I had a math teacher who argued that even if 10 and 9.[9 repeating] indicate the same point on a number line, they're not two names for the same number because a convergent infinite series is a different kind of thing than a number. And he'd disagree with your proof based on the argument that you can't subtract convergent infinite series without losing something because you can't find the rightmost digit to start subtracting at. That seemed like a reasonable philosophical view to hold.
The reason 10 = 9.9999r is because you sneak in the notion of INFINITY which can lead to many confusions. The notion of infinity ambiguous. 10 is not equal 9.9999r but 9.99999r is always an approximation of 10 no matter how big you chose your infinity to be. Infinity is inflammable be-careful while handling it.
Ir has to do with infty and limits but I think this is best looks as a "problem" with representation of numbers with simbols, and the construct of real numbers, when you write 10, you really mean 10.0000r, it's just not convention to write the 0's, this makes easier to accept that 9.9999r is equal to 10.0000r. (my comment is just that, a comment)
We are *not* 'more irrational than we'd like to admit'. We are **entirely** irrational. Logic and reasoning is a skill that we learn. Our societies have decided that this is a valuable skill - but only insofar as it doesn't threaten the status or power of the person or structure with which you are interacting. We are entirely capable of suspending any adherence to reason whenever it suits us - and we do so regularly and frequently. Logic is a skill.. like driving, or reading. We can choose to stop driving at any time. LIkewise, we can choose to stop following logical rules at any time - and we do.
Yes, because rationality informs how we make our decisions. Those decisions affect others, so if we don't attempt to hold people accountable for their irrationalities then we open the floodgates for Nihilism.
Rationality is good because you can effectively predict the future, therefore adapt to to the future and conquer your intentions since you're ready since you've adapted
If we do not cultivate rationality (the first option) will we be able to design the machines to help us with rationality? Is "rationality" a special trait like "genius" or "common sense"? Is it as rare?
Nope every one can be rational. You just have to choose to do so and to not take the easy way out. You simply have to look at things from both sides or to double check your work.
I work towards being rational and logical personally because of the consequences of my irrationality and illogical choices. I have done alot of really really stupid stuff, despite being "smart" or knowledgeable, because of irrational reasoning. Everyone else decides for themselves if it's important to try.
Even people that are rational a lot and very good at being rational are not rational in many of their choices day to day. I think the solution to your problem of having done stupid stuff, whatever that means, is more to understand what drove the bad choices and what allowed them to continue without any 'correction'. Knowing your emotional patterns and allowing for them will make you a better choice-maker than believing the nonsense that you can be rational at all times. You are human.
Unless we are already omniscient and perfectly rational, the crutches we design are going to be flawed. So yes, rationality is just as valuable as ever. It's same with strength or speed. You don't need it until you do :)
First: Aristotle never said that human beings are always rational, in the sense of making correct choices given their knowledge. What he said was that a major thing that separates man from the other animals is that man has the *capacity* for rationality. Second, human beings have to learn to use their minds, and this includes methods of thinking. So errors in method that lead to a wrong answer do not necessarily constitute irrationality. (Such errors only constitute irrationality if the proper thinking methods are _willfully_ ignored after one has understood them, and when one has the time to apply them.) Rationality consists of a dedication to using one's mind (proper thinking methods) to the best of one's ability and going by facts (that ultimately come through one's sensory experience.) (One fact relevant to reasoning, that a rational person must take into account, is that one does not have unlimited time to make decisions. Sometimes it is rational to limit one's reasoning to a split-second decision.) Third, people have to have the time and proper motivation to think through the problems, if anyone is to judge their real-life, deliberative problem solving skills (and especially, their commitment to rationality) by their giving correct answers to quiz questions. Wrong answers to a couple of tricky quiz questions thrown out in the middle of a UA-cam video says nothing about a person's rationality. Fourth, most boom-bust cycles are not caused by irrational speculation in a free market. Rather, they are caused by government intervention in the economy that creates perverse incentives for the various actors. The 2008 Financial Crisis, for example, was caused largely by the Federal Reserve's manipulation of interest rates and the actions of the government-sponsored Fannie Mae and Freddie Mac. I recommend this op-ed on the 2008 Financial Crisis: www.forbes.com/2008/07/18/fannie-freddie-regulation-oped-cx_yb_0718brook.html ...and this more in-depth course: estore.aynrand.org/p/134/the-financial-crisis-what-happened-and-why-mp3-download
Sword of Apollo 100% agreed. What do you think about describing rationality as a style of using one's mind? One's style could more or less consistently use facts, reason, focus, intelligence, etc. Intelligence would be the skill of abstraction into concepts and reason would be the skill of abstraction into principles/propositions.
***** Yes, in a way you could say that rationality is a style or way of using one's mind or consciousness. But I think, more fundamentally, it is consistency in using one's mind to deal with the facts one perceives and introspects, and acting on one's reasoned judgments. Ultimately, irrationality (emotionalism and/or dogmatic obedience) are failures to use one's mind--*qua* conceptual faculty--in regard to certain facts. The emotionalist's conceptual mental functioning is suspended in order to allow certain emotional responses to rule unchallenged in certain issues. (Though, in many cases, the suspension may be covered up through rationalization, which is actually pseudo-mental functioning, hiding the lapse in genuine reasoning.) As far as intelligence goes, I would say that intelligence in humans is an individual's capacity for abstract thought; i.e. for discovering, reasoning with, and/or applying abstract concepts at higher levels of abstraction; ("existence" or "momentum," (higher level) versus "chair," or "dog" (lower level).) How much of this capacity is the result of skill and how much is genetic and/or environmental is debatable and may vary from person to person.
Sword of Apollo "Though, in many cases, the suspension may be covered up through rationalization, which is actually pseudo-mental functioning, hiding the lapse in genuine reasoning." That's a trend I've observed. As one of countless examples, I had a friendly debate last night. In response to all my counterarguments, my opponent openly admits I'm logically right, but he still thinks I'm wrong. Hmm, if I'm logically right, then what else could possibly inform him I'm wrong? Seems to me he's an emotionalist or dogmatist (so also a subjectivist?). It's likely that his knowledge is organizationally and/or conceptually incorrect, so he's not able to understand the full implications, hence his persisting feeling that I'm wrong. The correct course of action is to examine and correct conflicts among his beliefs, which is part of the process of reprogramming one's subconscious. Further discussion revealed that he rejected the primacy of existence, hence his refusal for such corrective action. Suppose my opponent was an emotionalist. Per emotionalism, emotions/subconsciousness has primacy over reason/self-consciousness. And my opponent would be perplexed because he *thinks* he's rational because he uses reason, but it's secondary to emotions; in other words, reason occurs chronologically *after* emotions, playing not the role of evaluating the validity of thoughts against reality, but rather of rationalizing thoughts per emotions. Suppose my opponent was a subjectivist dogmatist. Per this strain of subjectivism, some minds are inherently superior to others. So it follows then to blindly accept what these superior minds say. Like with emotionalism, reason also takes a backseat; superior minds of others have primacy over reason. My opponent would be perplexed because he *thinks* he's rational because he uses reason, but because it takes a backseat to what he has deemed to be superior minds, he uses reason not to validate what others say but to rationalize what they say is true. So yes, I agree--rationality is fundamentally about consistency. The primacy of emotions or of the minds of others compartmentalizes reason, thus rationality is employed *inconsistently*.
Still, even a hunter gatherer had society. Perhaps he means simply hunter gatherer, but to imply they weren’t social is wrong. Even if they didn’t have languages, they’re still social. Humans are social creatures, as are most animal species. However humans are the only ones with discernible languages. To say that other species have a proper language could be wrong, but they still communicate through vocal intonations and actions. And if he’s meaning pre-community humans, I believe hunter gatherers also had communities, since the name somewhat implies that: someone hunts, someone gathers. Other species also have communities. Pack of wolves, pride of lions, flock of geese. All of these technically are communities. So to try to reason what he meant by that phrase could be irrational. 🤣
In the 10 = 9.99999 example, you said in your 3rd line that “Since x = 9.9999” and then subtracted x from both sides. In the fourth line you represent 10-9.9999 as equaling 9. That does not seem correct to me. How do you get 9 when you subtract 9.999999999 from 10? Thank you.
Here's a comment from a article addressing this issue which helped me surprisingly much to accept this proof. It's all about limits with x approaching infinity "This is the first time I have been exposed to the concept that 0.99999... = 1. The proofs given are hard to argue with. It makes some sense to me if I consider the chain of 0.999999999....etc. going on to infinity. As one approaches infinity, the difference between the .999999...number and 1 approaches zero, and they become essentially identical. This is all hard to swallow, and I am wary that there is some sort of mathematical trickery going on in the proofs given that I have failed to recognize. Very interesting, though! like 0 dislike 0"
You cannot add or subtract from infinite series. There is the error in your proof. If you can then every number can be proven same with every other numbers. For example, “1=2” because, “INF + 1 = INF + 2”. Please correct the video.
Wow, that was a bitter pill to swallow. That being said, what happens when the very people who establish those regulations and institutions you mentioned are just as irrational as the people they rule over?
You end up with a Dictatorship. Governments need a way to constantly cycle out leadership so the boom and busts can cancel out. If you are in a government where the leader abolishes term limits then you should worry.
9.99999... endlesly is defined as a limit here, the limit of function f (N)= 9.9999...( N times ) when N tends towards infinity. Which is indeed 10. The problem though is your proof .. it isn't valid because when you write X=9.99999... X already equals 10 by definition of X. So yeah same same.
I think that, provided some of our population is rational, the rest can benefit from their knowledge and input. It is a wasted effort to make everyone rational since not everyone could attain it. Instead we should focus on the strengths of each person and try to accommodate their weaknesses
Thank you for posing the question. In my opinion, a formal answer cannot be singularly rational, as it is a necessarily complex one; it must depend on a formal definition of the purpose of human life, which is arguably, completely indeterminable on the collective scale (although one must reason that it has to be something!). Complex systems exhibit chaos, and complex reasoning exhibits paradox. Here is the problem (as I see it now). Perfectly accurate reasoning requires infinite processing time to resolve a paradox in a linear time domain. Though the emergent problem is with irrationality, the essential problem is with the linearity (procedural time-bound action) of human thinking.
Again, thank you Ram :D I really appreciate that there are a lot of open questions in this video. I found the first reasoning challenge very compelling. I am no mathematician, but I understand there are contemporary mathematicians still interrogating such spaces as that of the second reasoning challenge. I find it very wise to acknowledge that the imperfection of human rationality is a fact, though we cannot say if it's terminal. I'll definitely check out Dan Ariely's book. Most of us know that we get better at reasoning with more effort and training over time, but even our greatest known complex problem solvers struggled with paradoxes which they were never able to resolve within their lifetimes. (I'm thinking of Albert Einstein and Bertrand Russell.) I argue that the whole approach of using a singular, linear train of thought to resolve inferences rationally is the essential limitation. It's like trying to be a fighter pilot with only one good eye, unable to properly judge depth and velocity without the advantage of parallax processing. The analogy is meant to imply that some hypothetical form of parallax reasoning would bring a very helpful salience to the dimension of complexity, although I have no such hypothesis to offer. Experts may have some sense going into the experience of a somewhat novel problem, constrained within their field of expertise, but I believe a more independent determination could be made from a less time-constrained frame of reference. The reality of typical biological life is that reasoning burns precious calories, which might be better spent running or fighting. Reasoning can be cost prohibitive. That said, we take that debt upon ourselves when we plan for long term goals, as humans. There are these rabbit holes in the landscape of logical reasoning. What if we could tell how deep the rabbit holes are before we blindly start down them? We may never be able to get to the bottom of every problem, but I believe we can get much better at prioritizing our problems in order of difficulty - problems which may not be optional at all. Simply being aware of the essential challenges and possible limitations of the human mind is of enormous importance, and I would think, generally easier to teach than reasoning skills - not to kill the dream of perfection, but to place it properly outside the reach of the linear rational mind. This is an important caveat to the question of how to approach a solution from a social engineering standpoint. Perhaps the first thing to implement in order to benefit society are innocuous environmental challenges to basic reasoning skills. If an AI counterpart is to be of assistance in daily human living, without becoming an unhealthy addiction, perhaps it should be programmed to constructively challenge our intelligence in exchange for access. I'm sure you were leading on to a lot more information by posing these questions, which I may or may not find time to consume. Thank you however.
2:40 Bad math is bad! You cannot do that to a limit. You can show that when you are *approaching* a limit that you can state that 9.999... Will *approach* 10. That doesn't mean the same thing as 9.99.... is 10.
2:29 What the heck!?!? If 10x=99.9999 shouldn't 9x=89.9999!?!?!?!? 10x9.9999=99.9999 and 9x9.9999=99.9999 This makes no sense! Can someone please help me understand what I don't understand?
Yes, we should learn to improve our rationality. It would lead to better outcomes during crises like Covid, elections and getting rid of religious beliefs. 3 things that have shown us lately just how irrational we are.
I completely disagree with 10 and 9.999... example, mathematically speaking they are two different numbers, they are very close numbers but they are still different, they often produce the same result but this doesn't mean that they're the same number as upon further investigation it is discovered that they do in fact differ in the answers they give. This is why scientist and mathematicians use more decimal places for accuracy because they're not the same number.
+Ashley ASHLEYM What's 10-9.99...? Dont' tell me its .000...1 because that's not a real number. If you want a clearer proof of equivalence, just express 9.99... as the infinite sum of 9/10^(i-1) where i ranges from 1 to infinity. This is a geometric series which can easily be seen to be equal to 10.
The key thing to understand is, rationality is more energy intensive than irrationality. People aren't strictly rational and irrational; We're mostly irrational (because typically it's more energy-efficient) but if we're well nourished, we can afford to expend some energy into short bursts of rationality. With these short bursts, we can design tools, systems and rules to overcome our irrational behaviour. Scientific method is an easy example of a system designed to iron out irrationality.
Step 9x = 90 is to suppose the truth of the conclusion among the premises (we have to accept that 9 x 9.9999... equals 90, while anyone's calculator will plainly show it equals only 89.9999....). That's a classic example of irrational reasoning called Begging the Question.
+Appleblade 9x=90 was deducted from the previous step 10x=99.99... So it doesn't assume the conclusion at all. It simply assumes that x=9.99... and 99.99...=90+9.99...
I know you were trying to show us how we dont actually are that logical showing examples, but... at 2:45, you showed use 99.999-x=90. I will just remind you that you cant subtract a variable from a KNOWN NUMBER
+Wireless Philosophy I watched the supplemented video, but I still think there is neglect in the step where you subtracted x from 10x. This should equal 9.000000 with an eventual, but never coming 1 at the end (admittedly, I don't know a proper way to notate that). Although that 1 never coming, it still seems vital to accept that it is different than the whole number 9. I am sympathetic to apathy, but I hardly think it has a place in math.
+Wireless Philosophy This is the equavilent of stating pi= 3.14 heres why thats not acurrate: 9.99... recuring is an irrational number like subtracting pi whatever number you actually subtract, or add or multiply for that matter, is only an approximation of pi and the result will always be inacurate like with pi. This is the case for any number that cant be written down as a fraction or in standard form.
+Wireless Philosophy I was skeptical until the example given was 1 = 1/3 * 3 = .33333333... * 3 = .9999999 I never realized that this is what I was learning in limits. The problem with people disagreeing with you seems to be that we should have learned something so interesting and simple when at the elementary level. #USEducationSucks
+Ghost Emblem 9.99... is not irrational. To identify an irrational number in decimal form, it has to be an infinite decimal with no indefinitely repeating patterns. Pi has no such patters, but 9.99... clearly does. If you're wondering what fraction represents it, well, it's 10. Just think of 9.99... as being the infinite sum of 9/10^(i-1). This sum can easily be shown to be 10.
+Nathan Klein "an eventural, but never coming 1 at the end" does not make sense in the real numbers. It' simply isn't a thing. A clearer way of seeing the equality is to express 9.99... as the infinite sum of 9/10^(i-1) with i ranging from 1 to infinity. This is a geometric series which can easily be seen to be equal to 10.
At a deep level, logic and rationality breaks down. If you examine the example of the 'married person' long enough you may realize words do not contain the full truth of the subject; What is the full definition of 'married'? Where precisely are all the limits of that property? If a womans husband died is she still married before she finds out about his death? In the middle of a marriage ceremony between the words 'I' and 'do', what is the martial status? I think its reasonable to assume their are some edge cases in which a person can be considered neither married nor unmarried. Trying to force the state of marriage into a boolean variable seems like an error. Our words should expand to correctly define the target, but instead I find most people force their perceptions to conform to the known word. Human language relies heavily on shared information which goes unspoken, leaving it to the listener to make assumptions and inferences on what is meant. And sometimes our words themselves do not correctly map onto reality. For example: 'vitalism' , modern science has disproven this concept (which was common knowledge in ancient egypt) . That leaves a LOT of ambiguity... how do we know for certain what someone IS saying, what they MEAN, or even the validity of the words used. As to the multiple choice 'married person' question, NOTHING is certain.
+judgeomega Well married and non-married are an either or, and you're not married until the signing of the legal agreement, until that very second that's completely you are non-married and the very second it's completed you are married.
Given that physical exercise to increase strength is good for you, whether you are actually strong or not, and given that using your mind, in much the same way, is good for you, whether you are rational or not, I'd suggest that attempting to be rational for its own sake is important, whether we have systems that support us in our shortcomings, or not. Indeed, allowing people to wallow in their irrationality is what is making Trump a viable candidate.
One would need rational people to design systems that allow people to be irrational without suffering negative consequences. This would fail, of course, if the designers were themselves irrational in their designs. Which, by your argument that "people are not as rational as they think," would seem to be the relevant case. Putting this aside for a moment, are you saying that if such irrationality-proof systems were designed there would not be any more need for further systems? Because as long as the need for further designs continued (e.g., if flaws were found, or a need arose to deal with a nascent problem) there would be need for rational people to design the systems. Who, of course, would not be as rational as they think their are, and thus incompetent to design such systems, or even recognize flaws in their designs - making your entire thesis internally inconsistent and, well, ludicrous.
Although we don't rely on our physical prowess like our ancestors did, some people are as fit or even more fit than most cavemen were. Similarly, even if devices replace the need for rationality, some people will be as smart or smarter than most people alive today. And they will be correct: because rationality isn't just about knowing what the right answer is, but it's also about going through the process that leads to the right answer. That is valuable in itself, just like the right answer is valuable in itself, or like being comfortable is valuable in itself.
i disagree with the first example. while the question was meant as "is any of these three people (guaranteed to be) looking at a person of opposite marital status?" i understood it as "can you tell which one of them is looking at a person with an opposite marital status" the actual answer can be determined, but it is pratically useless, so my engineer brain discarded it
i suspect that the reason most people give wrong answers is that they understand it like i did, and not as it was meant. if you phrase the question differently, you should get a lot more correct answers.
ok yea that makes sense... taht was maybe the reason that I felt like I have been fooled after the soluition is presented... its a trick question but maybe some questions that are to be answerd are constructed like trick questions. So that out of the box thinking is required.
A good question to ask is how do we understand the meaning of the word rationality? If we understand the meaning of rationality as it is defined as our capacity to reason, isn’t our ability to infer, to inquire, and to use logic, a manifestation of our capacity to reason, of our rationality? We rational beings make mistakes but making mistakes does not imply incapacity to reason. Does it? This questioning on whether we are rational or not, is irrelevant and quite foolish. Having said that, I think a more sensible question to ask is that which inquires about the degree of the objectivity and the quality of what our rationality can achieve.
Peter Miller Those who claim 10 is not equal to 9.999... is indeed making this error, or an error similar to it, in holding on to a naive idea of 'infinity' being something tangible.
Peter Miller There is no flaw in the proof use in the video, but here is one you might find more intuitive. 10/3 = 3.333... (10/3)*3 = (3.333...)*3 10 = 9.9999...
Delta X ah yes. now it is correct. just as long as you realize that there is literally no difference between 9.999... (ie an infinite number of 9's after the decimal point) and 10. if any of those 9's were to be an 8 or a 0 then they would not be the same number.
You didn't address the initial question(well you sort of did, but I suppose it's debatable), which is: why be rational? It seems that this question would have no satisfying answer because: Let's suppose that you do have an answer and call that X, now X must be sustained by some other premise, namely Y- which must also be predicated on something else,- and so on ad infinitum. So my question to you is, how do you circumvent the infinite regression of justification argument?
lol 9x=89.999.. not 90. Also, the algebra is wrong. You cannot randomly decide to substract X, that will make a whole other equation, one where x does = 10. What you should of done to find x is x=99.9999..../10, which equals 9.9999...not 10
hmm. Well, the way the brain interprets information would lead to something like the "is a married person looking at an unmarried person" question to be sort of misleading. What my immediate thought process was was "is a person known to be married looking at a person known to be unmarried?" which has nothing to do with logic, but more to do with pure interpretative error. With more explanation, my guess is that most people would have gotten it right (i.e. phrasing it differently, perhaps by drawing less attention to the married/unmarried "state" of the individuals in question and instead saying something like "given that *person in middle* might or might not be married..." This would ideally force the listener to consider possibilities instead of only considering the information given to them and not studying the actual possibilities). Regardless, humans are not perfect at reasoning (or even slightly good at it in general), or even interpretation for that matter, so I'm not claiming that either. lol
+pcred567 Yes it would indeed force them to do as much, but that also relieves some of the burden of reasoning which would allow them to arrive at that conclusion alone much easier, hence his point: It's not easy to reason effectively and be always rational. Perhaps your suggestion to adjust the phrasing would be an example of the robustness he suggests we could implement into our systems in order to accommodate for the predictable effects of human irrationality.
Investors during a bubble mostly don't hold irrational views of the true value of an asset. Instead, they see the price rising hope to sell the asset to some less-cautious investor before it begins to fall. It's gambling, a sort of chicken with the market price, but if you time things just right you can potentially make a lot of money off it.
On the Left hand side, the value if x you deducted is 10, and that is not equal to the right-hand side of 9.99… (Ie you didnt prove that 10 and 9.99 is equal)
Greetings Mario De La Barcena, Well, we can argue about mistakes and/or the semantic language all day. In any case, you’ve not addressed my main point: This was a red herring to a straw man-from a professor of philosophy, no less. So yes or no, was it an example of irrational behavior-and one which Professor Dan Ariely (who the professor mentions) would endorse? Clearly it’s not-and easily understood as not if you’ve taken philosophy, psychology, and behavioral economics-including studying Dan’s work. yYM
it seems that thinking rationally is governed with regard to the potential impact by the level of actually real and illusory elements and their relationship. the divisions initially imposed must be reconciled subsequent to development which if achieved will occur in late 20s early 30s. meanwhile the general public after being brainwashed is urged to assume massive amounts of debt which will usually inhibit the quality of development and emotional intelligence. so to me the effectiveness of rational thought is percieved differently depending on the individual and their interpretation of experience. Shortsighted opinion is fostered by the structures put in place by those that depend on this deception to enjoy life divorced from nature. my suspicion is that the status projected by those in power is a fascad that is ultimately detrimental to health. reluctance to violate boundaries imposed by archaic beliefs inhibits progress and perpetuates conflict in an insidious manner. efforts to challenge the status quo are mitigated through the development of syntheticaly developed environments possibly stemming from various goals and objectives which may be necessary to maintain quality of life. I dont see how that question could suffiently be answered with out unwarranted assumptions.
Investors don't often make irrational decisions and lose money. Of course they lose money because no one can predict the future. Their expectations at the time they make the decision is rational to them. Of course your expectations do not always become reality but if you knowingly make irrational decisions, knowing that you will lose, that makes you stupid. In the investment world, the future is always uncertain...and there are risks. The fact that the market moves in the opposite direction of your expectation does not make your expectations irrational.
Lack of physical strength is no longer a character flaw, due to power tools, if in the future we have rational power tools so human irrationality is no longer a character flaw... Then what are prosthetics? Just because deaf persons can hear the same as non-deaf persons, does not mean we shouldn't find ways to actually fix their ears? We could look at humans, normal humans, average humans, not as normal humans, but rather rationally crippled persons... Sure systems can help them function well enough in the ever demanding world, but they are still not the same as the real thing, in the sense that hearing aids are not equal to biological ears... Hearing aids could run out of batteries, be disabled much more easily, short-circuit... and so on... The systems helping with our human fallibility could be compromised in the same way, for example, in times of war or catastrophe, when our rational aids, like ethics, and law, are taken out of action... Or when the person is emotionally compromised, or the lights went out, or so on... Thus I argue for fundamentally improving our rationality... Of course, by improving here I am not talking about, "operator, I need an academic program for 20th century postmodern philosophy, alright, let's argue! I know kung fu" what I mean is, like, if you want to improve ethics fundamentally, then you don't install Aristotle ethics 1.2, you increase the base capacity for empathy or something, to walk a mile in someone else's shoes... By rationality, maybe we at least boost the proclivity towards reasoning and thinking things through, sit down and write it down, maybe increase base capacity for systematizing and spatial and imagination, what ifs, and so on...?
Rationality is required for empathy because at its heart rationality proposes a world objective of the perceiver and thus the inference of other minds.
This explains why some people think that the solution to solving irrationality are regulations and institutions that "save us" from our own irrationality - but wait a minute, don't those same people also suffer from thinking that their reasoning is better than everyone else's, when in fact it's more likely the case that everyone else is right? So how is it that suddenly a few people in positions of power are now "more rational" than the rest of society? Hmm - methinks there is potential for serious problems there.
Should we value rationality? It's a stupid question, of course we should. You may not want to be rational but you want everyone else to be. The alternative is to live in chaos and fear. Feat because you don't know if that person in front of you is going to keep or walking or turn around and attack you for no reason.
***** You argued that the only way to come to "that conclusion" (I am assuming "that" refers to: reason should be valued) was to assume reason is valuable. And I suppose a claim of circular reasoning could be made against such an argument. But it should be noted that claiming an argument is circular does not address the veracity of either the assumptions or the conclusion. But actually what I did was state as a fact fact that rationality should be valued. I think it also might be a fact that any argument against rationality would also be invalid because the act of making such an argument assumes reason is valuable. So any argument against rationality would be subject to a reductio ad absurdum fallacy. That does address veracity because with reductio ad absurdum either the conclusion or the assumption is wrong.
Rational is a relative term. Next to a person who thinks they are Alexander the Great, I am rational. I know Alexander the Great is a historical figure. I know he is dead. Therefore, the guy next to me is wrong in his believe of being Alexander the Great. I now know this person next to me is irrational. I know I am not Alexander the Great. I do not claim to be him. Therefore, I am more rational than he is. Since I am more rational than the person next to me, I am therefor at a different level of rationality. Since rationality is relative, I can only be considered rational or not by comparison. Therefor, without comparison, I could not be rational or irrational. In conclusion, am I rational? Comparatively yes.
Why on Earth would we want to stop developing our skill of being rational!? Do we have anything better to do, or anything that does not benefit from added rationality?
Many of you have objected to my proof that 9.9(repeating) = 10. Let me approach the same issue by a different route. You all agree that 1/3 = .3(repeating). And you agree that 3/3 = 1 Now, what is .3(repeating) multiplied by 3?
Although your argument seems correct but unfortunately you have just committed the fallacy of begging the question.Let me restate your argument in a simpler way:P1: P is QC1: 3P is 3QEven though the whole argument may seem sound, the premise and the conclusion are equivalent, meaning that you did not actually prove anything but rather assert the premise in another form. Moreover, you did not show how P1 is true.However, I agree that 1=0.999..... is true. There are plenty of explanations using limits.A slightly more intuitive way to think about the statement is that, according to the denseness of real number, there does not exist a real number T such that 1>T>0.999.....
Patrick Ding isn't saying "1>T>0.999... where T does not exist" similar to saying "there is no letter between A and B in the English alphabet therefore A=B"? Your argument is convincing other than that one issue I have with it.
still I find irrationality to be impossible, we all, or I think, behave as rational as can be in coherence with our senses and immediate glitches in thought process. to take your own life seems rational, even though the majority does not support this. or I will take my boat to sea without my life vest and phone and turn of the radio comm seems rational, even though the majority does not support this. is this proof of irrationality? or is irrationality and rationality only a rational thought along the lines of opposite, up imply down, left imply right 1 imply -1, heaven imply hell :-)
a problem in proof... lets say x = 9.9999....(billions times repeated) , then 10x = 99.999....({bilion - 1} times repeated) so 10x - x = 89.999....({billion - 1} times repeated)...1
Greeting Ram Neta, I'm sorry sir, but your second example is incorrect. Let's start with A.C. Grayling's idea of Fred-a twist on the Socratic question theme. So first, what do you mean by name/Fred? Second, what do you mean by number/Fred? And third, what do you mean by same/Fred? Example One: * "10" a Blake Edwards movie from 1979. vs. * 9.99999… [nine point nine repeating]. Was Bo Derek a "10" or a 9.99999…? Example Two: Go to Texas Instruments, Google, or Apple and try to program with this logic. Right! Thought Three: The fact that you had to use algebra [formulas with X and other symbols] as an illustration reveals numerous fallacies-one being equivocation. Thought Four: Your ability to rationalize using such an example, in my opinion, was an example of "Predictably Irrational" university professors. Dan talks about this too, as you know. :-) yYM
Mattias Sollerman What does equal and non-equal mean, respectfully? Listen to the sentence for starters: "Consider the number ten and the number nine point nine repeating..." * What does "and the" mean in American English? * Now, put each in a calculator and use it in a computation. Are they the "same?" So, playing with equivocation, definitions, or using semantics, I can make anything true and then argue irrationality. The videos's example is not what behavioral economics (a course I've taken) and Dan Ariely (whose books I've read) do not explain irrationality in this way. They do explain argue that minds did not evolve to do complex math and see certain concepts together well, but the example of 10 vs. 9.99999... is a bad example of this.
yinYangMountain The question was whether or not 10 and 9.999... are different names for the same number. The answer to this is, I believe, very clearly yes, they are. In the context of mathematics they are equal. Not in the synthetic sense bachelor and unmarried man are equal, but in an analytical sense. Mathematics would not make sense unless this is true. The same number _can_ have different names, we can for instance write the same number in different bases. This does not mean all names of a number are of equal practical use or have the same meaning outside of mathematics. Most devices are not even built to comprehend repeating decimals, or roman numerals, or names for mathematical constants, etc. So one can discuss whether or not this question about 9.999... is a good example of (ir)rational thinking. I'd say it is similar to the Monty Hall problem. There might be several reasons why one does not produce the correct answer, the question can for instance be malformed or misunderstood. But as soon as one has the answer explained to him/her it should become fairly easy to understand, given enough thought is invested. It's a clear example of how our intuition fools us and how faulty intuition can be overcome by rational reasoning.
The answer " A)Yes" to question 1 is based on the ASSUMPTION that Chris is either married or married. The argument doesn't not consider other legal marital status including WIDOWED, DIVORCED etc. which are different from married or unmarried. Thus, in my opinion answer "C) Not Enough Information" is still a better reasoning than answer A) Yes.
Just that I say...No way that Irracional or Emocional people this kind off video can understand! I had both kind of people and with them you have to do with metaphor and than, they maybe can understand. TJ
The sophist bypasses the self knowledge of the soul, thereby removing knowledge from her psychological foundation. This phenomenon of course is not Knowledge, but an energetic abberation. Data is not knowledge. Knowledge is a pre existing energy that doesn't ask for money in exchange. D minus.
Bro i admit that the first question was a bit tricky and we fell for it but THE SECOND is wrong. Cause you made a math mistake which deviated the answer Now Let x = 9.999... 10x= 99.999... But 9x = 9×9.999 = 89.991 ÷9 ÷9 x = 9.999... x=9.999... SO NO x=10🙅♂️
9.999... and 10 are both the representation of the same real number. It becomes evident when one thinks of the representation of real numbers as a result from a bisection process.
It's not fair to equate wisdom and rationality. What you've just compared together are only someones power of reasoning[generaly](rationality) and his or her ability for the aptitude of it[wisdom], if you look af it this way, then not many will make the comparison. and your unclear phrading of the question is also at fault, what did you mean by that question? Was the starting question the same question as the question you've asked later? The question is very vague. It could have been reffering to them individually. Or it could not... I don't think the question was clear enough. What did you mean whether someone could tell or is there was an answer at all? This is just a trick question. Rationality is just the ability, or rather actually only our inability, of ever actually thinking of something in terms of not being. We are only ever able to think of things of in terms of what they are and are never able to think of them in terms of something that doesn't exist, this is not something that we can do, such things, are literally, absurd, or unthinkable. [Parmenides, Peri physis(De natura)] So if all thought must be thought of in terms of something which exists, then how can we think that something doesn't exist? We do this by never thinking about something that doesn't exist as if does exist, but rahter in thinking about it's inexistence as the existence of it's inexistence, or of just simply speaking, the absence of such a thing. [Aristotle, De interpretatione - Organon] If we take rationality only to mean our property of making judgments, then we are all rational. I would alson then further argue that this must always and necessarily be the case. But if by rationality(de re) you just mean that we can make a foolish decision now and then(de dicto) then thisnquestion just turns into a triviality that sometimes people may make mistakes and will[must] be held responsible, lecutred, and forgiven, from time and time again(possibly). As surely no-one would argue against the fact that people can make foolish decisions, then this video is just very ridiculous! Then it does not and will never mean that anyone is actually or will ever be dispossesed of their power of reasoning and their rightful potential for wisdom in any way whatsoever, ever.
Peter Miller I've read a bunch of Austrian economics, but is there something in that literature that explains booms and busts without appeal to irrationality? Thanks in advance for any help you can offer on this point.
Of course there are business cycles, but the ups and downs of the business cycle are magnified by irrational group think. Warren Buffett urges investors to be fearful when others are greedy and greedy when others are fearful: that would be the rational response to the vicissitudes of the business cycle. Sadly, irrational groupthink makes the ups higher and the downs lower.
+Ram Neta I'm not sure if you know what the austrian business cycle is? millions of people aiming to go north following a compass that points north is not being irrational anymore than millions of people taking out loans when rates are low or saving when rates are high. interest rates are supposed to be "the price of money over time" but when the prices are fixed then there are no price signals to follow, just like a broken compass.
Peter Miller: I've been wondering why my efforts in this conversation have been such a failure so far, and my current hypothesis is that I have not adopted your straightforward style of communication. So let me start over: oh ffs. Learn some psychology before claiming that business cycles don't involve irrationality. Do you know what Irrationality is? I suggest reading some of Keith Stanovich's work on rationality, and its relation to our tendency to trust broken price signals. Does that help?
![PHILOSOPHY - Epistemology: The Will to Believe [HD]](http://i.ytimg.com/vi/uzmLXIuAspQ/mqdefault.jpg)
I had a math teacher who argued that even if 10 and 9.[9 repeating] indicate the same point on a number line, they're not two names for the same number because a convergent infinite series is a different kind of thing than a number. And he'd disagree with your proof based on the argument that you can't subtract convergent infinite series without losing something because you can't find the rightmost digit to start subtracting at. That seemed like a reasonable philosophical view to hold.
Just definitionally too... aside from being or not being functionally identical, one is an integer, one isn't.
The reason 10 = 9.9999r is because you sneak in the notion of INFINITY which can lead to many confusions. The notion of infinity ambiguous. 10 is not equal 9.9999r but 9.99999r is always an approximation of 10 no matter how big you chose your infinity to be. Infinity is inflammable be-careful while handling it.
Ir has to do with infty and limits but I think this is best looks as a "problem" with representation of numbers with simbols, and the construct of real numbers, when you write 10, you really mean 10.0000r, it's just not convention to write the 0's, this makes easier to accept that 9.9999r is equal to 10.0000r. (my comment is just that, a comment)
Yep. I knew the answer was 10 because I went to school and learned you can not have math without Infinity and zero.
We are *not* 'more irrational than we'd like to admit'. We are **entirely** irrational. Logic and reasoning is a skill that we learn. Our societies have decided that this is a valuable skill - but only insofar as it doesn't threaten the status or power of the person or structure with which you are interacting. We are entirely capable of suspending any adherence to reason whenever it suits us - and we do so regularly and frequently.
Logic is a skill.. like driving, or reading. We can choose to stop driving at any time. LIkewise, we can choose to stop following logical rules at any time - and we do.
Yes, because rationality informs how we make our decisions. Those decisions affect others, so if we don't attempt to hold people accountable for their irrationalities then we open the floodgates for Nihilism.
Rationality is good because you can effectively predict the future, therefore adapt to to the future and conquer your intentions since you're ready since you've adapted
Assuming you reason based on fact
If we do not cultivate rationality (the first option) will we be able to design the machines to help us with rationality?
Is "rationality" a special trait like "genius" or "common sense"? Is it as rare?
Nope every one can be rational. You just have to choose to do so and to not take the easy way out. You simply have to look at things from both sides or to double check your work.
I work towards being rational and logical personally because of the consequences of my irrationality and illogical choices. I have done alot of really really stupid stuff, despite being "smart" or knowledgeable, because of irrational reasoning. Everyone else decides for themselves if it's important to try.
I to try to be rational
@@lolteaz I also try to be rational.
Even people that are rational a lot and very good at being rational are not rational in many of their choices day to day.
I think the solution to your problem of having done stupid stuff, whatever that means, is more to understand what drove the bad choices and what allowed them to continue without any 'correction'. Knowing your emotional patterns and allowing for them will make you a better choice-maker than believing the nonsense that you can be rational at all times. You are human.
Unless we are already omniscient and perfectly rational, the crutches we design are going to be flawed. So yes, rationality is just as valuable as ever. It's same with strength or speed. You don't need it until you do :)
First: Aristotle never said that human beings are always rational, in the sense of making correct choices given their knowledge. What he said was that a major thing that separates man from the other animals is that man has the *capacity* for rationality.
Second, human beings have to learn to use their minds, and this includes methods of thinking. So errors in method that lead to a wrong answer do not necessarily constitute irrationality. (Such errors only constitute irrationality if the proper thinking methods are _willfully_ ignored after one has understood them, and when one has the time to apply them.) Rationality consists of a dedication to using one's mind (proper thinking methods) to the best of one's ability and going by facts (that ultimately come through one's sensory experience.) (One fact relevant to reasoning, that a rational person must take into account, is that one does not have unlimited time to make decisions. Sometimes it is rational to limit one's reasoning to a split-second decision.)
Third, people have to have the time and proper motivation to think through the problems, if anyone is to judge their real-life, deliberative problem solving skills (and especially, their commitment to rationality) by their giving correct answers to quiz questions. Wrong answers to a couple of tricky quiz questions thrown out in the middle of a UA-cam video says nothing about a person's rationality.
Fourth, most boom-bust cycles are not caused by irrational speculation in a free market. Rather, they are caused by government intervention in the economy that creates perverse incentives for the various actors. The 2008 Financial Crisis, for example, was caused largely by the Federal Reserve's manipulation of interest rates and the actions of the government-sponsored Fannie Mae and Freddie Mac. I recommend this op-ed on the 2008 Financial Crisis: www.forbes.com/2008/07/18/fannie-freddie-regulation-oped-cx_yb_0718brook.html
...and this more in-depth course: estore.aynrand.org/p/134/the-financial-crisis-what-happened-and-why-mp3-download
Sword of Apollo 100% agreed.
What do you think about describing rationality as a style of using one's mind? One's style could more or less consistently use facts, reason, focus, intelligence, etc. Intelligence would be the skill of abstraction into concepts and reason would be the skill of abstraction into principles/propositions.
***** Yes, in a way you could say that rationality is a style or way of using one's mind or consciousness. But I think, more fundamentally, it is consistency in using one's mind to deal with the facts one perceives and introspects, and acting on one's reasoned judgments. Ultimately, irrationality (emotionalism and/or dogmatic obedience) are failures to use one's mind--*qua* conceptual faculty--in regard to certain facts. The emotionalist's conceptual mental functioning is suspended in order to allow certain emotional responses to rule unchallenged in certain issues. (Though, in many cases, the suspension may be covered up through rationalization, which is actually pseudo-mental functioning, hiding the lapse in genuine reasoning.)
As far as intelligence goes, I would say that intelligence in humans is an individual's capacity for abstract thought; i.e. for discovering, reasoning with, and/or applying abstract concepts at higher levels of abstraction; ("existence" or "momentum," (higher level) versus "chair," or "dog" (lower level).) How much of this capacity is the result of skill and how much is genetic and/or environmental is debatable and may vary from person to person.
Sword of Apollo "Though, in many cases, the suspension may be covered up through rationalization, which is actually pseudo-mental functioning, hiding the lapse in genuine reasoning."
That's a trend I've observed. As one of countless examples, I had a friendly debate last night. In response to all my counterarguments, my opponent openly admits I'm logically right, but he still thinks I'm wrong. Hmm, if I'm logically right, then what else could possibly inform him I'm wrong? Seems to me he's an emotionalist or dogmatist (so also a subjectivist?). It's likely that his knowledge is organizationally and/or conceptually incorrect, so he's not able to understand the full implications, hence his persisting feeling that I'm wrong. The correct course of action is to examine and correct conflicts among his beliefs, which is part of the process of reprogramming one's subconscious. Further discussion revealed that he rejected the primacy of existence, hence his refusal for such corrective action.
Suppose my opponent was an emotionalist. Per emotionalism, emotions/subconsciousness has primacy over reason/self-consciousness. And my opponent would be perplexed because he *thinks* he's rational because he uses reason, but it's secondary to emotions; in other words, reason occurs chronologically *after* emotions, playing not the role of evaluating the validity of thoughts against reality, but rather of rationalizing thoughts per emotions.
Suppose my opponent was a subjectivist dogmatist. Per this strain of subjectivism, some minds are inherently superior to others. So it follows then to blindly accept what these superior minds say. Like with emotionalism, reason also takes a backseat; superior minds of others have primacy over reason. My opponent would be perplexed because he *thinks* he's rational because he uses reason, but because it takes a backseat to what he has deemed to be superior minds, he uses reason not to validate what others say but to rationalize what they say is true.
So yes, I agree--rationality is fundamentally about consistency. The primacy of emotions or of the minds of others compartmentalizes reason, thus rationality is employed *inconsistently*.
@timjung640 Great explanation, thanks
What is this mythical "pre-social human" you're speaking of?
Hunter gatherer
Still, even a hunter gatherer had society. Perhaps he means simply hunter gatherer, but to imply they weren’t social is wrong. Even if they didn’t have languages, they’re still social. Humans are social creatures, as are most animal species. However humans are the only ones with discernible languages. To say that other species have a proper language could be wrong, but they still communicate through vocal intonations and actions. And if he’s meaning pre-community humans, I believe hunter gatherers also had communities, since the name somewhat implies that: someone hunts, someone gathers. Other species also have communities. Pack of wolves, pride of lions, flock of geese. All of these technically are communities. So to try to reason what he meant by that phrase could be irrational. 🤣
In the 10 = 9.99999 example, you said in your 3rd line that “Since x = 9.9999” and then subtracted x from both sides. In the fourth line you represent 10-9.9999 as equaling 9. That does not seem correct to me. How do you get 9 when you subtract 9.999999999 from 10? Thank you.
Here's a comment from a article addressing this issue which helped me surprisingly much to accept this proof. It's all about limits with x approaching infinity
"This is the first time I have been exposed to the concept that 0.99999... = 1.
The proofs given are hard to argue with.
It makes some sense to me if I consider the chain of 0.999999999....etc. going on to infinity. As one approaches infinity, the difference between the .999999...number and 1 approaches zero, and they become essentially identical. This is all hard to swallow, and I am wary that there is some sort of mathematical trickery going on in the proofs given that I have failed to recognize. Very interesting, though!
like 0 dislike 0"
You cannot add or subtract from infinite series. There is the error in your proof. If you can then every number can be proven same with every other numbers. For example, “1=2” because, “INF + 1 = INF + 2”. Please correct the video.
Wow, that was a bitter pill to swallow.
That being said, what happens when the very people who establish those regulations and institutions you mentioned are just as irrational as the people they rule over?
Then, you have something called: Goverment, every country has two or more institutions with irrational leaders
You end up with a Dictatorship. Governments need a way to constantly cycle out leadership so the boom and busts can cancel out. If you are in a government where the leader abolishes term limits then you should worry.
Philosophers: you're either married or unmarried
Post structuralists: 🙃🙃🙃
9.99999... endlesly is defined as a limit here, the limit of function f (N)= 9.9999...( N times ) when N tends towards infinity. Which is indeed 10. The problem though is your proof .. it isn't valid because when you write X=9.99999... X already equals 10 by definition of X. So yeah same same.
I think that, provided some of our population is rational, the rest can benefit from their knowledge and input. It is a wasted effort to make everyone rational since not everyone could attain it. Instead we should focus on the strengths of each person and try to accommodate their weaknesses
Thank you for posing the question. In my opinion, a formal answer cannot be singularly rational, as it is a necessarily complex one; it must depend on a formal definition of the purpose of human life, which is arguably, completely indeterminable on the collective scale (although one must reason that it has to be something!). Complex systems exhibit chaos, and complex reasoning exhibits paradox. Here is the problem (as I see it now). Perfectly accurate reasoning requires infinite processing time to resolve a paradox in a linear time domain. Though the emergent problem is with irrationality, the essential problem is with the linearity (procedural time-bound action) of human thinking.
Again, thank you Ram :D I really appreciate that there are a lot of open questions in this video. I found the first reasoning challenge very compelling. I am no mathematician, but I understand there are contemporary mathematicians still interrogating such spaces as that of the second reasoning challenge.
I find it very wise to acknowledge that the imperfection of human rationality is a fact, though we cannot say if it's terminal. I'll definitely check out Dan Ariely's book. Most of us know that we get better at reasoning with more effort and training over time, but even our greatest known complex problem solvers struggled with paradoxes which they were never able to resolve within their lifetimes. (I'm thinking of Albert Einstein and Bertrand Russell.)
I argue that the whole approach of using a singular, linear train of thought to resolve inferences rationally is the essential limitation. It's like trying to be a fighter pilot with only one good eye, unable to properly judge depth and velocity without the advantage of parallax processing. The analogy is meant to imply that some hypothetical form of parallax reasoning would bring a very helpful salience to the dimension of complexity, although I have no such hypothesis to offer. Experts may have some sense going into the experience of a somewhat novel problem, constrained within their field of expertise, but I believe a more independent determination could be made from a less time-constrained frame of reference.
The reality of typical biological life is that reasoning burns precious calories, which might be better spent running or fighting. Reasoning can be cost prohibitive. That said, we take that debt upon ourselves when we plan for long term goals, as humans. There are these rabbit holes in the landscape of logical reasoning. What if we could tell how deep the rabbit holes are before we blindly start down them? We may never be able to get to the bottom of every problem, but I believe we can get much better at prioritizing our problems in order of difficulty - problems which may not be optional at all.
Simply being aware of the essential challenges and possible limitations of the human mind is of enormous importance, and I would think, generally easier to teach than reasoning skills - not to kill the dream of perfection, but to place it properly outside the reach of the linear rational mind. This is an important caveat to the question of how to approach a solution from a social engineering standpoint. Perhaps the first thing to implement in order to benefit society are innocuous environmental challenges to basic reasoning skills.
If an AI counterpart is to be of assistance in daily human living, without becoming an unhealthy addiction, perhaps it should be programmed to constructively challenge our intelligence in exchange for access.
I'm sure you were leading on to a lot more information by posing these questions, which I may or may not find time to consume. Thank you however.
2:40 Bad math is bad!
You cannot do that to a limit. You can show that when you are *approaching* a limit that you can state that 9.999... Will *approach* 10. That doesn't mean the same thing as 9.99.... is 10.
The complete expectations of rationality and "logic" are unreasonable
2:29 What the heck!?!?
If 10x=99.9999 shouldn't 9x=89.9999!?!?!?!?
10x9.9999=99.9999 and 9x9.9999=99.9999
This makes no sense! Can someone please help me understand what I don't understand?
Yes, we should learn to improve our rationality. It would lead to better outcomes during crises like Covid, elections and getting rid of religious beliefs. 3 things that have shown us lately just how irrational we are.
I completely disagree with 10 and 9.999... example, mathematically speaking they are two different numbers, they are very close numbers but they are still different, they often produce the same result but this doesn't mean that they're the same number as upon further investigation it is discovered that they do in fact differ in the answers they give. This is why scientist and mathematicians use more decimal places for accuracy because they're not the same number.
+Ashley ASHLEYM What's 10-9.99...? Dont' tell me its .000...1 because that's not a real number.
If you want a clearer proof of equivalence, just express 9.99... as the infinite sum of 9/10^(i-1) where i ranges from 1 to infinity. This is a geometric series which can easily be seen to be equal to 10.
The key thing to understand is, rationality is more energy intensive than irrationality. People aren't strictly rational and irrational; We're mostly irrational (because typically it's more energy-efficient) but if we're well nourished, we can afford to expend some energy into short bursts of rationality. With these short bursts, we can design tools, systems and rules to overcome our irrational behaviour. Scientific method is an easy example of a system designed to iron out irrationality.
Agree. We're also selectively more or less rational depending on the perceived importance of the problem/situation
Step 9x = 90 is to suppose the truth of the conclusion among the premises (we have to accept that 9 x 9.9999... equals 90, while anyone's calculator will plainly show it equals only 89.9999....). That's a classic example of irrational reasoning called Begging the Question.
+Appleblade 9x=90 was deducted from the previous step 10x=99.99...
So it doesn't assume the conclusion at all. It simply assumes that x=9.99... and 99.99...=90+9.99...
I know you were trying to show us how we dont actually are that logical showing examples, but... at 2:45, you showed use 99.999-x=90. I will just remind you that you cant subtract a variable from a KNOWN NUMBER
Here is an excellent video by Vi Hart that explains the 9.999...repeating = 10 example: ua-cam.com/video/TINfzxSnnIE/v-deo.html
+Wireless Philosophy I watched the supplemented video, but I still think there is neglect in the step where you subtracted x from 10x. This should equal 9.000000 with an eventual, but never coming 1 at the end (admittedly, I don't know a proper way to notate that). Although that 1 never coming, it still seems vital to accept that it is different than the whole number 9.
I am sympathetic to apathy, but I hardly think it has a place in math.
+Wireless Philosophy This is the equavilent of stating pi= 3.14 heres why thats not acurrate:
9.99... recuring is an irrational number like subtracting pi whatever number you actually subtract, or add or multiply for that matter, is only an approximation of pi and the result will always be inacurate like with pi. This is the case for any number that cant be written down as a fraction or in standard form.
+Wireless Philosophy I was skeptical until the example given was 1 = 1/3 * 3 = .33333333... * 3 = .9999999 I never realized that this is what I was learning in limits. The problem with people disagreeing with you seems to be that we should have learned something so interesting and simple when at the elementary level. #USEducationSucks
+Ghost Emblem 9.99... is not irrational. To identify an irrational number in decimal form, it has to be an infinite decimal with no indefinitely repeating patterns. Pi has no such patters, but 9.99... clearly does. If you're wondering what fraction represents it, well, it's 10. Just think of 9.99... as being the infinite sum of 9/10^(i-1). This sum can easily be shown to be 10.
+Nathan Klein "an eventural, but never coming 1 at the end" does not make sense in the real numbers. It' simply isn't a thing.
A clearer way of seeing the equality is to express 9.99... as the infinite sum of 9/10^(i-1) with i ranging from 1 to infinity. This is a geometric series which can easily be seen to be equal to 10.
At a deep level, logic and rationality breaks down. If you examine the example of the 'married person' long enough you may realize words do not contain the full truth of the subject;
What is the full definition of 'married'? Where precisely are all the limits of that property? If a womans husband died is she still married before she finds out about his death? In the middle of a marriage ceremony between the words 'I' and 'do', what is the martial status? I think its reasonable to assume their are some edge cases in which a person can be considered neither married nor unmarried. Trying to force the state of marriage into a boolean variable seems like an error. Our words should expand to correctly define the target, but instead I find most people force their perceptions to conform to the known word.
Human language relies heavily on shared information which goes unspoken, leaving it to the listener to make assumptions and inferences on what is meant. And sometimes our words themselves do not correctly map onto reality. For example: 'vitalism' , modern science has disproven this concept (which was common knowledge in ancient egypt) . That leaves a LOT of ambiguity... how do we know for certain what someone IS saying, what they MEAN, or even the validity of the words used.
As to the multiple choice 'married person' question, NOTHING is certain.
+judgeomega Well married and non-married are an either or, and you're not married until the signing of the legal agreement, until that very second that's completely you are non-married and the very second it's completed you are married.
Very insightful! Thanks
Given that physical exercise to increase strength is good for you, whether you are actually strong or not, and given that using your mind, in much the same way, is good for you, whether you are rational or not, I'd suggest that attempting to be rational for its own sake is important, whether we have systems that support us in our shortcomings, or not. Indeed, allowing people to wallow in their irrationality is what is making Trump a viable candidate.
One would need rational people to design systems that allow people to be irrational without suffering negative consequences. This would fail, of course, if the designers were themselves irrational in their designs. Which, by your argument that "people are not as rational as they think," would seem to be the relevant case.
Putting this aside for a moment, are you saying that if such irrationality-proof systems were designed there would not be any more need for further systems? Because as long as the need for further designs continued (e.g., if flaws were found, or a need arose to deal with a nascent problem) there would be need for rational people to design the systems. Who, of course, would not be as rational as they think their are, and thus incompetent to design such systems, or even recognize flaws in their designs - making your entire thesis internally inconsistent and, well, ludicrous.
Although we don't rely on our physical prowess like our ancestors did, some people are as fit or even more fit than most cavemen were. Similarly, even if devices replace the need for rationality, some people will be as smart or smarter than most people alive today. And they will be correct: because rationality isn't just about knowing what the right answer is, but it's also about going through the process that leads to the right answer. That is valuable in itself, just like the right answer is valuable in itself, or like being comfortable is valuable in itself.
i disagree with the first example. while the question was meant as "is any of these three people (guaranteed to be) looking at a person of opposite marital status?" i understood it as "can you tell which one of them is looking at a person with an opposite marital status"
the actual answer can be determined, but it is pratically useless, so my engineer brain discarded it
dose your missunderstanding of the question make it a bad example?
i suspect that the reason most people give wrong answers is that they understand it like i did, and not as it was meant.
if you phrase the question differently, you should get a lot more correct answers.
ok yea that makes sense... taht was maybe the reason that I felt like I have been fooled after the soluition is presented... its a trick question
but maybe some questions that are to be answerd are constructed like trick questions. So that out of the box thinking is required.
A good question to ask is how do we understand the meaning of the word rationality? If we understand the meaning of rationality as it is defined as our capacity to reason, isn’t our ability to infer, to inquire, and to use logic, a manifestation of our capacity to reason, of our rationality? We rational beings make mistakes but making mistakes does not imply incapacity to reason. Does it?
This questioning on whether we are rational or not, is irrelevant and quite foolish. Having said that, I think a more sensible question to ask is that which inquires about the degree of the objectivity and the quality of what our rationality can achieve.
2:52 - pretty sure this example makes the following error: 1/0 = infinity, and 2/0 = infinity, therefore 1=2.
Peter Miller Those who claim 10 is not equal to 9.999... is indeed making this error, or an error similar to it, in holding on to a naive idea of 'infinity' being something tangible.
Peter Miller There is no flaw in the proof use in the video, but here is one you might find more intuitive.
10/3 = 3.333...
(10/3)*3 = (3.333...)*3
10 = 9.9999...
Delta X ah ok. but that is wrong. (3.333...)*3 does not equal 9.999, it equals 10. since "..." means infinitely recurring.
Peter Miller sorry, I added the '...' to the last line, is that what you were referring to?
Delta X ah yes. now it is correct. just as long as you realize that there is literally no difference between 9.999... (ie an infinite number of 9's after the decimal point) and 10. if any of those 9's were to be an 8 or a 0 then they would not be the same number.
You didn't address the initial question(well you sort of did, but I suppose it's debatable), which is: why be rational?
It seems that this question would have no satisfying answer because:
Let's suppose that you do have an answer and call that X, now X must be sustained by some other premise, namely Y- which must also be predicated on something else,-
and so on ad infinitum.
So my question to you is, how do you circumvent the infinite regression of justification argument?
I need to know why you're asking me the question. So I can making a rational decision.
lol 9x=89.999.. not 90.
Also, the algebra is wrong. You cannot randomly decide to substract X, that will make a whole other equation, one where x does = 10.
What you should of done to find x is x=99.9999..../10, which equals 9.9999...not 10
9x=80.999...=90
huge difference, know what a derivative is?
Yes, but I fail to see how that's relevant considering both sides of the equations are constants.
Can you do a research study whitout epistemology?
hmm. Well, the way the brain interprets information would lead to something like the "is a married person looking at an unmarried person" question to be sort of misleading. What my immediate thought process was was "is a person known to be married looking at a person known to be unmarried?" which has nothing to do with logic, but more to do with pure interpretative error. With more explanation, my guess is that most people would have gotten it right (i.e. phrasing it differently, perhaps by drawing less attention to the married/unmarried "state" of the individuals in question and instead saying something like "given that *person in middle* might or might not be married..." This would ideally force the listener to consider possibilities instead of only considering the information given to them and not studying the actual possibilities). Regardless, humans are not perfect at reasoning (or even slightly good at it in general), or even interpretation for that matter, so I'm not claiming that either. lol
+pcred567 Yes it would indeed force them to do as much, but that also relieves some of the burden of reasoning which would allow them to arrive at that conclusion alone much easier, hence his point: It's not easy to reason effectively and be always rational.
Perhaps your suggestion to adjust the phrasing would be an example of the robustness he suggests we could implement into our systems in order to accommodate for the predictable effects of human irrationality.
This is a good video!!
Way to equivocate technology and social structures! Was spotting that part of your reasoning test?
Investors during a bubble mostly don't hold irrational views of the true value of an asset. Instead, they see the price rising hope to sell the asset to some less-cautious investor before it begins to fall. It's gambling, a sort of chicken with the market price, but if you time things just right you can potentially make a lot of money off it.
On the Left hand side, the value if x you deducted is 10, and that is not equal to the right-hand side of 9.99… (Ie you didnt prove that 10 and 9.99 is equal)
Greetings Mario De La Barcena,
Well, we can argue about mistakes and/or the semantic language all day. In any case, you’ve not addressed my main point: This was a red herring to a straw man-from a professor of philosophy, no less.
So yes or no, was it an example of irrational behavior-and one which Professor Dan Ariely (who the professor mentions) would endorse?
Clearly it’s not-and easily understood as not if you’ve taken philosophy, psychology, and behavioral economics-including studying Dan’s work.
yYM
Here is the real proof.
10/3 = 3.3333333....
Multiply both by 3.
10/3 (* 3) = 3.33333333.... (* 3)
10 = 9.99999999999999....
lol the calculator said 10 not 3,3333........ joint the science math major in college thn we talk again
3.3333 (*3) does not equal 9.999
that is not accurate
OBRIGADA DE NADA
How does 9x = 90 when x is= to 9.999r ? I got it as 89.9r :-$
99.999r - 9.999r = 90 :) I got confused here too but figured it out after
it seems that thinking rationally is governed with regard to the potential impact by the level of actually real and illusory elements and their relationship. the divisions initially imposed must be reconciled subsequent to development which if achieved will occur in late 20s early 30s. meanwhile the general public after being brainwashed is urged to assume massive amounts of debt which will usually inhibit the quality of development and emotional intelligence. so to me the effectiveness of rational thought is percieved differently depending on the individual and their interpretation of experience. Shortsighted opinion is fostered by the structures put in place by those that depend on this deception to enjoy life divorced from nature. my suspicion is that the status projected by those in power is a fascad that is ultimately detrimental to health. reluctance to violate boundaries imposed by archaic beliefs inhibits progress and perpetuates conflict in an insidious manner. efforts to challenge the status quo are mitigated through the development of syntheticaly developed environments possibly stemming from various goals and objectives which may be necessary to maintain quality of life. I dont see how that question could suffiently be answered with out unwarranted assumptions.
There is a limit to the small of the universe, otherwise things get odd. There just has to be.
Investors don't often make irrational decisions and lose money. Of course they lose money because no one can predict the future. Their expectations at the time they make the decision is rational to them. Of course your expectations do not always become reality but if you knowingly make irrational decisions, knowing that you will lose, that makes you stupid. In the investment world, the future is always uncertain...and there are risks. The fact that the market moves in the opposite direction of your expectation does not make your expectations irrational.
Lack of physical strength is no longer a character flaw, due to power tools, if in the future we have rational power tools so human irrationality is no longer a character flaw... Then what are prosthetics? Just because deaf persons can hear the same as non-deaf persons, does not mean we shouldn't find ways to actually fix their ears? We could look at humans, normal humans, average humans, not as normal humans, but rather rationally crippled persons... Sure systems can help them function well enough in the ever demanding world, but they are still not the same as the real thing, in the sense that hearing aids are not equal to biological ears... Hearing aids could run out of batteries, be disabled much more easily, short-circuit... and so on... The systems helping with our human fallibility could be compromised in the same way, for example, in times of war or catastrophe, when our rational aids, like ethics, and law, are taken out of action... Or when the person is emotionally compromised, or the lights went out, or so on... Thus I argue for fundamentally improving our rationality... Of course, by improving here I am not talking about, "operator, I need an academic program for 20th century postmodern philosophy, alright, let's argue! I know kung fu" what I mean is, like, if you want to improve ethics fundamentally, then you don't install Aristotle ethics 1.2, you increase the base capacity for empathy or something, to walk a mile in someone else's shoes... By rationality, maybe we at least boost the proclivity towards reasoning and thinking things through, sit down and write it down, maybe increase base capacity for systematizing and spatial and imagination, what ifs, and so on...?
Rationality is required for empathy because at its heart rationality proposes a world objective of the perceiver and thus the inference of other minds.
- Imagine of a human being, thinking himself rational and living for no reason.....
- oh, It's me!
dude you are following "rational" methods to endorse irrationality. this video is confusing :)
Is it just me or did he not even define rationality?
I think it should be more common knowledge that rationality itself falls to circularity. Meaning it's taken as an axiom, or taken on faith.
When I see wrong usage of math, is it rational to stop the video right there?
In case someone cares, the correct answer is yes, and I knew that by being irrational...
This explains why some people think that the solution to solving irrationality are regulations and institutions that "save us" from our own irrationality - but wait a minute, don't those same people also suffer from thinking that their reasoning is better than everyone else's, when in fact it's more likely the case that everyone else is right? So how is it that suddenly a few people in positions of power are now "more rational" than the rest of society? Hmm - methinks there is potential for serious problems there.
Should we value rationality? It's a stupid question, of course we should. You may not want to be rational but you want everyone else to be. The alternative is to live in chaos and fear. Feat because you don't know if that person in front of you is going to keep or walking or turn around and attack you for no reason.
+cgm778 I think his question could be rephrased as, "How much effort should we expend in improving our rationality?"
Oh, in that case the answer is clearly half as much as we spend on misleading ads.
***** Do you realize that without the assumption of rationality your argument is pointless?
***** You argued that the only way to come to "that conclusion" (I am assuming "that" refers to: reason should be valued) was to assume reason is valuable. And I suppose a claim of circular reasoning could be made against such an argument. But it should be noted that claiming an argument is circular does not address the veracity of either the assumptions or the conclusion. But actually what I did was state as a fact fact that rationality should be valued.
I think it also might be a fact that any argument against rationality would also be invalid because the act of making such an argument assumes reason is valuable. So any argument against rationality would be subject to a reductio ad absurdum fallacy. That does address veracity because with reductio ad absurdum either the conclusion or the assumption is wrong.
Rational is a relative term.
Next to a person who thinks they are Alexander the Great, I am rational. I know Alexander the Great is a historical figure. I know he is dead. Therefore, the guy next to me is wrong in his believe of being Alexander the Great.
I now know this person next to me is irrational.
I know I am not Alexander the Great. I do not claim to be him. Therefore, I am more rational than he is.
Since I am more rational than the person next to me, I am therefor at a different level of rationality.
Since rationality is relative, I can only be considered rational or not by comparison. Therefor, without comparison, I could not be rational or irrational.
In conclusion, am I rational? Comparatively yes.
Ration is needed by all if not rationality. Ration is rational.
great video. thanks.
Why on Earth would we want to stop developing our skill of being rational!? Do we have anything better to do, or anything that does not benefit from added rationality?
PRECISO DE 18 NO TRABALHO DE FILOSOFIA
:(
Our brains want to do what is 1) the Easiest and 2) what is in the best interest for our selves now and not later.
We're Rational until somebody does us WRONG or we see a pretty girl. 👸
Many of you have objected to my proof that 9.9(repeating) = 10.
Let me approach the same issue by a different route. You all agree that 1/3 = .3(repeating).
And you agree that 3/3 = 1
Now, what is .3(repeating) multiplied by 3?
1/3 is actually not exactly 0.3(repeating) but approximately 0.3(repeating). But nonetheless 0.9(repeating)=1 and 9.9(repeating)=10.
1/3 is exactly equal to .3 (repeating)
Although your argument seems correct but unfortunately you have just committed the fallacy of begging the question.Let me restate your argument in a simpler way:P1: P is QC1: 3P is 3QEven though the whole argument may seem sound, the premise and the conclusion are equivalent, meaning that you did not actually prove anything but rather assert the premise in another form. Moreover, you did not show how P1 is true.However, I agree that 1=0.999..... is true. There are plenty of explanations using limits.A slightly more intuitive way to think about the statement is that, according to the denseness of real number, there does not exist a real number T such that 1>T>0.999.....
Patrick Ding isn't saying "1>T>0.999... where T does not exist" similar to saying "there is no letter between A and B in the English alphabet therefore A=B"? Your argument is convincing other than that one issue I have with it.
still I find irrationality to be impossible, we all, or I think, behave as rational as can be in coherence with our senses and immediate glitches in thought process.
to take your own life seems rational, even though the majority does not support this.
or I will take my boat to sea without my life vest and phone and turn of the radio comm seems rational, even though the majority does not support this.
is this proof of irrationality? or is irrationality and rationality only a rational thought along the lines of opposite, up imply down, left imply right 1 imply -1, heaven imply hell :-)
12/12 in the logic game :D
the error is multiplying 3.333... or 9.999... it cannot be multiplied to give an 100% accurate answer.
It certainly can. How'd you represent 10/3 using the same notation?
a problem in proof...
lets say x = 9.9999....(billions times repeated) , then
10x = 99.999....({bilion - 1} times repeated)
so 10x - x = 89.999....({billion - 1} times repeated)...1
Isn’t that math equation only true because it’s a system. Not that 9.999 actually equals 10
QUERO LEGENDAS EM TUGA!!!!!!!!
EXATO CONCORDO!!!!
TAMBÉM QUERO
lol, you have to be irrational to be rational.
Greeting Ram Neta,
I'm sorry sir, but your second example is incorrect. Let's start with A.C. Grayling's idea of Fred-a twist on the Socratic question theme. So first, what do you mean by name/Fred? Second, what do you mean by number/Fred? And third, what do you mean by same/Fred?
Example One:
* "10" a Blake Edwards movie from 1979.
vs.
* 9.99999… [nine point nine repeating].
Was Bo Derek a "10" or a 9.99999…?
Example Two:
Go to Texas Instruments, Google, or Apple and try to program with this logic. Right!
Thought Three:
The fact that you had to use algebra [formulas with X and other symbols] as an illustration reveals numerous fallacies-one being equivocation.
Thought Four:
Your ability to rationalize using such an example, in my opinion, was an example of "Predictably Irrational" university professors. Dan talks about this too, as you know. :-)
yYM
yinYangMountain I'm curious, do you mean 1 is not equal to 0.999... ? Or am I completely misunderstanding your comment?
yinYangMountain Watch this excellent video by Vi Hart, if you need more information about this: ua-cam.com/video/TINfzxSnnIE/v-deo.html
Wireless Philosophy
Thanks for the link!
Mattias Sollerman
What does equal and non-equal mean, respectfully?
Listen to the sentence for starters:
"Consider the number ten and the number nine point nine repeating..."
* What does "and the" mean in American English?
* Now, put each in a calculator and use it in a computation. Are they the "same?"
So, playing with equivocation, definitions, or using semantics, I can make anything true and then argue irrationality. The videos's example is not what behavioral economics (a course I've taken) and Dan Ariely (whose books I've read) do not explain irrationality in this way.
They do explain argue that minds did not evolve to do complex math and see certain concepts together well, but the example of 10 vs. 9.99999... is a bad example of this.
yinYangMountain The question was whether or not 10 and 9.999... are different names for the same number. The answer to this is, I believe, very clearly yes, they are. In the context of mathematics they are equal. Not in the synthetic sense bachelor and unmarried man are equal, but in an analytical sense. Mathematics would not make sense unless this is true.
The same number _can_ have different names, we can for instance write the same number in different bases. This does not mean all names of a number are of equal practical use or have the same meaning outside of mathematics.
Most devices are not even built to comprehend repeating decimals, or roman numerals, or names for mathematical constants, etc.
So one can discuss whether or not this question about 9.999... is a good example of (ir)rational thinking. I'd say it is similar to the Monty Hall problem. There might be several reasons why one does not produce the correct answer, the question can for instance be malformed or misunderstood. But as soon as one has the answer explained to him/her it should become fairly easy to understand, given enough thought is invested.
It's a clear example of how our intuition fools us and how faulty intuition can be overcome by rational reasoning.
I am not convinced about the Math problem
i thought i was slick picking c for the 1st one lmao
The answer " A)Yes" to question 1 is based on the ASSUMPTION that Chris is either married or married. The argument doesn't not consider other legal marital status including WIDOWED, DIVORCED etc. which are different from married or unmarried. Thus, in my opinion answer "C) Not Enough Information" is still a better reasoning than answer A) Yes.
Those math problems were different.
Just that I say...No way that Irracional or Emocional people this kind off video can understand! I had both kind of people and with them you have to do with metaphor and than, they maybe can understand. TJ
The sophist bypasses the self knowledge of the soul, thereby removing knowledge from her psychological foundation. This phenomenon of course is not Knowledge, but an energetic abberation. Data is not knowledge. Knowledge is a pre existing energy that doesn't ask for money in exchange. D minus.
9.999 is not equal to 10. use 1 for x. then use 10 for x
Are we rational? NO. Next question...
9x= 9×9.999 = 89.991
Protestant vs the One True Faith of the Holy Catholic Church
Bro i admit that the first question was a bit tricky and we fell for it but THE SECOND is wrong. Cause you made a math mistake which deviated the answer
Now
Let x = 9.999...
10x= 99.999...
But 9x = 9×9.999 = 89.991
÷9 ÷9
x = 9.999...
x=9.999...
SO NO x=10🙅♂️
9.999... and 10 are both the representation of the same real number. It becomes evident when one thinks of the representation of real numbers as a result from a bisection process.
It's not fair to equate wisdom and rationality.
What you've just compared together are only someones power of reasoning[generaly](rationality) and his or her ability for the aptitude of it[wisdom], if you look af it this way, then not many will make the comparison. and your unclear phrading of the question is also at fault, what did you mean by that question? Was the starting question the same question as the question you've asked later? The question is very vague. It could have been reffering to them individually. Or it could not... I don't think the question was clear enough. What did you mean whether someone could tell or is there was an answer at all? This is just a trick question.
Rationality is just the ability, or rather actually only our inability, of ever actually thinking of something in terms of not being. We are only ever able to think of things of in terms of what they are and are never able to think of them in terms of something that doesn't exist, this is not something that we can do, such things, are literally, absurd, or unthinkable. [Parmenides, Peri physis(De natura)]
So if all thought must be thought of in terms of something which exists, then how can we think that something doesn't exist? We do this by never thinking about something that doesn't exist as if does exist, but rahter in thinking about it's inexistence as the existence of it's inexistence, or of just simply speaking, the absence of such a thing. [Aristotle, De interpretatione - Organon]
If we take rationality only to mean our property of making judgments, then we are all rational. I would alson then further argue that this must always and necessarily be the case. But if by rationality(de re) you just mean that we can make a foolish decision now and then(de dicto) then thisnquestion just turns into a triviality that sometimes people may make mistakes and will[must] be held responsible, lecutred, and forgiven, from time and time again(possibly). As surely no-one would argue against the fact that people can make foolish decisions, then this video is just very ridiculous! Then it does not and will never mean that anyone is actually or will ever be dispossesed of their power of reasoning and their rightful potential for wisdom in any way whatsoever, ever.
4:06 - oh ffs. lean some economics before blaming irrationality. i suggest reading some minsky or mises
Peter Miller I've read a bunch of Austrian economics, but is there something in that literature that explains booms and busts without appeal to irrationality? Thanks in advance for any help you can offer on this point.
well yeah - the whole austrian business cycle theory. its pretty much the same conclusion that minsky came to as well.
Of course there are business cycles, but the ups and downs of the business cycle are magnified by irrational group think. Warren Buffett urges investors to be fearful when others are greedy and greedy when others are fearful: that would be the rational response to the vicissitudes of the business cycle. Sadly, irrational groupthink makes the ups higher and the downs lower.
+Ram Neta I'm not sure if you know what the austrian business cycle is? millions of people aiming to go north following a compass that points north is not being irrational anymore than millions of people taking out loans when rates are low or saving when rates are high. interest rates are supposed to be "the price of money over time" but when the prices are fixed then there are no price signals to follow, just like a broken compass.
Peter Miller: I've been wondering why my efforts in this conversation have been such a failure so far, and my current hypothesis is that I have not adopted your straightforward style of communication. So let me start over:
oh ffs. Learn some psychology before claiming that business cycles don't involve irrationality. Do you know what Irrationality is? I suggest reading some of Keith Stanovich's work on rationality, and its relation to our tendency to trust broken price signals.
Does that help?
“If so, then why?”... because god damned trump and his supporters happen. We need a critically adept citizenry.
10 x 9.999 = 99.99, not 99.999. 🤷
10 does NOT equal 9.999...
That math is so bad.
I really agree with your conclusion, but if you're trying to prove that x≠x then I'm going to go ahead and say your the irrational one here.
This video made everything worse