that makes me think the Germans are doing better. Such as you saying the German president does not have as much power as a US president and I think that means the Germans are doing something right that US is not doing. I read education in Germany encourages the young to pay attention to their personal experience instead of the US's excessive focus on empirical information.

    Trump did not just promise to overturn the constitutional order, he acted on the willingness to do so. What is alarming to me is some people do not see that, and states that attempted to keep Trump off the ballot were prevented from doing so. How some can not see the danger Trump presents is a mystery to me. People who know he is a liar still believe he will keep his promises. That amazes me. It is his followers that lead me to say he is our Hitler. What is happening is more than the story of one man. It is also a story of our political climate.

    So what steps can be taken to better protect our institutions?

    I have to add, I don't think a presidential candidate should promise to raise minimum wages because I don't see how that can be done without creating inflation. I would like to know what others think of that.
  • What should the EU do when Trump wins the next election?
    do you think they are on the same level of constitutionality?Tobias

    What a delicious question. :nerd: Also what does the US Constitution have to do with the power of a president? US presidents gained a lot of power during the Roosevelt administration and again with Reagan and again after 911. Hum, I am thinking I need to be more careful because this is a serious subject and I hope you demand a good reply and don't let me slide with unsupported insinuations. I found a link that makes my point.

    For most of the nineteenth century, the presidency was a weak institution. In unusual circumstances, a Jefferson, a Jackson, or a Lincoln might exercise extraordinary power, but most presidents held little influence over the congressional barons or provincial chieftains who actually steered the government. The president’s job was to execute policy, rarely to make it. Policy making was the responsibility of legislators, particularly the leaders of the House and Senate.

    Today, the presidency has become the dominant force in national policy formation, not all domestic policy springs from the White House but none is made without the president’s involvement. And when it comes to foreign policy and, particularly security policy, there can be little doubt about presidential primacy. Of course, Congress retains the constitutional power to declare war, but the power has not been exercised in sixty-five years. During this period American military forces have been engaged in numerous conflicts all over the world—at the behest of the president....

    while the power to persuade and other leadership abilities wax and wane with successive presidents, the power of the presidency has increased inexorably, perhaps growing more rapidly under the Roosevelts and Reagans and less so under the Fillmores and Carters of American politics but growing nonetheless.
    https://yalebooks.yale.edu/2016/05/17/the-growth-of-presidential-power/

    That is not a full explanation but I doubt anyone regular citizen can provide a more detailed explanation and it is citizen ignorance and complacy that gives the President so much power. We are not politically aware and Trump shares a lot with Hitler. If you want to question me, I will attempt to give answers.

    What would make you say that? A fascist order is an order in which the state is held in supreme regard. The body politic is mass mobilized for the good of the state and individual rights are abolished in the name of some kind of social unity, it is generally a nationalist and militarist creed.Tobias

    That is an agreeable statement. Now we can make abortion illegal and we can ban books and in some states, Christianity can control education but fortunately, Texas teachers did win their supreme court battle with the Texas' efforts to mandate Creationism be taught as legitimate science. "Some kind of "social unity" is Christianity. Education for technology does not defend democracy in the classroom and Trump is our Hitler. I hope you take into consideration Germany was a Christian Republic. The book "The Founding Myth" by Andrew L. Seidel explains "Why Christian Nationalism is Un-American".Yes it is a nationalist and militarist creed doing God's "power and glory" with high-tech military abilities that can be used without a congressional declaration of war.

    I should say, I write with concerns, not facts that I am sure of. Unless people are working with the bible and for the kingdom of God, how can they imagine it is a good thing that someone running for the presidency would think it is a good thing for this person to announce once he is elected they will never have to vote again? Constitutionally "The Twenty-second Amendment to the United States Constitution limits the number of terms a person can serve as President to two." What is Trump promising us when he says we will never have to vote again?
  • What should the EU do when Trump wins the next election?
    Have you no highly skilled assassins?BC

    :lol:
  • What should the EU do when Trump wins the next election?
    I myself also do like the D'Hondt method which takes into account how much the party in general has won and how much the individual candidates have won. Of course this way has funny result that if in an electoral district there's a hugely popular candidate of one party, let's say Josef Stalin, and the party has also with him totally unknown or hated candidates that get just a few votes, they'll go in assisted by the result of the huge electoral winner. The method (called also the Jefferson method) isn't easy to understand itself (the calculation method) and it makes coalitions useful, but I think it works.

    What I don't like are these political systems where ruling parties make it extremely hard for new parties to get seats. And (unfortunately) in the case of the US, the POTUS has this "Superman" image as if one person could make a huge change to the system. True political change starts actually from the communal level.
    ssu

    Thank you. We have the problem of one candidate getting the popular vote and the other one winning because of the Electoral College which gives some states more importance than others.

    [/quote]The Electoral College is not a physical place. It is a process which includes the: Selection of electors. Meeting of electors who cast votes for the president and vice president. Counting of the electors' votes by Congress.

    Electoral College | USAGov

    USA.gov
    https://www.usa.gov › ... › How the president is elected [/quote]

    We have red states and blue states and I don't think the Electoral College was designed with this culture division in mind? And the economic division is interesting. Democratic states have done better economically making our argument about the President's impact on the economy skewed. People in different states have different realities and it is kind of nuts we argue so much about the President's impact when the reality is different in different states. https://gppreview.com/2020/02/21/growing-divide-red-states-vs-blue-states/
  • What should the EU do when Trump wins the next election?
    The American economy was actually good when Trump was president.
    — L'éléphant
    L'éléphant

    [quot3= Relativist
    ..until the pandemic shutdown. I think it's overly simplistic to either blame or give credit for the state of the economy. Business cycles are inevitable, and anomalies (like COVID) occur. Better to evaluate what policies a President implemented (or tried to implement).

    What exactly is a president supposed to do for the economy? Isn't that fascist? The government running the economy? Is that what we want?

    How about the international concerns like the US banking crashes that pull down other economies? Don't we need to govern against such disaster? By we I mean the whole world. Do we know enough to make good economic decisions?
  • Identity of numbers and information
    I agree that many dogs are very smart. It's hard for us, an animal capable of abstracting and reflecting on our experiences, an ability which seems to be reliant on symbolic language, to understand animal intelligence on its own terms, and not to underestimate it. No doubt we have it there somewhere.Janus

    I just order a book that explains math and animals. If I could get to understanding math at least as well as a dog I will have achieved something while I sit at home with COVID.

    I hope we always have a math thread to sustain my interest in math.
  • Identity of numbers and information
    Of course I don't really know you and you should consider the following a matter of speculation on my part. If there is something that resonates with you it might be worthwhile to consider it more, if not I won't be offended if you tell me you can't relate to what I say. That said...

    I don't think IQ works the way you think. We all have different constellations of cognitive strengths and weaknesses, with the consequence that learning some things may be harder or easier for us than for others. It seems plausible to me that math just doesn't come as easy for you as it does for some or even most. There is no failure on your part in that. Furthermore, it sound to me like the results of what you have learned are beautiful, and I hope you can be less hard on yourself.
    wonderer1

    Thank you so much for your concern about my feelings. That is something lacking in forums and yet science is making us aware of how important our emotions are and that we are healthier and happier when we reach out to others. And your nice words make me want to try even harder. I have math games I can put in my computer and I can give some time to using them. If we kept a running thread about math, the social aspect might help me stay motivated.

    The weird thing is I am fascinated by math. I have books and DVD's about math. I want to learn the language of math and I understand learning a language is one way to keep our mental powers as we age. And oh shit, I am in trouble. Your encouragement led to looking for books and I have to have at least 2 of them. These are some thrift books offerings...

    The Language of Mathematics: Making the Invisible Visible
    by Keith Devlin
    "The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden...

    The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs)
    by Keith Devlin

    There are two kinds of math: the hard kind and the easy kind. The easy kind, practiced by ants, shrimp, Welsh corgis -- and us -- is innate. What innate calculating skills do we humans have? Leaving aside built-in mathematics, such as the visual system, ordinary people do just fine when faced with mathematical tasks in the course of the day. Yet when they are confronted with the same tasks presented as "math," their accuracy often drops. But if we have innate mathematical ability, why do we have to teach math and why do most of us find it so hard to learn? Are there tricks or strategies that the ordinary person can do to improve mathematical ability? Can we improve our math skills by learning from dogs, cats, and other creatures that "do math"? The answer to each of these questions is a qualified yes. All these examples of animal math suggest that if we want to do better in the formal kind of math, we should see how it arises from natural mathematics. From NPR's "Math Guy" -- The Math Instinct will provide even the most number-phobic among us with confidence in our own mathematical abilities. This description may be from another edition of this product.

    In one of my sets of college lectures, the professor can talk about knots for at least an hour. This is using math to understand the unseen, such as to explore DNA with math.
  • Antinatalism Arguments
    Anti-life discussions (personal or otherwise) will be merged below. Please join this discussion rather than starting any new threads on this theme.Baden

    That really bites! I usually avoid threads that are too long. I really don't care what all the important people here have to say about anything. If I want to participate in a discussion of something, I want that to be my experience, not your only spoken thoughts. My thoughts and your reaction to them is what makes being here fun. If all I want is knowledge, I will buy a book that is highly recommended and read that. I do not come to forums and look for subjects to read that were closed discussions 5 years ago. If any of you have written books I should read, let me know.
  • Antinatalism Arguments
    I get that, but how does one differentiate between all the threads of argument dealing with the subject?schopenhauer1

    Loose one's memory, then each time is the first time and new things can be discovered. I just called old age purgatory but I am also enjoying, thinking, and rethinking things and noticing changes and new awareness. What really matters is if am enjoying the moment.

    New people are constantly coming into the arguments and really can't we treat each day as a new day? It really sucks to be enjoying a thread and then reading the subject has already been covered and a grumpy demand that the discussion end. If someone doesn't want to cover the subject again, just stay out of the discussion but there is no reason to ruin everyone else's fun. Especially not a newcomer's first-time experience of the subject. We can not be a part of the past discussions, only the present ones.